Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls-Nabarro （P-N） theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.

APPLICATION OF PARAMETRIC DERIVATION METHOD TO THE CALCULATION OF PEIERLS ENERGY AND PEIERLS STRESS IN LATTICE THEORY

Applying the parametric derivation method, Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory, while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law. The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow. Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law. Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.

Correlation of Critical Loci for Water-Hydrocarbon Binary Systems by EOS Based on the Multi-Fluid Nonrandom Lattice Theory

Quantitative representation of complicated behavior of fluid mixtures in the critical region by any of equation-of-state theories re-mains as a difficult thermodynamic topics to date. In the present work, a computational efforts were made for representing various types of critical loci of binary water with hydrocarbon systems showing Type II and Type III phase behavior by an elementary equation of state [called multi-fluid nonrandom lattice fluid EOS (MF-NLF EOS)] based on the lattice statistical mechanical theory. The model EOS requires two mo-lecular parameters which representing molecular size and interaction energy for a pure component and single adjustable interaction energy pa-rameter for binary mixtures. Critical temperature and pressure data were used to obtain molecular size parameter and vapor pressure data were used to obtain interaction energy parameter. The MF-NLF EOS model adapted in the present study correlated quantitatively well the critical loci of various binary water with hydrocarbon systems.

ENTROPIC CONTRIBUTION TO THE INTERACTION PARAMETER x IN THE POLYMER/OLIGOMER SYSTEM:A LATTICE CLUSTER THEORY CONSIDERATION

Entropic contribution to the interaction parameter (?) in the model incompressible polymer/oligomer system iscalculated by the lattice cluster theory(LCT).It is found that in the oligomer solvent,there exists a wide concentration rangethat the non-combinatorial“entropic interaction”term (?)φ_1φ_2 perceptibly counteracts the mean field combinary entropy△S_(MF).With the increase of the solvent size,both (?) and the ratio (?)φ_1φ_2/△S_(MF) first reach their maximum and finallybecome trivially to zero.It is worth noting that no any demixing was found in the current calculation.This makes thecontroversial idea“entropically driven demixing”even elusive.However,we propose that further work on compressiblepolymer solution with structured monomer will witness the demixing owning to an increased configurational correlation.

Rough Set Theory over Fuzzy Lattices

Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.

EFFECT OF HYDROGEN ON DEBYE TEMPERATURE AND LATTICE PARAMETER OF Ti-30Mo ALLOY

The variations of Debye temperature and lattice parameter of Ti-30Mo alloy with different hydrogen contents were measured by means of X-ray diffraction.It was found that as the hydrogen content increases,the Debye temperature decreases,but the lattice parameter of the aUoy increases.The above results experimentally support the decohesion theory that the in- crease of hydrogen in metals will weaken the cohesive force between the atoms and make met- als brittle.

Quantum simulation of lattice gauge theories on superconducting circuits:Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.

Pressure Effect on Elastic and Lattice Dynamic Properties of Beryllium Selenide from First Principles

The lattice dynamic, elastic, and thermodynamic properties of Be Se were investigated with first principles calculations. The phase transition pressure from the zinc blende（B3） to the nickel arsenide（B8） structure of Be Se was determined. The elastic stability analysis suggests that the B3 structure Be Se is mechanically stable in the applied pressure range of 0-50 GPa. Our lattice dynamic calculations show that the B3 structure is lattice dynamically stable under high pressure. Within the quasiharmonic approximation, the thermodynamic properties including the constant volume heat capacity and constant pressure heat capacity are predicted.

Theoretical Study of Electron Paramagnetic Resonance Spectra and Local Lattice Distortion for Mn^(2+) in Zn(ClO_4)_2·6(H_2O)Mg(ClO_4)_2·6(H_2O)

The electron paramagnetic resonance（EPR） spectra of trigonal Mn^（2＋） centers in Zn（ClO4）2·6（H2O） and Mg（ClO4）2·6（H2O） crystals were studied on the basis of the complete energy matrices for a d^5 configuration ion in a trigonal ligand field. It was demonstrated that the local lattice structure around a trigonal Mn^（2＋） center has an compressed distortion along the crystalline c3 axis, and when Mn^（2＋） is doped in the Zn（ClO4）2·6（H2O） and Mg（ClO4）2·6（H2O） crystals, there is a similar local distortion. From the EPR calculation, the local lattice structure parameters R=2.183 2 ？, for Zn（ClO4）2·6（H2O）, R=2.130 2 ？, for Mg（ClO4）2·6（H2O） have been determined.

Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational electromagnetism,which is concerned withthe numerical study of Maxwell equations.By discrete exterior calculus and the lattice gauge theory with coefficient R,we obtain the Bianchi identity on prism lattice.By defining an inner product of discrete differential forms,we derivethe source equation and continuity equation.Those equations compose the discrete Maxwell equations in vacuum caseon discrete manifold,which are implemented on Java development platform to simulate the Gaussian pulse radiation onantennaes.

Static strength of gold compressed up to 127 GPa

Gold powder is compressed non-hydrostatically up to 127 GPa in a diamond anvil cell （DAC）, and its angle dispersive X-ray diffraction patterns are recorded. The compressive strength of gold is investigated in a framework of the lattice strain theory by the line shift analysis. The result shows that the compressive strength of gold increases continuously with the pressure up to 106 GPa and reaches 2.8 GPa at the highest experimental pressure （127 GPa） achieved in our study. This result is in good agreement with our previous experimental result in a relevant pressure range. The compressive strength of gold may be the major source of the error in the equation-of-state measurement in various pressure environments.

Vector meson masses in two-dimensional SU(N_C)lattice gauge theory with massive quarks

Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in two-dimensional SU（Nc） lattice gauge theory. The numerical results show that for Nc = 2, 3, 4, 5, 6, 7, ..., in the scaling window 1 ≤ 1/g^2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r （this differs from the quark condensate）. Particularly for m → 0 our numerical results agree very well with Bhattacharya＇s analytical strong coupling result in the continuum, and the value of （δMv/δm） ｜m=0 in two-dimensional SU（Nc） lattice gauge theory is very close to that in Schwinger model.

Constrained lattice density functional theory and its applications on vapor–liquid nucleations

Vapor-liquid phase transition occurs via a nucleation process, and depending on the role of foreign objects, nucleation can be either homogeneous or heterogeneous. In this review, we focus on the recently developed constrained lattice density functional theory （CLDFT） and its applications on vapor-liquid nucleation. We also review the recent theoretical advance on the stability of nanobubbles. Based on CLDFT, a pinning and supersaturation mechanism has proposed to interpret the surprising stability of surface nanobubbles. The mechanism can interpret most characteristics of nanobubbles. More importantly, the mechanism suggests that the critical nucleus can be stabilized under the condition of contact line pinning. Thus, CLDFT studies provide an alternative way to measure the critical nucleus that is difficult to measure experimentally in the bulk solution, through stabilizing it with surface roughness or heterogeneities.

A review of recent theoretical and computational studies on pinned surface nanobubbles

The observations of long-lived surface nanobubbles in various experiments have presented a theoretical challenge, as they were supposed to be dissolved in microseconds owing to the high Laplace pressure. However, an increasing number of studies suggest that contact line pinning, together with certain levels of oversaturation, is responsible for the anomalous stability of surface nanobubbles. This mechanism can interpret most characteristics of surface nanobubbles. Here, we summarize recent theoretical and computational work to explain how the surface nanobubbles become stable with contact line pinning. Other related work devoted to understanding the unusual behaviors of pinned surface nanobubbles is also reviewed here.

Towards the continuum coupling in nuclear lattice effective field theory Ⅰ: A three-particle model

Weakly bound states often occur in nuclear physics.To precisely understand their properties,the coupling to the continuum should be worked out explicitly.As the first step,we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core.Our approach is consistent with the Lüscher formalism.

Effective charge from lattice QCD

Using lattice configurations for quantum chromodynamics(QCD)generated with three domain-wall fermions at a physical pion mass,we obtain a parameter-free prediction of QCD’s renormalisation-group-invariant process-independent effective charge,α^(k2).Owing to the dynamical breaking of scale invariance,evident in the emergence of a gluon mass-scale,m0=0.43(1)GeV,this coupling saturates at infrared momenta:α^(0)/π=0.97(4).Amongst other things:α^(k2)is almost identical to the process-dependent(PD)effective charge defined via the Bjorken sum rule;and also that PD charge which,employed in the one-loop evolution equations,delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment.The diversity of unifying roles played byα^(k^2)suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale;and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

Effect of external field on phase behavior of ternary systems involving polypeptide

The lattice theory regarding ternary systems involving a conformationally variable polypeptide and a randomly coiled polymer presented recently is extended to the case where an external orientational field is present.Chemical potentials of the components in the isotropic and anisotropic phases were obtained.The calculations carried out show that the external field exerts a marked effect on the phase behavior of the ternary systems.The isotropic-anisotropic biphasic gap is predicted to shift to lower polymer concentrations and become narrower when the external field exists.The entrance of the randomly coiled polymers into the anisotropic phase is promoted.Influences of chain conformation of polypeptide,chain length and temperature have been studied in the presence of the external field.The comparison between theory and experimental results was also carried out.

Thermodynamic properties and constitutive relations of crystals at finite temperature

The dynamics equation for each individual atom is established directly around the equilibrium state of the system of N atoms based on the inter-atomic potential energy of EAM model.Using the theory of lattice dynamics and periodical boundary condition,the 3N×3N stiffness matrix in eigen equations of vibration frequencies for a parallelepiped crystal is reduced to a 3n×3n matrix of eigen equations of vibration frequencies for a unit lattice.The constitutive relation of the crystal at finite temperature is extracted based on the quantum-mechanical principle.The thermodynamic properties and the stress-strain relationships of crystal Cu with large plastic deformation at different temperatures are calculated,the calculation results agree well with experimental data.