Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

We derive analytical expressions for the propagation speed of downward combustion fronts of thin solid fuels with a background flow initially at rest. The classical combustion model for thin solid fuels that consists of five coupled reaction-convection-diffusion equations is here reduced into a single equation with the gas temperature as the single variable. For doing so we apply a two-zone combustion model that divides the system into a preheating region and a pyrolyzing region. The speed of the combustion front is obtained after matching the temperature and its derivative at the location that separates both regions.We also derive a simplified version of this analytical expression expected to be valid for a wide range of cases. Flame front velocities predicted by our analyticalexpressions agree well with experimental data found in the literature for a large variety of cases and substantially improve the results obtained from a previous well-known analytical expression

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry (nuclear relaxation contribution) and vibrational motion (vibrational contribution) of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties (the so-called AEEP method), results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values

Compact matrix expressions for generalized Wald tests of equality of moment vectors

Asymptotic chi-squared test statistics for testing the equality ofmoment vectors are developed. The test statistics proposed aregeneralizedWald test statistics that specialize for different settings by inserting andappropriate asymptotic variance matrix of sample moments. Scaled teststatisticsare also considered for dealing with situations of non-iid sampling. Thespecializationwill be carried out for testing the equality of multinomial populations, andtheequality of variance and correlation matrices for both normal andnon-normaldata. When testing the equality of correlation matrices, a scaled versionofthe normal theory chi-squared statistic is proven to be an asymptoticallyexactchi-squared statistic in the case of elliptical data.

Deciding analytically or trusting your intuition? The advantadges and disadvantadges of analytic and intuitive thought

Recent research has highlighted the notion that people can make judgmentsand choices by means of two systems that are labeled here tacit(or intuitive) and deliberate (or analytic). Whereas most decisionstypically involve both systems, this chapter examines the conditions underwhich each system is liable to be more effective. This aims to illuminatethe age-old issue of whether and when people should trust intuition or analysis. To do this, a framework is presented to understand how thetacit and deliberate systems work in tandem. Distinctions are also madebetween the types of information typically used by both systems as wellas the characteristics of environments that facilitate or hinder accuratelearning by the tacit system. Next, several experiments that havecontrasted intuitive and analytic modes on the same tasks are reviewed.Together, the theoretical framework and experimental evidence leads tospecifying the trade-off that characterizes their relative effectiveness.Tacit system responses can be subject to biases. In making deliberate systemresponses, however, people might not be aware of the correct rule to dealwith the task they are facing and/or make errors in executing it. Whethertacit or deliberate responses are more valid in particular circumstancesrequires assessing this trade-off. In this, the probability of making errorsin deliberate thought is postulated to be a function of the analytical complexityof the task as perceived by the person. Thus the trade-off is one of bias (inimplicit responses) versus analytical complexity (when tasks are handled indeliberate mode). Finally, it is noted that whereas much attention has beenpaid in the past to helping people make decisions in deliberate mode, effortsshould also be directed toward improving ability to make decisions intacit mode since the effectiveness of decisions clearly depends on both. Thistherefore represents an important frontier for research.

On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

Analytic behavior of the QED polarizability function at finite temperature

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Black holes by analytic continuation

In the context of a two-dimensional exactly solvable model, the dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model in the region where the outgoing modes arise from the horizon with Planck-order frequencies. This occurs early in the evaporation process, and the resulting physical picture is unconventional. The theory predicts that black holes will only radiate out an energy of Planck mass order, stabilizing after a transitory period. The continuation from a regime without black hole formationaccessible in the 1+1 gravity theory consideredis implicit in an S-matrix approach and suggests in this way a possible solution to the problem of information loss.

La música i la multiculturalitat a l'aula. Com la pràctica de les diferents expressions musicals dels infants a l'aula pot ajudar al coneixement mutu en el grup- classe

Actualment, vivim en una societat on hi conviuen diferents cultures i la música és un llenguatge que s’utilitza en totes elles. Aquest treball tractarà el tema de la música i la multiculturalitat a l’aula per investigar si és possible, a partir de la música dels diferents països d’origen dels infants, conèixer-se millor i conèixer millor als companys. Com a mestres hem de tenir en compte totes les cultures de la nostra aula per tal d’ajudar als infants a respectar i valorar cada una d’elles. En aquesta investigació trobarem quina ha estat la metodologia d’estudi, quina ha estat la intervenció a l’aula i quins són els resultats que hem obtingut.

Weight filtration on the cohomology of complex analytic spaces

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.