Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Material processing by plasma shock wave generated in an inverse Z-pinch plasma expander

The applicability of plasma shock wave for material processing was investigated using modified inverse Z-pinch device. Shock wave expanding speed and plasma spectral analysis were studied using an internal magnetic,probe and spatially collimated light spectroscopy. The material processing capability of the device was shown by many different surface analysis techniques such as AES, IRS, EPM and SEM. The interactions between a plasma shock wave of similar to4x10(6) cm/s speed with a Si substrate surface shows some ion implantation capability using a nitrogen plasma and thin film formation using a methane plasma.

Ultrastructural and immunocytochemical evaluation of the effects of extracorporeal shock wave treatment in the hind limbs of horses with experimentally induced suspensory ligament desmitis

Objective-To evaluate the effects of extracorporeal shock wave therapy (ESWT) on affected ligaments in the hind limbs of horses with experimentally induced suspensory ligament desmitis by use of ultrasonographic, ultrastructural, and immunocytochemical techniques.Animals-10 horses.Procedure-Suspensory ligament desmitis was induced in both hind limbs of each horse by use of 2 collagenase injections (administered 2 weeks apart) in each suspensory ligament. Two weeks after the second injection, the right hind limb of each horse was treated with ESWT (3 treatments at 3-week intervals)- the left hind limb was not treated (control limb). Periodically during the study, the healing process was monitored ultrasonographically and the proportions of ligaments affected with lesions were assessed. Four weeks after the last ESWT treatment, biopsy specimens were collected from all ligaments for ultrastructural evaluation and immunocytochemical analysis of transforming growth factor beta-1.Results-The difference in the proportion of the lesion-affected ligament between ESWT-treated and control limbs was significant (P < 0.05) from 3 weeks after the second ESWT treatment to the end of the study. Compared with control ligaments, ESWT-treated ligaments had more small, newly formed collagen fibrils and greater expression of transforming growth factor beta-1 4 weeks after the last ESWT treatment was administered.Conclusions and Clinical Relevance-Results have indicated that ESWT appears to facilitate the healing process in horses with experimentally induced hind limb suspensory ligament desmitis.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

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

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.

Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Surface analysis of alumina ceramic exposed to shock waves produced by plasma expander

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Weak-field approximation of effective gravitational theory with local Galilean invariance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.

Avaliação histológica e morfométrica do retalho axial oris angularis e da terapia por ondas de choque aplicados a defeito palpebral experimental em cães

Considering that the cutaneous flap can be affected by isquemic complications the extra corporeal shock wave therapy (ESWT) was described as rescue techniques. The present study was developed to analyze histological and with morfometry, twenty one skin samples treated or not with the shock wave therapy, obtained from flap's distal border, used in this study to repair eyelids' experimental defects in dogs. The flap with or without ESWT did not show any histological sign of inflammatory or atrophic alterations. Both group treated showed similar morphometrical characteristics. The ESWT with the protocol used in this study (2500 impulses at 0,15 mJ/mm 2) did not demonstrate significant clinical outcomes as a rescue technique when applied over the oris angularis flap, however results showed no signals of collateral deleterious effects.

Determinação da densidade mineral e da elasticidade óssea após a aplicação de ondas de choque extracorpóreas no terceiro metacarpiano de equinos atletas

The porpoise of this study was to evaluate the effects of extracorporeal shock waves in third metacarpus bone from healthy horses by determination of bone elasticity. It were used 20 Thoroughbred horses, male and female, with two years old, on top of training and selected as the state healthy. At the beginning of the experiment (D0), all animals were submitted for evaluation of bone elasticity held in the third metacarpus bone. The animals were divided into two groups (Control Group - CG and Experimental Group - EG). The application of extracorporeal shock wave therapy (ESWT) was performed on the right forelimb of the animals in the experimental group in the same place evaluated for bone elasticity and was used apparatus for extracorporeal therapy of waves with 0.15 mJ/mm2 energy flux density and 2000 pulses with E6R20 probe, with focus feature of the shock wave of 20 mm. The ESWT were repeated every 21 days, a total of three sessions (D0, D21 and D42). The analysis of bone elasticity determination was realized at D21, D42 and D72. The average of speed ultrasound differed between groups at D21, D42 and D72, and the animals from EG had lower bone mineral density after applications of ESWT. There was also difference in the analysis of bone mass (Z-Score) between the groups at D21 and D42, which animals from EG showed a significant decrease in bone mass. The risk of fracture was higher in animals from experimental group at D21. It was concluded that ESWT is able to promote change in bone mineral density.

Modelagem matemática da doença do caranguejo letárgico via ondas viajantes

Pós-graduação em Biometria - IBB

Uso do retalho axial Oris angularis em defeitos palpebrais, associado ou não a aplicação de terapia por ondas de choque extracorpóreas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efeito das ondas de choque extracorpóreas na desmite experimentalmente induzida em eqüinos

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