A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity

Traveling waves in one-dimensional non-linear models of strain-limiting viscoelasticity

In this paper we investigate traveling wave solutions of a non-linear differential equation describing the behaviour of one-dimensional viscoelastic medium with implicit constitutive relations. We focus on a subclass of such models known as the strain-limiting models introduced by Rajagopal. To describe the response of viscoelastic solids we assume a non-linear relationship among the linearized...

Strain Softening in Viscoelasticity of the Rate Type

A Consistent One-dimensional Model for the Turbulent Tachocline

The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to the strongly stable stratification, the mean radial shear is stable, while the horizontal shear is expected to drive predominantly horizontal, quasi-2D moti...

Thermodynamically Consistent Quasi-Newton Formulae

Newton and quasi-Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton-based fixed-point methods have been used to solve many different kinds of chemical process design and optimization problems, perhaps the point of singl...

The cardiac Na$^+$/K$^+$ ATPase: An updated, thermodynamically consistent model

The Na+/K+ ATPase is an essential component of cardiac electrophysiology, maintaining physiological Na+ and K+ concentrations over successive heart beats. Terkildsen et al. (2007) developed a model of the ventricular myocyte Na+/K+ ATPase to study extracellular potassium accumulation during ischaemia, demonstrating the ability to recapitulate a wide range of experimental data, but unfortunately...