Table of contents

This focus issue of New Journal of Physics concentrates on recent developments in microfluidics, and related small-scale flow themes. This subject touches on many areas with the common element that they are engaged with understanding, measuring or manipulating flows at the scale of a few hundred microns or smaller.

Microfluidics is of interest to many scientists and engineers from many disciplines because it is a toolbox from which they can investigate basic questions in their respective fields. In particular, the field has led to new studies of small-scale fluid flows, especially those dominated by surface effects, which is crucial for understanding electrokinetics, chemical reactions and phase changes, and multiphase systems, including those involving dispersed liquid and gas phases, suspended particles, cells, vesicles, capsules, etc. The lower length scale of these kinds of flows concerns nanoscale manipulation of objects such as DNA or nanoparticles, nanofabrication of surfaces, studies of the flow within nanometers of substrates, etc.

Microfluidics has also given rise to technologies because it enables design and implementation of new devices for sensing, detection, measurement, materials characterization, combinatorial discovery, cellular-scale manipulation, miniaturization of reactors, etc. The fact that these systems are small, cheap, physically flexible, portable, multifunctional, and, when they are working, produce measurements quickly, offers many new avenues for innovation.

In this issue we highlight contributions from around the world that explore research directions inspired by the manifold possibilities of microfluidics. In particular, the papers include reports of single-phase flows that are driven by electrical fields, so-called electrokinetics. Although the field has its origins in the 19th century, if not even earlier, new theoretical ideas are required to understand dynamics close to charged surfaces, and new applications of the basic ideas are being introduced for driving flows and manipulating suspended particles (e.g. DNA). In addition, the subject of mixing and the study of transport processes coupling diffusion and convection is a necessary component of many studies aimed at lab-on-a-chip environments. At the other extreme from mixing there is interest in the precise placement of particles in microfluidic flows. Although the majority of microfluidic studies focus on the consequences of low Reynolds number motions, the flows can frequently have large enough particle-scale Reynolds numbers that inertial effects can appear. Also, chemical gradients, via osmotic effects, can be significant, and, where surface effects are significant, particle deposition can occur.

Multiphase flows constitute another major area of microfluidic research. For example, there has been great interest in using drops as individual containers since both the chemical composition inside and outside the drop can be controlled. Also, the interface between the two phases provides both a natural chemical barrier (surfactants are generally added to reduce the probability of coalescence between drops) as well as potentially being the site for reactions or localized organization of particles suspended in solution. Thus, there is interest in both the controlled breakup of liquid threads, the dynamics of such a thread, which can fold or buckle, and application of these processes to fabricating new materials. Not surprisingly the themes mentioned in this short summary are just a small window into the myriad of ideas being investigated in the research world of small-scale flows that is the playground of micro- and nanofluidics.

We are grateful to all of the contributors for their efforts and to the referees, whose feedback has added value to every contribution. We hope you, as readers, will find benefit in the many ideas discussed in this Focus on Micro- and Nanofluidics, which represents a sampling of current activity, including experiment, simulation and theory, in this rapidly developing field.

Focus on Micro- and Nanofluidics Contents

The anti-lotus leaf effect in nanohydrodynamic bump arrays Keith Morton, Ophelia K C Tsui, Chih-Kuan Tung, James C Sturm, Stephen Y Chou and Robert Austin

Transport in nanofluidic systems: a review of theory and applications W Sparreboom, A van den Berg and J C T Eijkel

The effects of polymer molecular weight on filament thinning and drop breakup in microchannels P E Arratia, L-A Cramer, J P Gollub and D J Durian

Mass transfer and interfacial properties in two-phase microchannel flows Jeffrey D Martin and Steven D Hudson

Temporal response of an initially deflected PDMS channel Priyadarshi Panda, Kai P Yuet, Dhananjay Dendukuri, T Alan Hatton and Patrick S Doyle

Gas–liquid two-phase flow patterns in rectangular polymeric microchannels: effect of surface wetting properties D Huh, C-H Kuo, J B Grotberg and S Takayama

Mixing via thermocapillary generation of flow patterns inside a microfluidic drop María Luisa Cordero, Hans Olav Rolfsnes, Daniel R Burnham, Paul A Campbell, David McGloin and Charles N Baroud

Pressure-driven DNA transport across an artificial nanotopography J T Del Bonis-O'Donnell, W Reisner and D Stein

Eulerian indicators for predicting and optimizing mixing quality Rob Sturman and Stephen Wiggins

Asymmetric flows over symmetric surfaces: capacitive coupling in induced-charge electro-osmosis T S Mansuripur, A J Pascall and T M Squires

High-viscosity fluid threads in weakly diffusive microfluidic systems T Cubaud and T G Mason

Interfacial mass transport in steady three-dimensional flows in microchannels Joseph D Kirtland, Corey R Siegel and Abraham D Stroock

Active connectors for microfluidic drops on demand Jean-Christophe Galas, Denis Bartolo and Vincent Studer

Electrokinetic control of sample splitting at a channel bifurcation using isotachophoresis Alexandre Persat and Juan G Santiago

Differential inertial focusing of particles in curved low-aspect-ratio microchannels Aman Russom, Amit K Gupta, Sunitha Nagrath, Dino Di Carlo, Jon F Edd and Mehmet Toner

Capillary instability on a hydrophilic stripe Raymond L Speth and Eric Lauga

Universal nanocolloid deposition patterns: can you see the harmonics of a Taylor cone? Xinguang Cheng and Hsueh-Chia Chang

Osmotic manipulation of particles for microfluidic applications B Abécassis, C Cottin-Bizonne, C Ybert, A Ajdari and L Bocquet

Scaling the drop size in coflow experiments E Castro-Hernández, V Gundabala, A Fernández-Nieves and J M Gordillo

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study Rajneesh Bhardwaj, Xiaohua Fang and Daniel Attinger

Topology and shape optimization of induced-charge electro-osmotic micropumps M M Gregersen, F Okkels, M Z Bazant and H Bruus

Fabrication of multiphasic and regio-specifically functionalized PRINT® particles of controlled size and shape H Zhang, J K Nunes, S E A Gratton, K P Herlihy, P D Pohlhaus and J M DeSimone

Using TIRF microscopy to quantify and confirm efficient mass transfer at the substrate surface of the chemistrode Delai Chen, Wenbin Du and Rustem F Ismagilov

Nonlinear electrokinetics at large voltages Martin Z Bazant, Mustafa Sabri Kilic, Brian D Storey and Armand Ajdari

Interdiffusion of liquids of different viscosities in a microchannel J Dambrine, B Géraud and J-B Salmon

Microfluidic fabrication of microparticles with structural complexity using photocurable emulsion droplets Shin-Hyun Kim, Jae Won Shim, Jong-Min Lim, Su Yeon Lee and Seung-Man Yang

Here we map gas–liquid two-phase flow regimes observed in polymeric microchannels with different wetting properties. We utilized video and confocal microscopy to examine two-phase flow patterns produced by parallel injection of air and water through a Y-shaped junction into a rectangular microchannel made of poly(dimethylsiloxane) (PDMS). We observed seven flow regimes in microchannels with hydrophobic walls, whereas only two flow patterns were identified in hydrophilic microchannels. Our study demonstrates that surface wettability has a profound influence on the spatial distribution of air and water moving in microchannels.

