Table of contents

Thin layer membranes with controllable features and material arrangements are often used as target materials for laser driven particle accelerators. Reduced cost, large scale fabrication of such membranes with high reproducibility, and good stability are central for the efficient production of proton beams. These characteristics are of growing importance in the context of advanced laser light sources where increased repetition rates boost the need for consumable targets with design and properties adjusted to study the different phenomena arising in ultra-intense laser-plasma interaction. We present the fabrication of sub-micrometric thin-layer gold or aluminum membranes in a silicon wafer frame by using nano/micro-electro-mechanical-system (N/MEMS) processing which are suitable for rapid patterning and machining of many samples at the same time and allowing for high-throughput production of targets for laser-driven acceleration. Obtained targets were tested for laser-proton acceleration through the Target Normal Sheath Acceleration mechanism (TNSA) in a series of experiments carried out on a purpose-made table-top Ti:Sa running at 3 TW peak power and 10 Hz diode pump rate with a contrast over ASE of 10⁸.

In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The information of the distance between the target and the observer, however, is lost in the large-distance asymptotic approximation. In this paper, we provide a rigorous theory of acoustic scattering without the large-distance asymptotic approximation. The acoustic scattering treatment developed in this paper provides an improved description for the acoustic wave outside the target. Moreover, as examples, we consider acoustic scattering on a rigid sphere and on a nonrigid sphere. We also illustrate the influence of the near target effect on the angular distribution of outgoing waves. It is shown that for long wavelength acoustic scattering, the near target effect must be reckoned in.

The head-on collision of ion-acoustic solitary waves in a collisionless plasma with cold ions and Boltzmann electrons is studied using the particle-in-cell (PIC) simulation. It is shown that solitary waves of sufficiently large amplitudes do not retain their identity after a collision. Their amplitudes decrease and their forms change. In the collision of solitary waves, accelerated ions are formed. The ion velocities can reach three speeds of sound. Dependences of amplitudes of the potential and densities of ions and electrons after a head-on collision of identical solitary waves on their initial amplitude are presented.

General relationship between mean Boltzmann entropy and Gibbs entropy is established. It is found that their difference is equal to fluctuation entropy, which is a Gibbs-like entropy of macroscopic quantities. The ratio of the fluctuation entropy and mean Boltzmann, or Gibbs entropy vanishes in the thermodynamic limit for a system of distinguishable and independent particles. It is argued that large fluctuation entropy clearly indicates the limit where standard statistical approach should be modified, or extended using other methods like renormalization group.

Quantum dots, quantum rings, and, most recently, quantum dot-ring nanostructures have been studied for their interesting potential applications in nanoelectronic applications. Here, the electronic properties of a dot-ring hetero-nanostructure consisting of a graphene ring and graphene dot with a hexagonal boron nitride (h-BN) ring serving as barrier between ring and dot are investigated using density functional theory. Analysis of the character of the wave functions near the Fermi level and of the charge distribution of this dot-ring structure and calculations of the quantum transport properties find asymmetry in the conductance resonances leading to asymmetric I–V characteristics which can be modified by applying a negative voltage potential to the central graphene dot.

Layered materials have huge potential in various applications due to their extraordinary properties. To determine the interlayer interaction (or equivalently the layer spacing under different perturbations) is of critical importance. In this paper, we focus on one of the most prominent layered materials, graphite, and theoretically quantify the relationship between its interlayer spacing and the vibrational frequencies of its layer breathing and shear modes, which are measures of the interlayer interaction. The method used here to determine the interlayer interaction can be further applied to other layered materials.

