146 research outputs found
Chaotic transitions in deterministic and stochastic dynamical systems: applications of Melnikov processes in engineering, physics, and neuroscience
No full textThe classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology
Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles
No full textWe give sufficient conditions in terms of the Melnikov functions in order that an analytic or a polynomial differential system in the real plane has a period annulus. We study the first nonzero Melnikov function of the analytic differential systems in the real plane obtained by perturbing a Hamiltonian system having either a nondegenerate center, a heteroclinic cycle, a homoclinic cycle, or three cycles obtained connecting the four separatrices of a saddle. All the singular points of these cycles are hyperbolic saddles. Finally, using the first nonzero Melnikov function we give a new proof of a result of Roussarie on the finite cyclicity of the homoclinic orbit of the integrable system when we perturb it inside the class of analytic differential systems.MathematicsSCI(E)0ARTICLE149-7721
Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations
No full textAgraïments: The author would like to thank the Centre de Recerca Matemàtica for their support and hospitality during the period in which the main results of this paper were obtained.In this paper we consider polynomial perturbations of a family of polynomial Hamiltonian equations whose associated Hamiltonian is not transversal to infinity, and its complexification is not a Morse polynomial. We look for an algorithm to compute the first non-vanishing Poincaré-Pontryagin-Melnikov function of the displacement function associated with the perturbed equation. We show that the algorithm of the case when the Hamiltonian is transversal to infinity and its complexification is a Morse polynomial can be extended to our family of perturbed equations. We apply the result to study the maximum number of zeros of the first non-vanishing Poincaré-Pontryagin-Melnikov function associated with some perturbed Hamiltonian equations
Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations
No full textAgraïments: The author would like to thank the Centre de Recerca Matemàtica for their support and hospitality during the period in which the main results of this paper were obtained.In this paper we consider polynomial perturbations of a family of polynomial Hamiltonian equations whose associated Hamiltonian is not transversal to infinity, and its complexification is not a Morse polynomial. We look for an algorithm to compute the first non-vanishing Poincaré-Pontryagin-Melnikov function of the displacement function associated with the perturbed equation. We show that the algorithm of the case when the Hamiltonian is transversal to infinity and its complexification is a Morse polynomial can be extended to our family of perturbed equations. We apply the result to study the maximum number of zeros of the first non-vanishing Poincaré-Pontryagin-Melnikov function associated with some perturbed Hamiltonian equations
The third order Melnikov function of a quadratic center under quadratic perturbations
No full textAbstractWe study quadratic perturbations of the integrable system (1+x)dH, where H=(x2+y2)/2. We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles
Warped throat geometries and low-energy spectrum of confining gauge theories
No full textString theory on the warped deformed conifold, which in the low-energy limit was described by Klebanov and Strassler, is by now the only known consistent example of the supergravity dual of a four dimensional confining (supersymmetric) gauge theory. In this work bosonic supergravity excitations over the Klebanov-Strassler background are studied. The excitation correspond to the low-energy states of a dual N=1 supersymmetric gauge theory. Discovered states are distributed among seven supermultiplets, for which the gauge theory description is determined. This investigation is in particular motivated by an example of the low-energy spectrum in the pure glue gauge theory in the model that might be relevant for the new physics at the LHC.Ph.D.Includes bibliographical references (p. 92-96)
Codimension one intersections of the components of a Springer fiber for the two-column case
No full textAbstractThis paper is a subsequent paper of Melnikov and Pagnon: Reducibility of the intersections of components of a Springer fiber, Indag. Mathem. 19 (4) (2008) 611–631. Here we consider the irreducible components of a Springer fibre (or orbital varieties) for the two-column case in GLn (ℂ). We describe the intersection of two irreducible components, and specially give the necessary and sufficient condition for this intersection to be of codimension one. Since an orbital variety in the two-column case is a finite union of the Borel orbits, we solve the initial question by determining orbits of codimension one in the closure of a given orbit. We show that they are parameterized by a specific set of involutions called descendants, already introduced by the first author in a previous work. Applying this result we show that the codimension one intersection of two components is irreducible and provide the combinatorial description in terms of Young tableaux of the pairs of such components
Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
No full textAgraïments: The first and fourth author are partially supported by a FAPESP grant 2013/34541-0. The first and fourth authors are supported by a CAPES PROCAD grant 88881.068462/2014-01. The second author is partially supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01. The third author is supported by a FAPESP grant 2015/02517-6.We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms
Thermal and Signal Integrity Analysis of Novel 3D Crossbar Resistive Random Access Memories
No full textThe resistive random access memory (RRAM) device is a fundamental building block of novel nonvolatile memories. This paper addresses the design of suitable 3D crossbar structures, in view of their monolithic integration into large memory modules. In fact, a full 3D electro-thermal model is here adopted to simulate and study the thermal and signal integrity of a 1Diode-1Resistor RRAM x-point crossbar structure. These analysis are carried out by considering different RESET biasing schemes and heatsink locations. In addition, two different materials are considered for realizing the contact electrode material wires of the 3D crossbar: Nickel and/or Carbon nanotubes. In particular, we investigate the worst-case scenario in the electro-thermal analysis by comparing the performance results in terms of resistive voltage drop and of temperature distribution. The achieved simulation results demonstrate that the use of carbon interconnects not only provides excellent signal and thermal integrity performances, but also enables the simplest solutions for an effective biasing scheme
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