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Browsing Mathematics (Scholarly Articles) by Title

Now showing items 74-85 of 85

Temperature effects on brain tissue in compression

Destrade, Michel; Gilchrist, Michael (2012)

Extensive research has been carried out for at least 50 years to understand the mechanical properties of brain tissue in order to understand the mechanisms of traumatic brain injury (TBI). The observed large variability ...
Third and fourth-order elasticity of biological soft tissues

Destrade, Michel; Gilchrist, Michael D. (Acoustical Society of America, 2010-01-24)

In the theory of weakly nonlinear elasticity, Hamilton et al. [J. Acoust. Soc. Am. 116, 41-44 (2004)] identified W = -I2+(A/3)I3+DI22 as the fourth-order expansion of the strain-energy density for incompressible isotropic ...
Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect.

Destrade, Michel; Gilchrist, Michael D. (Acoustical Society of America, 2010-02)

Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination ...
Torus Chiral n-Point Functions for Free Boson and Lattice Vertex Operator Algebras

Mason, Geoffrey; Tuite, Michael P. (2002)

We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions.
Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

Mason, Geoffrey; Tuite, Michael P.; Zuevsky, Alexander (2007)

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, ...
Transverse waves in nonlinearly elastic solids and the Milne-Pinney equation

Destrade, Michel (SAGE Journals, 2011-08-17)

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 ...
A two-weight scheme for a time-dependent advection-diffusion problem

Chadha, Naresh M.; Madden, Niall (2011)

We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion parameters, ...
Vertex Operators and Modular Forms

Mason, Geoffrey; Tuite, Michael P. (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

Tuite, Michael P. (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

Hurley, Donny; Tuite, Michael P. (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

Destrade, Michel (2008)

It is shown that in the Love-Kirchhoff 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

Destrade, Michel (American Physical Society, 2007-04-17)

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 ...