We study whether or not the Center-of-Mass (CM) motion and the relative motion can be separated for hydrogen atoms in a nonuniform electric field. First, we show that in the general problem of two charges in a nonuniform electric field, the CM and relative motions, rigorously speaking, cannot be separated. Second, we use an approximate analytical method of the separation of rapid and slow subsystems to achieve a pseudoseparation of the CM and relative motions for hydrogenic atoms/ions in an arbitrary nonuniform electric field. Third, we further develop these results for the case of a hydrogen atom in the nonuniform electric field, where the field is due to the nearest (to the hydrogen atom) ion in a plasma. Fourth, we apply the results to the ion dynamical Stark broadening of hydrogen lines in plasmas. Fifth, we present specific examples of laboratory plasmas (e.g., magnetic fusion plasmas or radiofrequency discharges) and astrophysical plasmas (e.g., in atmospheres of flare stars) where the allowance for these CM effects leads to a significant increase of the width of hydrogen spectral lines.

The magnetic properties of mixed spin-1/2 and spin-1 Ising 2D-nanoparticles (circle and square) with core–shell structure are examined by the use of the Monte Carlo simulation. The phase diagrams are investigated and show qualitatively interesting features. In particular, three and four physically different phases are identified for the square and circle nanoparticles, respectively. These phases are separated by different transitions that could be called ordinary, core and shell transitions according to the strengths of the exchange interactions.

We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction, a^d (0 < a < 1) decays with metric distance d between particle pair, and the interaction is short range. At a = 1.0, our model reduces to the famous Vicsek model. For all a > 0, the system shows a transition from a disordered to an ordered state as a function of noise strength. We calculate the critical noise strength, η_c(a) for different a and compare it with the mean-field result. Nature of the disorder-to-order transition continuously changes from discontinuous to continuous with decreasing a. We numerically estimate tri-critical point a_TCP at which the nature of transition changes from discontinuous to continuous. The density phase separation is large for a close to unity, and it decays with decreasing a. We also write the coarse-grained hydrodynamic equations of motion for general a, and find that the homogeneous ordered state is unstable to small perturbation as a approaches to 1. The instability in the homogeneous ordered state is consistent with the large density phase separation for a close to unity.

We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f-sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.

We describe the process of selecting a silicon photomultiplier (SiPM) as the light sensor for an ultrathin (≈2 mm) highly efficient cold neutron detector. The neutron detector consists of ⁶LiF:ZnS(Ag) scintillator in which wavelength shifting (WLS) fibers have been embedded. The WLS fibers conduct the scintillation light out from the scintillator to the SiPM photosensor. In addition to the many benefits of using silicon photomultipliers as photosensors (low cost, compact size, insensitivity to magnetic fields), their selection also presents many challenges (thermally induced dark noise, delayed cross talk, afterpulsing, etc) which are not shared by traditional photomultiplier tubes. In this work, we discuss the considerations for the selection of the appropriate silicon photomultiplier to achieve the best net neutron sensitivity and gamma ray discrimination. Important characteristics for these devices include short recovery time (≈35 ns), high photodetection efficiency (>30% at the target wavelength), low thermal noise (<35 kHz mm⁻² at ambient temperatures), and low crosstalk.

We present an analytical solution for the full spectrum of Kitaev's one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude and chemical potential in the case of an open chain. We also discuss the structure of the zero-modes in the presence of both phase gradients and next nearest neighbor hopping and pairing terms. As observed by Sticlet et al, one feature of such models is that in a part of the phase diagram, zero-modes are present at one end of the system, while there are none on the other side. We explain the presence of this feature analytically, and show that it requires some fine-tuning of the parameters in the model. Thus as expected, these 'one-sided' zero-modes are neither protected by topology, nor by symmetry.

I investigate the scattering properties of transformation devices as the impedance matching criteria are altered. Starting from an analysis of traditional impedance calculations, we see how to preserve the cloak's 'steering' refractive index profile whilst adjusting the 'scattering' impedance profile. Results are presented for transformation devices in a cylindrical geometry, but the lessons apply to both simpler and more complicated transformation devices. One technique used here is the use of impulsive field inputs, so that scattered fields are more easily distinguished from non-scattered fields. A two-axis continuous range of impedance profiles is shown to cover the three most important cases. This range is investigated numerically, with the summed scattering field being used as an indicator of device performance. We see that the standard '${\boldsymbol{\kappa }}$-medium' case where ${\boldsymbol{\varepsilon }}={\boldsymbol{\mu }}$ gives best performance, but with different rescalings giving different levels of deterioration.

We show in this note that the asymptotic spectral distribution, location and distribution of the largest eigenvalue of a large class of random density matrices coincide with that of Wishart-type random matrices using proper scaling. As an application, we show that the asymptotic entropy production rate is logarithmic. These results are generalizations of those of Nechita, and Sommers and Życzkowski.

It was suggested in the literature that the self-diffusion coefficient of simple fluids can be approximated as a ratio of the squared thermal velocity of the atoms to the 'fluid Einstein frequency,' which can thus serve as a rough estimate of the friction (momentum transfer) rate in the dense fluid phase. In this article we test this suggestion using a single-component Yukawa fluid as a reference system. The available simulation data on self-diffusion in Yukawa fluids, complemented with new data for Yukawa melts (Yukawa fluids near the freezing phase transition), are carefully analyzed. It is shown that although not exact, this earlier suggestion nevertheless provides a very sensible way of normalization of the self-diffusion constant. Additionally, we demonstrate that certain quantitative properties of self-diffusion in Yukawa melts are also shared by systems like one-component plasma and liquid metals at freezing, providing support to an emerging dynamical freezing indicator for simple soft matter systems. The obtained results are also briefly discussed in the context of the theory of momentum transfer in complex (dusty) plasmas.

We investigated the l-type doubling in the (14²0) ← (02²0) weak hot band transition of carbonyl sulphide (OCS) for l = 2 (i.e. Δ state) vibrational state. High-resolution spectroscopic measurements of l-doublet splittings of OCS were carried out using cavity ring-down spectroscopy (CRDS) technique employing a continuous-wave (cw) external-cavity quantum cascade laser (EC-QCL) operating at ∼5.2 μm. The rotationally resolved spectra of l-doublet splittings between the parity doublet e and f sub-states of OCS were recorded by probing the rotational lines from J = 22 to J = 29 in the R branch belonging to the weak hot band transition. Subsequently, we determined the l-type doubling constant, transition dipole moment, rotational constant and centrifugal distortion constant for both e and f components of the (14²0) vibrational state with relatively high rotational states of OCS. As the measurement of l-doublet splitting in l = 2 or higher states of OCS remains challenging due to extremely small splitting, therefore our findings suggest that the observation of the l-type doubling in Δ vibrational state (l = 2) with new values of the several spectroscopic parameters as mentioned above will be useful for better understanding of linear polyatomic molecular properties in general from high-resolution spectroscopic data.

The ability to carry transport current in a magnetic field is the most important aspect of a superconductor. We present a detailed analysis of the upper critical field (H_c2(0)) and vortex dynamics in superconducting boron doped diamond (BDD) films. H_c2(0) measured on the samples of different doping levels revealed a high critical field of up to 7.3 T. Pinning potential U₀, estimated using thermally activated flux-flow (TAFF) model shows that U₀ is of the order of 10² K. Self-field critical current density (J_c) estimated for the superconducting BDD films showed large J_c ∼ 10⁷ A/cm² due to enhanced flux trapping.

