K. Rajagopal - Academia.edu (original) (raw)

Papers by K. Rajagopal

Physical Review D, 2006

We construct strangelets, taking into account electrostatic effects, including Debye screening, a... more We construct strangelets, taking into account electrostatic effects, including Debye screening, and arbitrary surface tension σ of the interface between vacuum and quark matter. We find that there is a critical surface tension σcrit below which large strangelets are unstable to fragmentation and below which quark star surfaces will fragment into a crystalline crust made of charged strangelets immersed in an electron gas. We derive a model-independent relationship between σcrit and two parameters that characterize any quark matter equation of state. For reasonable model equations of state, we find σcrit typically of order a few MeV/fm 2 . If σ σcrit, the size-distribution of strangelets in cosmic rays could feature a peak corresponding to the stable strangelets that we construct.

Physical Review D, 2002

We demonstrate that crystalline color superconductivity may arise as a result of pairing between ... more We demonstrate that crystalline color superconductivity may arise as a result of pairing between massless quarks and quarks with nonzero mass m s. Previous analyses of this phase of cold dense quark matter have all utilized a chemical potential difference δµ to favor crystalline color superconductivity over ordinary BCS pairing. In any context in which crystalline color superconductivity occurs in nature, however, it will be m s-induced. The effect of m s is qualitatively different from that of δµ in one crucial respect: m s depresses the value of the BCS gap ∆ 0 whereas δµ leaves ∆ 0 unchanged. This effect in the BCS phase must be taken into account before m s-induced and δµ-induced crystalline color superconductivity can sensibly be compared.

Physical Review D, 2001

At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium i... more At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium is made of neutrons, protons and electrons. At sufficiently high density, such matter is made of up, down and strange quarks in the colorflavor locked phase, with no electrons. As a function of increasing density (or, perhaps, increasing depth in a compact star) other phases may intervene between these two phases which are guaranteed to be present. The simplest possibility, however, is a single first order phase transition between CFL and nuclear matter. Such a transition, in space, could take place either through a mixed phase region or at a single sharp interface with electron-free CFL and electron-rich nuclear matter in stable contact. Here we construct a model for such an interface. It is characterized by a region of separated charge, similar to an inversion layer at a metal-insulator boundary. On the CFL side, the charged boundary layer is dominated by a condensate of negative kaons. We then consider the energetics of the mixed phase alternative. We find that the mixed phase will occur only if the nuclear-CFL surface tension is significantly smaller than dimensional analysis would indicate.

Nuclear Physics A, 2003

We develop the Ginzburg-Landau approach to comparing different possible crystal structures for th... more We develop the Ginzburg-Landau approach to comparing different possible crystal structures for the crystalline color superconducting phase of QCD, the QCD incarnation of the Larkin-Ovchinnikov-Fulde-Ferrell phase. In this phase, quarks of different flavor with differing Fermi momenta form Cooper pairs with nonzero total momentum, yielding a condensate that varies in space like a sum of plane waves. We work at zero temperature, as is relevant for compact star physics. The Ginzburg-Landau approach predicts a strong first-order phase transition (as a function of the chemical potential difference between quarks) and for this reason is not under quantitative control. Nevertheless, by organizing the comparison between different possible arrangements of plane waves (i.e. different crystal structures) it provides considerable qualitative insight into what makes a crystal structure favorable. Together, the qualitative insights and the quantitative, but not controlled, calculations make a compelling case that the favored pairing pattern yields a condensate which is a sum of eight plane waves forming a face-centered cubic structure. They also predict that the phase is quite robust, with gaps comparable in magnitude to the BCS gap that would form if the Fermi momenta were degenerate. These predictions may be tested in ultracold gases made of fermionic atoms. In a QCD context, our results lay the foundation for a calculation of vortex pinning in a crystalline color superconductor, and thus for the analysis of pulsar glitches that may originate within the core of a compact star.

Series on Advances in Quantum Many-Body Theory, 2006

At ultra-high density, matter is expected to form a degenerate Fermi gas of quarks in which there... more At ultra-high density, matter is expected to form a degenerate Fermi gas of quarks in which there is a condensate of Cooper pairs of quarks near the Fermi surface: color superconductivity. In this chapter we review some of the underlying physics, and discuss outstanding questions about the phase structure of ultradense quark matter. We then focus on describing recent results on the crystalline color superconducting phase that may be the preferred form of cold, dense but not asymptotically dense, three-flavor quark matter. The gap parameter and free energy for this phase have recently been evaluated within a Ginzburg-Landau approximation for many candidate crystal structures. We describe the two that are most favorable. The robustness of these phases results in their being favored over wide ranges of density. However, it also implies that the Ginzburg-Landau approximation is not quantitatively reliable. We describe qualitative insights into what makes a crystal structure favorable which can be used to winnow the possibilities. We close with a look ahead at the calculations that remain to be done in order to make quantitative contact with observations of compact stars.

