Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Dynamics of convectively driven banded jets in the laboratory

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

Observations of the depth of ice particle evaporation beneath frontal cloud to improve NWP modelling

The evaporation (sublimation) of ice particles beneath frontal ice cloud can provide a significant source of diabatic cooling which can lead to enhanced slantwise descent below the frontal surface. The strength and vertical extent of the cooling play a role in determining the dynamic response of the atmosphere, and an adequate representation is required in numerical weather-prediction (NWP) models for accurate forecasts of frontal dynamics. In this paper, data from a vertically pointing 94 GHz radar are used to determine the characteristic depth-scale of ice particle sublimation beneath frontal ice cloud. A statistical comparison is made with equivalent data extracted from the NWP mesoscale model operational at the Met Office, defining the evaporation depth-scale as the distance for the ice water content to fall to 10% of its peak value in the cloud. The results show that the depth of the ice evaporation zone derived from observations is less than 1 km for 90% of the time. The model significantly overestimates the sublimation depth-scales by a factor of between two and three, and underestimates the local ice water content by a factor of between two and four. Consequently the results suggest the model significantly underestimates the strength of the evaporative cooling, with implications for the prediction of frontal dynamics. A number of reasons for the model discrepancy are suggested. A comparison with radiosonde relative humidity data suggests part of the overestimation in evaporation depth may be due to a high RH bias in the dry slot beneath the frontal cloud, but other possible reasons include poor vertical resolution and deficiencies in the evaporation rate or ice particle fall-speed parametrizations.

Remarkable dynamics of nanoparticles in the urban atmosphere

Nanoparticles emitted from road traffic are the largest source of respiratory exposure for the general public living in urban areas. It has been suggested that the adverse health effects of airborne particles may scale with the airborne particle number, which if correct, focuses attention on the nanoparticle (less than 100 nm) size range which dominates the number count in urban areas. Urban measurements of particle size distributions have tended to show a broadly similar pattern dominated by a mode centred on 20–30 nm diameter particles emitted by diesel engine exhaust. In this paper we report the results of measurements of particle number concentration and size distribution made in a major London park as well as on the BT Tower, 160 m high. These measurements taken during the REPARTEE project (Regents Park and BT Tower experiment) show a remarkable shift in particle size distributions with major losses of the smallest particle class as particles are advected away from the traffic source. In the Park, the traffic related mode at 20–30 nm diameter is much reduced with a new mode at <10 nm. Size distribution measurements also revealed higher number concentrations of sub-50 nm particles at the BT Tower during days affected by higher turbulence as determined by Doppler Lidar measurements and indicate a loss of nanoparticles from air aged during less turbulent conditions. These results suggest that nanoparticles are lost by evaporation, rather than coagulation processes. The results have major implications for understanding the impacts of traffic-generated particulate matter on human health.

Remarkable dynamics of nanoparticles in the urban atmosphere

Nanoparticles emitted from road traffic are the largest source of respiratory exposure for the general public living in urban areas. It has been suggested that adverse health effects of airborne particles may scale with airborne particle number, which if correct, focuses attention on the nanoparticle (less than 100 nm) size range which dominates the number count in urban areas. Urban measurements of particle size distributions have tended to show a broadly similar pattern dominated by a mode centred on 20–30 nm diameter emitted by diesel engine exhaust. In this paper we report the results of measurements of particle number concentration and size distribution made in a major London park as well as on the BT Tower, 160 m aloft. These measurements taken during the REPARTEE project (Regents Park and BT Tower experiment) show a remarkable shift in particle size distributions with major losses of the smallest particle class as particles are advected away from the traffic source. In the Park, the traffic related mode at 20–30 nm diameter is much reduced with a new mode at <10 nm. Size distribution measurements also revealed higher number concentrations of sub-50 nm particles at the BT Tower during days affected by higher turbulence as determined by Doppler Lidar measurements and are indicative of loss of nanoparticles from air aged during less turbulent conditions. These results are suggestive of nanoparticle loss by evaporation, rather than coagulation processes. The results have major implications for understanding the impacts of traffic-generated particulate matter on human health.

TNF-α influences the lateral dynamics of TNF receptor I in living cells

In mammalian cells, inflammation is mainly mediated by the binding of tumor necrosis factor alpha to tumor necrosis factor receptor 1. In this study, we investigated lateral dynamics of TNF-R1 before and after ligand binding using high-density single-particle tracking in combination with photoactivated localization microscopy. Our single-molecule data indicates the presence of tumor necrosis factor receptor 1 with different mobilities in the plasma membrane, suggesting different molecular organizations. Cholesterol depletion led to a decrease of slow receptor species and a strong increase in the average diffusion coefficient. Moreover, as a consequence of tumor necrosis factor-alpha treatment, the mean diffusion coefficient moderately increased while its distribution narrowed. Based on our observation, we propose a refined mechanism on the structural arrangement and activation of tumor necrosis factor receptor 1 in the plasma membrane.

Dynamical properties for the problem of a particle in an electric field of wave packet: Low velocity and relativistic approach

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

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.

Dynamics of hypernuclear nonmesonic weak decay

Simple and coincidence spectra of the NM weak decay of light hypernuclei have been evaluated in a systematic way for the first time. We have only considered 1N induced processes, neglecting entirely the events induced by 2N emission, as well as the effects of the FSIt's. As the theoretical frameworkwe have used the IPSM with three different parametrizations for the transition potential. The comparison with data strongly suggests that the soft π + K exchange model could be a good starting point to describe the dynamics in the NM weak decays of s- and p-shell hypernuclei. © 2012 American Institute of Physics.

Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

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

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.