In recent years, nanolasers based on plasmonic crystal nanocavity structures have attracted significant interest. However, the performance of such lasers is affected significantly by the coupling of the lasing emission to both reflection and transmission sides of the device and to multiple spatial modes in the far field due to higher-order diffraction from plasmonic crystals as well. In this work, we propose a nanolaser design that overcomes the performance degradation of plasmonic crystal based nanolasers and increases the emission intensity significantly. In the proposed nanolaser structure, a nanometer-thick gain medium has a one-dimensional photonic crystal on one side and a metal nanohole array on the other side. An incident pump pulse through the one-dimensional photonic crystal excites optical Tamm states at the metal-gain medium interface that are amplified by the stimulated emission of the gain medium. We find that the intensity of the extraordinary optical transmission through the metal nanohole array increases significantly due to the excitation of optical Tamm states with wavevector perpendicular to the nanohole array surface. We also find that the subwavelength periodicity in the nanohole array confines the lasing emission to the zero-th order mode only, and hence, makes the far-field pattern highly directional. Moreover, the laser emission wavelength can be tuned over a broad range by changing the thicknesses of the photonic crystal layers, gain medium, and in real-time, by changing the angle of incidence of the pump pulse.

There does not exist a general positive correlation between important life-supporting properties and the entropy production rate. The simple reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing optimal functioning. In fact those aspects are even crucial in the nonlinear regimes around equilibrium where we find biological processing on mesoscopic scales. We make these claims specific via examples of molecular motors, of circadian cycles and of sensory adaptation, whose performance in some regimes is indeed spoiled by increasing the dissipated power. We use the relation between dissipation and the amount of time-reversal breaking to keep the discussion quantitative also in effective models where the physical entropy production is not clearly identifiable.

The analytical procedures previously developed by the authors (see references) in order to evaluate the short-range interaction energy of two protons bound by one electron are briefly reviewed. The Hamilton-Jacobi-Riccati outer equation is solved perturbatively up to fifth order in the perturbation parameter, where the zero-order function is the He⁺ ground-state function. The inner equation is solved by expanding Hylleraas determinant. The results are consistent with those of similar treatments and with accurate numerical calculations.

The aim of this investigation is to provide improved mathematical series expansions of the longitudinal and transverse acoustic radiation forces for a rigid cylindrical particle in 2D of arbitrary cross-section located near a planar rigid wall. Incident plane progressive waves with variable angle of incidence are considered in a non-viscous fluid. The multiple scattering effects occurring between the particle and the rigid boundary are described using the partial-wave decomposition in cylindrical coordinates, the method of images and the translational addition theorem. Initially, an effective acoustic field incident on the particle is defined, which includes the primary incident field, the reflected waves from the flat wall and the scattered field from the image object. Subsequently, the incident effective field along with the scattered field from the object are utilized to obtain closed-form mathematical expressions for the longitudinal and transverse radiation force functions, based on a scattering approach in the far-field. The radiation force vector components are formulated in partial-wave series in cylindrical coordinates, which involve the incidence angle, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a rigid circular cylinder are considered. Computations for the longitudinal and transverse non-dimensional radiation force functions are performed. Emphasis is given on varying the size of the particle, the incidence angle of the source field and the particle-wall distance. Depending on the particle-wall distance and incidence angle, zero-longitudinal and transverse force components arise, thus, the particle becomes unaffected by the linear momentum transfer. Moreover, pushing or pulling forces between the particle and wall are predicted depending on the particle-wall distance, the incidence angle and size parameter. The results may find possible applications in the development of acousto-fluidic devices, acoustic levitation of particles nearby a boundary, cloaking/invisibility, and underwater acoustics to name a few areas, where most investigations resort initially to numerical simulations to guide the experimental design processes.

The present study proposes a generalized mean-field approach to examine the significant effect of the finite supply of particles on multi-lane coupled system with non-conserving dynamics. The steady-state behavior is analyzed by exploring vital characteristics such as phase diagrams, density profiles, residence time and power spectra. Despite the fully asymmetrical coupling environment, symmetrical phases are identified along with asymmetrical phases. The emergence of shock results in the breaking of symmetry prevailing among the lanes for a critical value of the total number of particles in the system. Additionally, bulk induced phase transition results in the shifting from low density to high density regime. As expected, jamming length increases with increase in the total number of particles in the system. Particles follow the pseudo-Gaussian distribution with decreasing variance exhibiting the significant effect of limited resources on the system properties. For the lower values of the total number of particles, the current initially increases and then saturate beyond its critical value. Through power spectra damped oscillations are observed in the particles occupancy in one of the lanes while other lane and reservoir show undamped profile with non-conserving dynamics in the bulk.

Quasi-two dimensional nano-structures are characterized by radical changes in electron and phonon properties. Electron behavior in Q-2D nano-structures is modified by the presence of multiple sub-bands. For well widths smaller than 50 Å simplified model calculations based on the assumption of electrons occupying the lowest sub-band appears to be quite reasonable. For larger width others, parabolic sub-bands need to be considered. The present paper investigates the thermoelectric figure-of-merit of bismuth telluride which is five layered (Te-Bi-Te-Bi-Te) crystal with hexagonal symmetry with six equivalent valleys, in the range 40–300 Å and observe that for 100 Å well width three sub-band model and for 200 Å well width six sub-band model are good approximation at room temperature. Further it is observed that optimum carrier density for 200 Å well width is $3.2\times {10}^{24}\,{{\rm{m}}}^{-3}$ and maximum of ZT shifts towards lower concentration; and discusses the acceptability of single band approximation.

The model combining power balance equations, coupling amplitude equations and stimulated Brillouin scattering (SBS) equation is established to simulate the spectrum evolution and SBS threshold in the amplifier stage. Four typical phase modulation seeds are employed to calculate the SBS spectrum evolution in fiber amplifier. The spectrum evolution results show that the top-hat shaped spectrum seed is optimal to suppress the SBS effect and scale the SBS threshold. The SBS threshold is studied in co-pumped and counter-pumped amplifiers. Simulation results show that counter-pumped amplifier is capable of generating about 2.5 times more output than co-pumped amplifier. The results provide theoretical basis on the design and experiment of continuous wave high power narrow linewidth fiber laser.

This paper investigates the fluctuation-induced interaction between flexible ideal polymer chains on membranes. Tiny fluctuations happen in the vicinity of the curved surface of the membrane where the potential energy is in the lowest value. The fluctuations are governed by the Helfrich effective surface energy and the effective interaction energy. Under this viewpoint, the energy and the entropy corresponds to one-point and two-point Green function, respectively. The variations of surface energy and the leading-term interaction between chains are calculated with chains anchored to a membrane and strongly confined between two planar membranes in the three dimensional space.

XUV nonlinear spectroscopy has recently discovered that there is more than one collective dipole resonance state in the energy range of the giant dipole resonance (GDR) of atomic Xe. This resonance-state substructure, hidden in the linear regime, raises imminent questions regarding our understanding of the collective electronic behavior of Xe, which has been largely founded on linear spectroscopic studies. Here, we approach the collective response of Xe from a new perspective: we study directly the resonance eigenstates, and then analyze their spectroscopic manifestations. We find that linear spectroscopy captures only partial information on the resonance substructure as a result of quantum interferences. Moreover, we show that the resonance state dominating the GDR in linear spectroscopy has no adiabatic connection to the resonance state governing the corresponding cross section when multielectron interactions are neglected. Going beyond the dipole-allowed correlated electronic structure, we predict the existence of collective multipole resonances of Xe. Unlike any known collective feature in atoms, these resonances live exceptionally long (more than 100 attoseconds), thus providing a new playground for studying the collective nonlinear response of Xe using advanced light sources.

Dielectric elastomers, a special class of electroactive polymers, have viscoelastic properties that strongly affect their dynamic performance. This paper contributes a high-order linear solid model together with an optimised parameter identification method to aid the selection of the model parameters. The paper also demonstrates that accurate modelling of the viscoelastic characteristics for commonly used dielectric elastomer (DE) material requires additional spring-damper combinations within a standard linear solid model. The effect of key parameters on the system dynamics in the frequency domain is elaborated and used to guide the parameter identification of the models. The increased effectiveness of higher order models that incorporate multiple spring-damper combinations is demonstrated using three experiments; (a) mechanical loading of a stacked sample over 0.01–5 Hz with strain variations up to 50%; (b) mechanical loading of a single-layer sample over 1–100 Hz with strain variations up to 10%; and (c) electrical actuation of a single-layer sample over 1–100 Hz using electric fields up to 20 MV m⁻¹. Silicone and polyacrylate samples were tested to show the effect of viscoelastic properties in the frequency domain. The proposed method of parameter identification is optimised to capture the frequency response.

The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a dynamical system whose set of states forms a topological space and whose law of evolution is a self-homeomorphism. Assuming the system is infinitesimally reducible—specifying the state and the dynamics of the whole system is equivalent to giving the state and the dynamics of its infinitesimal parts—will give us a classical Hamiltonian system. Assuming the system is irreducible—specifying the state and the dynamics of the whole system tells us nothing about the state and the dynamics of its substructure—will give us a quantum Hamiltonian system. Assuming kinematic equivalence, that studying trajectories is equivalent to studying state evolution, will give us Lagrangian mechanics and limit the form of the Hamiltonian/Lagrangian to the one with scalar and vector potential forces.

Based on an observer-centric methodology, we pinpoint the basic origin of the spectral Planckianity of the asymptotic Hawking modes in the conventional treatments of the evaporating horizons. By considering an observer who analyzes a causal horizon in a generic spacetime, we first clarify how the asymptotic Planckian spectrum is imposed on the exponentially redshifted Hawking modes through a geometric dispersion mechanism developed by a semiclassical environment which is composed by all the modes that build up the curvature of the causal patch of the asymptotic observer. We also discuss the actual microscopic phenomenon of the Hawking evaporation of generic causal horizons. Our quantum description is based on a novel holographic scheme of gravitational open quantum systems in which the degrees of freedom that build up the curvature of the observer's causal patch interact with the radiated Hawking modes, initially as environmental quanta, and after a crossover time, as quantum defects. Planckian dispersion of the modes would only be developed in the strict thermodynamic limit of this quantum environment, called optimal disperser, which is nevertheless avoided holographically. Finally, we outline and characterize how our microscopic formulation of the observer-centric holography, beyond the AdS/CFT examples and for generic causal patches, does realize the information-theoretic processing of unitarity.

Doping has been regarded as one of the most important band structure engineering methods for graphene and its derivatives. Here, we theoretically investigate the chevron-type graphene nanoribbon (CGNR) which is doped by nitrogen in its edges (N-CGNR). The impurity effect can be activated by hydrogen efficiently. When each N atom is adsorbed by a H atom, the σ bond of N induced by self-hybridization is replaced by the N-H sp² bond, leaving two p_z electrons perpendicular to the CGNR plane. Only one p_z electron can be bonded with the nearest C atom. Therefore, the residual p_z electron is delocalized from the N atom and induces the n-type impurity effect. We have calculated the binding energies of N-H bonds and found they are stable and can be manipulated independently without impacting the other bonds. A molecular dynamic (MD) simulation under high temperature further verifies that the N-H bonds in some specific positions can even be stable at 2000 K. Finally, the activated impurity effect is exhibited in the transport properties of CGNR based devices, indicating its wide application prospects.

Silicon-on-insulator is an attractive choice for developing mid-infrared photonic integrated circuits. It benefits from mature fabrication technologies and integration with on-chip electronics. We report the development of SOI channel and rib waveguides for mid-infrared wavelengths centered at 3.7 μm. Propagation loss of ∼1.44 dB/cm and ∼1.2 dB/cm has been measured for TE and TM polarizations in channel waveguides, respectively. Similarly, propagation loss of ∼1.39 dB/cm and ∼2.82 dB/cm has been measured for TE and TM polarized light in rib waveguides. The propagation loss is consistent with the measurements obtained using a different characterization setup and for the same waveguide structures on a different chip. Given the tightly confined single-mode in our 400 nm thick Si core, this propagation loss is among the lowest losses reported in literature. We also report the development of Ge-on-SOI strip waveguides for mid-infrared wavelengths centered at 3.7 μm. Minimum propagation loss of ∼8 dB/cm has been measured which commensurate with that required for high power mid-infrared sensing. Ge-on-SOI waveguides provide an opportunity to realize monolithically integrated circuit with on-chip light source and photodetector.

Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical calculation and only solving the Dirac-Weyl equation for the zero modes. Specifically, the eigenstates associated to the negative magnetic field configurations may be constructed from the zero mode with positive chirality. In addition, we obtain that the eigenstates associated to the positive magnetic field configurations may be constructed from the zero mode with negative chirality. Finally, we show that our mechanism may be used to obtain the eigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system.

Mathematical relations linking electric and magnetic field-dependent physical properties of molecules have been unveiled. These relations are analogous to Maxwell relations in thermodynamics and are derived from mixed third-order partial derivatives of every alternative Legendre representation of the energy of molecules with respect to the electric or magnetic field and normal coordinates. Some of these novel physical relationships have practical applications in the low computational cost calculation of parameters commonly used in vibrational spectroscopy like the Stark and Zeeman Tuning Rates. Furthermore, other equalities have shown connections and alternative ways of computing physical properties used in electrodynamics as permanent dipolar moments and polarizabilities.

Unsteady characteristics of shock waves in metals, for example elastic precursor decay, have often eluded a complete model description. Historic continuum elastic-plastic theories tend to require excessive initial dislocation densities in order to match experimental observations. Studies incorporating superposition of linear elastodynamic solutions for dislocations, either in analytical solutions or in discrete numerical simulations, omit nonlinear elastic effects and only consider effects of defects immediately at the elastic shock front. Prior analytical treatments of hydrodynamic attenuation consider nonlinearity manifesting as effects of stress gradients or particle velocity gradients immediately behind the front. The present analysis seeks to augment the predictive precursor decay equation from linear elastodynamics to account for elastic nonlinearity and dislocation nucleation in the wake of the precursor shock. A complete solution for the precursor magnitude at a material point is shown to require consideration of the prior history of dislocation generation and the entire flow field behind the elastic shock up to that material point. However, introduction of reasonable simplifying assumptions and basic models for dislocation generation and glide resistance enable derivation of a mathematically tractable relation for precursor decay. This relation is a nonlinear first-order ordinary differential equation that, in non-dimensional form, contains only one scalar parameter controlling the rate of dislocation generation behind the shock. Model predictions that include nonlinear effects are shown to provide a better match to experimental data for three metals. Effects of nonlinearity are shown to emerge early, but not immediately, in the shock attenuation process, and these effects increase in prominence with increasing impact stress.

A reactive fluid flowing through porous or fractured rocks causes changes in its porosity and permeability. Experimental studies on the effects of reactive flow in porous systems are normally confined to finite size rock samples in laboratories as actual field data is not sufficiently available. Such laboratory data and simulations based on them, may not always correctly predict or explain changes that take place in rock basins in geological time. In this study we simulate two cases- transient and steady. In a transient case, reactions occur as soon as a reactive fluid is injected into the rock, whereas in the steady case, reactions begin only after the injected fluid percolates through the sample length. The transient case is comparable to real rock basins, while the steady case mimics the situation in laboratory experiments. Variation of the hydrodynamic parameters such as porosity, permeability and surface area, and their inter-relationships at different temperatures, are discussed in both cases. We establish that for every temperature, there exists a threshold flux above which the two cases give similar results. Prediction of changes in rock property due to reactive flow in real situations can be made from laboratory experiments provided the flux is kept above this threshold value. When the fluid flux is kept above this threshold value, the porosity-permeability relation follows a power law behaviour. While the threshold flux is independent of temperature and channel width, the exponent of the power law is a slow decreasing function of temperature.