Search results for "Discretization"
showing 10 items of 237 documents
Some structural properties of a formal model of measurement procedure
1996
Three kinds of a model structure for a measurement procedure are analyzed, i.e. one-cyclic, tree-like and multicyclic. For a multicyclic structure a method of the choice of the optimal strategy for partitioning the uncertainty interval is constructed. An example of a measurement procedure using the suggested strategy is given. Some specific cases of the strategies under different initial conditions are discussed.
F4E load transfer procedure among finite element models different in topology or in discretization
2019
Abstract In this paper, a methodology developed in Fusion for Energy (F4E) for interpolating mechanical loads both between compatible (i.e. from solid to solid models different in discretization) and incompatible (e.g. from solid models to shell/beam models) FE models is described. This novel procedure is able of transferring a force vector field (i.e. Lorentz forces) from a three-dimensional solid mesh (e.g. electromagnetic model) onto a target mesh (e.g. mechanical model), being it either three-dimensional solid or simplified beam/shell model. This interpolation procedure is developed with the aim of preserving both the global and local mechanical equilibrium of the system in terms of res…
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
A 3D mesoscopic approach for discrete dislocation dynamics
2001
In recent years a noticeable renewed interest in modeling dislocations at the mesoscopic scale has been developed leading to significant advances in the field. This interest has arisen from a desire to link the atomistic and macroscopic length scales. In this context, we have recently developed a 3D-discrete dislocation dynamics model (DDD) based on a nodal discretization of the dislocations. We present here the basis of our DDD model and two examples of studies with single and multiple slip planes.
Modelling of Orientational Ordering in Lipid Monolayers
1993
Lipid monolayers at high densities are modelled as rigid rods grafted to an interface at the sites of a regular lattice. The transition between the state where the rods are uniformly tilted to a disordered state with no (average) tilt is studied by computer simulation methods. For the one-dimensional model, the molecular dynamics approach is found much less suitable to equilibrate the system rather than Monte Carlo methods. Both in d=2 discretized versions of Monte Carlo codes are much more efficient than continuum Monte Carlo methods, in spite of huge storage requirements. While in d=l the transition occurs at temperature T=0 via the spontaneous creation of solitons, at d=2 a finite temper…
Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures
2017
We present a new second-order energy dissipative numerical scheme to treat macroscopic equations aiming at the modeling of the dynamics of complex polymer–solvent mixtures. These partial differential equations are the Cahn-Hilliard equation for diffuse interface phase fields and the Oldroyd-B equations for the hydrodynamics of the polymeric mixture. A second-order combined finite volume/finite difference method is applied for the spatial discretization. A complementary approach to study the same physical system is realized by simulations of a microscopic model based on a hybrid Lattice Boltzmann/Molecular Dynamics scheme. These latter simulations provide initial conditions for the numerical…
A NEW SOLVER FOR NON-ISOTHERMAL FLOWS IN NATURAL AND MIXED CONVECTION
2022
Most thermal fluid flow of real-life practical problems fall in the category of low Mach-number or incompressible flow (e.g., industrial flows inside ducts, or around stationary/moving objects, flows in biological/biomedical problems, or atmospheric flows). Several numerical techniques have been proposed for simulation of thermal flows, Finite Difference (FDM), Finite Element (FEM), Finite Volume (FVM) and Lattice Boltzmann (LBM) methods. Unlike the FVMs and FEMs, the classical FDMs show some difficulties in handling irregular geometries. Conventional formulation of FEMs (e.g., Galerkin FEMs) suffers from the lack of local mass balance, recovered by modified formulations (Narasimhan & W…
High-quality discretizations for microwave simulations
2016
We apply high-quality discretizations to simulate electromagnetic microwaves. Instead of the vector field presentations, we focus on differential forms and discretize the model in the spatial domain using the discrete exterior calculus. At the discrete level, both the Hodge operators and the time discretization are optimized for time-harmonic simulations. Non-uniform spatial and temporal discretization are applied in problems in which the wavelength is highly-variable and geometry contains sub-wavelength structures. peerReviewed
Exponential synchronization of master-slave neural networks with time-delays
2009
This paper establishes an exponential H ∞ synchronization method for a class of master and slave neural networks (MSNNs) with mixed time-delays, where the delays comprise different neutral, discrete and distributed time-delays and the class covers the Lipschitz-type nonlinearity case. By introducing a novel discretized Lyapunov-Krasovskii functional in order to minimize the conservatism in the stability problem of the system and also using some free weighting matrices, new delay-dependent sufficient conditions are derived for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities (LMIs). The controller guarantees the exponential H ∞ synchr…
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
2004
A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.