scholarly journals A local existence result for a plasma physics model containing a fully coupled magnetic field

2009 ◽  
Vol 2 (3) ◽  
pp. 503-520
Author(s):  
Martin Seehafer ◽  
Keyword(s):  
Magnetic Field ◽  
Plasma Physics ◽  
Existence Result ◽  
Local Existence ◽  
Physics Model ◽  
Fully Coupled

scholarly journals A local existence result for Poincaré-Einstein metrics

2020 ◽  
Vol 361 ◽  
pp. 106912 ◽  
Author(s):  
Matthew J. Gursky ◽  
Gábor Székelyhidi
Keyword(s):  
Existence Result ◽  
Einstein Metrics ◽  
Local Existence

Coupled Magneto-mechanical Modeling of Composites Containing Aligned Ferromagnetic Particles

2003 ◽  
Vol 785 ◽  
Author(s):  
Huiming Yin ◽  
Lizhi Sun
Keyword(s):  
Magnetic Field ◽  
Elastic Interaction ◽  
Mechanical Modeling ◽  
Mechanical Loads ◽  
Elastic Fields ◽  
Particle Chain ◽  
Proposed Model ◽  
Fully Coupled ◽  
Ferromagnetic Particles ◽  
Soft Elastomer

ABSTRACTThe objective of this paper is to investigate effective magneto-mechanical behavior of composites containing aligned ferromagnetic particles. The effective magneto-elastic properties and the overall magnetostriction of the composites are derived by considering the pair-wise interaction between ferromagnetic particles. For the composites with soft elastomer matrix, the microstructural configuration rapidly changes with the magnetic and mechanical loads so that the local magnetic and elastic fields are fully coupled. This model accounts for the coupled magneto-elastic interaction and pair-wise interaction between particles. The results show that the Young's modulus along the particle-chain direction is reduced and the shear modulus is increased under the applied magnetic field. Predictions from the proposed model are compared with available experimental data and other models.

Non-isothermal flows in porous media with curing

1997 ◽  
Vol 8 (6) ◽  
pp. 623-637 ◽  
Author(s):  
LUCA BILLI
Keyword(s):  
Local Existence ◽  
Coupled System ◽  
Discontinuous Coefficients ◽  
Heat Diffusion ◽  
Weak Formulation ◽  
Heat Diffusion Equation ◽  
A Free Boundary Problem ◽  
Kinetics Of ◽  
Fully Coupled ◽  
Local Existence Of Solutions

The motivation for this work arises from the study of the processes involved in the manufacturing of a class of composite materials, in particular, those that are obtained by injecting a resin through a porous preform. A one-dimensional model that describes the non-isothermal filtration of an incompressible fluid is presented, and it also includes the possibility of curing, i.e. the polymerization of the penetrating resin. It comes out a fully coupled system consisting of the heat diffusion equation, Darcy's law and an equation related to the kinetics of the chemical reaction. The system is regarded as a free boundary problem for the heat equation with non-constant discontinuous coefficients. Its weak formulation is studied and the local existence of solutions is proved.

scholarly journals LOCAL EXISTENCE AND CONTINUATION CRITERIA FOR SOLUTIONS OF THE EINSTEIN–VLASOV-SCALAR FIELD SYSTEM WITH SURFACE SYMMETRY

2004 ◽  
Vol 01 (04) ◽  
pp. 691-724 ◽  
Author(s):  
D. TEGANKONG ◽  
N. NOUTCHEGUEME ◽  
A. D. RENDALL
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Wave Equations ◽  
Existence Result ◽  
General Theorem ◽  
Local Existence ◽  
Field System ◽  
Cosmological Solutions ◽  
Time Existence ◽  
Global Existence Result

We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein–Vlasov-scalar field system, with the sources generated by a distribution function and a scalar field, subject to the Vlasov and wave equations respectively. This system describes the evolution of self-gravitating collisionless matter and scalar waves within the context of general relativity. In the case where the only source is a scalar field it is shown that a global existence result can be deduced from the general theorem.

scholarly journals Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry

1996 ◽  
Vol 119 (4) ◽  
pp. 739-762 ◽  
Author(s):  
Gerhard Rein
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Existence Result ◽  
Local Existence ◽  
Space Distribution ◽  
Initial Value ◽  
Small Initial Data ◽  
Phase Space Distribution ◽  
Spacetime Singularity ◽  
Cosmological Solutions

AbstractThe Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and prove that for small initial data solutions exist up to a spacetime singularity which is a curvature and a crushing singularity. An important tool in the analysis is a local existence result with a continuation criterion saying that solutions can be extended as long as the momenta in the support of the phase-space distribution of the matter remain bounded.

Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation

2020 ◽  
pp. 2050069
Author(s):  
Reinhard Racke ◽  
Belkacem Said-Houari
Keyword(s):  
Cauchy Problem ◽  
Existence Result ◽  
Local Existence ◽  
Decay Rates ◽  
Polynomial Decay ◽  
Small Data ◽  
Third Order ◽  
Bootstrap Argument ◽  
The Cauchy Problem ◽  
Linear Decay

We consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan–Moore–Gibson–Thompson (JMGT) equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained.

scholarly journals Magnetospheric plasma boundaries: a test of the frozen-in magnetic field theorem

2005 ◽  
Vol 23 (7) ◽  
pp. 2565-2578 ◽  
Author(s):  
R. Lundin ◽  
M. Yamauchi ◽  
J.-A. Sauvaud ◽  
A. Balogh
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Magnetic Flux ◽  
Plasma Physics ◽  
Electric Fields ◽  
Measurement Data ◽  
Space Plasma ◽  
Space Plasma Physics ◽  
Macroscopic System ◽  
Ideal Mhd

Abstract. The notion of frozen-in magnetic field originates from H. Alfvén, the result of a work on electromagnetic-hydrodynamic waves published in 1942. After that, the notion of frozen-in magnetic field, or ideal MHD, has become widely used in space plasma physics. The controversy on the applicability of ideal MHD started in the late 1950s and has continued ever since. The applicability of ideal MHD is particularly interesting in regions where solar wind plasma may cross the magnetopause and access the magnetosphere. It is generally assumed that a macroscopic system can be described by ideal MHD provided that the violations of ideal MHD are sufficiently small-sized near magnetic x-points (magnetic reconnection). On the other hand, localized departure from ideal MHD also enables other processes to take place, such that plasma may cross the separatrix and access neighbouring magnetic flux tubes. It is therefore important to be able to quantify from direct measurements ideal MHD, a task that has turned out to be a major challenge. An obvious test is to compare the perpendicular electric field with the plasma drift, i.e. to test if E=–v×B. Yet another aspect is to rule out the existence of parallel (to B) electric fields. These two tests have been subject to extensive research for decades. However, the ultimate test of the "frozen-in" condition, based on measurement data, is yet to be identified. We combine Cluster CIS-data and FGM-data, estimating the change in magnetic flux (δB/δt) and the curl of plasma –v×B(∇×(v×B)), the terms in the "frozen-in equation". Our test suggests that ideal MHD applies in a macroscopic sense in major parts of the outer magnetosphere, for instance, in the external cusp and in the high-latitude magnetosheath. However, we also find significant departures from ideal MHD, as expected on smaller scales, but also on larger scales, near the cusp and in the magnetosphere-boundary layer. We discuss the importance of these findings. Keywords. Magnetospheric physics (Magnetopause, cusp and boundary layers; Solar wind-magnetosphere interactions) – Space plasma physics

scholarly journals The Interaction of Cometary Plasma with Interplanetary Medium - A Post-Halley View

1990 ◽  
Vol 142 ◽  
pp. 429-434
Author(s):  
Debi Prasad
Keyword(s):  
Magnetic Field ◽  
Plasma Physics ◽  
Recent Work ◽  
Strong Interaction ◽  
Interplanetary Medium ◽  
Heliospheric Magnetic Field ◽  
Cometary Plasma ◽  
Plasma Tail ◽  
Comet Halley

The strong interaction of cometary plasma with the interplanetary medium results the disconnection events and other features observed in plasma tail and the coma of comets. The understanding of these features provide direct probe of the heliospheric magnetic field. However the interpretation of these events is not without ambiguity, as revealed in the recent work with comet Halley. In this paper a review of the “Post-Halley era” developments of the cometary plasma physics is presented.

scholarly journals Satellite observations of plasma physics near the magnetic field reconnection X line

2011 ◽  
Vol 116 (A12) ◽  
pp. n/a-n/a ◽  
Author(s):  
F. S. Mozer ◽  
D. Sundkvist ◽  
J. P. McFadden ◽  
P. L. Pritchett ◽  
I. Roth
Keyword(s):  
Magnetic Field ◽  
Plasma Physics ◽  
Satellite Observations ◽  
The Magnetic Field
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