Approximate solutions for the single soliton in a Skyrmion-type model with a dilaton scalar field

We consider the analytical properties of the single-soliton solution in a Skyrmion-type Lagrangian that incorporates the scaling properties of quantum chromodynamics (QCD) through the coupling of the chiral field to a scalar field interpreted as a bound state of gluons. The model was proposed in previous works to describe the Goldstone pions in a dense medium, being also useful for studying the properties of nuclear matter and the in-medium properties of mesons and nucleons. Guided by an asymptotic analysis of the Euler-Lagrange equations, we propose approximate analytical representations for the single soliton solution in terms of rational approximants exponentially localized. Following the Pad\'e method, we construct a sequence of approximants from the exact power series solutions near the origin. We find that the convergence of the approximate representations to the numerical solutions is considerably improved by taking the expansion coefficients as free parameters and then minimizing the mass of the Skyrmion using our ans\"atze for the fields. We also perform an analysis of convergence by computation of physical quantities showing that the proposed analytical representations are very useful useful for phenomenological calculations.Comment: 13 pages, 3 eps figures, version to be published in Phys.Rev.

Towards understanding Regge trajectories in holographic QCD

We reassess a work done by Migdal on the spectrum of low-energy vector mesons in QCD in the light of the AdS-QCD correspondence. Recently, a tantalizing parallelism was suggested between Migdal's work and a family of holographic duals of QCD. Despite the intriguing similarities, both approaches face a major drawback: the spectrum is in conflict with well-tested Regge scaling. However, it has recently been shown that holographic duals can be modified to accomodate Regge behavior. Therefore, it is interesting to understand whether Regge behavior can also be achieved in Migdal's approach. In this paper we investigate this issue. We find that Migdal's approach, which is based on a modified Pade approximant, is closely related to the issue of quark-hadron duality breakdown in QCD.Comment: 17 pages, 1 figure. Typos fixed, references added, improved discussion. Minor changes to match the journal versio

Ignition of binary alloys of uranium

Experiments determine the effect of alloying additives on the ignition of uranium. Data on oxidation rates, ignition temperatures, and burning curves are provided in the report

Shallow Binding in LISP 1.5

Key Words and Phrases: LISP 1.5, environment structures, FUNARGs, shallow and deep binding, multiprogramming, cache. CR Categories: 4.13, 4.22, 4.32 This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0522.Shallow binding is a scheme which allows the value of a variable to be accessed in a bounded amount of computation. An elegant model for shallow binding in LISP 1.5 is presented in which context-switching is an environment structure transformation called "re-rooting". Re-rooting is completely general and reversible, and is optional in the sense that a LISP 1.5 interpreter will operate correctly whether or not re-rooting is invoked on every context change. Since re-rooting leaves (ASSOC X A) invariant, for all variables X and all environments A, the programmer can have access to a re-rooting primitive, (SHALLOW), which gives him dynamic control over whether accesses are shallow or deep, and which effects only the speed of execution of a program, not its semantics. So long as re-rooting is an indivisible operation, multiple processes can be active in the same environment structure. The re-rooting scheme is compared to a cache scheme for shallow binding and the two are found to be compatible. Finally, the concept of re-rooting is shown not to depend upon LISP's choice of dynamic instead of lexical binding for free variables; hence it can be used in an Algol interpreter, for example.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

A Note on the Optimal Allocation of Spaces in MACLISP

Key Words and Phrases: garbage collection, list processing, virtual memory, storage management, storage allocation, LISP. CR Categories: 3.50, 3.60, 3.73, 3.80, 4.13, 422, 4.32, 4.33, 4.35, 4.49 This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0522.This note describes a method for allocating storage among the various spaces in the MACLISP Implementation of LISP. The optimal strategy which minimizes garbage collector effort allocates free storage among the various spaces in such a way that they all run out at the same time. In an equilibrium situation, this corresponds to allocating free storage to the spaces in proportion to their usage. Methods are investigated by which the rates of usage can be inferred, and a gc-daemon interrupt handler is developed which implements an approximately optimal strategy in MACLISP. Finally, the sensitivity of this method to rapidly varying differential rates of cell usage is discussed.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

A computer program for plotting stress-strain data from compression, tension, and torsion tests of materials

A computer program for plotting stress-strain curves obtained from compression and tension tests on rectangular (flat) specimens and circular-cross-section specimens (rods and tubes) and both stress-strain and torque-twist curves obtained from torsion tests on tubes is presented in detail. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 110000 octal locations of core storage. The program has the capability of plotting individual strain-gage outputs and/or the average output of several strain gages and the capability of computing the slope of a straight line which provides a least-squares fit to a specified section of the plotted curve. In addition, the program can compute the slope of the stress-strain curve at any point along the curve. The computer program input and output for three sample problems are presented

On the properties of compacton-anticompacton collisions

We study the properties of compacton-anticompacton collision processes. We compare and con- trast results for the case of compacton-anticompacton solutions of the K(l, p) Rosenau-Hyman (RH) equation for l = p = 2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard- Sodano (CSS) equation for p = 1 and l = 3. This study is performed using a Pad\'e discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton- anticompacton scattering. For the CSS equation, the scattering can be interpreted as "annihila- tion" as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision which eventually lead to "blowup" of the resulting waveform.Comment: 8 pages, 7 figure

Stability and dynamical properties of Rosenau-Hyman compactons using Pade approximants

We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Pad\'e approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-differences formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman (RH) compactons including the collision of two compactons and resultant shock formation. Our approach uses a differencing scheme involving only nearest and next-to-nearest neighbors on a uniform spatial grid. The partial differential equation for the compactons involves first, second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth-order methods which differ in the possibility of increasing the degree of accuracy (or not) of one of the spatial derivatives to sixth order. A method designed to reduce roundoff errors was found to be the most accurate approximation in stability studies of single solitary waves, even though all derivates are accurate only to fourth order. Simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity. For those problems the different choices lead to different amounts of "spurious" radiation and we compare the virtues of the different choices.Comment: 12 figure

Method for comparing finite temperature field theory results with lattice data

The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one Tc, they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying Pade-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop barMS beta function for alpha_s by its Borel-Pade resummation, eliminating thus the unphysical Landau singularities of alpha_s. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results -- for the pressure (p), the chemical potential contribution (delta p) to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to Tc.Comment: 24 pages, 17 figures, revtex4; Ref.[25] is new; the ordering of the references and grammatic and stylistic errors are corrected - version as it appears in PR

Gamma-ray halos as a measure of intergalactic magnetic fields: a classical moment problem

The presence of weak intergalactic magnetic fields can be studied by their effect on electro-magnetic cascades induced by multi-TeV gamma-rays in the cosmic radiation background. Small deflections of secondary electrons and positrons as the cascade develops extend the apparent size of the emission region of distant TeV gamma-ray sources. These gamma-ray halos can be resolvable in imaging atmospheric Cherenkov telescopes and serve as a measure of the intergalactic magnetic field strength and coherence length. We present a method of calculating the gamma-ray halo for isotropically emitting sources by treating magnetic deflections in the cascade as a diffusion process. With this ansatz the moments of the halo follow from a set of simple diffusion-cascade equations. The reconstruction of the angular distribution is then equivalent to a classical moment problem. We present a simple solution using Pade approximations of the moment's generating function.Comment: 12 pages, 6 figure