Force-versus-time curves during collisions between two identical steel balls

We describe a numerical procedure for plotting the force-versus-time curves in elastic collisions between identical conducting balls. A system of parametric equations relating the force and the time to a dimensionless parameter is derived from the assumption of a force compatible with Hertz's theory of collision. A simple experimental arrangement consisting of a mechanical system of colliding balls and an electrical circuit containing a crystal oscillator and an electronic counter is used to measure the collision time as a function of the energy of impact. From the data we can determine the relevant parameters. The calculated results agree very well with the expected values and are consistent with the assumption that the collisions are elastic. (C) 2006 American Association of Physics Teachers.

Usando um voltímetro para medir tempo

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

The thermohydrodynamical picture of a charged Brownian particle

We study a charged Brownian gas with a non uniform bath temperature, and present a thermohydrodynamical picture. Expansion on the collision time probes the validity of the local equilibrium approach and the relevant thermodynamical variables. For the linear regime we present several applications (some novel).

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

Portadores quentes: modelo browniano

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Advantages of using nested collision induced dissociation/post-source decay with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry: sequencing of novel peptides from wasp venom

We have examined the applicability of the 'nested' collision induced dissociation/post-source decay (CID/PSD) method to the sequencing of novel peptides from solitary wasps which have neurotoxic venom for paralyzing other insects. The CID/PSD spectrum of a ladder peptide derived from an exopeptidase digest was compared with that of the intact peptide. The mass peaks observed only in the CID/PSD spectrum of a ladder peptide were extracted as C-terminal fragment ions. Assignment of C-terminal fragment ions enabled calculation of N-terminal fragment masses, leading to differentiation between N-terminal fragment ions and internal fragment ions. This methodology allowed rapid and sensitive identification by removing ambiguity in the assignment of the fragment ions, and proved useful for sequencing unknown peptides, in particular those available as natural products with a limited supply. Copyright (C) 2000 John Wiley & Sons, Ltd.

SPH simulations of clumps formation by dissipative collision of molecular clouds - I. Non magnetic case

Computer experiments of interstellar cloud collisions were performed with a new smoothed-particle-hydrodynamics (SPH) code. The SPH quantities were calculated by using spatially adaptive smoothing lengths and the SPH fluid equations of motion were solved by means of a hierarchical multiple time-scale leapfrog. Such a combination of methods allows the code to deal with a large range of hydrodynamic quantities. A careful treatment of gas cooling by H, H(2), CO and H II, as well as a heating mechanism by cosmic rays and by H(2) production on grains surface, were also included in the code. The gas model reproduces approximately the typical environment of dark molecular clouds. The experiments were performed by impinging two dynamically identical spherical clouds onto each other with a relative velocity of 10 km s(-1) but with a different impact parameter for each case. Each object has an initial density profile obeying an r(-1)-law with a cutoff radius of 10 pc and with an initial temperature of 20 K. As a main result, cloud-cloud collision triggers fragmentation but in expense of a large amount of energy dissipated, which occurred in the head-on case only. Off-center collision did not allow remnants to fragment along the considered time (similar to 6 Myr). However, it dissipated a considerable amount of orbital energy. Structures as small as 0.1 pc, with densities of similar to 10(4) cm(-3), were observed in the more energetic collision.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.