A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

Effect of Low-Level Laser Therapy on Malondialdehyde Concentration in Random Cutaneous Flap Viability

Objective: The aim of this study was to assess the effects of 830 and 670 nm laser on malondialdehyde (MDA) concentration in random skin-flap survival. Background Data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and activating superoxide-dismutase delivery, thus helping the inhibition of free-radical action and consequently reducing necrosis. Materials and Methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each one. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group; group 2 received 830 nm laser radiation; and group 3 was submitted to 670 nm laser radiation. The animals underwent laser therapy with 36 J/cm(2) energy density immediately after surgery and on the 4 days subsequent to surgery. The application site of the laser radiation was 1 point, 2.5 cm from the flap's cranial base. The percentage of the skin-flap necrosis area was calculated 7 days postoperative using the paper-template method, and a skin sample was collected immediately after as a way of determining the MDA concentration. Results: Statistically significant differences were found between the necrosis percentages, with higher values seen in group 1 compared with groups 2 and 3. Groups 2 and 3 did not present statistically significant differences (p > 0.05). Group 3 had a lower concentration of MDA values compared to the control group (p < 0.05). Conclusion: LLLT was effective in increasing the random skin-flap viability in rats, and the 670 nm laser was efficient in reducing the MDA concentration.

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.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.

Simulation of the Barkhausen Noise using random field Ising model with long-range interaction

We present a method to simulate the Magnetic Barkhausen Noise using the Random Field Ising Model with magnetic long-range interaction. The method allows calculating the magnetic flux density behavior in particular sections of the lattice reticule. The results show an internal demagnetizing effect that proceeds from the magnetic long-range interactions. This demagnetizing effect induces the appearing of a magnetic pattern in the region of magnetic avalanches. When compared with the traditional method, the proposed numerical procedure neatly reduces computational costs of simulation. (c) 2008 Published by Elsevier B.V.

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform triangular, and exponential random variables. (C) 2008 Elsevier B.V. All rights reserved.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.