On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

Stability analysis of aperiodic messages scheduled in the dynamic segment of flex ray protocol

In a cyber physical system like vehicles number of signals to be communicated in a network system has an increasing trend. More and more mechanical and hydraulic parts are replaced by electronic control units and infotainment and multimedia applications has increased in vehicles. Safety critical hard real time messages and aperiodic messages communicated between electronic control units have been increased in recent times. Flexray is a high bandwidth protocol consisting of static segment for supporting hard real time messages and a dynamic segment for transmitting soft and non real time messages. In this paper, a method to obtain the stability region for the random arrival of messages in each electronic control units which is scheduled in the dynamic segment of Flexray protocol is presented. Number of mini slots available in the dynamic segment of Flexray restricts the arrival rate of tasks to the micro controllers or the number of micro controllers connected to the Flexray bus. Stability region of mathematical model of the system is compared with the Flexray protocol simulation results.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

SELF-ORGANIZATION AND FRICTION DURING SLIDING

In self-organized sliding processes, the surfaces align to each other during sliding. This alignment leads to a more ordered contact state and significantly influences the frictional behavior. To understand the self-organization sliding processes, experiments were conducted on a pin-on-plate reciprocating sliding tester for various numbers of cycles. In the experiments, soft magnesium pins were slid against hard steel plates of various surface textures (undirectional, 8-ground, and random). Experimental results showed that the transfer layer formation on the steel plates increased with increasing number of cycles for all surfaces textures under both dry and lubricated conditions. The friction also increased with the number of cycles under dry conditions for all of the textures studied. During lubricated conditions, the friction decreased for unidirectional and 8-ground surfaces and increased for random surfaces with the number of cycles. Furthermore, the friction and transfer layer formation depend on the surface textures under both dry and lubricated conditions during the first few sliding cycles. Later on, it is less dependent of surface textures. The variation in the coefficient of friction under both dry and lubrication conditions were attributed to the self-organization process that occurred during repeated sliding.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.

Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box 0, L](3) is addressed through four sets of numerical simulations that calculate a new set of variables defined by D-m(t) = (pi(-1)(0) Omega(m))(alpha m) for 1 <= m <= infinity where alpha(m) = 2m/(4m - 3) and Omega(m)(t)](2m) = L-3 integral(v) vertical bar omega vertical bar(2m) dV with pi(0) = vL(-2). All four simulations unexpectedly show that the D-m are ordered for m = 1,..., 9 such that Dm+1 < D-m. Moreover, the D-m squeeze together such that Dm+1/D-m NE arrow 1 as m increases. The values of D-1 lie far above the values of the rest of the D-m, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 4096(3).

A Novel Monte-Carlo-Sampling-Based Receiver for Large-Scale Uplink Multiuser MIMO Systems

In this paper, we propose low-complexity algorithms based on Monte Carlo sampling for signal detection and channel estimation on the uplink in large-scale multiuser multiple-input-multiple-output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and a similar number of uplink users. A BS receiver that employs a novel mixed sampling technique (which makes a probabilistic choice between Gibbs sampling and random uniform sampling in each coordinate update) for detection and a Gibbs-sampling-based method for channel estimation is proposed. The algorithm proposed for detection alleviates the stalling problem encountered at high signal-to-noise ratios (SNRs) in conventional Gibbs-sampling-based detection and achieves near-optimal performance in large systems with M-ary quadrature amplitude modulation (M-QAM). A novel ingredient in the detection algorithm that is responsible for achieving near-optimal performance at low complexity is the joint use of a mixed Gibbs sampling (MGS) strategy coupled with a multiple restart (MR) strategy with an efficient restart criterion. Near-optimal detection performance is demonstrated for a large number of BS antennas and users (e. g., 64 and 128 BS antennas and users). The proposed Gibbs-sampling-based channel estimation algorithm refines an initial estimate of the channel obtained during the pilot phase through iterations with the proposed MGS-based detection during the data phase. In time-division duplex systems where channel reciprocity holds, these channel estimates can be used for multiuser MIMO precoding on the downlink. The proposed receiver is shown to achieve good performance and scale well for large dimensions.

