Time scale analysis for fluidized bed melt granulation I: granule-granule and granule-droplet collision rates

Fluidized bed spray granulators (FBMG) are widely used in the process industry for particle size growth; a desirable feature in many products, such as granulated food and medical tablets. In this paper, the first in a series of four discussing the rate of various microscopic events occurring in FBMG, theoretical analysis coupled with CFD simulations have been used to predict granule–granule and droplet–granule collision time scales. The granule–granule collision time scale was derived from principles of kinetic theory of granular flow (KTGF). For the droplet–granule collisions, two limiting models were derived; one is for the case of fast droplet velocity, where the granule velocity is considerable lower than that of the droplet (ballistic model) and another for the case where the droplet is traveling with a velocity similar to the velocity of the granules. The hydrodynamic parameters used in the solution of the above models were obtained from the CFD predictions for a typical spray fluidized bed system. The granule–granule collision rate within an identified spray zone was found to fall approximately within the range of 10-2–10-3 s, while the droplet–granule collision was found to be much faster, however, slowing rapidly (exponentially) when moving away from the spray nozzle tip. Such information, together with the time scale analysis of droplet solidification and spreading, discussed in part II and III of this study, are useful for probability analysis of the various event occurring during a granulation process, which then lead to be better qualitative and, in part IV, quantitative prediction of the aggregation rate.

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.

Proactive safety assessment in roadwork zones : a synthesis of surrogate measures of safety

Work zone safety studies have traditionally relied on historical crash records—an approach which is reactive in nature as it requires crashes to accumulate first before taking any preventive actions. However, detailed and accurate data on work zone crashes are often not available, as is the case for Australian road work zones. The lack of reliable safety records and the reactive nature of the crash-based safety analysis approach motivated this research to seek alternative and proactive measures of safety. Various surrogate measures of safety have been developed in the traffic safety literature including time to collision, time to accident, gap time, post encroachment time, required deceleration rate, proportion of stopping distances, lateral distance to departure, and time to departure. These measures express how close road-user(s) are from a potential crash by analysing their movement trajectories. A review of this fast-growing literature is presented in this paper from the viewpoint of applying the measures to untangle work zone safety issues. The review revealed that the use of the surrogate measures is very limited for analysing work zone safety, although numerous studies have used these measures for analysing safety in other parts of the road network, such as intersections and motorway ramps. There exist great opportunities for adopting this proactive safety assessment approach to transform work zone safety for both roadworkers and motorists.

Monte Carlo simulation of cooling induced by parametric resonance

We demonstrate that the parametric resonance in a magnetic quadrupole trap can be exploited to cool atoms by using Bird's method. In our programme the parametric resonance was realized by anisotropically modulating the trap potential. The modulation frequency dependences of temperature and fraction of the trapped atoms are explored. Furthermore, the temperature after the modulation as functions of the modulation amplitude and the mean elastic collision time are also studied. These results are valuable for the experiment of parametric resonance in a quadrupole trap.

Nuclear stopping and compression in heavy-ion collisions at intermediate energies

The nuclear stopping and the radial flow are investigated with an isospin-dependent quantum molecular dynamics (IQMD) model for Ni + Ni and Pb + Pb from 0.4 to and 1.2 GeV/u. The expansion velocity as well as the degree of nuclear stopping are higher in the heavier system at all energies. The ratio between the flow energy and the total available energy in center of mass of the colliding systems exhibits a positive correlation to the degree of nuclear stopping. The maximum density (rho(max)) achieved in the compression is comparable to the hydrodynamics prediction only if the non-zero collision time effect is taken into account in the later. Due to the partial transparency, the growing of the maximum density achieved in the central region of the fireball with the increase of beam energy becomes gradually flat in the 1 GeV/u energy regime. (C) 2008 Elsevier B.V. All rights reserved.

Modeling relativistic soliton interactions in overdense plasmas: A perturbed nonlinear Schrodinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrodinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrodinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

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)

Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Using time-to-contact information to assess potential collision modulates both visual and temporal prediction networks

Accurate estimates of the time-to-contact (TTC) of approaching objects are crucial for survival. We used an ecologically valid driving simulation to compare and contrast the neural substrates of egocentric (head-on approach) and allocentric (lateral approach) TTC tasks in a fully factorial, event-related fMRI design. Compared to colour control tasks, both egocentric and allocentric TTC tasks activated left ventral premotor cortex/frontal operculum and inferior parietal cortex, the same areas that have previously been implicated in temporal attentional orienting. Despite differences in visual and cognitive demands, both TTC and temporal orienting paradigms encourage the use of temporally predictive information to guide behaviour, suggesting these areas may form a core network for temporal prediction. We also demonstrated that the temporal derivative of the perceptual index tau (tau-dot) held predictive value for making collision judgements and varied inversely with activity in primary visual cortex (V1). Specifically, V1 activity increased with the increasing likelihood of reporting a collision, suggesting top-down attentional modulation of early visual processing areas as a function of subjective collision. Finally, egocentric viewpoints provoked a response bias for reporting collisions, rather than no-collisions, reflecting increased caution for head-on approaches. Associated increases in SMA activity suggest motor preparation mechanisms were engaged, despite the perceptual nature of the task.

The time-dependent close-coupling method for atomic and molecular collision processes

We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

Perceiving time to collision activates the sensorimotor cortex

The survival of many animals hinges upon their ability to avoid collisions with other animals or objects or to precisely control the timing of collisions. Optical expansion provides a compelling impression of object approach and in principle can provide the basis for judgments of time to collision (TTC) [1]. It has been demonstrated that pigeons [2] and houseflies [3] have neural systems that can initiate rapid coordinated actions on the basis of optical expansion. In the case of humans, the linkage between judgments of TTC and coordinated action has not been established at a cortical level. Using functional magnetic resonance imaging (fMRI), we identified superior-parietal and motor-cortex areas that are selectively active during perceptual TTC judgments, some of which are normally involved in producing reach-to-grasp responses. These activations could not be attributed to actual movement of participants. We demonstrate that networks involved in the computational problem of extracting TTC from expansion information have close correspondence with the sensorimotor systems that would be involved in preparing a timed motor response, such as catching a ball or avoiding collision.