Showing papers on "Critical radius published in 2004"
TL;DR: In this article, the authors investigated the character of plastic deformation in metallic glasses through instrumented nanoindentation experiments on amorphous Pd40Ni40P20 and Mg65Cu25Gd10.
429 citations
01 Nov 2004
TL;DR: It is shown that a drop larger than a critical radius cannot be trapped by a fiber whatever its velocity, and this critical size is determined as a function of the fiber radius.
Abstract: We study experimentally the dynamics of drops impacting horizontal fibers and characterize the ability of these objects to capture the drops. We first show that a drop larger than a critical radius cannot be trapped by a fiber whatever its velocity. We determine this critical size as a function of the fiber radius. Then we show that for smaller drops, different situations can occur: at a low impact velocity, the drop is entirely captured by the fiber, whereas some liquid is ejected when arriving faster. We quantify the threshold velocity of capture.
141 citations
120 citations
TL;DR: In this article, the authors extended previous work on the theory of heterogeneous ice nucleation and provided a suitable framework for modeling and parameterizing the icicle nucleation process in cloud-scale and large-scale atmospheric models.
Abstract: This paper extends previous work on the theory of heterogenous ice nucleation. The goals of this analysis are to explain empirical observations of ice nucleation and to provide a suitable framework for modeling and parameterizing the ice nucleation process in cloud-scale and large-scale atmospheric models. Considered are the processes of heterogeneous freezing of deliquescent mixed cloud condensation nuclei that may serve as ice nuclei, and the properties of an ice germ critical radius, energy, and nucleation rate of ice crystals are examined as functions of temperature and supersaturation. Expressions for nucleation in a polydisperse aerosol for the deliquescence-freezing mode are developed. Equations are derived for the threshold and critical saturation ratios as functions of temperature and nucleation rate, and for the threshold and critical temperatures as functions of saturation ratio. Equivalence of the new formulation for the freezing point depression with traditional expressions is shown ...
100 citations
TL;DR: In this paper, the authors proposed a critical disk for supercritical accretion, where the mass-accretion rate is regulated just at the critical rate with the help of wind mass-loss.
Abstract: For a supercritical accretion regime, we propose a critical accretion disk, where the mass-accretion rate is regulated just at the critical rate with the help of wind mass-loss. We first derive a critical radius, inside of which the standard picture is violated, using the condition that the radiative force is balanced by the gravity in the vertical direction. The critical radius rcr is found to be rcr =( 9 √ 3σT/16 πcm p) u
87 citations
TL;DR: In this paper, Liu et al. derived an analytical expression for the critical radius associated with Kessler-type parameterizations of the autoconversion process and used it to predict critical radius from the cloud liquid water content and the droplet number concentration.
Abstract: Received 19 November 2003; revised 7 January 2004; accepted 25 February 2004; published 25 March 2004. [1] An analytical expression for the critical radius associated with Kessler-type parameterizations of the autoconversion process is derived. The expression can be used to predict the critical radius from the cloud liquid water content and the droplet number concentration, eliminating the need to prescribe the critical radius as an empirical constant in numerical models. Data from stratiform clouds are analyzed, indicating that on average continental clouds have larger critical radii than maritime clouds. This work further suggests that anthropogenic aerosols affect the autoconversion process by increasing the critical radius and decreasing the characteristic radius, which in turn inhibits the initiation of embryonic raindrops, and by decreasing the autoconversion rate after the initiation process. The potential impact of this work on the evaluation of the second indirect aerosol effect is discussed. INDEX TERMS: 1600 Global Change; 1640 Global Change: Remote sensing; 1655 Global Change: Water cycles (1836); 1704 History of Geophysics: Atmospheric sciences; 1854 Hydrology: Precipitation (3354). Citation: Liu, Y., P. H. Daum, and R. McGraw (2004), An analytical expression for predicting the c ritical r adius i n t he autoconversion parameterization, Geophys. Res. Lett., 31, L06121, doi:10.1029/ 2003GL019117.
70 citations
TL;DR: The limit of crystal lattice coherency of a cross-sectional heteroepitaxial junction in a nanowire is calculated in terms of the critical radius R c, based on a general calculation of elastic stresses in a long cylindrical rod as discussed by the authors.
Abstract: The limit of crystal lattice coherency of a cross-sectional heteroepitaxial junction in a nanowire is calculated in terms of the critical nanowire radius R c, based on a general calculation of elastic stresses in a long cylindrical rod. R c is derived from the kinetics of a possible misfit dislocation which can slip in the heterointerface and rest in an energetic minimum, if it occurs at all, regardless of whether it is of zero total energy as assumed in the literature. A close comparison is made with the known models for the critical radius of a dislocation half-loop and the critical thickness h c of a heteroepitaxial film, where all models are refined by including the energy of the slip step formed or accidentally annihilated. For a symmetrical, abrupt heterojunction, we obtain R c as a lower and, therefore, quite safe limit, about five times larger than h c of a comparable thin film. An even larger R c is found for junctions of finite transition width instead of abrupt transitions. It is estimated that...
58 citations
TL;DR: In this article, the critical radius and critical dilatation for a dot and a wire were derived by considering the energy of a circular prismatic dislocation loop nucleation in the inclusions.
Abstract: Quantum dots and wires, having a mismatch of crystal lattice parameters with respect to the surrounding matrix, are modelled by spherical and cylindrical inclusions, respectively. By considering the energy of a circular prismatic dislocation loop nucleation in the inclusions, the critical radius and critical dilatation for a dot and a wire are calculated. The results are compared with similar critical parameters for a mismatched film on a substrate.
43 citations
TL;DR: It is shown that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate, and the minimum radius of the stationary bubble, whose collapse leads to vortexucleation, was found to be 28+/-1 healing lengths.
Abstract: Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be $28\ifmmode\pm\else\textpm\fi{}1$ healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.
27 citations
29 Nov 2004
TL;DR: It is shown that the size of this exclusion zone has a large impact on the transmission capacity of ad hoc networks, and an optimal critical radius is found using stochastic geometry.
Abstract: In ad hoc networks, it is necessary to suppress transmissions by nodes around the desired receiver in order to achieve successful communication. This minimum separation, the critical radius, has important implications on carrier sensing and other MAC-level protocols. Previously, the critical radius has not been well understood. The critical radius is investigated in CDMA ad hoc networks, with non-spread spectrum ad hoc networks being a special case where the spreading gain is unity. It is shown that the size of this exclusion zone has a large impact on the transmission capacity of ad hoc networks, and an optimal critical radius is found using stochastic geometry.
19 citations
TL;DR: In this article, the crossover insulation radius is defined as a radius greater than the critical radius such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system.
TL;DR: It is demonstrated that splay deformations around the particle significantly influence nematic wetting of curved surfaces and a good estimate is formed for the critical temperature as a function of the inverse particle radius.
Abstract: We discuss how the curvature of a substrate influences wetting by a nematic liquid crystal concentrating on the surface of a spherical particle. Our investigation is based on Landau\char21{}de Gennes free energy formulated in terms of second-rank nematic order parameter ${Q}_{\mathrm{ij}}.$ We review the method to treat wetting transitions in curved geometries and calculate the wetting phase diagram in terms of the temperature and a surface coupling parameter. We find that the length of the prewetting line which corresponds to the boundary-layer transitions introduced by Sheng [Phys. Rev. A 26, 1610 (1982)] gradually decreases with a decrease in particle radius until it vanishes completely below a critical radius of about 100 nm. The prewetting line ends at a critical point which we study in detail. By interpreting the effect of curvature as an effective shift in temperature in Landau\char21{}de Gennes theory, we are able to formulate a good estimate for the critical temperature as a function of the inverse particle radius. It demonstrates that splay deformations around the particle significantly influence nematic wetting of curved surfaces.
TL;DR: In this paper, an energy criterion for the nucleation of a circular prismatic misfit dislocation loop in a spheroidal inclusion modeling a quantum dot is considered, and the critical radius of the inclusion for which the misfit loop can nucleate is studied as a function of the lattice misfit between the inclusion and the matrix.
Abstract: An energy criterion for the nucleation of a circular prismatic misfit dislocation loop in a spheroidal inclusion modeling a quantum dot is considered. The critical radius of the inclusion, for which the misfit dislocation loop can nucleate, is studied as a function of the lattice misfit between the inclusion and the matrix.
TL;DR: In this article, a breakdown of the Gromov hyperbolicity of the graph as seen by the simple random walk on the sphere of radius $n/4 was shown.
