Non-local effects in the mean-field disc dynamo: II – numerical and asymptotic solutions

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

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Mean-field models for segregation dynamics

European Journal of Applied Mathematics ◽

10.1017/s095679252000039x ◽

2020 ◽

pp. 1-22

Author(s):

MARTIN BURGER ◽

JAN-FREDERIK PIETSCHMANN ◽

HELENE RANETBAUER ◽

CHRISTIAN SCHMEISER ◽

MARIE-THERESE WOLFRAM

Keyword(s):

Random Walk ◽

Mean Field ◽

Single Species ◽

Random Motion ◽

Local Effects ◽

Mean Field Models ◽

Existence And Stability ◽

Non Local ◽

The Rich ◽

Multiple Species

In this paper, we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well as the available space. All individuals have the tendency to stay within their own group and avoid the others. These interactions lead to the formation of aggregates in case of a single species and to segregation in the case of multiple species. We derive two different mean-field models, which are based on these interactions and weigh local and non-local effects differently. We discuss existence and stability properties of solutions for both models and illustrate the rich dynamics with numerical simulations.

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A non-local mixing-length theory able to compute core overshooting

Astronomy and Astrophysics ◽

10.1051/0004-6361/201731835 ◽

2018 ◽

Vol 612 ◽

pp. A21 ◽

Cited By ~ 3

Author(s):

M. Gabriel ◽

K. Belkacem

Keyword(s):

Temperature Gradient ◽

Mean Field ◽

Mixing Length ◽

Field Equations ◽

Mean Field Equations ◽

Convective Core ◽

Non Local ◽

The Mean ◽

Free Parameters ◽

Mixing Length Theory

Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars. A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylor’s closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models.

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Non-local effects in the fermion dynamical mean-field framework; application to the two-dimensional Falicov-Kimball model

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/12/10/306 ◽

2000 ◽

Vol 12 (10) ◽

pp. 2209-2216 ◽

Cited By ~ 2

Author(s):

Mukul S Laad ◽

Mathias van den Bossche

Keyword(s):

Mean Field ◽

Two Dimensional ◽

Local Effects ◽

Non Local

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On the mean-field theory of the Karlsruhe dynamo experiment I. Kinematic theory

Magnetohydrodynamics ◽

10.22364/mhd.38.1-2.6 ◽

2002 ◽

Vol 38 (1-2) ◽

pp. 41-71 ◽

Cited By ~ 16

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Kinematic Theory ◽

The Mean

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Path Integral Method in the Mean-field Model for the Magnetic Vector Potential

Geomagnetism and Aeronomy ◽

10.1134/s0016793220070300 ◽

2020 ◽

Vol 60 (7) ◽

pp. 989-992

Author(s):

E. V. Yushkov ◽

C. R. Kamaletdinov ◽

D. D. Sokoloff

Keyword(s):

Path Integral ◽

Vector Potential ◽

Integral Method ◽

Field Model ◽

Mean Field ◽

Magnetic Vector Potential ◽

Magnetic Vector ◽

Mean Field Model ◽

The Mean ◽

Path Integral Method

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Classical Kinetic Theory

10.1093/oso/9780198797241.003.0003 ◽

2018 ◽

Author(s):

Klaus Morawetz

Keyword(s):

Kinetic Equation ◽

Equation Of State ◽

Mean Field ◽

Ideal Gas ◽

Hydrodynamic Equations ◽

Free Particles ◽

Internal Mechanism ◽

The Mean ◽

Energy Gains ◽

Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

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