Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Effect of vehicle pretreatment on the flux, retention, and diffusion of topically applied penetrants in vitro

Purpose. The flux of a topically applied drug depends on the activity in the skin and the interaction between the vehicle and skin. Permeation of vehicle into the skin can alter the activity of drug and the properties of the skin barrier. The aim of this in vitro study was to separate and quantify these effects. Methods. The flux of four radiolabeled permeants (water, phenol, diflunisal, and diazepam) with log K-oct/water values from 1.4 to 4.3 was measured over 4 h through heat-separated human epidermis pretreated for 30 min with vehicles having Hildebrand solubility parameters from 7.9 to 23.4 (cal/cm(3))(1/2). Results. Enhancement was greatest after pretreatment with the more lipophilic vehicles. A synergistic enhancement was observed using binary mixtures. The flux of diazepam was not enhanced to the same extent as the other permeants, possibly because its partitioning into the epidermis is close to optimal (log K-oct 2.96). Conclusion. An analysis of the permeant remaining in the epidermis revealed that the enhancement can be the result of either increased partitioning of permeant into the epidermis or an increasing diffusivity of permeants through the epidermis.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B-k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B(mum)s) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B(mum)s for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the surface diffusion mechanism in activated carbon. (C) 2003 Elsevier Ltd. All rights reserved.

Hydrodynamic origin of diffusion in nanopores

We study the transport of a subcritical Lennard-Jones fluid in a cylindrical nanopore, using a combination of equilibrium and nonequilibrium as well as dual control volume grand canonical molecular dynamics methods. We show that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. We also demonstrate that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Annotation taken, in the perspective of criminal and constitutional law, as well as in criminology, to the decision of the portuguese constitutional court, of January 13, 2011 – with respect to the problems of “consent” and “medical act”

1 – Summary of the decision taken by the Portuguese Constitutional Court, of January 13, 2011; 2 – Complete text of the decision of the Portuguese Constitutional Court, of January 13, 2011, Judge Maria João ANTUNES (Reporter), Judge Carlos Pamplona de OLIVEIRA, Judge José Borges SOEIRO, Judge Gil GALVÃO, Judge Rui Manuel Moura RAMOS (President) –in terms of the tribunalconstitucional.pt, August 1, 2011; 3 – Brief annotation to the problem of the “medical act”; 3.1 – Plus some conclusions on the brief annotation to the problem of the “medical act”; 3.2 – Brief annotation to the problem of “consent”– continuation of the previous comments; 4 – Conclusions. It must never be forgotten that “consent” does not stand as the only cause of exclusion of unlawfulness.

Modeling the Diffusion of Energy Performance Contracting

The Portuguese Energy Policy considers the development of a commercially viable and competitive market for energy performance contracting (EPC) as a main mechanism to achieve the objectives of energy efficiency improvement. This paper proposes a study to investigate how to achieve widespread adoption of energy performance contracting by means of system dynamics modelling and simulation. To explore and gather insights on this question, a system dynamics model representing the system of the Portuguese EPC market at industry level will be created. The simulation of that model will provide a helpful basis for analysing and explaining the development of key variables, and accelerating learning on the managerial, organizational and political adaptation processes that foster the diffusion of EPC adoption. The first phase of this research project aims at identifying and analysing the key factors and critical cause-effect relations that drive the adoption of EPC. With this purpose, a qualitative content analysis on relevant documents was performed and a set of interviews was conducted. That data was analysed to capture the critical variables and its interrelation to formulate a preliminary representation of the system structure as stock and flow diagrams.

Mortality problems in Brazil and in Germany: past-present-future. Learning from each other?

This article was written by a Swiss-German historical demographer after having visited different Brazilian Universities in 1984 as a guest-professor. It aims at promoting a real dialog between developed and developing countries, commencing the discussion with the question: Can we learn from each other? An affirmative answer is given, but not in the superficial manner in which the discussion partners simply want to give each other some "good advice" or in which the one declares his country's own development to be the solely valid standard. Three points are emphasized: 1. Using infant mortality in S. Paulo from 1908 to 1983 as an example, it is shown that Brazil has at its disposal excellent, highly varied research literature that is unjustifiably unknown to us (in Europe) for the most part. Brazil by no means needs our tutoring lessons as regards the causal relationships; rather, we could learn two things from Brazil about this. For one, it becomes clear that our almost exclusively medical-biological view is inappropriate for passing a judgment on the present-day problems in Brazil and that any conclusions so derived are thus only transferable to a limited extent. For another, we need to reinterpret the history of infant mortality in our own countries up to the past few decades in a much more encompassing "Brazilian" sense. 2. A fruitful dialog can only take place if both partners frankly present their problems. For this reason, the article refers with much emprasis to our present problems in dealing with death and dying - problems arising near the end of the demographic and epidemiologic transitions: the superanuation of the population, chronic-incurable illnesses as the main causes of death, the manifold dependencies of more and more elderly and really old people at the end of a long life. Brazil seems to be catching up to us in this and will be confronted with these problems sooner or later. A far-sighted discussion already at this time seems thus to be useful. 3. The article, however, does not want to conclude with the rather depressing state of affairs of problems alternatingly superseding each other. Despite the caution which definitely has a place when prognoses are being made on the basis of extrapolations from historical findings, the foreseeable development especially of the epidemiologic transition in the direction of a rectangular survival curve does nevertheless provide good reason for being rather optimistic towards the future: first in regards to the development in our own countries, but then - assuming that the present similar tendencies of development are stuck to - also in regard to Brazil.

Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.