STOCHSIMGPU Parallel stochastic simulation for the Systems\ud Biology Toolbox 2 for MATLAB

Motivation: The importance of stochasticity in biological systems is becoming increasingly recognised and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU which exploits graphics processing units (GPUs)for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB.\ud \ud Results: The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM), and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user’s models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2

Liquid Crystal Theory and Modelling Discussion Meeting

In this report, we describe the main highlights of the international, multidisciplinary "Liquid Crystal Theory and Modelling, Discussion Meeting'' held in Oxford from the 29th-30th October 2009. This meeting had six separate themed sessions, with a total of seventeen invited speakers and over fifty participants. The proceedings of this meeting will be published as a special issue of the European Journal of Applied Mathematics. Contact [email protected] and [email protected] for more details

Dynamics of colloidal particles in ice

We use X-ray Photon Correlation Spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high-particle-density, where some of the colloids were forced into contact and formed disordered aggregates. We find that the particles in these high density regions underwent ballistic motion coupled with both stretched and compressed exponential decays of the intensity autocorrelation function, and that the particles’ characteristic velocity increased with temperature. We explain this behavior in terms of ice grain boundary migration

Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics

All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems

Time-dependent partial differential equations (PDEs) play an important role in applied mathematics and many other areas of science. One-shot methods try to compute the solution to these problems in a single iteration that solves for all time-steps at the same time. In this paper, we look at one-shot approaches for the optimal control of time-dependent PDEs and focus on the fast solution of these problems. The use of Krylov subspace solvers together with an efficient preconditioner allows for minimal storage requirements. We solve only approximate time-evolutions for both forward and adjoint problem and compute accurate solutions of a given control problem only at convergence of the overall Krylov subspace iteration. We show that our approach can give competitive results for a variety of problem formulations

Order parameters in the Landau-de Gennes theory - the static and dynamic scenarios

We obtain quantitative estimates for the scalar order parameters of liquid crystal configurations in three-dimensional geometries, within the Landau-de Gennes framework. We consider both static equilibria and non-equilibrium dynamics and we include external fields and surface anchoring energies into our formulation. Using maximum principle-type arguments, we obtain explicit bounds for the corresponding scalar order parameters in both static and dynamic situations; these bounds are given in terms of the material-dependent thermotropic coefficients, electric field strength and surface anchoring coefficients. These bounds provide estimates for the degree of orientational ordering, quantify the competing effects of the different energetic contributions and can be used to test the accuracy of numerical simulations

Adsorption and desorption dynamics of citric acid anions in soil

The functional role of organic acid anions (e.g. citrate, oxalate, malonate, etc) in soil has been intensively investigated with special focus either on (i) microbial respiration and soil carbon dynamics, (ii) nutrient solubilization, or (iii) metal detoxification. Considering the potential impact of sorption processes on the functional significance of these effects, comparatively little is known about the adsorption and desorption dynamics of organic acid anions in soils. The aim of this study therefore was to experimentally characterize the adsorption and desorption dynamics of organic acid anions in different soils using citrate as a model carboxylate. Results showed that both adsorption and desorption processes were fast, reaching a steady state equilibrium solution concentration within approximately 1 hour. However, for a given total soil citrate concentration(ctot) the steady state value obtained was critically dependent on the starting conditions of the experiment (i.e. whether most of the citrate was initially present in solution (cl) or held on the solid phase (cs)). Specifically, desorption-led processes resulted in significantly lower equilibrium solution concentrations than adsorption led processes indicating time-dependent sorption hysteresis. As it is not possible to experimentally distinguish between different sorption pools in soil (i.e. fast, slow, irreversible adsorption/desorption), a new dynamic hysteresis model was developed that relies only on measured soil solution concentrations. The model satisfactorily explained experimental data and was able to predict dynamic adsorption and desorption behaviour. To demonstrate its use we applied the model to two relevant scenarios (exudation and microbial degradation), where the dynamic sorption behaviour of citrate occurs. Overall, this study highlights the complex nature of citrate sorption in soil and concludes that existing models need to incorporate both a temporal and sorption hysteresis component to realistically describe the role and fate of organic acids in soil processes

Spin coating of an evaporating polymer solution

We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent volume fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system.\ud \ud The main practical interest is in controlling the appearance and development of a ``skin'' on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. The critical parameters controlling this behaviour are found to be $\epsilon$ the ratio of the diffusion to advection time scales, $\delta$ the ratio of the evaporation to advection time scales and $\exp(\gamma)$, the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with $\delta << \exp(-3/(4\gamma)) \epsilon^{3/4}$ skin formation can be prevented

A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored