scholarly journals Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field

2011 ◽  
Author(s):  
Hong Qin and Ronald C. Davidson
Keyword(s):  
Time Dependent ◽  
Nonlinear Dynamical ◽  
Self Similar ◽  
Nonneutral Plasma

Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration

2004 ◽  
Vol 126 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
R. Saleh ◽  
A. B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Velocity ◽  
Time Dependent ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Self Similar ◽  
Suction Rate ◽  
Axial Speed

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity and with uniform normal transpiration Uo are investigated. The impinging free stream is steady and with a constant strain rate k¯. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may move with constant speed, with exponentially increasing–decreasing axial velocity, with harmonically varying axial speed, or with accelerating–decelerating oscillatory axial speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semisimilar solutions of the unsteady Navier–Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers, Re=ka¯2/2υ, ranging from 0.1 to 100 for different values of dimensionless transpiration rate, S=Uo/ka¯, where a is cylinder radius and υ is kinematic viscosity of the fluid. Absolute value of the shear-stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear- stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain exponential axial velocity function at any particular value of Reynolds number and suction rate is axially stress-free. The heat transfer coefficient increases with the increasing suction rate, Reynolds number, Prandtl number, oscillation frequency and amplitude. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration. It is shown that a cylinder with certain type of exponential wall temperature exposed to a temperature difference has no heat transfer.

scholarly journals A general buoyancy–drag model for the evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities

2003 ◽  
Vol 21 (3) ◽  
pp. 347-353 ◽  
Author(s):  
YAIR SREBRO ◽  
YONI ELBAZ ◽  
OREN SADOT ◽  
LIOR ARAZI ◽  
DOV SHVARTS
Keyword(s):  
Temporal Evolution ◽  
Random Noise ◽  
Single Mode ◽  
Time Dependent ◽  
Late Time ◽  
Random Perturbations ◽  
Linear Stage ◽  
Drag Model ◽  
Characteristic Wavelength ◽  
Self Similar

The growth of a single-mode perturbation is described by a buoyancy–drag equation, which describes all instability stages (linear, nonlinear and asymptotic) at time-dependent Atwood number and acceleration profile. The evolution of a multimode spectrum of perturbations from a short wavelength random noise is described using a single characteristic wavelength. The temporal evolution of this wavelength allows the description of both the linear stage and the late time self-similar behavior. Model results are compared to full two-dimensional numerical simulations and shock-tube experiments of random perturbations, studying the various stages of the evolution. Extensions to the model for more complicated flows are suggested.

LOGISTIC MAPPING WITH A TIME-DEPENDENT SYSTEM-PARAMETER AND ITS ATTRACTOR BASINS WITH SELF-SIMILAR STRUCTURE

2004 ◽  
Vol 14 (07) ◽  
pp. 2407-2416 ◽  
Author(s):  
JOUSUKE KUROIWA ◽  
TAKAFUMI MIKI
Keyword(s):  
System Parameter ◽  
Time Dependent ◽  
Chaotic Attractors ◽  
Self Similarity ◽  
Initial Values ◽  
Logistic Mapping ◽  
Periodic Attractors ◽  
Self Similar ◽  
Basins Of Attractions ◽  
Time Dependent System

In this paper, logistic mapping with a time-dependent system-parameter (referred as "LMTD") is proposed. In various choices of time dependence, the periodic one has been tried in order to investigate the dynamical properties of LMTD. In certain parameter regions, two different attractors coexist depending on the initial values, for instances, two different chaotic attractors, two different periodic attractors, or two periodic/chaotic attractors. In addition, the whole configuration space of the initial values forms basins of attractions of which structures indicate self-similarity.

scholarly journals Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Gianni Mattioli ◽  
Massimo Scalia ◽  
Carlo Cattani
Keyword(s):  
Dynamical System ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
High Amplitude ◽  
Time Dependent ◽  
Third Order ◽  
Time Intervals ◽  
Nonlinear Dynamical ◽  
Short Time ◽  
Third Order Approximation

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

scholarly journals Signal processing of nonlinear dynamic systems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022057
Author(s):  
S V Sarkisov ◽  
S Z El-Salim ◽  
A V Bondarev ◽  
A N Korpusov ◽  
P A Putilin
Keyword(s):  
Wavelet Decomposition ◽  
Nonlinear Dynamical Systems ◽  
Hermite Polynomials ◽  
Nonlinear Dynamical ◽  
Self Similar ◽  
Quality Of Approximation ◽  
Approximation Coefficients ◽  
Similar Basis ◽  
Decomposition Of Functions

Abstract The paper considers Hermite polynomials that act as a self-similar basis for the decomposition of functions in phase space. It is shown that the equations of behavior of nonlinear dynamical systems are simplified. It is also noted that the wavelet decomposition over Hermite polynomials reduces the number of approximation coefficients and improves the quality of approximation.

scholarly journals Particle acceleration at colliding shock waves

2020 ◽  
Vol 494 (3) ◽  
pp. 3166-3176 ◽  
Author(s):  
T Vieu ◽  
S Gabici ◽  
V Tatischeff
Keyword(s):  
Shock Waves ◽  
High Energy ◽  
Time Dependent ◽  
Shock Acceleration ◽  
Diffusive Shock Acceleration ◽  
Mathematical Methods ◽  
Accretion Flows ◽  
Self Similar Solution ◽  
Self Similar ◽  
Accelerated Particles

ABSTRACT We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular, we show that in this limit the problem can be analysed with the help of a self-similar solution. While a number of recent works predict hard (E−1) spectra for the accelerated particles in the stationary limit, or the appearance of spectral breaks, we found instead that the spectrum of accelerated particles in a time-dependent collision follows quite closely the canonical E−2 prediction of diffusive shock acceleration at a single shock, except at the highest energy, where a hardening appears, originating a bumpy feature just before the exponential cut-off. We also investigated the effect of the reacceleration of pre-existing cosmic rays by a system of two shocks, and found that under certain conditions spectral features can appear in the cut-off region. Finally, the mathematical methods presented here are very general and could be easily applied to a variety of astrophysical situations, including for instance standing shocks in accretion flows, diverging shocks, backward collisions of a slow shock by a faster shock, and wind–wind or shock–wind collisions.

scholarly journals The structure of nearly isothermal, adiabatic shock waves

2020 ◽  
Vol 496 (1) ◽  
pp. L43-L47
Author(s):  
Eric R Coughlin
Keyword(s):  
Shock Wave ◽  
Contact Discontinuity ◽  
Time Dependent ◽  
Fluid Density ◽  
Leading Order ◽  
Energy Conserving ◽  
Post Shock ◽  
Adiabatic Shock ◽  
Self Similar ◽  
Ambient Gas

ABSTRACT An explosively generated shock wave with time-dependent radius R(t) is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index γ ≃ 1. Using the result that the post-shock gas is compressed into a shell of width ΔR/R ≃ δ, where δ = γ − 1, we show that a choice of self-similar variable that exploits this compressive behaviour in the limit that γ → 1 naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity δ. We demonstrate that the leading-order (in δ) solutions, which are increasingly accurate as γ → 1, can be written in simple, closed forms when the fluid is still approximated to be in the energy-conserving regime (i.e. the Sedov–Taylor limit), and that the density declines exponentially rapidly with distance behind the shock. We also analyse the solutions for the bubble surrounding a stellar or galactic wind that interacts with its surroundings, and derive expressions for the location of the contact discontinuity that separates the shocked ambient gas from the shocked wind. We discuss the implications of our findings in the context of the dynamical stability of nearly isothermal shocks.

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