Mean-field optimal multi-modes switching problem: A balance sheet

2019 ◽  
Vol 19 (04) ◽  
pp. 1950026 ◽  
Author(s):  
M’hamed Eddahbi ◽  
Imade Fakhouri ◽  
Youssef Ouknine
Keyword(s):  
Balance Sheet ◽  
Mean Field ◽  
Field Approximation ◽  
Expected Profit ◽  
Picard Iteration ◽  
Mean Field Approximation ◽  
Coupling Term ◽  
Snell Envelope ◽  
The Mean ◽  
Backward Sdes

We study a finite horizon optimal multi-modes switching problem with many nodes. The switching is based on the optimal expected profit and cost yields, moreover both sides of the balance sheet are considered. The profit and cost yields per unit time are respectively assumed to be coupled through a coupling term which is the average of profit and cost yields. The corresponding system of Snell envelopes is highly complex, so we consider the aggregated yields where a mean-field approximation is used for the coupling term. First, the problem is formulated by the mean of the Snell envelope of processes. Then, in terms of backward SDEs, the problem is equivalent to a system of mean-field reflected backward SDEs with interconnected and nonlinear obstacles. More precisely, the driver function depends also on the mean of the unknown process (expected profit or cost yields) which makes the mean-field interaction in the driver nonlinear. The first main result of this paper, is to show the existence of a continuous minimal solution of the system of mean-field reflected backward SDEs, which is done by using the Picard iteration method. The second main result concerns the optimality of the switching strategies which we fully characterize.

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 Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals UNDERSTANDING MAGNETIC INSTABILITY IN GAPLESS SUPERCONDUCTORS

2006 ◽  
Vol 21 (04) ◽  
pp. 910-913 ◽  
Author(s):  
Mei Huang
Keyword(s):  
Superconducting State ◽  
Phase Fluctuation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Bcs Theory ◽  
Magnetic Instability ◽  
Fermi Surfaces ◽  
Strong Phase ◽  
The Mean

Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected. The mean-field BCS theory describes very well the strongly coherent or rigid superconducting state. With the increase of mismatch between the Fermi surfaces of pairing fermions, the phase fluctuation plays more and more important role, and "soften" the superconductor. The strong phase fluctuation will eventually quantum disorder the superconducting state, and turn the system into a phase-decoherent pseudogap state.

Quartetting in Fermionic Matter and Alpha-Particle Condensation in Nuclear Systems

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2513-2546 ◽  
Author(s):  
G. Röpke ◽  
P. Schuck
Keyword(s):  
Nuclear Matter ◽  
Cluster Formation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Density Region ◽  
Nuclear Matter Density ◽  
Nuclear Systems ◽  
The Mean ◽  
Finite Nuclei

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

scholarly journals Several Physical Properties of Two Interacting Complex Scalar Fields at Finite Density

2011 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Tran Huu Phat ◽  
Phan Thi Duyen
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Meissner Effect ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Goldstone Theorem ◽  
Complex Scalar ◽  
Finite Density ◽  
Chemical Potentials ◽  
The Mean

The two interacting complex scalar fields at finite density is considered in the mean field approximation. It is shown that although the symmetry is spontaneously broken for the chemical potentials bigger than the meson masses in vacuum, but the Goldstone theorem is not preserved in broken phase. Then two mesons are condensed and their condensates turn out to be two-gap superconductor which is signaled by the appearance of the Meissner effect as well as the Abrikosov and non-Abrikosov vortices. Finally, there exhibits domain wall which is the plane, where two condensates flowing in opposite directions collide and generate two types of vortices with cores in the wall.

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