Strain limiting for clustered shape matching

journal articleIn this paper, we advocate explicit symplectic Euler integration and strain limiting in a shape matching simulation framework. The resulting approach resembles not only previous work on shape matching and strain limiting, but also the recently popular position-based dynamics. However, unlike this previous work, our approach reduces to explicit integration under small strains, but remains stable in the presence of non-linearities

On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed

Phase transitions during fruiting body formation in Myxococcus xanthus

The formation of a collectively moving group benefits individuals within a population in a variety of ways such as ultra-sensitivity to perturbation, collective modes of feeding, and protection from environmental stress. While some collective groups use a single organizing principle, others can dynamically shift the behavior of the group by modifying the interaction rules at the individual level. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behavior, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. This multi-step developmental process most likely involves several different single-celled behaviors as the population condenses from a loose, two-dimensional sheet to a three-dimensional mound. Here, we use high-resolution microscopy and computer vision software to spatiotemporally track the motion of thousands of individuals during the initial stages of fruiting body formation. We find that a combination of cell-contact-mediated alignment and internal timing mechanisms drive a phase transition from exploratory flocking, in which cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into streams, which act as slow-spreading, quasi-one-dimensional nematic fluids. These observations lead us to an active liquid crystal description of the myxobacterial development cycle.Comment: 16 pages, 5 figure

Clustering of Ly-alpha emitters around luminous quasars at z = 2-3: an alternative probe of reionization on galaxy formation

Narrowband observations have detected no Ly-alpha emission within a 70 pMpc^3 volume centered on the z = 2.168 quasar PKS 0424-131. This is in contrast to surveys of Ly-alpha emitters in the field at similar redshifts and flux limits, which indicate that tens of sources should be visible within the same volume. The observed difference indicates that the quasar environment has a significant influence on the observed density of Ly-alpha emitters. To quantify this effect we have constructed a semi-analytic model to simulate the effect of a luminous quasar on nearby Ly-alpha emitters. We find the null detection around PKS 0424-131 implies that the minimum isothermal temperature of Ly-alpha emitter host halos is greater than 3.4 x 10^6 K (68% level), corresponding to a virial mass of ~1.2 x 10^12 M_solar. This indicates that the intense UV emission of the quasar may be suppressing the star formation in nearby galaxies. Our study illustrates that low redshift quasar environments may serve as a surrogate for studying the radiative suppression of galaxy formation during the epoch of reionization.Comment: 9 pages, 5 figures, submitted to MNRA

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256^3, 512^3 and 1024^3 grid points, with k_(max)η(overbar) approximately 1, 2 and 4, respectively, the same initial conditions and Re_λ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256^3 grid resolution case (k_(max)η(overbar) ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [A_ij]_+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024^3 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [A_ij]_+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented

Large-Eddy Simulations of Flow and Heat Transfer in Complex Three-Dimensional Multilouvered Fins

The paper describes the computational procedure and results from large-eddy simulations in a complex three-dimensional louver geometry. The three-dimensionality in the louver geometry occurs along the height of the fin, where the angled louver transitions to the flat landing and joins with the tube surface. The transition region is characterized by a swept leading edge and decreasing flow area between louvers. Preliminary results show a high energy compact vortex jet forming in this region. The jet forms in the vicinity of the louver junction with the flat landing and is drawn under the louver in the transition region. Its interaction with the surface of the louver produces vorticity of the opposite sign, which aids in augmenting heat transfer on the louver surface. The top surface of the louver in the transition region experiences large velocities in the vicinity of the surface and exhibits higher heat transfer coefficients than the bottom surface.Air Conditioning and Refrigeration Project 9

Three-dimensional structure and flexibility of a membrane-coating module of the nuclear pore complex.

The nuclear pore complex mediates nucleocytoplasmic transport in all eukaryotes and is among the largest cellular assemblies of proteins, collectively known as nucleoporins. Nucleoporins are organized into distinct subcomplexes. We optimized the isolation of a putative membrane-coating subcomplex of the nuclear pore complex, the heptameric Nup84 complex, and analyzed its structure by EM. Our data confirmed the previously reported 'Y' shape. We discerned additional structural details, including specific hinge regions at which the particle shows great flexibility. We determined the three-dimensional structures of two conformers, mapped the localization of two nucleoporins within the subcomplex and docked known crystal structures into the EM maps. The free ends of the Y-shaped particle are formed by beta-propellers; the connecting segments consist of alpha-solenoids. Notably, the same organizational principle is found in the clathrin triskelion, which may share a common evolutionary origin with the heptameric complex

Scaling of the buckling transition of ridges in thin sheets

When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work required to crumple the sheet is consumed in breaking the folding lines or ``ridges''. To understand crumpling it is then necessary to understand the strength of ridges. In this work, we consider the buckling of a single ridge under the action of inward forcing applied at its ends. We demonstrate a simple scaling relation for the response of the ridge to the force prior to buckling. We also show that the buckling instability depends only on the ratio of strain along the ridge to curvature across it. Numerically, we find for a wide range of boundary conditions that ridges buckle when our forcing has increased their elastic energy by 20% over their resting state value. We also observe a correlation between neighbor interactions and the location of initial buckling. Analytic arguments and numerical simulations are employed to prove these results. Implications for the strength of ridges as structural elements are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev