Methods for deriving differential equations of arbitrary dynamic processes

2009 ◽  
Vol 45 (12) ◽  
pp. 1738-1749 ◽  
Author(s):  
E. R. Smol’yakov
Keyword(s):  
Differential Equations ◽  
Dynamic Processes

scholarly journals Laser Opto-Electronic Oscillator and the Modulation of a Laser Emission

2021 ◽  
Author(s):  
Alexander Bortsov
Keyword(s):  
Spectral Line ◽  
Differential Equations ◽  
Low Noise ◽  
Noise Generator ◽  
Dynamic Processes ◽  
Nonlinear Method ◽  
External Modulation ◽  
Mach Zehnder Modulator ◽  
Electronic Oscillator

The autonomous optoelectronic generator (OEO) is considered in the chapter as a source of low-noise oscillations. Differential equations are considered and methods with OEO modulation with direct and external modulation are analyzed. The complexity of both approaches is related to the non-standard way of description of the nonlinear method modulation for the internal (direct) structure and the utilization of the specific Mach-Zehnder modulator for the first stage on external modulation. The purpose of the presentation is to consider the main features of OEO as a low-noise generator. This includes consideration based on the study of differential equations, the study of transients in OEO, and the calculation of phase noise. It is shown that different types of fibers with low losses at small bending radii can be used as a FOLD in OEO. The important role of the choice of a coherent laser for OEO with a small spectral line width is shown. The prospects of using structured fibers with low losses at bends of less than 10 mm in OEO are described. The results of modeling dynamic processes in OEO with direct modulation are presented.

scholarly journals Robust Low-Rank Discovery of Data-Driven Partial Differential Equations

2020 ◽  
Vol 34 (01) ◽  
pp. 767-774
Author(s):  
Jun Li ◽  
Gan Sun ◽  
Guoshuai Zhao ◽  
Li-wei H. Lehman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minimization Problem ◽  
Real World ◽  
Low Rank ◽  
Dynamic Processes ◽  
Complex Data ◽  
Sparse Regression ◽  
Partial Differential ◽  
Regression Methods

Partial differential equations (PDEs) are essential foundations to model dynamic processes in natural sciences. Discovering the underlying PDEs of complex data collected from real world is key to understanding the dynamic processes of natural laws or behaviors. However, both the collected data and their partial derivatives are often corrupted by noise, especially from sparse outlying entries, due to measurement/process noise in the real-world applications. Our work is motivated by the observation that the underlying data modeled by PDEs are in fact often low rank. We thus develop a robust low-rank discovery framework to recover both the low-rank data and the sparse outlying entries by integrating double low-rank and sparse recoveries with a (group) sparse regression method, which is implemented as a minimization problem using mixed nuclear norms with ℓ1 and ℓ0 norms. We propose a low-rank sequential (grouped) threshold ridge regression algorithm to solve the minimization problem. Results from several experiments on seven canonical models (i.e., four PDEs and three parametric PDEs) verify that our framework outperforms the state-of-art sparse and group sparse regression methods. Code is available at https://github.com/junli2019/Robust-Discovery-of-PDEs

Solutions of ordinary differential equations as limits of pure jump markov processes

1970 ◽  
Vol 7 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Thomas G. Kurtz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Markov Processes ◽  
Radioactive Decay ◽  
Dynamic Processes ◽  
Deterministic Models ◽  
Image Position ◽  
Jump Markov Processes

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

Mass Dynamics of U.S. Presidential Competitions, 1928–1936

1988 ◽  
Vol 82 (4) ◽  
pp. 1153-1181 ◽  
Author(s):  
Courtney Brown
Keyword(s):  
United States ◽  
Differential Equations ◽  
Republican Party ◽  
Democratic Party ◽  
Formal System ◽  
Electoral Politics ◽  
The United States ◽  
Dynamic Processes ◽  
Dominant Characteristic ◽  
Modeling Strategy

This analysis investigates the mass dynamics of competitive electoral politics with respect to the presidential vote during the 1928–36 realigning period for the United States. A formal system of three interdependent differential equations is employed to characterize the dynamic processes of the aggregate voter shifts between the Republican, Democratic, and nonvoter populations. The modeling strategy is used to locate substantial variations in the mass dynamics between large subgroups in the electorate as well as to identify both national and socially interactive components to the patterns of voter movements. The results show that the overall realignment period was quite complex. Vote switching from the Republican party to the Democratic party was the dominant characteristic of the 1932 election, whereas additional Democratic gains in 1936 came mostly from new voters.

Modeling of dynamic processes on the market of goods and services

2019 ◽  
Vol 39 (2) ◽  
pp. 158-162
Author(s):  
N. A. Volkova ◽  
N. T. Katanaev
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Market Research ◽  
Dynamic Processes ◽  
Goods And Services ◽  
Multidimensional Models ◽  
Market Volume

The work is aimed at solving problems related to dynamic market research with a limited number of participants and domestic factors, which are used in market volume, the release of the product and its price. Lists the mathematical description of "logistics functions" in the form of analyses and solutions of differential equations processes on the market of goods and services. Given the necessity of transition to multidimensional models of market.

WAVELET-BASED ADAPTIVE COLLOCATION METHOD FOR THE RESOLUTION OF NONLINEAR PDEs

2007 ◽  
Vol 05 (06) ◽  
pp. 957-973 ◽  
Author(s):  
A. KARAMI ◽  
H. R. KARIMI ◽  
B. MOSHIRI ◽  
P. JABEDAR MARALANI
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Multiresolution Analysis ◽  
Chemical Engineering ◽  
Nonlinear Pdes ◽  
Dynamic Processes ◽  
Partial Differential ◽  
Numeric Solution ◽  
Interpolating Wavelets

Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. An efficient adaptive multiresolution numerical method is described for solving systems of partial differential equations. This method is based on multiresolution analysis and interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. Space derivatives were computed in an irregular grid by cubic splines method. The effectiveness of the method is demonstrated with some relevant examples in a chemical engineering context.

Global and local analysis of control programs on dynamic processes described by differential equations with a discrete set of controls

Cybernetics ◽  
1985 ◽  
Vol 21 (2) ◽  
pp. 147-153
Author(s):  
V. S. Mikhalevich ◽  
V. I. Popadinets ◽  
A. N. Golodnikov ◽  
A. V. Ishchenko
Keyword(s):  
Differential Equations ◽  
Local Analysis ◽  
Dynamic Processes ◽  
Control Programs ◽  
Global And Local

Solutions of ordinary differential equations as limits of pure jump markov processes

1970 ◽  
Vol 7 (01) ◽  
pp. 49-58 ◽  
Author(s):  
Thomas G. Kurtz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Markov Processes ◽  
Radioactive Decay ◽  
Dynamic Processes ◽  
Deterministic Models ◽  
Image Position ◽  
Jump Markov Processes

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

Dynamics of exit section of automatic mill of pipe rolling line

2021 ◽  
Vol 77 (2) ◽  
pp. 175-186
Author(s):  
S. R. Rakhmanov
Keyword(s):  
Differential Equations ◽  
Mechanical System ◽  
Technological Process ◽  
Dynamic Models ◽  
Dynamic Processes ◽  
Exit Section ◽  
Pipe Rolling ◽  
Automatic Mill ◽  
Hollow Billet ◽  
Rolling Line

Nonuniformity of pipe wall thickness is one of significant indices, determining quality of hot-rolled seamless pipes. One of the reasons of increased nonuniformity arising is dynamics of exit section mechanisms of pipe rolling line (PRL). Results of study of mandrel holding mechanism dynamics of PRL presented. Dynamic models of exit section, accounting parameters of technological process and inertia of a rolled hollow billet elaborated, which enabled to determine the character of dynamic processes at the exit section of PRL automatic mill. Differential equations of exit section elements motion at the exit section of PRL automatic mill were made up. The solution of the differential equations system was obtained in a numerical form by application of Runge‒Kutta method for correspondent dynamic models of exit section based on the example of calculations for ТПА-350 automatic mill. The pattern of dynamic processes arising at the exit section was specified at realization of the whole technological process of a hollow billet rolling at automatic mill, taking into consideration alternative action from the side of deformation center and mass of the rolled hollow billet. It was shown, that the specified solution of the task for three advanced dynamic models of mechanical system considerably differs from those of the known mathematical models. It was established, that the dynamics of the mandrel holding mechanism of ТПА-350 automatic mill equivalently form the mechanism of finished pipes geometry forming. Analysis of dynamic models of the mill exit section enabled to select the necessary technological and dynamic parameters of the mechanical system, to determine stable modes of hollow billets rolling at the ТПА-350 automatic mill. Results of the study of dynamics of exit section ТПА-350 automatic mill presented. A scheme of modernization of the exit section ТПА-350 automatic mill proposed, which enables to realize rational modes of operation accounting level of mechanical system dynamics and to control quality (geometric parameters) of the rolled pipes.

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