1,720,971 research outputs found
A class of linear viscoelastic models based on Bessel functions
No full textIn this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter . Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times
Prabhakar-like fractional viscoelasticity
No full textThe aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the Prabhakar one. Furthermore, we also discuss how to recover a formal equivalence between the new model and the known classical models of linear viscoelasticity by means of a suitable choice of the parameters in the Prabhakar derivative. Moreover, we also underline an interesting connection between the theory of Prabhakar fractional integrals and the recently introduced Caputo-Fabrizio differential operator
On variable-order fractional linear viscoelasticity
Full text linkA generalization of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions
Scott-Blair models with time-varying viscosity
No full textIn a recent paper, Zhou et al. (2017) studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheological model with a time-dependent viscosity coefficient. This rheological model is essentially based on a generalized Scott-Blair body with a time-dependent viscosity coefficient. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo-type fractional derivatives of a function with respect to another function. This new mathematical approach can be useful in viscoelasticity and diffusion processes in order to model systems with time-dependent features. In this paper we also provide the general solution of the creep experiment for our improved Scott-Blair model together with some explicit examples and illuminating plots
On the propagation of transient waves in a viscoelastic Bessel medium
No full textIn this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen–Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes
On transient waves in linear viscoelasticity
No full textThe aim of this paper is to present a comprehensive review of method of the wave-front expansion, also known in the literature as the Buchen-Mainardi algorithm. In particular, many applications of this technique to the fundamental models of both ordinary and fractional linear viscoelasticity are thoroughly presented and discussed
Le rappresentazioni in meccanica quantistica
Full text linkLo scopo di questo elaborato è compiere un viaggio virtuale attraverso le tappe principali dello sviluppo della teoria dei quanti e approfondirla nelle sue diverse rappresentazioni, quella di Erwin Schrodinger, quella di Werner Karl Heisenberg e quella di Paul Adrien Maurice Dirac, fino ad arrivare, nella fase conclusiva, a diverse applicazione delle rappresentazioni, sfiorando marginalmente la Teoria dei Campi e, di conseguenza, introducendo un parziale superamento della stessa Teoria Quantistica
Time-like definition of quaternions in exterior algebra
Full text linkA formal description of quaternions by means of exterior calculus is
presented. Considering a three-dimensional space-time characterized by three
time-like coordinates, we have been able to consistently recover a suitable
formulation of quaternions by means of the properties arising from exterior
algebra and calculus. As an application, it is also illustrated how rotations
may be written in terms of quaternions, in accordance with definition provided
in exterior algebra.Comment: 7 page
Generalized exterior-algebraic electromagnetism in (k, n)-dimensional spacetime
No full textThis doctoral thesis aims to find a connection between two different disciplines. On the one hand, the electromagnetic theory, one of the most known and most applied theories in physics, properly described by the famous Maxwell equations. On the other hand, the theory of information and communication, provided of a mathematical structure which mainly includes the concepts of probability and statistics. In order to establish a contact point between the two, we first decided to develop a suitable mathematical framework, which could accomodate the two theories in the appropriate context. We therefore chose to use the mathematical theory of exterior algebra, because it allows to combine a simple and intuitive method coming from a classical vector conception, with more advanced but equally effective mathematical tools. Having to build a theory from the beginning, we have opted to consider a procedure as general as possible and, therefore, we proceed in a space-time with arbitrary dimensions, both as regards time and as regards space. We formulate our theory in this space-time, utilizing multivector fields, also of arbitrary degree, in order to broaden the classical concept of vector field. The electromagnetic theory is thus generalized through these multivectors and the fact of having several free parameters, such as the dimensions of space-time and the grade of the multivectoral field, allows to identify various models, obtaining the known ones and opening the doors to new horizons. In practice, to build our theory we can follow two distinct but complementary approaches. In the first place, making an analogy with the classical theory, we can directly use the generalized definitions of exterior algebra to postulate a natural extension of the electromagnetic theory in arbitrary dimensions. Secondly, we have developed in parallel a dynamical theory, so-called Lagrangian, purposely built for multivector fields of arbitrary grade. Regardless of the path chosen, we have obtained a consistent theory that presents its equations of motion, corresponding to the generalized Maxwell equations, and all the equivalent physical quantities resulting from new conservation laws, which identify the quantities of the system that remain unchanged, such as energy and momentum. The connection point with the theory of communication emerges in dealing with the electromagnetic waves coming from the solutions of Maxwell equations. Studied from the multivectoral point of view of exterior algebra, these waves might open the doors to a new interpretation of the transmission of signals from a different perspective.Esta tesis doctoral tiene el objetivo de encontrar un vínculo entre dos disciplinas diferentes. Por un lado, la teoría electromagnética, una de las teorías más conocidas y aplicadas de la física y debidamente descrita por las famosas ecuaciones de Maxwell. Por otro lado, la teoría de la información y de la comunicación, dotada de una estructura matemática que comprende mayormente los conceptos de probabilidad y estadística. Para establecer un punto de encuentro entre las dos, primero decidimos desarrollar una estructura matemática apropiada, que pudiera conciliar las dos teorías en el contexto adecuado. Por lo tanto, decidimos utilizar la teoría matemática del álgebra exterior, porque es capaz de combinar un método simple e intuitivo proveniente de una concepción vectorial clásica, con herramientas matemáticas más avanzadas pero igualmente efectivas. Al tener que construir una teoría desde el principio, hemos optado por considerar un tratamiento lo más general posible y, por tanto, procedemos en un espacio-tiempo con dimensiones arbitrarias, tanto en el tiempo como en el espacio. Construimos nuestra teoría en este espacio-tiempo, basándonos en campos multivectoriales, también de grado arbitrario, para ampliar el concepto clásico de campo vectorial. La teoría electromagnética se generaliza a través de estos multivectores y el hecho de tener varios parámetros libres, como las dimensiones del espacio-tiempo y el grado del campo multivectorial, permite identificar varios modelos, obteniendo los ya conocidos y abriendo las puertas a nuevos horizontes. Operacionalmente, para construir nuestra teoría podemos seguir dos enfoques distintos pero complementarios. En primer lugar, haciendo una analogía con la teoría clásica, podemos utilizar directamente las definiciones generalizadas del álgebra exterior para postular una extensión natural de la teoría electromagnética en dimensiones arbitrarias. En segundo lugar, hemos desarrollado, en paralelo, una teoría dinámica, llamada Lagrangiana, construida a propósito para campos multivectoriales de grado arbitrario. Independientemente del enfoque elegido, hemos obtenido una teoría consistente que presenta sus ecuaciones de movimiento, es decir, las ecuaciones de Maxwell generalizadas, y todas las cantidades físicas equivalentes resultantes de las nuevas leyes de conservación, que identifican las cantidades del sistema que permanecen sin alterar, tales como energía y momento. El punto de conexión con la teoría de la comunicación surge al estudiar las ondas electromagnéticas provenientes de las soluciones de las ecuaciones de Maxwell. Consideradas desde el punto de vista multivectorial del álgebra exterior, estas ondas pueden abrir las puertas a una nueva interpretación de la transmisión de señales desde una perspectiva diferente.Programa de doctorat en Tecnologies de la Informació i les Comunicacion
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