Abstract: Turn the set of permutations of $n$ objects into a graph $G_n$ by connecting two permutations that differ by one transposition, and let $\sigma_t$ be the simple random walk on this graph. In a previous paper, Berestycki and Durrett [In Discrete Random Walks (2005) 17--26] showed that the limiting behavior of the distance from the identity at time $cn/2$ has a phase transition at $c=1$. Here we investigate some consequences of this result for the geometry of $G_n$. Our first result can be interpreted as a breakdown for the Gromov hyperbolicity of the graph as seen by the random walk, which occurs at a critical radius equal to $n/4$. Let $T$ be a triangle formed by the origin and two points sampled independently from the hitting distribution on the sphere of radius $an$ for a constant $0 0$, whereas it is always O(n)-thick when $a>1/4$. We also show that the hitting distribution of the sphere of radius $an$ is asymptotically singular with respect to the uniform distribution. Finally, we prove that the critical behavior of this Gromov-like hyperbolicity constant persists if the two endpoints are sampled from the uniform measure on the sphere of radius $an$. However, in this case, the critical radius is $a=1-\log2$.
TL;DR: In this paper, the time dependence of the fraction of crystallization in supercooled liquid at several temperatures is analyzed by the Johnson-Mehl-Avrami form and the Avrami number is 2.8 ± 0.4 for the present samples.
Abstract: Crystal nucleation and its time evolution during isothermal annealing in supercooled liquid of glassy metals Zr 55 Al 10 Cu 30 Ni 5 and Zr 55 Al 10 Cu 35 are examined using a technique of differential thermal analysis. Time dependence of the fraction of crystallization in supercooled liquid at several temperatures is analyzed by the Johnson–Mehl–Avrami form. The Avrami number is 2.8 ± 0.4 for the present samples. Since crystallites growing in the supercooled liquid with time are found to be Zr 2 Cu crystals, it is suggested that the crystal growth in supercooled liquid is ruled by a long range diffusion process of elements. Plots of the fraction of crystallized volume versus a scaled time normalized by the half time of full crystallization almost collapse on an almost single curve . The temperature dependence of the half time is discussed using a Williams–Landel–Ferry function. The excitation energy for crystal nuclei with a critical radius is estimated.
TL;DR: In this article, a weakly nonlinear analysis of the morphological stability of a two-dimensional cylindrical crystal growing from solution in an arbitrary regime (with the growth rate proportional to supersaturation) is presented, and a quadratic correction to the critical radius of a stable crystal determined in the linear theory is obtained in an analytical form and studied as a function of the per-turbation frequency and the growth regime.
Abstract: We present the first weakly nonlinear analysis of the morphological stability of a two-dimensional cylindrical crystal growing from solution in an arbitrary regime (with the growth rate proportional to supersaturation). A quadratic (with respect to the perturbation amplitude) correction to the critical radius of a stable crystal determined in the linear theory is obtained in an analytical form and studied as a function of the per-turbation frequency and the growth regime. It is established that an increase in the perturbation amplitude vir-tually always leads to a decrease in the critical radius. Factors accounting for this nontrivial effect are consid-ered.
TL;DR: The relation between the propagation velocity (or cooling rate) and the critical radius (or pore size) is summarized in a chart for applications in capillary-porous media, such as in the freezing of biological tissues.
Abstract: An experiment was designed to compare the freezing of an aqueous solution in glass microcapillaries and in thin films. The velocity dependence of the ice front propagation in glass capillaries with radii of 87.5 microm-1.5 microm was observed. A critical capillary radius r(0), corresponding to certain thermal conditions, was obtained, below which the ice growth inside the capillaries was retarded. This critical capillary radius is further related to lambda(0), the smallest wavelength used in the Mullins-Sekerka criterion for the instability analysis of bulk solidifications [Mullins and Sekerka, J. Appl. Phys. 35, 444 (1964)]. It was found that for the present hypothesis, r(0)=lambda(0)/4 gives good predictions. The relation between the propagation velocity (or cooling rate) and the critical radius (or pore size) is summarized in a chart for applications in capillary-porous media, such as in the freezing of biological tissues.
01 Jan 2004
TL;DR: In this paper, the nucleation site density is measured on roughly polished brass and stainless steel surfaces for gas nucleation and pool boiling over a large parameter space, and it is shown that there is no large difference for the measured nucleation sites density.
