Delay-Optimal Random Access in Large-Scale Energy Harvesting IoT Networks Based on Mean Field Game

With energy harvesting capability, the Internet of things(IoT) devices transmit data depending on their available energy, which leads to a more complicated coupling and brings new technical challenges to delay optimization. In this paper,we study the delay-optimal random access(RA) in large-scale energy harvesting IoT networks. We model a two-dimensional Markov decision process(MDP)to address the coupling between the data and energy queues, and adopt the mean field game(MFG) theory to reveal the coupling among the devices by utilizing the large-scale property. Specifically, to obtain the optimal access strategy for each device, we derive the Hamilton-Jacobi-Bellman(HJB) equation which requires the statistical information of other devices.Moreover, to model the evolution of the states distribution in the system, we derive the Fokker-PlanckKolmogorov(FPK) equation based on the access strategy of devices. By solving the two coupled equations,we obtain the delay-optimal random access solution in an iterative manner with Lax-Friedrichs method. Finally, the simulation results show that the proposed scheme achieves significant performance gain compared with the conventional schemes.

A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games

Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.

Fast impurity solver for dynamical mean field theory based on second order perturbation around the atomic limit

This paper proposes an impurity solver for the dynamical mean field theory （DMFT） study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA （local density approximation） ＋ DMFT studies of the Mort insulators with long range order.

Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach （AMFP）. Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential （DE） model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.

Investigations on Nuclei near Z = 82 in Relativistic Mean Field Theory with FSUGold

In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field （RMF） theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.

Method of accurately calculating mean field operator in multi-configuration time-dependent Hartree-Fock frame

The accurate theoretical expressions of the mean field operator associated with the multi-configuration time-dependent Hartree-Fock （MCTDHF） method are presented in this paper. By using a theoretical formula, derived without approxima- tion, we can study the multi-electron correlation dynamics accurately. Some illustrative calculations are carried out to check the accuracy of the expression of the mean field operator. The results of illustrative calculations indicate the reliability of the accurate expression of the mean field operator. This theoretical calculation method for the mean field operator may be of considerable help in future studies of the correlated dynamics of many-electron systems in strong laser fields.

Data Security Defense and Algorithm for Edge Computing Based on Mean Field Game

With the development of the Internet of Things,the edge devices are increasing.Cyber security issues in edge computing have also emerged and caused great concern.We propose a defense strategy based on Mean field game to solve the security issues of edge user data during edge computing.Firstly,an individual cost function is formulated to build an edge user data security defense model.Secondly,we research the𝜀𝜀-Nash equilibrium of the individual cost function with finite players and prove the existence of the optimal defense strategy.Finally,by analyzing the stability of edge user data loss,it proves that the proposed defense strategy is effective.

Relativistic Consistent Angular-Momentum Projected Shell-Model： Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ^16O and ^208Pb,the deformed nucleus 20~Ne. Good agreement is obtained.

Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter

我们为核子数量介子系统，一个任意的吝啬的分级的介子领域在被介绍建议一个量子化过程。有平常的这个过程的等价为任何给定的价值被证明。由这个过程的使用，在 Walecka 的 MFA 并且在下巴的 RHA 的分级的介子领域在保持的平均数附近被使量子化。它这些理论上的修正被不安考虑直到第二份订单。任意使我们自由在计算在任何阶段修理它。当我们以 Walecka 的 MFA 的方法修理它时，量修正大，并且结果不收敛。当我们以下巴的 RHA 的方法修理它时，量修正是微不足道的小的，并且集中是优秀的。它证明 RHA 为原子系统盖住量地理论的领先的部分并且是为进一步的量修正的优秀 zeroth 顺序近似，当 Walecka 的 MFA 不做时。我们建议由为有限原子核为原子事或全部的精力最小化全部的精力每核子在整个计算的目的修理参数，到使使量子化的相对论的吝啬的地理论(QRMFT ) 成为一个变化方法。

Mean field game of optimal relative investment with jump risk

In this paper,we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth,in which the interaction occurs by peer competition.In the model with n agents,the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modeled by a multi-dimensional nonlinear Hawkes process.With a continuum of agents,we formulate the mean field game problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions,allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications.Moreover,based on the mean field equilibrium,we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large.The explicit order of the approximation error is also derived.

