Effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below

The effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below are investigated. It is shown that the (2+1)-dimensional Burgers equation may appear as the equation governing the upper free surface perturbations of a Bénard system, even when the viscosity is assumed to depend on temperature. The critical Rayleigh number for the appearance of waves governed by the Kadomtsev-Petviashvili equation, however, will be smaller than R=30, which is the critical number obtained for a constant viscosity. © 1992.

Characterization of heat waves affecting mortality rates of broilers between 29 days and market age

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Damage Detection in Flexible Plate Using Lamb Waves

This paper presents an experimental technique for structural health monitoring (SHM) based on Lamb waves approach in an aluminum plate using piezoelectric material as actuators and sensors. Lamb waves are a form of elastic perturbation that remains guided between two parallel free surfaces, such as the upper and lower surfaces of a plate, beam or shelf. Lamb waves are formed when the actuator excites the surface of the structure with a pulse after receiving a signal. Two PZTs were placed in the plate surface and one of them was used to send a predefined wave through the structure. Thus, the other PZT (adjacent) becomes the sensor. Using this methodology, this paper presents one case of damage detection considering the aluminum plate in the free-free-free-free boundary condition. The damage was simulated by adding additional mass on the plate. It is proposed two damage detection indexes obtained from the experimental signal, involving the Fast Fourier Transform (FFT) and the power spectral density (PSD) that were computed using the output signal. The results show the viability of the presented methodology to damage detection in smart structures

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Traveling waves in the Lethargic Crab Disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.

Absorption cross section of electromagnetic waves for Schwarzschild black holes

The absorption cross section of black holes has been investigated for various fields. Nevertheless, the absorption cross section of Schwarzschild black holes for the electromagnetic field has been only calculated in the low- and high-frequency approximations until now. Here we compute it numerically for arbitrary frequencies.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Mean-field model for the interference of matter-waves from a three-dimensional optical trap

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by, Greiner et al. [Nature (London 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three. (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps. (C) 2003 Elsevier B.V. All rights reserved.

Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the net field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value u(0) of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L, u(0)), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.

Universal scaling in Bardeen-Cooper-Schrieffer superconductivity in two dimensions in non-s waves

The solutions of a renormalized BCS model are studied in two space dimensions for s, p and d waves for finite-range separable potentials. The gap parameter, the critical temperature T-c, the coherence length xi and the jump in specific heat at T-c as a function of the zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small xi and large T-c, appropriate for high-T-c cuprates. The specific heat, penetration depth and thermal conductivity as functions of temperature show universal scaling for p and d waves.

The nonlinear essence of gravitational waves

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that-analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge-a gravitational wave must necessarily be nonlinear to transport its own charge-that is, energy-momentum.