Development of three dimensional constitutive theories based on lower dimensional experimental data

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate of entropy production, etc. In this paper we show different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers to describe the viscoelastic behavior of bodies.Comment: 23 pages, 6 figure

A thermodynamic framework to develop rate-type models for fluids without instantaneous elasticity

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. Given specific forms for the Helmholtz potential and the rate of dissipation, the rate of dissipation is maximized with the constraint that the difference between the stress power and the rate of change of Helmholtz potential is equal to the rate of dissipation and any other constraint that may be applicable such as incompressibility. We show that the model that is developed exhibits fluid-like characteristics and is incapable of instantaneous elastic response. It also includes Maxwell-like and Kelvin-Voigt-like viscoelastic materials (when certain material moduli take special values).Comment: 18 pages, 5 figure

A model for the degradation of polyimides due to oxidation

Polyimides, due to their superior mechanical behavior at high temperatures, are used in a variety of applications that include aerospace, automobile and electronic packaging industries, as matrices for composites, as adhesives etc. In this paper, we extend our previous model in [S. Karra, K. R. Rajagopal, Modeling the non-linear viscoelastic response of high temperature polyimides, Mechanics of Materials, In press, doi:10.1016/j.mechmat.2010.09.006], to include oxidative degradation of these high temperature polyimides. Appropriate forms for the Helmholtz potential and the rate of dissipation are chosen to describe the degradation. The results for a specific boundary value problem, using our model compares well with the experimental creep data for PMR-15 resin that is aged in air.Comment: 13 pages, 2 figures, submitted to Mechanics of Time-dependent Material

Age and growth of the venus clam Gafrarium tumidum (Roding) from south-east coast of India

Age and growth of the Venus clam Gafrarium tumidum was studied in detail employing four conventional methods and an electronic package ELEFAN – 1. The growth rate obtained by all the methods was more or less similar and comparable with one another. The clam reached a length of 24.4, 31.9 and 37.7 mm at the end of 1st, 2nd and 3rd year of its life. Growth rates of male and female clams were similar and observed to be faster in the first year and then tended to slow down with age. The life span of Gafrarium tumidum was estimated to be 3 years

Reproductive biology of Venus clam Gafrarium tumidum (Roding, 1798) from Southeast coast of India

The reproductive biology of tumid venus clamGafrarium tumidum (Roding) was studied in detail from the Southeast coast of India. Sample size ranged from 10.3 to 41.3mm. Sexes are separate but not di¡erentiated externally. Annual sex ratio male:female (M:F) deviated signi¢cantly from the 1:1 ratio with females dominating. Based on ova diameter progression of gonad smear and histology, four and two maturity stages of gonads were di¡erentiated in female and male clams, respectively. Peak spawning was observed during November and a minor one in April

The Crystallography of Strange Quark Matter

Cold three-flavor quark matter at large (but not asymptotically large) densities may exist as a crystalline color superconductor. We explore this possibility by calculating the gap parameter Delta and free energy Omega(Delta) for possible crystal structures within a Ginzburg-Landau approximation, evaluating Omega(Delta) to order Delta^6. We develop a qualitative understanding of what makes a crystal structure stable, and find two structures with particularly large values of Delta and the condensation energy, within a factor of two of those for the CFL phase known to characterize QCD at asymptotically large densities. The robustness of these phases results in their being favored over wide ranges of density and though it also implies that the Ginzburg-Landau approximation is not quantitatively reliable, previous work suggests that it can be trusted for qualitative comparisons between crystal structures. We close with a look ahead at the calculations that remain to be done in order to make contact with observed pulsar glitches and neutron star cooling.Comment: 6 pages, 3 figures. Contribution to the proceedings of Strangeness in Quark Matter 2006, UCLA. Talk given by Rishi Sharm

Neutrality of a magnetized two-flavor quark superconductor

We investigate the effect of electric and color charge neutrality on the two-flavor color superconducting (2SC) phase of cold and dense quark matter in presence of constant external magnetic fields and at moderate baryon densities. Within the framework of the Nambu-Jona-Lasinio (NJL) model, we study the inter-dependent evolution of the quark's BCS gap and constituent mass with increasing density and magnetic field. While confirming previous results derived for the highly magnetized 2SC phase with color neutrality alone, we obtain new results as a consequence of imposing charge neutrality. In the charge neutral gapless 2SC phase (g2SC), a large magnetic field drives the color superconducting phase transition to a crossover, while the chiral phase transition is first order. At larger diquark-to-scalar coupling ratio $G_D/G_S$, where the 2SC phase is preferred, we see hints of the Clogston-Chandrasekhar limit at a very large value of the magnetic field ($B\sim 10^{19}$G), but this limit is strongly affected by Shubnikov de Haas-van Alphen oscillations of the gap, indicating the transition to a domain-like state.Comment: 19 pages, 7 figures, Matches with the published versio

Thermal Conductivity and Chiral Critical Point in Heavy Ion Collisions

Background: Quantum Chromodynamics is expected to have a phase transition in the same static universality class as the 3D Ising model and the liquid-gas phase transition. The properties of the equation of state, the transport coefficients, and especially the location of the critical point are under intense theoretical investigation. Some experiments are underway, and many more are planned, at high energy heavy ion accelerators. Purpose: Develop a model of the thermal conductivity, which diverges at the critical point, and use it to study the impact of hydrodynamic fluctuations on observables in high energy heavy ion collisions. Methods: We apply mode coupling theory, together with a previously developed model of the free energy that incorporates the critical exponents and amplitudes, to construct a model of the thermal conductivity in the vicinity of the critical point. The effect of the thermal conductivity on correlation functions in heavy ion collisions is studied in a boost invariant hydrodynamic model via fluctuations, or noise. Results: We find that the closer a thermodynamic trajectory comes to the critical point the greater is the magnitude of the fluctuations in thermodynamic variables and in the 2-particle correlation functions in momentum space. Conclusions: It may be possible to discern the existence of a critical point, its location, and thermodynamic and transport properties near to it in heavy ion collisions using the methods developed here.Comment: 36 pages, 8 figures. Version published in Phys.Rev.C86, 054911 (2012). It contains some minor improvements with respect to v1: further clarifications, small changes on figures and two extra reference

Prelude to Compressed Baryonic Matter

This is intended to appear as the introduction to "The CBM Physics Book: compressed baryonic matter in laboratory experiments" (ed. B. Friman, C. H\"ohne, S. Leupold, J. Knoll, J. Randrup, R. Rapp, P. Senger), to be published by Springer. At the end there is a new proposal for numerically tractable models of interacting many-body systems.Comment: 12 pages, to appear in "The CBM Book: compressed baryonic matter in laboratory experiments