scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals On Magnetic Inhibition of Thermal Convection

1972 ◽  
Vol 25 (6) ◽  
pp. 703 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy ◽  
EA Spiegel
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Quantitative Estimates ◽  
Wide Range ◽  
The Face ◽  
The Mean ◽  
The Magnetic Field

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.

Processus de branchement en champ moyen et réaction PCR

2001 ◽  
Vol 33 (2) ◽  
pp. 391-403 ◽  
Author(s):  
Didier Piau
Keyword(s):  
Branching Process ◽  
Random Number ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Process Mean ◽  
Dna Mutations ◽  
Wide Range ◽  
The Mean ◽  
Efficiency Rate

Sun and Waterman model DNA mutations during the PCR reaction by a non-canonical branching process. Mean-field approximated values fit the simulated values surprisingly well. We prove this as a theoretical result, for a wide range of the parameters. Thus, we bound explicitly the biases, in law and in the mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule, as a function of the initial number of molecules, of the number of PCR cycles, of the efficiency rate and of the mutation rate. The range where we prove that the approximation is good contains the observed mutation rates in many actual PCR reactions.

scholarly journals WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

2011 ◽  
Vol 09 (04) ◽  
pp. 1047-1056 ◽  
Author(s):  
D. O. SOARES-PINTO ◽  
J. TELES ◽  
A. M. SOUZA ◽  
E. R. DEAZEVEDO ◽  
R. S. SARTHOUR ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Order Transition ◽  
Mean Field Approximation ◽  
Temperature Hysteresis ◽  
First Case ◽  
The Matrix ◽  
The Mean

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B0 + λM and (ii) B = B0 + λM + λ′M3, where B0 is the external magnetic field, and λ, λ′ are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

scholarly journals PARITY VIOLATION AND THE MEAN FIELD APPROXIMATION FOR THE ANYON GAS

1993 ◽  
Vol 08 (20) ◽  
pp. 1909-1915 ◽  
Author(s):  
DIDIER CAENEPEEL ◽  
RICHARD MACKENZIE
Keyword(s):  
Magnetic Field ◽  
Parity Violation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Radius Of Curvature ◽  
Interparticle Separation ◽  
The Mean ◽  
The One ◽  
Self Consistency

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.

A MEAN FIELD APPROACH FOR ISING MODELS ON SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (07) ◽  
pp. 453-464 ◽  
Author(s):  
G. IANNONE ◽  
ORLANDO LUONGO
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Practical Applications ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
The Mean ◽  
Mean Field Approximations

Recently, the study of complex networks led to the analysis of the so-called scale-free models in statistical mechanics. This study has increased its importance, thanks to the wide range of applications in numerous physical contexts; for example, one important question is to understand the behavior of various models on such networks. We start first by investigating the Ising model in the mean field approximation and on scale-free networks, studying especially the Ising model with annealed dilution and Clock model, with particular attention devoted to focusing on similarities between the mean field approximations with or without scale-free statistics. A particular emphasis is given to the possible practical applications of these results in other disciplines such as medicine and social science.

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