We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat flux law is of Gurtin–Pipkin type and the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to describe, for instance, ...

We investigate Hopf bifurcations in a delayed Nicholson’s blowflies equation of neutral type, derived from the Gurtin–MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Global extension of local Hopf branches is established by combining a global Hopf bifurcation theorem with a Bendixson criteri...

We prove the existence of a quasistatic evolution for a model in strain gradient plasticity proposed by Gurtin and Anand concerning isotropic, plastically irrotational materials under small deformations. This is done by means of the energetic approach to rate-independent evolution problems. Finally we study the asymptotic behavior of the evolution as the strain gradient length scales tend to ze...

We consider, in an abstract setting, an instance of the Coleman-Gurtin model for heat conduction with memory, that is, the Volterra integro-differential equation ∂tu(t)− β∆u(t)− ∫ t 0 k(s)∆u(t− s)ds = 0. We establish new results for the exponential and polynomial decay of solutions, by means of conditions on the convolution kernel which are weaker than the classical differential inequalities.

Anand & Gurtin (2002) have recently developed a continuum theory for the elasticviscoplastic deformation of amorphous solids. Their theory is motivated by and builds on the work of Parks, Argon, Boyce, Arruda, and their co-workers (e.g. Boyce et al., 1988; Arruda & Boyce, 1993) on modeling the plastic deformation of amorphous polymers. The theory of Anand & Gurtin (2002) carefully accounts for ...

The Hugh Williamson Gait Analysis Laboratory is a world leader in the analysis of walking disorders in children. Using state of the art equipment, highly specialised staff are able to determine why children walk the way they do. Knowing this, it is then possible to plan treatment individually for each child. Gait Lab aims to make thorough and reliable measurements of children’s walking ability ...

Hyperbolic curvature flow is a geometric evolution equation that in the plane can be viewed as natural hyperbolic analogue of curve shortening flow. It was proposed by Gurtin and Podio-Guidugli (1991) to model certain wave phenomena solid-liquid interfaces. We introduce semidiscrete finite difference method for approximation prove error bounds discrete norms. also present numerical simulations,...

by considering the fact that the surface tension of a real fluid arises from a combination of both repulsive and attractive forces between molecules, a new expression for the interfacial tension has been derived from scaled particle theory (spt)  based on the work of cavity formation and the interaction energy between molecules. at the critical temperature, the interfacial tension between coexi...