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

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 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

Spatial bunching of same-charge polarization singularities in two-dimensional random vector waves

Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the ellipse becomes degenerate and light's electric field vector describes a perfect circle in time. In 2D slices of 3D random fields the distribution in space of the C points is reminiscent of that of interacting particles. With near-field experiments we show that when light becomes truly 2D, this has severe consequences for the distribution of C points in space. The most notable change is that the probability of finding two C points with the same topological charge at a vanishing distance is enhanced in a 2D field. This is an unusual finding for any system which exhibits topological singularities as same-charge repulsion is typically observed. All our experimental findings are supported with theory and excellent agreement is found between theory and experiment

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