Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.

Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Gough, John; Van Handel, R., (2007) 'Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode', Journal of Statistical Physics 127(3) pp.575-607 RAE2008

Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space–time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham–Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as designing a targeted drug delivery system.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Harnessing naturally randomized transcription to infer regulatory relationships among genes

We develop an approach utilizing randomized genotypes to rigorously infer causal regulatory relationships among genes at the transcriptional level, based on experiments in which genotyping and expression profiling are performed. This approach can be used to build transcriptional regulatory networks and to identify putative regulators of genes. We apply the method to an experiment in yeast, in which genes known to be in the same processes and functions are recovered in the resulting transcriptional regulatory network.

Interfacing cellular networks of S. cerevisiae and E. coli: Connecting dynamic and genetic information

Background: In recent years, various types of cellular networks have penetrated biology and are nowadays used omnipresently for studying eukaryote and prokaryote organisms. Still, the relation and the biological overlap among phenomenological and inferential gene networks, e.g., between the protein interaction network and the gene regulatory network inferred from large-scale transcriptomic data, is largely unexplored.

Results: We provide in this study an in-depth analysis of the structural, functional and chromosomal relationship between a protein-protein network, a transcriptional regulatory network and an inferred gene regulatory network, for S. cerevisiae and E. coli. Further, we study global and local aspects of these networks and their biological information overlap by comparing, e.g., the functional co-occurrence of Gene Ontology terms by exploiting the available interaction structure among the genes.

Conclusions: Although the individual networks represent different levels of cellular interactions with global structural and functional dissimilarities, we observe crucial functions of their network interfaces for the assembly of protein complexes, proteolysis, transcription, translation, metabolic and regulatory interactions. Overall, our results shed light on the integrability of these networks and their interfacing biological processes.

GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

Activité des cellules souches : identification de nouveaux effecteurs dans le système hématopoïétique

Les cellules souches somatiques présentent habituellement un comportement très différent des cellules souches pluripotentes. Les bases moléculaires de l’auto-renouvellement des cellules souches embryonnaires ont été récemment déchiffrées grâce à la facilité avec laquelle nous pouvons maintenant les purifier et les maintenir en culture durant de longues périodes de temps. Par contre, il en va tout autrement pour les cellules souches hématopoïétiques. Dans le but d’en apprendre davantage sur le fonctionnement moléculaire de l’auto-renouvellement des cellules souches hématopoïétiques, j’ai d’abord conçu une nouvelle méthode de criblage gain-de-fonction qui répond aux caprices particuliers de ces cellules. Partant d’une liste de plus de 700 facteurs nucléaires et facteurs de division asymétrique candidats, j’ai identifié 24 nouveaux facteurs qui augmentent l’activité des cellules souches hématopoïétiques lorsqu’ils sont surexprimés. J’ai par la suite démontré que neuf de ces facteurs agissent de manière extrinsèque aux cellules souches hématopoïétiques, c’est-à-dire que l’effet provient des cellules nourricières modifiées en co-culture. J’ai également mis à jour un nouveau réseau de régulation de transcription qui implique cinq des facteurs identifiés, c’est-à-dire PRDM16, SPI1, KLF10, FOS et TFEC. Ce réseau ressemble étrangement à celui soutenant l’ostéoclastogénèse. Ces résultats soulèvent l’hypothèse selon laquelle les ostéoclastes pourraient aussi faire partie de la niche fonctionnelle des cellules souches hématopoïétiques dans la moelle osseuse. De plus, j’ai identifié un second réseau de régulation impliquant SOX4, SMARCC1 et plusieurs facteurs identifiés précédemment dans le laboratoire, c’est-à-dire BMI1, MSI2 et KDM5B. D’autre part, plusieurs indices accumulés tendent à démontrer qu’il existe des différences fondamentales entre le fonctionnement des cellules souches hématopoïétiques murines et humaines.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Revisiting university students' knowledge that involves basic differential equation questions. 'Conocimiento de los estudiantes universitarios con respecto a preguntas que implican ecuaciones diferenciales : una revisión'.

Resumen basado en el de la publicación