Microscopic dissipation in a cohesionless granular jet impact

Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. We investigate the continuum limit of an unconfined, dense granular flow. To do this we use as a test system a two-dimensional dense cohesionless granular jet impinging upon a target. We simulate this via a timestep driven hard sphere method, and apply a mean-field theoretical approach to connect the macroscopic flow with the microscopic material parameters of the grains. We observe that the flow separates into a cone with an interior cone angle determined by the conservation of momentum and the dissipation of energy. From the cone angle we extract a dimensionless quantity $A-B$ that characterizes the flow. We find that this quantity depends both on whether or not a deadzone --- a stationary region near the target --- is present, and on the value of the coefficient of dynamic friction. We present a theory for the scaling of $A-B$ with the coefficient of friction that suggests that dissipation is primarily a perturbative effect in this flow, rather than the source of qualitatively different behavior.Comment: 9 pages, 11 figure

Combinatorial Topology Of Multipartite Entangled States

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separability polytopes for 3-partite systems are explicitly provided. It turns out that this characterisation of entanglement is associated with simulation of arbitrary unitary operations by 1- and 2-qubit gates. A topological description of how entanglement changes in course of such simulation is provided.Comment: 14 pages, LaTeX2e. Slightly revised version of the poster resented on the International Conference on Quantum Information, Oviedo, Spain, 13-18 July, 2002. To appear in the special issue of Journal of Modern Optic

Inductive Algebras for Finite Heisenberg Groups

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.Comment: 5 page

Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene

We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a \pi -band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiments. Furthermore, we argue that the expressions obtained can be useful in the analysis of future measurements of cyclotron resonance of electrons and holes in trilayer graphene.Comment: 10 pages, 8 figure

Classification of finite congruence-simple semirings with zero

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We also investigate those subsemirings further, addressing e.g. the question of isomorphy.Comment: 16 page

Phase Diagrams for Sonoluminescing Bubbles

Sound driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL. We present phase diagrams in the gas concentration vs forcing pressure state space and also in the ambient radius vs gas concentration and vs forcing pressure state spaces. These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude $P_a \sim 1.2 - 1.5$atm and low gas concentration of less than $0.4\%$ of the saturation. The upper concentration threshold becomes smaller with increasing forcing. Our results quantitatively agree with experimental results of Putterman's UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered. -- All statements are based on the Rayleigh-Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects. This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive. Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusion PDE and find good agreement.Comment: Phys. Fluids, in press; latex; 46 pages, 16 eps-figures, small figures tarred and gzipped and uuencoded; large ones replaced by dummies; full version can by obtained from: http://staff-www.uni-marburg.de/~lohse

Families of Graphs With Chromatic Zeros Lying on Circles

We define an infinite set of families of graphs, which we call $p$-wheels and denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$) graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at $q=0,1,...p+1$ for $n-p$ even and $q=0,1,...p+2$ for $n-p$ odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle $|q-(p+1)|=1$ in the complex $q$ plane. In the $n \to \infty$ limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function $W(\{(Wh)^{(p)}\},q)$ is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late

The Gravitational Horizon for a Universe with Phantom Energy

The Universe has a gravitational horizon, coincident with the Hubble sphere, that plays an important role in how we interpret the cosmological data. Recently, however, its significance as a true horizon has been called into question, even for cosmologies with an equation-of-state w = p/rho > -1, where p and rho are the total pressure and energy density, respectively. The claim behind this argument is that its radius R_h does not constitute a limit to our observability when the Universe contains phantom energy, i.e., when w < -1, as if somehow that mitigates the relevance of R_h to the observations when w > -1. In this paper, we reaffirm the role of R_h as the limit to how far we can see sources in the cosmos, regardless of the Universe's equation of state, and point out that claims to the contrary are simply based on an improper interpretation of the null geodesics.Comment: 9 pages, 1 figure. Slight revisions in refereed version. Accepted for publication in JCAP. arXiv admin note: text overlap with arXiv:1112.477