Renato Spigler - Profile on Academia.edu (original) (raw)

Papers by Renato Spigler

Communications in Applied and Industrial Mathematics, Dec 31, 2022

We survey results concerning the problem of identifying depth profiles at coastal zone, which evo... more We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of real observed and measured data, available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.

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 .

Mathematical Inequalities & Applications, 2023

The region of validity of Spira's strict inequality, given by |ζ (1 − s)| = g(s) |ζ (s)| where g(... more The region of validity of Spira's strict inequality, given by |ζ (1 − s)| = g(s) |ζ (s)| where g(s) := 2 1−s π −s cos(πs/2) Γ(s) , with g(s) > 1 , involving the size of the Riemann zetafunction, ζ (s) , at places symmetric with respect to the critical line, is enlarged to the subset H t * := H ∩{t > t * } of the semi-infinite critical half-strip H := {(σ ,t) ∈ C : 1/2 < σ < 1,t > 0} , where s = σ + it and t * = 2π + ε = 6.380685 +. It is conjectured that a smooth line, , exists in H such that the Spira's inequality holds above , while the opposite inequality holds below , and equality holds on. Moreover, if a nontrivial zero, s 0 , of ζ (s) of multiplicity k exists in H t * , it is shown that |ζ (k) (1 − s 0)| > |ζ (k) (s 0)|. Mathematics subject classification (2020): 11M06, 11M99, 11M26. Keywords and phrases: Spira's inequality, zeros of the derivatives of Riemann zeta function, modulus of ζ (s) in the critical strip.

On the Relation between the Lifshitz--Slyozov and the Lifshitz--Slyozov--Wagner Models for Supersaturated Solutions

Siam Journal on Applied Mathematics, 2021

Computational & Applied Mathematics, Jul 13, 2018

An asymptotic-numerical method to solve the initial-boundary value problems for systems of balanc... more An asymptotic-numerical method to solve the initial-boundary value problems for systems of balance laws in one space dimension, on the half space is developed. Expansions in powers of t −1/2 are used, in view of the precise asymptotic behavior recently established on theoretical bases. This approach increases considerably the efficiency of a previous one, where just expansions in inverse powers of t were made. Numerical examples and comparisons with the Godunov, the asymptotic high order, and the asymptotic-numerical method earlier developed are presented. Expanding the solution in powers of t −1/2 instead of t −1 , a saving of about one-half of the CPU time can be realized, still achieving the same accuracy.

Probabilistic and quasi-probabilistic domain decomposition methods for linear elliptic BV problems

Recent Results on Nonlinear Phenomena in Large Populations of Coupled Oscillators

$Research paper thumbnail of First considerations on regular and singular perturbations for fractional differential equations$

Regular and singular perturbations of fractional ordinary differential equations (fODEs) are cons... more Regular and singular perturbations of fractional ordinary differential equations (fODEs) are considered. This is likely the first attempt to describe these problems. Similarities and differences between these cases and the analogous ones for classical (integer-order) differential equations are pointed out. Examples, including the celebrated Bagley-Torvik equations are discussed. Asymptotic-numerical treatments for such problems are presented.

The Hyperbolic Schrödinger Equation and the Quantum Lattice Boltzmann Approximation

Communications in Computational Physics, Jun 1, 2022

Journal of Mathematical Analysis and Applications, Jul 1, 2018

Asymptotic approximations of "phase functions" for linear second-order differential equations, wh... more Asymptotic approximations of "phase functions" for linear second-order differential equations, whose solutions are highly oscillatory, can be obtained using Borůvka's theory of linear differential transformations coupled to Liouville-Green (WKB) asymptotics. A numerical method, very effective in case of asymptotically polynomial coefficients, is extended to other cases of rapidly growing coefficients. Zeros of solutions can be computed without prior evaluation of the solutions themselves, but the method can also be applied to Initial-and Boundary-Value problems, as well as to the case of forced oscillations. Numerical examples are given to illustrate the performance of the algorithm. In all cases, the error turns out to be of the order of that made approximating the phase functions.

Numerical treatment of a boundary-value problem for a certain singular parabolic partial differential equation

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.

Numerical Treatment of a Nonlinear Nonlocal Transport Equation Modeling Crystal Precipitation

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.

Recent advances in partial differential equations, Venice 1996 : proceedings of a conference in honor of the 70th birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

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.

Importance and Unpredictability of Self-organization Processes in Fusion Burning Plasmas

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)

Magneto Gravitational Modes Driven by the Modulated Gravitational Field of Compact Collapsing Binaries

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)

Numerical Functional Analysis and Optimization, 1995

The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hi... more The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like _ u = f (t; u; u) ; t 2 (0; T ] ; u (0) = u 0 , where f(t; ; v) is one-sided Lipschitz and R(I hf(t; ; v)) = H for h > 0 suciently small, and f(t; u;) is Lipschitz-continuous. Extension to Banach spaces is then pointed out. Ordinary and partial, dierential and integro-dierential equations or systems are included. For instance, _ u = A(t; u) + B (t; u), where A(t;) is [strongly] dissipative and maximal, and B(t;) is Lipschitz-continuous, fall into the previous class. The scheme is u n+1 = u n +t f ((n+1)t; u n+1 ; u n), n = 0 ; 1 ; :::; N 1, where t := T= N. T w o main computational advantages with respect to fully implicit methods are: (a) linearization of semilinear problems, and (b) decoupling of systems into lower-dimensional (stationary) subsystems, at each time step. In the latter case, parallelization becomes possible. A full error analysis is performed: consistency and stability are estabilished, and precise convergence estimates are obtained. Several applications, including reaction-diusion and hyperbolic systems, are nally given.

Comparing Cattaneo and Fractional Derivative Models for Heat Transfer Processes

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...

Journal of Integral Equations and Applications, Jun 1, 2013

In this paper, we apply the wavelet-Galerkin method to obtain approximate solutions to linear Vol... more In this paper, we apply the wavelet-Galerkin method to obtain approximate solutions to linear Volterra integral equations (VIEs) of the second kind. Daubechies wavelets are used to find such approximations. In this approach, we introduce some new connection coefficients and discuss their properties and propose algorithms to evaluate them. These coefficients can be computed just once and applied for solving every linear VIE of the second kind. Convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method.

High-Frequency Magnetohydrodynamics

Predicting coastal profiles evolution from a diffusion model based on real data

Applied Mathematical Modelling, Nov 1, 2022