Search results for "Boundary Conditions"
showing 10 items of 97 documents
Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry
1994
Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…
Green’s function and existence of solutions for a third-order three-point boundary value problem
2019
The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
CFD prediction of scalar transport in thin channels for reverse electrodialysis
2014
Reverse ElectroDialysis (RED) is a very promising technology allowing the electrochemical potential difference of a salinity gradient to be directly converted into electric energy. The fluid dynamics optimization of the thin channels used in RED is still an open problem. The present preliminary work focuses on the Computational Fluid Dynamics (CFD) simulation of the flow and concentration fields in these channels. In particular three different configurations were investigated: a channel unprovided with a spacer (empty channel) and two channels filled with spacers, one made of overlapped filaments the other of woven filaments. The transport of two passive scalars, representative of the ions …
A method to transform a nonlocal model into a gradient one within elasticity and plasticity
2014
Abstract A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kerne…
Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study
2017
We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are sudd…
Partition function of the trigonometric SOS model with reflecting end
2010
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Mass-flux-based outlet boundary conditions for the lattice Boltzmann method
2009
We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is fu…
Surface free energy of the open XXZ spin-1/2 chain
2012
We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representati…
A quantum particle in a box with moving walls
2013
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.