Browsing Mathematics (Scholarly Articles) by Title
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Transverse waves in nonlinearly elastic solids and the MilnePinney equation
(SAGE Journals, 20110817)We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc Amer Math Soc 1950; 1: 681]. As a starting point, we use the exact ... 
Tuning the pullin instability of soft dielectric elastomers through loading protocols
(Elsevier, 20190322)Pullin (or electromechanical) instability occurs when a drastic decrease in the thickness of a dielectric elastomer results in electrical breakdown, which limits the applications of dielectric devices. Here we derive the ... 
A twoweight scheme for a timedependent advectiondiffusion problem
(2011)We consider a family of twoweight finite difference schemes for a timedependent advectiondiffusion problem. For a given uniform gridspacing in time and space, and for a fixed value of advection and diffusion parameters, ... 
Uniform transmural strain in prestressed arteries occurs at physiological pressure
(Elsevier, 20120621)Residual deformation (strain) exists in arterial vessels, and has been previously proposed to induce homogeneous transmural strain distribution. In this work, we present analytical formulations that predict the existence ... 
Vertex algebras according to Isaac Newton
(IOP Publishing, 20170908)We give an introduction to vertex algebras using elementary forward difference methods originally due to Isaac Newton. 
Vertex Operators and Modular Forms
(2009)The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite ... 
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
(2006)We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series ... 
Virasoro Correlation Functions for Vertex Operator Algebras
(2011)We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially ... 
A wave near the edge of a circular disk
(2008)It is shown that in the LoveKirchhoff plate theory, an edge wave can travel in a circular thin disk made of an isotropic elastic material. This disk edge wave turns out to be faster than the classic flexural acoustic wave ... 
Weierstrass's criterion and compact solitary waves
(American Physical Society, 20070417)Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it ... 
The weighted fusion category algebra and the $q$Schur algebra for $\rm GL_2(q)$
(ScienceDirect, 200801)[no abstract available] 
Wrinkles and creases in the bending, unbending and eversion of soft sectors
(The Royal Society, 20180323)We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought ... 
Wrinkles in soft dielectric plates
(Elsevier, 20180704)We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through predeformation, the snapthrough behavior of their loading curve to deliver ... 
Wrinkles in the opening angle method
(Elsevier, 20170610)We investigate the stability of the deformation modeled by the opening angle method, often used to give a measure of residual stresses in arteries and other biological soft tubular structures. Specifically, we study the ... 
Zhu reduction for Jacobi npoint functions and applications
(20170623)We establish precise Zhu reduction formulas for Jacobi npoint functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly ...