The Self–similar Solution to Some Nonlinear Integro–differential Equations Corresponding to Fractional Order Time Derivative

2005 ◽  
Vol 21 (6) ◽  
pp. 1337-1350 ◽  
Author(s):  
Chang Xing Miao ◽  
Han Yang
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Time Derivative ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

On the continuity equation for electrons in microwave-afterglow plasmas

1992 ◽  
Vol 47 (2) ◽  
pp. 193-195 ◽  
Author(s):  
H. I. Abdel-Gawad
Keyword(s):  
Continuity Equation ◽  
Spherical Geometry ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar

We construct a continuity equation for electrons in microwave-afterglow plasmas. The self-similar solution of the equation is obtained for a plasma with plane, cylindrical or spherical geometry.

scholarly journals Phase-space structure of cold dark matter haloes inside splashback: multistream flows and self-similar solution

2020 ◽  
Vol 493 (2) ◽  
pp. 2765-2781 ◽  
Author(s):  
Hiromu Sugiura ◽  
Takahiro Nishimichi ◽  
Yann Rasera ◽  
Atsushi Taruya
Keyword(s):  
Dark Matter ◽  
Phase Space ◽  
Cold Dark Matter ◽  
The Self ◽  
Similar Solution ◽  
Sharp Drop ◽  
Self Similar Solution ◽  
Self Similar ◽  
Fitting Parameters ◽  
Radial Phase

ABSTRACT Using the motion of accreting particles on to haloes in cosmological N-body simulations, we study the radial phase-space structures of cold dark matter (CDM) haloes. In CDM cosmology, formation of virialized haloes generically produces radial caustics, followed by multistream flows of accreted dark matter inside the haloes. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multistream structure of CDM haloes inside the splashback radius. To analyse this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting on to the haloes, we count their number of apocentre passages, which is then used to reveal the multistream flows of the dark matter particles. The resultant multistream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim \!30{{\ \rm per\ cent}}$ of the simulated haloes satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterize physical properties of the haloes, including the mass accretion rate and the size of the outermost caustic (i.e. the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the N-body simulation.

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

1983 ◽  
Vol 29 (1) ◽  
pp. 139-142 ◽  
Author(s):  
J. R. Burgan ◽  
M. R. Feix ◽  
E. Fijalkow ◽  
A. Munier
Keyword(s):  
Asymptotic Solution ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Asymptotic Solutions ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
New Equation

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

On the self-similar solution of laser ablated plasma expansion

2010 ◽  
Author(s):  
R. Fermous ◽  
D. Doumaz ◽  
M. Djebli
Keyword(s):  
The Self ◽  
Similar Solution ◽  
Plasma Expansion ◽  
Self Similar Solution ◽  
Self Similar

The self-similar solutions to full compressible Navier–Stokes equations without heat conductivity

2019 ◽  
Vol 29 (12) ◽  
pp. 2271-2320
Author(s):  
Xin Liu ◽  
Yuan Yuan
Keyword(s):  
Small Perturbation ◽  
Heat Conductivity ◽  
Stokes Equations ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar ◽  
Similar Solutions

In this work, we establish a class of globally defined large solutions to the free boundary problem of compressible full Navier–Stokes equations with constant shear viscosity, vanishing bulk viscosity and heat conductivity. We establish such solutions with initial data perturbed around the self-similar solutions when [Formula: see text]. In the case when [Formula: see text], solutions with bounded entropy can be constructed. It should be pointed out that the solutions we obtain in this fashion do not in general keep being a small perturbation of the self-similar solution due to the second law of thermodynamics, i.e. the growth of entropy. If, in addition, in the case when [Formula: see text], we can construct a solution as a global-in-time small perturbation of the self-similar solution and the entropy is uniformly bounded in time. Our result extends the one of Hadžić and Jang [Expanding large global solutions of the equations of compressible fluid mechanics, J. Invent. Math. 214 (2018) 1205.] from the isentropic inviscid case to the non-isentropic viscous case.

Comments on the paper ‘Self-similar state of a weakly turbulent plasma’

1982 ◽  
Vol 27 (1) ◽  
pp. 189-190 ◽  
Author(s):  
G. E. Vekstein ◽  
D. D. Ryutov ◽  
R. Z. Sagdeev
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Collisionless Plasma ◽  
Turbulent Plasma ◽  
The Self ◽  
Similar Solution ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One

In a recent paper, Balescu (1980) criticizes the self-similar solution in the problem of anomalous plasma resistivity (Vekstein, Ryutov & Sagdeev 1970) and comes to the conclusion that this solution is not correct. The aim of this comment is to show why Balescu's arguments are erroneous.We consider here the simplest case of the one-dimensional collisionless plasma in the presence of an external electric field.

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