Quantum lattice models at intermediate temperatures

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our results are valid for discrete symmetry breaking only. Such phase transitions occur at intermediate temperatures where the continuous symmetry is not broken, while at very low temperature continuous symmetry breaking may occur.Comment: 25 pages, 6 figure

Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.Comment: 31 pages, 2 figure

A diffusion-split method to deal with thermal shocks using standard linear tetrahedral finite elements

International audienceThe thermal analysis using linear standard tetrahedral finite elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe way to directly discourage the use of these elements. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M-matrix form, which assures an oscillation-free solution. The performance of this method is evaluated by means of test case with analytical solution, as well as an industrial application, for which a well-behaved numerical solution is available

A two-phase two-dimensional finite element thermomechanics and macrosegregation model of mushy zone. Application to continuous casting

International audienceThe main lines of a coupled thermomechanical - solute transport model are first summarized. Macroscopic conservation equations for mass, momentum, energy and solute are obtained by a spatial averaging method. The mechanical model is a "sponge-like" one: assuming a semi-solid saturated mushy zone, the solid phase is macroscopically modeled as a compressible viscoplastic continuum, while the liquid phase flow obeys Darcy's law. Regarding solute transport, the study is limited to a binary alloy for which the solidification path is not given a priori but results from a microsegregation model (here the lever rule). A validation check of the correct implementation of this coupled model is achieved by comparing with an analytical solution in the case of a free compression of a saturated semi-solid medium. Application to the study of the solidification during secondary cooling in steel continuous casting is considered

Linear tetrahedral finite elements for thermal shock problems

International audiencePurpose - The paper seeks to present an original method for the numerical treatment of thermal shocks in non-linear heat transfer finite element analysis. Design/methodology/approach - The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M-matrix form, which ensures an oscillation-free solution. Findings - The proposed "diffusion-split" method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well as an industrial application, for which a well-behaved numerical solution is available. Originality/value - The proposed method should be helpful for computational engineers and software developers in the field of heat transfer analysis. It can be implemented in most existing finite element codes with minimal effort

An Extension of the Fluctuation Theorem

Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and white

Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMn3_3N clusters

Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements show that the incorporation of Mn strongly depends on the conditions of the growth. Hysteresis loops which persist at high temperature do not appear to be correlated to the presence of Mn. Samples with up to 2% Mn are purely substitutional Ga$_{1-x}$Mn$_x$N epilayers, and exhibit paramagnetic properties. At higher Mn contents, precipitates are formed which are identified as GaMn$_3$N clusters by x-ray diffraction and absorption: this induces a decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg exhibit a new feature: a ferromagnetic component is observed up to $T_c\sim175$ K, which cannot be related to superparamagnetism of unresolved magnetic precipitates.Comment: Revised versio

A 3D-fem model solving thermomechanics and macrosegregation in binary alloys solidification

International audienceThis paper introduces a three-dimensional numerical model for the coupled solution of momentum, energy and solute conservation equations, for binary alloys solidification. The spatial discretisation is carried out using linear tetrahedral finite elements, particularly those of P1+/P1 type for the velocity-pressure resolution of momentum equation. The liquid flow in the mushy zone is assumed to be governed by the Darcy's law. Thermal and buoyancy forces are taken into account by means of the Boussinesq's model. Microsegregation obeys the lever rule. The resulting solute transport equation is solved by the SUPG method. Coupling strategy between momentum, energy and solute equations is discussed and two applications are studied

A meaningful expansion around detailed balance

We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.Comment: 19 page

Impact of human bladder cancer cell architecture on autologous T-lymphocyte activation

To investigate the influence of tumor cell architecture on T-cell activation, we used an autologous human model based on 2 bladder tumor cell lines as targets for cytotoxic tumor-infiltrating lymphocytes (TILs). These tumor cell lines were grown in vitro as either standard 2-dimensional (2D) monolayers or 3-dimensional (3D) spheroids. T-cell activation was determined by measuring the production of three major cytokines (tumor necrosis factor, granulocyte/macrophage colony-stimulating factor and interferon-gamma), known to be secreted by most activated TILs. Changes in the architecture of target cells from 2D to 3D induced a dramatic decrease in their capacity for stimulating TILs. Interestingly, neither TIL infiltration nor MHC class I, B7.1 costimulatory or lymphocyte function-associated factor-3 adhesion molecule downregulation played a major role in this decrease. These findings demonstrate that tumor architecture has a major impact on T-cell activation and might be implicated in the escape of tumor cells from the immune system