The heating produced by a focused laser has been shown to provide a range of manipulation tools on droplets in microfluidic situations, through the generation of thermocapillary flows whose net result is to produce a force on the drop. In particular, droplets of water in oil that are produced in microchannels can be blocked in a special test section. Here, the manipulation of the flow within the droplet is explored through spatial and temporal modulation of the laser pattern used to block the drop. When a stationary pattern of two laser spots is used, the flow preserves the mirror symmetry inside the drop, as happens in the case of two alternating spots if the frequency of the switching is higher than the response rate of the fluid. Lower frequency switching produces a time periodic flow that breaks the mirror symmetry and which leads to efficient mixing inside the droplet. The mixing that is produced by this alternating flow is studied both experimentally and using numerical simulations of particle trajectories from measured velocity fields. This mixing can be optimized for certain parameter ranges, namely by varying the distance between the spots and the forcing frequency.

The pressure-driven transport of DNA was studied in slit-like nanochannels with an embedded nanotopography consisting of linear arrays of nanopits. We imaged individual DNA molecules moving single-file down the nanopit array, undergoing sequential pit-to-pit hops using fluorescence video microscopy. Distinct transport dynamics were observed depending on whether a molecule could occupy a single pit, or was forced to subtend multiple pits. We interpret these results in terms of a scaling theory of the free energy of polymer chains in a linear array of pits. Molecules contained within a single pit are predicted to face an entropic free energy barrier, and to hop between pits by thermally activated transport. Molecules that subtend multiple pits, on the other hand, can transfer DNA contour from upstream to downstream pits in response to an applied fluid flow, which lowers the energy barrier. When the trailing pit completely empties, or when the leading pit reaches its capacity, the energy barrier is predicted to vanish, and the low-pressure, thermally activated transport regime gives way to a high-pressure, dissipative transport regime. These results contribute to our understanding of polymers in nanoconfined environments, and may guide the development of nanoscale lab-on-a-chip applications.

Many different methods exist for measuring, quantifying and predicting the quality of a mixture resulting from a fluid mixing device. In general, these rely on Lagrangian information from the system, as they involve the evolution of individual trajectories. In this paper, we propose tools that are formulated using only Eulerian information, and yet can predict the Lagrangian mixing properties of a mixing device. The proposed Eulerian indicators are motivated by the recent linked twist map (LTM) formulation of fluid mixing. We describe their features and application in the context of four different fluid flows: the blinking vortex flow and the partitioned pipe mixer (two paradigm flows from the early studies of chaotic mixing), a model of a channel flow containing 'separatrices' in the cross-sectional flow (which is a common flow feature in a large number of micromixers), and a flow generated by pulsed source–sink pairs (which has been used as a model for mixing in DNA microarrays).

We report curious asymmetric induced-charge electro-osmotic (ICEO) flows over a symmetric, planar gate electrode under applied ac electric fields, whereas symmetric, counter-rotating rolls are expected. Furthermore, the asymmetric component of the flow is consistently directed towards the grounded electrode. We propose that capacitive coupling of the gate electrode to the microscope stage—a comparatively large equipotential surface that acts effectively as a ground—is responsible for this symmetry breaking. This stray capacitance drives the formation of a double layer whose zeta potential is proportional to the potential drop from the electrolyte directly above the gate electrode to the external stage. Therefore, the charge in this 'stray' double layer varies in phase with the driving field, resulting in a rectified, steady flow as with standard ICEO. We experimentally vary the stray capacitance, the electric potential of the stage and the location of the gate electrode, and find that the effect on the stray flow is qualitatively consistent with the predictions of the proposed mechanism. In the process, we demonstrate that capacitive coupling offers an additional means of manipulating fluid flow over a polarizable surface.

We provide an overview of the flow dynamics of highly viscous miscible liquids in microfluidic geometries. We focus on the lubricated transport of high-viscosity fluids interacting with less viscous fluids, and we review methods for producing and manipulating single and multiple core-annular flows, i.e. viscous threads, in compact and plane microgeometries. In diverging slit microchannels, a thread's buckling instabilities can be employed for generating ordered and disordered miscible microstructures, as well as for partially blending low- and high-viscosity materials. The shear-induced destabilization of a thread that flows off-center in a square microchannel is examined as a means for continuously producing miscible dispersions. We show original compound threads and viscous dendrites that are generated using three fluids, each of which has a large viscosity contrast with the others. Thread motions in zones of microchannel extensions are examined in both miscible and immiscible environments. We demonstrate that high-viscosity fluid threads in weakly diffusive microfluidic systems correspond to the viscous primary flow and can be used as a starting point for studying and understanding the destabilizing effects of interfacial tension as well as diffusion. Characteristic of lubricated transport, threads facilitate the transport of very viscous materials in small fluidic passages, while mitigating dissipation. Threads are also potentially promising for soft material synthesis and diagnostics with independent control of the thread specific surface and residence time in micro-flow reactors.

Rates of interfacial mass and heat transfer from uniaxial laminar flows through ducts at low Reynolds number follow the behaviour elucidated by Grætz: the local Sherwood (or Nusselt) number falls to an asymptotic value that is defined by the geometry and is independent of the Péclet number. In a previous study, we showed that analogous but distinct behaviour occurs in duct flows that exhibit Lagrangian chaos in the cross section due to spatially varying secondary flows: the Sherwood number follows the identical decay in the entrance region before passing to a Péclet-dependent value at larger axial distances; we called this behaviour, 'modified Grætz'. Here, we investigate the generality of this behaviour in chaotic and non-chaotic flows for transfer to moving interfaces and across internal interfaces between convectively disconnected sets in the flow. We present theoretical predictions of the transfer rates for these cases and verify the accuracy of these predictions with a tracer-based, numerical simulation. We also present a theoretical criterion for the modified Grætz behaviour in terms of the axial length associated with mixing and the axial length associated with the return of depleted fluid to the reactive interface; we exploit simulation to verify this criterion.

We introduce a simple and versatile microfluidic drop-on-demand solution that enables independent and dynamical control of both the drop size and the drop production rate. To do so, we combine a standard microfluidic T-junction and a novel active switching component that connects the microfluidic channel to the macroscopic liquid reservoirs. Firstly, we explain how to make this simple but accurate drop-on-demand device. Secondly, we carefully characterize its dynamic response and its range of operations. Finally, we show how to generate complex two-dimensional drop patterns dynamically in single or multiple synchronized drop-on-demand devices.

We present a novel method for accurately splitting ionic samples at microchannel bifurcations. We leverage isotachophoresis (ITP) to focus and transport sample through a one-inlet, two-outlet microchannel bifurcation. We actively control the proportion of splitting by controlling potentials at end-channel reservoirs (and thereby controlling the current ratio). We explore the effect of buffer chemistry and local electric field on splitting dynamics and propose and validate a simple Kirchoff-type rule controlling the split ratio. We explore the effects of large applied electric fields on sample splitting and attribute a loss of splitting accuracy to electrohydrodynamic instabilities. We propose a scaling analysis to characterize the onset of this instability. This scaling is potentially useful for other electrokinetic flow problems with self-sharpening interfaces.

Microfluidic-based manipulation of particles is of great interest due to the insight it provides into the physics of hydrodynamic forces. Here, we study a particle-size-dependent phenomenon based on differential inertial focusing that utilizes the flow characteristics of curved, low aspect ratio (channel width ≫ height), microfluidic channels. We report the emergence of two focusing points along the height of the channel (z-plane), where different sized particles are focused and ordered in evenly spaced trains at correspondingly different lateral positions within the channel cross-section. We applied the system for continuous ordering and separation of suspension particles.

