Search results for "boundary"
showing 10 items of 1626 documents
Domain wall splitting and creation of the fine domain structure
1998
Abstract The study of the movement of the paraelectric-ferroelectric interphase boundary in (Ba,Sr)TiO 3 with concentration change is provided in the framework of the mean-field theory. The analytical solution for the parameters of motion of the interphase boundary is applied to the calculations of the splitting of domain walls in (Ba,Sr)TiO 3 for different concentrations of Sr. The calculations are based on the experimental data for the Curie–Weiss constant and for the parameters of the Landau–Ginzburg expression for the free energy.
Topology guaranteeing manifold reconstruction using distance function to noisy data
2006
Given a smooth compact codimension one submanifold S of Rk and a compact approximation K of S, we prove that it is possible to reconstruct S and to approximate the medial axis of S with topological guarantees using unions of balls centered on K. We consider two notions of noisy-approximation that generalize sampling conditions introduced by Amenta & al. and Dey & al. Our results are based upon critical point theory for distance functions. For the two approximation conditions, we prove that the connected components of the boundary of unions of balls centered on K are isotopic to S. Our results allow to consider balls of different radii. For the first approximation condition, we also prove th…
High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles
2017
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.
Numerical propagator method solutions for the linear parabolic initial boundary-value problems
2007
On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are f…
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…
Dynamic analysis for axially moving viscoelastic panels
2012
In this study, stability and dynamic behaviour of axially moving viscoelastic panels are investigated with the help of the classical modal analysis. We use the flat panel theory combined with the Kelvin–Voigt viscoelastic constitutive model, and we include the material derivative in the viscoelastic relations. Complex eigenvalues for the moving viscoelastic panel are studied with respect to the panel velocity, and the corresponding eigenfunctions are found using central finite differences. The governing equation for the transverse displacement of the panel is of fifth order in space, and thus five boundary conditions are set for the problem. The fifth condition is derived and set at the in-…
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Fractional visco-elastic Euler–Bernoulli beam
2013
Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…
On Fixed Point (Trial) Methods for Free Boundary Problems
1992
In this note we consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.
On numerical simulation of the continuous casting process
1988
In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.