The Veronese Sequence of Analytic Solutions of the "Equation missing" Sigma Model Equations Described via Krawtchouk Polynomials

2021 ◽  
pp. 57-65
Author(s):  
Nicolas Crampé ◽  
Alfred Michel Grundland
Keyword(s):  
Sigma Model ◽  
Analytic Solutions ◽  
Krawtchouk Polynomials ◽  
Model Equations

scholarly journals Modeling nonlinear compressional waves in marine sediments

2009 ◽  
Vol 16 (1) ◽  
pp. 151-157 ◽  
Author(s):  
B. E. McDonald
Keyword(s):  
Marine Sediments ◽  
Plane Waves ◽  
High Stress ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Compressional Waves ◽  
Series Of Experiments ◽  
Model Equations ◽  
The Time Domain ◽  
Water Saturated

Abstract. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.

scholarly journals NUMERICAL SIMULATION OF DENGUE FEVER (SIR MODEL) USING DIFFERENTIAL TRANSFORM METHOD, MULTI-STEP DIFFERENTIAL TRANSFORM METHOD AND RK4 METHOD

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Gurpreet Singh Tuteja
Keyword(s):  
Dengue Fever ◽  
Transformation Method ◽  
Sir Model ◽  
Analytic Solutions ◽  
Differential Transform Method ◽  
Step Size ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Differential Transform ◽  
Model Equations

This study investigates the application of the differential transformation method(DTM), multi-step differential transform method(MsDTM) with step-size and RK4 method (Mathematica) for finding the numerical solution of the SIR model of dengue fever in epidemiology. This model is a system of non-linear ordinary differential equations that have no analytic solution. Both the methods DTM and MsDTM are applied directly without any linearization, perturbation or discretization in the model equations to obtain semi-analytic solutions. The accuracy of the MSDTM is excellent and comparable to the RK4 method of Mathematica.

SOLUTIONS TO YANG–MILLS EQUATIONS: QUASI-INSTANTONS, QUASI-MONOPOLES AND QUASI-VORTICES

1992 ◽  
Vol 07 (02) ◽  
pp. 269-285 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Lie Groups ◽  
Sigma Model ◽  
String Model ◽  
Gauge Fields ◽  
Relativistic String ◽  
Yang Mills ◽  
Self Duality ◽  
Model Equations ◽  
The One ◽  
Real Forms

Yang–Mills equations for semisimple gauge Lie groups G in d = 4 spaces with signatures (+ + + +) and (+ + − −) are considered. Generalizations of the one-monopole and one-instanton solutions to these equations for the group [Formula: see text] and for its real forms are obtained. For gauge fields of the vortex type, the Ansätze permitting the reduction of d = 4 self-duality equations to the d = 2 Liouville, sinh–Gordon and sine–Gordon, G/H sigma-model equations and to the equations of the relativistic string model are presented.

LINEAR GRAVITONS FROM STRINGS

1988 ◽  
Vol 03 (09) ◽  
pp. 917-928 ◽  
Author(s):  
JENNIE H. TRASCHEN
Keyword(s):  
Gauge Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Vertex Operators ◽  
Polarization Tensor ◽  
Conformal Field Theories ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Stress Energy ◽  
Model Equations

Linear gravitons and spin-two gauge invariance appear in several places in string theories. The purpose of this note is to clarify the connection between gravitons which are emitted by vertex operators in conformal field theories and those which appear in conformally invariant sigma models, and to compare the associated gauge invariances. The polarization tensor and scalar field of a graviton-dilaton vertex are shown to obey equations of motion which are identical to the sigma model equations of motion if, and only if, the trace of the polarization tensor is massless. The gauge invariance of this vertex is a restricted version of the normal spin-two gauge invariance, but is seen to be sufficient to imply conservation of spacetime stress energy of the string.

Model Equations for Quasi-Twodimensional Pattern Forming Systems

1994 ◽  
Vol 19 (6) ◽  
pp. 721-733 ◽  
Author(s):  
M. Neufeld ◽  
R. Friedrich
Keyword(s):  
Model Equations ◽  
Pattern Forming

Modelling Of Transport And Capture Of Particles In A Porous Medium

2019 ◽  
pp. 56-60
Keyword(s):  
Porous Medium ◽  
Asymptotic Solution ◽  
Retention Mechanism ◽  
Inverse Filtering ◽  
Underground Structures ◽  
Loose Soil ◽  
Monodisperse Suspension ◽  
Homogeneous Porous Medium ◽  
Model Equations ◽  
Pass Through

The study of the transport and capture of particles moving in a fluid flow in a porous medium is an important problem of underground hydromechanics, which occurs when strengthening loose soil and creating watertight partitions for building tunnels and underground structures. A one-dimensional mathematical model of long-term deep filtration of a monodisperse suspension in a homogeneous porous medium with a dimensional particle retention mechanism is considered. It is assumed that the particles freely pass through large pores and get stuck at the inlet of small pores whose diameter is smaller than the particle size. The model takes into account the change in the permeability of the porous medium and the permissible flow through the pores with increasing concentration of retained particles. A new spatial variable obtained by a special coordinate transformation in model equations is small at any time at each point of the porous medium. A global asymptotic solution of the model equations is constructed by the method of series expansion in a small parameter. The asymptotics found is everywhere close to a numerical solution. Global asymptotic solution can be used to solve the inverse filtering problem and when planning laboratory experiments.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

Reduction of Acquisition Time for RIL, SDL, and LADA

2007 ◽  
Author(s):  
Arjan Mels ◽  
Frank Zachariasse
Keyword(s):  
Background Noise ◽  
Signal Strength ◽  
Acquisition Time ◽  
Optimal Conditions ◽  
Signal Collection ◽  
Defect Localization ◽  
Model Equations ◽  
Set Up ◽  
Main Operating ◽  
Quantitative Tool

Abstract Although RIL, SDL and LADA are slightly different, the main operating principle is the same and the theory for defect localization presented in this paper is applicable to all three methods. Throughout this paper the authors refer to LADA, as all experimental results in this paper were obtained with a 1064nm laser on defect free circuits. This paper first defines mathematically what 'signal strength' actually means in LADA and then demonstrates a statistical model of the LADA situation that explains the optimal conditions for signal collection and the parameters involved. The model is tested against experimental data and is also used to optimise the acquisition time. Through this model, equations were derived for the acquisition time needed to discern a LADA response from the background noise. The model offers a quantitative tool to estimate the feasibility of a given LADA measurement and a guide to optimising the required experimental set-up.

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