Pion-pair formation and the pion dispersion relation in a hot pion gas

The possibility of pion--pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans--Rashid transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two--particle propagator. In bose systems there exists a second, lower critical temperature, associated with the appearance of the single--particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usual quasiparticle dispersion to a Bogoliubov--like dispersion relation at low momenta. This generalizes the non-relativistic result for an attractive bose gas by Evans et al. Possible consequences for the inclusive pion spectra measured in heavy--ion collisions at ultra--relativistic energies are discussed.Comment: 16 pages revtex, 7 Postscript figure

Short-Term Generation Asset Valuation

We present a method for valuing a power plant over a short term period using Monte Carlo simulation. The power plant valuation problem is formulated as a multi stage stochastic problem. We assume there are hourly markets for both electricity and the fuel used by the generator, and their prices follow some Ito processes. At each hour, the power plant operator must decide to run or not to run the unit so as to maximize expected profit. A certain lead time for commitment decision is necessary to start up a unit. The commitment decision, once made, is subject to physical constraints such as minimum uptime and downtime constraints. The generator\u27\u27s startup cost, is also taken into account in our model. The Monte Carlo method is employed not only in forward moving simulation, but also backward moving recursion of dynamic programming. We demonstrate through numerical tests how the physical constraints affect a power plant value

Size of Fireballs Created in High Energy Lead-Lead Collisions as Inferred from Coulomb Distortions of Pion Spectra

We compute the Coulomb effects produced by an expanding, highly charged fireball on the momentum distribution of pions. We compare our results to data on Au+Au at 11.6 A GeV from E866 at the BNL AGS and to data on Pb+Pb at 158 A GeV from NA44 at the CERN SPS. We conclude that the distortion of the spectra at low transverse momentum and mid-rapidity can be explained in both experiments by the effect of the large amount of participating charge in the central rapidity region. By adjusting the fireball expansion velocity to match the average transverse momentum of protons, we find a best fit when the fireball radius is about 10 fm, as determined by the moment when the pions undergo their last scattering. This value is common to both the AGS and CERN experiments.Comment: Enlarged discussion, new references added, includes new analysis of pi-/pi+ at AGS energies. 12 pages 5 figures, uses LaTex and epsfi

Coulomb Effect: A Possible Probe for the Evolution of Hadronic Matter

Electromagnetic field produced in high-energy heavy-ion collisions contains much useful information, because the field can be directly related to the motion of the matter in the whole stage of the reaction. One can divide the total electromagnetic field into three parts, i.e., the contributions from the incident nuclei, non-participating nucleons and charged fluid, the latter consisting of strongly interacting hadrons or quarks. Parametrizing the space-time evolution of the charged fluid based on hydrodynamic model, we study the development of the electromagnetic field which accompanies the high-energy heavy-ion collisions. We found that the incident nuclei bring a rather strong electromagnetic field to the interaction region of hadrons or quarks over a few fm after the collision. On the other hand, the observed charged hadrons' spectra are mostly affected (Coulomb effect) by the field of the charged fluid. We compare the result of our model with experimental data and found that the model reproduces them well. The pion yield ratio pi^-/pi+ at a RHIC energy, Au+Au 100+100 GeV/nucleon, is also predicted.Comment: 23 pages, RevTex, 19 eps figures, revised versio

Enthalpy as internal energy in plug flow reactor models: A long-lasting assumption defeated and its effects on models predictions in dynamic regime

In this paper, a general dynamic model of a pseudo-homogeneous catalytic plug flow reactor (PFR) is developed, which does not apply the traditional assumption of negligible difference between enthalpy and internal energy inside its energy balance. Such a model is then compared to a second dynamic PFR model, whose energy conservation equation identifies internal energy with enthalpy. The aim is that of quantitatively investigating the real suitability of the identification of these two thermodynamic quantities (internal energy and enthalpy) in PFR modeling problems. The Claus process is selected as a meaningful case study for the aforementioned purposes

Blurred femtoscopy in two-proton decay

We study the effects of final state interactions in two-proton emission by nuclei. Our approach is based on the solution the time-dependent Schr\"odinger equation. We show that the final relative energy between the protons is substantially influenced by the final state interactions. We also show that alternative correlation functions can be constructed showing large sensitivity to the spin of the diproton system.Comment: 5 pages. 4 figures, accepted for publication in Phys. Lett.

Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev

Freeze-Out Time in Ultrarelativistic Heavy Ion Collisions from Coulomb Effects in Transverse Pion Spectra

The influence of the nuclear Coulomb field on transverse spectra of $\pi^+$ and $\pi^-$ measured in $Pb+Pb$ reactions at 158 A GeV has been investigated. Pion trajectories are calculated in the field of an expanding fireball. The observed enhancement of the $\pi^-/\pi^+$ ratio at small momenta depends on the temperature and transverse expansion velocity of the source, the rapidity distribution of the net positive charge, and mainly the time of the freeze-out.Comment: 11 pages including 2 figure

Relativistic quantum kinetic equation of the Vlasov type for systems with internal degrees of freedom

We present an approach to derive a relativistic kinetic equation of the Vlasov type. Our approach is especially reliable for the description of quantum field systems with many internal degrees of freedom. The method is based on the Heisenberg picture and leads to a kinetic equation which fulfills the conservation laws. We apply the approach to the standard Walecka Lagrangian and an effective chiral Lagrangian.Comment: 11 pages, LaTeX, uses ijmpel.st

Resonance Model of πΔ→YK\pi \Delta \rightarrow Y K for Kaon Production in Heavy Ion Collisions

The elementary production cross sections $\pi \Delta \rightarrow Y K$ $(Y=\Sigma,\,\, \Lambda)$ and $\pi N \rightarrow Y K$ are needed to describe kaon production in heavy ion collisions. The $\pi N \rightarrow Y K$ reactions were studied previously by a resonance model. The model can explain the experimental data quite well \cite{tsu}. In this article, the total cross sections $\pi \Delta \rightarrow Y K$ at intermediate energies (from the kaon production threshold to3 GeV of $\pi \Delta$ center-of-mass energy) are calculated for the first time using the same resonance model. The resonances, $N(1710)\,I(J^P) = \frac{1}{2}(\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ for the $\pi \Delta \rightarrow \Sigma K$ reactions, and $N(1650)\, \frac{1}{2} (\frac{1}{2}^-)$, $N(1710)\, \frac{1}{2} (\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ for the $\pi \Delta \rightarrow \Lambda K$ reactions are taken into account coherently as the intermediate states in the calculations. Also t-channel $K^*(892) \frac{1}{2}(1^-)$ vector meson exchange is included. The results show that $K^*(892)$ exchange is neglegible for the $\pi \Delta \rightarrow \Sigma K$ reactions, whereas this meson does not contribute to the $\pi \Delta \rightarrow \Lambda K$ reactions. Furthemore, the $\pi \Delta \rightarrow Y K$ contributions to kaon production in heavy ion collisions are not only non-neglegible but also very different from the $\pi N \rightarrow Y K$ reactions. An argument valid for $\pi N \rightarrow Y K$ cannot be extended to $\pi \Delta \rightarrow Y K$ reactions. Therefore, cross sections for $\pi \Delta \rightarrow Y K$ including correctly the different isospins must beComment: ( Replaced with corrections of printing errors in the Table. ) 15 pages, Latex file with 4 figures, 1 figure is included in the text. A compressed uuencode file for 3 figures is appended. (A figure file format was changed.) Also available upon reques