Showing papers on "Critical radius published in 1999"

Dynamics of transient pores in stretched vesicles

Abstract: We image macroscopic transient pores in mechanically stretched giant vesicles. Holes open above a critical radius rc1, grow up to a radius rc2, and close. We interpret the upper limit rc2 by a relaxation of the membrane tension as the holes expand. The closing of the holes is caused by a further relaxation of the surface tension when the internal liquid leaks out. A dynamic model fits our data for the growth and closure of pores.

On acoustic cavitation of slightly subcritical bubbles

Abstract: The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of time-periodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequency-amplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh–Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed.

Chain formation in homogeneous gas–liquid nucleation of polar fluids

Abstract: We report a computer-simulation study of homogeneous gas–liquid nucleation in a model for strongly polar fluids. We find that the nucleation process is initiated by chain-like clusters. As the cluster size is increased, the chains become longer. However, beyond a certain size, the nuclei collapse to form compact, spherical clusters. Nevertheless, in the interface of the collapsed nuclei a high degree of chain formation is preserved. We compare the interface of the collapsed nuclei with the planar interface and find that the interface of the globule-like nuclei differs markedly from the flat interface. Classical nucleation theory underestimates both the size of the critical nucleus and the height of the nucleation barrier.

Mechanical behavior of a μm-sized single crystal silicon structure with sharp notches

Abstract: The mechanical behavior of μm-sized single crystal silicon structures is investigated in this paper. A new apparatus for microsample tensile testing is used to determine the mechanical properties of single crystal silicon microbars. Force and elongation are measured independently with high accuracy. Elastic constants as well as critical loads are determined. Failure of the sample occurs at the extremities of the microbar at a sharp notch. The stress field in the notch tip vicinity is therefore analyzed to characterize the load capacity of the structure. For this purpose, finite element computations are combined with approximate analytic solutions based on the Stroh formalism. Both the case of plane stress and two-dimensional displacements are considered. Comparison with the FEM solution shows that the plane stress assumption is better, leading to the determination of the critical stress intensity factor F cr for this case. Because F cr is dependent on the geometry, a new scalar failure criterion—i.e. a critical radius R cr —is introduced and derived from the calculated stress field at the notch. It is based on a comparison of stored elastic energy and surface energy at the critical location. Because it is a scalar criterion, it can be applied to single crystal microstructures with notches of arbitrary notch angle. For the case considered, experiments yield R cr = 0.8 nm. The proposed criterion can be considered as a step towards the definition of a design rule for sharp notches in single crystal structures, which is required for the optimized design of micromechanical devices.

Thinning transitions in free-standing liquid-crystal films as the successive formation of dislocation loops.

Abstract: We describe a model for the layer-thinning transition in free-standing liquid-crystal films based on the successive, spontaneous formation of dislocation loops. As the film temperature increases and the smectic order and layer compressional modulus decrease, the condition for creating a dislocation loop of critical radius is met and a thinning is nucleated. The resulting equation for N, the number of smectic layers, as a function of temperature yields good fitting results to the thinning transitions obtained from several fluorinated compounds.

Critical tube diameter for detonation transmission and critical initiation energy of spherical detonation

Abstract: Two experimental setups are used to study propagation and attenuation of blast waves. In the first one, the blast wave is generated by a spherical detonation, and in the second one, the blast wave is created by the diffraction of a planar detonation propagating in a tube. The similarity of these phenomena appears clearly by means of dimensionless space-time and pressure-space diagrams of shock wave propagation. Dimensionless variables are expressed as a function of the supplied energy. Two energy formulations are proposed: a piston model and a bulk energy model. The established diagrams cover a wide range of industrial applications. Under critical conditions, the energy released by a planar detonation is correlated to the ignition source energy supply and a relationship which links the critical radius of detonation to the critical tube diameter.

Enhanced protein crystallization around the metastable critical point

Abstract: We report on a computer-simulation study of homogeneous crystal nucleation in a model for globular proteins. We find that the presence of a metastable vapour-liquid critical point drastically changes the pathway for the formation of a critical nucleus. But what is more important, the large density fluctuations near the critical point also lowers the free-energy barrier to nucleation and hence increases the nucleation rate. As␣the location of the vapour-liquid critical point can be controlled by changing the solvent conditions, our simulation results suggest a guided approach to protein crystallization.

