Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Devienne i el fagot : una visió de les obres de fagot i el seu moment

L’objectiu del treball és conèixer millor la figura de François Devienne i la seva obra per a fagot. Per això es fa un recorregut per la seva biografia, context històric i musical, el fagot de l’època, amb el qual tocava i per al qual composava, el seu catàleg de l’obra musical per fagot i una anàlisi de dues de les seves obres, una sonata i un quartet. Aquesta darrera part no es tracta només d’una anàlisi formal, sinó que recull també la vessant interpretativa.

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.

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

High-momentum proton removal from 16 O and the (e,e'p) cross section

The cross section for the removal of high-momentum protons from 16O is calculated for high missing energies. The admixture of high-momentum nucleons in the 16O ground state is obtained by calculating the single-hole spectral function directly in the finite nucleus with the inclusion of short-range and tensor correlations induced by a realistic meson-exchange interaction. The presence of high-momentum nucleons in the transition to final states in 15N at 60¿100 MeV missing energy is converted to the coincidence cross section for the (e,e¿p) reaction by including the coupling to the electromagnetic probe and the final state interactions of the outgoing proton in the same way as in the standard analysis of the experimental data. Detectable cross sections for the removal of a single proton at these high missing energies are obtained which are considerably larger at higher missing momentum than the corresponding cross sections for the p-wave quasihole transitions. Cross sections for these quasihole transitions are compared with the most recent experimental data available.

Two nucleon induced Lambda decay and the proton to neutron induced ratio

We reanalyze the decay mode of Lambda hypernuclei induced by two nucleons modifying previous numerical results and the interpretation of the process. The repercussions of this channel in the ratio of neutron to proton induced Lambda decay is studied in detail in connection with the present experimental data. This leads to ratios that are in greater contradiction with usual one pion exchange models than those deduced before.

Kinematically complete analysis of the CLAS data on the proton structure Function F2 in a Regge-Dual model

The recently measured inclusive electron-proton cross section in the nucleon resonance region, performed with the CLAS detector at the Thomas Jefferson Laboratory, has provided new data for the nucleon structure function F2 with previously unavailable precision. In this paper we propose a description of these experimental data based on a Regge-dual model for F2. The basic inputs in the model are nonlinear complex Regge trajectories producing both isobar resonances and a smooth background. The model is tested against the experimental data, and the Q2 dependence of the moments is calculated. The fitted model for the structure function (inclusive cross section) is a limiting case of the more general scattering amplitude equally applicable to deeply virtual Compton scattering. The connection between the two is discussed.

Proton emission off nuclei induced by kaons in flight

We study the (K-, p) reaction on nuclei with a 1 GeV/c momentum kaon beam, paying special attention to the region of emitted protons having kinetic energy above 600 MeV, which was used to claim a deeply attractive kaon nucleus optical potential. Our model describes the nuclear reaction in the framework of a local density approach and the calculations are performed following two different procedures: one is based on a many-body method using the Lindhard function and the other is based on a Monte Carlo simulation. The simulation method offers flexibility to account for processes other than kaon quasielastic scattering, such as K- absorption by one and two nucleons, producing hyperons, and allows consideration of final-state interactions of the K-, the p, and all other primary and secondary particles on their way out of the nucleus, as well as the weak decay of the produced hyperons into pi N. We find a limited sensitivity of the cross section to the strength of the kaon optical potential. We also show a serious drawback in the experimental setup-the requirement for having, together with the energetic proton, at least one charged particle detected in the decay counter surrounding the target-as we find that the shape of the original cross section is appreciably distorted, to the point of invalidating the claims made in the experimental paper on the strength of the kaon nucleus optical.

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of p H and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.