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maximum-entropy principle for nonlinear hydrodynamic transport in semiconductors

CONTINUUM MECHANICS AND THERMODYNAMICS 2008年第8期19卷 511-532页

作者： Trovato, M. Falsaperla, P. Univ Catania Dipartimento Matemat & Informat I-95125 Catania Italy

We present, in a strong nonlinear context, a full-band hydrodynamic approach by using the first 13 moments of the distribution function in the framework of extended thermodynamics. Following this approach we show that: (1) the full-band effects of the band structure are described accurately up to high electric fields both in homogeneous and nonhomogeneous conditions;(2) the effectiveness of the dissipation processes can be properly investigated, in homogeneous conditions, only in a strong nonlinear context;and (3) the hyperbolicity region of the system is very large, also in the nonlinear conditions. In this way, by using a strong nonlinear closure, it is possible to describe accurately the transport phenomena in submicron devices, when very high electric fields and field gradients occur (E approximate to 220 kV/cm, E/(dE/dx) approximate to 100 angstrom).

关键词： extended thermodynamics maximum-entropy principle semiconductors

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maximum-entropy principle for Modeling Damage and Fracture in Solder Joints

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JOURNAL OF ELECTRONIC MATERIALS 2012年第2期41卷 398-411页

作者： Chan, D. Subbarayan, G. Nguyen, L. Purdue Univ W Lafayette IN 47906 USA Natl Semicond Corp Santa Clara CA 95051 USA

A maximum-entropy fracture model (MEFM) is derived from concepts of information theory and statistical thermodynamics. Exploiting the maximum-entropy principle enables life predictions for a structure in the presence of microstructural uncertainty. This single-parameter model relates the probability of fracture to accumulated entropic dissipation at a given material point. Using J (2) plasticity and equilibrium thermodynamics, entropic dissipation is related to inelastic dissipation. We demonstrate the MEFM by extracting the single damage accumulation parameter for Sn-3.8Ag-0.7Cu solder through cyclical fatigue testing. We then apply the model with the single parameter to numerically predict, in three dimensions, crack initiation and growth in Sn-3.8Ag-0.7Cu solder joints of a wafer-level chip-scale package (WLCSP). The simulated crack fronts are validated against experimentally observed crack fronts obtained by testing 64 packages under conditions identical to those used in the simulations. The model is shown to accurately predict the geometrical profile of the observed crack fronts, and the number of cycles corresponding to the observed crack profile to within 10% of the measured number of cycles.

关键词： maximum-entropy principle information theory microstructural uncertainty lead-free solder fatigue fracture

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maximum-entropy principle: ecological organization and evolution

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JOURNAL OF BIOLOGICAL PHYSICS 2010年第2期36卷 175-183页

作者： Chakrabarti, C. G. Ghosh, Koyel Univ Calcutta Dept Appl Math Kolkata 700009 W Bengal India

In the present paper, we have first studied the role of the maximum-entropy principle to explain the concept of organization of a physical system in the decreasing law of entropy with the increase of external constraints imposed on the system. We have then considered an open ecosystem (living) and determined a quantitative measure of ecological organization from the consideration of the thermodynamics of irreversible processes. Finally, we have tried to explain the evolution of the ecosystem in the light of Prigogine's principle of "order through fluctuation.".

关键词： maximum-entropy principle Open system Constraints Ecological organization Evolution

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maximum entropy principle and Landau free energy inequality

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LINEAR & MULTILINEAR ALGEBRA 2021年第6期69卷 1020-1034页

作者： Bebiano, N. da Providencia, J. Univ Coimbra CMUC Dept Math Coimbra Portugal Univ Coimbra Dept Phys CFisUc P-3004516 Coimbra Portugal

In this paper, the following problem is considered: given two Hermitian matrices H and K and two real numbers x and y, determine a positive semidefinite matrix rho such that the von Neumann entropy is maximum, subject to the condition that and . This question arises in information theory and in statistical mechanics in connection with the maximum-entropy inference principle. To answer it, we use this principle and numerical range methods.

