A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Constructing a new individual-based model of phosphine resistance in lesser grain borer (Rhyzopertha dominica): do we need to include two loci rather than one?

In this article, we describe and compare two individual-based models constructed to investigate how genetic factors influence the development of phosphine resistance in lesser grain borer (R. dominica). One model is based on the simplifying assumption that resistance is conferred by alleles at a single locus, while the other is based on the more realistic assumption that resistance is conferred by alleles at two separate loci. We simulated the population dynamic of R. dominica in the absence of phosphine fumigation, and under high and low dose phosphine treatments, and found important differences between the predictions of the two models in all three cases. In the absence of fumigation, starting from the same initial frequencies of genotypes, the two models tended to different stable frequencies, although both reached Hardy-Weinberg equilibrium. The one-locus model exaggerated the equilibrium proportion of strongly resistant beetles by 3.6 times, compared to the aggregated predictions of the two-locus model. Under a low dose treatment the one-locus model overestimated the proportion of strongly resistant individuals within the population and underestimated the total population numbers compared to the two-locus model. These results show the importance of basing resistance evolution models on realistic genetics and that using oversimplified one-locus models to develop pest control strategies runs the risk of not correctly identifying tactics to minimise the incidence of pest infestation.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Constitutive model for municipal solid waste incorporating mechanical creep and biodegradation-induced compression

A constitutive model is proposed to describe the stress-strain behavior of municipal solid waste (MSW) under loading using the critical state soil mechanics framework. The modified cam clay model is extended to incorporate the effects of mechanical creep and time dependent biodegradation to calculate total compression under loading. Model parameters are evaluated based on one-dimensional compression and triaxial consolidated undrained test series conducted on three types of MSW: (a) fresh MSW obtained from working phase of a landfill, (b) landfilled waste retrieved from a landfill after 1.5 years of degradation, and (c) synthetic MSW with controlled composition. The model captures the stress-strain and pore water pressure response of these three types of MSW adequately. The model is useful for assessing the deformation and stability of landfills and any post-closure development structures located on landfills.

A Model of Anomalous Chain Translocation Dynamics

A model of polymer translocation based on the stochastic dynamics of the number of monomers on one side of a pore-containing surface is formulated in terms of a one-dimensional generalized Langevin equation, in which the random force is assumed to be characterized by long-ranged temporal correlations. The model is introduced to rationalize anomalies in measured and simulated values of the average time of passage through the pore, which in general cannot be satisfactorily accounted for by simple Brownian diffusion mechanisms. Calculations are presented of the mean first passage time for barrier crossing and of the mean square displacement of a monomeric segment, in the limits of strong and weak diffusive bias. The calculations produce estimates of the exponents in various scaling relations that are in satisfactory agreement with available data.

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive-active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied. (c) 2005 Elsevier Ltd. All rights reserved.

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of noninteracting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials and show that nonadiabatic pumping violates the simple sin phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time-reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and nonresonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulklike condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is nonexponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments. (C) 2010 American Institute of Physics. doi: 10.1063/1.3474948]

Experimental validation of the 1-D acoustical model for conical concentric tube resonators with moving medium

Variable cross-sectional area ducts are often used for attenuation at lower frequencies (of the order of firing frequency), whereas concentric tube resonators provide attenuation at relatively higher frequencies. In this paper, analysis of one dimensional control volume approach of conical concentric tube resonators is validated experimentally. The effects of mean flow and taper are investigated. The experimental setup is specially designed to measure the pressure transfer function in the form of Level Difference or Noise Reduction across the test muffler. It is shown that there is a reasonably good agreement between the predicted values of the Noise Reduction and the measured ones for incompressible mean flow as well as stationary medium. (C) 2011 Institute of Noise Control Engineering.