Search Results - (Author, Cooperation:J. C. Fung)

2012-11-10

American Association for the Advancement of Science (AAAS)

0036-8075

1095-9203

Biology

Chemistry and Pharmacology

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Natural Sciences in General

Physics

G1 Phase ; Microscopy, Confocal ; Mitochondria/*metabolism/*ultrastructure ; *Mitochondrial Size ; Saccharomyces cerevisiae/cytology/*growth & development/*ultrastructure ; Saccharomyces cerevisiae Proteins/genetics/metabolism ; rab GTP-Binding Proteins/genetics/metabolism

1089-7666

AIP Digital Archive

Physics

The difference between locally self-similar fractals, called K fractals, and H fractals, which are globally self-similar fractals, is recalled . The self-similar cascade of energy [and enstrophy in the two-dimensional (2-D) case], which has been the original incentive for introducing fractals in the study of turbulence, does not seem to generate H-fractal interfaces in 2-D turbulent flows, according to the numerical evidence currently available. It only produces spiral singularities that are an example of K-fractal structures, and presumably a consequence of the structure of the turbulence that is neglected in pictures of the turbulence, based on a self-similar cascade of energy. It may be that the experimental evidence for fractal interfaces in 3-D turbulence is, in fact, evidence that these interfaces are K fractal. On the other hand, it could be that only very unsteady flows can produce H-fractal interfaces through a folding process that the unsteadiness adds to the stretching of the flow [see J. M. Ottino, The Kinematics of Mixing: Stretchings, Chaos and Transport (Cambridge U. P., Cambridge, 1989)]. That idea is investigated by releasing lines in a blinking vortex [J. Fluid Mech. 143, 1 (1984)] known to advect fluid elements "chaotically'' in a certain range of parameters. The numerical evidence obtained supports the claim that interfaces in chaotic advection are H fractal. The length of a line in a blinking vortex grows exponentially, whereas the length of a line in a single steady vortex only grows linearly. The two "fractal'' dimensions of the line investigated here increase with time, but they do not both asymptote to 2. The asymptotic value of the Kolmogorov capacity decreases as the time spent by the vortex in each location is decreased.

Electronic Resource

1089-7666

AIP Digital Archive

Physics

We release a line in a flow produced by a blinking vortex1 which is known to advect fluid elements "chaotically'' for a certain range of parameters. This is a similar problem to that of a line evolving in phase space through the action of an area-preserving map, addressed a decade ago by Berry et al.2 These authors have classified the convolutions of such a line as being either "tendril shaped'' or "whorl shaped.'' Recent numerical simulations of lines released in 2-D turbulence3 have shown that they only develop "whorls,'' i.e., spiral structures. These spiral structures are produced by the eddying regions of the flow4 and are responsible for the noninteger value of the "fractal'' dimension DK of the line, as measured by the box-counting algorithm. This "fractal'' dimension is actually a Kolmogorov capacity.It has also been shown recently3 that the Kolmogorov capacity is a measure of local self-similarity, whereas the Hausdorff dimension DH is a measure of global self-similarity. Spirals are a good example of locally self-similar objects, for which DK〉1 but DH=1. For conciseness we call a line H fractal when DH〉1, and K fractal when DK〉1. Most experimental and numerical evidence to date for "fractal'' interfaces in turbulent flows is in fact evidence showing these interfaces to be K fractal. In fact, in the numerical simulations of Vassilicos,3 lines have been found not to be H fractal. Whether a line in chaotic advection becomes K fractal or H fractal is not a trivial question. If one neglects the effect of the unsteadiness of the flow, and thinks in terms of a single vortex at a fixed point in space wrapping the line around it, then it is easy to show that the spiral thus created has a DK〉1 but DH=1 (and, in particular, that DK〈2; the question of whether a line in chaotic advection is space filling is therefore not a trivial one either). But if one concentrates on the similarity between Aref's blinking vortex and a two-dimensional map, then one may be reminded of the Hénon attractor5 which is known to have a transversal Cantor-like structure that is H fractal. In fact, pictures of the line in the blinking vortex flow show that line to have a comparable stretched and folded structure to that of the Hénon attractor.We measure DH by measuring the length of the line with various resolutions and find that DH grows with time above 1. By zooming into the pictures of our line we can see its self-similar structure, and are therefore inclined to conclude that lines in chaotic advection do become H fractal. We also measure DK by the box-counting algorithm, and find that it also grows with time above 1, but is not equal to DH. It is a known mathematical fact that in general DK≥DH, and our findings are consistent with this requirement. But we do not yet understand what this nonvanishing difference between DK and DH means for a line in chaotic advection. Furthermore, we find that both DK and DH increase as the switching of the vortex from one location to the other becomes faster. It is not clear whether these two fractal dimensions tend, asymptotically with time, toward a value strictly smaller than 2 or not. The interest of this work is to show how efficient unsteadiness (which is the central component of 2-D chaotic advection) can be for creating H fractal structures through a process of folding that it adds to stretching of the flow.6 We compare with numerical simulations of 2-D turbulence3 where the simulated, self-similar cascade of eddies fails to produce H fractal structures, and only produces K fractals.

