2,897 research outputs found
Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?
We investigate shear-induced crystallization in a very dense flow of
mono-disperse inelastic hard spheres. We consider a steady plane Couette flow
under constant pressure and neglect gravity. We assume that the granular
density is greater than the melting point of the equilibrium phase diagram of
elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive
relations all of which (except the shear viscosity) diverge at the crystal
packing density, while the shear viscosity diverges at a smaller density. The
phase diagram of the steady flow is described by three parameters: an effective
Mach number, a scaled energy loss parameter, and an integer number m: the
number of half-oscillations in a mechanical analogy that appears in this
problem. In a steady shear flow the viscous heating is balanced by energy
dissipation via inelastic collisions. This balance can have different forms,
producing either a uniform shear flow or a variety of more complicated,
nonlinear density, velocity and temperature profiles. In particular, the model
predicts a variety of multi-layer two-phase steady shear flows with sharp
interphase boundaries. Such a flow may include a few zero-shear (solid-like)
layers, each of which moving as a whole, separated by fluid-like regions. As we
are dealing with a hard sphere model, the granulate is fluidized within the
"solid" layers: the granular temperature is non-zero there, and there is energy
flow through the boundaries of the "solid" layers. A linear stability analysis
of the uniform steady shear flow is performed, and a plausible bifurcation
diagram of the system, for a fixed m, is suggested. The problem of selection of
m remains open.Comment: 11 pages, 7 eps figures, to appear in PR
Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
We present new singular solutions of the biharmonic nonlinear Schrodinger
equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions
collapse with the quasi self-similar ring profile, with ring width L(t) that
vanishes at singularity, and radius proportional to L^\alpha, where
\alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is
1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4.
These solutions are analogous to the ring-type solutions of the nonlinear
Schrodinger equation.Comment: 21 pages, 13 figures, research articl
Strong contraction of the representations of the three dimensional Lie algebras
For any Inonu-Wigner contraction of a three dimensional Lie algebra we
construct the corresponding contractions of representations. Our method is
quite canonical in the sense that in all cases we deal with realizations of the
representations on some spaces of functions; we contract the differential
operators on those spaces along with the representation spaces themselves by
taking certain pointwise limit of functions. We call such contractions strong
contractions. We show that this pointwise limit gives rise to a direct limit
space. Many of these contractions are new and in other examples we give a
different proof
Whatever did happen at Jaggersfontein? Or diamonds are forever - but gold is for now!
Paper presented at the Wits History Workshop: The Making of Class, 9-14 February, 198
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
Closed-Orbit Theory of Oscillations in Atomic Photoabsorption Cross Sections in a Strongelectric Field. I. Comparison Between Theory and Experiments on Hydrogen and Sodium Above Threshold
Using a simple analytic formula from closed-orbit theory, we calculate photoabsorption cross sections of hydrogen and sodium in a strong electric field. The theoretical spectra show good agreement with experimental results. A scaled variable measurement is also suggested
Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations
The position of a reaction front, propagating into a metastable state,
fluctuates because of the shot noise of reactions and diffusion. A recent
theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147
(2011)] gave a closed analytic expression for the front diffusion coefficient
in the weak noise limit. Here we test this theory in stochastic simulations
involving reacting and diffusing particles on a one-dimensional lattice. We
also investigate a small noise-induced systematic shift of the front velocity
compared to the prediction from the spatially continuous deterministic
reaction-diffusion equation.Comment: 5 pages, 5 figure
Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell
We investigate quasi-two-dimensional relaxation, by surface tension, of a
long straight stripe of inviscid fluid trapped inside a viscous fluid in a
Hele-Shaw cell. Combining analytical and numerical solutions, we describe the
emergence of a self-similar dumbbell shape and find non-trivial dynamic
exponents that characterize scaling behavior of the dumbbell dimensions.Comment: 4 pages, 5 figures, to appear in PR
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