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.

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.

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.

PARAMETER IDENTIFICATION TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 14 (06) ◽  
pp. 2053-2060 ◽  
Author(s):  
T. G. MÜLLER ◽  
J. TIMMER
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Parameter Estimates ◽  
Partial Differential ◽  
Physical Systems ◽  
Advantages And Disadvantages ◽  
Dynamical Parameters ◽  
Temporal And Spatial ◽  
Identification Techniques

Many physical systems exhibiting nonlinear spatiotemporal dynamics can be modeled by partial differential equations. Although information about the physical properties for many of these systems is available, normally not all dynamical parameters are known and, therefore, have to be estimated from experimental data. We analyze two prominent approaches to solve this problem and describe advantages and disadvantages of both methods. Specifically, we focus on the dependence of the quality of the parameter estimates with respect to noise and temporal and spatial resolution of the measurements.

Sign in / Sign up

Export Citation Format

Share Document