Narrow Results

Consider a queueing network with a large number $N$ nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the $M/M/1$ queue with a modified arrival rate when the queue length is around zero.

We suggest that the dark matter halo in some of the spiral galaxies can be described as the ground state of the Bose–Einstein condensate of ultra-light self-gravitating axions. We have also developed an effective “dissipative” algorithm for the solution of nonlinear integro-differential Schrödinger equation describing self-gravitating Bose–Einstein condensate. The mass of an ultra-light axion is estimated.

We consider a two-component dark matter halo (DMH) of a galaxy containing ultra-light axions (ULA) of different mass. The DMH is described as a Bose–Einstein condensate (BEC) in its ground state. In the mean-field (MF) limit, we have derived the integro-differential equations for the spherically symmetrical wave functions of the two DMH components. We studied, numerically, the radial distribution of the mass density of ULA and constructed the parameters which could be used to distinguish between the two- and one-component DMH. We also discuss an interesting connection between the BEC ground state of a one-component DMH and Black Hole temperature and entropy, and Unruh temperature.

We consider a dark matter halo (DMH) of a spherical galaxy as a Bose–Einstein condensate (BEC) of the ultra-light axions (ULA) interacting with the baryonic matter. In the mean-field (MF) limit, we have derived the integro-differential equation of the Hartree–Fock type for the spherically symmetrical wave function of the DMH component. This equation includes two independent dimensionless parameters: (i) $\beta$ is the ratio of baryon and axion total mases and (ii) $\xi$ is the ratio of characteristic baryon and axion spatial parameters. We extended our “dissipation algorithm” for studying numerically the ground state of the axion halo in the gravitational field produced by the baryonic component. We calculated the characteristic size, $x_c$ of DMH as a function of $\beta$ and $\xi$ and obtained an analytical approximation for $x_c$.

The spin-5/2 Blume–Capel model was studied using the mean-field approximation and the Migdal–Kadanoff renormalization group method for two- and three-dimensional systems. We determined the phase diagrams in the (crystal field, temperature) plane where the system exhibited first- and second-order phase transitions as well as isolated critical, bicritical and triple points. In order to show first-order transitions at low temperature, we presented the total magnetization per site and the derivative of the free energy as a function of the crystal field. Moreover, the critical exponents of the system were calculated by linearizing the renormalization transformation at the vicinity of the second-order fixed points.

Explosive death in coupled nonlinear oscillators has been an active area of extensive research in nonlinear dynamics in the recent decades. Depending on proper choice of network topology, coupling scenarios, and feedback strength, explosive death can be revealed. In this work, for the first time, we report the effect of delayed feedback on the death behavior in an ensemble of identical mean-field coupled van der Pol oscillators. In both systems with or without time delay, the normalized amplitude exhibits an abrupt transition between the oscillatory state and the death state. Intriguingly, the presence of time delay in the coupling may induce the normalized amplitude of all oscillators in the network to experience a step-like descent with small jumps in approaching the death state, pulling back the forward and backward transition points. The backward transition point has been explicitly obtained, which is confirmed by the numerical results.

The Maxwell and Glendenning construction scenarios of deconfinement phase transition in neutron star matter are investigated. The hadronic phase is described within the relativistic mean-field (RMF) theory, if the scalar-isovector δ-meson field is also taken into account. The strange quark phase is described in the frame of MIT bag model, including the effect of perturbative one-gluon exchange interactions. The influence of the δ-meson field on the deconfinement phase transition boundary characteristics is discussed.

Neutrinos propagate in astrophysical and cosmological environments modifying their flavor in intriguing ways. The study of neutrino propagation in media is based on the mean-field, extended mean-field and Boltzmann equations. We summarize salient features of these evolution equations and the methods employed so far to derive them. We emphasize applications to situations of observational interest.

The three-dimensional semi-infinite mixed spin-1/2 and spin-3/2 ferrimagnetic Ising system with crystal field is investigated using the mean-field approximation and the Monte Carlo simulation. According to the ratio $R$ of bulk and surface exchange interactions and the ratio $Y$ of bulk and surface crystal fields, we have classified four qualitative types of phase diagrams characterized by the presence or absence of ordinary, extraordinary, surface and special phase transitions. The critical behavior of the surface and bulk magnetizations has also been highlighted in the vicinity of these different transitions. At low temperatures, two critical end-points appear in the bulk and on the surface in the ordered region limiting two successive first-order phase transitions. Furthermore, we have made a comparison with other works on similar models in pure or mixed versions.

By the use of the Migdal–Kadanoff renormalization group technique and the mean field approximation, we have explored the critical behavior of the semi-infinite mixed spin-7/2 and spin-1/2 Blume–Capel model. As a function of the computation ratios (bulk-surface) R and Y, different phase diagrams in the bulk and on the surface are classified and determined in the (surface anisotropy, temperature) plane. We have found four types of phase diagrams characterized by ordinary, extraordinary, surface, and special phase transitions. The derivative of the free energy and the behavior of the bulk and surface magnetizations are plotted at very low temperatures proving the existence of first-order transitions for both the surface and bulk. We have also presented the related fixed points and the critical exponents manifesting several classes of universality at the surface. Otherwise, a comparison was made between the two methods as well as with previous studies.

We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.

The magnetic properties and phase diagrams of a ferrimagnetic cylindrical Ising nanotube with spin-1/2 core and spin-3/2 shell are studied using mean-field approximation and Monte Carlo simulation. The effects of shell and core-shell interface exchange couplings and crystal field on the magnetic properties of the system are examined. For some physical parameters, the critical and compensation behaviors are highlighted and first-order phase transitions are observed in the ferrimagnetic ordered region at low temperatures. A comparison between the two methods was performed.

Binding energies and even-odd mass differences of rare-earth ^160–170Er nuclei are calculated by using the exactly solvable mean-filed plus nearest-orbit pairing model and compared with the corresponding experimental values. And the ground state occupation probabilities of valence nucleon pairs with definite angular momentum quantum number for ^{160, 162, 164}Er in the model fitted are calculated. The analysis shows that the ground state occupation probabilities with even angular momenta are much larger than those with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.