Search results for "Boundary value problem"
showing 10 items of 551 documents
Theoretical studies of the propagation of sound in narrow channels filled with helium II. I. The dispersion relations of fourth sound and of the fift…
1971
The wave propagation in helium II bounded by two plane-parallel plates forming a narrow channel is considered. The theory is based on the complete linearized set of the Khalatnikov equations. These equations are exactly averaged over the width of the channel taking into account the boundary conditions and symmetry relations. It is shown that in narrow channels three solutions of these equations exist; (a) fourth sound, (b) the so-called fifth-wave mode, and (c) another wave mode, which is very strongly damped. The dispersion relations of these wave modes are calculated with regard to all kinetic coefficients and to the coefficient of thermal expansion. The phase velocities and absorption co…
Optical phonons and electron-phonon interaction in quantum wires.
1993
A unified macroscopic continuum theory for the treatment of optical-phonon modes in quantum-wire structures is established. The theory is based on a Lagrangian formalism from which the equations of motion are rigorously derived. They consist of four coupled second-order differential equations for the vibrational amplitude and electrostatic potential. The matching boundary conditions are obtained from the fundamental equations. It is shown that no incompatibility exists between mechanical and electrostatic matching boundary conditions when a correct mathematical treatment of the problem is given. The particular case of a GaAs quantum wire buried in AlAs, where the phonons can be considered c…
Moment‐based boundary conditions for straight on‐grid boundaries in three‐dimensional lattice Boltzmann simulations
2020
In this article, moment‐based boundary conditions for the lattice Boltzmann method are extended to three dimensions. Boundary conditions for velocity and pressure are explicitly derived for straight on‐grid boundaries for the D3Q19 lattice. The method is compared against the bounce‐back scheme using both single and two relaxation time collision schemes. The method is verified using classical benchmark test cases. The results show very good agreement with the data found in the literature. It is confirmed from the results that the derived moment‐based boundary scheme is of second‐order accuracy in grid spacing and does not produce numerical slip, and therefore offers a transparent way of accu…
Thermodynamic Approach to the Self-Diffusiophoresis of Colloidal Janus Particles
2019
Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here, we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit self-propulsion in a demixing binary solvent. At variance with a slip velocity, we find that propuls…
Theoretical Description of Primary Nanoferroics. Comparison of the Theory with Experiment
2013
This Chapter is devoted primarily to the theoretical description of the physical properties of nanoferroics. The theoretical approach that has been successful in describing the size- and shape-dependent effects observed experimentally in nanoferroics is Landau – Ginzburg – Devonshire phenomenological theory, operating on nanoferroics symmetry and order parameters. Our analysis of this theory applicability shows that it can be safely applied down to the sample sizes of few nanometers. The main peculiarity of theoretical description of nanoferroics is that the boundary conditions and terms containing gradients of order parameters cannot be omitted and play the vital role in the description of…
COMPUTER SIMULATION OF PROFILES OF INTERFACES BETWEEN COEXISTING PHASES: DO WE UNDERSTAND THEIR FINITE SIZE EFFECTS?
2000
Interfaces between coexisting phases are very common in condensed matter physics, and thus many simulations attempt to characterize their properties, in particular, the interfacial tension and the interfacial profile. However, while theory usually deals with the "intrinsic profile", the latter is not a straightforward output of a simulation: The actual profile (observed in simulations and/or experiments!) is broadened by lateral fluctuations. Therefore, in the usual simulation geometry of L × L × L (in three dimensions), where one chooses suitable boundary conditions to stabilize one or two interfaces of (minimal) area L × L, the profile (and in particular the interfacial width) depends on…
Anisotropies in thermal Casimir interactions: Ellipsoidal colloids trapped at a fluid interface
2009
We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long--ranged interface fluctuations by particles gives rise to fluctuation--induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuati…
Kac-potential treatment of nonintegrable interactions.
2000
We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potential treatment, leading to an exact, mean-field-like theory. This explains various numerical results recently obtained for finite systems in the context of ``nonextensive thermodynamics,'' and in passing exposes a strong regulator dependence not discussed in these studies. Our findings imply that, contrary to some claims, Boltzmann-Gibbs statistics are sufficient for a standard description of this cla…
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical …
1991
If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper. In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable. The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, th…
Polarization and modal attractors in conservative counterpropagating four-wave interaction
2005
An experimental and theoretical study of the resonant four-wave interaction scheme in the counterpropagating configuration reveals the existence of a novel attraction process in Hamiltonian systems. We show analytically that it is the specificity of the boundary conditions inherent in the counterpropagating configuration that makes attraction dynamics possible in spite of the reversible nature of the four-wave interaction. In the context of optics, this novel dynamical feature could be the basic mechanism of a universal polarizer performing total polarization conversion of unpolarized light with, in principle, 100% efficiency.