A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches 90° (Gau et al 1999 Science 283 46–9). Surprisingly, the fluid segments did not break up into droplets—as would be expected for a classical Rayleigh–Plateau instability—but instead displayed a long-wavelength instability where all excess fluid gathered in a single bulge along each stripe. We consider here the dynamics of the flow instability associated with this setup. We perform a linear stability analysis of the capillary flow problem in the inviscid limit. We first confirm previous work showing that all cylindrical segments are linearly unstable if (and only if) their apparent contact angle is larger than 90°. We then demonstrate that the most unstable wavenumber for the surface perturbation decreases to zero as the apparent contact angle of the fluid on the surface approaches 90°, allowing us to re-interpret the creation of bulges in the experiment as a zero-wavenumber capillary instability. A variation of the stability calculation is also considered for the case of a hydrophilic stripe located on a wedge-like geometry.

Specific harmonics of the Laplace equation are selected near a conducting Taylor cone with discrete polar angles for the field maxima. Charged nanocolloids ejected along the discrete electric field lines of these mode maxima are observed to deposit a universal spectrum of rings on an intersecting plane, with particles of different sizes occupying different spectral lines due to different residue charge. After an affine transformation, nanocolloids ejected into a microslit and deposited onto one substrate are also shown to exhibit the same universal line spectra.

Diffusiophoresis, i.e. the movement of macromolecules along a molecular gradient, is shown to be an efficient means to drive particles in microchannels. By using a generic microfluidic setup, we assess the displacement of silica particles under a controlled salt gradient and provide experimental evidence for a strongly enhanced migration process, the amplitude of which depends on the nature of the salt. A theoretical description shows quantitative agreement with the observed experimental features. Furthermore, we describe a set of microfluidic operations such as separation, sorting or focusing of a colloidal assembly which can be efficiently performed using diffusiophoresis.

We perform extensive experiments with coflowing liquids in microfluidic devices and provide a closed expression for the drop size as a function of measurable parameters in the jetting regime that accounts for the experimental observations; this expression works irrespective of how the jets are produced, providing a powerful design tool for this type of experiments.

An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit. In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier–Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. Laplace stresses and thermal Marangoni stresses are accounted for. The particle concentration is tracked by solving a continuum advection–diffusion equation. Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles. Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microspheres evaporating on glass and polydimethylsiloxane substrates, respectively. Measured evaporation times, deposit shapes and sizes and flow fields are in very good agreement with the numerical results. Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump.

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology-optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

Using Particle Replication In Nonwetting Templates (PRINT^®) technology, multiphasic and regio-specifically functionalized shape-controlled particles have been fabricated that include end-labeled particles via post-functionalization; biphasic Janus particles that integrate two compositionally different chemistries into a single particle; and more complex multiphasic shape-specific particles. Controlling the anisotropic distribution of matter within a particle creates an extra parameter in the colloidal particle design, providing opportunities to generate advanced particles with versatile and tunable compositions, properties, and thus functionalities. Owing to their robust characteristics, these multiphasic and regio-specifically functionalized PRINT particles should be promising platforms for applications in life science and materials science.

This paper describes experiments for characterizing mass transfer at the hydrophilic surface of the substrate in a chemistrode. The chemistrode uses microfluidic plugs to deliver pulses of chemicals to a substrate with high temporal resolution, which requires efficient mass transfer between the wetting layer and the hydrophilic surface of the substrate. Here, total internal reflection fluorescence microscopy (TIRFM) was used to image the hydrophilic surface of the substrate as plugs were made to flow over it. The surface of the substrate was rapidly saturated with a fluorescent dye as the fluroesecent plugs passed over the substrate, confirming effective mass transfer between the wetting layer and the surface of the substrate. The dynamics of saturation are consistent from cycle to cycle, indicating that the chemistrode can stimulate surfaces with high reproducibility. The number of plugs required to reach 90% saturation of the hydrophilic surface of the substrate, ϕ(90%), only weakly depended on experimental conditions (the Péclet number or the capillary number). Furthermore, over a wide range of operating conditions, ϕ(90%) was less than 4. These results are useful for improving the chemistrode and for understanding other phenomena that involve diffusional transfer in multiphase or recirculating flows near surfaces.

The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, k_BT/e=25 mV. In nonlinear 'induced-charge' electrokinetic phenomena, such as ac electro-osmosis, several volts ≈100k_BT/e are applied to the double layer, and the theory breaks down and cannot explain many observed features. We argue that, under such a large voltage, counterions 'condense' near the surface, even for dilute bulk solutions. Based on simple models, we predict that the double-layer capacitance decreases and the electro-osmotic mobility saturates at large voltages, due to steric repulsion and increased viscosity of the condensed layer, respectively. The former suffices to explain observed high-frequency flow reversal in ac electro-osmosis; the latter leads to a salt concentration dependence of induced-charge flows comparable to experiments, although a complete theory is still lacking.

We perform a detailed study of the interdiffusion of two miscible liquids of different viscosities, water and a water/glycerol mixture, flowing side by side within a pressure-driven microfluidic flow. Using Raman imaging, we measure cartographies of the concentration in glycerol for different imposed flow rates. The analysis of these experimental data confirms a classical diffusive mixing since the extent of the diffusion layer follows a power law regime with the streamwise coordinate x. However, the interdiffusion layer is not located in the center of the microchannel, and its mean position y_m evolves with x during the mixing. We also derive a theoretical model and present analytical arguments to explain the above results. We demonstrate that the displacement of the interdiffusion zone y_m(x) is due to the coupling between hydrodynamics and the mixing through the dependence of the viscosity with the glycerol concentration. Eventually, we perform numerical simulations of the theoretical model and compare the solutions with the experimental data in order to estimate quantitatively an interdiffusion coefficient.

Polymeric microparticles with hexagonal surface patterns comprising of colloids or dimples were fabricated using photocurable emulsion droplets. Colloidal silica particles within the interior of the photocurable emulsion droplets formed two-dimensional (2D) crystals at the droplet surface by anchoring on the emulsion interface, and the resulting composite structures were captured by rapid photopolymerization. A microfluidic device composed of two coaxial glass capillaries was used to generate monodisperse microparticles, with the evolution time determining the area of the anchored colloidal silica particles on the microparticle that was exposed to the continuous phase. The exposed region of silica particles could be modified by the introduction of desired functional groups such as dye molecules through simple chemical reaction with a silane coupling agent. This ability to modify the surface should prove useful in many applications such as chemical or biomolecular screening and colloidal barcoding systems.

It is well known that quantum mechanics is incompatible with local realistic theories. Svetlichny showed, through the development of a Bell-like inequality, that quantum mechanics is also incompatible with a restricted class of nonlocal realistic theories for three particles where any two-body nonlocal correlations are allowed (Svetlichny 1987 Phys. Rev. D 35 3066). In the present work, we experimentally generate three-photon GHZ states to test Svetlichny's inequality. Our states are fully characterized by quantum state tomography using an overcomplete set of measurements and have a fidelity of (84±1)% with the target state. We measure a convincing, 3.6σ, violation of Svetlichny's inequality and rule out this class of restricted nonlocal realistic models.

Applying time-dependent photoemission we unravel the graphene growth process on a metallic surface by chemical vapor deposition (CVD). Graphene CVD growth is in stark contrast to the standard growth process of two-dimensional films because it is self-limiting and stops as soon as a monolayer of graphene has been synthesized. Most importantly, a novel phase of metastable graphene was discovered that is characterized by permanent and simultaneous construction and deconstruction. The high quality and large area graphene flakes are characterized by angle-resolved photoemission, proving that they are indeed monolayer and cover the whole 1×1 cm Ni(111) substrate. These findings are of high relevance to the intensive search for reliable synthesis methods for large graphene flakes of controlled layer number.

