Search results for "Boundary value problem"
showing 10 items of 551 documents
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…
Casimir-Polder forces, boundary conditions and fluctuations
2008
We review different aspects of the atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited for extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation.
Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables
2014
28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…
Extended irreversible thermodynamics of liquid helium II: boundary condition and propagation of fourth sound
2001
Abstract The work deals with further developments of a study previously initiated, in which a macroscopic monofluid model of liquid helium II, based on extended irreversible thermodynamics, has been formulated. The transversal modes are investigated and a boundary condition, suggested in the natural way by their analysis, is formulated; the existence of the fourth sound is demonstrated too. A possible experimental determination of the coefficients appearing in the theory is proposed: it is shown that the model is able to express the velocities and the attenuations of the two sounds in bulk helium II, in accord with the experimental data, using a number of parameters smaller than those intro…
A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density
1986
Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the t…
Study of the thermo-mechanical performances of the IFMIF-EVEDA Lithium Test Loop target assembly
2012
Abstract Within the framework of the IFMIF R&D program and in close cooperation with ENEA-Brasimone, at the Department of Energy of the University of Palermo a research campaign has been launched to investigate the thermo-mechanical behavior of the target assembly under both steady state and start-up transient conditions. A theoretical approach based on the finite element method (FEM) has been followed and a well-known commercial code has been adopted. A realistic 3D FEM model of the target assembly has been set-up and optimized by running a mesh independency analysis. A proper set of loads and boundary conditions, mainly concerned with radiation heat transfer between the target assembly ex…
Mean-field games and two-point boundary value problems
2014
A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
2008
We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…
Surface effects, boundary conditions and evolution laws within second strain gradient plasticity
2014
Abstract The principle of the virtual power (PVP) is used in conjunction with the concepts of “energy residual” and “insulation condition” to address second strain gradient plasticity. The energy residual with its typical divergence format is an extra stress power playing the role of basic state variable to describe the gradient effects, whereas the insulation condition constitutes a global energy characterization of the body as part of the body/environment system. The microstructure of a second strain gradient material (but not of a first strain gradient one) is shown to exhibit surface effects with the formation of a thin boundary layer. This boundary layer is in local (and global) equili…
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …