scholarly journals Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation

Nonlinearity ◽  
2015 ◽  
Vol 28 (5) ◽  
pp. 1307-1350 ◽  
Author(s):  
Susana Gutiérrez ◽  
André de Laire
Keyword(s):  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

Theoretical modeling of the carbon dioxide injection into the porous medium saturated with methane and water taking into account the CO2 hydrate formation

2018 ◽  
Author(s):  
Gubaidullin A. A. ◽  
Musakaev N. G. ◽  
Duong Ngoc Hai ◽  
Borodin S. L. ◽  
Nguyen Quang Thai ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Hydrate Formation ◽  
Carbon Dioxide Injection ◽  
Reservoir Temperature ◽  
One Dimensional ◽  
Porous Reservoir ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Mathematical Model

In this work the mathematical model is constructed and the features of the injection of warm carbon dioxide (with the temperature higher than the initial reservoir temperature) into the porous reservoir initially saturated with methane gas and water are investigated. Self-similar solutions of the one-dimensional problem describing the distributions of the main parameters in the reservoir are constructed. The effect of the parameters of the injected carbon dioxide and the reservoir on the intensity of the CO2 hydrate formation is analyzed

On the stability of a class of self-similar solutions to the filtration-absorption equation

2002 ◽  
Vol 13 (2) ◽  
pp. 179-194 ◽  
Author(s):  
ALINA CHERTOCK
Keyword(s):  
The Self ◽  
Initial Condition ◽  
Cauchy Problems ◽  
One Dimensional ◽  
Self Similar ◽  
Analytical Result ◽  
Axisymmetric Solutions ◽  
The Stability ◽  
The One ◽  
Similar Solutions

We consider the one-dimensional and two-dimensional filtration-absorption equation ut = uΔu−(c−1)(∇u)2. The one-dimensional case was considered previously by Barenblatt et al. [4], where a special class of self-similar solutions was introduced. By the analogy with the 1D case we construct a family of axisymmetric solutions in 2D. We demonstrate numerically that the self-similar solutions obtained attract the solutions of non-self-similar Cauchy problems having the initial condition of compact support. The main analytical result we provide is the linear stability of the above self-similar solutions both in the 1D case and in the 2D case.

scholarly journals Impact of dust in the decay of blast waves produced by a nuclear explosion

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200105 ◽  
Author(s):  
Meera Chadha ◽  
J. Jena
Keyword(s):  
Radiation Effects ◽  
Nuclear Explosion ◽  
Blast Waves ◽  
Dust Particles ◽  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Impact ◽  
Relaxing Gas

In this paper, we have studied the impact created by the introduction of up to 5% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters.

Self-similar solutions for Vlasov and water-bag models

1978 ◽  
Vol 19 (1) ◽  
pp. 135-146 ◽  
Author(s):  
J. R. Burgan ◽  
J. Gutierrez ◽  
E. Fijalkow ◽  
M. Navet ◽  
M. R. Feix
Keyword(s):  
Single Species ◽  
Complete Agreement ◽  
Self Similarity ◽  
One Dimensional ◽  
Virtual Particle ◽  
Electron Plasmas ◽  
Finite Group Theory ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

Using finite group theory, self-similar solutions for the one-dimensional Vlasov– Poisson system are considered, both for electron plasmas, with a fixed ion background, and for a single species beam. Difficulties arising from the Poisson equation are pointed out and handled by using an exponential group of transformations. Introducing, for the beam, a water-bag model, we find that the boundary condition problem, imposed by self-similarity, can be solved through the introduction of a ‘virtual particle’ concept. In order to test the analytical solution obtained, we perform a numerical simulation using a particle code. Complete agreement is found.

A similarity problem of a porous material drying

2008 ◽  
Vol 6 ◽  
pp. 75-81
Author(s):  
D.Ye. Igoshin
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Gas Mixture ◽  
Dimensional Problem ◽  
Vapor Mixture ◽  
Initial State ◽  
One Dimensional ◽  
Similarity Problem ◽  
Self Similar ◽  
Similar Solutions

The plano-one-dimensional problem of heat and mass transfer is considered when a porous semi-infinite material layer dries. At the boundary, which is permeable for the gas-vapor mixture, the temperature and composition of the gas are kept constant. Self-similar solutions are set describing the propagation of the temperature field and the moisture content field arising when heat is supplied. The intensity of dry flows is studied, depending on the initial state of the wet-porous medium, as well as the temperature and concentration composition of the vapor-gas mixture at the boundary of the porous medium.

scholarly journals A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY

Fractals ◽  
2004 ◽  
Vol 12 (03) ◽  
pp. 331-346 ◽  
Author(s):  
SERGIO BIANCHI
Keyword(s):  
Necessary Conditions ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Probability Distribution Functions ◽  
Self Similar ◽  
The One ◽  
New Distribution

In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

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