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Full-Text Articles in Physical Sciences and Mathematics
A Discrete Nonlinear Model With Substrate Feedback, Panos Kevrekidis, B. A. Malomed, A. R. Bishop
A Discrete Nonlinear Model With Substrate Feedback, Panos Kevrekidis, B. A. Malomed, A. R. Bishop
Panos Kevrekidis
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial …
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Mathematics and Statistics Department Faculty Publication Series
In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions of Weyl’s dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan–Lusztig cells.
On The Minimum Ropelength Of Knots And Links, Jason Cantarella, Robert B. Kusner, John M. Sullivan
On The Minimum Ropelength Of Knots And Links, Jason Cantarella, Robert B. Kusner, John M. Sullivan
Robert Kusner
The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C 1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Mathematics and Statistics Department Faculty Publication Series
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one. The model with the static defect directly applies to an optical pulse in a long fiber link with an inserted additional section of a nonlinear fiber. A local breather which gives rise to the nonlinear defect affecting the propagation of a narrow optical pulse is possible in a molecular chain. In the case when the host waveguide is linear, the pulse has a Gaussian shape. In that case, an immediate result of …
On Thickness And Packing Density For Knots And Links, Robert Kusner
On Thickness And Packing Density For Knots And Links, Robert Kusner
Robert Kusner
We describe some problems, observations, and conjectures concerning density of the hexagonal packing of unit disks in R2.thickness and packing density of knots and links in S3 and R3. We prove the thickness of a nontrivial knot or link in S3 is no more than 4 , the thickness of a Hopf link. We also give arguments and evidence supporting the conjecture that the packing density of thick links in R3 or S3 is generally less than √12 , the density of the hexagonal packing of unit disks in R2.
Discrete Nonlinear Model With Substrate Feedback, P. G. Kevrekidis, B. A. Malomed, A. R. Bishop
Discrete Nonlinear Model With Substrate Feedback, P. G. Kevrekidis, B. A. Malomed, A. R. Bishop
Panos Kevrekidis
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial …
On The Reducibility Of Characteristic Varieties, Tom Braden
On The Reducibility Of Characteristic Varieties, Tom Braden
Tom Braden
We show that some monodromies in the Morse local systems of a conically stratified perverse sheaf imply that other Morse local systems for smaller strata do not vanish. This result is then used to explain the examples of reducible characteristic varieties of Schubert varieties given by Kashiwara and Saito in type A and by Boe and Fu for the Lagrangian Grassmannian.
A Smooth Space Of Tetrahedra, E Babson, Pe Gunnells, R Scott
A Smooth Space Of Tetrahedra, E Babson, Pe Gunnells, R Scott
Paul Gunnells
This is the pre-published version harvested from ArXiv. We construct a smooth symmetric compactification of the space of all labeled tetrahedra in 3.
Nonequivalent Statistical Equilibrium Ensembles And Refined Stability Theorems For Most Probable Flows, Richard S. Ellis, Kyle Haven, Bruce Turkington
Nonequivalent Statistical Equilibrium Ensembles And Refined Stability Theorems For Most Probable Flows, Richard S. Ellis, Kyle Haven, Bruce Turkington
Richard S. Ellis
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is investigated for these models. The main results show that models in which the energy and circulation invariants are treated microcanonically give richer families of equilibria than models in which they are treated canonically. For each model, a variational principle that characterizes its equilibrium states is derived by large deviation techniques. An analysis of the two different variational principles resulting from the canonical and microcanonical ensembles reveals that their equilibrium states coincide if and …