Showing 51 - 60 of 94 Items
Equivalence classes in the Weyl groups of type Bn
Date: 2008-04-01
Creator: Thomas Pietraho
Access: Open access
- We consider two families of equivalence classes in the Weyl groups of type B n which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by a non-negative integer r. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra when r=0; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters when r is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure of left cells for remaining choices of the Iwahori-Hecke algebra parameters. © 2007 Springer Science+Business Media, LLC.
Higher rank lamplighter groups are graph automatic
Date: 2018-02-15
Creator: Sophie Bérubé, Tara Palnitkar, Jennifer Taback
Access: Open access
- We show that the higher rank lamplighter groups, or Diestel–Leader groups Γd(q) for d≥3, are graph automatic. This introduces a new family of graph automatic groups which are not automatic.
Knuth relations for the hyperoctahedral groups
Date: 2009-06-01
Creator: Thomas Pietraho
Access: Open access
- C. Bonnafé, M. Geck, L. Iancu, and T. Lam have conjectured a description of Kazhdan-Lusztig cells in unequal parameter Hecke algebras of type B which is based on domino tableaux of arbitrary rank. In the integer case, this generalizes the work of D. Garfinkle. We adapt her methods and construct a family of operators which generate the equivalence classes on pairs of arbitrary rank domino tableaux described in the above conjecture. © 2008 Springer Science+Business Media, LLC.
Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
Date: 2009-01-15
Creator: C. Chong, R. Carretero-González, B. A. Malomed, P. G. Kevrekidis
Access: Open access
- We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss. © 2008 Elsevier B.V. All rights reserved.
Traveling waves in 2D hexagonal granular crystal lattices
Date: 2014-01-01
Creator: A. Leonard, C. Chong, P. G. Kevrekidis, C. Daraio
Access: Open access
- This study describes the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. The dynamics of the system are modeled using the Hertzian normal contact law. After the initial impact strikes the system, a characteristic wave structure emerges and continuously decays as it propagates through the lattice. Using an extension of the binary collision approximation for one-dimensional chains, we predict its decay rate, which compares well with numerical simulations and experimental data. While the hexagonal lattice does not support constant speed traveling waves, we provide scaling relations that characterize the directional power law decay of the wave velocity for various angles of impact. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates. © 2014 The Author(s).
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
Date: 2016-01-25
Creator: C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi Ping Ma
Access: Open access
- Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. The transition between these two types of propagation is explored.
Tempered, invariant, positive-definite distributions on SU(1, 1)/{± 1}
Date: 1984-01-01
Creator: William H. Barker
Access: Open access
An alternative almost sure construction of Gaussian stochastic processes in the L2([0,1]) space
Date: 2019-05-01
Creator: Kevin Chen
Access: Open access
Metric properties of diestel-leader groups
Date: 2013-06-01
Creator: Melanie Stein, Jennifer Taback
Access: Open access
Thompson's group F is not almost convex
Date: 2003-12-01
Creator: Sean Cleary, Jennifer Taback
Access: Open access
- We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any positive integer n with respect to the standard generating set with two elements. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our techniques rely upon Fordham's method for calculating the length of a word in F and upon an analysis of the generators' geometric actions on the tree pair diagrams representing elements of F. © 2003 Elsevier Inc. All rights reserved.