Giorgio Sonnino | Université libre de Bruxelles (original) (raw)

Papers by Giorgio Sonnino

Axioms, Feb 19, 2024

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

APS Division of Plasma Physics Meeting Abstracts, Nov 1, 2015

arXiv (Cornell University), Jun 5, 2023

Studies of mesoscopic structures have now become a leading and rapidly evolving research field ra... more Studies of mesoscopic structures have now become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few nanometers is leading to radical changes not only in the realization of new materials but also in shedding light on our understanding of the fundamental laws of nature that govern the dynamics of systems at the mesoscopic scale. On the basis of recent experimental results and previous theoretical research, we investigate thermodynamic processes in small systems in Onsager's region. We show that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff-Prigogine's dissipative variable may be discretized at the mesoscopic scale. We establish the canonical commutation rules (ccr) valid at the mesoscopic scale. The numerical value of the discretization constant is estimated experimentally. The ultraviolet divergence problem is solved by applying the correspondence principle with Einstein-Prigogine's fluctuations theory in the limit of macroscopic systems.

Mathematical and Computer Modelling, Mar 1, 1997

Experimental data on free convection of water in the region of maximum density are interpreted by... more Experimental data on free convection of water in the region of maximum density are interpreted by a theoretical model. The agreement between our theory and experimental data is excellent. Typical arrests in the temperature versus time curves and loops in warming-cooling cycles indicate large effects on convection generated by small changes in the space-time density profiles. These observations are fully explained by an extended theoretical approach which takes into account complex phenomena occurring in the boundary layer region. The comparison between theory and experiments indicates how the convective motion propagates from the boundary layer to the internal region of the fluid (central nucleus). Thanks to the extreme sensitivity of the temperature behaviour to relatively small density variations, a complete information about density profile around 4O C can be obtained by a quite simple experimental apparatus. Experimental data at temperature ranges between 0" C and 8O C can "feel" the asymmetry in the density curve around 4" C which is of about 8 parts per million. Our results can bring some light on the experiments performed by Azouni about the water hysteresis loop around 4' C.

The authors proposed a mathematical model with the aim to predict and control the Ebola Virus Dis... more The authors proposed a mathematical model with the aim to predict and control the Ebola Virus Disease (EVD) outbreak. More specifically, the dynamics of the six compartments Susceptible, Exposed, Infected, Treated, Recovered, and Death (SEITRD) is governed by space-independent ordinary differential equations with a convex incidence rate. Three control measures have been taken into account 1) Tracing of contacts; 2) The Lock-down measures;

The aim of this study is to investigate the spreading of the SARS-COV2 infection in Mauritius. To... more The aim of this study is to investigate the spreading of the SARS-COV2 infection in Mauritius. To this end, the author developed mathematical models of the progression of COVID-19 in Mauritius and numerous other countries primarily in Europe. By comparing similar models for numerous countries, the author found that, for the first COVID-19 wave, the ceiling value of the number of cases was inversely correlated to the slope of mathematical models fitted to the curve. He

We propose a protocol able to show publicly addition and multiplication on secretly shared values... more We propose a protocol able to show publicly addition and multiplication on secretly shared values. To this aim, we developed a protocol based on the use of masks and FMPC (Fourier Multi-Party Computation). FMPC is a novel multiparty computation protocol of arithmetic circuits based on secretsharing, capable to compute the addition and multiplication of secrets with no communication. We achieve this task by introducing the first generalization of Parseval's identity for Fourier series applicable to an arbitrary number of inputs and a new algebra referred to as the Θ [n]-algebra. FMPC operates in a setting where users wish to compute a function over some secret inputs by submitting the computation to a set of nodes, without revealing those inputs. FMPC offloads most of the computational complexity to the end users and includes an online phase that mainly consists of each node locally evaluating specific functions. FMPC paves the way for a new kind of multiparty computation protocol; making it possible to compute the addition and multiplication of secrets stepping away from circuit garbling and the traditional algebra introduced by Donald Beaver in 1991. Our protocol is capable to compute addition and multiplication with no communication and its simplicity provides efficiency and ease of implementation.

Bulletin of the American Physical Society, Oct 27, 2014

Submitted for the DPP14 Meeting of The American Physical Society Theoretical Issues for Plasma Re... more Submitted for the DPP14 Meeting of The American Physical Society Theoretical Issues for Plasma Regimes to be Explored by the Ignitor Experiment* A. CARDINALI, ENEA, B. COPPI, MIT, G. SONNINO, Université Libre de Bruxelles-At present, the Ignitor experiment is the only one designed and planned to approach and explore ignition regimes under controlled DT burning conditions. The machine parameters [1] have been established on the basis of existing knowledge of the confinement properties of high density plasmas. A variety of improved confinement regimes are expected to be accessible by means of the available ICRH heating power in addition to the prevalent programmable Ohmic heating power and relying on the injection of high velocity pellets for density profile control. The relevance of the various known confinement regimes to the objectives of Ignitor is discussed. Among other theoretical efforts, a non-linear thermal energy balance equation is investigated to study the onset of thermonuclear instability in the plasmas expected to be produced in Ignitor. The equation for the temperature profile in the equilibrium state is solved with the resulting profiles in agreement with those obtained by a full transport code and commonly adopted scalings for them. The evolution of the thermonuclear instability that relies on the solution of the time dependent energy balance equation is obtained. *Sponsored in part by the U.S. DOE.