We investigate the dependence of spin squeezing on the polar angle of the initial coherent spin state |θ₀, ϕ₀⟩ in a generalized one-axis twisting model, where the detuning δ is taken into account. We show explicitly that regardless of δ and ϕ₀, previous results of the ideal one-axis twisting are recovered as long as θ₀=π/2. For a small departure of θ₀ from π/2, however, the achievable variance (V₋)_min ∼N^2/3, which is larger than the ideal case N^1/3. We also find that the maximal squeezing time t_min scales as N^−5/6. Analytic expressions of (V₋)_min and t_min are presented and they agree with numerical simulations.

Most previous studies have focused on the effect of fertility selection on the evolution of cooperation. In fact, the payoff to an individual is in terms of the effect on fitness including survival and fecundity. In this paper, we introduce a model of strategy evolution with network dynamics based on mortality selection. The intensity β of mortality selection has a nontrivial role in the evolution of both cooperation and network structure. At a defector's temptation b=1, the system gains its maximal cooperation level at β→∞. Increasing b decreases β_max for the maximal cooperation level. For network structure, the average degrees of strategists and the self-organization of clusters are investigated to understand the connections of strategists and their effects on cooperation level. Furthermore, we introduce the cooperating k-core to describe the tight level of the cooperator cluster. Cooperation is enhanced by forming a tight cooperating k-core at moderate β, but there is a collapse of the cooperating k-core when β is too large. The results indicate that cooperators outside the cooperating k-core play an important role in maintaining that core to ensure a high cooperation level. So the formation and maintenance of the cooperating k-core coordinate with each other at maximum cooperation level at a specific value of β.

We have investigated spin and orbital magnetic moments of the Re 5d ion in the double perovskites A₂FeReO₆ (A=Ba, Sr, Ca) by x-ray magnetic circular dichroism (XMCD) at the Re L_{2, 3} edges. In these ferrimagnetic compounds, an unusually large negative spin and positive orbital magnetic moment at the Re atoms was detected. The presence of a finite spin magnetic moment in a 'non-magnetic' double perovskite as observed in the double perovskite Sr₂ScReO₆ proves that Re has also a small, but finite intrinsic magnetic moment. We further show for the examples of Ba and Ca that the usually neglected alkaline earth ions undoubtedly also contribute to the magnetism in the ferrimagnetic double perovskites.

We consider a two-band superconductor with relative phase π between the two order parameters as a model for the superconducting state in ferropnictides. Within this model we calculate the microwave response and the NMR relaxation rate. The influence of intra- and interband impurity scattering beyond the Born and unitary limits is taken into account. We show that, depending on the scattering rate, various types of power law temperature dependences of the magnetic field penetration depth and the NMR relaxation rate at low temperatures may take place.

A transverse ratchet effect has been measured in magnetic/superconducting hybrid films fabricated by electron beam lithography and magnetron sputtering techniques. The samples are Nb films grown on top of an array of Ni nanotriangles. Injecting an ac current parallel to the triangle reflection symmetry axis yields an output dc voltage perpendicular to the current, due to a net motion of flux vortices in the superconductor. The effect is reproduced by numerical simulations of vortices as Langevin particles with realistic parameters. Simulations provide an intuitive picture of the ratchet mechanism, revealing the fundamental role played by the random intrinsic pinning of the superconductor.

We study the decay of an atomic Bose–Einstein condensate (BEC) population N(τ) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Λ>Λ_b, discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N(τ), which for a whole range of Λ-values follow a scale-free distribution P(J=δN)∼1/J^α. A theoretical analysis of the mixed phase space of the system indicates that 1<α<3, in agreement with our numerical findings.

We report on the observation of strong exciton–photon coupling in a ZnO-based microresonator consisting of a half medium wavelength ZnO cavity embedded between two dielectric Bragg reflectors made of 10.5 layer pairs of yttria stabilized zirconia and Al₂O₃. The microresonator was investigated by photoluminescence and reflectivity measurements in a wide temperature range between 10 and 550 K. With both techniques a lower polariton branch (LPB) was observable. As expected no signal from an upper polariton branch could be detected caused by the strong absorption of ZnO in this spectral range. The dispersion behaviour of the LPB (in both energy and broadening) is well described by a model that takes into account the coupling between one exciton mode and one cavity-photon mode. From this analysis we can conclude that the microresonator is in the strong coupling regime up to 410 K. Maximum values of the coupling strength at 10 K of 51 meV, respectively 55 meV, could be derived from the photoluminescence and from the reflectivity. These results demonstrate the high potential of ZnO microresonators for the realization of a Bose–Einstein condensation at room temperature and above.

We present an experimental and theoretical study of the conductance and stability of Mg atomic-sized contacts. Using mechanically controllable break junctions (MCBJ), we observed that the room temperature conductance histograms exhibit a series of peaks, which suggests the existence of a shell effect. Its periodicity, however, cannot be simply explained in terms of either an atomic or electronic shell effect. We also found that at room temperature, contacts of the diameter of a single atom are absent. A possible interpretation could be the occurrence of a metal-to-insulator transition as the contact radius is reduced, in analogy with what is known in the context of Mg clusters. However, our first principles calculations show that while an infinite linear chain can be insulating, Mg wires with larger atomic coordinations, as in realistic atomic contacts, are always metallic. Finally, at liquid helium temperature, our measurements show that the conductance histogram is dominated by a pronounced peak at the quantum of conductance. This is in good agreement with our calculations based on a tight-binding model that indicated that the conductance of a Mg one-atom contact is dominated by a single fully open conduction channel.

The origin of ferromagnetism in Co-doped (La,Sr)TiO₃ epitaxial thin films is discussed. While the as-grown samples are not ferromagnetic at room temperature or at 10 K, ferromagnetism at room temperature appears after annealing the films in reducing conditions and disappears after annealing in oxidizing conditions. Magnetic measurements, x-ray absorption spectroscopy, x-ray photoemission spectroscopy and transmission electron microscopy experiments indicate that within the resolution of the instruments the activation of the ferromagnetism is not due to the presence of pure Co.

The lattice dynamical and allied properties of the multiferroic manganites SmMnO₃, EuMnO₃ and GdMnO₃ were investigated in this work by means of a shell model with transferable pairwise interionic interaction potential. This shell-model potential is able to reproduce the available crystal structure and phonon frequencies. A zone center imaginary A_u mode is observed in these lattice dynamics calculations that indicates metastability of the perovskite phase. Comparison of the Gibbs free energies in the orthorhombic and hexagonal phases points to the possible coexistence of the two phases of these manganites under ambient conditions.

We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.

We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities interested in investigating and characterizing multipartite entangled states by introducing realistic milestones for setup design and associated predictions.

We apply the wave-kinetic approach to study nonlinearly coupled Rossby wave-zonal flow fluid turbulence in a two-dimensional rotating fluid. Specifically, we consider for the first time nonlinear excitations of zonal flows by a broad spectrum of Rossby wave turbulence. Short-wavelength Rossby waves are described here as a fluid of quasi-particles, and are referred to as the 'Rossbyons'. It is shown that Reynolds stresses of Rossbyons can generate large-scale zonal flows. The result should be useful in understanding the origin of large-scale planetary and near-Earth atmospheric circulations. It also provides an example of a turbulent wave background driving a coherent structure.

We consider electronic transport through a suspended voltage-biased nanowire subject to an external magnetic field. In this paper, we show that the transverse magnetic field, which acts to induce coupling between the tunneling current and the vibrational modes of the wire, controls the current–voltage characteristics of the system in novel ways. In particular, we derive the quantum master equation for the reduced density matrix describing the nanowire vibrations. From this we find a temperature- and bias voltage-independent current deficit in the limit of high bias voltage since the current through the device is lower than its value at zero magnetic field. We also find that the corrections to the current from the back-action of the vibrating wire decay exponentially in the limit of high voltage. Furthermore, it is shown that the expression for the temperature- and bias voltage-independent current deficit holds even if the nanowire vibrational modes have been driven out of thermal equilibrium.

To consider the origin of a pseudo-gap and a superconducting gap found in the high-T_c cuprates, the momentum dependence of the singlet gap parameter and the superconductivity correlation function are evaluated in the t–J model by using an optimization variational Monte Carlo method. In the underdoped regime, the singlet gap is significantly modified from the simple d_{x²- y²}-wave gap (∝cos k_x-cos k_y) by the contributions of long-range pairings. Its angular dependence along the Fermi surface is qualitatively consistent with those experimentally observed in both hole- and electron-doped cuprates. This singlet gap will correspond to the pseudo-gap and its doping dependence agrees with that of the pseudo-gap. On the other hand, the superconductivity correlation function is dominant in the nearest-neighbor pairing and its Fourier transform preserves the original simple d_{x²- y²}-wave form. We argue that this superconductivity correlation function is closely related to the coherent superconductivity gap appearing below T_c in the 'Fermi arc' region. Its doping dependence is also consistent with the recent experimental observations.

Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here, we focus on variational approaches, but comparisons with both quantum cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the quantum cluster method. An interesting trend is found by comparing gap parameters Δ (antiferromagnetic or superconducting) obtained with different variational wave functions. Δ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.

In an accompanying paper (Sauls and Eschrig 2009 New J. Phys. 11 075008) we have studied the equilibrium properties of vortices in a chiral quasi-two-dimensional triplet superfluid/superconductor. Here we extend our studies to include the dynamical response of a vortex core in a chiral triplet superconductor to an external ac electromagnetic field. We consider in particular the response of a doubly quantized vortex with a homogeneous core in the time-reversed phase. The external frequencies are assumed to be comparable in magnitude to the superconducting gap frequency, such that the vortex motion is nonstationary but can be treated by linear response theory. We include broadening of the vortex-core bound states due to impurity scattering and consider the intermediate-clean regime, with a broadening comparable to or larger than the quantized energy level spacing. The response of the order parameter, impurity self-energy, induced fields and currents are obtained by a self-consistent calculation of the distribution functions and the excitation spectrum. Using these results we obtain the self-consistent dynamically induced charge distribution in the vicinity of the core. This charge density is related to the nonequilibrium response of the bound states and order parameter collective mode, and dominates the electromagnetic response of the vortex core.

Superconductors exhibit unconventional electronic and magnetic properties if the Cooper pair wave function breaks additional symmetries of the normal phase. Rotational symmetries in spin and orbital spaces, as well as discrete symmetries such as space and time inversion, may be spontaneously broken. When this occurs in conjunction with broken global U(1) gauge symmetry, new physical phenomena are exhibited below the superconducting transition that are characteristic of the broken symmetries of the pair condensate. This is particularly true of vortices and related defects. Superconductors with a multi-component order parameter exhibit a variety of different vortex structures and closely related defects that are not possible in condensates belonging to a one-dimensional (1D) representation. In this paper, we discuss the structure of vortices in fermionic superfluids and superconductors which break chiral symmetry, i.e. combined broken time inversion and 2D parity. In particular, we consider the structure of vortices and defects that might be realized in thin films of ³He-A and the layered superconductor Sr₂RuO₄, and identify some of the characteristic signatures of broken chiral symmetry that should be revealed by these defects.

We report upper critical field B_c2(T) data for LaO_0.9F_0.1FeAs_{1- δ} in a wide temperature and field range up to 60 T. The large slope of B_c2≈- 5.4 to -6.6 T K^-1 near an improved T_c≈28.5 K of the in-plane B_c2(T) contrasts with a flattening starting near 23 K above 30 T we regard as the onset of Pauli-limited behaviour (PLB) with B_c2(0)≈63–68 T. We interpret a similar hitherto unexplained flattening of the B_c2(T) curves reported for at least three other disordered closely related systems, Co-doped BaFe₂As₂, (Ba,K) Fe₂As₂ and NdO_0.7F_0.3FeAs (all single crystals), for applied fields H∥(a,b), also as a manifestation of PLB. Their Maki parameters have been estimated by analysing their B_c2(T) data within the Werthamer–Helfand–Hohenberg approach. The pronounced PLB of (Ba, K)Fe₂As₂ single crystals obtained from an Sn flux is attributed also to a significant As deficiency detected by wavelength dispersive x-ray spectroscopy as reported by Ni et al (2008 Phys. Rev. B 78 014507). Consequences of our results are discussed in terms of disorder effects within conventional superconductivity (CSC) and unconventional superconductivity (USC). USC scenarios with nodes on individual Fermi surface sheets (FSS), e.g. p- and d-wave SC, can be discarded for our samples. The increase of dB_c2/dT|_Tc by sizeable disorder provides evidence for an important intraband (intra-FSS) contribution to the orbital upper critical field. We suggest that it can be ascribed either to an impurity-driven transition from s_± USC to CSC of an extended s₊₊-wave state or to a stabilized s_±-state provided As-vacancies cause predominantly strong intraband scattering in the unitary limit. We compare our results with B_c2 data from the literature, which often show no PLB for fields below 60–70 T probed so far. A novel disorder-related scenario of a complex interplay of SC with two different competing magnetic instabilities is suggested.

We reveal a generic mechanism of generating sign-alternating intersite interactions mediated by strongly correlated lattice bosons. The ground-state phase diagram of the two-component hard-core Bose–Hubbard model on a square lattice at half-integer filling factor for each component, obtained by worm algorithm Monte Carlo simulations, is strongly modified by these interactions and features the solid+superfluid (SF) phase for strong asymmetry between the hopping amplitudes. The new phase is a direct consequence of the effective nearest-neighbor repulsion between 'heavy' atoms mediated by the 'light' SF component. Due to their sign-alternating character, mediated interactions lead to a rich variety of yet to be discovered quantum phases.

We have implemented an optical quantum eraser with the aim of studying this phenomenon in the context of state discrimination. An interfering single photon is entangled with another one serving as a which-path marker. As a consequence, the visibility of the interference as well as the which-path information are constrained by the overlap (measured by the inner product) between the which-path marker states, which in a more general situation are non-orthogonal. In order to perform which-path or quantum eraser measurements while analysing non-orthogonal states, we resort to a probabilistic method for the unambiguous modification of the inner product between the two states of the which-path marker in a discrimination-like process.

A general, twisted and tilted, grain boundary in copper has been simulated using the adaptive kinetic Monte Carlo method to study the atomistic structure of the non-crystalline region and the mechanism of annealing events that occur at low temperature. The simulated time interval spanned 67 μs at 135 K. Similar final configurations were obtained starting from different initial structures: (i) by bringing the two grains into contact without any intermediate layer, and (ii) by inserting an amorphous region between the grains. The results obtained were analyzed with a radial distribution function and a common neighbor analysis. Annealing events leading to lowering of the energy typically involved concerted displacement of several atoms—even as many as 10 atoms displaced by more than half an Ångström. Increased local icosahedral ordering is observed in the boundary layer, but local HCP coordination was also observed. In the final low-energy configurations, the thickness of the region separating the crystalline grains corresponds to just one atomic layer, in good agreement with reported experimental observations. The simulated system consists of 1307 atoms and atomic interactions were described using effective medium theory.