Determining Nuclear Form factor for Detection of Dark Matter in Relativistic Mean Field Theory

在这个工作，我们以相对论的吝啬的域(RMF ) 为在儒弱的人和原子核之间的纺纱无关的碰撞导出原子表格因素理论。有通常在文学被使用的传统的表格因素的比较被给，我们的结果稍微在上面，这被发现在4%～8%的 2PF 模型，但是为全部在15%～25%从舵柄表格因素背离撤退 0 ~的精力光谱 100 keV 。而且，作为例子拿 Xe 和 Ge，我们在 recoil 精力上显示出表格因素的依赖。

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

octupole 变丑和弄平甚至 Rn， Th 和 U 同位素的另外的扎根的州的性质在思考的框架以内系统地被调查不对称的相对论的吝啬的地(RAS-RMF ) 模型。计算结果复制有约束力的精力和四极变丑很好。计算结果在状态演变从的地面显示这些原子核将近球形(N = 130 ) 形状到有中子数字的增加的四极变丑形状。在 Rn 同位素之中，仅仅 222,224Rn 是使变形的 octupole，为他们的 octupole 变丑是小的，这也被发现。然而，在 Th 和 U 同位素的更多的原子核(N 134148 ) 是使变形的 octupole，为他们中的一些的 octupole 变丑是重要的(| 3 |~ 0.1 或甚至更大) 。

Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions

The influence of the chiral mean field on the K+ in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the inmedium kaon dynamics and strongly counterbalances the influence of the vector potential on the K+ in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization,which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the K+ in-plane flow.

A Trading Execution Model Based on Mean Field Games and Optimal Control

We present a trading execution model that describes the behaviour of a big trader and of a multitude of retail traders operating on the shares of a risky asset. The retail traders are modeled as a population of “conservative” investors that: 1) behave in a similar way, 2) try to avoid abrupt changes in their trading strategies, 3) want to limit the risk due to the fact of having open positions on the asset shares, 4) in the long run want to have a given position on the asset shares. The big trader wants to maximize the revenue resulting from the action of buying or selling a (large) block of asset shares in a given time interval. The behaviour of the retail traders and of the big trader is modeled using respectively a mean field game model and an optimal control problem. These models are coupled by the asset share price dynamic equation. The trading execution strategy adopted by the retail traders is obtained solving the mean field game model. This strategy is used to formulate the optimal control problem that determines the behaviour of the big trader. The previous mathematical models are solved using the dynamic programming principle. In some special cases explicit solutions of the previous models are found. An extensive numerical study of the trading execution model proposed is presented. The interested reader is referred to the website: http://www.econ.univpm.it/recchioni/finance/w19 to find material including animations, an interactive application and an app that helps the understanding of the paper. A general reference to the work of the authors and of their coauthors in mathematical finance is the website:?http://www.econ.univpm.it/recchioni/finance.

Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings

This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-particle levels of bound and resonant states,and neutron density distributions and shapes.Simultaneously,special attention is paid to the distinctive physical phenomena associated with these isotopes.The deformed relativistic mean field theory in complex momentum representations with BCS pairings(DRMF-CMR-BCS)employed in our research provides resonant states with real physics,offering insights into deformed halo nuclei.Four effective interactions(NL3,NL3^(*),PK1,and NLSH)were considered to assess the influence of continuum and deformation effects on halo structures.Calculations for odd-even nuclei ^(35–43)Na revealed the dependence on the chosen effective interaction and number of considered resonant states.Neutron occupation patterns near the Fermi surface,particularly in orbitals 1/2^(−)_(3) and 3/2^(−)_(2),were determined to be crucial in halo formation.The study provided detailed insights into the density distributions,shape evolution,and structure of neutron-rich sodium isotopes,contributing valuably to the field of nuclear physics.

Density-dependent relativistic mean field approach and its application to single-Λhypernuclei in oxygen hyperisotopes

The in-medium feature of nuclear force, which includes both nucleon-nucleon( NN) and hyperon-nucleon( ΛN) interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new ΛN effective interaction in the covariant density functional(CDF) theory, namely, DD-LZ1-Λ1, is obtained by fitting the experimental data ofΛ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of Λ1p spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of theΛ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei,and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium NN interactions and core polarization effects.

The boundary value problem for the mean field equation on a compact Riemann surface

Let(Σ,g)be a compact Riemann surface with smooth boundary■Σ,Δ_(g) be the Laplace-Beltrami operator,and h be a positive smooth function.Using a min-max scheme introduced by Djadli and Malchiodi(2008)and Djadli(2008),we prove that ifΣis non-contractible,then for anyρ∈(8kπ,8(k+1)π)with k∈N^(*),the mean field equation{Δgu=ρhe^(u)/∫∑he^(u)dv_(g)in∑,u=0 on■∑has a solution.This generalizes earlier existence results of Ding et al.(Ann Inst H PoincaréAnal Non Linéaire,1999)and Chen and Lin(2003)in the Euclidean domain.Also we consider the corresponding Neumann boundary value problem.If h is a positive smooth function,then for anyρ∈(4kπ,4(k+1)π)with k∈N^(*),the mean field equation{Δgu=ρhe^(u)/∫_(∑)he^(u)dv_(g)-1/|∑|in∑,■u/■v=0 on■∑has a solution,where v denotes the unit normal outward vector on ■Σ.Note that in this case we do not require the surface to be non-contractible.

Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.

On the mean field limit of the Random Batch Method for interacting particle systems

The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.