scholarly journals Stability of combustion waves in a simplified gas–solid combustion model in porous media

2018 ◽  
Vol 376 (2117) ◽  
pp. 20170185 ◽  
Author(s):  
Fatih Ozbag ◽  
Stephen Schecter
Keyword(s):  
Weight Function ◽  
Essential Spectrum ◽  
Parabolic Systems ◽  
Travelling Wave ◽  
Weight Functions ◽  
Combustion Model ◽  
Combustion Waves ◽  
Linearized System ◽  
The Stability ◽  
Linearized Operator

We study the stability of the combustion waves that occur in a simplified model for injection of air into a porous medium that initially contains some solid fuel. We determine the essential spectrum of the linearized system at a travelling wave. For certain waves, we are able to use a weight function to stabilize the essential spectrum. We perform a numerical computation of the Evans function to show that some of these waves have no unstable discrete spectrum. The system is partly parabolic, so the linearized operator is not sectorial, and the weight function decays at one end. We use an extension of a recent result about partly parabolic systems that are stabilized by such weight functions to show nonlinear stability. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

scholarly journals Spectrum of the M5-traveling waves

2020 ◽  
Vol 15 ◽  
pp. 66
Author(s):  
Salvador Cruz-García
Keyword(s):  
Essential Spectrum ◽  
Traveling Waves ◽  
Imaginary Axis ◽  
Weighted Space ◽  
Cell Movement ◽  
Mesenchymal Cell ◽  
Weight Functions ◽  
Dimensional Version ◽  
The One ◽  
Linearized Operator

In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M5-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in L2(ℝ; ℂ3) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space Lw2(ℝ; ℂ3) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space Lwα2(ℝ; ℂ2) × Lwε2(ℝ; ℂ) the essential spectrum lies on {Reλ<0}, outside the imaginary axis.

scholarly journals Fixed Point Root-Finding Methods of Fourth-Order of Convergence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 769 ◽  
Author(s):  
Alicia Cordero ◽  
Lucía Guasp ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Nonlinear Problems ◽  
Dynamical Analysis ◽  
Function Technique ◽  
Weight Functions ◽  
Good Tool ◽  
Quadratic Polynomials ◽  
Root Finding ◽  
The Stability

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub’s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.

scholarly journals Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 55 ◽  
Author(s):  
Francisco I. Chicharro ◽  
Alicia Cordero ◽  
Neus Garrido ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Weight Functions ◽  
Iterative Schemes ◽  
Numerical Tests ◽  
Low Degree ◽  
Second Order Convergence ◽  
The Stability ◽  
Low Degree Polynomials

In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are members of this family for particular choices of the weight function. The dynamical behavior of one of these choices is presented, analyzing the stability of the fixed points and the critical points of the rational function obtained when the iterative expression is applied on low degree polynomials. Several numerical tests are given to compare different elements of the proposed family on non-polynomial problems.

scholarly journals The stability of pure weights under conditioning

1974 ◽  
Vol 15 (1) ◽  
pp. 5-12 ◽  
Author(s):  
D. J. Foulis ◽  
C. H. Randall
Keyword(s):  
Weight Function ◽  
Stochastic Models ◽  
Convex Set ◽  
Extreme Points ◽  
Weight Functions ◽  
The Stability ◽  
Universe Of Discourse

In [1], we showed how a collection of physical operations or experiments could be represented by a nonempty set of nonempty sets satisfying certain conditions (irredundancy and coherence) and we called such sets . We also introduced “complete stochastic models” for the empirical universe of discourse represented by such a manual , namely, the so-called weight functions for . These weight functions form a convex set the extreme points of which are called pure weights. We also showed that there is a so-called logic ∏() affiliated with a manual and that each weight function for induces a state on this logic.

scholarly journals Experimental and theoretical progress in pipe flow transition

2008 ◽  
Vol 366 (1876) ◽  
pp. 2671-2684 ◽  
Author(s):  
A.P Willis ◽  
J Peixinho ◽  
R.R Kerswell ◽  
T Mullin
Keyword(s):  
Pipe Flow ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Turbulent Pipe Flow ◽  
Transition To Turbulence ◽  
Reynolds Number Flow ◽  
Threshold Amplitude ◽  
Number Flow ◽  
The Stability ◽  
Laminar State

There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

scholarly journals SYMPLECTIC STABILITY, ANALYTIC STABILITY IN NON-ALGEBRAIC COMPLEX GEOMETRY

2004 ◽  
Vol 15 (02) ◽  
pp. 183-209 ◽  
Author(s):  
ANDREI TELEMAN
Keyword(s):  
Weight Function ◽  
Complex Manifold ◽  
Stability Theory ◽  
Complex Geometry ◽  
Reductive Group ◽  
Hamiltonian Action ◽  
Maximal Weight ◽  
Analytic Stability ◽  
The Stability

We give a systematic presentation of the stability theory in the non-algebraic Kählerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a complex manifold one can associate a G-equivariant maximal weight function and prove a Hilbert criterion for semistability. In other words, for such actions, the symplectic semistability and analytic semistability conditions are equivalent.

scholarly journals Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor

1998 ◽  
Vol 120 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. D. Manring ◽  
G. R. Luecke
Keyword(s):  
Order System ◽  
Axial Piston Pump ◽  
Third Order ◽  
Stability Range ◽  
Hydrostatic Transmission ◽  
Control Gain ◽  
Variable Displacement ◽  
Linearized System ◽  
The Stability ◽  
Axial Piston

This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.

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