Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

Water Dynamics at Interfaces and Solutes: Disentangling Free Energy and Diffusivity Contributions

The dynamics of single water molecules in bulk and at interfaces is studied by means of molecular dynamics simulations. We use a recently developed stochastic method based on the Fokker-Planck equation to disentangle the contributions of the free energy and diffusivity profiles on the local dynamics. The strong variations found in the diffusivity profiles are crucial for accurately modeling the water kinetics. A comparison of hydrophobic and hydrophilic substrates and solutes yields significant differences in the diffusivities, which can be attributed to the presence of hydrogen bonds.     

Low Entropy Future Boundary Conditions

A number of ways to detect future, low-entropy, boundary conditions are considered. The most important of these is the use of slowly-decaying isotopes and the observation (or prediction) of galactic dynamics. There is the expectation that future developments in experimental or observational technique will yield positive results.     

Free Molecular Flow with Boundary Effect

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and constant boundary temperature, T _*. The geometry is also chosen to be the simplest ones, a bounded symmetric domain in ${\mathbb{R}^d}$ : an interval for d = 1, a disk for d = 2, and a ball for d = 3. It is shown that the solution converges to the global Maxwellian with the given boundary temperature T _*. We obtain the optimal convergence rates of (t + 1)^?d . The stochastic formulation of Shih-Hsien Yu is refined and generalized for our analysis.     

Zero-Flux Plane Kinetics at Multicomponent Interfaces

Zero flux planes (ZFP's) are the locations in a diffusion couple where fluxes of individual components vanish. The conditions required for developing ZFP's between interdiffusing multicomponent alloys are now well understood through the works of Dayananda and Morral. In this paper we analyze the kinetics of multicomponent diffusion near ZFP's. In contrast to the usual mixing that occurs between end-member alloys in a diffusion couple, where the average component compositions are approached through “global” exchange of atoms, the presence of a stationary ZFP requires instead that mixing of the blocked component occurs through the release of a pair of coupled diffusion waves. In classical (thick) couples these waves spread symmetrically away from the Matano plane. The wave pair consists of a “depletion” wave that reduces the blocked component concentration in the component-rich alloy, and a conjugate “repletion” wave that increases the concentration in the adjacent component-poor alloy. Curiously, each of these waves establishes the average (equilibrium) concentration unilaterally on either side of the Matano plane. A stationary ZFP precludes net transport of one component across the Matano plane—a circumstance that has practical and theoretically interesting implications for the design of stable multicomponent films and coatings that must resist diffusive loss of a component.     

Nonstandard Boundary Conditions in Quantum Mechanics

The class of boundary conditions for wave functions which follow from the quantum mechanical continuity equation for the probability density and the probability current is considered.     

Segregation of Aluminium at Nickel-Sapphire Interfaces

Sessile drop experiments of pure liquid Ni on the basal surface of pure sapphire were conducted under controlled atmosphere and temperature. This system has been traditionally considered as non-reactive, based on thermodynamic assessments. However, the results of this study demonstrate that a capillary driven interaction exists between the pure liquid Ni and the sapphire, which causes the dissolution of the sapphire substrate mainly at the triple junction. Oxygen and Al resulting from the dissolution process diffuse into Ni and segregate at its interfaces with the atmosphere and the sapphire (probably as Al _x O _y clusters), which reduces the interface energy. It is considered that this reduction is beneficial for the adhesion of both liquid and solid Ni on sapphire. The amount of Al introduced into the drop, and hence the segregation of Al that affects the interface energy (and adhesion), are related to the size of the sessile drop.     

Laser Gain for Inhomogeneous Boundary Conditions

Russian Physics Journal - The method proposed by the authors for solving the Helmholtz equation with homogeneous boundary conditions was verified for an elliptic cross section. The method is...     

