Showing papers on "Critical radius published in 1995"
TL;DR: For the first time, virus crystal growth dynamics and morphology have been investigated in real time on the nanometer scale and mechanisms for defect incorporation and suggest factors that limit growth rate and uniformity are suggested.
Abstract: For the first time, virus crystal growth dynamics and morphology have been investigated in real time on the nanometer scale. Individual monomers on the (111) face of cubic satellite tobacco mosaic virus (STMV) crystals were resolved and used to determine crystal packing. Growth of STMV proceeded by two- and three-dimensional nucleation to formed ``stacks'' of islands. No dislocations were observed. Small islands provided an estimate of critical radius size and the free energy of the step edge, \ensuremath{\alpha}. Step advancement rates were used to determinate the kinetic coefficient \ensuremath{\beta}. Images illustrate mechanisms for defect incorporation and suggest factors that limit growth rate and uniformity.
124 citations
TL;DR: In this article, the pore space of rocks was numerically simulated by varying the proportions of empty and filled bonds and nodes on a square lattice, where a filled bond could contain a tube or a crack or both, the dimensions of which were randomly chosen.
Abstract: The heterogeneous nature of the pore space of rocks was numerically simulated by varying the proportions of empty and filled bonds and nodes on a square lattice. A filled bond could contain a tube or a crack or both, the dimensions of which were randomly chosen. For each of 100 network realizations, the permeability, k, electrical formation factor, F, connected porosity, ϕ, specific surface area, A, and their pressure dependences were calculated. This large simulated database was then used for testing the validity of several models from the literature. The main result of this work is that permeability was well predicted by the relation k = R2/(8F), where R is an appropriate length scale. This relation was better satisfied by using the Katz-Thompson (KT) critical radius for R rather than the Schwartz-Sen-Johnson (SSJ) hydraulic radius. In particular, the SSJ model was found to be more sensitive to the pore shape heterogeneity than was the KT model. It yielded estimates of k of equal (if not better) quality than did the KT model when only one type of channel was considered (cracks or tubes), but more scattered results were obtained when it was applied to mixtures of cracks and tubes.
81 citations
TL;DR: The first-order phase transition between the $A$ and $B$ phases of superfluid helium has remained an outstanding mystery in helium physics for nearly 20 years as discussed by the authors, and the results of these experiments are discussed, along with the prospects for future work.
Abstract: The first-order phase transition between the $A$ and $B$ phases of superfluid $^{3}\mathrm{He}$ has remained an outstanding mystery in helium physics for nearly 20 years. The small difference in bulk free energies between the two phases, combined with the relatively large surface energy associated with the $\mathrm{AB}$ interface, leads to an anomalously large critical radius for nucleation, of order 1 \ensuremath{\mu}m, suggesting a lifetime for the super-cooled $A$ phase against homogeneous nucleation far beyond the age of the universe. Yet anisotropy of the high-temperature phase minimizes the depairing effects of surfaces, thus making conventional heterogeneous nucleation unlikely. Recent experiments have been reported that lend support to one of the more exotic nucleation mechanisms ever proposed: Leggett's "baked Alaska" model, in which the $B$ phase is nucleated by cosmic rays penetrating the supercooled $A$ phase. The results of these experiments are discussed, along with the prospects for future work.
21 citations
TL;DR: In this article, an extension of classical nucleation theory is presented which yields the shape of the critical intermediate phase nucleus and the critical work of formation, with the use of a simple example it is demonstrated that the formation decreases and hence the nucleation rate increases, with increasing interdiffusion time.
Abstract: The nucleation of an intermediate phase at the planar boundary of two other phases in a diffusion couple is considered. An extension of classical nucleation theory is presented which yields the shape of the critical intermediate phase nucleus and the critical work of formation. With the use of a simple example it is demonstrated that the work of formation decreases, and hence the nucleation rate increases, with increasing interdiffusion time.
19 citations
TL;DR: The instabilities found here imply the existence of stable solutions with nonzero vector fields outside the horizon; unless [ital q]=1 and [ital g][gt]0, these will not be spherically symmetric.
Abstract: The stability of the magnetically charged Reissner-Nordstr\"om black hole solution is investigated in the context of a theory with massive charged vector mesons. By exploiting the spherical symmetry of the problem, the linear perturbations about the Reissner-Nordstr\"om solution can be decomposed into modes of definite angular momentum J. For each value of J, unstable modes appear if the horizon radius is less than a critical value that depends on an anomalous magnetic moment coupling g and the monopole magnetic charge q/e. It is shown that such a critical radius exists (except in the case q=1/2 with 0\ensuremath{\le}g\ensuremath{\le}2), provided only that the vector meson mass is not too close to the Planck mass. The value of the critical radius is determined numerically for a number of values of J. The instabilities found here imply the existence of stable solutions with nonzero vector fields (``hair'') outside the horizon; unless q=1 and gg0, these will not be spherically symmetric.
14 citations
01 Sep 1995
TL;DR: In this article, the authors show that the critical radius is solely determined by the average concentration of the solute; thermal and convective contributions simply enhance the growth rate, whereas particle mass is conserved, whereas the particle number changes continuously.
Abstract: Simulation results for Ostwald ripening in liquids are presented. Thermal, diffusive, and convective contributions are considered simultaneously. We find that the critical radius is solely determined by the average concentration of the solute; thermal and convective contributions simply enhance the growth rate. Simulations based on a system of 20,000 particles show that a peak is sustained close to the critical radius, whereas particles with radii larger than the critical radius are hardly affected. For a closed system the particle mass is conserved, whereas the particle number changes continuously. Convective growth is stronger for smaller particles than for larger ones.
13 citations
TL;DR: A weakly nonlinear morphological stability analysis for a sphere growing from its pure undercooled melt and treats the anomalous case of a perturbation by a first-order spherical harmonic and observes that the second harmonic becomes unstable before the perturbing mode itself.
Abstract: We develop a weakly nonlinear morphological stability analysis for an infinitely long right circular cylinder growing from its pure undercooled melt. For a cylinder perturbed by a specific planform consisting of sinusoids, we perform an expansion in the planform amplitude A to calculate the nonlinear critical radius (above which the chosen planform will be unstable for finite A), to the lowest order in A, by setting the normal velocity corresponding to the fundamental perturbing mode to zero. We study the nonlinear critical radius as a function of the amplitude to identify the various bifurcations, which for the chosen sinusoidal planforms are subcritical or supercritical (requiring an expansion to third order in A), since the shapes for positive and negative amplitudes are related by rotation and translation. We find that the bifurcations are mostly subcritical. For the special case of axially symmetric perturbations, we encounter a generalization of the Rayleigh varicosity instability. \textcopyright{} 1996 The American Physical Society.
12 citations
15 Feb 1995-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the effects of notches and microstructure on the fracture behavior of TiAl-based alloys are systematically investigated, and the effect of the notch root radius on the apparent fracture toughness is explained very well.
Abstract: The effects of notches and microstructure on the fracture behavior of TiAl-based alloys are systematically investigated. It has been determined that the apparent fracture toughness, KA, for four typical microstructures—which include fully lamellar, nearly lamellar, duplex, and nearly gamma microstructures—exhibits similar variational trends with the notch root radius. KA is independent of the notch root radius ρ when ρ is smaller than the critical radius ρ0, and increases linearly with ρ 1 2 when ρ is larger than ρ0. The value of ρ0 is of the same order of magnitude as the grain size, and the slope of the K A -ρ 1 2 curve is dependent on the microstructure type. The good agreement between the statistical data of the crack initiation site in the blunt bent bar and the peak stress location indicates that the fracture of TiAl-based alloys is controlled by the maximum tensile stress rather than the strain or strain gradients as in Ti3Al-Nb-based alloys. By using the Tetelman model of stress-controlled fracture, the effect of the notch root radius on the apparent fracture toughness can be explained very well.
12 citations
TL;DR: In this article, a model of transient cross-flow filtration in a permeable cylindrical tube based on a force balance analysis is presented, where a slip boundary condition is applied at the interface between the flow and the porous surface of the tube, which represents the hydrodynamic effect of the porosity of tube wall and cake on the crossflow.
Abstract: A model of transient cross-flow filtration in a permeable cylindrical tube based on a force balance analysis is presented. Particle layer (or cake) formation on the tube is simulated. A slip boundary condition for cross-flow is applied at the interface between the flow and the porous surface of the tube, which represents the hydrodynamic effect of the porosity of the tube wall and cake on the cross-flow. For a given particle size distribution in the fluid, the mean radius of particles at different depths in the cake and at different positions along the tube is calculated. It is found that when a slip boundary condition is applied, the critical radius of particles is reduced, resulting in a slower growth of cake on the surface of the tube. In the model, the thickness of the cake can either increase or decrease along the axial direction of the tube depending on the conditions, pressures, permeability of the tube etc. This differs from results of concentration polarization models, which predict a continuously increasing particle layer.
11 citations
TL;DR: In this article, the effect of strong anisotropic scattering law on the variation of the critical radius in onespeed neutron transport theory was studied using a synthetic kernel, and the results indicated that low-order Legendre approximations are sufficient to show the effects of strong scattering on the radius variation of critical radius.
10 citations
TL;DR: In this paper, the authors define surface area = surface area of needle frost = height of the needle frost, and radius of needle-frost = average electric field, where the electric field at the tip of a needle is defined as the Helmholtz free energy.
Abstract: Nomenclature = surface area = height of the needle frost = radius of the needle frost = average electric field Et, = electric field at the tip F = Helmholtz free energy / = driving force of sublimation G = Gibbs free energy g = specific Gibbs free energy Kvc = electric field coefficient m — mass p = saturation pressure p* pressure of water vapor near the frost surface R = universal gas constant r(. = critical radius of ice nucleation T — temperature or saturation temperature y = interfacial energy of unit area defined by Eq. (9) £() = dielectric constant A = latent heat p = density X = polarization rate co = specific electric energy
TL;DR: In this article, the solid phase reaction of Fe thin films with (111) Si substrate was investigated at constant annealing temperature and time (700°C, 7 minutes) as a function of the initial iron film thickness.
Abstract: The solid phase reaction of Fe thin films with (111) Si substrate was investigated at constant annealing temperature and time (700°C, 7 minutes) as a function of the initial iron film thickness (from 5 nm to 27.5 nm in 2.5 nm steps). The formed phases were analysed by X-ray diffraction, Rutherford backscattering and transmission electron microscopy and optical microscopy. After annealing FeSi phase was detected in the thinner samples. Samples with Fe layers thicker than 12.5 nm contained a β-FeSi2 phase. This special phase sequence was explained with the help of a nucleation controlled phase formation model, taking into consideration the critical radius of nuclei of the new phase. The advantages of using the film thickness as a variable during investigation of solid phase thin film reactions and the probable substrate effects are also discussed.
TL;DR: In this article, a quasi-steady (q-s) state approximation for a characteristic time scale much larger than the reaction time scale is presented, and two branches of q-s solutions are exhibited with a C-shaped curve and a critical radius below which generalised Chapman-Jouguet (CJ) solutions cannot exist.
Abstract: A theoretical analysis of the direct initiation of gaseous detonations by an energy source has been published recently, the results are recalled here. Nonlinear curvature effects are proved to be essential mechanisms controlling the critical condition. These effects are first studied in a quasi-steady (q-s) state approximation valid for a characteristic time scale much larger than the reaction time scale. Two branches of q-s solutions are exhibited with a C-shaped curve and a critical radius below which generalised Chapman-Jouguet (CJ) solutions cannot exist. At ordinary conditions this critical radius is much larger than the thickness of the plane CJ detonation front (typically 300 to 500 times larger). Direct numerical simulations show that the upper branch of q-s solutions, acts as an attractor of the unsteady blast waves originating from a sufficiently strong energy source. The criterion of initiation derived here works to a good approximation and exhibits the huge numerical factor (10 6 -10 8 ) which is observed in the experimental data of the critical energy source and which was not explained up to now. Transient may induce additional failure mechanisms close to the critical condition.
01 Jan 1995
TL;DR: In this article, the authors investigated the direct initiation of cylindrical and spherical detonations by an ideal point energy source, for a one-step irreversible reaction, based on nonlinear curvature effects on the detonation structure.