Abstract: It has been well established that the rate of heat transfer associated with boiling systems is strongly dependent on the nucleation site density. Over many years attempts have been made to predict nucleation site density in boiling systems using a variety of techniques. With the exception of specially prepared surfaces, these attempts have met with little success. This paper presents an experimental investigation of nucleation site density measured on roughly polished brass and stainless steel surfaces for gas nucleation and pool boiling over a large parameter space. The fluids used for this study, distilled water and ethanol, are moderately wetting and highly wetting, respectively. Using distilled water it has been observed that the trends of nucleation site density versus the inverse of the critical radius are similar for pool boiling and gas nucleation. The nucleation site density is higher for gas nucleation than for pool boiling. An unexpected result has been observed with ethanol as the heat transfer fluid, which casts doubt on the general validity of heterogeneous nucleation theory. Due to flooding, few sites are active on the brass surface and at most two are active on the stainless steel surface during gas nucleation experiments. However, nucleation sites readily form in large concentration on both the brass and stainless steel surfaces during pool boiling. The nucleation site densities for the rough and mirror polished brass surfaces are also compared. It shows that there is no large difference for the measured nucleation site density.Copyright © 2004 by ASME
TL;DR: In this paper, the critical radii of nuclei of zeolite A and the amorphous phase were estimated based on the nucleation rates determined in previous studies and the classical theory of homogeneous nucleation.
Abstract: As a fundamental study of zeolite crystallization from aluminosilicate solutions, the critical radii of nuclei of zeolite A and the amorphous phase were estimated based on the nucleation rates determined in our previous studies and the classical theory of homogeneous nucleation.The calculated critical radii of nucleus of zeolite A crystals were 0.4–0.8 nm under the conditions examined, and its diameter is found to be almost equal to the half of the edge length of a unit cell of zeolite A crystals. Meanwhile the radii of the critical nucleus of the amorphous phase were 0.8–1.6 nm with the surface energy of 12–23 mJ·m–2.These calculated results imply the following phase transformation processes. For the case of zeolite A nucleation, several growth units assemble together and result in a formation of a zeolite A nucleus. In the case of the amorphous phase, a greater number of growth units are needed for nucleation and the induction time of the nucleation of the amorphous phase is shorter than that of zeolite A probably due to the random structures of the amorphous phase.
TL;DR: By assuming a balance in molar flux at a solid-liquid interface layer with thickness δ in a binary liquid alloy, this paper studied the interfacial instability and a critical radius of a homogeneous nucleation.
Patent•
24 Dec 2004
TL;DR: In this article, the authors proposed a method to predict the density distribution and size distribution of oxygen precipitation nuclei in a single crystal accurately using a computer from the pulling time of the single crystal to the finish time of cooling while taking account of the convection of the melt.
Abstract: PROBLEM TO BE SOLVED: To predict the density distribution and size distribution of oxygen precipitation nuclei in a single crystal accurately. SOLUTION: At first to seventh steps, temperature distribution in a single crystal 14 growing from melt 12 is determined using a computer from the pulling time of the single crystal to the finish time of cooling while taking account of the convection of the melt. At eighth to fourteenth steps, void density is determined using the computer by taking account of the cooling process of the single crystal separated from the melt and reflecting the effect of gradual and quick cooling of the single crystal on the result, and then the void radius and the thickness of an inner wall oxide film growing around the void are determined in relation to each other using the computer. At fifteenth to seventeenth steps, the generation of oxygen precipitation nuclei per unit time and the critical radius are determined using the computer. When the generation of the oxygen precipitation nuclei per unit time exceeds zero, calculations of the void radius and the thickness of the inner wall oxide film are stopped and the radius of the oxygen precipitation nucleus is determined using the computer. COPYRIGHT: (C)2005,JPO&NCIPI
TL;DR: In this paper, a metastable system is described as an ensemble of locally isolated statistically independent centers, with a possibility of one and only one nucleus of a close-to critical radius emerging on each one of these centers.
Abstract: A metastable system is described as an ensemble of locally isolated statistically independent centers, with a possibility of one and only one nucleus of a close-to- critical radius emerging on each one of these centers. It is assumed that this event occurs as a result of fluctuations in a heterophase subsystem and leads to the formation of a viable nucleus at a given point in space. The process of the emergence of this nucleus is treated as the first crossing of the potential barrier by a Brownian particle. Proceeding from the principles of nonequilibrium thermodynamics, dynamic equations of bubble (droplet) growth are derived, which correspond to the Onsager relations. These formulas are used as Langevin equations in multidimensional phase space and are related to the respective Fokker-Planck equation whose solution enables one to determine the local rate of emergence of a viable nucleus and, as a consequence, the rate of its emergence in the entire system. An alternative expression is given for the rate of homogeneous steady-state nucleation, which differs from the classical expression by the pre-exponential factor and, in the case where one parameter (radius) may be sufficient, gives close limits of attainable superheat (supersaturation). Given the expression for the nonequilibrium work of bubble (droplet) and the distribution of heterogeneous centers, the obtained result may be readily generalized to the case of heterogeneous nucleation.