Phenomenological models of holographic superconductors and hall currents

We study general models of holographic superconductivity parametrized by four arbitrary functions of a neutral scalar field of the bulk theory. The models can accommodate several features of real superconductors, like arbitrary critical temperatures and critical exponents in a certain range, and perhaps impurities or boundary or thickness effects. We find analytical expressions for the critical exponents of the general model and show that they satisfy the Rushbrooke identity. An important subclass of models exhibit second order phase transitions. A study of the specific heat shows that general models can also describe holographic superconductors undergoing first, second and third (or higher) order phase transitions. We discuss how small deformations of the HHH model can lead to the appearance of resonance peaks in the conductivity, which increase in number and become narrower as the temperature is gradually decreased, without the need for tuning mass of the scalar to be close to the Breitenlohner-Freedman bound. Finally, we investigate the inclusion of a generalized ¿theta term¿ producing Hall effect without magnetic field.

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

Friedman's Excess energy and the McMillan-Mayer theory of solutions:Thermodynamics

In his version of the theory of multicomponent systems, Friedman used the analogy which exists between the virial expansion for the osmotic pressure obtained from the McMillan-Mayer (MM) theory of solutions in the grand canonical ensemble and the virial expansion for the pressure of a real gas. For the calculation of the thermodynamic properties of the solution, Friedman proposed a definition for the"excess free energy" that is a reminder of the ancient idea for the"osmotic work". However, the precise meaning to be attached to his free energy is, within other reasons, not well defined because in osmotic equilibrium the solution is not a closed system and for a given process the total amount of solvent in the solution varies. In this paper, an analysis based on thermodynamics is presented in order to obtain the exact and precise definition for Friedman"s excess free energy and its use in the comparison with the experimental data.

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme inter-actions and from relativistic mean field theory. VWK consist s of the Thomas-Fermi part plus a pure, perturbative h 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total en energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of h 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g.208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an adhoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

The role of intramolecular barriers on the glass transition of polymers: computer simulations versus mode coupling theory

We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are analyzed within the framework of the mode coupling theory (MCT). Critical nonergodicity parameters, critical temperatures, and dynamic exponents are obtained from consistent fits of simulation data to MCT asymptotic laws. The so-obtained MCT λ-exponent increases from standard values for fully flexible chains to values close to the upper limit for stiff chains. In analogy with systems exhibiting higher-order MCT transitions, we suggest that the observed large λ-values arise form the interplay between two distinct mechanisms for dynamic arrest: general packing effects and polymer-specific intramolecular barriers. We compare simulation results with numerical solutions of the MCT equations for polymer systems, within the polymer reference interaction site model (PRISM) for static correlations. We verify that the approximations introduced by the PRISM are fulfilled by simulations, with the same quality for all the range of investigated barrier strength. The numerical solutions reproduce the qualitative trends of simulations for the dependence of the nonergodicity parameters and critical temperatures on the barrier strength. In particular, the increase in the barrier strength at fixed density increases the localization length and the critical temperature. However the qualitative agreement between theory and simulation breaks in the limit of stiff chains. We discuss the possible origin of this feature.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Versatility of field theory motivated nuclear effective Lagrangian approach

We analyze the results for infinite nuclear and neutron matter using the standard relativistic mean field model and its recent effective field theory motivated generalization. For the first time, we show quantitatively that the inclusion in the effective theory of vector meson self-interactions and scalar-vector cross-interactions explains naturally the recent experimental observations of the softness of the nuclear equation of state, without losing the advantages of the standard relativistic model for finite nuclei.

Sidelobe elimination for generalized synthetic discriminant functions by a two-filter correlation and subsequent postprocessing of the intensity distributions

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Adsorption energy and spin state of first-row transition metals adsorbed on MgO(100)

Slab and cluster model spin-polarized calculations have been carried out to study various properties of isolated first-row transition metal atoms adsorbed on the anionic sites of the regular MgO(100) surface. The calculated adsorption energies follow the trend of the metal cohesive energies, indicating that the changes in the metal-support and metal-metal interactions along the series are dominated by atomic properties. In all cases, except for Ni at the generalized gradient approximation level, the number of unpaired electron is maintained as in the isolated metal atom. The energy required to change the atomic state from high to low spin has been computed using the PW91 and B3LYP density-functional-theory-based methods. PW91 fails to predict the proper ground state of V and Ni, but the results for the isolated and adsorbed atom are consistent within the method. B3LYP properly predicts the ground state of all first-row transition atom the high- to low-spin transition considered is comparable to experiment. In all cases, the interaction with the surface results in a reduced high- to low-spin transition energy.

A Write-Based Solver for SAT Modulo the Theory of Arrays

The extensional theory of arrays is one of the most important ones for applications of SAT Modulo Theories (SMT) to hardware and software verification. Here we present a new T-solver for arrays in the context of the DPLL(T) approach to SMT. The main characteristics of our solver are: (i) no translation of writes into reads is needed, (ii) there is no axiom instantiation, and (iii) the T-solver interacts with the Boolean engine by asking to split on equality literals between indices. As far as we know, this is the first accurate description of an array solver integrated in a state-of-the-art SMT solver and, unlike most state-of-the-art solvers, it is not based on a lazy instantiation of the array axioms. Moreover, it is very competitive in practice, specially on problems that require heavy reasoning on array literals

Approximation to the theory of affinities to manage the problems of the groupping process

New economic and enterprise needs have increased the interest and utility of the methods of the grouping process based on the theory of uncertainty. A fuzzy grouping (clustering) process is a key phase of knowledge acquisition and reduction complexity regarding different groups of objects. Here, we considered some elements of the theory of affinities and uncertain pretopology that form a significant support tool for a fuzzy clustering process. A Galois lattice is introduced in order to provide a clearer vision of the results. We made an homogeneous grouping process of the economic regions of Russian Federation and Ukraine. The obtained results gave us a large panorama of a regional economic situation of two countries as well as the key guidelines for the decision-making. The mathematical method is very sensible to any changes the regional economy can have. We gave an alternative method of the grouping process under uncertainty.