Material Issues of the Metal Printing Process, MPP

The metal printing process, MPP; is a novel Rapid Manufacturing process under development at SINTEF and NTNU in Trondheim, Norway. The process, which aims at the manufacturing of end-use products for demanding applications in metallic and CerMet materials, consists of two separate parts; The layer fabrication, based on electrostatic attraction of powder materials, and the consolidation, consisting of the compression and sintering of each layer in a heated die. This approach leads to a number of issues regarding the interaction between the process solutions and the materials. This paper addresses some of the most critical material issues at the current development stage of MPP, and the present solutions to these.Mechanical Engineerin

Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Convergent finite difference schemes for stochastic transport equations

We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The $L^2$ estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes

Global existence of dissipative solutions to the Camassa--Holm equation with transport noise

We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for dissipative weak martingale solutions to this SPDE, with general finite-energy initial data. The solution is obtained as the limit of classical solutions to parabolic SPDEs. The proof combines model-specific statistical estimates with stochastic propagation of compactness techniques, along with the systematic use of tightness and a.s. representations of random variables on specific quasi-Polish spaces. The spatial dependence of the noise function makes more difficult the analysis of a priori estimates and various renormalisations, giving rise to nonlinear terms induced by the martingale part of the equation and the second-order Stratonovich--It\^{o} correction term.Comment: 86 page

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Consistently computing the K -> pi long distance weak transition

First we extract the long-distance (LD) weak matrix element from certain data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale and then test the latter SQL scale against the decuplet weak decay amplitude ratio. Finally, we study LD decay. All of these experimental and theoretical values are in good agreement. We deduce an average value from eleven experimental determinations compared to the theoretical SQL values average.Comment: 19 pages, 9 figures minor change to the Conclusions and abstract sectio

Polynomial Cointegration among Stationary Processes with Long Memory

n this paper we consider polynomial cointegrating relationships among stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and we consider a form of spectral regression around frequency zero. For these estimates, we establish consistency by means of a more general result on continuously averaged estimates of the spectral density matrix at frequency zeroComment: 25 pages, 7 figures. Submitted in August 200

Hyperon Nonleptonic Weak Decays Revisited

We first review the current algebra - PCAC approach to nonleptonic octet baryon 14 weak decay B (\to) (B^{\prime})(\pi) amplitudes. The needed four parameters are independently determined by (\Omega \to \Xi \pi),(\Lambda K) and (\Xi ^{-}\to \Sigma ^{-}\gamma) weak decays in dispersion theory tree order. We also summarize the recent chiral perturbation theory (ChPT) version of the eight independent B (\to) (B^{\prime}\pi) weak (\Delta I) = 1/2 amplitudes containing considerably more than eight low-energy weak constants in one-loop order.Comment: 10 pages, RevTe

Remarks on the f_0(400-1200) scalar meson as the dynamically generated chiral partner of the pion

The quark-level linear sigma model is revisited, in particular concerning the identification of the f_0(400-1200) (or \sigma(600)) scalar meson as the chiral partner of the pion. We demonstrate the predictive power of the linear sigma model through the pi-pi and pi-N s-wave scattering lengths, as well as several electromagnetic, weak, and strong decays of pseudoscalar and vector mesons. The ease with which the data for these observables are reproduced in the linear sigma model lends credit to the necessity to include the sigma as a fundamental q\bar{q} degree of freedom, to be contrasted with approaches like chiral perturbation theory or the confining NJL model of Shakin and Wang.Comment: 15 pages, plain LaTeX, 3 EPS figure