Renato Spigler - Academia.edu (original) (raw)
Papers by Renato Spigler
Communications in Applied and Industrial Mathematics, Dec 31, 2022
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Physics Letters, Sep 1, 2023
We consider the case that the displacement current is not neglected in the classical MHD equation... more We consider the case that the displacement current is not neglected in the classical MHD equations, as it is
usually done. This amounts to cast them in the relativistic framework of a finite speed of light. We show
some consequences in describing magnetic reconnection phenomena and for hydromagnetic waves. In
the first case, the equation for the magnetic induction is changed from (formally) parabolic to (formally)
hyperbolic, in the second case both, the perturbed magnetic field and the particle velocity, obey to a
certain third-order in time partial differential equation, rather than to the classical wave equation. We
stress the role of two typically small but nonzero parameters, the magnetic diffusivity, η (corresponding
to large values of the Lundquist number), and ε := c − 2 .
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Mathematical Inequalities & Applications, 2023
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Siam Journal on Applied Mathematics, 2021
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Computational & Applied Mathematics, Jul 13, 2018
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Communications in Computational Physics, Jun 1, 2022
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Journal of Mathematical Analysis and Applications, Jul 1, 2018
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Journal of Computational Physics, 1988
We solve a boundary-value problem for a certain linear singular partial differential equation of ... more We solve a boundary-value problem for a certain linear singular partial differential equation of parabolic type by a suitable implicit finite-difference scheme. This allows us to obtain precise tabulated values for the mean powers reflected and transmitted by a slab of random medium. This is relevant, e.g., to Plasma Physics. copyright 1988 Academic Press, Inc.
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Mathematical Models and Methods in Applied Sciences, Sep 1, 2008
Numerical methods to solve certain nonlinear nonlocal transport equations (hyperbolic partial dif... more Numerical methods to solve certain nonlinear nonlocal transport equations (hyperbolic partial differential equations with smooth solutions), even singular at the boundary, are developed and analyzed. As a typical case, a model equation used to describe certain crystal precipitation phenomena (a slight variant of the so-called Lifshitz–Slyozov–Wagner model) is considered. Choosing a train of few delta functions as initial crystal size distribution, one can model the technologically important case of having only a modest number of crystal sizes. This leads to the reduction of the transport equation to a system of ordinary differential equations, and suggests a new method of solution for the transport equation, based on Shannon sampling, which is widely used in communication theory.
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American Mathematical Society eBooks, 1998
Scaling laws and vanishing viscosity limits in turbulence theory by G. I. Barenblatt and A. J. Ch... more Scaling laws and vanishing viscosity limits in turbulence theory by G. I. Barenblatt and A. J. Chorin Potential theory in Hilbert spaces by P. Cannarsa and G. Da Prato Recent developments in the theory of the Boltzmann equation by C. Cercignani New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method by P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin Evolution of trajectory correlations in steady random flows by A. Fannjiang, L. Ryzhik, and G. Papanicolaou Integrability: From d'Alembert to Lax by A. S. Fokas Methods in the theory of quasi periodic motions by G. Gallavotti Fourier analysis and nonlinear wave equations by S. Klainerman The KdV zero-dispersion limit and densities of Dirichlet spectra by C. D. Levermore On Boltzmann equation and its applications by P.-L. Lions Simplified asymptotic equations for slender vortex filaments by A. J. Majda Homoclinic orbits for pde's by D. W. McLaughlin and J. Shatah Lagrangian metrics on fractals by U. Mosco Approximate solutions of nonlinear conservation laws and related equations by E. Tadmor The small dispersion KdV equation with decaying initial data by S. Venakides.
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Self-organization processes are considered to have an important role in well confined plasmas pro... more Self-organization processes are considered to have an important role in well confined plasmas produced by present day experiments where the heating source is externally applied. The observation of ``Profile Consistency'' [1] is viewed as a manifestation of the presence of these processes. In the case of fusion burning plasmas close to self-sustainment (ignition) most of the heating due to fusion products is strongly dependent on the evolution of both the plasma temperature and density profiles. Therefore, self-organization is expected to be of considerably greater importance than in the case of non-reacting plasmas. This fact involves a significant degree of unpredictability on the outcome of envisioned experiments on burning plasmas that has to be added to the complexity of the collective modes that are expected to emerge. Thus, one of the motivations for the Ignitor program is to shed light on these issues and minimize the uncertainties for the design of more ambitious undertakings such as a Compact Pilot Plant. *Sponsored in part by CNR of Italy. [1] B. Coppi, Comm. Plasma Phys. Cont. Fusion extbf{5}, 261 (1980)
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APS, 2019
A new theoretical process [1], to create high energy particle populations during the collapse of ... more A new theoretical process [1], to create high energy particle populations during the collapse of neutron star - neutron star or black hole - black hole binaries, has been identified. The oscillatory gravitational potential that is associated with the rotating binary is characterized by two frequencies, in the case where the masses of the two components are not equal, that reduce to one (the main) when the two masses are equal. Consequently the gravitationally confined plasma surrounding the considered binary will oscillate with the same frequencies. When one of these (e.g. the main) will become about equal to the frequency (about that of the compressional Alfv\ue9n wave) of a newly identified vertically localized ballooning mode, the amplitude of this can be sustained by the gravitationally induced plasma density oscillations. Then the involved characteristic mode-particle resonances can raise the energy of a super-thermal fraction of the electron distribution up to relativistic values and lead to produce observable high energy radiation emission. [1] B. Coppi, Plasma Physics Reports, 45, 5 (2019)
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Numerical Functional Analysis and Optimization, 1995
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Siam Journal on Applied Mathematics, 2018
We compare the model of heat transfer proposed by Cattaneo, Maxwell, and Vernotte with another on... more We compare the model of heat transfer proposed by Cattaneo, Maxwell, and Vernotte with another one, formulated in terms of fractional differential equations, in one and two dimensions. These are only some of the numerous models that have been proposed in the literature over many decades to model heat transport and possibly heat waves, in place of the classical heat equation due to Fourier. These models are characterized by sound as well as by critical properties. In particular, we found that the Cattaneo model does not exhibit necessarily oscillations or negative values of the (absolute) temperature when the relaxation parameter, tau\tautau, drops below some value. On the other hand, the fractional derivative model may be affected by oscillations, depending on the specific initial profile. We also estimate the error made when the Cattaneo equation is adopted in place of the heat equation, and show that the approximation error is of order tau\tautau. Moreover, the solution of the Cattaneo equation converges unifor...
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Journal of Integral Equations and Applications, Jun 1, 2013
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Applied Mathematical Modelling, Nov 1, 2022
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Communications in Applied and Industrial Mathematics, Dec 31, 2022
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Physics Letters, Sep 1, 2023
We consider the case that the displacement current is not neglected in the classical MHD equation... more We consider the case that the displacement current is not neglected in the classical MHD equations, as it is
usually done. This amounts to cast them in the relativistic framework of a finite speed of light. We show
some consequences in describing magnetic reconnection phenomena and for hydromagnetic waves. In
the first case, the equation for the magnetic induction is changed from (formally) parabolic to (formally)
hyperbolic, in the second case both, the perturbed magnetic field and the particle velocity, obey to a
certain third-order in time partial differential equation, rather than to the classical wave equation. We
stress the role of two typically small but nonzero parameters, the magnetic diffusivity, η (corresponding
to large values of the Lundquist number), and ε := c − 2 .
Bookmarks Related papers MentionsView impact
Mathematical Inequalities & Applications, 2023
Bookmarks Related papers MentionsView impact
Siam Journal on Applied Mathematics, 2021
Bookmarks Related papers MentionsView impact
Computational & Applied Mathematics, Jul 13, 2018
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Communications in Computational Physics, Jun 1, 2022
Bookmarks Related papers MentionsView impact
Journal of Mathematical Analysis and Applications, Jul 1, 2018
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Journal of Computational Physics, 1988
We solve a boundary-value problem for a certain linear singular partial differential equation of ... more We solve a boundary-value problem for a certain linear singular partial differential equation of parabolic type by a suitable implicit finite-difference scheme. This allows us to obtain precise tabulated values for the mean powers reflected and transmitted by a slab of random medium. This is relevant, e.g., to Plasma Physics. copyright 1988 Academic Press, Inc.
Bookmarks Related papers MentionsView impact
Mathematical Models and Methods in Applied Sciences, Sep 1, 2008
Numerical methods to solve certain nonlinear nonlocal transport equations (hyperbolic partial dif... more Numerical methods to solve certain nonlinear nonlocal transport equations (hyperbolic partial differential equations with smooth solutions), even singular at the boundary, are developed and analyzed. As a typical case, a model equation used to describe certain crystal precipitation phenomena (a slight variant of the so-called Lifshitz–Slyozov–Wagner model) is considered. Choosing a train of few delta functions as initial crystal size distribution, one can model the technologically important case of having only a modest number of crystal sizes. This leads to the reduction of the transport equation to a system of ordinary differential equations, and suggests a new method of solution for the transport equation, based on Shannon sampling, which is widely used in communication theory.
Bookmarks Related papers MentionsView impact
American Mathematical Society eBooks, 1998
Scaling laws and vanishing viscosity limits in turbulence theory by G. I. Barenblatt and A. J. Ch... more Scaling laws and vanishing viscosity limits in turbulence theory by G. I. Barenblatt and A. J. Chorin Potential theory in Hilbert spaces by P. Cannarsa and G. Da Prato Recent developments in the theory of the Boltzmann equation by C. Cercignani New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method by P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin Evolution of trajectory correlations in steady random flows by A. Fannjiang, L. Ryzhik, and G. Papanicolaou Integrability: From d'Alembert to Lax by A. S. Fokas Methods in the theory of quasi periodic motions by G. Gallavotti Fourier analysis and nonlinear wave equations by S. Klainerman The KdV zero-dispersion limit and densities of Dirichlet spectra by C. D. Levermore On Boltzmann equation and its applications by P.-L. Lions Simplified asymptotic equations for slender vortex filaments by A. J. Majda Homoclinic orbits for pde's by D. W. McLaughlin and J. Shatah Lagrangian metrics on fractals by U. Mosco Approximate solutions of nonlinear conservation laws and related equations by E. Tadmor The small dispersion KdV equation with decaying initial data by S. Venakides.
Bookmarks Related papers MentionsView impact
Self-organization processes are considered to have an important role in well confined plasmas pro... more Self-organization processes are considered to have an important role in well confined plasmas produced by present day experiments where the heating source is externally applied. The observation of ``Profile Consistency'' [1] is viewed as a manifestation of the presence of these processes. In the case of fusion burning plasmas close to self-sustainment (ignition) most of the heating due to fusion products is strongly dependent on the evolution of both the plasma temperature and density profiles. Therefore, self-organization is expected to be of considerably greater importance than in the case of non-reacting plasmas. This fact involves a significant degree of unpredictability on the outcome of envisioned experiments on burning plasmas that has to be added to the complexity of the collective modes that are expected to emerge. Thus, one of the motivations for the Ignitor program is to shed light on these issues and minimize the uncertainties for the design of more ambitious undertakings such as a Compact Pilot Plant. *Sponsored in part by CNR of Italy. [1] B. Coppi, Comm. Plasma Phys. Cont. Fusion extbf{5}, 261 (1980)
Bookmarks Related papers MentionsView impact
APS, 2019
A new theoretical process [1], to create high energy particle populations during the collapse of ... more A new theoretical process [1], to create high energy particle populations during the collapse of neutron star - neutron star or black hole - black hole binaries, has been identified. The oscillatory gravitational potential that is associated with the rotating binary is characterized by two frequencies, in the case where the masses of the two components are not equal, that reduce to one (the main) when the two masses are equal. Consequently the gravitationally confined plasma surrounding the considered binary will oscillate with the same frequencies. When one of these (e.g. the main) will become about equal to the frequency (about that of the compressional Alfv\ue9n wave) of a newly identified vertically localized ballooning mode, the amplitude of this can be sustained by the gravitationally induced plasma density oscillations. Then the involved characteristic mode-particle resonances can raise the energy of a super-thermal fraction of the electron distribution up to relativistic values and lead to produce observable high energy radiation emission. [1] B. Coppi, Plasma Physics Reports, 45, 5 (2019)
Bookmarks Related papers MentionsView impact
Numerical Functional Analysis and Optimization, 1995
Bookmarks Related papers MentionsView impact
Siam Journal on Applied Mathematics, 2018
We compare the model of heat transfer proposed by Cattaneo, Maxwell, and Vernotte with another on... more We compare the model of heat transfer proposed by Cattaneo, Maxwell, and Vernotte with another one, formulated in terms of fractional differential equations, in one and two dimensions. These are only some of the numerous models that have been proposed in the literature over many decades to model heat transport and possibly heat waves, in place of the classical heat equation due to Fourier. These models are characterized by sound as well as by critical properties. In particular, we found that the Cattaneo model does not exhibit necessarily oscillations or negative values of the (absolute) temperature when the relaxation parameter, tau\tautau, drops below some value. On the other hand, the fractional derivative model may be affected by oscillations, depending on the specific initial profile. We also estimate the error made when the Cattaneo equation is adopted in place of the heat equation, and show that the approximation error is of order tau\tautau. Moreover, the solution of the Cattaneo equation converges unifor...
Bookmarks Related papers MentionsView impact
Journal of Integral Equations and Applications, Jun 1, 2013
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Applied Mathematical Modelling, Nov 1, 2022
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