Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.     

Upper bound on the heat transport in a layer of fluid of infinite prandtl number, rigid lower boundary, and stress-free upper boundary

We obtain an upper bound on the convective heat transport in a heated from below horizontal fluid layer of infinite Prandtl number with rigid lower boundary and stress-free upper boundary. Because of the asymmetric boundary conditions the solutions of the Euler-Lagrange equations of the corresponding variational problem are also asymmetric with different thicknesses of the boundary layers on the upper and lower boundary of the fluid. The obtained bound on the convective heat transport and the corresponding wave number are between the values for a fluid layer with two rigid boundaries and a fluid layer with two stress-free boundaries.     

Asymmetric tilt grain boundary structure and energy in copper and aluminium

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the ? 100 ? misorientation axis, and the Σ9 and Σ11 systems rotated about the ? 110 ? misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the ? 100 ? system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the ? 110 ? system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.     

Modification of the spin-wave dispersion law in multilayer films by changes in the symmetry of the boundary conditions

The present paper is the first attempt to study the transformation of spin-wave resonance spectra when symmetric boundary conditions are smoothly replaced by asymmetric. The transition is done by gradually reducing the thickness of one of the layers in a three-layer film. Spin deexcitation is caused by a dissipation mechanism. We find that in the transition region between symmetric and asymmetric boundary conditions the dispersion curve experiences a break, whose position depends on the degree of deexcitation (the thickness of the upper layer). The break is caused by the appearance of asymmetric transitional spin-wave modes, which cannot be excited under symmetric boundary conditions. Zh. éksp. Teor. Fiz. 111, 1667–1673 (May 1997)     

Hydrodynamic Limit for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities.     

Symmetry-breaking for solutions of semilinear elliptic equations with general boundary conditions

We study the bifurcation of radially symmetric solutions of +f(u)=0 onn-balls, into asymmetric ones. We show that ifu satisfies homogeneous Neumann boundary conditions, the asymmetric components in the kernel of the linearized operators can have arbitrarily high dimension. For general boundary conditions, we prove some theorems which give bounds on the dimensions of the set of asymmetric solutions, and on the structure of the kernels of the linearized operators.Research supported in part by the NSF under Grant No. MCS-800 2337     

Dynamical Large Deviations for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities.     

Minimal standard heterotic string models

Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z₂×Z₂ orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.     

Finite-size effects in the three-state quantum asymmetric clock model

The one-dimensional quantum hamiltonian of the asymmetric three-state clock model is studied using finite-size scaling. Various boundary conditions are considered on chains containing up to eight sites. We calculate the boundary of the commensurate phase and the mass gap index. The model shows an interesting finite-size dependence in connexion with the presence of the incommensurate phase indicating that for the infinite system there is no Lifshitz point.     

Boundary force effects exerted on solitons in highly nonlinear media

We study the effects caused by remote boundaries on soliton dynamics in nonlinear media with a large range of nonlocality, and demonstrate theoretically and experimentally how asymmetric boundary forces can lead to soliton steering and oscillation in predetermined trajectories.     

Josephson (001) tilt grain boundary junctions of high-temperature superconductors

We calculate the Josephson critical current I_c across in-plane (001) tilt grain boundary junctions of high-temperature superconductors. We solve for the electronic states corresponding to the electron-doped cuprates, two slightly different hole-doped cuprates, and an extremely underdoped hole-doped cuprate in each half-space, and weakly connect the two half-spaces by either specular or random Josephson tunnelling. We treat symmetric, straight, and fully asymmetric junctions with s-, extended-s, or d _{x ²?y ²} -wave order parameters. For symmetric junctions with random grain boundary tunnelling, our results are generally in agreement with the Sigrist–Rice form for ideal junctions that has been used to interpret ‘phase-sensitive’ experiments consisting of such in-plane grain boundary junctions. For specular grain boundary tunnelling across symmetric junctions, our results depend upon the Fermi surface topology, but are usually rather consistent with the random facet model of Tsuei et al. Our results for asymmetric junctions of electron-doped cuprates are in agreement with the Sigrist–Rice form. However, our results for asymmetric junctions of hole-doped cuprates show that the details of the Fermi surface topology and of the tunnelling processes are both very important, so that the ‘phase-sensitive’ experiments based upon in-plane Josephson junctions are less definitive than has generally been thought.     

