Search results for "Calculus"
showing 10 items of 617 documents
Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes
1993
In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Itoˆ’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.
Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses
2015
In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta.
Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions
2007
Abstract A gradient elastic material model exhibiting gradient kinematic and isotropic hardening is addressed within a thermodynamic framework suitable to cope with nonlocal-type continua. The Clausius–Duhem inequality is used, in conjunction with the concepts of energy residual, insulation condition and locality recovery condition, to derive all the pertinent restrictions upon the constitutive equations, including the PDEs and the related higher order (HO) boundary conditions that govern the gradient material behaviour. Through a suitable limiting procedure, the HO boundary conditions are shown to interpret the action, upon the body's boundary surface, of idealized extra HO constraints cap…
Stochastic response of a fractional vibroimpact system
2017
Abstract The paper proposes a method to investigate the stochastic dynamics of a vibroimpact single-degree-of-freedom fractional system under a Gaussian white noise input. It is assumed that the system has a hard type impact against a one-sided motionless barrier, which is located at the system’s equilibrium position; furthermore, the system under study is endowed with an element modeled with fractional derivative. The proposed method is based on stochastic averaging technique and overcome the particular difficulty due to the presence of fractional derivative of an absolute value function; particularly an analytical expression for the system’s mean squared response amplitude is presented an…
Computer algebra and large scale perturbation theory
1998
This work presents a brief resume of our applications of computer algebra to the study of large-scale perturbation theory in quantum mechanical systems, both in the small and in the strong coupling regimes.
Dynamic shakedown by modal analysis
1984
Dynamic shakedown of discrete elastic-perfectly plastic structures under a specified load history is studied using the dynamic characteristics of the structure provided by modal analysis. Several statical and kinematical theorems are presented, including lower and upper bound theorems for the minimum adaptation time of the structure. In the formulation of the kinematical theorems a crucial role is played by the appropriate definition of ≪admissible plastic strain cycle≫.
New insights on Neolithic food and mobility patterns in Mediterranean coastal populations
2020
OBJECTIVES The aims of this research are to explore the diet, mobility, social organization, and environmental exploitation patterns of early Mediterranean farmers, particularly the role of marine and plant resources in these foodways. In addition, this work strives to document possible gendered patterns of behavior linked to the neolithization of this ecologically rich area. To achieve this, a set of multiproxy analyses (isotopic analyses, dental calculus, microremains analysis, ancient DNA) were performed on an exceptional deposit (n = 61) of human remains from the Les Breguieres site (France), dating to the transition of the sixth to the fifth millennium BCE. MATERIALS AND METHODS The sa…
Exotic foods reveal contact between South Asia and the Near East during the second millennium BCE
2020
Aunque el papel clave del comercio a larga distancia en la transformación de las cocinas en todo el mundo está bien documentado desde al menos la época romana, la prehistoria del comercio de alimentos euroasiático es menos visible. Con el fin de arrojar luz sobre la transformación de las cocinas del Mediterráneo oriental durante la Edad del Bronce y la Edad del Hierro Temprana, analizamos los microrestos y las proteínas conservadas en el cálculo dental de individuos que vivieron durante el segundo milenio a. Nuestros resultados proporcionan evidencia clara del consumo de alimentos básicos esperados, como cereales (Triticeae), sésamo ( Sesamum ) y dátiles ( Phoenix ). Además, informamos evid…
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
Fokker Planck equation solved in terms of complex fractional moments
2014
Abstract In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones, the solution of the FPK equation in terms of a finite number of complex moments may be easily found. It is shown that the probability density function (PDF) solution of the FPK equation is restored in the whole domain, including the trend at infinity with the exception of the value of the PDF in zero.