DYNAMICAL SCALING IN FRAGMENTATION

The dynamics of a fragmentation model is examined from the point of view of numerical simulation and rate equations. The model includes effects of temperature. The number n (s,t) of fragments of size s at time t is obtained and is found to obey the scaling form n(s,t) approximately s(-tau)t(omegasgamma e(-rhot) f(s/t(z)) where f(x) is a crossover function satisfying f(x) congruent-to 1 for x much less than and f(x) much less than 1 for x much greater than 1. The dependence of the critical exponents tau, omega, gamma and z on space dimensionality d is studied from d = 1 to 5. The result of the dynamics on fractal and nonfractal objects as well as on square and triangular lattices is also examined.

Finns growth dynamics, competition and power-law scaling

We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive business world. The detailed quantitative agreement of the theory with empirical results of firms growth based on a large economic database spanning over 20 years is good with a single set of the parameters for all the curves. Further, the empirical data of the variation of the standard deviation of the growth rate with the size of the firm are in accordance with the present theory rather than a simple power law. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Describing Fermi acceleration with a scaling approach: The Bouncer model revisited

The behavior of average velocities on a dissipative version of the classical bouncer model is described using scaling arguments. The description of the model is made by use of a two-dimensional nonlinear area contracting map. Our results reveal that the model experiences a transition from limited to unlimited energy growth as the dissipation vanishes. (c) 2007 Elsevier B.V. All rights reserved.

Scaling investigation of Fermi acceleration on a dissipative bouncer model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fermi acceleration and scaling properties of a time dependent oval billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time evolution of the structure function and dynamical scaling in porous SnO2 dry gels

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

Scaling in the BCS to Bose crossover problem in different partial waves

The BCS superconductivity to Bose condensation crossover problem is studied in two dimensions in S, P, and D waves, for a simple anisotropic pairing, with a finite-range separable potential at zero temperature. The gap parameter and the chemical potential as a function of Cooper-pair binding B c exhibit universal scaling. In the BCS limit the results for coherence length ξ and the critical temperature T c are appropriate for highT c cuprate superconductors and also exhibit universal scaling as a function of B c.

Scaling law for baryon coupling to its current and its possible applications

The baryon coupling to its current (λB), in conventional QCD sum rule calculations (QCDSR), is shown to scale as the cubic power of the baryon mass, MB. Some theoretical justification for it comes from a simple light-cone model and also general scaling arguments for QCD. But more importantly, taken as a phenomenological ansatz for the present, this may find very good use in current explorations of possible applications of QCDSR to baryon physics both at temperature T = 0, T ≠ 0 and/or density ρ = 0, ρ ≠ 0. © World Scientific Publishing Company.

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length ξ and a large critical temperature, T c, appropriate for some high-T c materials. The BCS gap, T c, ξ and specific heat C s(T c) as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below T c in p and d waves.

Extended Hierarchical Censored Production Rules (EHCPRs) system: An approach toward generalized knowledge representation

One common problem in all basic techniques of knowledge representation is the handling of the trade-off between precision of inferences and resource constraints, such as time and memory. Michalski and Winston (1986) suggested the Censored Production Rule (CPR) as an underlying representation and computational mechanism to enable logic based systems to exhibit variable precision in which certainty varies while specificity stays constant. As an extension of CPR, the Hierarchical Censored Production Rules (HCPRs) system of knowledge representation, proposed by Bharadwaj & Jain (1992), exhibits both variable certainty as well as variable specificity and offers mechanisms for handling the trade-off between the two. An HCPR has the form: Decision If(preconditions) Unless(censor) Generality(general_information) Specificity(specific_information). As an attempt towards evolving a generalized knowledge representation, an Extended Hierarchical Censored Production Rules (EHCPRs) system is suggested in this paper. With the inclusion of new operators, an Extended Hierarchical Censored Production Rule (EHCPR) takes the general form: Concept If (Preconditions) Unless (Exceptions) Generality (General-Concept) Specificity (Specific Concepts) Has_part (default: structural-parts) Has_property (default:characteristic-properties) Has_instance (instances). How semantic networks and frames are represented in terms of an EHCPRs is shown. Multiple inheritance, inheritance with and without cancellation, recognition with partial match, and a few default logic problems are shown to be tackled efficiently in the proposed system.

Inversely symmetric interpolatory quadrature rules

We consider interpolatory quadrature rules with nodes and weights satisfying symmetric properties in terms of the division operator. Information concerning these quadrature rules is obtained using a transformation that exists between these rules and classical symmetric interpolatory quadrature rules. In particular, we study those interpolatory quadrature rules with two fixed nodes. We obtain specific examples of such quadrature rules.

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.