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Research Interests: Mathematics and Scala
ABSTRACT
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When a soil saturated with water is subject to freezing, a volume expansion can generally be observed. The increase in volume is due not only to the different densities of water and ice, but mainly to a water migration process that is... more
When a soil saturated with water is subject to freezing, a volume expansion can generally be observed. The increase in volume is due not only to the different densities of water and ice, but mainly to a water migration process that is transported from the base of the soil up to an intermediate region where the change of phase occurs. It is generally accepted that a transition region, called frozen fringe, where ice and water coexist in the porous space, separates the unfrozen from the frozen part of the soil. Immediately over the frozen fringe a pure segregated layer of ice (ice lens) can form. If the freezing process is too fast or the weight acting on the soil (overburden pressure) is relevant, the porous matrix does not separate and the shifting of the frozen fringe towards the base of the soil (frost penetration) is observed. Many mathematical models have been proposed for the frost heave process. The main features of the one-dimensional model we are considering are summarized in Sec. 1. In Ref. 9 the case of assignment of the boundary thermal fluxes (at the base and on top of the soil) is studied. In practical cases, sometime the boundary temperatures, instead of the thermal fluxes, can be registered or imposed: in this paper we will investigate the model in such case. The main purpose is to detect which are the boundary values for temperature that determine the process of lens formation or frost penetration, once the properties of the soil are known.
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When a soil saturated with water is subject to freezing, a volume expansion can generally be observed. The increase in volume is due not only to the different densities of water and ice, but mainly to a water migration process that is... more
When a soil saturated with water is subject to freezing, a volume expansion can generally be observed. The increase in volume is due not only to the different densities of water and ice, but mainly to a water migration process that is transported from the base of the soil up to an intermediate region where the change of phase occurs. It is generally accepted that a transition region, called frozen fringe, where ice and water coexist in the porous space, separates the unfrozen from the frozen part of the soil. Immediately over the frozen fringe a pure segregated layer of ice (ice lens) can form. If the freezing process is too fast or the weight acting on the soil (overburden pressure) is relevant, the porous matrix does not separate and the shifting of the frozen fringe towards the base of the soil (frost penetration) is observed. Many mathematical models have been proposed for the frost heave process. The main features of the one-dimensional model we are considering are summarized i...
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Dottorato di ricerca in matematica. 7. ciclo. A.a. 1991-95. Direttore della ricerca A. Fasano. Coordinatore C. PucciConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za... more
Dottorato di ricerca in matematica. 7. ciclo. A.a. 1991-95. Direttore della ricerca A. Fasano. Coordinatore C. PucciConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
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This work is based on the “Notes for the course of dynamic systems” written by Professor Riccardo Ricci in 2005 and subsequently reworked until the year of his death, which occurred in 2013. Starting from the latest version, the scholars... more
This work is based on the “Notes for the course of dynamic systems” written by Professor Riccardo Ricci in 2005 and subsequently reworked until the year of his death, which occurred in 2013. Starting from the latest version, the scholars have undertaken a review and expansion that led to this manual. The text is aimed at bachelor students of the courses in Mathematics, Physics and Engineering. Moreover, it presents the fundamental topics of Lagrangian mechanics and the dynamics of rigid bodies and variational principles, with a hint at Hamiltonian mechanics.
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A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide... more
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the lagrangian components, in the classical sense of the Newton's law, for a quite general class of forces. At the same time, the generalized equations of motions recover some of the classical alternative formulations of the Lagrangian equations.
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One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems,... more
One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems, the Voronec equations are probably less frequent and common with respect to the prevalent methods of quasi--coordinates (Hamel--Boltzmann equations) and of the acceleration energy (Gibbs--Appell equations). In this paper we start from the case of linear nonholonomic constraints, in order to extend the Voronec equations to nonlinear nonholonomic systems. The comparison between two ways of expressing the equations of motion is performed. We finally comment that the adopted procedure is appropriated to implement further extensions.
The equable, Pythagorean and natural scales are built on the basis of a mathematical logic.
One of the earliest formulations of dynamics of nonholonomic systems traces back to 1895 and is due to Chaplygin, who developed his analysis under the assumption that a certain number of the generalized coordinates do not occur either in... more
One of the earliest formulations of dynamics of nonholonomic systems traces back to 1895 and is due to Chaplygin, who developed his analysis under the assumption that a certain number of the generalized coordinates do not occur either in the kinematic constraints or in the Lagrange function. A few years later Voronec derived equations of motion for nonholonomic systems removing the restrictions demanded by the Chaplygin systems. Although the methods encountered in the following years favor the use of the quasi-coordinates, we will pursue the Voronec method, which deals with the generalized coordinates directly. The aim is to establish a procedure for extending the equations of motion to nonlinear nonholonomic systems, even in the rheonomic case.
We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the... more
We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance of the mechanical energy induced by the equations of motion; the conservation of the energy on the basis of the tipology of the constraint equations is discussed. Several examples are performed.
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We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the... more
We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance of the mechanical energy induced by the equations of motion; the conservation of the energy on the basis of the tipology of the constraint equations is discussed. Several examples are performed.