格子Boltzmann方法中的边界条件

比较并讨论了几种格子Boltzmann方法(LBM)中的边界条件处理方法,对标准的壁面全反弹方法进行了改进,提高了壁面反弹方法的精度．通过采用d2q9模型对Poiseuille流和非定常Coueue流进行数值模拟,获得了与分析解比较吻合的结果．针对不同的松弛时间τ和Re数,还给出了采取不同边界条件处理时的收敛精度,验证了小Re数时,LBM可以完全模拟N-S方程,由计算发现松弛时间τ接近1时的精度最高,τ较大时,误差较大。     

Coherency Strain-Assisted Equilibrium Segregation at Heterophase Interfaces

Theoretical work in the field of interfacial segregation is focused mainly on the sharp interface approach beginning with the Gibbs' introduction of the dividing surface. In this paper a continuum approach to the problem of interfacial segregation, which deals with continuous distributions of quantities at interfaces, is developed. The current study concentrates on heterophase interfaces in alloys as opposed to grain boundaries or antiphase domain boundaries. The important effect of coherency strains is taken into account. The Gibbs adsorption theorem is discussed in the framework of a continuum approach. A comparison is made between the sharp (Gibbsian) and diffuse interface approaches.     

Orthogonality and Boundary Conditions in Quantum Mechanics

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets) depend on two quantum numbers: energy and parity (+ or —). With the aid of projection operators the particles are confined to a constrained region, in a way similar to the action of an infinite well potential. From the resulting overcomplete basis, only the mutually orthogonal states are selected. Four solutions are found, corresponding to different non-commuting Hamiltonians. Their energy eigenstates are labeled with the main quantum number n and parity + or —. The energy eigenvalues are functions of n only. The four cases correspond to different boundary conditions: (I) The wave function vanishes on the boundary (energy levels: l⁺,2^–,3⁺,4^–,...), (II) the derivative of the wavefunction vanishes on the boundary (energy levels 0⁺,l^–,2⁺,3^–,...), (III) periodic boundary conditions (energy levels: 0⁺,2⁺,2^–,4⁺,4^–6⁺,6^–,...), (IV) periodic boundary conditions (energy levels: l⁺,1^–,3⁺,3^–,5⁺,5^–,...). Among the four cases, only solution (III) forms a complete basis in the sense that any function in the constrained region, can be expanded with it. By extending the boundaries of the constrained region to infinity, only solution (III) converges uniformly to the free particle states. Orthogonality seems to be a more basic requirement than boundary conditions. By using projection operators, confinement of the particle to a definite region can be achieved in a conceptually simple and unambiguous way, and physical operators can be written so that they act only in the confined region.     

Symmetries and Boundary Conditions with a Twist

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2–7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.     

Ordering at Solid-Liquid Interfaces Between Dissimilar Materials

In an earlier report we explored structural correlations at a liquid-solid interface with molecular dynamics simulations of a model aluminium system using the Ercolessi-Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium fcc crystalline positions while liquid atoms were free to move. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found. In the present paper we extend this study to the case of a fixed bcc substrate in contact with liquid aluminium. We find surprisingly similar results for the density profiles of both (100) and (110) substrates. However, there is a far greater in-plane ordering in the (100) than for the (110) system. For the (100) substrates we observe adsorption of liquid atoms into the terminating plane of the bcc (100) substrate, effectively transforming the bcc (100) plane into an fcc (100) plane.     

A Free Boundary Problem with Non Local Interaction

We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, (Phys. Rev. E 56, 2597D2604, 1997) and Durrett and Remenik, (Ann. Probab. 39, 2043–2078, 2011). The problem we consider describes the limit evolution of branching brownian particles on the line with death of the leftmost particle at each creation time as studied in De Masi et al. (2017). We use extensively results in Cannon (1984) and Fasano (2008).     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

超对称系统的边界条件与可积性

通过研究反射方程的解,构造了一类具有不同边界条件的超对称系统,同时证明了在一维情况下,这类系统是完全可积的.     

Chiral Anomaly with MIT Bag Boundary Conditions

After a brief review of the heat kernel approach we obtain a chiral anomaly for local MIT bag boundary conditions.     

Asymptotic Analysis of Lattice Boltzmann Boundary Conditions

In this article, we use a general method for the analysis of finite difference schemes to investigate lattice Boltzmann algorithms for Navier–Stokes problems with Dirichlet boundary conditions. Several link based boundary conditions for commonly used lattice Boltzmann BGK models are considered. With our method, the accuracy of the algorithms can be exactly predicted. Moreover, the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity. The analysis is applicable to general geometries and instationary flows