Phase separation frustrated by the long range Coulomb interaction II: Applications

The theory of first order density-driven phase transitions with frustration due to the long range Coulomb (LRC) interaction develop on paper I of this series is applied to the following physical systems: i) the low density electron gas ii) electronic phase separation in the low density three dimensional $t-J$ model iii) in the manganites near the charge ordered phase. We work in the approximation that the density within each phase is uniform and we assume that the system separates in spherical drops of one phase hosted by the other phase with the distance between drops and the drop radius much larger than the interparticle distance. For i) we study a well known apparent instability related to a negative compressibility at low densities. We show that this does not lead to macroscopic drop formation as one could expect naively and the system is stable from this point of view. For ii) we find that the LRC interaction significantly modifies the phase diagram favoring uniform phases and mixed states of antiferromagnetic (AF) regions surrounded by metallic regions over AF regions surrounded by empty space. For iii) we show that the dependence of local densities of the phases on the overall density found in paper I gives a non-monotonous behavior of the Curie temperature on doping in agreement with experiments.Comment: Second part of cond-mat/0010092 12 pages, 12 figure

A second order cone formulation of continuous CTA model

The final publication is available at link.springer.comIn this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using l1 or l2 norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the l1 -CTA using Pseudo-Huber func- tion was introduced in an attempt to combine positive characteristics of both l1 -CTA and l2 -CTA. All three models can be solved using appro- priate versions of Interior-Point Methods (IPM). It is known that IPM in general works better on well structured problems such as conic op- timization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and l1 -CTA as Second-Order Cone (SOC) op- timization problems and test the validity of the approach on the small example of two-dimensional tabular data set.Peer ReviewedPostprint (author's final draft

Coarse grained models in Coulomb-frustrated phase separation

Competition between interactions on different length scales leads to self-organized textures in classical as well as quantum systems. This pattern formation phenomenon has been invoked to explain some intriguing properties of a large variety of strongly correlated electronic systems that includes for example high temperature superconductors and colossal magnetoresistance manganites. We classify the more common situations in which Coulomb frustrated phase separation can occur and review their properties.Comment: 13 pages, 4 figures. Presented at "Phase Separation in Electronic Systems", Crete 200

Phase separation frustrated by the long range Coulomb interaction I: Theory

We analyze the combined effect of the long range Coulomb (LRC) interaction and of surface energy on first order density-driven phase transitions in the presence of a compensating rigid background. We study mixed states formed by regions of one phase surrounded by the other in the case in which the scale of the inhomogeneities is much larger than the interparticle distance. Two geometries are studied in detail: spherical drops of one phase into the other and a layered structure of one phase alternating with the other. We find the optimum density profile in an approximation in which the free energy is a functional of the local density (LDA). It is shown that an approximation in which the density is assumed to be uniform (UDA) within each phase region gives results very similar to those of the more involved LDA approach. Within the UDA we derive the general equations for the chemical potential and the pressures of each phase which generalize the Maxwell construction to this situation. The equations are valid for a rather arbitrary geometry. We find that the transition to the mixed state is quite abrupt i.e. inhomogeneities of the first phase appear with a finite value of the radius and of the phase volume fraction. The maximum size of the inhomogeneities is found to be on the scale of a few electric field screening lengths. Contrary to the ordinary Maxwell construction, the inverse specific volume of each phase depends here on the global density in the coexistence region and can decrease as the global density increases. The range of densities in which coexistence is observed shrinks as the LRC interaction increases until it reduces to a singular point. We argue that close to this singular point the system undergoes a lattice instability as long as the inverse lattice compressibility is finite.Comment: 17 pages, 14 figures. We added a section were the density profile of inhomogeneities is arbitrary and included other geometries. The applications of the original version are in a separate pape

On the limits of engine analysis for cheating detection in chess

The integrity of online games has important economic consequences for both the gaming industry and players of all levels, from professionals to amateurs. Where there is a high likelihood of cheating, there is a loss of trust and players will be reluctant to participate — particularly if this is likely to cost them money. Chess is a game that has been established online for around 25 years and is played over the Internet commercially. In that environment, where players are not physically present “over the board” (OTB), chess is one of the most easily exploitable games by those who wish to cheat, because of the widespread availability of very strong chess-playing programs. Allegations of cheating even in OTB games have increased significantly in recent years, and even led to recent changes in the laws of the game that potentially impinge upon players’ privacy. In this work, we examine some of the difficulties inherent in identifying the covert use of chess-playing programs purely from an analysis of the moves of a game. Our approach is to deeply examine a large collection of games where there is confidence that cheating has not taken place, and analyse those that could be easily misclassified. We conclude that there is a serious risk of finding numerous “false positives” and that, in general, it is unsafe to use just the moves of a single game as prima facie evidence of cheating. We also demonstrate that it is impossible to compute definitive values of the figures currently employed to measure similarity to a chess-engine for a particular game, as values inevitably vary at different depths and, even under identical conditions, when multi-threading evaluation is used

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654

Binding energy corrections in positronium decays

Positronium annihilation amplitudes that are computed by assuming a factorization approximation with on-shell intermediate leptons, do not exhibit good analytical behavior. We propose an ansatz which allows to include binding energy corrections and obtain the correct analytical and gauge invariance behavior of these QED amplitudes. As a consequence of these non-perturbative corrections, the parapositronium and orthopositronium decay rates receive corrections of order alpha^4 and alpha^2, respectively. These new corrections for orthopositronium are relevant in view of a precise comparison between recent theoretical and experimental developments. Implications are pointed out for analogous decays of quarkonia .Comment: 11 pages, 1 .ps figure, submitted for publicatio