Table of contents

Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of the parameters.

The main goal of this work is to model a homogeneous computer material with well-defined mechanical properties. To carry out the model material, an internal structure arranged in layers with different atom sizes is implemented using a simple interatomic law of Lennard-Jones type (LJ). We show that imposing an appropriate scaling law between the interatomic potentials from different layers, we obtain the same mechanical properties as if the material was homogeneous. Employing this scheme, given a fixed space volume to be occupied by the solid, this structural arrangement allows to decrease drastically (∼30–80%) the required number of atoms as compared with the case of a homogeneous solid, decreasing the computational effort and speeding up calculations. In that respect, this procedure is an analogous to mesh refinements methodologies usually applied in the continuum approaches.

The dynamics of small-amplitude solitons in one-dimensional arrays of short Josephson junctions with negative group velocity is reported. Analytical expression of the solitons are derived. Dynamics of bright and dark solitons is numerically studied. Very high soliton velocities are observed. The effect of the modulation instability on the envelope shape is analyzed and the effect of loss is discussed.

We use the Swift-Hohenberg model and normal-form equations to study wave-number locking in two-dimensional systems as a result of one-dimensional spatially periodic weak forcing. The freedom of the system to respond in a direction transverse to the forcing leads to wave-number locking in a wide range of forcing wave-numbers, even for weak forcing, unlike the locking in a set of narrow Arnold tongues in one-dimensional systems. Multi-stability ranges of stripe, rectangular, and oblique patterns produce a variety of resonant patterns. The results shed new light on rehabilitation practices of banded vegetation in drylands.

We consider elementary excitations of an interacting Bose-Einstein condensate in the mean-field framework. As a building block for understanding the dynamics of systems comprising interaction and disorder, we study the scattering of Bogoliubov excitations by a single external impurity potential. A numerical integration of the Gross-Pitaevskii equation shows that the single-scattering amplitude has a marked angular anisotropy. By a saddle point expansion of the hydrodynamic mean-field energy functional, we derive the relevant scattering amplitude including the crossover from sound-like to particle-like excitations. The very different scattering properties of these limiting cases are smoothly connected by an angular envelope function with a well-defined node of vanishing scattering amplitude. We find that the overall scattering is most efficient at the crossover from phonon-like to particle-like Bogoliubov excitations.

It is shown that on a finite phase plane the kq-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number M defining the size of the phase plane can be expressed as a product, M=M₁M₂, with M₁ and M₂ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.

The Schwarzschild metric has a divergent energy density at the horizon, which motivates a new approach to black holes. If matter is spread uniformly throughout the interior of a supermassive black hole, with mass M∼M_⋆=2.34 10⁸M_⊙, it may arise from a Bose-Einstein condensate of densely packed H atoms. Within the relativistic theory of gravitation with a positive cosmological constant, a bosonic quantum field is coupled to the curvature scalar. In the Bose-Einstein condensed ground state an exact, self-consistent solution for the metric is presented. It is regular with a specific shape at the origin. The redshift at the horizon is finite but large, z∼10¹⁴M_⋆/M. The binding energy remains as an additional parameter to characterize the BH; alternatively, the mass observed at infinity can be any fraction of the rest mass of its constituents.

We report the transport of ultracold atoms with optical tweezers in the non-adiabatic regime, i.e. on a time scale on the order of the oscillation period. We have found a set of discrete transport durations for which the transport is not accompanied by any excitation of the centre of mass of the cloud after the transport. We show that the residual amplitude of oscillation of the dipole mode is given by the Fourier transform of the velocity profile imposed to the trap for the transport. This formalism leads to a simple interpretation of our data and simple methods for optimizing trapped particles displacement in the non-adiabatic regime.

I present a method to simulate complex-shaped interacting bodies, a problem which appears in many areas, including molecular dynamics, material science, virtual reality, geo- and astrophysics. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well-defined conservative and frictional interaction between these bodies is derived. The model (particles+interactions) is much more efficient, accurate and easier to implement than other models. Simulations with conservative interactions comply with the statistical mechanical principles for conservative systems. Simulations with frictional forces show that particle shape strongly affects the jamming phenomena in granular flow.

We show the formation of bright and dark slow optical solitons based on intersubband transitions in a semiconductor quantum well (SQW). Using the coupled Schrödinger-Maxwell approach, we provide both analytical and numerical results. Such a nonlinear optical process may be used for the control technology of optical delay lines and optical buffers in the SQW solid-state system. With appropriate parameters, we also show the generation of a large cross-phase modulation (XPM). Since the intersubband energy level can be easily tuned by an external bias voltage, the present investigation may open possibilities for electrically controlled phase modulators in solid systems.

We propose a simple model of the dynamics of a contact line under evaporation and partial wetting conditions, taking into account the divergent nature of evaporation near the contact line, as evidenced by Deegan et al. (Nature, 389 (1997) 827). We show that evaporation can induce a non-negligible change of the contact angle together with modification of the flow near the contact line. We apply our results to dip-coating of a substrate with non volatile solutes. We show that at small velocities the coating thickness increases and scales like the inverse of the square of the velocity which implies a minimum of the coating thickness at the cross-over with the more familiar Landau-Levich regime.

With dielectric-constant gas thermometry (DCGT) a sudden change in the low-temperature properties of gaseous ⁴He has been observed. Below 3.3 K, the usual real-gas behavior ends. The change can be explained by the assumption of clustering ⁴He atoms. Such clusters influence the molar polarizability and the dielectric virial coefficients. This causes wrong thermodynamic temperature results of DCGT with ⁴He. Consistency checks with ³He revealed the best experimental value for the polarizability of ³He up to now and confirmed the feasibility of DCGT in the treated temperature range.

We present a simplified model for the electron-ion energy relaxation in dense two-temperature systems that includes the effects of coupled collective modes. It also extends the standard Spitzer result to both degenerate and strongly coupled systems. Starting from the general coupled-mode description, we are able to solve analytically for the temperature relaxation time in warm dense matter and strongly coupled plasmas. This was achieved by decoupling the electron-ion dynamics and by representing the ion response in terms of the mode frequencies. The presented reduced model allows for a fast description of temperature equilibration within hydrodynamic simulations and an easy comparison for experimental investigations. For warm dense matter, both fluid and solid, the model gives a slower electron-ion equilibration than predicted by the classical Spitzer result.

Results from recent measurements of carbon impurity ion toroidal and poloidal rotation velocities, ion temperature, ion density and the resulting radial electric field (E_r) profiles are presented from an evolving Joint European Torus (JET) tokamak plasma over a range of energy and particle confinement regimes. Significant levels of edge plasma poloidal rotation velocity have been measured for the first time on JET, with maximum values of ±9 km s^{- 1}. Such values of poloidal rotation provide an important contribution to the total edge plasma E_r profiles. Large values of shear in the measured E_r profiles are observed to arise as a consequence of the presence of the edge transport barrier (ETB) and do not appear to be necessary for their formation or destruction. These results have an important impact on potential mechanisms for transport barrier triggering and sustainment in present-day and future high-performance fusion plasmas.

Some time ago, we found an exact solution for nonlinear cold-plasma oscillations against a periodic ion background. The main and somewhat surprising physical effect due to the fixed ion background was the appearance of unbounded-electron density and electric-field intensity peaks. Along with others, we then tried to understand this in terms of realistic physical situations. Here we present a calculation indicating that these infinities can be removed by inclusion of viscous effects. A discussion of possible regions of validity of the model is given. For removal of infinities, the viscosity must be larger than a critical value depending on both the amplitude and spacing of the periodic ion background. Lagrangian coordinates are crucial in this calculation.

A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. The problem of linear fluctuations of charges on the surface of the dust grain is discussed.

The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.

In this study, the phase field model of crack propagation is used to study the dynamic branching instability in the case of inplane loading in two dimensions. Simulation results are in good agreement with theoretical predictions and experimental findings. Namely, the critical speed at which the instability starts is about 0.48c_s. They also show that a full 3D approach is needed to fully understand the branching instability. The finite interface effects are found to be neglectable in the large system size limit even though they are stronger than the one expected from a simple one-dimensional calculation.

The thermomechanical Lehmann coefficient ν is directly measured as a function of temperature in a compensated cholesteric liquid crystal. The method consists of observing the continuous rotation of the director in samples treated for planar sliding anchoring when a temperature gradient is applied perpendicularly to the director. The main result is that there is no relationship between the Lehmann coefficient and the equilibrium twist q. In particular, we confirm that ν does not vanish at the compensation temperature at which q=0, in agreement with previous static measurements of Éber and Jánossy (Mol. Cryst. Liq. Cryst., 72 (1982) 233) and of ourselves (Europhys. Lett., 80 (2007) 26001). In addition, the sign of the Lehmann coefficient is determined by observing between crossed polarizers the sense of rotation of the extinction branches of the disclination lines.

