Hadron Production in Ultra-relativistic Nuclear Collisions: Quarkyonic Matter and a Triple Point in the Phase Diagram of QCD

We argue that features of hadron production in relativistic nuclear collisions, mainly at CERN-SPS energies, may be explained by the existence of three forms of matter: Hadronic Matter, Quarkyonic Matter, and a Quark-Gluon Plasma. We suggest that these meet at a triple point in the QCD phase diagram. Some of the features explained, both qualitatively and semi-quantitatively, include the curve for the decoupling of chemical equilibrium, along with the non-monotonic behavior of strange particle multiplicity ratios at center of mass energies near 10 GeV. If the transition(s) between the three phases are merely crossover(s), the triple point is only approximate.Comment: 28 pages, 9 figures; submitted to Nucl. Phys. A; v2 to eliminate obsolete figs. inadvertently attached at the end of the paper; v3: final version accepted for publicatio

ShapeWright--finite element based free-form shape design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1990.Includes bibliographical references (p. 179-192).by George Celniker.Ph.D

Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation

Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.Comment: 98 pages, 6 appendices. v2: typos corrected; v3: significant changes made to results section using simpler arguments, added discussion of real structures, additional references, 2 new appendice

The Quark-Gluon Plasma in Equilibrium

Our current knowledge of the quark-gluon plasma in thermodynamical equilibrium is reviewed. The phase diagram of strongly interacting matter is discussed, with emphasis on the quark-hadron phase transition and the color-superconducting phases of quark matter. Lattice QCD results on the order of the phase transition, the thermodynamical functions, the heavy quark free energy, mesonic spectral functions, and recent results for nonzero quark chemical potential are presented. Analytic attempts to compute the thermodynamical properties of strongly interacting matter, such as perturbation theory, quasiparticle models, ``hard-thermal-loop''(HTL)-resummed perturbation theory, the Polyakov-loop model, as well as linear sigma models are discussed. Finally, color-superconducting quark matter is considered in the limit of weak coupling. The gap equation and the excitation spectrum are derived. The solution of the gap equation, gap parameters in various color-superconducting phases, and critical temperatures for the transition to normal-conducting quark matter are presented. A summary of gluon and photon properties in color superconductors is given.Comment: 89 pages, 26 figures, review for Prog. Part. Nucl. Phys, minor revisions to text, correction of typos, refs. adde

Modelling dependance in collateralied debt obligations with copulas

In this paper we provide a review of credit derivatives, and some of the tools used to model them. We give a basic introduction to copulas and how they are used to model the depedence between single name credit derivatives. We then investigate various features of Gaussian and t copula dependence using numerical results obtained from Monte-Carlo simulation

Obtaining Optimal Mobile-Robot Paths with Non-Smooth Anisotropic Cost Functions Using Qualitative-State Reasoning

This paper appeared in the International Journal of Robotics Research, 16, 3 (June 1997), 375-399. The equations were reconstructed in 2007 for better readability.Realistic path-planning problems frequently show anisotropism, dependency of traversal cost or feasibility on the traversal heading. Gravity, friction, visibility, and safety are often anisotropic for mobile robots. Anisotropism often differs qualitatively with heading, as when a vehicle has insufficient power to go uphill or must brake to avoid accelerating downhill. Modeling qualitative distinctions requires discontinuities in either the cost-per-traversal-distance function or its derivatives, preventing direct application of most results of the calculus of variations. We present a new approach to optimal anisotropic path planning that first identifies qualitative states and permissible transitions between them. If the qualitative states are chosen appropriately, our approach replaces an optimization problem with such discontinuities by a set of subproblems without discontinuities, subproblems for which optimization is likely to be faster and less troublesome. Then the state space in the near neighborhood of any particular state can be partitioned into "behavioral regions" representing states optimally reachable by single qualitative "behaviors", sequences of qualitative states in a finite-state diagram. Simplification of inequalities and other methods can find the behavioral regions. Our ideas solve problems not easily solvable any other way, especially those with what we define as "turn-hostile" anisotropism. We illustrate our methods on two examples, navigation on an arbitrarily curved surface with gravity and friction effects (for which we show much better performance than a previously-published program 22 times longer), and flight of a simple missile.This work was supported in part by the U.S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86. This work was also prepared in part in conjunction with research conducted for the Naval Air Systems Commandfunded by the Naval Postgraduate SchoolApproved for public release; distribution is unlimited

Studies of two-phase flow with soluble surfactant

Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this limit, that scales out the Péclet number dependence, is adapted to resolve the drop interior flow, the bulk surfactant evolution, and the transfer of surfactant between the bulk and surface phases. A more traditional numerical method that solves the full governing equations without the asymptotic reduction is also developed. This is designed to achieve high accuracy at large Péclet number by use of complex variable techniques that map the evolving drop shape and flow velocity onto the fixed domain of the unit disk, where a Chebyshev-Fourier spectral method is developed to resolve the bulk phase surfactant evolution. Results of the two methods are compared for 2D simulations of drop dynamics, when the drop is stretched or deformed in either a strain flow or in a shear flow. Recirculation of the interior flow and surfactant exchange on the interior of the drop induce more intricate dynamics than when bulk surfactant is present in the exterior phase