Massimo Tessarotto | Università degli Studi di Trieste (original) (raw)

Papers by Massimo Tessarotto

Toroidal differential rotation (shear flow) produced by E x B drift in tokamak plasmas is current... more Toroidal differential rotation (shear flow) produced by E x B drift in tokamak plasmas is currently regarded important for its role in plasma equilibrium, stability and transport. Experimental observations of enhanced confinement and transport regimes in Tokamaks, especially during H-modes and reverse magnetic shear configurations demonstrate, however, evidence of the existence of strong drifts, corresponding not only to the E x B drift, but also produced by steep radial profiles of density [N{sub s}], temperature [T{sub s}] and mass flow [V = {omega}Re{sub {var_phi}}, with e{sub {var_phi}} the toroidal unit vector, R the distance for the symmetry axis of the torus and {omega} being the toroidal angular rotation velocity]. Thus, a fundamental problem appears the formulation of the gyrokinetic equation in the presence of strong drifts, based on a consistent formulation of guiding-center mechanics. A further potentially important feature which seems desirable to address in this connection is the treatment of weakly relativistic corrections to the electron dynamics in such a general case, extending recent work on the weakly relativistic.

Symmetry, Oct 6, 2022

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

Symmetry, Jun 7, 2023

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, 1983

M assim o T e s s a r o t to , Equilibria with non-rigid motions, ecc. 61 Fisica matem atica.-Equ... more M assim o T e s s a r o t to , Equilibria with non-rigid motions, ecc. 61 Fisica matem atica.-Equilibria w ith non-rigid motions in a magnetoplasma <•). Nota ((*) **> di M assimo T essarotto <***>, presen tata dal Socio D. G raffi. R ia s s u n to .-Si studiano soluzioni perturbative deirequazione cinetica di Fokker-Planck nella approssimazione « di raggio di Larmor piccolo » che corrispon dono a stati iniziali in presenza di moti non rigidi del plasma. Quali esempi si consi derano, in particolare, configurazioni di equilibrio idromagnetico spazialmente sim metriche. (*) Research performed in the framework of the author's participation in the activities of the « Gruppo Nazionale per la Fisica Matematica » of the Italian «Consiglio Nazionale delle Ricerche». (**) Pervenuta all'Accademia il 2 agosto 1983.

Bulletin of the American Physical Society, Nov 19, 2007

Several issues concerning the foundations of hydrodynamics still remain unanswered. A significant... more Several issues concerning the foundations of hydrodynamics still remain unanswered. A significant aspect is the determination of the fluid pressure in isothermal incompressible fluids and the construction of algorithms with permit to time-advance the same fluid pressure. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. However, the interesting question arises whether there exists actually an evolution equation for the fluid pressure which is exactly equivalent to the Poisson equation (i.e., is a Poisson solver). The search of an exact pressure-evolution equation, besides being a still unsolved mathematical problem, is potentially relevant in fluid dynamics. In this note we intend to show that, based on an inverse kinetic theory (IKT) recently proposed for the incompressible Navier-Stokes equations [M. Ellero and M. Tessarotto, Physica A 355, 233 (2005)], a solution to this problem can actually be reached. Basic consequences of the result are presented.

Advances in Mathematical Physics, Dec 2, 2018

The conditions for the occurrence of the so-called macroscopic irreversibility property and the r... more The conditions for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the 1-body probability density function (PDF) associated with hard-sphere systems are investigated. The problem is set in the framework of the axiomatic "ab initio" theory of classical statistical mechanics developed recently and the related establishment of an exact kinetic equation realized by the Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the 1-body PDF, identified here with the Master kinetic information. It is then proved that, provided the same PDF is prescribed in terms of suitably smooth, i.e., stochastic, solution of the Master kinetic equation, the two properties indicated above are indeed realized.

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, 1983

Journal of Applied Mechanics, Mar 1, 1960

Comparison of Equation (14) with Equations (8), (10), and (16) of the paper shows analytically th... more Comparison of Equation (14) with Equations (8), (10), and (16) of the paper shows analytically that the first two acceleration influence coefficients, a "d piF, are the same as the corresponding velocity influence coefficients, since they are the same pair of partial derivatives. _ Also it is seen that the third acceleration influence coefficient, /3;d, is equal to D 2 R j/DdD-, which is of a different nature from the other influence coefficients, since it gives the effect clue to two interrelated inputs [coc and coFas related by Equation (10) ] rather than the effect due to a single input. As in the velocity solution, these influence coefficients can be evaluated by graphical solutions, and then the constraint which was removed to obtain a second degree of freedom can be reintroduced to evaluate coF in terms of coc and cofl. For the example in the paper, this can be accomplished analytically by setting Fs = 0 in Equation (13) of this discussion. When the velocity influence coefficients are identified as partial derivatives, it is seen that the application of influence coefficients for synthesis of mechanisms by variation, as suggested in the final paragraph of the paper, is similar in principle to the method described by Svoboda, 6 by Nickson, 6 and by Hall and Tao. 7 A. S. HALL. 8 The writer has always been troubled by the fact that there seemed to be in the literature no method guaranteed to solve the problems of velocity' and acceleration analysis in all conceivable plane mechanisms. The paper by Goodman, author's reference [3], was an excellent step in the right direction and probably his method will take care of most practical mechanisms. However, there still remained the (possibly academic) question of whether we could conceive mechanisms which could not be analyzed. The author has answered the question to the writer's satisfaction. It now appears that suitable use of the suggested superposition ideas should lead to a solution for any plane mechanism.

Physics Letters, May 1, 2017

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings ... more In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large N −body system of hard spheres, i.e., formed by N ≡ 1 ε ≫ 1 particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto et al., 2013-2016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the 1−body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of ε for all the physically-relevant parameters. The goal is that of identifying the relevant physically-meaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by small-size or finite-size identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of ε.

Foundations of Physics, Mar 14, 2022

Symmetry, Apr 24, 2019

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Grav... more The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder-Weyl variational formulation (2015-2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g µν being realized by the third-order 4-tensor Π α µν. It is shown that this generates a corresponding Hamilton-Jacobi theory in which the Hamilton principal function is a 4-tensor S α. However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton-Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field.

Entropy, Oct 26, 2020

The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy... more The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.

Entropy, Apr 19, 2019

Based on the introduction of a suitable quantum functional, identified here with the Boltzmann-Sh... more Based on the introduction of a suitable quantum functional, identified here with the Boltzmann-Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.

Entropy, Apr 23, 2021

Foundations of Physics, Feb 2, 2016

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is form... more In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1-or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.

Symmetry, May 19, 2023

arXiv (Cornell University), Mar 14, 2017

In this paper the conditions are investigated for the occurrence of the so-called macroscopic irr... more In this paper the conditions are investigated for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the 1−body probability density function (PDF) associated with hard-sphere systems. The problem is set in the framework of the axiomatic "ab initio" approach to classical statistical mechanics recently developed [Tessarotto et al., 2013-2017] and the related establishment of an exact kinetic equation realized by Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the 1−body PDF here identified with the Master kinetic information. The goal is to show that, provided the same PDF is realized in terms of an arbitrary suitably-smooth particular solution of the Master kinetic equation the two properties indicated above are indeed realized and that the same functional is unrelated either with the Boltzmann-Shannon entropy and the Fisher information.