Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Transient Ventilation Dynamics Following a Change in Strength of a Point Source of Heat

We investigate the transient ventilation flow within a confined ventilated space, with high- and low-level openings, when the strength of a low-level point source of heat is changed instantaneously. The steady-flow regime in the space involves a turbulent buoyant plume, which rises from the point source to a well-mixed warm upper layer. The steady-state height of the interface between this layer and the lower layer of exterior fluid is independent of the heat flux, but the upper layer becomes progressively warmer with heat flux. New analogue laboratory experiments of the transient adjustment between steady states identify that if the heat flux is increased, the continuing plume propagates to the top of the room forming a new, warmer layer. This layer gradually deepens, and as the turbulent plume entrains fluid from the original warm layer, the original layer is gradually depleted and disappears, and a new steady state is established. In contrast, if the source buoyancy flux is decreased, the continuing plume is cooler than the original plume, so that on reaching the interface it is of intermediate density between the original warm layer and the external fluid. The plume supplies a new intermediate layer, which gradually deepens with the continuing flow. In turn, the original upper layer becomes depleted, both as a result of being vented through the upper opening of the space, but also due to some penetrative entrainment of this layer by the plume, as the plume overshoots the interface before falling back to supply the new intermediate layer. We develop quantitative models which are in good accord with our experimental data, by combining classical plume theory with models of the penetrative entrainment for the case of a decrease in heating. Typically, we find that the effect of penetrative entrainment on the density of the intruding layer is relatively weak, provided the change in source strength is sufficiently large. However, penetrative entrainment measurably increases the rate at which the depth of the draining layer decreases. We conclude with a discussion of the importance of these results for the control of naturally ventilated spaces.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Know thy neighbour: A normative theory of synaptic depression

Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a fixed computational operation in a network, this seems like a most unacceptable degree of added variability. We suggest an alternative theory according to which short-term synaptic plasticity plays a normatively-justifiable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quantity that contains all the critical information, namely its membrane potential. We suggest that a synapse solves the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives, acting as a recursive filter. We show that the dynamics of short-term synaptic depression closely resemble those required for optimal filtering, and that they indeed support high quality estimation. Under this account, the local postsynaptic potential and the level of synaptic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential fluctuations and the form of spiking non-linearity should be related to the properties of short-term plasticity in any particular cell type.

Theory and simulation in neuroscience.

Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model, ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Material point method for coupled hydromechanical problems

This paper describes a new formulation of the material point method (MPM) for solving coupled hydromechanical problems of fluid-saturated soil subjected to large deformation. A soil-pore fluid coupled MPM algorithm based on Biot's mixture theory is proposed for solving hydromechanical interaction problems that include changes in water table location with time. The accuracy of the proposed method is examined by comparing the results of the simulation of a one-dimensional consolidation test with the corresponding analytical solution. A sensitivity analysis of the MPM parameters used in the proposed method is carried out for examining the effect of the number of particles per mesh and mesh size on solution accuracy. For demonstrating the capability of the proposed method, a physical model experiment of a large-scale levee failure by seepage is simulated. The behavior of the levee model with time-dependent changes in water table matches well to the experimental observations. The mechanisms of seepage-induced failure are discussed by examining the pore-water pressures, as well as the effective stresses computed from the simulations © 2013 American Society of Civil Engineers.