Papers by Aniello Fedullo
About Practical Stability of Solutions of Systems with Impulse Influences
Il mistero e la verità sulle onde e i corpuscoli
This paper is devoted to the study of the following problem. We have set of diffusion processes w... more This paper is devoted to the study of the following problem. We have set of diffusion processes with absorption on boundaries in some region at initial time $t=0$. It is required to estimate of number of the unabsorbed processes for the fixed time ~$\tau>0$. The number of initial processes is considered as function of $\tau$ and $\tau\to\infty$.
Nonlinear mechanism of purposeful energy redistribution for suppression of oscillations of structures on movable foundation
We consider a possible mechanism of energy redistribution on the basis of the problem relative to... more We consider a possible mechanism of energy redistribution on the basis of the problem relative to the problem of suppression of oscillation of a containment of a nuclear power station under abnormal loading. The proposed mechanism is based on the insertion of a unilateral interaction in the mechanical system. This mechanism presents a particular type of nonlinearity, which can be described only by means of inequalities. The numerical analytical approach shows that the insertion of such an external unilateral interaction makes it possible to change the general behaviour of oscillations and suppress an undesirable development of processes.
Topics on Chaotic Systems
On dynamical behavior of two-junction interferometers in presence of colored noises
The article is devoted to investigation of solution of the Fokker-Plank equations (FPE) with smal... more The article is devoted to investigation of solution of the Fokker-Plank equations (FPE) with small parameter for stochastic differential equations (SDE) connected with the properties of d.c. SQUIDs (Superconductive QUantum Interference Devices), where SQUID are superconducting loops interrupted by two Josephson junctions (JJ).
Asymptotic Expansions of Transition Densities of the Superconducting Phase Differences in d. c. SQUID in Presence of White Noise
Topics on Chaotic Systems - Selected Papers from CHAOS 2008 International Conference, 2009
ABSTRACT This paper deals with the Fokker-Plank equations for the probability density function of... more ABSTRACT This paper deals with the Fokker-Plank equations for the probability density function of the superconducting phase differences of a two junction quantum interferometer in presence of white noises. The authors argue that opportune choice of scales for time and space variables allows to construct effective algorithm of approximation of solutions to these equations in the case of small or large inductance values. The estimations of approximations are also obtained in the present paper.
Slow Rotation of Viscous Liquid with a Free Surface in a Cylindrical Tank
Physics Letters A, 2011
Comparing the stationary states of a mechanical pendulum and of a small under-damped Josephson ju... more Comparing the stationary states of a mechanical pendulum and of a small under-damped Josephson junction, parametric resonance in the latter system due to an oscillating magnetic field is studied by means of a Gedanken-experiment. A second conceptual experiment shows that for rapidly oscillating magnetic fields the superconducting phase difference φ across the junction in the absence of bias current can attain values of ±π in the vicinity of the lower lying stationary state at φ = 0.
Physica C: Superconductivity, 2010
We illustrate, in the limit of small values of the parameter b, a method to analyze the stochasti... more We illustrate, in the limit of small values of the parameter b, a method to analyze the stochastic equations governing the time evolution of a two-junction quantum interferometer in the presence of noise. The analysis takes into account the different characteristic times of the two processes involved in the system, in such a way that the appropriate probability density function for each process is derived by means of one-dimensional Fokker-Planck equations. Therefore, the present analysis is equivalent to a generalization of the reduced single-junction model in the case of thermal fluctuations in the junctions. Voltagecurrent characteristics, transfer functions and circulating currents in 0-SQUIDs and p-SQUIDs are calculated by means of the proposed analytic approach.
… Science, Part B, Jan 1, 2005
The profile functions expected in diffraction patterns of axially oriented semicrystalline fibers... more The profile functions expected in diffraction patterns of axially oriented semicrystalline fibers are discussed. Attention is focused on a Gaussian distribution of the crystallite unique axes. The limits of applicability of known approximations to the computationally demanding theoretical profile function have been found and a simple correction has been proposed enabling the computation of the profile functions near the meridian and on the meridian itself. Test calculations show that this correction leads to better agreement with the theoretical profile functions.
The inclusion-exclusion principle
Journal of Interdisciplinary Mathematics, 2002
ABSTRACT The inclusion-exclusion principle, which finds in measure theory its most general formul... more ABSTRACT The inclusion-exclusion principle, which finds in measure theory its most general formulation, is an important result in probability theory and in combinatorics. In the present paper various formulations are given of the principle which are deduced as corollaries of an abstract version of the principle itself. Many applications in different areas are presented, including matches, ménages and occupancy problems, chromatic polynomials, constrained permutations, Euler function and reliability evaluation. Finally, notable inequalities conclude the paper.
The European Physical Journal B, 2008
The magnetic states of multi-junction superconducting quantum interference device containing 2N i... more The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φex. The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φex. The stability of these states is qualitatively studied by means of the effective potential notion for the system.
Pertubation analysis of the dynamical behavior of two-junction interferometers
The European Physical Journal B, 2007
The dynamical properties of symmetric quantum interferometers with equal junctions of negligible ... more The dynamical properties of symmetric quantum interferometers with equal junctions of negligible capacitance have been studied by means of perturbation analysis in the limit of small values of the parameter beta . In this limit, two characteristic time constants arise. These quantities may be linked to two different dynamical processes in the system: the first is related to the time evolution of the average superconducting phase difference across the two junctions; the second defines the time scale for flux motion. The response of the system to constant and time-dependent externally applied magnetic fields is considered and a general perturbed solution for the average superconducting phase difference and the fluxon number variable is derived to first order in beta .
Focusing light rays back to the vertex of a reflecting parabolic collector: the equivalent of Dionysius ear effect in optical systems
European Journal of Physics, 2009
ABSTRACT A vertical light ray coming from infinity is reflected by a primary parabolic mirror M1 ... more ABSTRACT A vertical light ray coming from infinity is reflected by a primary parabolic mirror M1 having focus at F1. At a small distance from F1 a secondary mirror M2, symmetric with respect to the vertical axis, is placed. One would like to find the analytic equation of the mirror M2, so that all rays from infinity, incident on M1, could be sent back to the vertex V1 of the primary mirror M1. We denote the mirror M2 with the name of zozzaroid, after P Zozzaro, who first proposed the problem. Recalling the famous legend about Dionysius ear, we find that M2 has either an elliptic or a hyperbolic profile.
Central European Journal of Mathematics, 2006
We have random number of independent diffusion processes with absorption on boundaries in some re... more We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to estimate of number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.
ricevuto il 2 novembre 1981)
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Papers by Aniello Fedullo