A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration

Some dynamical properties of a bouncing ball model under the presence of an external force modelled by two nonlinear terms are studied. The description of the model is made by the use of a two-dimensional nonlinear measure-preserving map on the variable's velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

Competition between suppression and production of Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Suppressing Fermi acceleration in two-dimensional driven billiards

We consider a dissipative oval-like shaped billiard with a periodically moving boundary. The dissipation considered is proportional to a power of the velocity V of the particle. The three specific types of power laws used are: (i) F proportional to-V; (ii) F proportional to-V-2 and (iii) F proportional to-V-delta with 1 < delta < 2. In the course of the dynamics of the particle, if a large initial velocity is considered, case (i) shows that the decay of the particle's velocity is a linear function of the number of collisions with the boundary. For case (ii), an exponential decay is observed, and for 1 < delta < 2, an powerlike decay is observed. Scaling laws were used to characterize a phase transition from limited to unlimited energy gain for cases (ii) and (iii). The critical exponents obtained for the phase transition in the case (ii) are the same as those obtained for the dissipative bouncer model. Therefore near this phase transition, these two rather different models belong to the same class of universality. For all types of dissipation, the results obtained allow us to conclude that suppression of the unlimited energy growth is indeed observed.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

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

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

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

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Crystal Structures of Xanthomonas Small Heat Shock Protein Provide a Structural Basis for an Active Molecular Chaperone Oligomer

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

Economic design of (X)over-bar and R charts under Weibull shock models

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

SURFACE SOLITARY WAVES IN A DOUBLE DIFFUSIVE SYSTEM

We show that a surface solitary wave governed by the Korteweg-de Vries equation can develop in a fluid acted upon by fluxes of heat and of a second diffusive element. This solitary wave appears as a manifestation of a hydrodynamical instability which sets in only when a certain relation involving the parameters of the system is satisfied.

Crystallization and preliminary X-ray diffraction analysis of XAC1151, a small heat-shock protein from Xanthomonas axonopodis pv. citri belonging to the alpha-crystallin family

The hspA gene (XAC1151) from Xanthomonas axonopodis pv. citri encodes a protein of 158 amino acids that belongs to the small heat-shock protein ( sHSP) family of proteins. These proteins function as molecular chaperones by preventing protein aggregation. The protein was crystallized using the sitting-drop vapour-diffusion method in the presence of ammonium phosphate. X-ray diffraction data were collected to 1.65 angstrom resolution using a synchrotron-radiation source. The crystal belongs to the rhombohedral space group R3, with unit-cell parameters a = b = 128.7, c = 55.3 angstrom. The crystal structure was solved by molecular-replacement methods. Structure refinement is in progress.

Effect of acute heat stress on heat shock protein 70 messenger RNA and on heat shock protein expression in the liver of broilers

1. The synthesis of heat shock protein 70 (Hsp70) mRNA and the expression of Hsp70 in the liver of broiler chickens submitted to acute heat stress (35 degrees C for 5 h) was investigated.2. Hsp70 expression was detected by SDS-PAGE and Western blot analysis using a polyclonal antiserum against Hsp70 of Blastocladiella emersonii. The specific signal of Hsp70 mRNA was analysed by Northern blot using as probe a Hsp70 cDNA of B. emersonii.3. An increase in the amount of Hsp70 was detected from the first up to the fifth hour of acute heat exposure. This increase in the amount of Hsp70 was accompanied by an increase in Hsp70 mRNA which peaked at 3 h.4. This study shows that the heat induced increase in Hsp70 mRNA and protein in broiler liver, in vivo, are time dependent, similar to that in mammals.

LESION OF THE ANTEROVENTRAL 3RD VENTRICLE REGION IMPAIRS THE RECOVERY OF ARTERIAL-PRESSURE INDUCED BY HYPERTONIC SALINE IN RATS SUBMITTED TO HEMORRHAGIC-SHOCK

The effect of intravenous infusion of hypertonic saline (HS, 7.5% NaCl) on the recovery of mean arteria pressure (MAP) after hemorrhage was studied in sham-operated rats and in rats with electrolytic lesion of the anteroventral third ventricle (AV3V) region (4 h, 4 and 20 days). Rats anesthetized with thiopental sodium were bled (about 2.8 ml/100 g) until the MAP was stabilized at the level of 60 mmHg for 30 min. In sham-lesioned rats, MAP increased to 90 mmHg and became stable near this level after intravenous infusion of 7.5% NaCl (4 ml/kg b.wt.). In AV3V-lesioned rats, the same infusion induced a smaller increase in MAP (80 mmHg) and the MAP returned to pre-infusion levels within 30 min. These results show that the AV3V region plays an important role in the recovery of arterial pressure induced by hypertonic saline in rats submitted to hemorrhagic shock.

Joint conomic design of (x)over-bar and R charts under Weibull shock models

This paper deals with the joint economic design of (x) over bar and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating, or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, a sensitivity analysis of the model is conducted, and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated.