arXiv subjects

R. Vilela Mendes

Publications and source records attributed to R. Vilela Mendes.

104 records · Page 6Linked to original sources

arXiv1998

Feigenbaum networks

We study dynamical systems composed of a set of linearly coupled quadratic maps which, if uncoupled, would be on the Feigenbaum accumulation point. For two units we prove the existence of an infinite number of sinks for an open set of coupling parameters. In the limit of many units a mean field analysis also implies the stabilization in periodic orbits of, at least, a subset of the coupled units. Possible applications in the fields of control of chaos, signal processing through complex dynamics and as models of self-organization, are discussed.

chao-dyn↗

arXiv1998

Conditional exponents, entropies and a measure of dynamical self-organization

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants.

adap-org↗

arXiv1998

Gluon condensate and the vacuum structure of QCD

Phenomenological evidence and analytic approximations to the QCD ground state suggest a complex gluon condensate structure. Exclusion of elementary fermion excitations by the generation of infinite mass corrections is a consequence. In addition the existence of vacuum condensates in unbroken non-abelian gauge theories, endows SU(3) and higher order groups with a non-trivial structure in the manifold of possible vacuum solutions, which is not present in SU(2). This may be related to the existence of particle generations.

hep-th↗

arXiv1997

Characteristic functions and process identification by neural networks

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide only incomplete or misleading information on the statistical properties of the data. To handle such situations we propose neural network algorithms, with an hybrid (supervised and unsupervised) learning scheme, which constructs the characteristic function of the probability distribution and the transition functions of the stochastic process. Illustrative examples are presented, which include Cauchy and Levy-type processes

physics.data-an↗

arXiv1997

Non-commutative time-frequency tomography

The characterization of non-stationary signals requires joint time and frequency information. However, time (t) and frequency (omega) being non-commuting variables there cannot be a joint probability density in the (t,omega) plane and the time-frequency distributions, that have been proposed, have difficult interpretation problems arising from negative or complex values and spurious components. As an alternative we propose to obtain time-frequency information by looking at the marginal distributions along rotated directions in the (t,omega) plane. The rigorous probability interpretation of the marginal distributions avoids all interpretation ambiguities. Applications to signal analysis and signal detection are discussed as well as an extension of the method to other pairs of non-commuting variables.

physics.data-an↗

arXiv1997

On the computation of quantum characteristic exponents

A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are discussed as well as the problems encountered in the numerical computation of the quantum exponents. Although an example of true quantum chaos may be exhibited, the taming effect of quantum mechanics on chaos is quite apparent in the computation of the quantum exponents. However, even when the exponents vanish, the functionals used for their definition may still provide a characterization of distinct complexity classes for quantum behavior.

quant-ph↗

arXiv1997

Saddle scars: Existence and applications

A quantum scar is a wave function which displays an high intensity in the region of a classical unstable periodic orbit. Saddle scars are states related to the unstable harmonic motions along the stable manifold of a saddle point of the potential. Using a semiclassical method it is shown that, independently of the overall structure of the potential, the local dynamics of the saddle point is sufficient to insure the general existence of this type of scars and their factorized structure is obtained. Potentially useful situations are identified, where these states appear (directly or in disguise) and might be used for quantum control purposes.

quant-ph↗

arXiv1997

Active control of ionized boundary layers

The challenging problems, in the field of control of chaos or of transition to chaos, lie in the domain of infinite-dimensional systems. Access to all variables being impossible in this case and the controlling action being limited to a few collective variables, it will not in general be possible to drive the whole system to the desired behaviour. A paradigmatic problem of this type is the control of the transition to turbulence in the boundary layer of fluid motion. By analysing a boundary layer flow for an ionized fluid near an airfoil, one concludes that active control of the transition amounts to the resolution of an generalized integro-differential eigenvalue problem. To cope with the required response times and phase accuracy, electromagnetic control, whenever possible, seems more appropriate than mechanical control by microactuators.

chao-dyn↗

arXiv1997

Collision states and scar effects in charged three-body problems

Semiclassical methods form a bridge between classical systems and their quantum counterparts. An interesting phenomenon discovered in this connection is the scar effect, whereby energy eigenstates display enhancement structures resembling the path of unstable periodic orbits. This paper deals with collision states in charged three-body problems, in periodic media, which are scarred by unstable classical orbits. The scar effect has a potential for practical applications because orbits corresponding to zero measure classical configurations may be reached and stabilized by resonant excitation. It may be used, for example, to induce reactions that are favoured by unstable configurations.

quant-ph↗

arXiv1997

On the nonlinearity interpretation of q- and f-deformation and some applications

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.

quant-ph↗

arXiv1997

Boundary-layer control by electric fields: A feasibility study

A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boundary layer control for realistic physical parameters. Practical design formulas and criteria are obtained. We also discuss the perspectives for active control of the laminar-to-turbulent transition fluctuations by electromagnetic field modulation.

physics.flu-dyn↗

arXiv1994

A Stochastic Process for the Dynamics of the Turbulent Cascade

Velocity increments over a distance r and turbulent energy dissipation on a box of size r are well described by the multifractal models of fully developed turbulence. These quantities and models however, do not involve time-correlations and therefore are not a detailed test of the dynamics of the turbulent cascade. If the time development of the turbulent cascade, in the inertial range, is related to the lifetime of the eddies at different length scales, the time correlations may be described by a stochastic process on a tree with jumping kernels which are a function of the ultrametric (tree) distance. We obtain the solutions of the Chapman-Kolmogorov equation for such a stochastic process, with jumping kernels depending on the ultrametric distance, but with an arbitrarily specified invariant probability measure. We then show how to use these solutions to compute the time correlations in the turbulent cascade.

chao-dyn↗

arXiv1994

Texture Segmentation by Local Bi-Orthogonal Decomposition

We investigate the ability of a local bi-orthogonal decomposition to build texture segmentation of images. Using the structures associated to the local decomposition of the image independent row and columns we perform a segmentation, where the regions are defined by the property of having a smooth variation of the corresponding entropy. Examples are choosen in texture made and also in real life images. The size of the local analysis is also determined by the properties of the (global) bi-orthogonal decomposition.

chao-dyn↗

arXiv1993

q-Deformed Brownian Motion

Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.

hep-th↗