Search results for " Boundary conditions"
showing 10 items of 87 documents
Energy localization in a nonlinear discrete system
1996
International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.
Method of Lines and Finite Difference Schemes with Exact Spectrum for Solving Some Linear Problems of Mathematical Physics
2013
In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions BCs and periodic boundary conditions PBCs are studied. The finite difference scheme FDS and the finite difference scheme with exact spectrum FDSES are used for the space discretization. The solution in the time is obtained analytically and numerically, using the method of lines and continuous and discrete Fourier methods.
Short chaotic strings and their behaviour in the scaling region
2008
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary conditions, called chaotic strings. In this short note we show that the fine structure of the self energy of this chaotic string in the scaling region (i.e. for very small coupling) is retained if we reduce the length of the string to three lattice points.
Assessment of methodologies and data used to calculate desalination costs
2017
Abstract In desalination, similarly with other industries, the cost of the final product is one of the most important criteria that define the commercial success of a specific technology. Therefore, when new projects are planned or new technologies are proposed, the analysis of the expected costs attracts a lot of attention and is compared to (perceived) costs of state-of-the-art desalination or costs of alternative fresh water supply options. This comparison only makes sense if the cost assessment methodologies are based on the same principles and use common assumptions. This paper assesses: (i) the methodologies used to calculate the water cost; (ii) the boundary conditions and (iii) the …
General framework for testing Poisson-Voronoi assumption for real microstructures
2020
Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single phase steel microstructures. The aim of this paper is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of 2D sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, thre…
Convergence of the finite volume method for a conductive-radiative heat transfer problem
2013
We show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then, by obtaining uniform boundedness of discrete solutions and their discrete gradients with respect to mesh size, we finally get L 2type convergence of discrete solutions.
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.
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…
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…