Secondary Perturbation Effects in Keplerian Accretion Disks: Elliptical Instability

Origin of turbulence in cold accretion disks, particularly in 3D, which is expected to be hydrodynamic but not magnetohydrodynamic, is a big puzzle. While the flow must exhibit some turbulence in support of the transfer of mass inward and angular momentum outward, according to the linear perturbation theory it should always be stable. We demonstrate that the 3D secondary disturbance to the primarily perturbed disk which exhibits elliptical vortices into the system solves the problem. This result is essentially applicable to the outer region of accretion disks in active galactic nuclei where the gas is significantly cold and neutral in charge and the magnetic Reynolds number is smaller than 10^4.

Exploiting Programmable Network Interfaces for Parallel Query Execution in Workstation Clusters

Workstation clusters equipped with high performance interconnect having programmable network processors facilitate interesting opportunities to enhance the performance of parallel application run on them. In this paper, we propose schemes where certain application level processing in parallel database query execution is performed on the network processor. We evaluate the performance of TPC-H queries executing on a high end cluster where all tuple processing is done on the host processor, using a timed Petri net model, and find that tuple processing costs on the host processor dominate the execution time. These results are validated using a small cluster. We therefore propose 4 schemes where certain tuple processing activity is offloaded to the network processor. The first 2 schemes offload the tuple splitting activity - computation to identify the node on which to process the tuples, resulting in an execution time speedup of 1.09 relative to the base scheme, but with I/O bus becoming the bottleneck resource. In the 3rd scheme in addition to offloading tuple processing activity, the disk and network interface are combined to avoid the I/O bus bottleneck, which results in speedups up to 1.16, but with high host processor utilization. Our 4th scheme where the network processor also performs apart of join operation along with the host processor, gives a speedup of 1.47 along with balanced system resource utilizations. Further we observe that the proposed schemes perform equally well even in a scaled architecture i.e., when the number of processors is increased from 2 to 64

Molecular Dynamics of Thermotropic Liquid Crystals: Anomalous relaxation dynamics of calamitic and discotic liquid crystals

Recent optical kerr effect (OKE) studies have demonstrated that orientational relaxation of rod-like nematogens exhibits temporal power law decay at intermediate times not only near the isotropic–nematic (I–N) phase boundary but also in the nematic phase. Such behaviour has drawn an intriguing analogy with supercooled liquids. We have investigated both collective and single-particle orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I–N phase boundary, the system behaves remarkably like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system. A model liquid crystal, consisting of disk-like molecules, has also been investigated in molecular dynamics simulations for orientational relaxation along two isobars starting from the high temperature isotropic phase. The isobars have been so chosen that the phase sequence isotropic (I)–nematic (N)–columnar (C) appears upon cooling along one of them and the sequence isotropic (I)–columnar(C) along the other. While the orientational relaxation in the isotropic phase near the I–N phase transition shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I–C phase boundary. The origin of the power law decay in the single-particle second-rank orientational time correlation function (OTCF) is traced to the growth of the orientational pair distribution functions near the I–N phase boundary. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.

Impact on spinning discs

The initial local response of a spinning disk subjected to impact is presented to highlight the effect of centrifugal stress. The impact generated deflection falls after reaching a peak unlike in the case of a stationary plate. The peak deflection at a given radius occurs around the time when the membrane wave reaches that location. This paper demonstrates the absorption of impact vibration transients in a spinning disk by the membrane wave action.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

Efficient external memory structures for range-aggregate queries

We present external memory data structures for efficiently answering range-aggregate queries. The range-aggregate problem is defined as follows: Given a set of weighted points in R-d, compute the aggregate of the weights of the points that lie inside a d-dimensional orthogonal query rectangle. The aggregates we consider in this paper include COUNT, sum, and MAX. First, we develop a structure for answering two-dimensional range-COUNT queries that uses O(N/B) disk blocks and answers a query in O(log(B) N) I/Os, where N is the number of input points and B is the disk block size. The structure can be extended to obtain a near-linear-size structure for answering range-sum queries using O(log(B) N) I/Os, and a linear-size structure for answering range-MAX queries in O(log(B)(2) N) I/Os. Our structures can be made dynamic and extended to higher dimensions. (C) 2012 Elsevier B.V. All rights reserved.

Virtually cool ternary content addressable memory

Fast content addressable data access mechanisms have compelling applications in today's systems. Many of these exploit the powerful wildcard matching capabilities provided by ternary content addressable memories. For example, TCAM based implementations of important algorithms in data mining been developed in recent years; these achieve an an order of magnitude speedup over prevalent techniques. However, large hardware TCAMs are still prohibitively expensive in terms of power consumption and cost per bit. This has been a barrier to extending their exploitation beyond niche and special purpose systems. We propose an approach to overcome this barrier by extending the traditional virtual memory hierarchy to scale up the user visible capacity of TCAMs while mitigating the power consumption overhead. By exploiting the notion of content locality (as opposed to spatial locality), we devise a novel combination of software and hardware techniques to provide an abstraction of a large virtual ternary content addressable space. In the long run, such abstractions enable applications to disassociate considerations of spatial locality and contiguity from the way data is referenced. If successful, ideas for making content addressability a first class abstraction in computing systems can open up a radical shift in the way applications are optimized for memory locality, just as storage class memories are soon expected to shift away from the way in which applications are typically optimized for disk access locality.

Studies on the Aging Characteristics of Base Oil with Amine Based Antioxidant in Steel-on-Steel Lubricated Sliding

An industrial base oil, a blend of different paraffin fractions, is heated to 130 degrees C (1) in the ambient and (2) for use as a lubricant in a steel pin on a steel disk sliding experiment. The base oil was tested with and without test antioxidants: dimethyl disulfide (DMDS) and alkylated diphenylamine (ADPA). Primary and secondary oxidation products were monitored continuously by FTIR over a 100 h period. In addition, friction and wear of the steel pin were monitored over the same period and the chemical transformation of the pin surface was monitored by XPS. The objective of this work is to observe the catalytic action of the steel components on the oil aging process and the efficacy of the antioxidant to reduce oxidation of oil used in tribology as a lubricant. Possible mechanistic explanations of the aging process as well as its impact on friction and wear are discussed.

Another look at tightness

We examine a natural, but non-tight, reductionist security proof for deterministic message authentication code (MAC) schemes in the multi-user setting. If security parameters for the MAC scheme are selected without accounting for the non-tightness in the reduction, then the MAC scheme is shown to provide a level of security that is less than desirable in the multi-user setting. We find similar deficiencies in the security assurances provided by non-tight proofs when we analyze some protocols in the literature including ones for network authentication and aggregate MACs. Our observations call into question the practical value of non-tight reductionist security proofs. We also exhibit attacks on authenticated encryption schemes, disk encryption schemes, and stream ciphers in the multi-user setting.

Enabling node repair in any erasure code for distributed storage

Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The codes perform poorly though, when repair of a failed node is called for, as they typically require the entire file to be downloaded to repair a failed node. A new class of erasure codes, termed as regenerating codes were recently introduced, that do much better in this respect. However, given the variety of efficient erasure codes available in the literature, there is considerable interest in the construction of coding schemes that would enable traditional erasure codes to be used, while retaining the feature that only a fraction of the data need be downloaded for node repair. In this paper, we present a simple, yet powerful, framework that does precisely this. Under this framework, the nodes are partitioned into two types and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes. Depending upon the choice of the two codes, the framework can be used to avail one or more of the following advantages: simultaneous minimization of storage space and repair-bandwidth, low complexity of operation, fewer disk reads at helper nodes during repair, and error detection and correction.

Enabling node repair in any erasure code for distributed storage

Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The codes perform poorly though, when repair of a failed node is called for, as they typically require the entire file to be downloaded to repair a failed node. A new class of erasure codes, termed as regenerating codes were recently introduced, that do much better in this respect. However, given the variety of efficient erasure codes available in the literature, there is considerable interest in the construction of coding schemes that would enable traditional erasure codes to be used, while retaining the feature that only a fraction of the data need be downloaded for node repair. In this paper, we present a simple, yet powerful, framework that does precisely this. Under this framework, the nodes are partitioned into two types and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes. Depending upon the choice of the two codes, the framework can be used to avail one or more of the following advantages: simultaneous minimization of storage space and repair-bandwidth, low complexity of operation, fewer disk reads at helper nodes during repair, and error detection and correction.

Totally geodesic discs in strongly convex domains

We prove that every isometry from the unit disk Delta in , endowed with the Poincar, distance, to a strongly convex bounded domain Omega of class in , endowed with the Kobayashi distance, is the composition of a complex geodesic of Omega with either a conformal or an anti-conformal automorphism of Delta. As a corollary we obtain that every isometry for the Kobayashi distance, from a strongly convex bounded domain of class in to a strongly convex bounded domain of class in , is either holomorphic or anti-holomorphic.

Interleaved winding and suppression of natural frequencies

Ideally, it is desirable to design and manufacture a transformer winding that can render all its internal resonances non-excitable. This study examines the effectiveness of an interleaved winding in achieving this goal. While investigating its effectiveness, it led to the establishment of a much desired theoretical basis that reinforces the reasons put forward in the literature to explain internal insulation failures observed in interleaved windings used in extra high voltage (EHV) transformers. Numerical calculations along with experimental verification on actual transformer windings are presented. This study reveals that most of the natural frequencies that are normally non-excitable in the line and neutral current responses of an interleaved winding have been rendered excitable in the disk-to-disk voltages, thus, providing favourable conditions for insulation overstress because of resonant overvoltages. Prevalence of such a condition is an inherent characteristic of interleaved windings.

Magnetohydrodynamic stability of stochastically driven accretion flows

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.