Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

We perform molecular dynamics simulations of model granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time $t_l$ required for the velocity profiles to become linear and find that $t_l$ increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.Comment: 11 pages, 14 figure

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

A Model for the Moving `Wisps' in the Crab Nebula

I propose that the moving `wisps' near the center of the Crab Nebula result from nonlinear Kelvin-Helmholtz instabilities in the equatorial plane of the shocked pulsar wind. Recent observations suggest that the wisps trace out circular wavefronts in this plane, expanding radially at speeds approximately less than c/3. Instabilities could develop if there is sufficient velocity shear between a faster-moving equatorial zone and a slower moving shocked pulsar wind at higher latitudes. The development of shear could be related to the existence of a neutral sheet -- with weak magnetic field -- in the equatorial zone, and could also be related to a recent suggestion by Begelman that the magnetic field in the Crab pulsar wind is much stronger than had been thought. I show that plausible conditions could lead to the growth of instabilities at the radii and speeds observed, and that their nonlinear development could lead to the appearance of sharp wisplike features.Comment: 7 pages; 3 postscript figures; LaTex, uses emulateapj.sty; to Appear in the Astrophysical Journal, Feb. 20, 1999, Vol. 51

An Information Model for Geographic Greedy Forwarding in Wireless Ad-Hoc Sensor Networks

In wireless ad-hoc sensor networks, an important issue often faced in geographic greedy forwarding routing is the "local minimum phenomenon" which is caused by deployment holes and blocks the forwarding process. In this paper, we provide a new information model for the geographic greedy forwarding routing that only forwards the packet within the so-called request zone. Under this new information model, the hole and its affected area are identified easily and quickly in an unsafe area with a labeling process. The greedy forwarding will be blocked if and only if a node inside the unsafe area is used. Due to the shape of the request zone, an unsafe area can be estimated as a rectangular region in the local view of unsafe nodes. With such estimate information, the new routing method proposed in this paper will avoid blocking by holes and achieve better performance in routing time while the cost of information construction is greatly reduced compared with the best results known to date.Department of ComputingRefereed conference pape

Variational ground states of 2D antiferromagnets in the valence bond basis

We study a variational wave function for the ground state of the two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h(x,y) for valence bonds connecting spins separated by (x,y) lattice spacings. In contrast to previous studies, in which a functional form for h(x,y) was assumed, we here optimize all the amplitudes for lattices with up to 32*32 spins. We use two different schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a stochastic method which requires only the signs of the first derivatives of the energy. The latter method performs significantly better. The energy for large systems deviates by only approx. 0.06% from its exact value (calculated using unbiased quantum Monte Carlo simulations). The spin correlations are also well reproduced, falling approx. 2% below the exact ones at long distances. The amplitudes h(r) for valence bonds of long length r decay as 1/r^3. We also discuss some results for small frustrated lattices.Comment: v2: 8 pages, 5 figures, significantly expanded, new optimization method, improved result

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Note on the hydrodynamic description of thin nematic films: strong anchoring model

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion

From nothing to something: discrete integrable systems

Chinese ancient sage Laozi said that everything comes from `nothing'. Einstein believes the principle of nature is simple. Quantum physics proves that the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to deriving a number of discrete models, including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP, and special Viallet equations, from `nothing' via simple principles. It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra, model-independent nonlinear superpositions of a trivial integrable system (Riccati equation), index homogeneous decompositions of the simplest geometric theorem (the angle bisector theorem), as well as the M\"obious transformation invariants.Comment: 11 pages, side 10 repor

MHD tidal waves on a spinning magnetic compact star

In an X-ray binary system, the companion star feeds the compact neutron star with plasma materials via accretions. The spinning neutron star is likely covered with a thin "magnetized ocean" and may support {\it magnetohydrodynamic (MHD) tidal waves}. While modulating the thermal properties of the ocean, MHD tidal waves periodically shake the base of the stellar magnetosphere that traps energetic particles, including radiating relativistic electrons. For a radio pulsar, MHD tidal waves in the stellar surface layer may modulate radio emission processes and leave indelible signatures on timescales different from the spin period. Accretion activities are capable of exciting these waves but may also obstruct or obscure their detections meanwhile. Under fortuitous conditions, MHD tidal waves might be detectable and offer valuable means to probe properties of the underlying neutron star. Similar situations may also occur for a cataclysmic variable -- an accretion binary system that contains a rotating magnetic white dwarf. This Letter presents the theory for MHD tidal waves in the magnetized ocean of a rotating degenerate star and emphasizes their potential diagnostics in X-ray and radio emissions.Comment: ApJ Letter paper already publishe

Interference-free wakeup scheduling with consecutive constraints in wireless sensor networks

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe