429 research outputs found
Electrification in granular gases leads to constrained fractal growth
The empirical observation of aggregation of dielectric particles under the
influence of electrostatic forces lies at the origin of the theory of
electricity. The growth of clusters formed of small grains underpins a range of
phenomena from the early stages of planetesimal formation to aerosols. However,
the collective effects of Coulomb forces on the nonequilibrium dynamics and
aggregation process in a granular gas -- a model representative of the above
physical processes -- have so far evaded theoretical scrutiny. Here, we
establish a hydrodynamic description of aggregating granular gases that
exchange charges upon collisions and interact via the long-ranged Coulomb
forces. We analytically derive the governing equations for the evolution of
granular temperature, charge variance, and number density for homogeneous and
quasi-monodisperse aggregation. We find that, once the aggregates are formed,
the system obeys a physical constraint of nearly constant dimensionless ratio
of characteristic electrostatic to kinetic energy . This
constraint on the collective evolution of charged clusters is confirmed both by
the theory and the detailed molecular dynamics simulations. The inhomogeneous
aggregation of monomers and clusters in their mutual electrostatic field
proceeds in a fractal manner. Our theoretical framework is extendable to more
precise charge exchange mechanism, a current focus of extensive
experimentation. Furthermore, it illustrates the collective role of long-ranged
interactions in dissipative gases and can lead to novel designing principles in
particulate systems
Stochastic Rotation Dynamics for Nematic Liquid Crystals
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We
extend the particle-based stochastic rotation dynamics method, which reproduces
the Navier-Stokes equation, to anisotropic fluids by including a simplified
Ericksen-Leslie formulation of nematodynamics. We verify the applicability of
this hybrid model by studying the equilibrium isotropic-nematic phase
transition and nonequilibrium problems, such as the dynamics of topological
defects, and the rheology of sheared LCs. Our simulation results show that this
hybrid model captures many essential aspects of LC physics at the mesoscopic
scale, while preserving microscopic thermal fluctuations
A universal scaling law for the evolution of granular gases
Dry, freely evolving granular materials in a dilute gaseous state coalesce
into dense clusters only due to dissipative interactions. This clustering
transition is important for a number of problems ranging from geophysics to
cosmology. Here we show that the evolution of a dilute, freely cooling granular
gas is determined in a universal way by the ratio of inertial flow and thermal
velocities, that is, the Mach number. Theoretical calculations and direct
numerical simulations of the granular Navier--Stokes equations show that
irrespective of the coefficient of restitution, density or initial velocity
distribution, the density fluctuations follow a universal quadratic dependence
on the system's Mach number. We find that the clustering exhibits a scale-free
dynamics but the clustered state becomes observable when the Mach number is
approximately of . Our results provide a method to determine
the age of a granular gas and predict the macroscopic appearance of clusters
Multiparticle Collision Dynamics for Tensorial Nematodynamics
Liquid crystals establish a nearly unique combination of thermodynamic,
hydrodynamic, and topological behavior. This poses a challenge to their
theoretical understanding and modeling. The arena where these effects come
together is the mesoscopic (micron) scale. It is then important to develop
models aimed at capturing this variety of dynamics. We have generalized the
particle-based multiparticle collision dynamics (MPCD) method to model the
dynamics of nematic liquid crystals. Following the Qian--Sheng theory of
nematics, the spatial and temporal variations of the nematic director field and
order parameter are described by a tensor order parameter. The key idea is to
assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic
average is the tensor order parameter. This new nematic-MPCD method includes
backflow effect, velocity-orientation coupling and thermal fluctuations. We
validate the applicability of this method by testing: (i) the nematic-isotropic
phase transition, (ii) the flow alignment of the director in shear and
Poiseuille flows, and (iii) the annihilation dynamics of a pair of line
defects. We find excellent agreement with existing literature. We also
investigate the flow field around a force dipole in a nematic liquid crystal,
which represents the leading-order flow field around a force-free microswimmer.
The anisotropy of the medium not only affects the magnitude of velocity field
around the force dipole, but can also induce hydrodynamic torques depending on
the orientation of dipole axis relative to director field. A force dipole
experiences a hydrodynamic torque when the dipole axis is tilted with respect
to the far-field director. The direction of hydrodynamic toque is such that the
pusher- (or puller-) type force dipole tends to orient along (or perpendicular
to) the director field
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