Existence of Traveling Waves in Lattice Dynamical Systems

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c*>0 such that for each c≥c*, the systems under consideration admit monotonic nondecreasing traveling waves.

Uniform Exponential Attractors for Second Order Non-autonomous Lattice Dynamical Systems

In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.

Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for κ-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-SchrSdinger Equation

In this paper, we establish the existence of a global attractor for a coupled κ-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-SchrSdinger Equation. An estimate of the upper bound of the Kohnogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented .

Random Attractors for Partly Dissipative Stochastic Lattice Dynamical Systems with Multiplicative White Noises

The present paper is devoted to the existence of the random attractor for partly dissipative stochastic lattice dynamical systems with multiplicative white noises.

Effects of Rattling Behavior of K and Cd Atoms along Different Directions in Anisotropic KCdAs on Lattice Thermal Transport and Thermoelectric Properties

We employ advanced first principles methodology,merging self-consistent phonon theory and the Boltzmann transport equation,to comprehensively explore the thermal transport and thermoelectric properties of KCdAs.Notably,the study accounts for the impact of quartic anharmonicity on phonon group velocities in the pursuit of lattice thermal conductivity and investigates 3ph and 4ph scattering processes on phonon lifetimes.Through various methodologies,including examining atomic vibrational modes and analyzing 3ph and 4ph scattering processes,the article unveils microphysical mechanisms contributing to the lowκL within KCdAs.Key features include significant anisotropy in Cd atoms,pronounced anharmonicity in K atoms,and relative vibrations in non-equivalent As atomic layers.Cd atoms,situated between As layers,exhibit rattling modes and strong lattice anharmonicity,contributing to the observed lowκL.Remarkably flat bands near the valence band maximum translate into high PF,aligning with ultralowκL for exceptional thermoelectric performance.Under optimal temperature and carrier concentration doping,outstanding ZT values are achieved:4.25(a(b)-axis,p-type,3×10^(19)cm^(−3),500 K),0.90(c-axis,p-type,5×10^(20)cm^(−3),700 K),1.61(a(b)-axis,n-type,2×10^(18)cm^(−3),700 K),and 3.06(c-axis,n-type,9×10^(17)cm^(−3),700 K).

Global attractor for Klein-Gordon-Schrodinger lattice system

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schroedinger equation （KGS lattice system）. We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using ＂End Tails＂ of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.

Lattice dynamical and thermodynamical properties of ReB_2,RuB_2,and OsB_2 compounds in the ReB_2 structure

Structural and lattice dynamical properties of ReB2,RuB2,and OsB2 in the ReB2 structure are studied in the framework of density functional theory within the generalized gradient approximation.The present results show that these compounds are dynamically stable for the considered structure.The temperature-dependent behaviors of thermodynamical properties such as internal energy,free energy,entropy,and heat capacity are also presented.The obtained results are in good agreement with the available experimental and theoretical data.

The Structural,Dielectric,Lattice Dynamical and Thermodynamic Properties of Zinc-Blende CdX(X=S,Se,Te) from First-Principles Analysis

The structural, dielectric, lattice dynamical and thermodynamic properties of zinc-blende CdX （X=S, Se, Te） are studied by using a plane-wave pseudopotential method within the density-functional theory. Our calculated lattice constants and bulk modulus are compared with the pubfished experimental and theoretical data. In addition, the Born effective charges, electronic dielectric tensors, phonon frequencies, and longitudinal opticaltransverse optical splitting are calculated by the linear-response approach. Some of the characteristics of the phonon-dispersion curves for zinc-blende CdX （X= S, Se, Te） are summarized. What is more, based on the lattice dynamical properties, we investigate the thermodynamic properties of CdX （X= S, Se, Te） and analyze the temperature dependences of the Helmholtz free energy F, the internal energy E, the entropy S and the constant-volume specific heat Cv. The results show that the heat capacities for CdTe, CdSe, and CdS approach approximately to the Petit-Dulong limit 6R.

Lattice dynamical simulation of methane hydrate

INS （Inelastic Neutron Scattering） spectrum of methane hydrate was measured on MARI （a direct-geometry chopper spectrometer） at Ruther-ford Appleton Laboratory, UK. Compared with ice Ih, it is found that the whole spectrum of methane hydrate moves toward high-energy by about 1.5 meV. Using lattice dynamical （LD） technique, computer simulations of methane hydrate were carried out. In the simulations, four potential models （BE TIP3P, TIP4P, MCY） were employed to calculate the phonon density of states （PDOS）. Comparing the calculated PDOS spectrum with the experimental spectrum, it is found that BF, TIP4P, and TIP3P potential lattices give out well-separated translational and librational bands while MCY potential lattice is unstable to do so and this model is not suitable to describe hydrate system.

From molecular dynamics to lattice Boltzmann:a new approach for pore-scale modeling of multi-phase flow

Most current lattice Boltzmann （LBM） models suffer from the deficiency that their parameters have to be obtained by fitting experimental results. In this paper, we propose a new method that integrates the molecular dynamics （MD） simulation and LBM to avoid such defect. The basic idea is to first construct a molecular model based on the actual components of the rock-fluid system, then to compute the interaction force between the rock and the fluid of different densities through the MD simulation. This calculated rock-fluid interaction force, combined with the fluid-fluid force determined from the equation of state, is then used in LBM modeling. Without parameter fitting, this study presents a new systematic approach for pore-scale modeling of multi-phase flow. We have validated this ap- proach by simulating a two-phase separation process and gas-liquid-solid three-phase contact angle. Based on an actual X-ray CT image of a reservoir core, we applied our workflow to calculate the absolute permeability of the core, vapor-liquid H20 relative permeability, and capillary pressure curves.

Density functional theory investigation on lattice dynamics,elastic properties and origin of vanished magnetism in Heusler compounds CoMnVZ(Z=Al,Ga)

The lattice dynamics,elastic properties and the origin of vanished magnetism in equiatomic quaternary Heusler compounds CoMnVZ(Z=Al,Ga)are investigated by first principle calculations in this work.Due to the similar constituent atoms in CoMnVAl and CoMnVGa compounds,they are both stable in LiMgPdSn-type structure with comparable lattice size,phonon dispersions and electronic structures.Comparatively,we find that CoMnVAl is more structurally stable than CoMnVGa.Meanwhile,the increased covalent bonding component in CoMnVAl enhances its mechanical strength and Vickers hardness,which leads to better comprehensive mechanical properties than those of CoMnVGa.Practically and importantly,structural and chemical compatibilities at the interface make non-magnetic semiconductor CoMnVAl and magnetic topological semimetals Co2MnAl/Ga more suitable to be grown in heterostructures.Owing to atomic preferential occupation in CoMnVAl/Ga,the localized atoms Mn occupy C(0.5,0.5,0.5)Wyckoff site rather than B(0.25,0.25,0.25)and D(0.75,0.75,0.75)Wyckoff sites in LiMgPdSn-type structure,which results in symmetric band filling and consequently drives them to be non-magnetic.Correspondingly,by tuning localized atoms Mn to occupy B(0.25,0.25,0.25)or/and D(0.75,0.75,0.75)Wyckoff sites in off-stoichiometric Co-Mn-V-Al/Ga compounds and keeping the total valence electrons as 24,newly compensated ferrimagnetic compounds are theoretically achieved.We hope that our work will provide more choices for spintronic applications.

Lattice dynamics study of low energy guest-host coupling in clathrate hydrate

Our lattice dynamics simulation of Xe-hydrate with four-site TIP4P oxygen-shell model can accurately reproduce each peak position in the inelastic incoherent neutron scattering spectrum at the acoustic band （below 15 meV） and yield correct relative intensity. Based on the results, the uncertain profile at ～6 meV is assigned to anharmonic guest modes coupled strongly to small cages. Blue shift is proposed in phonon dispersion sheet in the case of anticrossing and found to be an evident signal for guest-host coupling that explains the anomalous thermal conductivity of clathrate hydrate.

First-principles study of lattice dynamics and thermodynamics of osmium under pressure

We have performed the first-principles linear response calculations of the lattice dynamics, thermal equation of state and thermodynamical properties of hep Os metal by using the plane-wave pseudopotential method. The thermodynamical properties are deduced from the calculated Helmholtz free energy by taking into account the electronic contribution and lattice vibrational contribution. The phonon frequencies at Gamma point are consistent with ex- perimental values and the dispersion curves at various pressures have been determined. The calculated volume, bulk modulus and their pressure derivatives as a function of temperature are in excellent agreement with the experimental results. The calculated specific heat indicates that the electronic contribution is important not only at very low tem- peratures but also at high temperatures due to the electronic thermal excitation. The calculated Debye temperature at a very low temperature is in good agreement with experimental values and drops to a constant until 100 K.

Lattice Dynamics at Zone-Center of Sulphide and Selenide Spinels

A rigid-ion model is used to calculate the force constants and effective dynamical charges of sulphide and selenide spinels. The Raman and infrared phonon modes of normal cubic sulphide spinels MCr2S4 （M = Mn, Co, Fe, Hg, Zn, and Cd） and selenide spinels MCr2Se4 （M = Hg, Zn, and Cd） are calculated at the first Brillouin zone-centre using above model, The significant outcome of the present work is （i） the interatomic interaction between Cr-S （Se） dominates over the Cr-S（Se） and S-S（Se-Se） type of interatomic interactions, （ii） the effective dynamical charges of the bivalent metal ions are nearly zero, and （iii） the selenide spinels are less ionic than the sulphide spinels and the ionicity decreases as MnCr2S4 〉 FeCr2S4 〉 CoCr2S4 〉 and CdOr2C4 〉 ZnCr2C4 〉 HgCr2C4 （C = S and Se）. The zone-center phonon frequencies, calculated using these parameters, are found to be in very good agreement with the observed results.

Guest-Host Interaction Study in Clathrate Hydrates Using Lattice Dynamics Simulation

Lattice dynamics simulation of several gas hydrates （helium, argon, and methane） with different occupancy rates has been performed using TIP3P potential model. Results show that the coupling between the guest and host is not simple as depicted by the conventional viewpoints. For clathrate hydrate enclosing small guest, the small cages are dominantly responsible for the thermodynamic stability of clathrate hydrates. And the spectrum of methane hydrate is studied compared with argon hydrate, then as a result, shrink effect from positive hydrogen shell is proposed.

A comparison study on the electronic structures, lattice dynamics and thermoelectric properties of bulk silicon and silicon nanotubes

In order to investigate the mechanism of the electron and phonon transport in a silicon nanotube （SiNT）, the elec- tronic structures, the lattice dynamics, and the thermoelectric properties of bulk silicon （bulk Si） and a SiNT have been calculated in this work using density functional theory and Boltzmann transport theory. Our results suggest that the thermal conductivity of a SiNT is reduced by a factor of 1, while its electrical conductivity is improved significantly, although the Seebeck coefficient is increased slightly as compared to those of the bulk Si. As a consequence, the figure of merit （ZT） of a SiNT at 1200 K is enhanced by 12 times from 0.08 for bulk Si to 1.10. The large enhancement in electrical conductivity originates from the largely increased density of states at the Fermi energy level and the obviously narrowed band gap. The significant reduction in thermal conductivity is ascribed to the remarkably suppressed phonon thermal conductivity caused by a weakened covalent bonding, a decreased phonon density of states, a reduced phonon vibration frequency, as well as a shortened mean free path of phonons. The other factors influencing the thermoelectric properties have also been studied from the perspective of electronic structures and lattice dynamics.

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by （N＋ 1 ）-dimensional nonlinear Schr6dinger （NLS） equation. In particular, the resonant mode interaction of （2＋l）-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the （2＋ I ）- dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.

Site preferences and lattice vibrations of Nd_6Fe_(13-x)T_xSi(x=Co, Ni)

The site preferences of the rare earth intermetallics Nd6Fe13-xTxSi（T = Co, Ni） are investigated by using interatomic pair potentials which are converted from a lattice-inversion method. Calculation shows that the order of the site preference of Co is 4d, 16 k, 16l1, and 16l2 and that of Ni is 16l2, 16l1, 16 k, and 4d in Nd6Fe13-xTxSi. Calculated lattice and positional parameters are found to agree with those reported in the literature. Furthermore, the phonon density of states for Nd6Fe13-xTxSiis also evaluated, and a qualitative analysis featuring the coordination and the relevant potentials is carried out.

The pressure dependences of elastic and lattice dynamic properties of AlAs from ab initio calculations

Ab initio calculations,based on norm-conserving nonlocal pseudopotentials and density functional theory（DFT）,are performed to investigate the structural,elastic,dielectric,and vibrational properties of aluminum arsenide（AlAs） with a zinc-blende（B3） structure and a nickel arsenide（B81） structure under hydrostatic pressure.Firstly,the path for the phase transition from B3 to B81 is confirmed by analyzing the energies of different structures,which is in good agreement with previous theoretical results.Secondly,we find that the elastic constants,bulk modulus,static dielectric constants,and the optical phonon frequencies vary in a nearly linear manner under hydrostatic pressure.What is more,the softening mode of the transversal acoustic mode at the X point supports the phase transition in AlAs.

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.