Mean Field Approximation

The generalized Heusler compounds Mn2CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb) with the Hg2CuTi structure are of large interest due to their half-metallic ferrimagnetism. The complex magnetic interactions between the constituents are studied by first principles calculations of the Heisenberg exchange coupling parameters, and Curie temperatures are calculated from those. Due to the direct Mn-Mn exchange interaction in Mn2CoZ, the Curie temperature decreases, while the total moment increases when changing Z from one group to another. The exchange interactions are dominated by a strong direct exchange between Co and its nearest neighbor Mn on the B site, which is nearly constant. The coupling between the nearest-neighbor Mn atoms scales with the magnetic moment of the Mn atom on the C site. Calculations with different lattice parameters suggest a negative pressure dependence of the Curie temperature, which follows from decreasing magnetic moments. Curie temperatures of more than 800 K are predicted for Mn2CoAl (890 K), Mn2CoGa (886 K), and Mn2CoIn (845 K).

With this paper we will try to introduce the foundations and the formalism of relativistic mean field theory and its applications. We begin by discussing the formulation of the theory of special relativity. Then we derive the Lagrangian formulation of a field from the continuous limit of a discrete system. Afterwards, we formulate a relativistically invariant Lagrangian for a field and use the previous formalism to investigate several problems of continuous systems. Finally, reference is made to the application of the mean field approximation to the nuclear model of Quantum Hadrodynamics (QHD).

This study aims to model the methane partial oxidation process in the burner and combustion chamber of autothermal reactor. The numerical simulation based on this model offers a powerful tool that can assist in reactor design and optimization and scale up of the process saving expensive pilot work. The steady-state governing equations were solved using the SIMPLE algorithm and the effect of turbulence on the mean flow field was accounted for using the RNG k–ε model. A two-step reaction mechanism was used for the gas combustion with CO as the intermediate species. The reaction rates were modeled using an Eddy-Dissipation Model. In terms of the geometrical model, a 3D model for burner was developed while an axis-symmetric model for the combustion chamber was implemented to reduce the computational costs. The model formulated was validated against a currently operating autothermal reactor and then has been used to investigate different aspects of these reactors. Results show that effect of oxygen to methane ratio is more than that of feed temperature. It is demonstrated that a 60% increase in O2/CH4 ratio causes a 15.4% decrease and 42.7% increase in H2/CO ratio and methane conversion, respectively. In contrast, a 60% increase in feed temperature does not have a significant effect on the process.

A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered (O) and disordered (D) forms of water are treated as two components, and we assume that the density of the D component is larger. The density of the sample is determined by the fraction of cells occupied by the O and D forms of water. Due to the larger density of the D state, the strength of the van der Waals (vdW) interactions increases in the direction O-O<O-D<D-D . On the other hand, the H-bond interactions are assumed only for the O-O pairs. For the vdW and H-bond interaction parameters and the density ratio of the close-packed and ice forms of water compatible with experimentally known values, we find liquid-vapor and liquid-liquid transitions and the corresponding critical points in good agreement with other approaches. Water anomalies are correctly predicted within the mean-field approximation on a qualitative level.

A theory of inhomogeneous multicomponent systems containing weakly charged polyelectrolytes is developed. The theory treats the polymer conformation and the electrostatics simutaneously using a functional integral representation of the partition function. A mean-field approximation to the theory leads to two sets of coupled mean-field equations: a generalized Poisson-Boltzmann equation describing the electrostatic potential, and a set of self-consistent field equations describing the equilibrium densities. The theory can be used to study the interfacial properties, microphase structures, and adsorptions of a variety of weakly charged polyelectrolyte systems. As a simple application, the interfaces between the polymer-rich and polymer-poor phases of a polyelectrolyte solution is studied.

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.

Dilute ferromagnetic oxides having Curie temperatures far in excess of 300 K and exceptionally large ordered moments per transition-metal cation challenge our understanding of magnetism in solids. These materials are high-k dielectrics with degenerate or thermally activated n-...

In this article the Ginzburg-Landau theory ideas are considered in their application to the description of fluctuations influence on the superfluid density in superconductor. The conclusion about the availability of two incompatible mathematical definitions of the superfluid density is made. That is why, it is suggested not to consider the fluctuating part of order parameter, while calculating the superconductor thermodynamical characteristics in the Mean Field Approximation. Comment: 5 pages, 0 figures

We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zig-zag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin, $S$, consistent with Lieb's theorem for bipartite lattices. Triangles have a finite $S$ for all sizes whereas hexagons have S=0 and develop local moments above a critical size of $\approx 1.5$ nm.

The transport of particles moving out of equilibrium in an asymmetric substrate potential has been studied intensively for a variety of different systems [1, 2] in order to achieve an efficient control of the net particle flow. Various realizations of rachet systems working out of equilibrium have been proposed involving different rectification mechanisms, like temporal temperature oscillations (temperature ratchet [3]), zeroaverage sinusoidal ac forces (ac tilted or rocked ratchet [4]), stochastic and deterministic fluctuations of the ratchet potentials [5], ...

The Heisenberg nearest-neighbor antiferromagnet on the pyrochlore (three-dimensional) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI&#39;s) may be present in pyrochlore compounds as is shown, and the consequences of such interactions on the magnetic properties are investigated through mean-field approximation and Monte Carlo simulations. It is found that

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand vs. price, the bid-ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behavior than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero-intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic-zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.