General Dissipative Materials for Simple Histories

A material with memory typically has a set of many free energy functionals associated with it, all members of which yield the same constitutive relations. An alternative interpretation of this set is explored in the present work. Explicit formulae are derived for the free energy and total dissipation of an arbitrary material in the cases of step function and sinusoidal/exponential histories. Expressions for the fraction of stored and dissipated energy are deduced. Also, various formulae are given for discrete spectrum materials. For materials with relaxation function containing one decaying exponential, the associated Day functional is the physical free energy. For more general materials, we seek a best fit of the relaxation function with one decaying expo- nential to that chosen for the general case. The free energy, total dissipation and fractions of stored and dissipated energies relating to the Day material are derived for the various histories. Similar data, in the case of the general mate- rial, are explored for the minimum and maximum free energies and also for a centrally located free energy given in the literature. Various plots of aspects of this data, including comparisons between the behaviour for general and Day materials, are presented and discussed

Second Gradient Viscoelastic Fluids: Dissipation Principle and Free Energies

We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they differ from the standard Graffi conditions. Various free energy functionals, which are well-known in relation to simple materials, are generalized so that they apply to this fluid. In particular, expressions for the minimum free energy and a more recently introduced explicit functional of the minimal state are proposed. Derivations of various formulae are abbreviated if closely analogous proofs already exist in the literature

Energy balance criteria for viscoelastic fracture

An energy balance criterion of the Griffith type has been used to derive conditions that are valid, in the isothermal non-inertial approximation, for the growth of cracks in viscoelastic bodies. These bodies are acted upon by general position and time-dependent load. The conditions obtained have the same form as the instability conditions obtained for the corresponding problems in elasticity theory and, in particular are independent of crack velocity. The analysis relies upon an exact calculation of the displacement and stress fields that is derived in the appendix with the aid of extensions to viscoelasticity of the Kolosov-Muskhelishvili equations of elasticity theory

High Speed Phase-Resolved 2-d UBV Photometry of the Crab pulsar

We report a phase-resolved photometric and morphological analysis of UBV data of the Crab pulsar obtained with the 2-d TRIFFID high speed optical photometer mounted on the Russian 6m telescope. By being able to accurately isolate the pulsar from the nebular background at an unprecedented temporal resolution (1 \mu s), the various light curve components were accurately fluxed via phase-resolved photometry. Within the $UBV$ range, our datasets are consistent with the existing trends reported elsewhere in the literature. In terms of flux and phase duration, both the peak Full Width Half Maxima and Half Width Half Maxima decrease as a function of photon energy. This is similarly the case for the flux associated with the bridge of emission. Power-law fits to the various light curve components are as follows; \alpha = 0.07 \pm 0.19 (peak 1), \alpha = -0.06 \pm 0.19 (peak 2) and \alpha = -0.44 \pm 0.19 (bridge) - the uncertainty here being dominated by the integrated CCD photometry used to independently reference the TRIFFID data. Temporally, the main peaks are coincident to \le 10 \mu s although an accurate phase lag with respect to the radio main peak is compromised by radio timing uncertainties. The plateau on the Crab's main peak was definitively determined to be \leq 55 \mu s in extent and may decrease as a function of photon energy. There is no evidence for non-stochastic activity over the light curves or within various phase regions, nor is there evidence of anything akin to the giant pulses noted in the radio. Finally, there is no evidence to support the existence of a reported 60 second modulation suggested to be as a consequence of free precession.Comment: 13 pages, 12 figures, accepted for publication in Astronomy & Astrophysic

Implications of the Optical Observations of Neutron Stars

We show that observations of pulsars with pulsed optical emission indicate that the peak flux scales according to the magnetic field strength at the light cylinder. The derived relationships indicate that the emission mechanism is common across all of the observed pulsars with periods ranging from 33ms to 385 ms and ages of 1000-300,000 years. It is noted that similar trends exist for $\gamma$ ray pulsars. Furthermore the model proposed by Pacini (1971) and developed by Pacini and Salvati (1983,1987) still has validity and gives an adequate explanation of the optical phenomena.Comment: 23 pages, 6 figures, accepted for publication in the Astrophysical Journa

Odor sampling strategies in mice with genetically altered olfactory responses

Peripheral sensory cells and the central neuronal circuits that monitor environmental changes to drive behaviors should be adapted to match the behaviorally relevant kinetics of incoming stimuli, be it the detection of sound frequencies, the speed of moving objects or local temperature changes. Detection of odorants begins with the activation of olfactory receptor neurons in the nasal cavity following inhalation of air and airborne odorants carried therein. Thus, olfactory receptor neurons are stimulated in a rhythmic and repeated fashion that is determined by the breathing or sniffing frequency that can be controlled and altered by the animal. This raises the question of how the response kinetics of olfactory receptor neurons are matched to the imposed stimulation frequency and if, vice versa, the kinetics of olfactory receptor neuron responses determine the sniffing frequency. We addressed this question by using a mouse model that lacks the K+-dependent Na+/Ca2+ exchanger 4 (NCKX4), which results in markedly slowed response termination of olfactory receptor neuron responses and hence changes the temporal response kinetics of these neurons. We monitored sniffing behaviors of freely moving wildtype and NCKX4 knockout mice while they performed olfactory Go/NoGo discrimination tasks. Knockout mice performed with similar or, surprisingly, better accuracy compared to wildtype mice, but chose, depending on the task, different odorant sampling durations depending on the behavioral demands of the odorant identification task. Similarly, depending on the demands of the behavioral task, knockout mice displayed a lower basal breathing frequency prior to odorant sampling, a possible mechanism to increase the dynamic range for changes in sniffing frequency during odorant sampling. Overall, changes in sniffing behavior between wildtype and NCKX4 knockout mice were subtle, suggesting that, at least for the particular odorant-driven task we used, slowed response termination of the odorant-induced receptor neuron response either has a limited detrimental effect on odorant-driven behavior or mice are able to compensate via an as yet unknown mechanism