Mean-field Approximation Schemes Research Articles

Analytical and 3D numerical analysis of the thermoviscoelastic behavior of concrete-like materials including interfaces

We investigate in this paper analytically and numerically by means of 3D simulations the viscoelastic behavior of concrete and mortar subjected to creep loading and moderate temperatures at mesoscale. These heterogeneous materials are assumed to be composed of thermoelastic aggregates distributed in a linear thermoviscoelastic matrix; moreover, the Interfacial Transition Zones (ITZ) between aggregates and matrix, whose behavior is also considered as linear thermoviscoelastic, are explicitly introduced. The numerical specimens consist in unstructured periodic meshes containing polyhedral aggregates with various size and shapes randomly distributed in a box. Zero-thickness interface finite elements are introduced between aggregates and matrix to model the ITZ. Macroscopic response and averaged stresses and strains in the matrix and aggregate phases are compared to analytical estimations obtained with classical mean-field approximation schemes applied in the Laplace–Carson space, in which the ITZ are introduced via imperfect interfaces modeled with the Linear Spring Model (LSM). The effects of ITZ thickness, aggregate shape and uniform temperature increase are then studied to evaluate their respective influence on the local and macroscopic creep behavior of mortar and concrete. Globally, it is found that the model response is in relatively good agreement with numerical simulations results, and that as expected while the ITZ do not affect significantly the concrete behavior, they have a non-negligible impact on the mortar one.

Thermoviscoelastic Analysis of Concrete Creep at Mesoscale

Concrete is a heterogeneous material made up at mesoscale of linear elastic aggregates distributed in a mortar matrix whose behavior is time and temperature dependent. The Interfacial Transition Zone (ITZ) between aggregates and matrix also influences the overall behavior. We investigate here analytically and numerically by means of 3D simulations the creep behavior of concrete and mortar subjected to moderate temperatures at mesoscale. The numerical specimens consist in unstructured periodic meshes of polyhedral aggregates with various size and shapes randomly distributed in a box. Specific interface finite elements are introduced between aggregates and matrix to model the ITZ. Both matrix and ITZ are considered as linear thermoviscoelastic materials. Averaged stresses and strains in the matrix and aggregate phases are compared to analytical estimations obtained with classical mean-field approximation schemes applied in the Laplace-Carson space, where the ITZ are introduced via imperfect interfaces modelled with the Linear Spring Model (LSM). The effects of ITZ thickness, aggregate shape and temperature are then studied to evaluate their respective influence on mortar and concrete creep behavior.

Magnetocaloric effect in Ni-Zn ferrite nanoparticles prepared by using solution combustion

Ni x Zn1−x Fe2O4 (x = 0.2 and 0.3) ferrite nanoparticles with sizes ranging from 65 to 70 nm were synthesized employing the solution combustion route. The magnetocaloric behavior was investigated within the 50 K ≤ T ≤ 400 K range of temperatures (T). The entropy change (ΔS) and the adiabatic temperature change (ΔT) were derived from magnetization (M) and specific heat (C P ) measurements. Both compositions exhibited broad peaks for the isothermal entropy change. The magnetic field (H)-dependent ΔT was analyzed within the mean-field approximation scheme, and the observed magnetocaloric properties of the nanoparticle samples were compared with those of a bulk sample. Our study suggests that the magnetocaloric properties of magnetic oxides strongly depend on the particle size; thus, particle size should be considered as a key tuning parameter in the optimization of magnetic refrigeration.

Mixed State in t-U-J-V Model

The mean-field approximation (MFA) is one of the most widespread methods in the theory of the condensed matter. It is relatively simple but quite crude, so the need for more refined treatments emerges. One of them is renormalized mean-field approximation (RMFA) [1, 2], similar in use to MFA but in spirit reminding the Gutzwiller method or its slave-boson variations [3]. Applied to Hubbardor t−J-like models amounts to adding a doping-dependent weighting factors both to the hopping and to the interaction parts of the Hamiltonian, followed by the MFA scheme. The hopping-term weighting factor is precisely the band-narrowing factor of the slaveboson theory [4]. In the present paper the RMFA method is applied to the t−U−J−V model in the U → ∞ limit. The results are applicable also to t−J-like models in general. Keeping finite on-site repulsion U during intermediate stages of calculations, to take U → ∞ limit in the end enables us to obtain proper low density limit (i.e., two-electron bound state with finite critical value), incorrectly given in standard t−J model treatment [5]. Considering the V-term is equivalent to using anisotropic t−J model.

A dynamically extending exclusion process

An extension of the totally asymmetric exclusion process, which incorporatesa dynamically extending lattice, is explored. Although originally inspired as amodel for filamentous fungal growth, here the dynamically extending exclusionprocess (DEEP) is studied in its own right as a nontrivial addition to the class ofnonequilibrium exclusion process models. Here we discuss various mean-field approximationschemes and elucidate the steady state behaviour of the model and its associatedphase diagram. Of particular note is that the dynamics of the extending latticeleads to a new region in the phase diagram in which a shock discontinuity inthe density travels forward with a velocity that is lower than the velocity of thetip of the lattice. Thus in this region the shock recedes from both boundaries.

Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.

A mean-field approximation scheme containing the spatial parameter and its application to a surface-reaction-like cellular automaton model

Using an AB2 surface-reaction-like cellular automaton model, we present a modified mean-field approximation scheme for describing some dynamic lattice models, in which a lattice freedom parameter N is introduced as a variable. We obtain the phase diagrams of the example model for linear, hexagonal, square and triangular lattices and we reveal a second-order phase transition which has not been found using traditional approaches.

Black hole entropy from nonperturbative gauge theory

We present the details of a mean-field approximation scheme for the quantum mechanics of N D0-branes at finite temperature. The approximation can be applied at strong 't Hooft coupling. We find that the resulting entropy is in good agreement with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with a 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We study the spectrum of single-string excitations within quantum mechanics, and find evidence for a clear separation between light and heavy degrees of freedom. We also present a way of identifying the black hole horizon.

New macroeconomic modeling approaches: Hierarchical dynamics and mean-field approximation

This paper proposes hierarchical structures and mean-field approximation schemes as two potentially useful ways of modeling collective behavior in macroeconomics. Economics systems with hierarchically organized state spaces or agents can exhibit the sluggish response patterns typical of economic time series with unit or near-unit roots. We describe how such hierarchies may arise in several ways, and how dynamics can exhibit behavior with multiple time scales. Then, we describe the use of the mean-field approximation method to model a system composed of many (heterogeneous) agents subject to nonlocalized externalities, and give two brief examples.

On the independent particle approximation of gauge theories

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

An improved mean field approach to the phase structure in Z N gauge theory in four dimensions

We extend the mean field approximation scheme to include the effect of fluctuation of the gauge field. As a consequence, we successfully obtain for the Z N theory ( N > 5) the phase transition which separates the Coulomb phase from the ordered phase, as well as that separating the Coulomb and disordered phases. The former transition shows characteristics of higher-order phase transitions.