Abstract: The direct initiation of cylindrical and spherical detonations by an ideal point energy source, is investigated numerically for a one-step irreversible reaction. The study is based on nonlinear curvature effects on the detonation structure. Our results obtained from solving the steady curved detonation front structures, exhibit a critical radius below which generalised ChapmanJouguet (CJ) solutions cannot exist. For sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 500 times larger at ordinary conditions). Numerical simulations of detonation initiation by an energy source, show that a critical energy is associated with the critical solution described above. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of a detonation requires a larger source energy. Transient phenomena which are associated with the intrinsic instability of the detonation front, develop on a short time scale and may induce additional failure mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions and the criterion of initiation based on the nonlinear curvature effects, works with a quite good approximation in cylindrical and spherical geometry.
TL;DR: In this paper, a kinetic model is used to describe the growth via nucleation process, and the set of finite difference equations describing the growth are solved exactly for an equilibrium and a steady state.
TL;DR: In this paper, the authors studied the stability range for a coherent interface between Ge quantum dots and an epitaxial Si shell and found that the system is coherent up to a Ge nanocrystallite radius of about 100 A, irrespective of the Si shell thickness.
Abstract: We study the stability range for a coherent interface between Ge quantum dots and an epitaxial Si shell. The critical radius at which coherency is lost is evaluated as a function of Si shell thickness and Ge nanocrystallite radius by comparing the energy of the system in the coherent and incoherent state. We find that the system is coherent up to a Ge nanocrystallite radius of about 100 A, irrespective of the Si shell thickness. Nanocrystallites of radii larger than 270 A lose coherency by the generation of perfect dislocation loops. In nanocrystallites of intermediate radii ( between 100 A and 270 A), the coherency is lost by the introduction of partial dislocation loops enclosing a stacking fault. As the shell thickness decreases, the critical radius increases.
TL;DR: In this article, the relative stability of single graphite sheets of zero, positive and negative curvature was investigated through a simple model where both strain and dangling bond energy were taken into account.
Abstract: The relative stability of single graphite sheets of zero, positive and negative curvature is investigated through a simple model where both strain and dangling bond energy are taken into account. Although it is found that flat sheets are always more stable than negatively curved ones, calculations show that above a critical radius of curvature there is a crossover from positive to negative curvature as the more stable geometry for a single sheet. A maximum size for a negatively curved sheet is also predicted. Similarly, positive curvature is found to be energetically favored over zero curvature below some value of the curvature radius and above a certain number of atoms of the sheet. These results are discussed in view of available transmission electron microscopy observations of sp2 amorphous carbon.
TL;DR: In this paper, it was shown that the critical radius is of the order of the diffusion length (in 2-dimensions), and smaller than the diffusion long (in 1-dimension).
Abstract: Nucleation in phase transition is a classical problem. Close to the transition point, the critical radius is known to be much larger than the diffusion length. In this paper, we focus on the case far from the critical point, as it is the case in a supercooled liquid, or in the related context of excitable media. We show that the physics of nucleation is different from the classical case. The critical radius is of the order of the diffusion length (in 2-dimensions), and smaller than the diffusion length (in 1-dimension). As a result, diffusion first leads to a decrease in amplitude of the initial seed, before a propagating pulse (or front) is initiated. This results in different laws for the critical radius. The relevance of these effects to stimulation in biological tissues, such as cardiac muscle, is discussed.
TL;DR: In this article, it was shown that the magnetic bipolaron can be formed if the distance between two polarons is less than some critical value, i.e., the larger the lower the dimensionality of the system, lower the temperature, and larger the single-polaron radius.
Abstract: Interaction of two magnetic polarons formed either by single carriers or by excitons is considered in bulk crystal, quantum well and quantum wire. It is shown that the magnetic bipolaron can be formed if the distance between two polarons is less than some critical value. This critical radius is the larger the lower the dimensionality of the system, the lower the temperature and the larger the single-polaron radius. The critical distance for the neutral-magnetic-bipolaron formation is much longer than for the charged bipolaron.