Unexpected large thermal rectification in asymmetric grain boundary of graphene

We have investigated the lattice thermal transport across the asymmetric tilt grain boundary between armchair and zigzag graphene by nonequilibrium molecular dynamics (NEMD). We have observed significant temperature drop and ultra-low temperature-dependent thermal boundary resistance. More importantly, we find an unexpected thermal rectification phenomenon. The thermal conductivity and Kapitza conductance is direction-dependent. The effect of thermal rectification could be amplified by increasing the difference of temperature imposed on two sides. Our results propose a promising kind of thermal rectifier and phonon diodes based on polycrystalline graphene without delicate manipulation of the atomic structure.     

Temperature dependence of the structure and shear response of a Σ11 asymmetric tilt grain boundary in copper from molecular-dynamics

We investigate the effect of temperature on the structure and shear response of a Σ11 asymmetric tilt grain boundary in a classical embedded-atom model of elemental copper using molecular dynamics simulations. As the temperature is increased the structure of the boundary disorders considerably, but with a boundary width that remains finite at the melting point. The disordering of the boundary structure becomes significant for homologous temperatures above 0.83 (1100?K). As temperature increases above this point the boundary width and roughness increases monotonically. Near the temperature where the boundary starts to disorder we observe a change in the temperature dependence of the ideal shear strength of the boundary, as well as the value of the coupling parameter β, defined as the ratio of the velocity of relative translation of the grains parallel to the boundary plane to that corresponding to the motion of the boundary normal to its plane.     

Large Deviation Functional of the Weakly Asymmetric Exclusion Process

We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like _L ¹ . We recover as limiting cases the expressions derived recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP limit, the nonlinear differential equation one needs to solve can be analysed by a method which resembles the WKB method.     

Topological Phase Transition and Eigenstates Localization in a Generalized Non‐Hermitian Su–Schrieffer–Heeger Model

The topological properties of a generalized non‐Hermitian Su–Schrieffer–Heeger model are investigated and it is demonstrated that the non‐Hermitian phase transition and the non‐Hermitian skin effect can be induced by intra‐cell asymmetric coupling under open boundary conditions. Through investigating and calculating the non‐Hermitian winding number with generalized Brillouin zone theory, it is found that the present non‐Hermitian system has an exact bulk‐boundary correspondence relationship. Meanwhile, the non‐Hermitian winding number is used to characterize the non‐Hermitian phase transition and determine the phase transition boundary, and it is found that the non‐Hermitian phase transition is not completely induced by the asymmetric coupling strength. By means of the mean inverse participation ratio, the factors that affect the eigenstates localization are shown and it is revealed that large system size or large asymmetric coupling strength can leave the system in the localized state. Additionally, it is found that for the asymmetric coupling strength and the system size, the eigenstates localization is much more sensitive to the asymmetric coupling strength.     

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions.Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters,we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations,which give the specific boundary conditions.Our analytical results show that the wave functions take simple forms and are independent of hopping range,while the eigenvalue spectra display rich model-dependent structures.Particularly,we find the existence of a special point coined as pseudo-periodic boundary condition,for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions,whereas the eigenstates display the non-Hermitian skin effect.     

Enhancement of ohmic and stochastic heating by resonance effects in capacitive radio frequency discharges: a theoretical approach

In low-pressure capacitive radio frequency discharges, two mechanisms of electron heating are dominant: (i) Ohmic heating due to collisions of electrons with neutrals of the background gas and (ii) stochastic heating due to momentum transfer from the oscillating boundary sheath. In this work we show by means of a nonlinear global model that the self-excitation of the plasma series resonance which arises in asymmetric capacitive discharges due to nonlinear interaction of plasma bulk and sheath significantly affects both Ohmic heating and stochastic heating. We observe that the series resonance effect increases the dissipation by factors of 2-5. We conclude that the nonlinear plasma dynamics should be taken into account in order to describe quantitatively correct electron heating in asymmetric capacitive radio frequency discharges.     

Boundary layer analysis for non-equilibrium phase transitions

In this review, we discuss some of the recent developments in understanding various boundary induced phase transitions in asymmetric simple exclusion processes using boundary layer analysis. The boundary layer analysis is shown to be useful in gaining a lot of physical insights regarding the formation of shock, the critical point and the dual boundary transition.     

Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries

For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line.