The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Robert W. Finkel - One of the best experts on this subject based on the ideXlab platform.
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Kinetic Equations in Hamiltonian Treatments
The Journal of Physical Chemistry A, 2001Co-Authors: Robert W. FinkelAbstract:Chemical Kinetic Equations are easily cast in a Hamiltonian form, making them amenable to a wealth of established techniques. The formalism allows for canonical transformations to simplify the rate...
Lorenzo Pareschi - One of the best experts on this subject based on the ideXlab platform.
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An introduction to uncertainty quantification for Kinetic Equations and related problems
arXiv: Numerical Analysis, 2020Co-Authors: Lorenzo PareschiAbstract:We overview some recent results in the field of uncertainty quantification for Kinetic Equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction details or incomplete information at the boundaries or on the initial data. These uncertainties contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. After a brief introduction on the main numerical techniques for uncertainty quantification in partial differential Equations, we focus our survey on some of the recent progress on multi-fidelity methods and stochastic Galerkin methods for Kinetic Equations.
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Kinetic Equations: Computation
Encyclopedia of Applied and Computational Mathematics, 2015Co-Authors: Lorenzo PareschiAbstract:Kinetic Equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
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Numerical methods for Kinetic Equations
Acta Numerica, 2014Co-Authors: Giacomo Dimarco, Lorenzo PareschiAbstract:In this survey we consider the development and mathematical analysis of numerical methods for Kinetic partial differential Equations. Kinetic Equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Here we review the basic numerical techniques for dealing with such Equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for Kinetic Equations. This covers the derivation of fast algorithms, the notion of asymptotic-preserving methods and the construction of hybrid schemes.
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interacting multiagent systems Kinetic Equations and monte carlo methods
2014Co-Authors: Lorenzo Pareschi, Giuseppe ToscaniAbstract:PART I: Kinetic MODELLING AND SIMULATION 1. A short introduction to Kinetic Equations 2. Mathematical tools 3. Monte Carlo strategies 4. Monte Carlo methods for Kinetic Equations PART II: MULTIAGENT Kinetic Equations 5. Models for wealth distribution 6. Opinion modelling and consensus formation 7. A further insight into economy and social sciences 8. Modelling in life sciences Appendix A: Basic arguments on Fourier transforms Appendix B: Important probability distributions
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Numerical methods for Kinetic Equations
Acta Numerica, 2014Co-Authors: Giacomo Dimarco, Lorenzo PareschiAbstract:In this survey we consider the development and the mathematical analysis of numerical methods for Kinetic partial differential Equations. Kinetic Equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their in- trinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computa- tional complexity. Here we review the basic numerical techniques for dealing with such Equations, including the case of semi-Lagrangian methods, discrete velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for Kinetic Equations. This covers the derivation of fast algorithms, the notion of asymptotic preserving methods and the construction of hybrid schemes.
Vladimir N Chernega - One of the best experts on this subject based on the ideXlab platform.
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spin Kinetic Equations in the probability representation of quantum mechanics
Journal of Russian Laser Research, 2019Co-Authors: Vladimir N Chernega, V I MankoAbstract:We discuss the possibility to formulate the dynamics of spin states described by the Schr¨odinger equation for pure states and the von Neumann equation (as well as the GKSL equation) for mixed states in the form of quantum Kinetic Equations for probability distributions. We review an approach to the spin-state description by means of the probability distributions of dichotomic random variables.
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tomographic representation of Kinetic Equations in classical statistical mechanics
Moscow University Physics Bulletin, 2010Co-Authors: V I Manko, Boris I. Sadovnikov, Vladimir N ChernegaAbstract:A tomographic representation of Kinetic Equations is constructed using the Radon transform. Liouville’s equation is considered for one and many particles. The reduced Liouville’s equation is obtained in the tomographic representation and the Bogolyubov chain is investigated in this representation. An example of the relativistic Kinetic equation in the tomographic representation is considered.
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Radon transform and Kinetic Equations in the tomographic representation
Journal of Russian Laser Research, 2009Co-Authors: Vladimir N Chernega, Vladimir I. Man’ko, Boris I. SadovnikovAbstract:Statistical properties of classical random processes are considered in the tomographic representation. The Radon integral transform is used to construct the tomographic form of the Kinetic Equations. The relationship between the probability density on the phase space for classical systems and the tomographic probability distribution is elucidated. Examples of simple Kinetic Equations like the Liouville Equations for one and many particles are studied in detail.
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Radon transform and Kinetic Equations in tomographic representation
arXiv: Quantum Physics, 2009Co-Authors: Vladimir N Chernega, Vladimir I. Man’ko, Boris I. SadovnikovAbstract:Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of Kinetic Equations. Relation of probability density on phase space for classical systems with tomographic probability distributions is elucidated. Examples of simple Kinetic Equations like Liouville Equations for one and many particles are studied in detail.
L N Tsintsadze - One of the best experts on this subject based on the ideXlab platform.
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novel quantum Kinetic Equations of the fermi particles
EPL, 2009Co-Authors: N L Tsintsadze, L N TsintsadzeAbstract:New types of quantum Kinetic Equations of the Fermi particles are derived. Bogolyubov's type of dispersion relation, which is valid for the Bose fluid, is disclosed. A model of neutral Bose atoms in dense strongly coupled plasmas with attractive interaction is discussed. A set of fluid Equations describing the quantum plasmas is obtained. Furthermore, the equation of the internal energy of degenerate Fermi plasma particles is derived.
Julien Vovelle - One of the best experts on this subject based on the ideXlab platform.
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Regularity of stochastic Kinetic Equations
Electronic Journal of Probability, 2017Co-Authors: Ennio Fedrizzi, Franco Flandoli, Enrico Priola, Julien VovelleAbstract:We consider regularity properties of stochastic Kinetic Equations with multiplicative noise and drift term which belongs to a space of mixed regularity (Lp-regularity in the velocity-variable and Sobolev regularity in the space-variable). We prove that, in contrast with the deterministic case, the SPDE admits a unique weakly differentiable solution which preserves a certain degree of Sobolev regularity of the initial condition without developing discontinuities. To prove the result we also study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable stochastic flow.
