Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

We suggest employing the first-order stable RC filters, based on a single capacitor, for control of unstable fixed points in an array of oscillators. A single capacitor is sufficient to stabilize an entire array, if the oscillators are coupled strongly enough. An array, composed of 24 to 30 mean-field coupled FitzHugh–Nagumo (FHN) type asymmetric oscillators, is considered as a case study. The investigation has been performed using analytical, numerical, and experimental methods. The analytical study is based on the mean-field approach, characteristic equation for finding the eigenvalue spectrum, and the Routh–Hurwitz stability criteria using low-rank Hurwitz matrix to calculate the threshold value of the coupling coefficient. Experiments have been performed with a hardware electronic analog, imitating dynamical behavior of an array of the FHN oscillators.

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The Second-Order Master Equation

The Master Equation and the Convergence Problem in Mean Field Games ◽

10.23943/princeton/9780691190716.003.0005 ◽

2019 ◽

pp. 128-158

Author(s):

Pierre Cardaliaguet ◽

François Delarue ◽

Jean-Michel Lasry ◽

Pierre-Louis Lions

Keyword(s):

Master Equation ◽

Mean Field ◽

Second Order ◽

Well Posedness ◽

Mean Field Game ◽

First Order ◽

Common Noise ◽

System P ◽

The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

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Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.172-174.608 ◽

2011 ◽

Vol 172-174 ◽

pp. 608-617 ◽

Cited By ~ 3

Author(s):

William A. Soffa ◽

David E. Laughlin ◽

Nitin Singh

Keyword(s):

Nearest Neighbor ◽

Binary Solution ◽

Mean Field ◽

Lattice Relaxation ◽

Two Phase ◽

First Order ◽

Tetragonal Lattice ◽

Wide Range ◽

Third Law Of Thermodynamics ◽

The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

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Microstructure Evaluation for Time Dependent Nucleation Protocols in KJMA Kinetics

MRS Proceedings ◽

10.1557/proc-580-321 ◽

1999 ◽

Vol 580 ◽

Author(s):

Eloi Pineda ◽

Daniel Crespo

Keyword(s):

Mean Field ◽

Quantitative Agreement ◽

Nucleation And Growth ◽

Time Dependent ◽

First Order ◽

Microstructure Evaluation ◽

The Mean ◽

Dependent Growth ◽

First Order Phase

AbstractThe microstructure developed in a first order phase transformation is obtained using a populational extension of the Kolmogorov, Johnson-Mehl and Avrami (KJMA) model, PKJMA. PKJMA allows one to determine the grain size distribution resulting from nucleation and growth kinetics. PKJMA is grounded on the mean field hypothesis that the free space around the growing grains is randomly distributed, independent of the grain radius. Although this approach is perfectly valid for the case of constant nucleation, a detailed analysis of the model shows that this hypothesis does not hold in the case of time dependent nucleation protocols or pre-existing nuclei. In this work, the PKJMA model has been improved by estimating the average free surface around the grains as a function of their radius and the time elapsed since nucleation. The resulting model gives quantitative determination of the microstructure developed under a variety of nucleation and growth processes: pre-existing nuclei, constant nucleation, and the combination of both mechanisms, constant and radius dependent growth rates. Comparison with Monte Carlo simulations, showing a quantitative agreement will be presented.

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Convergence to the mean field game limit: A case study

The Annals of Applied Probability ◽

10.1214/19-aap1501 ◽

2020 ◽

Vol 30 (1) ◽

pp. 259-286 ◽

Cited By ~ 3

Author(s):

Marcel Nutz ◽

Jaime San Martin ◽

Xiaowei Tan

Keyword(s):

Mean Field ◽

Mean Field Game ◽

The Mean

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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

International Journal of Modern Physics B ◽

10.1142/s0217979219501030 ◽

2019 ◽

Vol 33 (11) ◽

pp. 1950103 ◽

Cited By ~ 4

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.

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Relation of the average interaction field with the coercive and interaction field distributions in First order reversal curve diagrams of nanowire arrays

Scientific Reports ◽

10.1038/s41598-020-78279-1 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Y. G. Velázquez ◽

A. Lobo Guerrero ◽

J. M. Martínez ◽

E. Araujo ◽

M. R. Tabasum ◽

...

Keyword(s):

Field Distribution ◽

Coercive Field ◽

Mean Field ◽

Full Width ◽

Switching Field ◽

Distribution Profile ◽

First Order ◽

Interaction Field ◽

The Mean ◽

Switching Field Distribution

AbstractFirst-order reversal curve diagrams, or FORC diagrams, have been studied to determine if the widths of their distributions along the interaction and coercivity axes can be related to the mean-field magnetization dependent interaction field (MDIF). Arrays of nanowires with diameters ranging from 18 up to 100 nm and packing fractions varying from 0.4 to 12% have been analyzed. The mean-field MDIF has been measured using the remanence curves and used as a measuring scale on the FORC diagrams. Based on these measurements, the full width of the interaction field distribution and the full width at half maximum (FWHM) of the FORC distribution profile along the interaction field direction are shown to be proportional to the MDIF, and the relation between them is found. Moreover, by interpreting the full width of the coercive field distribution in terms of the dipolar induced shearing, a simple relation is found between the width of this distribution and the MDIF. Furthermore, we show that the width of the FORC distribution along the coercive field axis is equal to the width of the switching field distribution obtained by the derivation of the DC remanence curve. This was further verified with the switching field distribution determined using in-field magnetic force microscopy (MFM) for very low density nanowires. The results are further supported by the good agreement found between the experiments and the values calculated using the mean-field model, which provides analytical expressions for both FORC distributions.

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A FIRST ORDER PHASE TRANSITION IN ISING FERRIMAGNETS

Modern Physics Letters B ◽

10.1142/s0217984995001339 ◽

1995 ◽

Vol 09 (21) ◽

pp. 1347-1351 ◽

Cited By ~ 1

Author(s):

HASAN M. AL MUKADAM ◽

DIMO I. UZUNOV

Keyword(s):

Phase Transition ◽

Order Parameter ◽

Mean Field Theory ◽

Mean Field ◽

First Order ◽

First Order Phase Transition ◽

Exchange Constants ◽

The Mean ◽

First Order Phase ◽

Ising Spins

The mean field theory is used for the analysis of a two-sublattice system of Ising spins, which describes ferro-, antiferro-, and ferrimagnetic orderings. It is proven that the phase transition in these systems is of a first order when the exchange constants of the sublattices are different. The free energy, the order parameter profiles and the latent heat of the phase transition are calculated for almost equivalent sublattices.

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Mean Field Approximation for the Dense Charged Drop

Advances in High Energy Physics ◽

10.1155/2017/7374909 ◽

2017 ◽

Vol 2017 ◽

pp. 1-5

Author(s):

S. Bondarenko ◽

K. Komoshvili

Keyword(s):

Charged Particle ◽

Schrödinger Equation ◽

Spherical Symmetry ◽

Schrodinger Equation ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Charged Drop ◽

First Order ◽

The Mean

We consider in this note the mean field approximation for the description of the probe charged particle in a dense charged drop. We solve the corresponding Schrödinger equation for the drop with spherical symmetry in the first order of mean field approximation and discuss the obtained results.

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Notizen: Monte-Carlo Simulation of a Two-dimensional Dipolar Lattice

Zeitschrift für Naturforschung A ◽

10.1515/zna-1977-1119 ◽

1977 ◽

Vol 32 (11) ◽

pp. 1320-1322 ◽

Cited By ~ 1

Author(s):

S. Romano

Keyword(s):

Monte Carlo ◽

Mean Field Theory ◽

Mean Field ◽

Square Lattice ◽

Electrostatic Energy ◽

Two Dimensional ◽

First Order ◽

First Order Phase Transition ◽

The Mean ◽

First Order Phase

Abstract Monte-Carlo calculations were carried out on a system consisting of 256 point-dipoles, whose centres are fixed in a two-dimensional square lattice with the usual boundary condition; the Epstein-Ewald-Kornfeld algorithm was used in evaluating the electrostatic energy. No evidence of a first-order phase transition was found, and the results suggest there might be a second-order one. Additional calculations were carrierd out using the mean-field theory, which was found to overestimate the transition temperature by about a factor two.

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DENSITY FLUCTUATIONS AND A FIRST-ORDER CHIRAL PHASE TRANSITION IN NON-EQUILIBRIUM

Modern Physics Letters A ◽

10.1142/s0217732308029605 ◽

2008 ◽

Vol 23 (27n30) ◽

pp. 2469-2472 ◽

Cited By ~ 1

Author(s):

CHIHIRO SASAKI ◽

BENGT FRIMAN ◽

KRZYSZTOF REDLICH

Keyword(s):

Phase Transition ◽

Mean Field ◽

Field Approximation ◽

Density Fluctuations ◽

Mean Field Approximation ◽

Chiral Phase ◽

Chiral Phase Transition ◽

First Order ◽

The Mean ◽

Non Equilibrium

The thermodynamics of a first-order chiral phase transition is considered in the presence of spinodal phase separation using the Nambu-Jona-Lasinio model in the mean field approximation. We focus on the behavior of conserved charge fluctuations. We show that in non-equilibrium the specific heat and charge susceptibilities diverge as the system crosses the isothermal spinodal lines.

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