The Thermal Explosion Revisited

Abstract: The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction $\a$ of its wall is ideally thermally conducting while the remaining fraction $1-\a$ is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive $\a$ and isolated $1-\a$ parts of the boundary occupy together the segments $2\pi/N$ ($N$ is the number of segments) of the boundary. A numerical investigation is performed. It is shown that at small $\a$ and large $N$ the critical radius obeys a scaling law with the coefficients depending upon $N$. For large $N$ is obtained that in the central core of the vessel the temperature distribution is axisymmetric. In the boundary layer near the wall having the thickness $\approx 2\pi r_0/N$ ($r_0$--the radius of the vessel) the temperature distribution varies sharply in the peripheral direction. The temperature distribution in the axisymmetric core at the critical value of the vessel radius is subcritical

The influence of the flow of the reacting gas on the conditions for a Thermal Explosion

Abstract: The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor's length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Critical radius of loop defects in homeotropic nematic liquid crystals

Abstract: We describe an experimental situation with a looped line defect in nematic liquid crystals observed by polarizing optical microscopy. We measured the critical size of the loop below which it spontaneously shrinks and transforms into a point defect. The experiment was done with 5CB which gives rise to twist disclinations as do most of the usual nematics. For this kind of disclination an in-plane force due to the boundary conditions acts on the line and influences the critical radius. W e have constructed a model which is in good agreement with experimental measurements and deduced the line tension of the disclination.

On acoustic cavitation of slightly subcritical bubbles

Abstract: The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of time-periodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequency-amplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh-Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed.

Inconel 718レーザ溶接性に及ぼす溶接条件の影響-Ni基耐熱超合金のレーザ溶接性に関する研究(第1報)-

Abstract: This study was carried out to know the laser weldability of Ni-base superalloy, Inconel 718. Inconel 718 whose thickness and grain size were 2 mm and 84 μm were prepared for a bead on plate test using CO2 laser welding with a power of 1 to 3 kW and with a traveling speed of 0.5 to 5 m/min. The testing plate was solution heat-treated at the temperature of 1340 K for 3.6 ks before welding.The shape of penetration depended on traveling speed and was typically classified into two types of Type C and Type N by specialized shape. Type C had low depth to width ratio like a champagne glass and Type N had high depth to width ratio like a nail head. Type C and Type N weld beads are seen at a side of low welding speed and at a high welding speed side, respectively and the critical welding speed between Type C and Type N is 1.5 m/min in the present study.Liquation cracks easily occurred at HAZ in the case of nail head like penetration. We used a radius of curvature of fusion boundary at neck zone of penetration to represent a feature of penetration. It can be seen that a critical radius of curvature exists by which whether cracks occur or not in HAZ can be judged. No weld cracks were found when the radius of curvature exceeded the critical value of ρcr. Furthermore, as a countermeasure welding cracks can be prevented by increasing the laser heat input over the valus of 100 kJ/m in the present study. According to observation of grain boundary liquation at HAZ, liquation crack was related to grain boundary liquation.

Estimation of The Critical Radius for The Nucleation of the C54 Phase in C49 TiSi2: Role of The Difference in Density

Abstract: We discuss the rather scattered measurements of the lattice parameters for C49 TiSi 2 , which are reported in literature, along with new and accurate X-ray diffraction measurements and ab-initio calculations. Both agree in indicating that the density of the metastable C49 structure cannot be much smaller than the one for the polymorphic C54 phase, as it is commonly reported. We conclude by demonstrating that only in the case of such a smaller difference in density between the two phases, the elastic strain contribution to the nucleation energy of the C54 structure in the C49 matrix can be neglected. The estimation of the critical radius strongly depends on this issue.

Regular article Enhanced protein crystallization around the metastable critical point

Abstract: We report on a computer-simulation study of homogeneous crystal nucleation in a model for globular proteins. We find that the presence of a metastable vapour-liquid critical point drastically changes the pathway for the formation of a critical nucleus. But what is more important, the large density fluctuations near the critical point also lowers the free-energy barrier to nucleation and hence increases the nucleation rate. As the location of the vapour-liquid critical point can be controlled by changing the solvent conditions, our simulation results suggest a guided approach to protein crystallization.

Tail Probability via Tube Formula and Euler Characteristic Method when Critical Radius is Zero

Abstract: In Takemura and Kuriki(1999b) we have established that the tube formula and the Euler characteristic method give identical and valid asymptotic expansion of tail probability of the maximum of Gaussian random field when the random field has finite Karhunen-Loeve expansion and the index set has positive critical radius. The purpose of this paper is to show that the positiveness of the critical radius is an essential condition. Namely, we prove that if the critical radius is zero, only the main term is valid and other higher order terms are generally not valid in the formal asymptotic expansion based on the tube formula or the Euler characteristic method. Our examples show that index sets with zero critical radius are commonly used in statistics.