Simulated three-component granular segregation in a rotating drum

Discrete particle simulations are used to model segregation in granular mixtures of three different particle species in a horizontal rotating drum. Axial band formation is observed, with medium-size particles tending to be located between alternating bands of big and small particles. Partial radial segregation also appears; it precedes the axial segregation and is characterized by an inner core region richer in small particles. Axial bands are seen to merge during the long simulation runs, leading to a coarsening of the band pattern; the relocation of particles involved in one such merging event is examined. Overall, the behavior is similar to experiment and represents a generalization of what occurs in the simpler two-component mixture.Comment: 7 pages, 11 figures (low resolution color figures only; originals at author's website http://www.ph.biu.ac.il/~rapaport/research/granular.html) [revised version contains extra figures

Microscale swimming: The molecular dynamics approach

The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms.Comment: 5 pages, 3 figures (minor changes to text

Molecular dynamics simulations of the evaporation of particle-laden droplets

We use molecular dynamics simulations to study the evaporation of particle-laden droplets on a heated surface. The droplets are composed of a Lennard-Jones fluid containing rigid particles which are spherical sections of an atomic lattice, and heating is controlled through the temperature of an atomistic substrate. We observe that sufficiently large (but still nano-sized) particle-laden drops exhibit contact line pinning, measure the outward fluid flow field which advects particle to the drop rim, and find that the structure of the resulting aggregate varies with inter-particle interactions. In addition, the profile of the evaporative fluid flux is measured with and without particles present, and is also found to be in qualitative agreement with earlier theory. The compatibility of simple nanoscale calculations and micron-scale experiments indicates that molecular simulation may be used to predict aggregate structure in evaporative growth processes

Self-similar measures associated to a homogeneous system of three maps

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and B\'ar\'any, K\"aenm\"aki. To overcome the difficulties stemming form these, we develop novel techniques, including an extension of Hochman's entropy increase method to a function field setup.Comment: 82 page

DAMAGES - INJUNCTION BOND - ATTORNEY\u27S FEES AS DAMAGES

Frequently, when a litigant seeks to establish rights with respect to particular property, it is possible for the opposing party so to act with respect to the property involved, while litigation is pending, as to deprive the plaintiff of the substantial benefit of his remedy should he prevail. Consequently, on prima facie showing of right, courts of equity will grant a temporary injunction to freeze the situation until the rights of the parties are finally determined. Since the temporary injunction is issued without a final determination of the rights of the parties, the enjoined party is deprived of dominion over the subject matter before it is finally decided that dominion is not rightfully his. Therefore, should he ultimately prevail in the action, he is deprived of whatever benefits he might have gained through the exercise of his rights in connection with the subject matter during the interim between the issuance of the temporary injunction and the final hearing. Courts of equity, recognizing this source of hardship, have required as a condition precedent to the issuance of a temporary injunction that the plaintiff execute a bond conditioned on payment of all damages the defendant might sustain by reason of the temporary injunction, should it be finally determined that such injunction ought not to have been issued. In an action on the injunction bond, it is obvious that such injuries as are occasioned by defendant\u27s being deprived of dominion over the property are compensable. However, a more difficult problem is put to the court when it must decide whether attorney fees incurred for procuring dissolution of the temporary injunction are similarly within the condition of the bond. It is with this latter problem that this comment is concerned

The influence of bond-rigidity and cluster diffusion on the self-diffusion of hard spheres with square-well interaction

Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength

Electrostatic traps for dipolar excitons

We consider the design of two-dimensional electrostatic traps for dipolar indirect excitons. We show that the excitons dipole-dipole interaction, combined with the in-plane electric fields that arise due to the trap geometry, constrain the maximal density and lifetime of trapped excitons. We derive an analytic estimate of these values and determine their dependence on the trap geometry, thus suggesting the optimal design for high density trapping as a route for observing excitonic Bose-Einstein condensation.Comment: 5 pages, 3 figures. This 2nd version contains a revised Fig.3 + minor revisions to the discussion and abstrac