Electronic Resource

1089-7666

AIP Digital Archive

Physics

We study the topology, and in particular the self-similar and space-filling properties of the topology of line-interfaces passively advected by five different 2-D turbulent-like velocity fields. Special attention is given to three fundamental aspects of the flow: the time unsteadiness, the classification of local spatial flow structure in terms of hyperbolic and elliptic points borrowed from the study of phase spaces in dynamical systems and a classification of flow structure in wavenumber space derived from the studies of Weierstrass and related functions. The methods of analysis are based on a classification of interfacial scaling topologies in terms of K- and H- fractals, and on two interfacial scaling exponents, the Kolmogorov capacity DK and the dimension D introduced by Fung and Vassilicos [Phys. Fluids 11, 2725 (1991)] who conjectured that D(approximately-greater-than)1 implies that the interface is H-fractal. An argument is presented (in the Appendix) to show that D(approximately-greater-than)1 is a necessary condition for the evolving interface to be H-fractal through the action of the flow, and that D(approximately-greater-than)1 is also sufficient provided that no isolated regions exist where the flow velocity is either unbounded or undefined in finite time. D is interpreted to be a degree of H-fractality and is different from the Hausdorff dimension DH. In all our flows, steady and unsteady, interfaces in particular realisations of the flow reach a non-space-filling steady self-similar state where D and DK are both constant in time even though the interface continues to be advected and deformed by the flow.It is found that D is equal to 1 in 2-D steady flows and always increases with unsteadiness, that DK generally decreases with unsteadiness where the interfacial topology is dominated by spirals, and that DK increases with unsteadiness where the interfacial topology is dominated by tendrils. In those flows with larger number of modes, DK is a non-increasing function of unsteadiness and a decreasing function of the exponent p of the flow's self-similar energy spectrum E(k)∼k−p. DK's decreasing dependences on unsteadiness and the exponent p can be explained by the presence of spirals in the eddy regions of the flow. The values of D and DK and their dependence on unsteadiness can change significantly only by changing the distribution of wavenumbers in wavenumber space while keeping the phases and energy spectrum constant. © 1995 American Institute of Physics.

Electronic Resource

1619-6937

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Physics

Zusammenfassung Die freien Schwingungen von einseitig eingespannten Trägern mit variablen Querschnitt werden betrachtet. Durch Zusammenziehung der Masse auf diskrete Punkte werden—im wesentlichen durch ein einfaches Iterationsschema—Näherungen für die Schwingungsformen und für die oberen und unteren Grenzen der Eigenfrequenzen gefunden. SowohlEuler-Bernoulli als auchTimoshenko-Träger werden betrachtet. Anhand von Beispielen wird der Vergleich mit bekannten Resultaten gezogen.

Summary The free oscillations of cantilever beams of variable cross-section are considered. By lumping the mass properties of the beam at discrete points, approximate modes and upper and lower bounds to approximate natural frequencies are obtained essentially by a simple iteration scheme. BothEuler-Bernoulli andTimoshenko beams are considered. Example problems are exhibited and compared to known results.

Electronic Resource

1573-7357

Springer Online Journal Archives 1860-2000

Physics

Abstract We have developed a Beliaev theory incorporating a semi-phenomenological roton backflow effect in order to examine the effect of the backflow on the Quantum Evaporation of atoms from the free surface of superfluid 4 He. A theory of Quantum Evaporation based on a real-space Beliaev theory neglecting roton backflow was recently developed by Sobnack et al. [Phys. Rev. B 60, 3465 (1999)], and in this paper we discuss the extension of the theory to include the backflow physics from the Aldrich-Pines polarization potential theory of the 1970's. The calculation of the effect of the backflow on Quantum Evaporation is presented elsewhere.

Electronic Resource

1573-7357

Springer Online Journal Archives 1860-2000

Physics

Abstract We investigate the effect of roton backflow on the scattering of atoms, rotons and phonons at the free surface of superfluid 4 He at T=0 K by including backflow semi-phenomenologically in the form of a backflow potential in the theory of Sobnack et al. [M. B. Sobnack, J. C. Inkson, and J. C. H. Fung, Phys. Rev. B 60, 3465 (1999)]. We assume that all the surface scattering processes are elastic and that the quasiparticles and atoms are incident obliquely to the free surface. We calculate probabilities for the various one-to-one surface scattering processes allowed for a range of energies and compare the scattering rates with those obtained when backflow is neglected.

Electronic Resource

1573-1987

turbulent transport ; turbulent diffusion ; concentration fluctuations

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Abstract A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows. An initial distribution of material is discretised into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by Kinematic Simulation or by a stochastic model for the motion of each cloud centroid. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by Kinematic Simulation. The ensemble of discrete clouds is periodically rediscretised, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow and in a coastal flow, and the results are compared with analytic, steady state solutions where available.

Electronic Resource

1573-1987

turbulence ; diffusion ; random Fourier modes ; random flight ; rapid distortion theory

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Abstract To investigate the diffusion of fluid particles around a cylinder in a turbulent flow, we have developed two new types of model for simulating the trajectory of particles:(1) a model combining random Fourier modes and random flight (RF); (2) a pure kinematic simulation (KS) by random Fourier modes. In model 1 the large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the small-scale random motion of particles is simply modelled by an Itô type of stochastic differential equation with a memory time comparable to the Lagrangian time scaleT s L of the small-scale motion. In model 2, both large- and small-scale turbulence is simulated using random Fourier modes. The change of turbulence around the cylinder is modelled by rapid distortion theory (RDT), although the small-scale motion of particles in the RF model is simply assumed to keep the homogeneous random behaviour. These models give very similar and realistic trajectories showing rapid changes of direction due to the small-scale motion.

Electronic Resource