关键词： maximum-entropy principle Landau free energy inequality Von Neumann entropy numerical range

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Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2006年第11期65卷 2169-2191页

作者： Blokhin, A. M. Bushmanov, R. S. Romano, V. Inst Math Novosibirsk 630090 Russia Novosibirsk State Univ Novosibirsk 630090 Russia Catania Univ Dipartimento Matemat & Informat I-95125 Catania Italy

Nonlinear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. I I (1999) 307-325;V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000) 31-51] is proven for a typical 1-D problem. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： maximum-entropy principle PARABOLIC BAND TRANSPORT HYDRODYNAMICAL MODEL CARRIER TRANSPORT MOMENT EQUATIONS SIMULATION DEVICE RELAXATION BEHAVIOR CLOSURE

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Chaos control of ferroresonance system based on RBF-maximum entropy clustering algorithm

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PHYSICS LETTERS A 2006年第3期357卷 218-223页

作者： Fan, Liu Sun Cai-xin Wen-xia, Si-ma Liao Rui-jin Fei, Guo Chongqing Univ Minist Educ Key Lab High Voltage & Elect New Technol Chongqing 400044 Peoples R China

With regards to the ferroresonance overvoltage of neutral grounded power system, a maximum-entropy learning algorithm based on radial basis function neural networks is used to control the chaotic system. The algorithm optimizes the object function to derive learning rule of central vectors, and uses the clustering function of network hidden layers. It improves the regression and learning ability of neural networks. The numerical experiment of ferroresonance system testifies the effectiveness and feasibility of using the algorithm to control chaos in neutral grounded system. (c) 2006 Elsevier B.V. All rights reserved.

关键词： neutral grounded power system chaos control radial basis function maximum-entropy principle

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Derivatives of maximum-entropy basis functions on the boundary: Theory and computations

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2013年第12期94卷 1123-1149页

作者： Greco, F. Sukumar, N. Univ Calabria Dept Mech Engn I-87036 Arcavacata Di Rende CS Italy Univ Calif Davis Dept Civil & Environm Engn Davis CA 95616 USA

In this paper, we obtain explicit expressions to evaluate the derivatives of maximum-entropy (max-ent) basis function on the boundary of a convex domain. In the max-ent formulation, the basis functions are obtained by maximizing a concave functional subjected to linear constraints (reproducing conditions). In doing so, it is found that the Lagrange multipliers blow up when x, and the expressions for the derivatives of the max-ent basis functions in are of an indeterminate form for points on . We appeal to l'Hopital's rule to derive expressions to determine the derivatives of the basis functions. We consider the Shannon entropy functional and the relative entropy functional with different choices of the prior weight function. The first-order derivatives of all basis functions are bounded. In contrast, on an irregular grid with a certain nodal spacing, some of the second derivatives of the basis functions are unbounded on the boundary. Necessary and sufficient conditions on the priors to obtain bounded Lagrange multipliers are established. Optimal convergence rates for fourth-order problems are demonstrated for a Galerkin approach with a quadratically complete partition-of-unity enriched max-ent *** (c) 2013 John Wiley & Sons, Ltd.

关键词： maximum-entropy principle relative entropy convex approximation plate bending meshfree method l'Hopital'srule

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Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2006年第5期65卷 1018-1038页

作者： Blokhin, A. M. Bushmanov, R. S. Rudometova, A. S. Romano, V. Inst Math Novosibirsk 630090 Russia Novosibirsk State Univ Novosibirsk 630090 Russia Univ Catania Dipartimento Matemat & Informat I-95125 Catania Italy

Linear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999) 307-325;V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000) 31-51] is proven for a typical two-dimensional problem. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： maximum-entropy principle PARABOLIC BAND TRANSPORT CARRIER TRANSPORT MOMENT EQUATIONS SIMULATION SILICON CLOSURE DEVICES

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Enhanced reconstruction of weighted networks from strengths and degrees

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NEW JOURNAL OF PHYSICS 2014年第4期16卷 1-16页

作者： Mastrandrea, Rossana Squartini, Tiziano Fagiolo, Giorgio Garlaschelli, Diego Scuola Super Sant Anna Inst Econ I-56127 Pisa Italy Scuola Super Sant Anna LEM I-56127 Pisa Italy Leiden Univ Inst Lorentz Theoret Phys NL-2333 CA Leiden Netherlands

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.

关键词： network reconstruction null models of networks maximum-entropy principle maximum-likelihood principle enhanced configuration model

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maximum-entropy clustering algorithm and its global convergence analysis

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Science China(Technological Sciences) 2001年第1期44卷 89-101页

作者：张志华郑南宁史罡 1. Institute of Artificial Intelligence & Robotics Xi’ an Jiaotong University 710049 Xi’an China

Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.

关键词： clustering algorithm maximum-entropy principle optimization method entropy function convergence

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