3,988 research outputs found
Nonequilibrium dynamics of mixtures of active and passive colloidal particles
We develop a mesoscopic field theory for the collective nonequilibrium
dynamics of multicomponent mixtures of interacting active (i.e., motile) and
passive (i.e., nonmotile) colloidal particles with isometric shape in two
spatial dimensions. By a stability analysis of the field theory, we obtain
equations for the spinodal that describes the onset of a motility-induced
instability leading to cluster formation in such mixtures. The prediction for
the spinodal is found to be in good agreement with particle-resolved computer
simulations. Furthermore, we show that in active-passive mixtures the spinodal
instability can be of two different types. One type is associated with a
stationary bifurcation and occurs also in one-component active systems, whereas
the other type is associated with a Hopf bifurcation and can occur only in
active-passive mixtures. Remarkably, the Hopf bifurcation leads to moving
clusters. This explains recent results from simulations of active-passive
particle mixtures, where moving clusters and interfaces that are not seen in
the corresponding one-component systems have been observed.Comment: 17 pages, 3 figure
Granular Solid Hydrodynamics
Granular elasticity, an elasticity theory useful for calculating static
stress distribution in granular media, is generalized to the dynamic case by
including the plastic contribution of the strain. A complete hydrodynamic
theory is derived based on the hypothesis that granular medium turns
transiently elastic when deformed. This theory includes both the true and the
granular temperatures, and employs a free energy expression that encapsulates a
full jamming phase diagram, in the space spanned by pressure, shear stress,
density and granular temperature. For the special case of stationary granular
temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity},
a state-of-the-art engineering model.Comment: 42 pages 3 fi
Colloquium: Trapped ions as quantum bits -- essential numerical tools
Trapped, laser-cooled atoms and ions are quantum systems which can be
experimentally controlled with an as yet unmatched degree of precision. Due to
the control of the motion and the internal degrees of freedom, these quantum
systems can be adequately described by a well known Hamiltonian. In this
colloquium, we present powerful numerical tools for the optimization of the
external control of the motional and internal states of trapped neutral atoms,
explicitly applied to the case of trapped laser-cooled ions in a segmented
ion-trap. We then delve into solving inverse problems, when optimizing trapping
potentials for ions. Our presentation is complemented by a quantum mechanical
treatment of the wavepacket dynamics of a trapped ion. Efficient numerical
solvers for both time-independent and time-dependent problems are provided.
Shaping the motional wavefunctions and optimizing a quantum gate is realized by
the application of quantum optimal control techniques. The numerical methods
presented can also be used to gain an intuitive understanding of quantum
experiments with trapped ions by performing virtual simulated experiments on a
personal computer. Code and executables are supplied as supplementary online
material (http://kilian-singer.de/ent).Comment: accepted for publication in Review of Modern Physics 201
Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
The linear integral equations defining the Navier-Stokes (NS) transport
coefficients for polydisperse granular mixtures of smooth inelastic hard disks
or spheres are solved by using the leading terms in a Sonine polynomial
expansion. Explicit expressions for all the NS transport coefficients are given
in terms of the sizes, masses, compositions, density and restitution
coefficients. In addition, the cooling rate is also evaluated to first order in
the gradients. The results hold for arbitrary degree of inelasticity and are
not limited to specific values of the parameters of the mixture. Finally, a
detailed comparison between the derivation of the current theory and previous
theories for mixtures is made, with attention paid to the implication of the
various treatments employed to date.Comment: 26 pages, to be published in Phys. Rev.
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