Predictions Of Continuum Models Research Articles

Phase Diagrams for Multi-Component Membrane Vesicles: A Coarse-Grained Modeling Study

We develop a multicomponent membrane coarse-grained model in which the effects of spontaneous curvature and fluidity are included. This model is used to perform computer simulations to study the phase segregation, domain coarsening, budding and budding off of multicomponent membrane vesicles. Three types of phase diagram are presented with variation of composition, spontaneous curvature, and line tension (the unlike bond energy). Various phases have been observed, including, sphere, biconcave, starfish, capsule, budding, and budding off. Our simulations show that budding off occurs only when the size of a domain is larger than a critical value, and the critical condition is closely related to the spontaneous curvature and line tension. A continuum model is used to predict the critical condition for budding off. Quantitative comparisons are made between the present simulation results and the continuum model predictions, and good agreements have been achieved.

A SPATIALLY RESOLVED INNER HOLE IN THE DISK AROUND GM AURIGAE

We present 0.3 arcsec resolution observations of the disk around GM Aurigae with the Submillimeter Array (SMA) at a wavelength of 860 um and with the Plateau de Bure Interferometer at a wavelength of 1.3 mm. These observations probe the distribution of disk material on spatial scales commensurate with the size of the inner hole predicted by models of the spectral energy distribution. The data clearly indicate a sharp decrease in millimeter optical depth at the disk center, consistent with a deficit of material at distances less than ~20 AU from the star. We refine the accretion disk model of Calvet et al. (2005) based on the unresolved spectral energy distribution (SED) and demonstrate that it reproduces well the spatially resolved millimeter continuum data at both available wavelengths. We also present complementary SMA observations of CO J=3-2 and J=2-1 emission from the disk at 2" resolution. The observed CO morphology is consistent with the continuum model prediction, with two significant deviations: (1) the emission displays a larger CO J=3-2/J=2-1 line ratio than predicted, which may indicate additional heating of gas in the upper disk layers; and (2) the position angle of the kinematic rotation pattern differs by 11 +/- 2 degrees from that measured at smaller scales from the dust continuum, which may indicate the presence of a warp. We note that photoevaporation, grain growth, and binarity are unlikely mechanisms for inducing the observed sharp decrease in opacity or surface density at the disk center. The inner hole plausibly results from the dynamical influence of a planet on the disk material. Warping induced by a planet could also potentially explain the difference in position angle between the continuum and CO data sets.

Making waves: Kinetic processes controlling surface evolution during low energy ion sputtering

When collimated beams of low energy ions are used to bombard materials, the surface often develops a periodic pattern or “ripple” structure. Different types of patterns are observed to develop under different conditions, with characteristic features that depend on the substrate material, the ion beam parameters, and the processing conditions. Because the patterns develop spontaneously, without applying any external mask or template, their formation is the expression of a dynamic balance among fundamental surface kinetic processes, e.g., erosion of material from the surface, ion-induced defect creation, and defect-mediated evolution of the surface morphology. In recent years, a comprehensive picture of the different kinetic mechanisms that control the different types of patterns that form has begun to emerge. In this article, we provide a review of different mechanisms that have been proposed and how they fit together in terms of the kinetic regimes in which they dominate. These are grouped into regions of behavior dominated by the directionality of the ion beam, the crystallinity of the surface, the barriers to surface roughening, and nonlinear effects. In sections devoted to each type of behavior, we relate experimental observations of patterning in these regimes to predictions of continuum models and to computer simulations. A comparison between theory and experiment is used to highlight strengths and weaknesses in our understanding. We also discuss the patterning behavior that falls outside the scope of the current understanding and opportunities for advancement.

Control of stress propagation in the cytoplasm by prestress and loading frequency.

One fundamental question in cell biology is how mechanical stresses are distributed inside the cytoplasm. Recently we have developed a synchronous detection approach to map cytoplasmic displacements and stresses using yellow fluorescent protein tagged mitochondria as fiducial markers of the cytoskeleton (CSK) in response to a localized load applied via an RGD-coated magnetic bead (7). We have shown that stresses are propagated to remote sites in the cytoplasm, a finding that contradicts continuum model predictions. Here we show that long distance force propagation in the cytoplasm was abolished when the contractile prestress in the CSK was lowered by relaxing agents and enhanced when the prestress was increased by contractile agonists. Surprisingly, when the loading frequency was varied from 0.03 Hz to 30 Hz, the total area of induced displacements (an index of the extent of stress propagation) first increased with loading frequency and then decreased with loading frequency. These results demonstrate that the long distance force propagation in living adherent cells might be controlled by the level of contractile prestress in the CSK and by the loading frequency.

Scaling Law in Carbon Nanotube Electromechanical Devices

We report a method for probing electromechanical properties of multiwalled carbon nanotubes (CNTs). This method is based on atomic force microscopy measurements on a doubly clamped suspended CNT electrostatically deflected by a gate electrode. We measure the maximum deflection as a function of the applied gate voltage. Data from different CNTs scale into an universal curve within the experimental accuracy, in agreement with a continuum model prediction. This method and the general validity of the scaling law constitute a very useful tool for designing actuators and in general conducting nanowire-based nanoelectromechanical systems.

Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory

We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the (100) surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion (PD) of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness (reflecting the energetics and adsorption site lattice structure in the atomistic model), and can also account for anisotropy in the step edge mobility (reflecting details of the kinetics). In such continuum treatments, the characteristic time τ e q for relaxation of clusters with linear size of order L satisfies τ e q ∼L 4 . Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters (formed by corner-to-corner coalescence of square clusters), atomistic simulations for PD with no kink rounding barrier (δ=0) reveal that τ e q ∼L 4 always applies. In contrast, atomistic simulations with a large kink rounding barrier (δ>0) reveal distinct scaling with τ e q ∼L 3 , for low T or small L, thus providing an effective way to test for δ>0. For the relaxation of faceted rectangular clusters (formed by side-to-side coalescence of square clusters), atomistic simulations for PD with δ=0 reveal that τ e q ∼L 2 , for low T or small L. This is consistent with a recent proposal by Combe and Larralde. For large δ>0, τ e q has an even weaker dependence on L. We elucidate scaling behavior and the effective activation barrier for relaxation in terms of the individual atomistic PD processes and their barriers.

Conformational equilibria of polar and charged flexible polymer chains in water

Continuum model predictions of the conformational equilibria of idealized polar and charged linear polymers in water are compared to complementary simulations in explicit water. The continuum model of hydration predicts with reasonable accuracy the conformational dependence of the hydration free energy of these solutes observed in the simulations. However, a prerequisite for accurate predictions is the optimization of the phenomenological parameters inherent to the continuum model using the simulation results for a subset of the solutes, in this case the uncharged polymer and two amphiphilic polymer chains with a single positive or negative charge on one terminal group. Our results demonstrate that the continuum model can be used to discriminate among the conformational preferences for different sequences of backbone charges. Finally, an unexpected finding of this study is the stabilization in water of the more compact conformations of the polymer chains with a fixed dipole moment. The driving force for this behavior is greater than the hydrophobic driving force and is electrostatic in nature.

Effect of Undulations on Surface Tension in Simulated Bilayers

To understand the effect of the finite size of simulation cells on the equilibrium properties of bilayers, an extensive series of glycerolmonoolein bilayer molecular dynamics simulations in which the surface area and system size were systematically changed have been conducted. Systems ranging from 200 to 1800 lipids were simulated, covering length scales up to 20 nm. The dependence of the surface tension on the area per lipid is shown, although long simulation times were needed (up to 40 ns) to obtain reliable estimates. As the size of simulated patches increases, long wavelength undulatory modes appear with a concomitant increase in the area compressibility due to coupling of undulation modes to area fluctuations. Both the undulatory intensities and the peristaltic intensities of the bilayer fluctuations can be fitted in the long wavelength limit to continuum model predictions. The effect of system size on surface tension appears to depend on the stress conditions.

Characterizing the performance of industrial-scale columns

The performance of a large commercial chromatographic column was investigated using a short pulse of a tracer and an extension of the reverse-flow technique. This technique permits separate determination of the unavoidable irreversible microscopic processes and the reversible effects of flow maldistribution, and allows for the separation of flow maldistribution in the flow distributors from flow maldistribution inside the packed bed. This analysis was performed on a 0.44 m Millipore IsoPak column using Cellufine GC 700, cellulosic-based media with an average particle diameter of 75 μm, for the stationary phase. The column efficiency was quantified by analysis of the effluent curve from a short pulse of a 5% aqueous acetone tracer. The study examined behavior of beds of different lengths (10–24 cm) and beds packed from different slurry concentrations (10–75% v/v). The slurry-packed columns were very uniform, and no significant macroscopic flow maldistribution was observed inside the column. The observed bed plate heights conformed to the predictions of available one-dimensional continuum models. Dispersion in the flow distributors was significant, corresponding to 15–25% of the intracolumn dispersion when the full 24 cm available bed length was used and a proportionally larger increase for shorter bed lengths. Thus, the headers are shown to produce a significant increase in the observed plate height.

Convergence of Molecular and Macroscopic Continuum Descriptions of Ion Hydration

Using computer simulations we study the boundary between explicit molecular and macroscopic continuum dielectric descriptions of ion hydration. The continuum model reasonably describes electrostatic potential fluctuation contributions to the hydration free energy, but fails to capture first-order potential contributions in the uncharged state. Once this contribution is accounted for, cationic and anionic free energies become indistinguishable with increasing size, in agreement with continuum model predictions. The ion radius at which the hydration free energies converge scales as the square root of the absolute charge (υ = 0.54 ± 0.04) and compares to the length scale ion−water dipole interactions equal the thermal energy.

Controlled Firing of Reaction‐Bonded Aluminum Oxide (RBAO) Ceramics: Part I, Continuum‐Model Predictions

The reaction‐bonded aluminum oxide (RBAO) process is a novel, reaction‐forming technique for producing monolithic, alumina‐based ceramics. Although there has been extensive work on the RBAO process, it is often difficult to reproduce the process and avoid sample cracking. To solve the problems that are associated with the RBAO process, it is necessary to have a fundamental understanding of the reaction‐bonding process and the effects of various processing parameters on the reaction behavior. To gain some insight into the process, a continuum model has been developed. The model, which considers the interaction between the macroscopic material and energy balances, is used to predict conditions under which RBAO bodies may be fired in a controlled manner, i.e., avoiding the runaway reaction. In particular, the effects of the oxygen content of the atmosphere, the heat loss by convection and radiation, the heating cycle, and scale (sample size) have been investigated. For small sample sizes, model predictions indicate that the reaction may be controlled by reducing the oxygen content of the atmosphere, increasing the heat loss, and/or incorporating an isothermal hold into the heating cycle at a temperature just below the ignition temperature. For larger sample sizes, model predictions indicate the need for multiple low‐temperature holds at increasing temperatures. It is believed that firing RBAO bodies in a controlled manner will allow one to avoid sample cracking. Part II of this work presents a complementary experimental study that investigates the reaction behavior and structural integrity of samples that have been fired under the predicted conditions.

Atomistic Simulations of Integranular Fracture in Symmetric-Tilt Grain Boundaries

Fracture experiments on symmetric-tilt grain boundaries in Cu are interpreted using the Peierls-Nabarro continuum model of dislocation nucleation as a starting point. Good agreement is found only when the continuum model is modified according to the results of atomistic simulations. The same experiments are also reproduced by direct Molecular Dynamics simulations of fracture propagation and dislocation emission from a microcrack placed in the interface plane of the symmetric-tilt (221)(221) grain boundary in fcc Cu. Direction-dependent fracture response is observed, namely the microcrack advancing by brittle fracture along the [11 $$\bar 4$$ ] direction and being blunted by dislocation emission along the opposite [ $$\bar 1\bar 1$$ 4] direction. Moreover, the simulations allow us to establish important differences with respect to the continuum-model predictions due to the shielding of the stress field at the crack-tip and to the presence of the residual stress at the interface.

Dynamic overshoot in -iron by atomistic simulations

We present large-scale molecular dynamic simulations of microcrack growth in -iron based on an N-body potential model which gives a good description of defect energetics, anisotropic elasticity and phonon frequency spectra. We demonstrate dynamic overshoot of a pre-existing microcrack under impact loading. We show that the basic behaviour of the simulations is in agreement with the predictions of continuum models. Dynamic phenomena, such as scattering of stress waves at crack faces, acoustic emission (due to bond breakage) and reflections of the stress waves from sample borders, are studied here in detail. The results on microcrack growth, unimpeded by the wave reflections from external sample borders, indicate that under fast loading or at high crack velocities, i.e. under high strain rates, transient twin formation is possible from the crack tip with later detwinning at free crack faces as the crack advances: a twinning equivalent to virtual Knott dislocations.

