Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

An Analysis of a Boundary Layer Diffusion Flame Over a Porous Flat Plate in a Confined Flow

A numerical analysis of the gas dynamic structure of a two-dimensional laminar boundary layer diffusion flame over a porous flat plate in a confined flow is made on the basis of the familiar boundary layer and flame sheet approximations neglecting buoyancy effects. The governing equations of aerothermochemistry with the appropriate boundary conditions are solved using the Patankar-Spalding method. The analysis predicts the flame shape, profiles of temperature, concentrations of variousspecies, and the density of the mixture across the boundary layer. In addition, it also predicts the pressure gradient in the flow direction arising from the confinement ofthe flow and the consequent velocity overshoot near the flame surface. The results of thecomputation performed for an n-pentane-air system are compared with experimental data andthe agreement is found to be satisfactory.

Inhibition of self-quenching in thioketones by micellar compartmentalization

The technique of micellar compartmentalization has been used to inhibit the diffusion-controlled self-quenching process in thioketones. By adjusting the ratio of the bulk concentration of the thioketone solute to the bulk concentration of micelles multiple occupancy of the micelles was avoided. Under these conditions enhanced phosphorescence intensity was observed in nitrogen-purged micellar solutions compared with that in acetonitrile solutions, indicating that the thioketone triple was indeed protected from deactivation by a ground statet

nvestigations on the Stability and Extinction of a Laminar Diffusion Flame Over a Porous Flat Plate

The limits of stability and extinction of a laminar diffusion flame have been experimentally studied in a two-dimensional laminar boundary layer over a porous flat plate through which n-pentane vapour was uniformly injected. The stability and extinction boundaries are mapped on a plot of free stream oxidant velocity versus fuel injection velocity. Effects of free stream temperature and of dilution of fuel and oxidant on these boundaries have been examined. The results show that there exists a limiting oxidant flux beyond which the diffusion flame cannot be sustained. This limiting oxidant flux has been found to depend_on the free stream oxygen concentration, fuel concentration and injection'velocity of the fuel.

Structure, energetics and diffusion properties of isomers of trimethyl benzene in beta zeolite: Uptake and Monte Carlo simulation study

A Monte Carlo study along with experimental uptake measurements of 1,2,3-trimethyl benzene, 1,2,4-trimethyl benzene and 1,3,5-trimethyl benzene (TMB) in beta zeolite is reported. The TraPPE potential has been employed for hydrocarbon interaction and harmonic potential of Demontis for modeling framework of the zeolite. Structure, energetics and dynamics of TMB in zeolite beta from Monte Carlo runs reveal interesting information about the diameter, properties of these isomers on confinement. Of the three isomers, 135TMB is supposed to have the largest diameter. It is seen TraPPE with Demontis potential predicts a restricted motion of 135TMB in the channels of zeolite beta.Experimentally, 135TMB has the highest transport diffusivity whereas MID results suggest this has the lowest self diffusivity. (C) 2009 Elsevier Inc. Ail rights reserved.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

Investigation of surface activity and photoinduced diffusion of metals in solution deposited amorphous films of As2S3

Surface activity of solution deposited (SD) amorphous films of As2S3 has been investigated. Silver and copper are readily deposited on such films from appropriate aqueous ionic solutions. The metals diffuse into the films upon irradiation with energetic photons. Structure and properties of SD films have been investigated using electron microscopy, optical spectroscopy and differential scanning calorimetry. The amorphous films tend to crystallize upon metal diffusion. The stability of amorphous films, the deposition of metals on their active surfaces and the photo-induced diffusion may all be attributed to the presence or production of charged defects in amorphous chalcogenide films.

Dendritic structures produced on solidification of multicomponent aqueous solutions

Dendrite structures of ice produced on undirectional solidification of ternary and quaternary aqueous solutions have been studied. Upon freezing, solutions containing more than one solute produce plate-shaped dendrites of ice. The spacing between dendrites increase linearly with the distance from the chill surface and the square root of local solidification time (or square root of inverse freezing rate) for any fixed composition. For fixed freezing conditions, the dendrite spacings from multicomponent aqueous solutions were a function of the concentrations and diffusion coefficients of the individual solutes. The dendrite spacing produced by freezing of a solution was changed by the addition of a solute different from those already present. If the main diffusion coefficient of the added solute is higher than that of solutes already present, the dendrite spacing is increased and vice versa. The dendrite spacing in multi-component systems increases with the total solute concentration if the constituent solutes are present in equal amounts. The dendrite spacing obtained on freezing of these dilute multicomponent solutions can be expressed by regression equations of the type Image Full-size image (2K) where L is the dendrite spacing in microns, C1, C2 and C3 are concentrations of individual solutes, Θf is the total freezing time and A1 −A8 are constants. A Yates analysis of the dendrite spacings in a factorial design of quaternary solutions indicates that there are strong interactions between individual solutes in regard to their effect on the dendrite spacings. A mass transport analysis has been used to calculate the interdendritic supersaturation ΔC of the individual solutes, the supercooling in the interdendritic liquid ΔT, and the transverse growth velocity of the dendrites, VT. In ternary solutions if two solutes are present in equal amount the supersaturation of the solute with higher main diffusion coefficient is lower, and vice versa. If a solute with higher main diffusion coefficient is added to a binary solution, the interface growth velocity, the interdendritic supersaturation of the base solute and the interdendritic supercooling increase with the quantity of solute added.

Quantum diffusion in thin disordered wires

Quantum Ohmic residual resistance of a thin disordered wire, approximated as a one-dimensional multichannel conductor, is known to scale exponentially with length. This nonadditivity is shown to imply (i) a low-frequency noise-power spectrum proportional to -ln(Ω)/Ω, and (ii) a dispersive capacitative impedance proportional to tanh(√iΩ )/ √iΩ. A deep connection to the quantum Brownian motion with linear dynamical frictional coupling to a harmonic-oscillator bath is pointed out and interpreted in physical terms.

Copper Diffusion Barrier Deposition on Integrated Circuit Devices by Atomic Layer Deposition Technique

Transfer from aluminum to copper metallization and decreasing feature size of integrated circuit devices generated a need for new diffusion barrier process. Copper metallization comprised entirely new process flow with new materials such as low-k insulators and etch stoppers, which made the diffusion barrier integration demanding. Atomic Layer Deposition technique was seen as one of the most promising techniques to deposit copper diffusion barrier for future devices. Atomic Layer Deposition technique was utilized to deposit titanium nitride, tungsten nitride, and tungsten nitride carbide diffusion barriers. Titanium nitride was deposited with a conventional process, and also with new in situ reduction process where titanium metal was used as a reducing agent. Tungsten nitride was deposited with a well-known process from tungsten hexafluoride and ammonia, but tungsten nitride carbide as a new material required a new process chemistry. In addition to material properties, the process integration for the copper metallization was studied making compatibility experiments on different surface materials. Based on these studies, titanium nitride and tungsten nitride processes were found to be incompatible with copper metal. However, tungsten nitride carbide film was compatible with copper and exhibited the most promising properties to be integrated for the copper metallization scheme. The process scale-up on 300 mm wafer comprised extensive film uniformity studies, which improved understanding of non-uniformity sources of the ALD growth and the process-specific requirements for the ALD reactor design. Based on these studies, it was discovered that the TiN process from titanium tetrachloride and ammonia required the reactor design of perpendicular flow for successful scale-up. The copper metallization scheme also includes process steps of the copper oxide reduction prior to the barrier deposition and the copper seed deposition prior to the copper metal deposition. Easy and simple copper oxide reduction process was developed, where the substrate was exposed gaseous reducing agent under vacuum and at elevated temperature. Because the reduction was observed efficient enough to reduce thick copper oxide film, the process was considered also as an alternative method to make the copper seed film via copper oxide reduction.