Shared information in stationary states of stochastic processes

We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

LIMIT THEOREMS FOR A GENERAL STOCHASTIC RUMOUR MODEL

We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.

Batch cooling crystallization of xylitol produced by biotechnological route

BACKGROUND: This work deals with the xylitol production by biotechnological routes emphasizing the purification process using crystallization. RESULTS: Xylitol volumetric productivity of 0.665 g L(-1) h(-1) and yield of 0.7024 g g(-1) were obtained after 92 h fermentation. The fermented broth (61.3 g L(-1) xylitol) was centrifuged, treated and concentrated obtain a syrup (745.3 g L(-1) xylitol) which was crystallized twice, xylitol crystals with 98.5-99.2% purity being obtained. CONCLUSION: The hypothetical distribution obtained permits the determination of modeling parameters, which make possible the estimation of crystal dominant size from different initial experimental conditions. (C) 2008 Society of Chemical Industry

Niobium hydrogenation process Effect of temperature and cooling rate from the hydrogenation temperature

High-purity niobium powder can be produced via the hydrogenation and dehydrogenation processes The present work aimed at the effect of temperature and cooling rate conditions on the niobium hydrogenation process using hydrogen gas The hydrogen contents of the materials were evaluated by weight change and chemical analysis X ray diffraction (XRD) was performed to identify and determine the lattice parameters of the formed hydride phases No hydrogenation took place under isothermal conditions only during cooling of the materials Significant hydrogenation occurred in the 500 C and 700 C experiments leading to the formation of a beta NbH(x) single phase material (C) 2010 Elsevier Ltd All rights reserved

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Analysis of the behavior of transverse walls of socket base connections

This paper presents a theoretical and experimental analysis of socket base connections of precast concrete structures with regard to the behavior of transverse walls. The experimental program included seven specimens, for which the type of interface in contact with cast-in-place concrete, the load eccentricities and the embedded lengths were all varied, A design model was proposed to calculate the reinforcements of the transverse walls. Based on the obtained results, some conclusions can be drawn: (a) The top of the transverse wall on the compression side of the smooth connections and the top of the two transverse walls of the rough connections are submitted to a bending-tension and this tension prevails on the bending; (b) The design model proposed for the calculation of the reinforcement of the transverse wall on the compression side provides the best prediction of the experimental results for all specimens when compared to the current design models; (c) For rough interfaces, the top of the transverse wall on the tension side is more requested than the top of transverse wall on the compression side; (d) The results of the proposed design model for the reinforcement of the transverse wall on the tension side of rough connections were in close agreement with the experimental results. (C) 2008 Elsevier Ltd. All rights reserved.

Vegetable Oil Quenchants: Calculation and Comparison of The Cooling Properties of a Series of Vegetable Oils

The compositions of canola, soybean, corn, cottonseed and sunflower oils suggest that they exhibit substantially different propensity for oxidation following the order of Canola < corn < cottonseed < sunflower approximate to soybean. These data suggest that any of the vegetable oils evaluated could be blended with minimal impact on viscosity although compositional differences would surely affect oxidative stability. Cooling curve analysis showed that similar cooling profiles were obtained for different vegetable oils. Interestingly, no film boiling or transition nucleate boiling was observed with any of the vegetable oils and heat transfer occurs only by pure nucleate boiling and convection. High-temperature cooling properties of vegetable oils are considerable faster than those observed for petroleum oil-based quenchants. (C)2010 Journal of Mechanical Engineering. All rights reserved.

Fatigue behaviour of friction stir welded AA2024-T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024-T3 aluminium alloy have been studied under constant load amplitude (increasing-Delta K), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka`s method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold Delta K values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K-C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non-conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non-conservative crack growth rate predictions next to K-C instability. At threshold Delta K values non-conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.

Influence of Microstructures on Polarization Resistance and Hydrogen-Induced Cracking of a Micro-Alloyed Steel Submitted to Different Cooling Rates

The effect of different microstructures on the polarization resistance (Rp) and the hydrogen-induced cracking (HIC) of a micro-alloyed steel austenitized and submitted to different cooling rates was studied. Samples 19.1 x 6 x 2 mm, containing the whole thickness of the plate were extracted from a 20 mm plate and heat treated on a quenching dilatometer, were submitted to Rp and HIC corrosion tests. Both Rp and HIC tests followed as close as possible ASTM G59 and NACE standard TM0284-2003, in this case, modified only with regard to the size of the samples. Steel samples transformed from austenite by a slow cooling (cooling rate of 0.5 degrees C.s(-1)) showed higher susceptibility to hydrogen-induced cracking, with large cracks in the middle of the sample propagating along segregation bands, corresponding to the centerline of the plate thickness. For cooling rates of 10 degrees C.s(-1), only small cracks were found in the matrix and micro cracks nucleated at non-metallic inclusions. For higher cooling rates (40 degrees C.s(-1)) very few small cracks were detected, linked to non-metallic inclusions. This result suggests that structures formed by polygonal structures and segregation bands (were cutectoid microconstituents predominate) have higher susceptibility to HIC. Structures predominantly formed by acicular ferrite make it difficult to propagate the cracks among non-oriented and interlaced acicular ferrite crystals. Smaller segregation bands containing eutectoid products also help inhibit cracking and crack propagation; segregation bands can function as pipelines for hydrogen diffusion and offer a path of stress concentration for the propagation of cracks, frequently associated to non-metallic inclusions. Polarization resistance essays performed on the steel in theas received condition, prior to any heat treatment, showed larger differences between the regions of the plate, with a considerably lower Rp in the centerline. The austenitization heat treatments followed by cooling rates of 0.5 e 10 degrees C.s(-1) made more uniform the corrosion resistance along the thickness of the plate. The effects of heat treatments on the corrosion resistance are probably related to the microconstituent formed, allied to the chemical homogenization of the impurities concentrated on the centerline of the plate.

Integrated analysis of cooling water systems: Modeling and experimental validation

Cooling towers are widely used in many industrial and utility plants as a cooling medium, whose thermal performance is of vital importance. Despite the wide interest in cooling tower design, rating and its importance in energy conservation, there are few investigations concerning the integrated analysis of cooling systems. This work presents an approach for the systemic performance analysis of a cooling water system. The approach combines experimental design with mathematical modeling. An experimental investigation was carried out to characterize the mass transfer in the packing of the cooling tower as a function of the liquid and gas flow rates, whose results were within the range of the measurement accuracy. Then, an integrated model was developed that relies on the mass and heat transfer of the cooling tower, as well as on the hydraulic and thermal interactions with a heat exchanger network. The integrated model for the cooling water system was simulated and the temperature results agree with the experimental data of the real operation of the pilot plant. A case study illustrates the interaction in the system and the need for a systemic analysis of cooling water system. The proposed mathematical and experimental analysis should be useful for performance analysis of real-world cooling water systems. (C) 2009 Elsevier Ltd. All rights reserved.

A systemic approach for optimal cooling tower operation

The thermal performance of a cooling tower and its cooling water system is critical for industrial plants, and small deviations from the design conditions may cause severe instability in the operation and economics of the process. External disturbances such as variation in the thermal demand of the process or oscillations in atmospheric conditions may be suppressed in multiple ways. Nevertheless, such alternatives are hardly ever implemented in the industrial operation due to the poor coordination between the utility and process sectors. The complexity of the operation increases because of the strong interaction among the process variables. In the present work, an integrated model for the minimization of the operating costs of a cooling water system is developed. The system is composed of a cooling tower as well as a network of heat exchangers. After the model is verified, several cases are studied with the objective of determining the optimal operation. It is observed that the most important operational resources to mitigate disturbances in the thermal demand of the process are, in this order: the increase in recycle water flow rate, the increase in air flow rate and finally the forced removal of a portion of the water flow rate that enters the cooling tower with the corresponding make-up flow rate. (C) 2009 Elsevier Ltd. All rights reserved.