A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Investigations on the Equation of State of Neutron Star Matter with Density-dependent Relativistic Mean-field Model

The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius.In particular,the compact object with a mass of 2.50-2.67 M_(⊙)observed by LIGO Scientific and Virgo collaborations in GW190814,as well as the recent report of a light compact object with a mass and radius of M=0.77_(-0.17)^(+0.20)M_(⊙)and R=10.4_(-0.78)^(+0.86)km within the supernova remnant HESS J1731-347,have posed a great challenge to the investigations into the supranuclear matter.In the inner core of a neutron star,the strangeness degrees of freedom,such as the hyperons,can be present to form a hyperon star.In this work,the neutron star consisting of nucleons and leptons,and the hyperonic star including the hyperons will be studied in the framework of the density-dependent relativistic mean-field(DDRMF)model.Some popular DDRMF parameterizations will be adopted to investigate the properties of nuclear matter and the mass,radius,tidal deformability,and other properties of neutron star and hyperonic stars.We find that the maximum masses of neutron star calculated by DD-MEX,DD-MEX1,DD-MEX2,DD-MEXY and DD-LZ1 sets can be around 2.5-2.6 MM_(⊙)because they can produce quite stiff equations of state(EOSs)due to the strong repulsive contributions from vector potentials at high densities.Moreover,by investigating the influence of the crust EOS and core EOS on the neutron stars,we find that the observational data from HESS J1731-347 suggest the requirement of a crust EOS with a higher L parameter and a core EOS with a lower L parameter,and the M-R relations from the constructed EOSs can also be consistent with the observables of PSR J0740+6620,PSR J0030+0451 from NICER and the GW170817 event.With the inclusion of hyperons,the hyperonic star matter becomes softer compared to the neutron star matter,but the massive hyperonic star can also be obtained with DDRMF parameter sets if the vector meson coupling constants are strong.

Stoner-Wohlfarth模型的磁滞回线特征量分析

针对磁化强度的一致转动:Stoner-Wohlfarth模型,在磁滞回线不能严格求解的现实情况下,我们获得了描述磁滞回线的特征量:剩磁、矫顽力、饱和场的严格解.依据磁化强度一致转动过程的分析,我们提出了剩磁、矫顽力、饱和场这3个特征量的确定条件,并得到以上磁性材料的技术磁化特征量与材料内禀参量饱和磁化强度和各向异性等效场的关系.同时,我们利用磁滞回线在3个特殊角度下的严格解和一般情况下的数值解验证了以上特征量关系的正确性.本研究结果对于判断磁性材料的磁化反磁化过程和深入理解一致转动过程具有重要参考意义.

基于Stoner-Wohlfarth模型磁性纳米颗粒的磁化反转

纳米磁性材料由于其特殊的磁学性能,近年来,在许多领域受到了广泛的应用。在基础理论研究中,人们提出了各种描述纳米磁性材料的理论;另一方面,计算机计算能力以及实验手段的提高,使得应用计算机进行材料设计以及探测单个纳米颗粒的磁学特性成为可能。这使得人们对纳米磁性材料的理解更加深入。本篇论文介绍了磁性纳米颗粒的磁化反转机制的基本理论与实验研究的最新进展。本文首先从磁性材料中基本的相互作用入手说明这些相互作用在纳米尺度下的表现形式,随后详细介绍了基于Stoner-Wohlfarth模型计算机模拟方法,最后简单介绍两种可以用来研究单个纳米颗粒磁化反转实验手段以及相关的实验结果。

基于Stoner-Wohlfarth模型的纳米磁性颗粒系统磁化过程Monte Carlo模拟

采用SW模型以改进的Monte Carlo算法计算纳米磁性颗粒系统的磁学性质。改进的算法充分考虑低温时系统的热扰动以及具体磁化反转过程的反转路径。模拟的结果再现了系统的Néel驰豫特性,同时建立起了Monte Carlo步和实验测量时间之间的关系。对于无相互作用的纳米磁性颗粒系统,对于易磁化方向随机分布和同一分布的系统,二者的剩磁和矫顽场均随温度的增加而减小。改进算法能充分再现纳米磁性颗粒系统的磁学特性,为以后复杂系统的模拟提供了很好的基础。

Shape Coexistence in Neutron-Deficient At Isotopes in Relativistic Mean-Field Model

The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.

Application of Mean-Field Jordan-Wigner Transformation to Antiferromagnet System

By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.

A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus

This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.

Current-induced synchronized magnetization reversal of two-body Stoner particles with dipolar interaction

We investigate magnetization reversal of two-body uniaxial Stoner particles, by injecting spin-polarized current through a spin-valve structure. The two-body Stoner particles perform synchronized dynamics and can act as an information bit in computer technology. In the presence of magnetic dipole–dipole interaction（DDI） between the two particles,the critical switching current Ic for reversing the two dipoles is analytically obtained and numerically verified in two typical geometric configurations. The Ic bifurcates at a critical DDI strength, where Ic can decrease to about 70% of the usual value without DDI. Moreover, we also numerically investigate the magnetic hysteresis loop, magnetization self-precession,reversal time and synchronization stability phase diagram for the two-body system in the synchronized dynamics regime.

Nonlinear Effects in Quantum Dynamics of Atom Laser: Mean-Field Approach

Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.

多期动态资产负债管理模型的研究—Mean-Field方法的应用

本文在均值–方差准则下考虑有负债的多期有现金流追加的投资选择问题,该问题的目标函数含有盈余期望的平方这一非线性项,不能直接利用动态规划方法求解。本文通过利用mean-field方法,扩大状态空间和策略空间,使得原问题可以利用动态规划原理得出最佳策略,进而通过迭代计算,得到了有效前沿。

Exact analytical solutions to the mean-field model depicting microcavity containing semiconductor quantum wells

By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.

MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R^2

Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.

Resonant Continuum in the Relativistic Mean-Field Theory

Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory （MFT）. The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.

Shape Coexistence for ^179Hg in Relativistic Mean-Field Theory

The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.

Combining descriptor-based analyses and mean-field modeling of the electrochemical interface to comprehend trends of catalytic processes at the solid/liquid interface

Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/liquid interface.Most commonly,heuristic concepts in the realm of materials screening by the compilation of volcano plots are used,which rely on a plethora of simplifications and approximations of the complex electrochemical interface.While the investigation of the catalytic processes at the solid/liquid interface mainly relies on descriptor-based approaches,in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.

A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.