Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Separation by thermal diffusion in a rotary column

A rotary thermal diffusion column with the inner cylinder rotating and the outer cylinder static was used to separate n-heptane-benzene mixtures at different speeds of rotation. The results show that the column efficiency depends on the speed of rotation. For the optimum speed the increase in efficiency relative to the static column was of the order of 8%. The role of the geometric irregularities in the annulus width on performance of the rotary column is also discussed.

Nonsymmetrical separations in thermal diffusion columns

The influence of the feed composition upon the actual degrees of separation attained at the top and bottom sections of a thermogravitational column is discussed using the classical phenomenological theory of Furry, Jones, and Onsager. It is shown that, except for a feed composition of C 0 = 0.5 (mass fraction), the separation profile is nonsymmetric, i.e., the separations in the top and bottom sections of the column are nonsymmetric with respect to the feed composition, the asymmetry increasing as the feed composition moves away from C 0 = 0.5. An equation for the determination of the optimum feed location as a function of the feed composition is derived.

Some observations on asymmetrical separation in thermal diffusion columns

Data have been obtained in steady-state batch operated thermogravitational separation columns using different binary mixtures to test the theory recently published by Morgado et al. The experimental results confirm that separations by thermal diffusion are asymmetrical except when the initial concentration is 0.5 and that the asymmetry is larger as the initial concentration deviates from 0.5 and as the separation potential increases.

The application of the equivalent annulus width concept in thermal diffusion separations

The equivalent annulus width concept is used to characterize a small commercial thermogravitational hermal diffusion column and its validity checked experimentally by separating batchwise in the column mixtures of n-heptanebenzene with different initial concentrations. The equation of Ruppell and Coull was used to analyse the data in the short separation times range and determine the equivalent annulus width. Good agreement was obtained between the experimental and predicted time-separation curves when using the equivalent annulus width value and on averaged value of the thermal diffusion constant. A new method is presented for the simultaneous determination of the equivalent annulus width and the thermal diffusion constant of a binary mixture from a single set of experimental data.

Single molecule simulation of diffusion and enzyme kinetics

This work presents a molecular-scale agent-based model for the simulation of enzymatic reactions at experimentally measured concentrations. The model incorporates stochasticity and spatial dependence, using diffusing and reacting particles with physical dimensions. We developed strategies to adjust and validate the enzymatic rates and diffusion coefficients to the information required by the computational agents, i.e., collision efficiency, interaction logic between agents, the time scale associated with interactions (e.g., kinetics), and agent velocity. Also, we tested the impact of molecular location (a source of biological noise) in the speed at which the reactions take place. Simulations were conducted for experimental data on the 2-hydroxymuconate tautomerase (EC 5.3.2.6, UniProt ID Q01468) and the Steroid Delta-isomerase (EC 5.3.3.1, UniProt ID P07445). Obtained results demonstrate that our approach is in accordance to existing experimental data and long-term biophysical and biochemical assumptions.

Efeitos da exposição à fumaça lateral do cigarro sobre o barorreflexo em ratos adultos

FUNDAMENTO: Tem sido demonstrado na literatura que a exposição à fumaça do cigarro causa hipertensão em ratos; entretanto, ainda não foi demonstrado se a função barorreflexa está prejudicada antes do animal se tornar hipertenso. OBJETIVO: Avaliamos os efeitos de curto prazo da exposição à fumaça lateral do cigarro (FLC) sobre a função barorreflexa em ratos Wistar normotensos. MÉTODOS: Os ratos foram expostos à FLC durante três semanas, 180 minutos, cinco dias por semana, a uma concentração de monóxido de carbono entre 100-300 ppm. A pressão arterial média (PAM) e a freqüência cardíaca (FC) foram avaliadas através de canulação da veia e artéria femoral. RESULTADOS: Não houve diferença significante entre os grupos controle e FLC em relação à MAP e FC, componentes simpáticos e parassimpáticos da função barorreflexa. CONCLUSÃO: Nossos dados sugerem que três semanas de exposição à FLC não são suficientes para causar dano significante aos parâmetros cardiovasculares e sensibilidade barorreflexa em ratos Wistar normotensos.

Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Adaptive numerical simulation of reaction - diffusion systems

Fluidized beds, granulation, heat and mass transfer, calcium dynamics, stochastic process, finite element methods, Rosenbrock methods, multigrid methods, parallelization

Funktionelle Untersuchungen zur pulmonalen Diffusion, dem pulmonalen kapillären Blutvolumen und der Rolle des Endothelin-1 bei Patienten mit Leberzirrhose

Magdeburg, Univ., Med. Fak., Diss., 2015

Static diffusion models of the upper atmosphere with empirical temperature profiles.

v. 8 no. 9

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

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.

Critical evaluation of outcome scales to assess outcome after lateral ankle ligament repair

Introduction: Several scores are commonly used to evaluate patients' postoperative satisfaction after lateral ankle ligament repair, including: AOFAS, FAAM, CAIT and CAIS. Comparing published studies in the literature is difficult, as the same patient can have markedly different results depending on which scoring system is used. The current study aims to address this gap in the literature by developing a system to compare these tests, to allow better analysis and comparison of published studies. Patients and methods: This is a retrospective cohort study of 47 patients following lateral ankle ligament repair using a modified Broström-Gould technique. All patients were operated between 2005 and 2010 by a single surgeon and followed the same post operative rehabilitation protocol. Six patients were excluded from the study because of concomitant surgery. Patients were assessed by an independent observer. We used the Pearson correlation coefficient to analyse the concordance of the scores, as well as scatter plots to assess the linear relationship between them. Results: A linear distribution between the scores was found when the results were analysed using scatter plots. We were thus able to use the Pearson correlation coefficient to evaluate the relationship between each of the different postoperative scores. The correlation was found to be above 0.5 in all cases except for the comparison between the CAIT and the FAAM for the activities of daily living (0.39). We were, therefore, able to compare the results obtained and assess the relative concordance of the scoring systems. The results showed that the more specific the scale is, the worst the score is and inversely. So the CAIT and the CAIS appeared to be more severe than the AOFAS and the FAAM measuring the activities of daily living. The sports subscale of the FAAM demonstrated intermediate results. Conclusion: This study outlines a system to compare different postoperative scores commonly used to evaluate outcome after ankle stabilization surgery. The impact of this study is that it makes comparison of published studies easier, even though they use a variety of different clinical scores, thus facilitating better outcome analysis of operative techniques.