Closed form solution of the return mapping algorithm in elastoplasticity

In the present work a return mapping algorithm is discussed for small strain elastoplasticity boundary value problems with an exact closed form solution of the local constitutive equations. Nonlinear kinematic hardening rules are adopted in modelling kinematic hardening behavior of ductile materials. The local solution of the constitutive equations is expressed by only one nonlinear scalar equation which is subsequently reduced to a single variable algebraic equation. Due to the straightforward form of the nonlinear scalar equation the analytical solution of the algebraic equation is found in exact closed form. A remarkable advantage of the present approach is that no iterative solution method is used to solve the local constitutive equations in three-dimensional elastoplasticity. Numerical applications and computational results are reported in order to illustrate the robustness and effectiveness of the proposed algorithmic procedure

Why the xE distribution triggered by a leading particle does not measure the fragmentation function but does measure the ratio of the transverse momenta of the away-side jet to the trigger-side jet

Hard-scattering of point-like constituents (or partons) in p-p collisions was discovered at the CERN-ISR in 1972 by measurements utilizing inclusive single or pairs of hadrons with large transverse momentum ($p_T$). It was generally assumed, following Feynman, Field and Fox, as shown by data from the CERN-ISR experiments, that the $p_{T_a}$ distribution of away side hadrons from a single particle trigger [with $p_{T_t}$], corrected for of fragmentation would be the same as that from a jet-trigger and follow the same fragmentation function as observed in $e^+ e^-$ or DIS. PHENIX attempted to measure the fragmentation function from the away side $x_E\sim p_{T_a}/p_{T_t}$ distribution of charged particles triggered by a $\pi^0$ in p-p collisions at RHIC and showed by explicit calculation that the $x_E$ distribution is actually quite insensitive to the fragmentation function. Illustrations of the original arguments and ISR results will be presented. Then the lack of sensitivity to the fragmentation function will be explained, and an analytic formula for the $x_E$ distribution given, in terms of incomplete Gamma functions, for the case where the fragmentation function is exponential. The away-side distribution in this formulation has the nice property that it both exhibits $x_E$ scaling and is directly sensitive to the ratio of the away jet $\hat{p}_{T_a}$ to that of the trigger jet, $\hat{p}_{T_t}$, and thus can be used, for example, to measure the relative energy loss of the two jets from a hard-scattering which escape from the medium in A+A collisions. Comparisons of the analytical formula to RHIC measurements will be presented, including data from STAR and PHENIX, leading to some interesting conclusions.Comment: 6 pages, 5 figures, Proceedings of Poster Session, 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2006), November 14-20, 2006, Shanghai, P. R. Chin

A relativistically covariant stochastic model for systems with a fluctuating number of particles

We construct a relativistically covariant stochastic model for systems of non-interacting spinless particles whose number undergoes random fluctuations. The model is compared with the canonical quantization of the free scalar field in the limit of infinite volume.Comment: 5 Pages; no figures; Plain REVTeX style. To be published in Phys. Lett.

Comment on "Why quantum mechanics cannot be formulated as a Markov process"

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.Comment: Latex file, resubm. to Phys. Rev.

A Next-to-Leading-Order Study of Dihadron Production

The production of pairs of hadrons in hadronic collisions is studied using a next-to-leading-order Monte Carlo program based on the phase space slicing technique. Up-to-date fragmentation functions based on fits to LEP data are employed, together with several versions of current parton distribution functions. Good agreement is found with data for the dihadron mass distribution. A comparison is also made with data for the dihadron angular distribution. The scale dependence of the predictions and the dependence on the choices made for the fragmentation and parton distribution functions are also presented. The good agreement between theory and experiment is contrasted to the case for single $\pi^0$ production where significant deviations between theory and experiment have been observed.Comment: 22 pages, 15 figures; 3 references added, one figure modified for clarit

Weak nuclear forces cause the strong nuclear force

We determine the strength of the weak nuclear force which holds the lattices of the elementary particles together. We also determine the strength of the strong nuclear force which emanates from the sides of the nuclear lattices. The strong force is the sum of the unsaturated weak forces at the surface of the nuclear lattices. The strong force is then about ten to the power of 6 times stronger than the weak force between two lattice points.Comment: 12 pages, 1 figur

A statistical procedure for testing financial contagion

The analysis of the relationships among financial markets and the identification of financial contagion episodes are relatively recent in the economic analysis and have experienced a rapid development in the last decade, coinciding with the occurrence of relevant financial crises which had effects that spread outside the geographical areas where they originally started. The increasing interest in this topic has lead to the definition of different tests for detecting the existence of financial contagion (Corsetti et al., 2001; Forbes and Rigobon, 2001; Dungey et al., 2004; Allen and Gale, 2005; Rodriguez, 2007; Krishnamurthy, 2009; Sugihara, 2010). However, conclusions on both theoretical and statistical analyses of financial contagion are far from unique. The changes in the international dynamics of returns, which in the last decades has been characterized by increases in both volatilities and asset price synchronicities in different countries, have raised even further the scientific interest in this topic. In this paper, we propose a new methodology for the evaluation of contagion based on the extent of disequilibria in financial dynamics and, in this framework, we define an innovative test for the detection of contagion which specifically identifies the disequilibrium originated by the international transmission of financial crises and their relationships with the behaviours of market participants. Disequilibria exogenously generated by the spread of the effects of a crisis beyond the dynamic process describing endogenous amplification of volatility from one country to other countries are attributed to contagion phenomena. In this framework, contagion effects are separated from the endogenous transmission processes which have their genesis in both the pricing process system and the investor\u2019s behaviours and which are responsible for the amplification of cross-market financial interdependence. In this paper, we discuss the theoretical framework underlying our approach and define a new econometric model for evaluating contagion among countries