Travelling Waves within the Clifford Algebra

1993 ◽  
pp. 197-201
Author(s):  
Bernard Jancewicz
Keyword(s):  
Clifford Algebra ◽  
Travelling Waves

Bifurcations of travelling waves in population taxis models

1999 ◽  
Vol 169 (9) ◽  
pp. 1011 ◽  
Author(s):  
Faina S. Berezovskaya ◽  
G.P. Karev
Keyword(s):  
Travelling Waves

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals Qualitative Properties of Autocatalytic Reactions Occurring in a Flow System

1985 ◽  
Vol 40 (7) ◽  
pp. 736-747
Author(s):  
Sang H. Kim ◽  
Vladimir Hlavacek
Keyword(s):  
Chaotic Behavior ◽  
Flow System ◽  
Cell Model ◽  
Dispersion Model ◽  
Travelling Waves ◽  
Continuous Model ◽  
Product Inhibition ◽  
Stable Node ◽  
Qualitative Properties ◽  
Intermediate Value

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

Calculating the response of waveguides to base excitation using the wave and finite element method

2021 ◽  
pp. 107754632098131
Author(s):  
Jamil Renno ◽  
Sadok Sassi ◽  
Wael I Alnahhal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Functions ◽  
Travelling Waves ◽  
Model Free ◽  
Time Harmonic ◽  
Element Approach ◽  
Response Transfer ◽  
Free Wave Propagation ◽  
Element Method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

Fault location on transmission lines based on travelling waves using correlation and MODWT

2021 ◽  
Vol 197 ◽  
pp. 107308
Author(s):  
V.H. Gonzalez-Sanchez ◽  
V. Torres-García ◽  
D. Guillen
Keyword(s):  
Transmission Lines ◽  
Fault Location ◽  
Travelling Waves
Sign in / Sign up

Export Citation Format

Share Document