Much of optics depends on objects being much larger than the wavelength of light: shadows of opaque objects are sharp only if free of diffraction effects, and 'cat's eye' retroreflectors function only if they are large. Here, we show how to make theoretically arbitrarily small versions of these devices by exploiting the power of a negatively refracting lens to magnify objects that are smaller than the wavelength, thus creating the effect of a large object while keeping all physical dimensions small. We also give a new perspective on the 'perfect lens theorem' on which the paper is based.

We introduce a novel cooling technique capable of approaching the quantum ground state of a kilogram-scale system—an interferometric gravitational wave detector. The detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) operate within a factor of 10 of the standard quantum limit (SQL), providing a displacement sensitivity of 10⁻¹⁸ m in a 100 Hz band centered on 150 Hz. With a new feedback strategy, we dynamically shift the resonant frequency of a 2.7 kg pendulum mode to lie within this optimal band, where its effective temperature falls as low as 1.4 μK, and its occupation number reaches about 200 quanta. This work shows how the exquisite sensitivity necessary to detect gravitational waves can be made available to probe the validity of quantum mechanics on an enormous mass scale.

We show how to calculate the fraction of single-photon counts of the 3-intensity decoy-state quantum cryptography faithfully with both statistical fluctuations and source errors. Our results rely only on the bound values of a few parameters of the states of pulses.

We explore the quantum dynamics of heteronuclear atomic collisions in waveguides and demonstrate the existence of a novel mechanism for the resonant formation of polar molecules. The molecular formation probabilities can be tuned by changing the trap frequencies that characterize the transverse modes of the atomic species. The origin of this effect is the confinement-induced mixing of the relative and center of mass motions in the atomic collision process leading to a coupling of the diatomic continuum to the center of mass excited molecular states in closed transverse channels.

We show that the room temperature resistivity of Ba_0.5Sr_1.5Zn₂Fe₁₂O₂₂ single crystals increases by more than three orders of magnitude upon being subjected to optimized heat treatments. The increase in the resistivity allows the determination of magnetic field (H)-induced ferroelectric phase boundaries up to 310 K through measurements of dielectric constant at a frequency of 10 MHz. Between 280 and 310 K, the dielectric constant curve shows a peak centered at zero magnetic field and thereafter decreases monotonically up to 0.1 T, exhibiting a magnetodielectric effect of 1.1%. This effect is ascribed to the realization of magnetic field-induced ferroelectricity at an H value of less than 0.1 T near room temperature. Comparison between electric and magnetic phase diagrams in wide temperature- and field-windows suggests that the magnetic field for inducing ferroelectricity has decreased near its helical spin ordering temperature around 315 K due to the reduction of spin anisotropy in Ba_0.5Sr_1.5Zn₂Fe₁₂O₂₂.

We propose a new approach to the consistency test of dark energy models with observations. To test a category of dark energy models, we suggest introducing a characteristic Q(z) that, in general, varies with the redshift z but, in those models, plays the role of a (constant) distinct parameter. Then, by reconstructing dQ(z)/dz from observational data and comparing it with zero, we can assess the consistency between data and the models under consideration. For a category of models that passes the test, we can further constrain the distinct parameter of those models by reconstructing Q(z) from data. For demonstration, in this paper we concentrate on quintessence. In particular, we examine the exponential potential and the power-law potential via a widely used parameterization of the dark energy equation of state, w(z)=w₀+w_a(1−a), for data analysis. This method of the consistency test is particularly efficient because for all models we invoke the constraint of only a single parameter space that by choice can be easily accessed. The general principle of our approach is not limited to dark energy. It may also be applied to the testing of various cosmological models and even models in other fields beyond the scope of cosmology.

We investigated the ratio of the surface superconducting field (H_c3) to the bulk superconducting field (H_c2) in MgB₂ single crystals at different temperatures and at different angles between the field and the c-axis of the crystal by using electrical transport measurements. The temperature dependence of the ratio H_c3/H_c2 at different angles was qualitatively well described by a recent theory based on the two-gap nature of MgB₂. The angular dependence of the ratio shows that it can be both enhanced and reduced, which can be explained by the two-band theory. If slight deviations of H_c3/H_c2 from the value for the half-infinite geometry used in the theory are to be accommodated, effects due to the finite geometry and to the orientation of the applied field relative to the crystal plane need to be considered.

The Gutzwiller-projected BCS Hamiltonian is a useful model for high-temperature superconductivity due to its equivalence to the Heisenberg model at half filling and a close connection to the t–J model at moderate doping. In this work, a dynamical mean field theory (DMFT) is developed for the BCS Hamiltonian with d-wave pairing subject to on-site repulsive interaction, U, which we call the BCS+U model. The large-U limit corresponds to the Gutzwiller-projected BCS Hamiltonian. It is shown that the equivalence between the Heisenberg and the Gutzwiller-projected BCS model is a manifestation of a broader duality in the BCS+U model: for any finite U, the local dynamics of the BCS+U model is dual at half filling with respect to the exchange between the hopping parameter, t, and the pairing amplitude, Δ. It is explicitly demonstrated in our DMFT analysis that the real superconducting gap, determined from the sharp coherence peaks in the local density of states, shows strong renormalization from its bare value as a function of U.

We investigated the instability properties of ring-profile vortex solitons supported by Bessel lattices in defocusing cubic media. The instability domain of vortex solitons can be significantly suppressed by selecting the higher-order Bessel lattice as a linear refractive index guidance. The finding provides an effective way for the realization of stable vortex solitons with higher topological charges (e.g. m=5) by relatively shallow lattices.

Hard and soft x-ray photoelectron spectroscopy was performed for core and valence electrons in solid compounds containing V and O atoms. The single-nucleus recoil effects on photoelectron emission were observed in the form of recoil shifts for all core levels and the valence band in a heavy Fermion material LiV₂O₄, whereas such shifts were negligible in VO₂ even in the high-temperature metal phase. The valence band recoil shifts of V₅O₉ and V₂O₃ metal are found to be in between. These differences in the valence band are ascribable to the difference in the relative spectral weight of the O 2p component near the Fermi level.

The electronic structure single crystals of the new double perovskite Sr₂YRu_1−xCu_xO₆ (x = 0–0.05) has been investigated by x-ray absorption near-edge structure (XANES) spectroscopy. The Cu K-edge spectra show that Cu is incorporated as Cu¹⁺ and Cu²⁺ in the crystals grown in air and in an oxygen atmosphere and Ru⁵⁺ is seen in the Ru K-edge spectra. The O K-edge and the Ru L₃-edge spectra indicate an increase in the unoccupied states (hole concentration) as x is increased, accompanied by a lattice distortion from an increased O–Ru–O bond angle. These changes observed even with a small Cu addition are interpreted to result from the Cu 3d–O 2p hybridization as Cu replaces Ru in the octahedral sites.

We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique (Higgins et al 2007 Nature 450 393), our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes.

We demonstrate experimentally and theoretically the existence of slow chaotic spiking sequences in the dynamics of a semiconductor laser with ac-coupled optoelectronic feedback. The timescale of these dynamics is fully determined by the high-pass filter in the feedback loop and their erratic, though deterministic, nature is evidenced by means of the interspike interval (ISI) probability distribution. We eventually show that this regime is the result of an incomplete homoclinic scenario to a saddle-focus, where an exact homoclinic connection does not occur.

