The Experts below are selected from a list of 150 Experts worldwide ranked by ideXlab platform
Eugene H Stanley - One of the best experts on this subject based on the ideXlab platform.
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an alternate formulation of the static scaling hypothesis
International Journal of Quantum Chemistry, 2009Co-Authors: Alex Hankey, Eugene H StanleyAbstract:The static scaling law hypothesis for thermodynamic Functions is formulated by the statement that the singular part of any thermodynamic potential is a generalized Homogeneous Function (GHF), where by definition a Function f(x, y) is a GHF if there exist two numbers a, b such that for all positive values of λ, f (λax, λby) = λ f(x, y). We show that all Legendre transforms and all partial derivatives of a GHF are also GHF'S. Since every thermodynamic Function is related to a given thermodynamic potential by some combination of Legendre transforms and partial derivatives, it follows that all thermodynamic Functions are GHF'S. We then observe that every such Function has a simple power law singularity at the critical point, and that the value of every critical-point exponent can be written down by inspection in terms of the two initial numbers a, b. Consideration of different paths of approach to the critical point lead to an important class of direct tests of the scaling hypothesis; among these are the familiar relations among certain combinations of critical-point exponents. Finally, the problems of extension to Functions of more than two variables are discussed.
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barkhausen noise elementary signals power laws and scaling relations
Physical Review E, 1996Co-Authors: Eugene H Stanley, Djordje Spasojevic, Srdjan Bukvic, Sava MilosevicAbstract:We report extensive measurements, with sufficiently large statistics, of the Barkhausen noise ~BN! in the case of the commercial VITROVAC 6025 X metal glass sample. Applying a very scrutinized numerical procedure, we have extracted over one million of the BN elementary signals from the raw experimental data, whereby we made a rather precise estimation of the relevant power law exponents. In conjunction with the experimental part of the work, we have recognized a generic shape of a single BN elementary signal ~BNES!, and we have put forward, without invoking any existing model of BN, a simple mathematical expression for BNES. Using the proposed expression for BNES in a statistical analysis, we have been able to predict scaling relations and an elaborate formula for the power spectrum. We have also obtained these predictions within the generalized Homogeneous Function approach to the BNES’s probability distribution Function, which we have substantiated by the corresponding data collapsing analysis. Finally, we compare all our findings with results obtained within the current experimental and theoretical research of BN. @S1063-651X~96!13409-7#
N Sukumar - One of the best experts on this subject based on the ideXlab platform.
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spectral extended finite element method for band structure calculations in phononic crystals
Journal of Computational Physics, 2021Co-Authors: Eric B Chin, Amir Ashkan Mokhtari, Ankit Srivastava, N SukumarAbstract:Abstract In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bezier representation of curved (circular) geometries, and construct suitable material enrichment Functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the Homogeneous numerical integration scheme—a method that uses Euler's Homogeneous Function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band structure calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O ( 10 − 8 ) accuracy in frequency calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements.
Denis Efimov - One of the best experts on this subject based on the ideXlab platform.
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on finite time stability of Homogeneous systems with multiplicative bounded Function
European Control Conference, 2019Co-Authors: Youness Braidiz, Wilfrid Perruquetti, A Polyakov, Denis EfimovAbstract:In this paper, we study the finite-time stability of a class of nonlinear systems $\dot{x}=f({x})=H(x)b(x)$ , where $H$ is Homogeneous and $b$ is bounded. We define the Homogeneous extension of the non-Homogeneous Function $f$ and use this extension to prove that, under some conditions on b, if the system $\dot{x}\ =\ f(x)$ is globally asymptotically stable, then it is finite-time stable. An example of global asymptotic stable system with some additional conditions is presented in the last section to illustrate the obtained results.
O A Godin - One of the best experts on this subject based on the ideXlab platform.
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fermat principle for a nonstationary medium
Physical Review Letters, 2003Co-Authors: A G Voronovich, O A GodinAbstract:: One possible formulation of a variational principle of the Fermat type for systems with time-dependent parameters is suggested. In a stationary case, it reduces to the Mopertui-Lagrange least-action principle. A class of Hamiltonians (dispersion relations) is indicated, for which the variational principle reduces to the Fermat principle in a general nonstationary case. Hamiltonians that are Homogeneous Functions of momenta are in this category. For the important case of nondispersive waves (corresponding to Hamiltonians being Homogeneous Function of momenta order 1) the Fermat principle fully determines the geometry of the rays. Equations relating the variation of signal frequency with the rate of change of propagation time are established.
Eric B Chin - One of the best experts on this subject based on the ideXlab platform.
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spectral extended finite element method for band structure calculations in phononic crystals
Journal of Computational Physics, 2021Co-Authors: Eric B Chin, Amir Ashkan Mokhtari, Ankit Srivastava, N SukumarAbstract:Abstract In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bezier representation of curved (circular) geometries, and construct suitable material enrichment Functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the Homogeneous numerical integration scheme—a method that uses Euler's Homogeneous Function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band structure calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O ( 10 − 8 ) accuracy in frequency calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements.