Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Interfacial tension model for catalytically driven nanorods

We present an analysis of the interfacial tension model for the movement of the catalytically driven nanorod. The model considers the convective reaction-diffusion equation for the production and diffusion of oxygen around the bimetallic nanorod. We solve the equation and find the concentration difference, which drives the nanorod. We use our expression to calculate the force on the nanorod and find that the result is within 20% of the results found earlier [ W. Paxton et al., J. Am. Chem. Soc. 128, 14881 (2006) ] by an approximate method. Unlike the earlier results, our results are valid from short to long lengths of the nanorod.

A Model of Anomalous Enzyme-Catalyzed Gel Degradation Kinetics

We show that a model of target location involving n noninteracting particles moving subdiffusively along a line segment (a generalization of a model introduced by Sokolov et al. [Biophys. J. 2005, 89, 895.]) provides a basis for understanding recent experiments by Pelta et al. [Phys. Rev. Lett. 2007, 98, 228302.] on the kinetics of diffusion-limited gel degradation. These experiments find that the time t(c) taken by the enzyme thermolysin to completely hydrolyze a gel varies inversely as roughly the 3/2 power of the initial enzyme concentration [E]. In general, however, this time would be expected to vary either as [E](-1) or as [E](-2), depending on whether the Brownian diffusion of the enzyme to the site of cleavage took place along the network chains (1-d diffusion) or through the pore spaces (3-d diffusion). In our model, the unusual dependence of t(c) on [E] is explained in terms of a reaction-diffusion equation that is formulated in terms of fractional rather than ordinary time derivatives.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/ imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart. The analytical solutions were also shown to be capable of providing bulk optical properties through a numerical experiment using a realistic breast model. (C) 2013 Optical Society of America

Progress in the understanding of Ni silicide formation for advanced MOS structures

Metallic silicides have been used as contact materials on source/drain and gate in metal-oxide semiconductor (MOS) structure for 40 years. Since the 65 nm technology node, NiSi is the preferred material for contact in microelectronic due to low resistivity, low thermal budget, and low Si consumption. Ni(Pt)Si with 10 at.% Pt is currently employed in recent technologies since Pt allows to stabilize NiSi at high temperature. The presence of Pt and the very low thickness (<10 nm) needed for the device contacts bring new concerns for actual devices. In this work, in situ techniques [X-ray diffraction (XRD), X-ray reflectivity (XRR), sheet resistance, differential scanning calorimetry (DSC)] were combined with atom probe tomography (APT) to study the formation mechanisms as well as the redistribution of dopants and alloy elements (Pt, Pd.) during the silicide formation. Phenomena like nucleation, lateral growth, interfacial reaction, diffusion, precipitation, and transient phase formation are investigated. The effect of alloy elements (Pt, Pd.) and dopants (As, B.) as well as stress and defects induced by the confinement in devices on the silicide formation mechanism and alloying element redistribution is examined. In particular APT has been performed for the three-dimensional (3D) analysis of MOSFET at the atomic scale. The advances in the understanding of the mechanisms of formation and redistribution are discussed. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Experimental and numerical study on AlGaInAs/AlGaAs distributed feedback lasers with GaInP gratings

Ridge-waveguide AlGaInAs/AlGaAs distributed feedback lasers with lattice-matched GaInP gratings were fabricated and their light-current characteristics, spectrum and far-field characteristics were measured. On the basis of our experimental results we analyze the effect of the electron stopper layer on light-current performance using the commercial laser simulation software PICS3D. The simulator is based on the self-consistent solution of drift diffusion equations, the Schrodinger equation, and the photon rate equation. The simulation results suggest that, with the use of a 80 nm-width p-doped Al0.6GaAs electron stopper layer, the slope efficiency can be increased and the threshold current can be reduced by more than 10 mA.

Mechanisms of the sidewall facet evolution in lateral epitaxial overgrowth of GaN by MOCVD

The lateral epitaxial overgrowth of GaN was carried out by low-pressure metalorganic chemical vapor deposition, and the cross section shape of the stripes was characterized by scanning electron microscopy. Inclined {11-2n} facets (n approximate to 1-2.5) were observed in the initial growth, and they changed gradually into the vertical {11-20} sidewalls in accordance with the process of the lateral overgrowth. A model was proposed utilizing diffusion equations and boundary conditions to simulate the concentration of the Ga species constituent throughout the concentration boundary layer. Solutions to these equations are found using the two-dimensional, finite element method. We suggest that the observed evolution of sidewall facets results from the variation of the local V/III ratio during the process of lateral overgrowth induced by the lateral supply of the Ga species from the SiNx mask regions to the growing GaN regions.

Simulated morphological landscape of polymer single crystals by phase-field model

The novel phase field model with the "polymer characteristic" was established based on a nonconserved spatiotemporal Ginzburg-Landau equation (TDGL model A). Especially, we relate the diffusion equation with the crystal growth faces of polymer single crystals. Namely, the diffusion equations are discretized according to the diffusion coefficient of every lattice site in various crystal growth faces and the shape of lattice is selected based on the real proportion of the unit cell dimensions.

Extraction kinetics of rare earth elements with sec-octylphenoxy acetic acid

The kinetics of RE (La, Gd, Er, Yb and Y) extraction with sec-octylphenoxy acetic acid was investigated using a constant interfacial area cell with laminar flow at 303 K. The natures of the extracted complexes have some effect on the extraction rate which is controlled by the reaction rate of M(III) and extractant molecules at two-phase interface for Er(III), Yb(III) and Y(III), by a mixed chemical reaction-diffusion for Gd(III) and a diffusion for La( III). The extractant molecules tend to adsorb at the interface. So an interfacial extraction reaction model was derived.

Kinetics of cerium(IV) extraction from H2SO4-HF medium with Cyanex 923

Studies of the extraction kinetics of cerium(IV) from H2SO4-HF solutions with Cyanex 923 in n-heptane have been carried out using a constant interfacial area cell with laminar flow. The experimental hydrodynamic conditions were chosen so that the contribution of diffusion to the measured rate of reaction was minimized. The data were analyzed in terms of pseudo-first order constants. The results were compared with those of the system without HF. It was concluded that the addition of HF reduces the activation energy for the forward rate from 46.2 to 36.5 U mol(-1) while it has an opposite effect on the activation energy for the reverse process(the activation energy increased from 23.3 to 90.8 U mol(-1)). Thus, HF can accelerate the rate of cerium(IV) extraction. At the same time, the extraction rate is controlled by a mixed chemical reaction-diffusion rather than by a chemical reaction alone. A rate equation has also been obtained.

Optimized strong stability preserving IMEX Runge-Kutta methods

Esta es la versión no revisada del artículo: Inmaculada Higueras, Natalie Happenhofer, Othmar Koch, and Friedrich Kupka. 2014. Optimized strong stability preserving IMEX Runge-Kutta methods. J. Comput. Appl. Math. 272 (December 2014), 116-140. Se puede consultar la versión final en https://doi.org/10.1016/j.cam.2014.05.011

Sinkkirikasteen liuotusprosessin kineettinen mallinnus

Työssä on tehty kineettinen simulointimalli sinkkirikasteen liuotusprosessista. Prosessi on pieni osa Kokkolan sinkinvalmistusprosessia, jonka muita osia ovat: pasutus, neutraaliliuotus, konversio, liuospuhdistus ja elektrolyysi. Rikasteen liuotukseen tulee konversioprosessin liuos ja liuotuksesta lähtevä neste menee takaisin neutraaliliuotukseen. Saostunut jarosiitti läjitetään. Kokkolan liuotusprosessi koostuu liettoreaktorista ja kahdesta neljän liuotusreaktorin sarjasta. Liuotukseen syötetään paluuhappoa liettoreaktoriin ja liuotuspiirien ensimmäisiin liuotusreaktoreihin. Happea syötetään kaikkiin liuotusreaktoreihin. Prosessin mallintamiseen käytettiin Aspen Plus-simulointiohjelmaa, johon pystyttiin syöttämään kineettisiä yhtälöitä. Reaktionopeusyhtälöitä käytettiin raudan hapetuksen, sulfidien liuotuksen ja jarosiitiin saostumisen mallintamiseen, eli kaikkiin liuotusreaktoreissa tapahtuviin reaktioihin. Kineettiset yhtälöt etsittiin kirjallisuudesta. Liettoreaktori puolestaan mallinnettiin syöttämällä ohjelmaan reaktioyhtälöt ja antamalla niille etenemisasteet. Jarosiitin liukenemisesta työssä on tehty laboratoriokokeita, koska aiheesta ei kirjallisuudesta löytynyt kineettistä tietoa. Liuotuskokeissa käytetyn kiintoaineen kuitenkin todettiin sisältävän liikaa götiittiä, että tuloksista olisi voitu laskea kinetiikkaa jarosiitin liukenemiselle. Simulointimallilla laskettiin yksi tapaus vertailukohdaksi, johon malliin tehtyjä muutoksia verrattiin. Mallilla tutkittiin konversiosta tulevan jarosiitin määrän vaikutusta, reaktorikoon merkitystä ja rikasteen liuotuksen sekä jarosiitin saostuksen reaktionopeuksien muutoksen vaikutuksia. Käytetyillä kineettisillä yhtälöillä reaktioiden todettiin tarvitsevan vain ¾ käytetystä reaktiotilavuudesta, rikasteen liuotusnopeuden kohtalaisen pienellä hidastamisen todettiin vähentävän sinkin saantoa ja jarosiitin saostuksen reaktionopeuden kasvulla todettiin myös olevan negatiivinen vaikutus sinkin saantoon. Simulointimallissa käytettyjen reaktionopeusyhtälöiden varmentaminen kokeilla todettiin tarpeelliseksi, sillä jo kohtalaisen pienillä muutoksilla havaittiin olevan merkitystä prosessin toimivuuteen. Lisäksi todettiin jarosiitin liukenemisen huomioimisen olevan tarpeen.

Modélisation d'arythmies auriculaires modulées par le système nerveux autonome

La fibrillation auriculaire (FA) est la forme d’arythmie la plus fréquente et représente environ un tiers des hospitalisations attribuables aux troubles du rythme cardiaque. Les mécanismes d’initiation et de maintenance de la FA sont complexes et multiples. Parmi ceux-ci, une contribution du système nerveux autonome a été identifiée mais son rôle exact demeure mal compris. Ce travail cible l’étude de la modulation induite par l’acétylcholine (ACh) sur l’initiation et le maintien de la FA, en utilisant un modèle de tissu bidimensionnel. La propagation de l’influx électrique sur ce tissu est décrite par une équation réaction-diffusion non-linéaire résolue sur un maillage rectangulaire avec une méthode de différences finies, et la cinétique d'ACh suit une évolution temporelle prédéfinie qui correspond à l’activation du système parasympathique. Plus de 4400 simulations ont été réalisées sur la base de 4 épisodes d’arythmies, 5 tailles différentes de région modulée par l’ACh, 10 concentrations d’ACh et 22 constantes de temps de libération et de dégradation d’ACh. La complexité de la dynamique des réentrées est décrite en fonction de la constante de temps qui représente le taux de variation d’ACh. Les résultats obtenus suggèrent que la stimulation vagale peut mener soit à une dynamique plus complexe des réentrées soit à l’arrêt de la FA en fonction des quatre paramètres étudiés. Ils démontrent qu’une décharge vagale rapide, représentée par des constantes de temps faibles combinées à une quantité suffisamment grande d’ACh, a une forte probabilité de briser la réentrée primaire provoquant une activité fibrillatoire. Cette activité est caractérisée par la création de plusieurs ondelettes à partir d’un rotor primaire sous l’effet de l’hétérogénéité du gradient de repolarisation causé par l’activité autonomique.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.