Gibbsian Hypothesis in Turbulence

We show that Kolmogorov multipliers in turbulence cannot be statistically independent of others at adjacent scales (or even a finite range apart) by numerical simulation of a shell model and by theory. As the simplest generalization of independent distributions, we suppose that the steady-state statistics of multipliers in the shell model are given by a translation-invariant Gibbs measure with a short-range potential, when expressed in terms of suitable ``spin'' variables: real-valued spins that are logarithms of multipliers and XY-spins defined by local dynamical phases. Numerical evidence is presented in favor of the hypothesis for the shell model, in particular novel scaling laws and derivative relations predicted by the existence of a thermodynamic limit. The Gibbs measure appears to be in a high-temperature, unique-phase regime with ``paramagnetic'' spin order.Comment: 19 pages, 9 figures, greatly expanded content, accepted to appear in J. Stat. Phy

Kernel Spectral Curvature Clustering (KSCC)

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches exist for modeling data by mixtures of affine subspaces (which is often referred to as hybrid linear modeling). We translate some important instances of multi-manifold modeling to hybrid linear modeling in embedded spaces, without explicitly performing the embedding but applying the kernel trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses kernels at two levels - both as an implicit embedding method to linearize nonflat manifolds and as a principled method to convert a multiway affinity problem into a spectral clustering one. We demonstrate the effectiveness of the method by comparing it with other state-of-the-art methods on both synthetic data and a real-world problem of segmenting multiple motions from two perspective camera views.Comment: accepted to 2009 ICCV Workshop on Dynamical Visio

Simultaneous space charge and conduction current measurements in solid dielectrics under high dc electric field

The importance of space charge in solid dielectrics has been recognized for many years and various attempts have been made to map the distribution and assess its influence on the electrical performance of solid dielectrics. Significant development in non-destructive measurement techniques emerged two decades ago. Crosslinked polyethylene (XLPE) has been used for ac power cable insulation up to 500 kV for many years. There is a tendency to use XLPE for dc power cable. However, the easy formation of space charge under dc electric field within XLPE is a major concern for such an application. Space charge in insulation can distort electric field distribution, causing electric field increase in one region and reduction in another. The electric field enhancement could lead to degradation and result in premature failure. Electrical treeing in solid dielectrics is a typical example of local field enhancement due to space charge accumulation. In this report several popular non-destructive techniques are briefly reviewed. This is followed by detailed description of a modified pulsed electroacoustic (PEA) technique that allows simultaneous measurement of space charge and conduction current in a solid dielectric subjected to high dc electric fields. Finally, we report the relationship between space charge dynamics and electrical conduction current in XLPE using the modified PEA system. The effect of electrode material on both charge dynamics and current has been investigated using semiconducting material and aluminium. It has been found charge dynamics in the material depend on electrode configuration. More importantly, it has been noticed that the so called space charge limited transient current peaks are closely related to the meetings of negative and positive charge front in the bulk of the sample

Space Charge Modelling in Solid Dielectrics under High Electric Field Based on Double Charge Injection Model

Present study aims to develop a clear insight on factors that influence space charge dynamics in solid dielectrics through a numerical simulation. The model used for the simulation is proposed by Alison and Hill [1] which describes charge dynamics as a result of bipolar transport with single level trapping. In this model, a constant mobility and no detrapping have been assumed. The simulation results show that carrier mobility, trapping coefficient and Schottky barrier have a significant effect on the space charge dynamics. Many features of space charge profiles observed by experiments have been revealed in despite of over simplistic model. More importantly, the simulation allows us to study the role of each individual parameter in the formation of space charge in solid dielectrics, so that the experimental results can be better understood

Stability Of contact discontinuity for steady Euler System in infinite duct

In this paper, we prove structural stability of contact discontinuities for full Euler system

Comparison of the Geometrical Characters Inside Quark- and Gluon-jet Produced by Different Flavor Quarks

The characters of the angular distributions of quark jets and gluon jets with different flavors are carefully studied after introducing the cone angle of jets. The quark jets and gluon jets are identified from the 3-jet events which are produced by Monte Carlo simulation Jetset7.4 in e+e- collisions at $\sqrt s$=91.2GeV. It turns out that the ranges of angular distributions of gluon jets are obviously wider than that of quark jets at the same energies. The average cone angles of gluon jets are much larger than that of quark jets. As the multiplicity or the transverse momentum increases, the cone-angle distribution without momentum weight of both the quark jet and gluon jet all increases, i.e the positive linear correlation are present, but the cone-angle distribution with momentum weight decreases at first, then increases when n > 4 or p_t > 2 GeV. The characters of cone angular distributions of gluon jets produced by quarks with different flavors are the same, while there are obvious differences for that of the quark jets with different flavors.Comment: 13 pages, 6 figures, to be published on the International Journal of Modern Physics

Semantics-Space-Time Cube. A Conceptual Framework for Systematic Analysis of Texts in Space and Time

We propose an approach to analyzing data in which texts are associated with spatial and temporal references with the aim to understand how the text semantics vary over space and time. To represent the semantics, we apply probabilistic topic modeling. After extracting a set of topics and representing the texts by vectors of topic weights, we aggregate the data into a data cube with the dimensions corresponding to the set of topics, the set of spatial locations (e.g., regions), and the time divided into suitable intervals according to the scale of the planned analysis. Each cube cell corresponds to a combination (topic, location, time interval) and contains aggregate measures characterizing the subset of the texts concerning this topic and having the spatial and temporal references within these location and interval. Based on this structure, we systematically describe the space of analysis tasks on exploring the interrelationships among the three heterogeneous information facets, semantics, space, and time. We introduce the operations of projecting and slicing the cube, which are used to decompose complex tasks into simpler subtasks. We then present a design of a visual analytics system intended to support these subtasks. To reduce the complexity of the user interface, we apply the principles of structural, visual, and operational uniformity while respecting the specific properties of each facet. The aggregated data are represented in three parallel views corresponding to the three facets and providing different complementary perspectives on the data. The views have similar look-and-feel to the extent allowed by the facet specifics. Uniform interactive operations applicable to any view support establishing links between the facets. The uniformity principle is also applied in supporting the projecting and slicing operations on the data cube. We evaluate the feasibility and utility of the approach by applying it in two analysis scenarios using geolocated social media data for studying people's reactions to social and natural events of different spatial and temporal scales

Transonic Shocks In Multidimensional Divergent Nozzles

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity(non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Frechet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.Comment: 54 page

Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation