Prediction of the steady flame spread rate by the principle of minimal entropy production

The propagation of a two-dimensional diffusive flame over a combustible material is studied by solving steady-state conservation equations written in the coordinate system fixed on the flame front. The analysis of a two-dimensional problem featuring flame spread rate as an eigenvalue has shown that there is no unique solution relative to the flame spread rate unless some additional condition is involved. A novel approach to the prediction of flame spread rate is proposed using the principles of irreversible thermodynamics. The steady flame propagation is considered as a stationary non-equilibrium thermodynamic state, which can be characterized, according to the formulation of Prigogine, by minimal entropy production. A numerical algorithm for the prediction of flame spread rate has been developed and tested on the investigation of downward flame spread over thin sheets of paper. The adequate physical background of the proposed approach and satisfactory agreement with experimental data have been shown.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Minimum entropy production and logarithmic rate equations

A system interacting with a heat bath and radiation is considered. It is assumed that the steady state is exactly characterized by the principle of minimum entropy production. From this, the general form of the equations for the time rate of change of the probabilities of the states is derived and the rate equations are shown to be nonlinear and to involve the differences of the logarithms of the probabilities. Some properties of these equations are discussed and the specific cases of two- and three-state subsystems are considered and compared with results obtained from the usual linear rate equations.     

Relative entropy and hydrodynamics of Ginzburg-Landau models

We prove the hydrodynamic limit of Ginzburg-Landau models by considering relative entropy and its rate of change with respect to local Gibbs states. This provides a new understanding of the role played by relative entropy in the hydrodynamics of interacting particle systems.Work partially supported by U.S. National Science Foundation Grant. DMS-8806731 and Army Grant ARO-DAAL 03-88-K-0047.     

Spontaneous parity violation and minimal Higgs models

In this paper we present a model for the spontaneous breaking of parity with two Higgs doublets and two neutral Higgs singlets which are even and odd under -parity. The condition can be satisfied without introducing bidoublets, and it is induced by the breaking of -parity through the vacuum expectation value of the odd Higgs singlet. Examples of left–right symmetric and mirror fermions models in grand unified theories are presented. PACS 12.60.Cn; 14.80.Cp; 12.10.Dm     

Coupled minimal models with and without disorder

We analyze in this article the critical behavior of M q₁-state Potts models coupled to N q₂-state Potts models (q₁, q₂ ε [2, …, 4]) with and without disorder. The techniques we use are based on perturbed conformal theories. Calculations have been performed at two loops. We already find some interesting situations in the pure case for some peculiar values of M and N with new tricritical points. When adding weak disorder, the results we obtain tend to show that disorder makes the models decouple. Therefore, no relations emerges, at a perturbation level, between for example the disordered q₁ × q₂-state Potts model and the two disordered q₁, q₂-state Potts models (q₁ ≠ q₂), despite the fact that their central charges are similar according to recent numerical investigations.     

The dispersionless Lax equations and topological minimal models

It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions ofA _n topological minimal models are found. The Virasoro constraints for the analogue of the -function of the dispersionless Lax equation corresponding to these models are proved.     

Shannon entropy as a measure of uncertainty in positions and momenta

I start with a brief report of the topic of entropic uncertainty relations for the position and momentum variables. Then I investigate the discrete Shannon entropies related to the case of a finite number of detectors set to measure the probability distributions in the position and momentum spaces. I derive the uncertainty relation for the sum of the Shannon entropies which generalizes the previous approach by I. Bialynicki-Birula based on an infinite number of detectors (bins).     

The Fisher information measure and Shannon entropy for particulate matter measurements

We investigated the dynamics of particulate matter data, recorded in Tito, a small industrial area of southern Italy. The analysis of these signals was performed using the Fisher information measure (FIM), which is a powerful tool for investigating complex and nonstationary signals, and the Shannon entropy, which is a well-known tool for investigating the degree of disorder in dynamical systems. Our results point to an increase of disorder and complexity from fine to coarse particulates.     

Beliefs and stochastic modelling of interest rate scenario risk

We present a framework that allows for a systematic assessment of risk given a specific model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows for a (time-)local understanding of its level, together with a short term forecast. On the other hand, via a diffusion approximation, the time evolution of the probability density of risk is modeled by a Fokker-Planck equation. Then, as a final step, using Bayes theorem, beliefs are conditioned on the stationary probability density function as obtained from the Fokker-Planck equation. We believe this to be a highly rigorous framework to integrate subjective judgments of future market behavior and underlying models. In order to demonstrate the approach, we apply it to risk assessment of empirical interest rate scenario methodologies, i.e. the application of Principal Component Analysis to the the dynamics of bonds. Received 1st August 2000     

Two-site entropy and quantum phase transitions in low-dimensional models

We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters, or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group algorithm is used.     

Torus amplitudes in minimal Liouville gravity and matrix models

We evaluate one-point correlation numbers on the torus in the Liouville theory coupled to the conformal matter M(2,2p+1)$M(2,2p+1)$. We find agreement with the recent results obtained in the matrix model approach.     

Particle mass limits in minimal and nonminimal supersymmetric models

A review of the Higgs and neutralino sector of supersymmetric models is presented. This includes the upper limit on the mass of the lightest Higgs boson in the minimal supersymmetric standard model, as well as models based on the standard model gauge groupSU(2) _L xU(l) _Y with extended Higgs sectors. We then discuss the Higgs sector of left-right supersymmetric models, which conserveR-parity as a consequence of gauge invariance, and present a calculable upper bound on the mass of the lightest Higgs boson in these models. We also discuss the neutralino sector of general supersymmetric models based on the SM gauge group. We show that, as a consequence of gauge coupling unification, an upper bound on the mass of the lightest neutralino as a function of the gluino mass can be obtained.