Search results for "partial differential equation"
showing 10 items of 326 documents
Estimation of the mean crystal size and the moments of the crystal size distribution in batch crystallization processes
2016
International audience; A cascade high gain observer is designed to estimate the first four leading moments of the crystal size distribution (CSD) and the mean crystal size in batch crystallization processes. The proposed observer is based on a well-known transformation of the partial differential equation describing the CSD to a set of ordinary differential equations (the method of moments). Due to numerical difficulties resulting from the important differences in the magnitudes of the moments, a set of new variables is computed to allow a good estimation of the moments and thus the mean crystal size. In this work, only solute concentration and crystallizer temperature are used to estimate…
One-dimensional hydrodynamic modeling of coronal plasmas on transputer arrays
1990
Abstract We describe a concurrent implementation of the Palermo-Harvard hydrodynamic code on cost-effective and modularity expandable transputer arrays. We have tested the effectiveness of our approach by simulating an already well-studied compact solar-flare model on different transputer configurations and compared their performances with those of other machines. We have found that the speed of the concurrent program on a 16-T800 transputers array is ~1/9 of that of the equivalent code optimized for a CRAY X-MP/48. This work clearly shows that transputer-based arrays provide locally available high computing-power tools to extend the investigation of compact solar flares and similar astroph…
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…
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
On global solutions of the Maxwell-Dirac equations
1987
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.
Multiscale Particle Method in Solving Partial Differential Equations
2007
A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.
Lacunary bifurcation for operator equations and nonlinear boundary value problems on ℝN
1991
SynopsisWe consider nonlinear eigenvalue problems of the form Lu + F(u) = λu in a real Hilbert space, where L is a positive self-adjoint linear operator and F is a nonlinearity vanishing to higher order at u = 0. We suppose that there are gaps in the essential spectrum of L and use critical point theory for strongly indefinite functionals to derive conditions for the existence of non-zero solutions for λ belonging to such a gap, and for the bifurcation of such solutions from the line of trivial solutions at the boundary points of a gap. The abstract results are applied to the L2-theory of semilinear elliptic partial differential equations on ℝN. We obtain existence results for the general c…
Kleine periodische L�sungen bei nichtlinearen stark-elliptischen Systemen von partiellen Differentialgleichungen I
1971
Strongly elliptic systems of nonlinear partial differential equations are considered in the case when the derivatives of the solutions occuring in the nonlinear terms have the same order as those in the linear principal part. The existence of periodic solutions for such systems is investigated. It is shown that this problem can be reduced to the study of algebraic bifurcation equations, whose small solutions correspond to the classical solutions of the given problem. A discussion of the bifurcation equations will be given in a forthcoming paper.
Explicit solutions for second-order operator differential equations with two boundary-value conditions. II
1992
AbstractBoundary-value problems for second-order operator differential equations with two boundary-value conditions are studied for the case where the companion operator is similar to a block-diagonal operator. This case is strictly more general than the one treated in an earlier paper, and it provides explicit closed-form solutions of boundary-value problem in terms of data without increasing the dimension of the problem.
The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media
2009
A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection-diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations sy…