Differential rotation of nonlinear r-modes

Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction and Conclusions, references updated; to appear in Phys. Rev.

Emergence of communities on a coevolutive model of wealth interchange

We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is less than a threshold value that defines the width of the economic classes. If the interchange of wealth cannot be done, agents are reconnected with another randomly selected agent, allowing the network to evolve in time. On each interaction there is a probability of favoring the poorer agent, simulating the action of the government. We measure the Gini index, having real world values attached to reality. Besides the network structure showed a very close connection with the economic dynamic of the system.Comment: 5 pages, 7 figure

Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates

An effective multi-objective optimization methodology that combines the isogeometric analysis (IGA) and adaptive chaotic particle swarm algorithm is presented for optimizing ceramic volume fraction (CVF) distribution of functionally graded plates (FGPs) under eigenfrequencies. The CVF distribution is represented by the B-spline basis function. Mechanical behaviors of FGPs are obtained with NURBS-based IGA and the recently developed simple first-order shear theory. The design variables are the CVFs at control points in the thickness direction, and the optimization objective is to minimize the mass of structure and maximize the first natural frequency. A recently developed multi-objective adaptive chaotic particle swarm algorithm with high efficiency is employed as an optimizer. All desirable features of the developed approach will be illustrated through four numerical examples, confirming its effectiveness and reliability

Quantum Phase Transitions in the U(5)-O(6) Large N limit

The U(5)-O(6) transitional behavior of the Interacting Boson Model in the large N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B(E2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviors of these quantities are greatly enhanced with increasing of the total number of bosons N, especially fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n_d in the first excited 0^+ state and the ground state, and another quantity related to the isomer shift behave similarly in both the O(6)-U(5) large N and U(5)-SU(3) phase transitions.Comment: 7 Pages LaTeX, 3 figure

Collapse dynamics of trapped Bose-Einstein condensates

We analyze the implosion and subsequent explosion of a trapped condensate after the scattering length is switched to a negative value. Our results compare very well qualitatively and fairly well quantitatively with the results of recent experiments at JILA.Comment: 4 pages, 3 figure

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Pulsating flow and convective heat transfer in a cavity with inlet and outlet sections

This paper deals with the study of 2-D, laminar, pulsating flow inside a heated rectangular cavity with different aspect ratios. The cooling liquid (water with temperature dependent viscosity and thermal conductivity) comes and leaves the cavity via inlet and outlet ports. The flow topology is characterised by the large recirculation regions that exist at inner corners of the cavity. These low velocity regions cause the heat transfer to be small when compared, for instance, to that of a straight channel. We study the effect that a prescribed pulsation at the inlet port has on the cavity heat transfer. This pulsating boundary condition, of the unsteady Poiseuille type, is described by its frequency and the amplitude of the pressure gradient. The time averaged Reynolds number of the flow, based on the hydraulic diameter of the inlet channel, is 100 and we consider that the dimensionless pulsation frequency (Strouhal number) varies in the range from 0.0 to 0.4. We show that the prescribed pulsation enhances heat transfer in the cavity and that the mechanism that causes this enhancement appears to be the periodic change in the recirculation flow pattern generated by the pulsation. Regarding the quantitative extent of heat transfer recovery, we find that appropriate selection of the pulsation parameters allows for the cavity to behave like a straight channel that is the configuration with the highest Nusselt number

3-D elasto-plastic large deformations: IGA simulation by Bézier extraction of NURBS

This paper is devoted to the numerical simulation of elasto-plastic large deformation in three-dimensional (3-D) solids using isogeometric analysis (IGA) based on Bézier extraction of NURBS (non-uniform rational B-splines), due to some inherently desirable features. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C0-continuity Bézier elements. Consequently, the IGA based on Bézier extraction of NURBS can be embedded in existing FEM codes, and more importantly, as have been shown in literature that higher accuracy over traditional FEM can be gained. The main features distinguishing between the IGA and FEM are the exact geometry description with fewer control points, high-order continuity, high accuracy. Unlike the standard FEM, the NURBS basis functions are capable of precisely describing both geometry and solution fields. The present kinematic is based on the Total Lagrange description due to the elasto-plastic large deformation with deformation history. The results for the distributions of displacements, von Mises stress, yielded zones, and force-displacement curves are computed and analyzed. For the sake of comparison of the numerical results, the same numerical examples have additionally been computed with the FEM using ABAQUS. IGA numerical results show the robustness and accuracy of the technique

Thermodynamic perturbation theory for dipolar superparamagnets

Thermodynamic perturbation theory is employed to derive analytical expressions for the equilibrium linear susceptibility and specific heat of lattices of anisotropic classical spins weakly coupled by the dipole-dipole interaction. The calculation is carried out to the second order in the coupling constant over the temperature, while the single-spin anisotropy is treated exactly. The temperature range of applicability of the results is, for weak anisotropy (A/kT << 1), similar to that of ordinary high-temperature expansions, but for moderately and strongly anisotropic spins (A/kT > 1) it can extend down to the temperatures where the superparamagnetic blocking takes place (A/kT \sim 25), provided only the interaction strength is weak enough. Besides, taking exactly the anisotropy into account, the results describe as particular cases the effects of the interactions on isotropic (A = 0) as well as strongly anisotropic (A \to \infty) systems (discrete orientation model and plane rotators).Comment: 15 pages, 3 figure

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to "optical" metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.Comment: 24 pages, accepted for publication in GR