BPS Saturated Solitons in N=2 Two-Dimensional Theories on RxS (Domain Walls in Theories with Compactified Dimensions)

We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kahler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N=2 field theory includes an auxiliary N=1 quantum mechanics, Witten's index of which counts the number of the BPS particles.Comment: LaTeX, 23 pages, 7 Postscript figure

A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N+1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.Comment: Latex, 12 page

Chapman-Enskog expansion of the Boltzmann equation and its diagrammatic interpretation

We perform a Chapman-Enskog expansion of the Boltzmann equation keeping up to quadratic contributions. We obtain a generalized nonlinear Kubo formula, and a set of integral equations which resum ladder and extended ladder diagrams. We show that these two equations have exactly the same structure, and thus provide a diagrammatic interpretation of the Chapman-Enskog expansion of the Boltzmann equation, up to quadratic order.Comment: 5 pages, 2 figures in eps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL http://ismd31.ccnu.edu.cn

Chemoviscosity modeling for thermosetting resin systems, part 3

A new analytical model for simulating chemoviscosity resin has been formulated. The model is developed by modifying the well established Williams-Landel-Ferry (WLF) theory in polymer rheology for thermoplastic materials. By introducing a relationship between the glass transition temperature (T sub g (t)) and the degree of cure alpha(t) of the resin system under cure, the WLF theory can be modified to account for the factor of reaction time. Temperature-dependent functions of the modified WLF theory parameters C sub 1 (T) and C sub 2 (T) were determined from the isothermal cure data. Theoretical predictions of the model for the resin under dynamic heating cure cycles were shown to compare favorably with the experimental data. This work represents a progress toward establishing a chemoviscosity model which is capable of not only describing viscosity profiles accurately under various cure cycles, but also correlating viscosity data to the changes of physical properties associated with the structural transformations of the thermosetting resin systems during cure

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.Comment: 23 page

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Nuclear Structure of Bound States of Asymmetric Dark Matter

Models of Asymmetric Dark Matter (ADM) with a sufficiently attractive and long-range force gives rise to stable bound objects, analogous to nuclei in the Standard Model, called nuggets. We study the properties of these nuggets and compute their profiles and binding energies. Our approach, applicable to both elementary and composite fermionic ADM, utilizes relativistic mean field theory, and allows a more systematic computation of nugget properties, over a wider range of sizes and force mediator masses, compared to previous literature. We identify three separate regimes of nugget property behavior corresponding to (1) non-relativistic and (2) relativistic constituents in a Coulomb-like limit, and (3) saturation in an anti-Coulomb limit when the nuggets are large compared to the force range. We provide analytical descriptions for nuggets in each regime. Through numerical calculations, we are able to confirm our analytic descriptions and also obtain smooth transitions for the nugget profiles between all three regimes. We also find that over a wide range of parameter space, the binding energy in the saturation limit is an ${\cal O}(1)$ fraction of the constituent's mass, significantly larger than expectations in the non-relativistic case. In a companion paper, we apply our results to synthesis of ADM nuggets in the early Universe.Comment: 20 pages, 8 figures, 1 appendi

Making Asymmetric Dark Matter Gold: Early Universe Synthesis of Nuggets

We compute the mass function of bound states of Asymmetric Dark Matter--nuggets--synthesized in the early Universe. We apply our results for the nugget density and binding energy computed from a nuclear model to obtain analytic estimates of the typical nugget size exiting synthesis. We numerically solve the Boltzmann equation for synthesis including two-to-two fusion reactions, estimating the impact of bottlenecks on the mass function exiting synthesis. These results provide the basis for studying the late Universe cosmology of nuggets in a future companion paper.Comment: 27 pages, 11 figures, modified discussions in Section I

On the algebra A_{\hbar,\eta}(osp(2|2)^{(2)}) and free boson representations

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current algebra with the structure of a so-called infinite Hopf family of (super)algebras. A representation of this algebra at $c=1$ is realized in the product Fock space of two commuting sets of Heisenberg algebras.Comment: 14 pages, LaTe