Hydration and Conformational Equilibria of Simple Hydrophobic and Amphiphilic Solutes

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of ±1 e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.

A tight-binding model for calculations of structures and properties of graphitic nanotubes

A parameterized tight-binding model is applied to calculate the equilibrium structures, energies, band gaps and elastic properties of graphitic nanotubes with various helicities and radii. The structures, energies and band gaps for the tubes of large radii are in agreement with more accurate calculations. The elastic moduli depend only on the tube radius and follow the continuum model predictions.

Step-bunching instability of vicinal surfaces under stress.

On a vicinal surface under stress, elastic relaxation at steps produces a long-range attractive interaction between the steps. As a result, the surface is unstable against step bunching, driven by the energetics of the system rather than by the kinetics of step flow. This bunching instability differs from the predictions of previous continuum models by its lack of a characteristic wavelength. Instead, it evolves by progressive coalescence of step bunches. Flux can dramatically modify this evolution, limiting the growth of step bunches.

Capillary effects in drainage in heterogeneous porous media: continuum modelling, experiments and pore network simulations

We investigate effects of capillary heterogeneity induced by variations in permeability in the direction of displacement in porous media under condition of drainage. The investigation is three-pronged and uses macroscopic simulation, based on the standard continuum equations, experiments with the use of an acoustic technique and pore network numerical models. It is found that heterogeneity affects significantly the saturation profiles, the effect being stronger at lower rates. A good agreement is found between the continuum model predictions and the experimental results, based on which it can be postulated that capillary heterogeneity in the direction of displacement acts much like a body force (e.g. gravity). A qualitative agreement is also found between the continuum approach and the pore network numerical models, which is expected to improve when finite size effects in the pore network simulations diminish. The results are interpreted with the use of invasion percolation concepts.

Solvent dynamics following charge transfer at the liquid-liquid interface

The dynamics of solvent reorganization following charge transfer at the interface between two immiscible liquids, one polar and the other non-polar are investigated by molecular dynamics. Both charge separation and charge recombination processes in two different orientations at the surface are considered and are compared with the same processes in the bulk polar solvent. The relaxation at the surface is significantly slower than in the bulk, in contrast to predictions of continuum models. The linear response approximation works reasonably well in the bulk but fails at the interface. The Langevin model is in poor agreement with the exact equilibrium correlations, especially at short time, but can qualitatively account for the overall rate.

Theoretical study of ion solvation at the water liquid–vapor interface

Molecular dynamics calculations are reported for several ions at the liquid–vapor interface of water. The transition from the bulk to the interface region is investigated from structural, energetic, and dynamical points of view by calculating ion–water geometries, radial distribution functions, solvent molecular reorientation times, solvent polarization fluctuations, and solvation free energy as a function of distance from the interface. It is shown that ions tend to keep most of the structural and dynamical properties of their first solvation shell intact as they are moved into the interface, and that the tendency for negative adsorption (positive free energy of adsorption) is associated with weaker and fewer long range interactions. A comparison of some of the molecular dynamics results to predictions of simple continuum models is discussed, showing generally poor quantitative agreement.

The dynamics of polar solvation: Inhomogeneous dielectric continuum models

The influence of an inhomogeneous dielectric response on the dynamics of solvation of ions and dipoles is investigated. Solvent models considered include discrete shell models as well as models in which the solvent dielectric constant varies continuously as a function of distance from a spherical solute. The effect of such dielectric inhomogeneity is to introduce additional, slower relaxation times into the solvation response when compared to the homogeneous case. For all models studied, the deviation of the average relaxation time from that predicted for a homogeneous continuum solvent increases as the dielectric constant and the length parameter, which specifies the rapidity of approach to bulk behavior, increase. For a given solvent model the solvation response to a change in a point dipole moment is slower than the response to a charge jump. The continuum results are compared to a recent molecular model based on the mean spherical approximation. The comparison suggests that deviations from homogeneous continuum behavior in the molecular model can be accounted for by inhomogeneity of the solvent dielectric constant extending only over the first solvation shell. Predictions of inhomogeneous continuum models are also compared to experimental data. Both the observed dependence of average relaxation time on dielectric constant, and the detailed time dependence of the relaxation in high dielectric constant solvents can be rationalized on the basis of such models.