Applying a quasiclassical equation to carriers in graphene, we found a way how to distinguish between samples with the domination of short- and long-range scatterers from the conductivity measurements. The model proposed explains recent transport experiments with chemically doped as well as suspended graphene.

Here we report a new class of superconductors prepared by high-pressure synthesis in the quaternary family ReFeAsO_1−δ (Re=Sm, Nd, Pr, Ce, La) without fluorine doping. The onset superconducting critical temperature (T_c) in these compounds increases with the reduction of the Re atom size, and the highest T_c obtained so far is 55 K in SmFeAsO_1−δ. For the NdFeAsO_1−δ compound with different oxygen concentration a dome-shaped phase diagram was found.

A lateral shift, similar to a Goos-Hänchen shift, of a normally incident electromagnetic beam reflected off an antiferromagnet in the presence of an external magnetic field is predicted. This shift is interpreted in terms of nonreciprocity of the reflected phase, and is confirmed using numerical simulation. There is also a lateral displacement of the field within the antiferromagnet, but not of the beam transmitted through an antiferromagnetic slab.

We propose a theoretical scenario for pumping of fractionally charged quasi-particle in the context of ν=1/3 fractional quantum Hall liquid. We consider quasi-particle pumping across an anti-dot level tuned close to the resonance. Fractional charge pumping is achieved by slow and periodic modulation of coupling of the anti-dot level to left and right moving edges of a Hall bar set-up. This is attained by periodically modulating the gate voltages controlling the couplings. In order to obtain quantization of pumped charge in the unit of the electronic charge fraction (νe) per pumping cycle in the adiabatic limit, we argue that the only possibility is to tune the quasi-particle operator to be irrelevant from being relevant in the renormalization group sense, which can be accomplished by invoking quantum Hall line junctions into the Hall bar geometry. We also comment on the possibility for experimental realization of the above scenario.

Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be σ=σ₀(1+0.01g), where g is the dimensionless ("fine structure") coupling constant. The calculations are performed using three different methods: i) electron polarization function, ii) Kubo formula for the conductivity, iii) quantum transport equation. Surprisingly, these methods yield different results unless a proper ultraviolet cut-off procedure is implemented, which requires that the interaction potential in the effective Dirac Hamiltonian is cut-off at small distances (large momenta).

Fe films were grown by molecular beam epitaxy on {2×4}InP(001) at room temperature in the thickness range of 5–21 monolayer equivalent (ML). The magnetic anisotropy and magnetization were studied using in situ ferromagnetic resonance and in situ SQUID magnetometry, respectively. For the whole thickness range the magnetization was found to favor an in-plane alignment. The easy axis of magnetization is parallel to the []-direction below 7 ML, which rotates by 45^° towards the [100]-direction for thicker Fe layers. The magnetic anisotropy energy of the system has been quantitatively determined as a function of film thickness. The perpendicular magnetic anisotropy is strongly thickness dependent with a large surface-interface contribution which is comparable to that of Fe grown on GaAs. The cubic anisotropy K₄≈1×10⁴ J/m³, however, is small compared to that of bulk Fe over the whole thickness regime and almost thickness independent. The in-plane uniaxial anisotropy is strongly thickness dependent and originates at the Fe/InP interface.

We have investigated the electronic properties of defected boron nitride nanotubes (BNNTs) for spin-up and spin-down electrons by using the first-principle density functional theory. Two types of defects have been considered, vacancy and substitution of carbon and oxygen by boron or nitrogen. The formation energy calculation shows that for both vacancies defected zigzag and armchair BNNTs, the probability of the nitrogen vacancy case is higher than that of the boron vacancy. Also in the carbon doping process of BNNTs, the substitution of boron by carbon is more possible with respect to nitrogen by carbon. In the oxygen doping substitution process, substitution of boron by oxygen is less favorable than nitrogen by oxygen. For the higher-probability cases the spin-up and spin-down band structures show different features. For the first and second cases, the spin-up band structure shows a n-type semiconductor, while the spin-down band structure illustrates a wide band gap semiconductor. But for the oxygen-doped BNNTs case, the spin-up band structure shows a wide band gap semiconductor, while the spin-down band structure illustrates a n-type semiconductor. All defected BNNTs have a 1.0μ_B total magnetic moment.

