Macroscopic Profile Research Articles

Weak shocks of a BGK kinetic model for isentropic gas dynamics

We consider a one-dimensional BGK model as a regularization for the isentropic system of gas dynamics. Existence and dynamic stability of small amplitude travelling waves of the kinetic transport equation are proven. Their macroscopic moments approximate viscous shock profiles for the isentropic system. These results are also extended to the isothermal case.

Comparative pharmacognostic studies on the barks of four Ficus species

The barks of 4 Ficus species, namely F. racemosa, F. virens, F. religiosa and F. benghalensis, are important ingredients in many Ayurvedic and traditional formulations. The barks are considered to be very effective in various treatments, such as diabetes, skin diseases, ulcers, and nervous disorders. During market research, we observed that various species of Ficus barks were sold in Indian market under traditional names, such as Plaksah, Udumbarah, Asvatthah, and Vatah. The barks of the species mention above are usually interchanged or adulterated with other species of Ficus because of the limited knowledge in identification and differentiation. Therefore, a detailed comparative pharmacognostic evaluation of the 4 species has been carried out with the aim to establish the diagnostic keys of these important drugs based on the macroscopic, microscopic, and HPTLC profiles. Detailed diagnostic and distinctive characteristics for the differentiation of the 4 Ficus species are discussed.

X-ray and neutron reflectivity studies of self-assembled InAs quantum dots stacks on GaAs (1 0 0)

X-ray and neutron reflectometry are used for structural characterization of self-assembled InAs quantum dot stacks on GaAs (1 0 0), grown by molecular beam epitaxy. The macroscopic density profile of uncapped InAs layer is extracted and shows a three-dimensional pyramidal structure of maximum height of 5 nm. The ultra thin InAs buried layers are well approximated as a two-dimensional structure, indicating amalgamation between InAs and GaAs. The interface roughness of the capping layers is found smaller than 0.5 nm, showing the high quality of the epitaxial surfaces. The thicknesses of the capping GaAs layers are extracted in atomic scale level and are found in fine agreement with the nominal values.

Modeling two-stage bunch compression with wakefields: Macroscopic properties and microbunching instability

In a two-stage compression and acceleration system, where each stage compresses a chirped bunch in a magnetic chicane, wakefields affect high-current bunches. The longitudinal wakes affect the macroscopic energy and current profiles of the compressed bunch and cause microbunching at short wavelengths. For macroscopic wavelengths, impedance formulas and tracking simulations show that the wakefields can be dominated by the resistive impedance of coherent edge radiation. For this case, we calculate the minimum initial bunch length that can be compressed without producing an upright tail in phase space and associated current spike. Formulas are also obtained for the jitter in the bunch arrival time downstream of the compressors that results from the bunch-to-bunch variation of current, energy, and chirp. Microbunching may occur at short wavelengths where the longitudinal space-charge wakes dominate or at longer wavelengths dominated by edge radiation. We model this range of wavelengths with frequency-dependent impedance before and after each stage of compression. The growth of current and energy modulations is described by analytic gain formulas that agree with simulations.

Travelling fronts in stochastic Stokes’ drifts

By analytical methods we study the large time properties of the solution of a simple one-dimensional model of stochastic Stokes’ drift. Semi-explicit formulae allow us to characterize the behaviour of the solutions and compute global quantities such as the asymptotic speed of the center of mass or the effective diffusion coefficient. Using an equivalent tilted ratchet model, we observe that the speed of the center of mass converges exponentially to its limiting value. A diffuse, oscillating front attached to the center of mass appears. The description of the front is given using an asymptotic expansion. The asymptotic solution attracts all solutions at an algebraic rate which is determined by the effective diffusion coefficient. The proof relies on an entropy estimate based on homogenized logarithmic Sobolev inequalities. In the travelling frame, the macroscopic profile obeys to an isotropic diffusion. Compared with the original diffusion, diffusion is enhanced or reduced, depending on the regime. At least in the limit cases, the rate of convergence to the effective profile is always decreased. All these considerations allow us to define a notion of efficiency for coherent transport, characterized by a dimensionless number, which is illustrated on two simple examples of travelling potentials with a sinusoidal shape in the first case, and a sawtooth shape in the second case.

Equation‐free methods for molecular dynamics: a lifting procedure

AbstractWe present a lifting procedure for the initialization of molecular dynamics simulations of dense fluids in the context of equation‐free computing. As the macroscopic system description we use a smooth representation of the density and velocity profile using a kernel density estimation, of which the dimensionality is reduced via a spline fit. The proposed initialization procedure generates initial atom positions on a grid, as well as initial velocities, such that the desired macroscopic density and velocity profiles are well approximated. We illustrate the approach on a model problem, and point out some inherent caveats in the design of good lifting operators for molecular dynamics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hydrodynamic limit for a particle system with degenerate rates

We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of kinetically constrained lattice gases (KCLG) which have been introduced and intensively studied in physics literature as simple models for the liquid/glass transition. Due to the degeneracy of rates for KCLG there exists blocked configurations which do not evolve under the dynamics and in general the hyperplanes of configurations with a fixed number of particles can be decomposed into different irreducible sets. As a consequence, both the Entropy and Relative Entropy method cannot be straightforwardly applied to prove the hydrodynamic limit. In particular, some care should be put when proving the One and Two block Lemmas which guarantee local convergence to equilibrium. We show that, for initial profiles smooth enough and bounded away from zero and one, the macroscopic density profile for our KCLG evolves under the diffusive time scaling according to the porous medium equation. Then we prove the same result for more general profiles for a slightly perturbed dynamics obtained by adding jumps of the Symmetric Simple Exclusion. The role of the latter is to remove the degeneracy of rates and at the same time they are properly slowed down in order not to change the macroscopic behavior. The equilibrium fluctuations and the magnitude of the spectral gap for this perturbed model are also obtained.

Interfacial colloidal sedimentation equilibrium. II. Closure-based density functional theory

In Part I [R. E. Beckham and M. A. Bevan, J. Chem. Phys. 127, 164708 (2007)], results were presented for the sedimentation equilibrium of concentrated colloidal dispersions using confocal scanning laser microscopy experiments, Monte Carlo (MC) simulations, and a local density approximation perturbation theory. In this paper, we extended the modeling effort on those systems to include nonlocal density functional theory (DFT), which is capable of predicting the microstructure of the sediment at length scales comparable to the colloidal particle dimension. Specifically, we use a closure-based DFT formulation to predict interfacial colloidal sedimentation equilibrium density profiles. The colloid-colloid and colloid-surface interactions were modeled with DLVO screened electrostatic potentials using parameters taken directly from the experimental work. The DFT profiles were compared to the experimental and MC results from Part I. Good agreement was found for relatively dilute interfacial colloidal fluids, but agreement was less satisfactory as interfacial layering became more pronounced for conditions approaching the onset of interfacial crystallization. We also applied DFT in an inverse sense using the measured colloid density profile to extract the underlying colloid-surface potential; this can be thought of as a microscopic analog to the well-known procedure of using the macroscopic (coarse-grained) density profile to extract the osmotic equation of state. For the dilute interfacial fluid, the inverse DFT calculations reproduced the true colloid-surface potential to within 0.5kT at all elevations.

Dynamic protrusive cell behaviour generates force and drives early matrix contraction by fibroblasts

We investigated the cellular mechanisms underlying force generation and matrix contraction, using human corneal, Tenon's and scleral fibroblasts in a standard collagen matrix. We used timelapse light and confocal reflection microscopy to analyse concomitantly cell behaviour and matrix remodeling during contraction and devised a novel index to quantify dynamic cell behaviour in 3D. Based on the previously described culture force monitor, a novel simultaneous imaging and micro-culture force monitor system (SIM–CFM) was developed to measure the mechanical strain generated during matrix contraction whilst simultaneously recording cell and matrix behaviour. Ocular fibroblasts show marked differences in macroscopic matrix contraction profiles, with corneal fibroblasts inducing the strongest, and scleral the weakest, contraction. We identified four factors that determine the early matrix contraction profile: 1) cell size, 2) intrinsic cellular force, 3) dynamic cell protrusive activity and 4) net pericellular matrix displacement. Intrinsic cellular force and dynamic activity appear to be independent unique characteristics of each cell type and might serve as predictors of matrix contraction. The identification of these factors raises the fundamental new possibilities of predicting the ability of tissues to contract and scar and of modulating tissue contraction by targeting intracellular pathways linked to protrusive activity and force generation.

Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential

We consider a lattice gas in a periodic d-dimensional lattice of width γ −1 , γ > 0 , interacting via a Kac's type interaction, with range 1 γ and strength γ d , and under the influence of a random one body potential given by independent, bounded, random variables with translational invariant distribution. The system evolves through a conservative dynamics, i.e. particles jump to nearest neighbor empty sites, with rates satisfying detailed balance with respect to the equilibrium measures. In [M. Mourragui, E. Orlandi, E. Saada, Macroscopic evolution of particles systems with random field Kac interactions, Nonlinearity 16 (2003) 2123–2147] it has been shown that rescaling space as γ −1 and time as γ −2 , in the limit γ → 0 , for dimensions d ⩾ 3 , the macroscopic density profile ρ satisfies, a.s. with respect to the random field, a non-linear integral partial differential equation, having the diffusion matrix determined by the statistical properties of the external random field. Here we show an almost sure (with respect to the random field) large deviations principle for the empirical measures of such a process. The rate function, which depends on the statistical properties of the external random field, is lower semicontinuous and has compact level sets.

Homogenization of Linear Transport Equations in a Stationary Ergodic Setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.

Quick mapping of carrier concentration in InP substrate with large diameter by near-infrared transmittance measurement

In order to assess macroscopic and microscopic profiles of carrier concentration in n-type InP substrates, near-infrared (NIR) transmittance has been measured and quantitatively converted into the term of carrier concentration with the calibration curve determined experimentally in the range from 1×10 18 to 6.4×10 18 cm −3. The InP substrate assessed here was a 4-in S-doped substrate grown by the vapor-pressure-controlled Czochralski (VCZ) technique. It was found that the radial profile of carrier concentration was macroscopically concave. An elliptical striation pattern due to microscopic fluctuation of carrier concentration was observed, which seemed to be originating from unwanted asymmetry in the VCZ growth process. The macroscopic and microscopic profiles of carrier concentration may provide very important information about the crystal growth situations such as the shape of solid–liquid interface and the stability of crystal growth.

Holocene fire in the Scottish Highlands: evidence from macroscopic charcoal records

It has been hypothesized that the mid-Holocene decline of pine (Pinus sylvestris L.) woodland in the Scottish Highlands may have been the result of a change in the fire regime of the region. Little is known about the Holocene fire history of these forests, although a number of factors suggest that fire may have played a significant role. This study examines whether fire was a prevalent factor in Scotland over the course of the Holocene and its relationship with Highland vegetation communities. Both macroscopic and microscopic charcoal are analysed in conjunction with a full palynological investigation from four Holocene lake sedimentary sequences in locations throughout the Scottish Highlands. Comparison of macroscopic charcoal abundance profiles with those from areas of known wildfire activity and the consistent pattern of burning revealed across the four disparate Highland sites indicate that broad-scale burning of vegetation did occur. Charcoal abundance was related to vegetation composition at all four of the sites examined. The abundance of pine, however, was found to be unrelated to fire history. Instead, fire appears to be predominantly linked to the development of heath and blanket mire communities. Analysis of three different macroscopic charcoal size fractions (? 500 gm, 250-500 gm and 125-250 gm) revealed strong correlations between measures. Microscopic charcoal abundance, however, was more variable and was determined to be a less accurate measure of local catchment-scale burning within the region.

Three-dimensional resist development simulation with discrete models

Control and minimization of line-edge roughness (LER) is a crucial problem for further advancements in lithography. To simulate LER, a switch from continuous to discrete, molecular level resist models is required. This article presents a new algorithm for the discrete resist structure generation with nonoverlapping polymer distributions and a novel development simulation approach. The presented concept allows simultaneously the simulation of macroscopic profile dimensions as well as of microscopic roughness properties of the resist. Required microscopic dissolution times of the polymers are derived from the corresponding simulated local macroscopic development rates. By retaining all other resist parameters unchanged in the simulation, the isolated influence of varying the assumed polymer size, branching geometry, and dissolution time variations on LER is examined with this new method. Small, strongly tangled polymers lead to considerably lower LER values than bigger or less bended polymers. Compared to the investigated polymer size and geometry, the examined range of variances in the dissolution times has only a weak influence on LER.

Hydrodynamic limit for perturbation of a hyperbolic equilibrium point in two-component systems

We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the spectral gap which is quadratic in the size of the system. Under Eulerian scaling the hydrodynamic limit for the macroscopic density profiles leads to a two-component system of conservation laws. The resulting pde is hyperbolic inside the physical domain of the macroscopic densities, with possible loss of hyperbolicity at the boundary. We investigate the propagation of small perturbations around a hyperbolic equilibrium point. We prove that the perturbations essentially evolve according to two decoupled Burgers equations. The scaling is not Eulerian: if the lattice constant is n −1 , the perturbations are of order n − β then time is speeded up by n 1 + β . Our derivation holds for 0 < β < 1 5 . The proof relies on Yau's relative entropy method, thus it applies only in the regime of smooth solutions. This result is an extension of [T. Seppäläinen, Perturbation of the equilibrium for a totally asymmetric stick process in one dimension, Ann. Probab. 29 (2001) 176–204] and [B. Tóth, B. Valkó, Between equilibrium fluctuations and Eulerian scaling. Perturbation of equilibrium for a class of deposition models, J. Statist. Phys. 109 (2002) 177–205] where the analogue result was proved for systems with one conservation law. It also complements [B. Tóth, B. Valkó, Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit, Commun. Math. Phys. 256 (2005) 111–157] where it was shown that perturbations around a nonhyperbolic boundary equilibrium point are driven by a universal two-by-two system of conservation laws.

In Situ and Online Monitoring of Hydrodynamic Flow Profiles in Microfluidic Channels Based upon Microelectrochemistry: Concept, Theory, and Validation

Herein, we propose a method for reconstructing any plausible macroscopic hydrodynamic flow profile occurring locally within a rectangular microfluidic channel. The method is based on experimental currents measured at single or double microband electrodes embedded in one channel wall. A perfectly adequate quasiconformal mapping of spatial coordinates introduced in our previous work [Electrochem. Commun. 2004, 6, 1123] and an exponentially expanding time grid, initially proposed [J. Electroanal. Chem. 2003, 557, 75] in conjunction with the solution of the corresponding variational problem approached by the Ritz method are used for the numerical reconstruction of flow profiles. Herein, the concept of the method is presented and developed theoretically and its validity is tested on the basis of the use of pseudoexperimental currents emulated by simulation of the diffusion-convection problem in a channel flow cell, to which a random Gaussian current noise is added. The flow profiles reconstructed by our method compare successfully with those introduced a priori into the simulations, even when these include significant distortions compared with either classical Poiseuille or electro-osmotic flows.

Sensitivity of the stress response function to packing preparation

A granular assembly composed of a collection of identical grains may pack under differentmicroscopic configurations with microscopic features that are sensitive to the preparationhistory. A given configuration may also change in response to external actions such ascompression and shearing. We show, using a mechanical response function methoddeveloped experimentally and numerically, that the macroscopic stress profiles are stronglydependent on these preparation procedures. These results were obtained for both two andthree dimensions. The method reveals that, under a given preparation history, themacroscopic symmetries of the granular material is affected, and in most casessignificant departures from isotropy should be observed. This suggests a newpath towards a non-intrusive test of granular material constitutive properties.

Physical and chemical changes induced by osmotic dehydration in plant tissues

The osmotic processes induce not only water and solute fluxes in the tissue but also changes in cellular structure, depending on the ratio in which different transport mechanisms act in the system: osmo-diffusional transport of water and solutes and hydrodynamic gains of external solution. The latter is more important in porous tissues, especially when submitted to vacuum impregnation process. In macroscopic samples, different compositional and structural profiles are induced depending on process variables and tissue microstructure; cells near the sample interface are practically perfectly equilibrated in composition with the osmotic solution, whereas the more internal cells may remain unaltered. Compositional–structural profiles developed in the tissue during the process has a great impact on physical (such as optical and mechanical) and chemical properties (such as volatile profile) of the final product, in part due to differences in the number of cells depth, altered and unaltered. The degree in which gas–liquid exchanges occur in the tissue also plays a relevant role.

Restricted diffusion and release of aroma molecules from sol-gel-made porous silica particles

The aim of the current study is to predict the release kinetics of organic molecules entrapped in sol-gel-made silica particles using both pulsed field gradient-nuclear magnetic resonance (PFG-NMR) techniques and model calculations to describe restricted diffusion. The macroscopic release profile of aroma molecules from sol-gel-made particles is measured directly by UV-VIS spectroscopy, while the release kinetics are calculated by the Crank equation. The microscopic restricted pore diffusion coefficient of the aroma molecules in the Crank equation is obtained in situ by pulsed field gradient (PFG) magic angle spinning (MAS) nuclear magnetic resonance (NMR). Furthermore, restricted pore diffusion coefficients obtained by model calculations are in agreement with those measured by PFG-MAS-NMR, indicating the potential of the latter for characterization and screening of encapsulation formulations. Measured and calculated release profiles agree within experimental error.

Influence of moderate Joule heating on electroosmotic flow velocity, retention, and efficiency in capillary electrochromatography

The influence of Joule heating on electroosmotic flow velocity, the retention factor of neutral analytes, and separation efficiency in capillary electrochromatography was investigated theoretically and experimentally. A plot of electrical current against the applied electrical field strength was used to evaluate the Joule heating effect. When the mobile phase concentration of Tris buffer exceeded 5.0 mM in the studied capillary electrochromatography systems using particulate and monolithic columns (with an accompanying power level of heat dissipation higher than 0.35 W/m), the Joule heating effect became clearly noticeable. Theoretical models for describing the variation of electroosmotic flow velocity with increasing applied field strength and the change of retention factors for neutral analytes with electrical field strength at higher Tris buffer concentrations were analyzed to explain consequences of Joule heating in capillary electrochromatography. Qualitative agreement between experimental data and implications of the theoretical model analysis was observed. The decrease of separation efficiency in capillary electrochromatography with macroporous octadecylsilica particles at high buffer concentration can be also attributed to Joule heating mainly via the increased axial diffusion of the analyte molecules and dispersion of solute bands by a nonuniform electroosmotic flow profile over the column cross-section. However, within a moderate temperature range, the contribution of the macroscopic velocity profile in the column arising from radial temperature gradients is insignificant.