Search results for "Boundary condition"
showing 10 items of 235 documents
From Random Walker to Vehicular Traffic: Motion on a Circle
2014
Driving of cars on a highway is a complex process which can be described by deterministic and stochastic forces. It leads to equations of motion with asymmetric interaction and dissipation as well as to new energy flow law already presented at previous TRAFFIC AND GRANULAR FLOW meetings. Here we consider a model, where motion of an asymmetric random walker on a ring with periodic boundary conditions takes place. It is related to driven systems with active particles, energy input and depot. This simple model can be further developed towards more complicated ones, describing vehicular or pedestrian traffic. Three particular cases are considered, starting with discrete coordinate and time, the…
Natural convection heat transfer in a partially—or completely—partitioned vertical rectangular enclosure
1991
Abstract The effect of symmetric partitions protruding centrally from the end walls of a rectangular vertical enclosure on heat transfer rates is investigated numerically. The enclosure has opposite isothermal walls at different temperatures. The Rayleigh number is varied from 10 4 to 10 7 and the aspect ratio from 0.5 to 10. The thickness of the partitions is fixed and equal to one tenth of the width of the enclosure. Their non-dimensional length ( L / H ) is varied from 0 (non-partitioned enclosure) to 0.5 (two separate enclosures). The effect of different thermal boundary conditions at the end walls and at the partitions is included in the investigation.
Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
1991
for some x in [0, rr]. The guiding idea of this paper is to observe the changes in the stability behavior of the solutions if we perturb the autonomous problem intro- ducing a forcing term g. In [8] it was shown that iff and g are related by a boundedness condi- tion (see condition (* ) in Theorem 3.1) then there exists a stable solution of (1.1) “close” to each stable solution of (1.2). We want to call these stable solutions of (1.1)
Redox potentials and acidity constants from density functional theory based molecular dynamics.
2014
CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical refe…
Implicit-explicit and explicit projection schemes for the unsteady incompressible Navier–Stokes equations using a high-order dG method
2017
Abstract A modified version of the projection scheme [19] is proposed, which does not show a lower limit for the time step in contrast to the limits of stability observed numerically for some projection type schemes. An advantage of the proposed scheme is that the right-hand side of the Poisson equation for the pressure is independent of the time step. An explicit version of the current scheme is also provided besides the implicit-explicit one. For the implicit-explicit version, we retain divergence of the viscous terms on the right-hand side of the Poisson equation in order to achieve a higher accuracy for low Reynolds number flows. In this way, we also ensure that the Poisson equation wit…
Inflow/outflow pressure boundary conditions for smoothed particle hydrodynamics simulations of incompressible flows
2017
Abstract Open Boundary treatment is a well-known issue in the Smoothed Particle Hydrodynamics (SPH) method, mainly when the truly Incompressible (ISPH) approach is employed. In the paper a novel method is proposed to set pressure boundary conditions in the computational domain inlets and outlets, without requiring the velocity profile assignment. The new technique allows to treat in the same way inflow and outflow sections, effectively dealing with the release of new particles at inlets and the deactivation of the ones leaving the domain through the outlets. Several 3D numerical tests, both in the laminar and turbulent regimes, are carried out to validate the proposed numerical scheme consi…
Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2
2009
AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.
Infinitely many solutions for a mixed boundary value problem
2010
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions
2019
In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
Time-based Chern number in periodically driven systems in the adiabatic limit
2023
To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic two-dimensional (2D) Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic 2D Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via h…