We prove the non-equilibrium fluctuations for the one-dimensional symmetric simple exclusion process with a slow bond. This generalizes a result of [Stochastic Process. Appl. 123 (2013) 4156-4185;Stochastic Process. A...
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We prove the non-equilibrium fluctuations for the one-dimensional symmetric simple exclusion process with a slow bond. This generalizes a result of [Stochastic Process. Appl. 123 (2013) 4156-4185;Stochastic Process. Appl. 126 (2016) 3235-3242], which dealt with the equilibrium fluctuations. The foundation stone of our proof is a precise estimate on the correlations of the system, and that is by itself one of the main novelties of this paper. To obtain these estimates, we first deduce a spatially discrete PDE for the covariance function and we relate it to the local times of a random walk in a non-homogeneous environment via Duhamel's principle. Projection techniques and coupling arguments reduce the analysis to the problem of studying the local times of the classical random walk. We think that the method developed here can be applied to a variety of models, and we provide a discussion on this matter.
In this work, we intend to investigate the phase transition behavior in AdS spacetime of massive gravity. We found that it can exhibit different phase transitions in the T - S plane. We further study specific heat cap...
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In this work, we intend to investigate the phase transition behavior in AdS spacetime of massive gravity. We found that it can exhibit different phase transitions in the T - S plane. We further study specific heat capacity and free energy of the spacetime, and C-q - Sand F - T phase structures with different parameters are also plotted. The results show that the phase structures are related to the charge Q, the parameters gamma and lambda of the AdS spacetime of massive gravity. In addition, by utilizing two point correlation function, holographic phase transitions can also be displayed in the T - delta L plane, which means phase transition behavior can be detected by the two point correlation function. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
In the framework of holography, we survey the phase structure for a higher dimensional hairy black hole including the effects of the scalar field hair. It is worth emphasizing that, not only black hole entropy, but al...
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In the framework of holography, we survey the phase structure for a higher dimensional hairy black hole including the effects of the scalar field hair. It is worth emphasizing that, not only black hole entropy, but also entanglement entropy and two point correlation function exhibit the Van der Waals-like phase transition in a fixed scalar charge ensemble. Furthermore, by making use of numerical computation, we show that the Maxwell's equal area law is valid for the first order phase transition. In addition, we also discuss how the hair parameter affects the black hole's phase transition. (C) 2016 The Author( s). Published by Elsevier B.V.
This work presents a new functional approach to estimate the distance-disorientation correlationfunction of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by ...
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This work presents a new functional approach to estimate the distance-disorientation correlationfunction of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by its Euler angles () and geometrical domain defined by distance distribution function . The crystallographic domain is treated as independent (known) variable and an analytical estimate for the Euclidian distance distribution function is obtained. The proposed analytical solution for the estimation of is based on existing statistical growth models and the logistic probability distribution function. The solution is optimized for the measured experimental data and takes into account morphological features of the microstructure such as grain volume, grain radius and grain size as well as their distribution inside the material. An analytical model is proposed for constructing the distance-disorientation function (DDF) using the estimated Euclidian distance between pixel pairs. The new functional solution is a highly effective way to calculate DDF values, making it suitable for application to the real microstructure optimization problems. The DDF obtained by using the results of probabilistic solution is validated by comparing them with the DDF obtained from experimental electron back-scatter diffraction data.
A procedure to reconstruct two phase porous media, given the porosity and the two point correlation function of such media is described. The random media are modelled as a discrete valued random field Z((x) over right...
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A procedure to reconstruct two phase porous media, given the porosity and the two point correlation function of such media is described. The random media are modelled as a discrete valued random field Z((x) over right arrow), which takes value I in regions of pores and 0 in regions of solid phase. The field Z((x) over right arrow) is obtained by applying a non-linear filter - Nataf's transformation - to a correlated Gaussian random field Y((x) over right arrow). The two point correlation function R-YY of the Gaussian field Y is related to the two point correlation function R-ZZ of the field Z and can be calculated by expanding the bivariate Gaussian probability in terms of Hermite polynomials. The correlationfunction of the Gaussian field is decomposed into eigenfunctions and eigenvalues required by the Karhunen-Loeve expansion. The eigenfunctions and eigenvalues are used to generate as many samples of the Gaussian field as required and the discrete field corresponding to each such sample can be obtained by applying the non-linear filter mentioned above. The method was tested by generating a large number of samples of one and two dimensional Debye random media using different porosities and different correlation lengths and the statistics of the ensemble was found to agree favourably with the input data. Also one and two dimensional 'chess board' patterns were reconstructed to see how well the geometry is reconstructed. The one dimensional case was reconstructed very accurately, whereas the two dimensional case, though not very satisfactory, indicates that the method captures some of the essentials of the geometry. The method also has the advantage that it gives an analytical framework for the porous media in terms of the random fields. These random fields could be used for further studies related to porous media. (C) 2013 Elsevier Ltd. All rights reserved.
In this paper we introduce a toy model for understanding the growth of structures and the two point correlation functions in the cotext of the Quasi-Steady State Cosmology (QSSC). The paper first describes the essenti...
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In this paper we introduce a toy model for understanding the growth of structures and the two point correlation functions in the cotext of the Quasi-Steady State Cosmology (QSSC). The paper first describes the essential features of the QSSC and then addresses the problem of structure formation.
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