Interfaces and Free Boundaries, 2000

Crystallization and solidification in polymers is a problem of great importance to the polymer pr... more Crystallization and solidification in polymers is a problem of great importance to the polymer processing industry. In these processes, the melt is subjected to deformation while being cooled into the desired shape. The properties of the final product are strongly influenced by the deformation and thermal histories and the final solid is invariably anisotropic. In this work we present a model to capture the effects during solidification and crystallization in polymers within a purely mechanical setting, using the framework of multiple natural configurations that was introduced recently to study a variety of non-linear dissipative responses of materials undergoing phase transitions. Using this framework we present a consistent method to model the transition from a fluid-like behaviour to a solid-like behaviour. We also present a novel way of incorporating the formation of an anisotropic crystalline phase in the melt. The anisotropy of the crystalline phase, and consequently that of the final solid, depends on the deformation in the melt at the instant of crystallization, a fact that has been known for a long time and has been exploited in polymer processing. The proposed model is tested by solving three homogenous deformations.

Pathophysiology of Haemostasis and Thrombosis, 2005

Both biochemical and mechanical factors have to be taken into account if a meaningful model for t... more Both biochemical and mechanical factors have to be taken into account if a meaningful model for the formation, growth, and lysis of clots in flowing blood is to be developed. Most models that are currently in use neglect one or the other of these factors. We have previously reported a model [J Theoret Med 2003;5:183–218] that we believe is a step in this direction, incorporating many of the crucial biochemical and rheological factors that play a role in the formation, growth, and lysis of clots. While this model takes into account the extrinsic pathway of coagulation, it largely ignores the intrinsic pathway. Here, we discuss some of the general issues with respect to mathematical modeling of thrombus formation and lysis, as well as specific aspects of the model that we have developed.

SIAM Journal on Mathematical Analysis, 2009

In his treatise titled "The physics of high pressures" (1931), Bridgman carefully documented that... more In his treatise titled "The physics of high pressures" (1931), Bridgman carefully documented that the viscosity and the thermal conductivity of most liquids depend on the pressure and the temperature. The relevant experimental studies show that even at high pressures the variations of the values in the density are insignificant in comparison to that of the viscosity, and it is thus reasonable to assume that the liquids in question are incompressible fluids with pressure dependent viscosities. We rigorously investigate the mathematical properties of unsteady three-dimensional internal flows of such incompressible fluids. The model is expressed through a system of partial differential equations representing the balance of mass, the balance of linear momentum, the balance of energy and the equation for the entropy production. Assuming that we have Navier's slip at the impermeable boundary we establish the long-time existence of a (suitable) weak solution when the data are large.

In this short paper we study the linearized stability of the flow of a chemically reacting fluid ... more In this short paper we study the linearized stability of the flow of a chemically reacting fluid in a cylindrical pipe, under the assumption that the length of the pipe is far greater than its diameter. The fluid models that are considered have relevance to the flow of both polymeric liquids that are capable of undergoing chemical reactions and biological fluids such as the synovial fluid whose viscosity changes due to the concentration of the hyaluronan. The viscosity of the class of fluids that we consider can increase or decrease due to the concentration of the chemical that is being carried by the fluid and it can also shear thin or shear thicken. We non-dimensionalize the equations governing the motion of the fluid and then carry out an approximation wherein we retain terms that are of order unity in the Reynolds number and Péclet number. We further simplify the problem by seeking a special semi-inverse solution, in the same spirit as that which is used in the study of classical Hagen-Poiseuille flow, and look for solutions for the velocity field and the concentration that vary only with the radial coordinate. Under the above mentioned approximation, one can obtain an exact solution for the basic flow which then allows us to analytically consider the stability of the base flow to sufficiently small disturbances. On the basis of earlier studies of such fluids in the modeling of biological fluids, especially the synovial fluid, we consider two types of variation of the viscosity with the concentration. We find that flows in the cylindrical pipe, within the context of our approximation, are stable to sufficiently small disturbances, for both variations of the viscosity that are considered.