Worldlines and body points associated with an extensive property

Material structure of bodies that is usually assumed a-priory in continuum mechanics is constructed on the basis of a balance of a given extensive property on spacetime. Body points are identified with worldlines—the integral lines of the flux of the property. The geometric setting assumes that spacetime has only the structure of a differentiable manifold and no particular frame is assumed to be given.     

Semi-Iterative Minimum Cross-Entropy Algorithms for Rare-Events,Counting, Combinatorial and Integer Programming

We present a new generic minimum cross-entropy method, called the semi-iterative MinxEnt, or simply SME, for rare-event probability estimation, counting, and approximation of the optimal solutions of a broad class of NP-hard linear integer and combinatorial optimization problems (COP’s). The main idea of our approach is to associate with each original problem an auxiliary single-constrained convex MinxEnt program of a special type, which has a closed-form solution. We prove that the optimal pdf obtained from the solution of such a specially designed MinxEnt program is a zero variance pdf, provided the “temperature” parameter is set to minus infinity. In addition we prove that the parametric pdf based on the product of marginals obtained from the optimal zero variance pdf coincides with the parametric pdf of the standard cross-entropy (CE) method. Thus, originally designed at the end of 1990s as a heuristics for estimation of rare-events and COP’s, CE has strong connection with MinxEnt, and thus, strong mathematical foundation. The crucial difference between the proposed SME method and the standard CE counterparts lies in their simulation-based versions: in the latter we always require to generate (via Monte Carlo) a sequence of tuples including the temperature parameter and the parameter vector in the optimal marginal pdf’s, while in the former we can fix in advance the temperature parameter (to be set to a large negative number) and then generate (via Monte Carlo) a sequence of parameter vectors of the optimal marginal pdf’s alone. In addition, in contrast to CE, neither the elite sample no the rarity parameter is needed in SME. As result, the proposed SME algorithm becomes simpler, faster and at least as accurate as the standard CE. Motivated by the SME method we introduce a new updating rule for the parameter vector in the parametric pdf of the CE program. We show that the CE algorithm based on the new updating rule, called the combined CE (CCE), is at least as fast and accurate as its standard CE and SME counterparts. We also found numerically that the variance minimization (VM)-based algorithms are the most robust ones. We, finally, demonstrate numerically that the proposed algorithms, and in particular the CCE one, allows accurate estimation of counting quantities up to the order of hundred of decision variables and hundreds of constraints. This research was supported by the Israel Science Foundation (grant No 191-565).     

Are quantum processes cosmologically induced?

Why, among ～10 ¹⁶ possibilities, does a wave function of a fast ion, spread over several centimeters, collapse in a crystal within a region measuring a few angstroms across? The most direct answer to this question would be the existence in this region of a cosmic particle, called a dybbuk, which induces the collapse. If dybbuks exist, deviations from conventional theory might be expected to occur for experiments involving ultrasmall space-time intervals less than the characteristic space-time interval of a dybbuk. It is shown that a dybbuk theory having the above characteristics can be constructed and can be tested experimentally by the decay of a0 ^? (J ^P) meson into two vector mesons.     

On input-output stability of time-varying nonlinear systems

In this work the question of bounded input-output stability of systems is investigated. The main tool of analysis is the generalized impulse response representation. Necessary and sufficient conditions for the stability of the operator are given. The analysis is carried out first for the linear operator and then the nonlinear operator is pursued. As is expected, difficulties are encountered for the nonlinear operator which do not occur for the linear case.     

Joint decision on production and pricing for online dual channel supply chain system

Online dual channel supply chain system and its joint decision on production and pricing under information asymmetry are investigated. First, optimal production and pricing strategies are depicted according to the centralized system. Next, two kinds of contracts are designed for the decentralized system to coordinate the channel system, and their production and pricing decisions are depicted using a principle-agent method for the asymmetric information on the traditional channel. Finally, some interesting insights are found: the centralized system is not always being better than the decentralized system with a feasible contract if the traditional and professional retailer has lower selling cost. When uncertainty in the traditional channel information is higher, the manufacturer prefers a menu of contracts according to different channel settings. When uncertainty is lower, the manufacturer prefers a single contract. Furthermore, the higher the uncertainty in the traditional channel, the more the information welfare of the traditional retailer will gain. Performance with a menu of contracts cannot outperform that with a single contract integrating optimistic and pessimistic market setting well; their difference in performance is bigger when uncertainty in the traditional channel information is less.     

News and Views: Challenges of Relativistic Astrophysics

I discuss some of the most outstanding challenges in relativistic astrophysics in the subjects of compact objects (black holes and neutron stars), dark sector (dark matter and dark energy), plasma astrophysics (origin of jets, cosmic rays, and magnetic fields), and the primordial universe (physics at the beginning of the Universe). In these four subjects, I discuss 12 of the most important challenges. These challenges give us insight into new physics that can only be studied in the large scale universe. The near-future possibilities, in observations and theory, for addressing these challenges are also discussed.     

Modeling of the shape of infrared stimulated luminescence signals in feldspars

This paper presents a new empirical model describing infrared (IR) stimulation phenomena in feldspars. In the model electrons from the ground state of an electron trap are raised by infrared optical stimulation to the excited state, and subsequently recombine with a nearest-neighbor hole via a tunneling process, leading to the emission of light. The model explains the experimentally observed existence of two distinct time intervals in the luminescence intensity; a rapid initial decay of the signal followed by a much slower gradual decay of the signal with time.The initial fast decay region corresponds to a fast rate of recombination processes taking place along the infrared stimulated luminescence (IRSL) curves. The subsequent decay of the simulated IRSL signal is characterized by a much slower recombination rate, which can be described by a power-law type of equation.Several simulations of IRSL experiments are carried out by varying the parameters in the model. It is found that the shape of the IRSL signal is remarkably stable when the kinetic parameters are changed within the model; this is in agreement with several previous studies of these signals on feldspars, which showed that the shape of the IRSL curves does not change significantly under different experimental conditions. The relationship between the simulated IRSL signal and the well-known power-law dependence of relaxation processes in solids is also explored, by fitting the IRSL signal at long times with a power-law type of equation. The exponent in this power-law is found to depend very weakly on the various parameters in the model, in agreement with the results of experimental studies. The results from the model are compared with experimental IRSL curves obtained using different IR stimulating power, and good quantitative agreement is found between the simulation results and experimental data.     

Superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals in luminescence materials: An analytical approach

The phenomenon of superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals has been reported for several important dosimetric materials. We develop new analytical equations for the filling of traps and centers during irradiation and for the read-out stage of annealed luminescence materials, within the context of a two-trap and two-center model. The equations are applicable for both TL and OSL signals in annealed dosimetric materials, and are derived under the assumptions of low irradiation doses and dominant strong retrapping (weak recombination) processes. For low doses all traps and centers display linear dose response, which leads to quadratic dose response of the integrated TL/OSL signals. A new analytical expression is presented for this well-known quadratic dose dependence, in terms of the kinetic parameters in the model. The effect of elevated irradiation temperature on the integrated TL/OSL signals is also considered, and analytical expressions are obtained for this situation as well. A new type of dose-rate effect is reported based on the modeling results, which is due to irradiation during elevated temperatures. The accuracy of the analytical expressions is verified by comparing with the results of numerical simulations.