We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-state energy is often efficiently estimated. An introduction of quantum transitions to all states with equal weights is shown to greatly improve the situation, but with a sacrifice in annealing time. We also clarify the relation between the spin configurations in degenerate ground states and the probabilities that those states are obtained by quantum annealing. The strengths and weaknesses of quantum annealing for problems with degenerate ground states are discussed in comparison with classical simulated annealing.

We present measurements of conditional probability density functions (PDFs) that allow one to systematically bridge from Eulerian to Lagrangian statistics in fully developed 3D turbulence. The transition is investigated for hydro- as well as magnetohydrodynamic flows and comparisons are drawn. Significant differences in the transition PDFs are observed for these flows and traced back to the differing coherent structures. In particular, we address the problem of an increasing degree of intermittency going from Eulerian to Lagrangian coordinates by means of the conditional PDFs involved in this transformation. First simple models of these PDFs are investigated in order to distinguish different contributions to the degree of Lagrangian intermittency.

Supercurrents in superconducting flux threaded loops are expected to oscillate with the magnetic flux with a period of hc/2e. This is indeed true for s-wave superconductors larger than the coherence length ξ₀. Here, we show that for superconductors with gap nodes, there is no such strict condition for the supercurrent to be hc/2e rather than hc/e periodic. For nodal superconductors, the flux-induced Doppler shift of the near-nodal states leads to a flux-dependent occupation probability of quasi-particles circulating clockwise and counter clockwise around the loop, which leads to an hc/e periodic component of the supercurrent, even at zero temperature. We analyze this phenomenon on a cylinder in an approximative analytic approach and also numerically within the framework of the BCS theory. Specifically for d-wave pairing, we show that the hc/e periodic current component decreases with the inverse radius of the loop and investigate its temperature dependence.

We present ⁷⁵As nuclear magnetic resonance data in the paramagnetic and magnetic states of single-crystal CaFe₂As₂. The electric field gradient and the internal magnetic field at the As sites change discontinuously below the first-order structural transition at T₀=169 K. In the magnetic state, we find a single value of the internal hyperfine field consistent with commensurate antiferromagnetic order of Fe moments pointing in the ab plane. The spin lattice relaxation rate shows Korringa behavior for T≲T₀/3, reflecting the metallic nature of the ordered state. Surprisingly, T₁^-1 exhibits a small peak at 10 K, revealing the presence of slow spin fluctuations that may be associated with domain wall motion.

Nonstationary and steady-state transport through a mesoscopic sample connected to particle reservoirs via time-dependent barriers is investigated by the reduced density operator method. The generalized master equation is solved via the Crank–Nicolson algorithm by taking into account the memory kernel which embodies the non-Markovian effects that are commonly disregarded. The lead–sample coupling takes into account the match between the energy of the incident electrons and the levels of the isolated sample, as well as their overlap at the contacts. Using a tight-binding description of the system, we investigate the effects induced in the transient current by the spectral structure of the sample and by the localization properties of its eigenfunctions. In strong magnetic fields, the transient currents propagate along edge states. The behavior of populations and coherences is discussed, as well as their connection to the tunneling processes that are relevant for transport.

In this work, the quantum dot (QD) formation of InAs on In_0.5Ga_0.5As/InP(001) has been studied theoretically using a hybrid approach. The surface energies were calculated using density functional theory. For elastic relaxation energies, continuum elasticity theory was applied. This hybrid method, as already shown in the literature, takes into account the atomic structure of the various facets of the QDs as well as the wetting layer. Our study deals with the aspect of shape evolution of InAs QDs on a ternary substrate. It shows how the island shape close to equilibrium evolves with varying volume in InAs/In_0.5Ga_0.5As/InP (001) epitaxy. Overall, our study indicates that for this system, there may exist two paths for island growth: one path involves an early energetic stabilization of flat, hut-shaped islands with high-index facets (that may persist due to kinetic limitations), whereas the other path involves islands with larger height-to-base ratios that develop low-index facets. At large volumes, the steeper but more compact islands tend to be energetically more favourable compared to the elongated shapes.

We consider a dusty plasma where dust particles have a magnetic dipole moment. A Hall-MHD type of model, generalized to account for the intrinsic magnetization, is derived. The model is shown to be energy conserving, and the energy density and flux are derived. The general dispersion relation is then derived, and we show that kinetic dust-Alfvén waves exhibit instability for a low dust and ion temperature and high dust density. We discuss the implication of our results.

The frequencies of the 2S–3S two-photon transition for the stable lithium isotopes were measured by cavity-enhanced Doppler-free laser excitation that was controlled by a femtosecond frequency comb. The resulting values of 815 618 181.57(18) and 815 606 727.59(18) MHz, respectively, for ⁷Li and ⁶Li are in agreement with previous measurements but are more accurate by an order of magnitude. There is still a discrepancy of about 11.6 and 10.6 MHz from the latest theoretical values. This is comparable to the uncertainty in the theoretical calculations, while uncertainty in our experimental values is more than a hundred-fold smaller. More accurate theoretical calculation of the transition frequencies would allow extraction of the absolute charge radii for these stable isotopes, which in turn could improve nuclear charge radii values for the unstable lithium isotopes.

We investigate the ground state of one-dimensional few-atom Bose–Bose mixtures under harmonic confinement throughout the crossover from weak to strong inter-species attraction. The calculations are based on the numerically exact multi-configurational time-dependent Hartree method. For repulsive components, we detail the condition for the formation of a molecular Tonks–Girardeau gas in the regime of intermediate inter-species interactions, and the formation of a molecular condensate for stronger coupling. Beyond a critical inter-species attraction, the system collapses to an overall bound state. Different pathways emerge for unequal particle numbers and intra-species interactions. In particular, for mixtures with one attractive component, this species can be viewed as an effective potential dimple in the trap center for the other, repulsive component.

Studying generalized non-signaling theories brings insight into the foundations of quantum mechanics. Here we focus on a dynamical process in such general theories, namely non-locality swapping, the analogue of quantum entanglement swapping. In order to implement such a protocol, one needs to define a coupler, which performs the equivalent of quantum joint measurements on generalized 'box-like' states. Establishing a connection to Bell inequalities, we define consistent couplers for theories containing an arbitrary amount of non-locality, which leads us to introduce the concepts of perfect and minimal couplers. Remarkably, Tsirelson's bound for quantum non-locality naturally appears in our study.

A modification of the classical Bohm sheath criterion is investigated in complex plasmas containing Boltzmann electrons, cold fluid ions and strongly coupled microparticles. Equilibrium is provided by an effective 'temperature' associated with electrostatic interactions between charged grains. Using the small-potential expansion approach of the Sagdeev potential, a significant reduction of the ion Bohm velocity is obtained for complex plasma parameters relevant for experiments. The result is of consequence for all problems involving ion drag on microparticles, including parametric instability, structure formation, wave propagation, etc.

A follow-the-leader model of traffic flow on a closed loop is considered in the framework of the extended optimal velocity (OV) model where the driver reacts to both the following and the preceding car. Periodic wave train solutions that describe the formation of traffic congestion patterns are found analytically. Their velocity and amplitude are determined from a perturbation approach based on collective coordinates with the discrete modified Korteweg–de Vries equation as the zero order equation. This contains the standard OV model as a special case. The analytical results are in excellent agreement with numerical solutions.

