Application of Isovector Approach for the Solutions of Differential Equations of Physical Systems

1990 ◽  
pp. 12-19
Author(s):  
O. P. Bhutani ◽  
K. Vijaya Kumar
Keyword(s):  
Differential Equations ◽  
Physical Systems

On modelling physical systems with stochastic models: diffusion versus Lévy processes

2008 ◽  
Vol 366 (1875) ◽  
pp. 2455-2474 ◽  
Author(s):  
Cécile Penland ◽  
Brian D Ewald
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Lévy Processes ◽  
Numerical Models ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Physical Systems ◽  
Random Forcing ◽  
Weather And Climate ◽  
Made In

Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

scholarly journals Visiting Power Laws in Cyber-Physical Networking Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Upper Bound ◽  
Large Time ◽  
Power Laws ◽  
Point Of View ◽  
Fundamental Theory ◽  
Physical Systems ◽  
Time Scaling ◽  
Type Data

Cyber-physical networking systems (CPNSs) are made up of various physical systems that are heterogeneous in nature. Therefore, exploring universalities in CPNSs for either data or systems is desired in its fundamental theory. This paper is in the aspect of data, aiming at addressing that power laws may yet be a universality of data in CPNSs. The contributions of this paper are in triple folds. First, we provide a short tutorial about power laws. Then, we address the power laws related to some physical systems. Finally, we discuss that power-law-type data may be governed by stochastically differential equations of fractional order. As a side product, we present the point of view that the upper bound of data flow at large-time scaling and the small one also follows power laws.

scholarly journals The Conservation Theorems of a Damped Dynamical System

1923 ◽  
Vol 42 ◽  
pp. 61-68 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Dynamical System ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Calculus Of Variations ◽  
Least Action Principle ◽  
Partial Differential ◽  
Physical Systems ◽  
Least Action ◽  
Dissipation Of Energy ◽  
Dissipative Equation

The Partial Differential Equations of Physics may be defined as those equations which can be derived from a “least action principle,” that is, as those which are obtained by making a certain integral stationary by the methods of the Calculus of Variations. But, generally speaking, such equations belong to conservative physical systems, and not to those which involve dissipation of energy. In this note it is shewn that a certain class of dissipative equation, of which the best known example is the equation of telegraphy, can be derived from such a calculus of variations problem.

A Method to Find Non-Zero Operating Point Volterra Models for Port-Based Ordinary Differential Equations

2010 ◽  
Author(s):  
Eliot Motato ◽  
Clark Radcliffe ◽  
Jose Luis Viveros
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Functions ◽  
Operating Conditions ◽  
Operating Point ◽  
Input Output ◽  
Nonlinear Functions ◽  
Nonlinear Odes ◽  
Physical Systems ◽  
Volterra Models

Nonlinear physical systems frequently perform around constant non-zero input-output operating conditions. This local behavior can be modeled using port-based nonlinear ordinary differential equations (ODEs). An ODE local solution around an specific input-output operating point can be obtained through the Volterra transfer function (VTF) model. In a past work a procedure for obtaining MIMO Volterra models from port-based nonlinear ODEs was presented. This previous work considered only systems operating at zero input-output conditions subject to linear inputs. In this work the process for obtaining MIMO Volterra transfer functions is extended for systems operating at non-zero input-output conditions. This extension also allows systems that are nonlinear functions of their inputs and input derivatives.

Conservation laws and null divergences

1983 ◽  
Vol 94 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Existence Of Solutions ◽  
Complete Classification ◽  
Complete Analysis ◽  
Partial Differential ◽  
Physical Systems

For a system of partial differential equations, the existence of appropriate conservation laws is often a key ingredient in the investigation of its solutions and their properties. Conservation laws can be used in proving existence of solutions, decay and scattering properties, investigation of singularities, analysis of integrability properties of the system and so on. Representative applications, and more complete bibliographies on conservation laws, can be found in references [7], [8], [12], [19]. The more conservation laws known for a given system, the more tools available for the above investigations. Thus a complete classification of all conservation laws of a given system is of great interest. Not many physical systems have been subjected to such a complete analysis, but two examples can be found in [11] and [14]. The present paper arose from investigations ([15], [16]) into the conservation laws of the equations of elasticity.

The Response of Distributed—Lumped Parameter Systems

1988 ◽  
Vol 202 (6) ◽  
pp. 421-429 ◽  
Author(s):  
R Whalley
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Physical Systems ◽  
Lumped Parameter ◽  
Spatially Distributed ◽  
Lumped Elements ◽  
Mathematical Difficulties

Physical systems are constructed from a variety of components, some of which have relatively concentrated, pointwise features while others have spatially distributed characteristics. In contrast, models rarely reflect this structure, thereby avoiding the mathematical difficulties arising from the manipulation of sets of mixed algebraic, ordinary and partial differential equations which may generate irrational functions on transformation. In this paper general results are produced, enabling the response to systems comprising a series of distributed-lumped elements to be calculated. A simple example is included to illustrate the procedures outlined.

An Experimental Determination of Differential Equations to Describe Simple Nonlinear Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 393-398 ◽  
Author(s):  
L. L. Hoberock ◽  
R. H. Kohr
Keyword(s):  
Differential Equations ◽  
Continuous Functions ◽  
Nonlinear Functions ◽  
Physical Systems ◽  
Lumped Parameter ◽  
System Input ◽  
System Variables ◽  
Time Invariant ◽  
By Products

A method is presented for the determination of ordinary differential equations to describe the performance of existing lumped-parameter, time-invariant, nonlinear physical systems. It is assumed initially that the nonlinear elements can be described by products of continuous functions of system variables and these system variables themselves, which consist of the input and output of the system and their time derivatives. It is also assumed that the system input may be specified and that the output can be measured. The method yields graphical representations of unknown nonlinear functions in an assumed system differential equation. Examples illustrating the accuracy of the procedure are presented, and results obtained in the identification of two physical systems are given.

scholarly journals Some Differential Equations of Elasticity and their Lie Point Symmetry Generators

2014 ◽  
Vol 8 (2) ◽  
pp. 99-102
Author(s):  
Jozef Bocko ◽  
Iveta Glodová ◽  
Pavol Lengvarský
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Lie Group ◽  
Theory Of Elasticity ◽  
Systematic Method ◽  
Lie Group Theory ◽  
Physical Systems ◽  
Symmetries Of Differential Equations ◽  
Symmetry Generators ◽  
Group Symmetries

Abstract The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given.

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