Search results for "Equations"
showing 10 items of 955 documents
How to control stock markets
1994
This paper provides a different approach to the analysis of imperfect stock markets. The model we are concerned with is described by the interaction of three institutional classes of agents (the specialist trader, the professional trader and the non-professional trader), sharing different information. The dynamical discrete-time system obtained can be changed into a second-order linear difference equation forced by the fundamental value of the specialist trader. Using typical tools of control theory, we study the behaviour of the professional trader’s fundamental value influenced by the specialist’s one. © 1994 Taylor & Francis Group, LLC.
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…
A supramolecular system that strictly follows the binding mechanism of conformational selection
2020
Induced fit and conformational selection are two dominant binding mechanisms in biology. Although induced fit has been widely accepted by supramolecular chemists, conformational selection is rarely studied with synthetic systems. In the present research, we report a macrocyclic host whose binding mechanism is unambiguously assigned to conformational selection. The kinetic and thermodynamic aspects of this system are studied in great detail. It reveals that the kinetic equation commonly used for conformational selection is strictly followed here. In addition, two mathematical models are developed to determine the association constants of the same guest to the two host conformations. A “confo…
A new algorithm for a robust solution of the fully dynamic Saint-Venant equations
2003
A new procedure for the numerical solution of the fully dynamic shallow water equations is presented. The procedure is a fractional step methodology where the original system is split into two sequential ones. The first system differs from the original one because of the head gradient term, that is treated as constant and equal to the value computed at the end of the previous time step. The solution of this system, called kinematic, is computed in each element using a spatial zero order approximation for both the heads and the flow rates by means of integration of single ODEs. The second system is called diffusive, contains in the momentum equations only the complementary terms and can be e…
Viscosity solutions of the Monge-Ampère equation with the right hand side in Lp
2007
We compare various notions of solutions of Monge-Ampère equations with discontinuous functions on the right hand side. Precisely, we show that the weak solutions defined by Trudinger can be obtained by the vanishing viscosity approximation method. Moreover, we investigate existence and uniqueness of Lp-viscosity solutions.
Synthesis and characterization of indium oxide at high pressures
2018
Introducción: La naturaleza es sorprendente pero a la vez limitada. A mi entender, nada tiene más potencial que aplicar el ingenio humano para modificar lo que nos rodea y crear algo completamente nuevo. La Física de la Materia Condensada es un campo que actualmente está ganando importancia en la Física moderna. En virtud de los éxitos logrados en Física de la Materia Condensada se han producido enormes avances en el campo de la electrónica cuántica, de los semiconductores y de la ciencia de materiales, teniendo como resultado numerosas aplicaciones tecnológicas que han cambiado nuestras vidas drásticamente en los últimos 50 años. Una de las ramas de la Física de la Materia Condensada es el…
On Discovering Low Order Models in Biochemical Reaction Kinetics
2007
We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a st…
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.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
1992
The tradìtíonal splitting-up method or fractíonal step method is stuítable for sequentìal compulìng. Thís means that the computing of the present fractional step needs the value of the previous fractional steps. In thìs paper we propose a new splitting-up scheme for which the computing of the fractional steps is índependent of each other and therefore can be computed by parallel processors. We have proved the convergence estimates of this scheme both for steady state and nonsteady state linear and nonlinear problems. To use .finite element method to solve Navier-Stokes problems it is always dfficult to handle the zero-divergent finíte element spaces. Here, by using the splitting-up method w…