A comprehensive theoretical study of the optical properties and switching competence of double-shell photonic crystals (DSPC) and double-inverse-opal photonic crystals (DIOPC) is presented. Our analysis reveals that a DIOPC structure with a silicon (Si) background exhibits a complete photonic bandgap (PBG), which can be completely switched on and off by moving the core spheres inside the air pores of the inverse opal. We show that the size of this switchable PBG assumes a value of 3.78% upon judicious structural optimization, while its existence is almost independent of the radii of the interconnecting cylinders, whose sizes are difficult to control during the fabrication process. The Si-based DIOPC may thus offer a novel and practical route to complete PBG switching and optical functionality.

We present a dynamical model that successfully explains the observed time evolution of the magnetization in diluted magnetic semiconductor quantum wells after weak laser excitation. Based on the pseudo-fermion formalism and a second-order many-particle expansion of the exact p–d exchange interaction, our approach goes beyond the usual mean-field approximation. It includes both the sub-picosecond demagnetization dynamics and the slower relaxation processes that restore the initial ferromagnetic order in a nanosecond timescale. In agreement with experimental results, our numerical simulations show that, depending on the value of the initial lattice temperature, a subsequent enhancement of the total magnetization may be observed within the timescale of a few hundred picoseconds.

An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime.

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid for a wide family of initial conditions, such as canonical, constrained canonical, multi-canonical and grand canonical distributions, as well as both for classical and quantum systems.

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre–Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation.

We present theoretical and numerical studies of the acceleration of monoenergetic protons in a double layer formed by the laser irradiation of an ultra-thin film. The ponderomotive force of the laser light pushes the electrons forward, and the induced space charge electric field pulls the ions and makes the thin foil accelerate as a whole. The ions trapped by the combined electric field and inertial force in the accelerated frame, together with the electrons trapped in the well of the ponderomotive and ion electric field, form a stable double layer. The trapped ions are accelerated to monoenergetic energies up to 100 MeV and beyond, making them suitable for cancer treatment. We present an analytic theory for the laser-accelerated ion energy and for the amount of trapped ions as functions of the laser intensity, foil thickness and the plasma number density. We also discuss the underlying physics of the trapped and untrapped ions in a double layer. The analytical results are compared with those obtained from direct Vlasov simulations of the fully nonlinear electron and ion dynamics that is controlled by the laser light.

We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos–Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.

Two stationary, partially polarized electromagnetic beams with equal degrees of polarization may exhibit completely different time evolutions of the instantaneous polarization state. In this work, we derive a statistical quantity that describes the rate at which the field intensity in the beam, on average, is redistributed between the beam's polarization state at any time and the state orthogonal to it. This method allows one to treat the dynamical properties of the polarization fluctuations both theoretically and experimentally. We demonstrate the method by applying it to important special cases, such as fields obeying Gaussian statistics, black-body radiation pencils and depolarized laser beams. We also prove that a geometric approach introduced earlier is closely connected with the present model.

We present a detailed direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation with the incompressibility constraint and air-drag-induced Ekman friction; our DNS has been designed to investigate the combined effects of walls and such a friction on turbulence in forced thin films. We concentrate on the forward-cascade regime and show how to extract the isotropic parts of velocity and vorticity structure functions and hence the ratios of multiscaling exponents. We find that velocity structure functions display simple scaling, whereas their vorticity counterparts show multiscaling, and the probability distribution function of the Weiss parameter Λ, which distinguishes between regions with centers and saddles, is in quantitative agreement with experiments.

We present a fully automated quantum key distribution prototype running at 625 MHz clock rate. Taking advantage of ultra low loss (ULL) fibres and low-noise superconducting detectors, we can distribute 6000 secret bits s⁻¹ over 100 km and 15 bits s⁻¹ over 250 km.

A quantum key distribution (QKD) network is an infrastructure that allows the realization of the key distribution cryptographic primitive over long distances and at high rates with information-theoretic security. In this work, we consider QKD networks based on trusted repeaters from a topology viewpoint, and present a set of analytical models that can be used to optimize the spatial distribution of QKD devices and nodes in specific network configurations in order to guarantee a certain level of service to network users, at a minimum cost. We give details on new methods and original results regarding such cost minimization arguments applied to QKD networks. These results are likely to become of high importance when the deployment of QKD networks will be addressed by future quantum telecommunication operators. They will therefore have a strong impact on the design and requirements of the next generation of QKD devices.

In this paper, we present the quantum key distribution (QKD) network designed and implemented by the European project SEcure COmmunication based on Quantum Cryptography (SECOQC) (2004–2008), unifying the efforts of 41 research and industrial organizations. The paper summarizes the SECOQC approach to QKD networks with a focus on the trusted repeater paradigm. It discusses the architecture and functionality of the SECOQC trusted repeater prototype, which has been put into operation in Vienna in 2008 and publicly demonstrated in the framework of a SECOQC QKD conference held from October 8 to 10, 2008. The demonstration involved one-time pad encrypted telephone communication, a secure (AES encryption protected) video-conference with all deployed nodes and a number of rerouting experiments, highlighting basic mechanisms of the SECOQC network functionality.

The paper gives an overview of the eight point-to-point network links in the prototype and their underlying technology: three plug and play systems by id Quantique, a one way weak pulse system from Toshiba Research in the UK, a coherent one-way system by GAP Optique with the participation of id Quantique and the AIT Austrian Institute of Technology (formerly ARCAustrian Research Centers GmbH—ARC is now operating under the new name AIT Austrian Institute of Technology GmbH following a restructuring initiative.), an entangled photons system by the University of Vienna and the AIT, a continuous-variables system by Centre National de la Recherche Scientifique (CNRS) and THALES Research and Technology with the participation of Université Libre de Bruxelles, and a free space link by the Ludwig Maximillians University in Munich connecting two nodes situated in adjacent buildings (line of sight 80 m). The average link length is between 20 and 30 km, the longest link being 83 km.

The paper presents the architecture and functionality of the principal networking agent—the SECOQC node module, which enables the authentic classical communication required for key distillation, manages the generated key material, determines a communication path between any destinations in the network, and realizes end-to-end secure transport of key material between these destinations.

The paper also illustrates the operation of the network in a number of typical exploitation regimes and gives an initial estimate of the network transmission capacity, defined as the maximum amount of key that can be exchanged, or alternatively the amount of information that can be transmitted with information theoretic security, between two arbitrary nodes.

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a nonzero information centrality to be extensive/subextensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results for the information flow in social networks are discussed.

The paper demonstrates the possibility to control the collective behavior of a large network of excitable stochastic units, in which oscillations are induced merely by external random input. Each network element is represented by the FitzHugh–Nagumo system under the influence of noise, and the elements are coupled through the mean field. As known previously, the collective behavior of units in such a network can range from synchronous to non-synchronous spiking with a variety of states in between. We apply the Pyragas delayed feedback to the mean field of the network and demonstrate that this technique is capable of suppressing or weakening the collective synchrony, or of inducing the synchrony where it was absent. On the plane of control parameters we indicate the areas where suppression of synchrony is achieved. To explain the numerical observations on a qualitative level, we use the semi-analytic approach based on the cumulant expansion of the distribution density within Gaussian approximation. We perform bifurcation analysis of the obtained cumulant equations with delay and demonstrate that the regions of stability of its steady state have qualitatively the same structure as the regions of synchrony suppression of the original stochastic equations. We also demonstrate the delay-induced multistability in the stochastic network. These results are relevant to the control of unwanted behavior in neural networks.