Triangular-shaped mesoscopic superconductors are consistent with the symmetry of the Abrikosov vortex lattice resulting in a high stability of vortex patterns for commensurate vorticities. However, for non-commensurate vorticities, vortex configurations in triangles are not compatible with the sample shape. Here we present the first direct observation of vortex configurations in μm-sized niobium triangles using the Bitter decoration technique, and we analyze the vortex states in triangles by analytically solving the London equations and performing molecular-dynamics simulations. We found that filling rules with increasing vorticity can be formulated for triangles in a similar way as for mesoscopic disks where vortices form shells.

Scanning tunneling microscopy and spectroscopy were conducted over a broad temperature range on single crystals of Pr_0.68Pb_0.32MnO₃. Spectroscopic studies revealed inhomogeneous maps of the zero-bias conductance with a broad distribution of the local conductivities only within a narrow temperature range close to the metal-insulator transition. An analysis of the conductance histograms based on these maps gave direct evidence for phase separation into insulating and conducting areas. This phase separation was found to be confined only to the transition region.

We study here, both experimentally and theoretically, the anisotropy of magneto resistance in atomic contacts. Our measurements on iron break junctions reveal an abrupt and hysteretic switch between two conductance levels when a large applied field is continuously rotated. We propose that this behaviour stems from the coexistence of two metastable electronic states which result from the anisotropy of electronic interactions responsible for the enhancement of orbital magnetization. In both states giant orbital moments appear on the low coordinated central atom in a realistic contact geometry. However, they differ by their orientation, parallel or perpendicular, with respect to the axis of the contact. Our explanation is totally at variance with the usual model based on the band structure of a monatomic linear chain, which we argue cannot be applied to 3d ferromagnetic metals.

Typhoon Matsa (2005) is examined in terms of entropy flow through the entropy flow formula that is the organic component of the entropy balance equation derived from the Gibbs relation. The entropy flows in the various stages of their evolution are diagnosed based on the outputs of the Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) Mesoscale Model version 5 (MM5). The results show that: i) the vertical distribution of entropy flow for the typhoon is characterized by a predominant negative entropy flow (NEF) in a large portion of the troposphere with positive flow in the upper levels during its development; ii) the simulated centres of severe rainfall match well with the zones of large NEF, demonstrating that large NEF may be a significant indicator for severe weather events; and, iii) the typhoon, as a dissipative structure, develops only when the entropy flow from its surroundings is negative, and tends to decay when the NEF is weakened or replaced by positive entropy flow, suggesting that the self-organization of the typhoon is dependent on NEF.

That almost all language networks are small-world and scale-free raises the question of whether syntax plays a role to measure the complexity of a language network. To answer this question, we built up two random language (dependency) networks based on a dependency syntactic network and investigated the complexity of these three language networks to see if the non-syntactic ones have network indicators similar to the syntactic one. The results show that all the three networks are small-world and scale-free. While syntax influences the indicators of a complex network, scale-free is only a necessary but not sufficient condition to judge whether a network is syntactic or non-syntactic. The network analysis focuses on the global organization of a language, it may not reflect the subtle syntactic differences of the sentence structure.

Waves are a ubiquitous phenomenon in the cytoskeleton of cells crawling or spreading on a substrate. In theoretical analysis, cytoskeletal waves have been attributed to the action of molecular motors that actively cross-link cytoskeletal filaments. Motivated by recent observations of cytoskeletal waves in human neutrophils, we develop a description of treadmilling filaments in the presence of nucleating proteins that are active when bound to the membrane adjacent to the substrate. If these proteins bind cooperatively to the membrane, we find traveling waves even in the absence of molecular motors. In a confined domain the system can organize into a pair of counter-rotating spirals that emit planar waves.

Evidence is presented that reflection anisotropy spectroscopy (RAS) can provide real-time measurements of conformational change in proteins induced by electron transfer reactions. A bacterial electron transferring flavoprotein (ETF) has been modified so as to adsorb on an Au(110) electrode and enable reversible electron transfer to the protein cofactor in the absence of mediators. Reversible changes are observed in the RAS of this protein that are interpreted as arising from conformational changes accompanying the transfer of electrons.