Bulletin of the American Physical Society, Nov 12, 2013

Submitted for the DPP13 Meeting of The American Physical Society Analytical Model for the Thermon... more Submitted for the DPP13 Meeting of The American Physical Society Analytical Model for the Thermonuclear Instability in IGNI-TOR* A. CARDINALI, ENEA, G. SONNINO, Universite Libre de Bruxelles, B. COPPI, MIT-The non-linear energy balance equation for thermal equilibrium and stability, is analytically and numerically investigated in order to study the thermonuclear instability in the IGNITOR experiment facility. The expressions for the ion and the electron thermal coefficients, introduced in the thermal energy balance equation, are obtained by solving the nonlinear transport equations relevant to several collisional transport regimes (in particular the banana regime). The differential equation for the temperature profile at equilibrium is solved and the resulting profile is compared with the results obtained by a full transport code. The growth of the perturbation in the temperature is analyzed by integrating the equation in time. A scenario is considered where IGNITOR is led to operate in a slightly sub-critical regime by adding a small fraction of 3 He to the nominal 50-50 Deuterium-Tritium mixture and heating the plasma by ICRH power. *Sponsored in part by the US DOE.

Fundamental theories of physics, 2022

The first attempts to develop non-equilibrium thermodynamics theory occurred after the first obse... more The first attempts to develop non-equilibrium thermodynamics theory occurred after the first observations of some coupled phenomena of thermal diffusion and thermoelectric. However, the big obstacle to overcome is that the number of unknowns is greater than the number of equations expressing the conservation laws. So, it is crucial to determine the closure relations to make the problem solvable. The objective of this work is to determine the nonlinear flux-force relations for systems out of Onsager's region that respect the existing thermodynamic theorems for systems far from equilibrium. To this aim, a thermodynamic theory for irreversible processes [referred to as the Thermodynamical Field Theory (TFT)] has been developed. The TFT rests upon the concept of equivalence between thermodynamic systems. The equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called Thermodynamic Covariant Transformations (TCT). The TCT are the most general thermodynamic force transformations which leave unaltered both the entropy production and the Glansdorff-Prigogine dissipative quantity. In this work, we describe the Lie group and the group representations associated to the TCT. The TCT leads to the so-called Thermodynamic Covariance Principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, must be covariant under TCT. In this chapter, we provide the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients when the skew-symmetric piece is absent. The solution of these equations allows to determine the flux-force closure relations for systems out of the Onsager region. Since the proposed PDEs are obtained without neglecting

Auxiliary plasma heating by radio-frequency waves is a usual procedure in the modern tokamaks. In... more Auxiliary plasma heating by radio-frequency waves is a usual procedure in the modern tokamaks. In the case of 3 He minority heating is analysed the equilibrium distribution function for minority species and the factor modi…cation of the Maxwellian form is plotted for speci…c parameters values as function of radial coordinate and normalized velocity. The energetic minority tail develops with the heating.

The aim of this work is twice: i) To complete (making it easier) Verheest's derivation of the lin... more The aim of this work is twice: i) To complete (making it easier) Verheest's derivation of the linearity of the one-dimensional Lorentz transformations; ii) To show that there is no need to postulate "a priori" Einstein's light principle. The author replaced the postulate the speed of light in a vacuum is the same for all inertial observers with the principle: "the speed of propagation of interactions is finite". MAIN RESULTS OBTAINED By combining the special principle of relativity with the above postulate ii), the author showed that the interactions must propagate with the same speed in all inertial systems and that speed must be a universal constant.

Book Publisher International (a part of SCIENCEDOMAIN International), Mar 4, 2022

Medical Research Archives

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ap- peared in the Chinese region o... more A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ap- peared in the Chinese region of Wuhan at the end of 2019. Since then, the virus spread to other countries, including most of Europe and USA. This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dy- namics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quar- antine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process are derived by adopting the so-called kinetic-type reactions approach. The lockdown and the quarantine measures are modelled by some kind of in- hibitor reactions where susceptible and infected individuals can be trapped into inactive states. The dynamics for the recovered people is obtained b...

Chaos, Solitons & Fractals

In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriat... more In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose them as a good candidate for describing also transport in thermodynamic systems in turbulent regimes. As a special case, we derive the nonlinear PDEs for transport coefficients when the thermodynamic system is subjected to two thermodynamic forces. In this case, the obtained PDE is, in thermodynamical field theory (TFT), analogous to Liouville's equation in Riemannian (or pseudo-Riemannian) geometry. The validity of our model is tested by analyzing a concrete example where Onsager's relations manifestly disagree with experience: transport in Tokamak-plasmas. More specifically, we compute the electron mass and energy losses in turbulent FTU (Frascati Tokamak Upgrade)-plasmas.

Nonequilibrium Thermodynamics and Fluctuation Kinetics

Cornell University - arXiv, Aug 21, 2022

Based on the Bezout approach we propose a simple algorithm to determine the {\tt gcd} of two poly... more Based on the Bezout approach we propose a simple algorithm to determine the {\tt gcd} of two polynomials which doesn't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only nnn steps for polynomials of degree nnn. Formal manipulations give the discriminant or the resultant for any degree without needing division nor determinant calculation.