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

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

Single-Crystal Magnetic Properties of [Co(NH3)5(OH2)] [Cr(CN)6] Between 2 and 300 K

1992 ◽  
Vol 45 (11) ◽  
pp. 1899 ◽  
Author(s):  
PA Reynolds ◽  
CD Delfs ◽  
BN Figgis ◽  
B Moubaraki ◽  
KS Murray
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Mean Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Zero Field Splitting ◽  
Magnetic Exchange Interaction ◽  
Mean Field Model ◽  
Magnetic Exchange ◽  
The Mean

The magnetic susceptibilities along and perpendicular to the c axis (hexagonal setting) between 2.0 and 300 K at a magnetic field of 1.00 T, and the magnetizations at field strengths up to 5.00 T, are presented for single crystals of [Co(NH3)5(OH2)] [Cr(CN)6]. The results are interpreted in terms of zero-field splitting (2D) of the ground 4A2g term by spin-orbit coupling and of magnetic exchange interaction between the chromium atoms. The magnetic exchange is modelled as one of Ising or mean-field in type. The exchange is found to be quite small: J = -0.18(6) cm-1 if the Ising model is employed, and -0.03(1) cm-1 for the mean-field model. The model adopted for the exchange has a strong influence on the value of the parameter D obtained. When the Ising model is used D is deduced to be -0.28(9) cm-l; when the mean-field model is used D is -0.14(4) cm-l. The g-values deduced are in agreement with those from e.s.r. measurements at higher temperatures and do not depend on the exchange model. In any case, D is found to be sufficiently large that it must be considered in a polarized neutron diffraction experiment on the compound.

scholarly journals Phase diagram of the mean field model of simplicial gravity

1999 ◽  
Vol 542 (1-2) ◽  
pp. 413-424 ◽  
Author(s):  
P. Bialas ◽  
Z. Burda ◽  
D. Johnston
Keyword(s):  
Phase Diagram ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
The Mean

A Phase Diagram for the Ice VI–VII–VIII Transitions

1998 ◽  
Vol 12 (08) ◽  
pp. 271-279 ◽  
Author(s):  
H. Yurtseven ◽  
S. Salihoğlu
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Field Model ◽  
Mean Field ◽  
Calculated Phase Diagram ◽  
Mean Field Model ◽  
Phase Line ◽  
Calculated Phase ◽  
The Mean ◽  
T Phase

In this study we obtain the P–T phase diagram for the ice VI–VII–VIII phase transitions by means of the mean field model developed here. We have fitted the experimentally measured P–T data to our phase line equations. Our calculated phase diagram describes adequately the observed behavior of the ice VI–VII–VIII phase transitions.

COMPETITION AND PREDATION IN A THREE SPECIES MODEL

2006 ◽  
Vol 17 (11) ◽  
pp. 1629-1645 ◽  
Author(s):  
JANUSZ SZWABIǸSKI ◽  
ANDRZEJ PȨKALSKI ◽  
KAMIL TROJAN
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
Agent Based ◽  
Interacting Species ◽  
Stochastic Fluctuations ◽  
The Mean ◽  
Large Systems ◽  
Access To Food ◽  
Type Of Behavior

A model of dynamics of three interacting species is presented. Two of the species are prey and one is predator, which feeds on both prey, however with some preference to one type. Prey compete for space (breeding) although they always have access to food. Predators in order to survive and reproduce must catch prey, otherwise they die of hunger. The dynamics of the model is found via differential equations in the mean-field like approach and through computer simulations for agent-based method. We show that the coexistence of the three species is possible in the mean-field model, provided the preference of the predators is small, whereas from simulation it follows that the stochastic fluctuations drive, generally, one of the prey populations into extinction. We have found a different type of behavior for small and large systems and a rather unexpected dependence of the coexistence chance of the preference parameter in bigger lattices.

scholarly journals Mean field approximation of network of biophysical neurons driven by conductance-based ion exchange dynamics

2021 ◽  
Author(s):  
Abhirup Bandyopadhyay ◽  
Spase Petkoski ◽  
Viktor Jirsa
Keyword(s):  
Ion Exchange ◽  
Molecular Mechanisms ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Ion Concentrations ◽  
The Mean ◽  
Locally Homogeneous

Changes in extracellular ion concentrations are known to modulate neuronal excitability and play a major role in controlling the neuronal firing rate, not just during the healthy homeostasis, but also in pathological conditions such as epilepsy. The microscopic molecular mechanisms of field effects are understood, but the precise correspondence between the microscopic mechanisms of ion exchange in the cellular space of neurons and the macroscopic behavior of neuronal populations remains to be established. We derive a mean field model of a population of Hodgkin Huxley type neurons. This model links the neuronal intra- and extra-cellular ion concentrations to the mean membrane potential and the mean synaptic input in terms of the synaptic conductance of the locally homogeneous mesoscopic network and can describe various brain activities including multi-stability at resting states, as well as more pathological spiking and bursting behaviors, and depolarizations. The results from the analytical solution of the mean field model agree with the mean behavior of numerical simulations of large-scale networks of neurons. The mean field model is analytically exact for non-autonomous ion concentration variables and provides a mean field approximation in the thermodynamic limit, for locally homogeneous mesoscopic networks of biophysical neurons driven by an ion exchange mechanism. These results may provide the missing link between high-level neural mass approaches which are used in the brain network modeling and physiological parameters that drive the neuronal dynamics.

Calculation of the thermodynamic quantities of perovskite metal organics DMAKCr and perovskite HyFe close to the weakly first-order relaxor-like structural transformation using the mean field theory

2019 ◽  
Vol 33 (11) ◽  
pp. 1950103 ◽  
Author(s):  
H. Yurtseven ◽  
Ö. Tarı
Keyword(s):  
Field Theory ◽  
Field Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Excess Heat Capacity ◽  
Mean Field Model ◽  
First Order ◽  
Entropy Formula ◽  
Inverse Susceptibility ◽  
The Mean

Weakly first-order or nearly second-order phase transitions occurring in metal–organic frameworks (MOFs), particularly in DMAKCr and perovskite HyFe, are studied under the mean field model by using the observed data from the literature. In this work, mainly thermal and magnetic properties among various physical properties which have been reported in the literature for those MOFs are studied by the mean field theory. By expanding the free energy in terms of the magnetization (order parameter), the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S), latent heat (L), magnetization (M) and the inverse susceptibility ([Formula: see text]) are calculated as a function of temperature close to the weakly first-order phase transition within the Landau phenomenological model which is fitted to the experimental data from the literature for C[Formula: see text] (DMAKCr and perovskite HyFe) and for magnetization M (HyFe). Our predictions of the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S) agree below T[Formula: see text] with the observed data within the temperature intervals studied for DMAKCr and perovskite HyFe. From our predictions, we find that magnetization decreases continuously whereas the inverse susceptibility decreases linearly with increasing temperature toward the transition temperature in those MOFs as expected for a weakly first-order transition from the mean field model.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

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