Effect of myonuclear number and mitochondrial fusion on Drosophila indirect flight muscle organization and size

Mechanisms involved in establishing the organization and numbers of fibres in a muscle are not completely understood. During Drosophila indirect flight muscle (IFM) formation, muscle growth is achieved by both incorporating hundreds of nuclei, and hypertrophy. As a result, IFMs provide a good model with which to understand the mechanisms that govern overall muscle organization and growth. We present a detailed analysis of the organization of dorsal longitudinal muscles (DLMs), a subset of the IFMs. We show that each DLM is similar to a vertebrate fascicle and consists of multiple muscle fibres. However, increased fascicle size does not necessarily change the number of constituent fibres, but does increase the number of myofibrils packed within the fibres. We also find that altering the number of myoblasts available for fusion changes DLM fascicle size and fibres are loosely packed with myofibrils. Additionally, we show that knock down of genes required for mitochondrial fusion causes a severe reduction in the size of DLM fascicles and fibres. Our results establish the organization levels of DLMs and highlight the importance of the appropriate number of nuclei and mitochondrial fusion in determining the overall organization, growth and size of DLMs. (C) 2013 Elsevier Inc. All rights reserved.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Support vector clustering-based direct coherency identification of generators in a multi-machine power system

This study investigates the application of support vector clustering (SVC) for the direct identification of coherent synchronous generators in large interconnected multi-machine power systems. The clustering is based on coherency measure, which indicates the degree of coherency between any pair of generators. The proposed SVC algorithm processes the coherency measure matrix that is formulated using the generator rotor measurements to cluster the coherent generators. The proposed approach is demonstrated on IEEE 10 generator 39-bus system and an equivalent 35 generators, 246-bus system of practical Indian southern grid. The effect of number of data samples and fault locations are also examined for determining the accuracy of the proposed approach. An extended comparison with other clustering techniques is also included, to show the effectiveness of the proposed approach in grouping the data into coherent groups of generators. This effectiveness of the coherent clusters obtained with the proposed approach is compared in terms of a set of clustering validity indicators and in terms of statistical assessment that is based on the coherency degree of a generator pair.

Measurement Based Impromptu Deployment of a Multi-Hop Wireless Relay Network

We study the problem of optimal sequential (''as-you-go'') deployment of wireless relay nodes, as a person walks along a line of random length (with a known distribution). The objective is to create an impromptu multihop wireless network for connecting a packet source to be placed at the end of the line with a sink node located at the starting point, to operate in the light traffic regime. In walking from the sink towards the source, at every step, measurements yield the transmit powers required to establish links to one or more previously placed nodes. Based on these measurements, at every step, a decision is made to place a relay node, the overall system objective being to minimize a linear combination of the expected sum power (or the expected maximum power) required to deliver a packet from the source to the sink node and the expected number of relay nodes deployed. For each of these two objectives, two different relay selection strategies are considered: (i) each relay communicates with the sink via its immediate previous relay, (ii) the communication path can skip some of the deployed relays. With appropriate modeling assumptions, we formulate each of these problems as a Markov decision process (MDP). We provide the optimal policy structures for all these cases, and provide illustrations of the policies and their performance, via numerical results, for some typical parameters.

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

Variable field ion traps

This paper presents a technique to vary the electric field within a cylindrical ion trap (CIT) mass spectrometer while it is in operation. In this technique, the electrodes of the CIT are split into number of mini-electrodes and different voltages are applied to these split-electrodes to achieve the desired field. In our study we have investigated two geometries of the split-electrode CIT. In the first, we retain the flat endcap electrodes of the CIT but split the ring electrode into five mini-rings. In the second configuration, we split the ring electrode of the CIT into three mini-rings and also divide the endcaps into two mini-discs. By applying different potentials to the mini-rings and mini-discs of these geometries we have shown that the field within the trap can be optimized to desired values. In our study, two different types of fields were targeted. In the first, potentials were adjusted to obtain a linear electric field and, in the second, a controlled higher order even multipole field was obtained by adjusting the potential. We have shown that the different potentials required can be derived from a single RF generator by connecting appropriate capacitor terminations to split electrodes. The field within the trap can be modified by changing the values of the external capacitors. (C) 2013 Elsevier B.V. All rights reserved.

A novel MCMC algorithm for near-optimal detection in large-scale uplink mulituser MIMO systems

In this paper, we propose a low-complexity algorithm based on Markov chain Monte Carlo (MCMC) technique for signal detection on the uplink in large scale multiuser multiple input multiple output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and similar number of uplink users. The algorithm employs a randomized sampling method (which makes a probabilistic choice between Gibbs sampling and random sampling in each iteration) for detection. The proposed algorithm alleviates the stalling problem encountered at high SNRs in conventional MCMC algorithm and achieves near-optimal performance in large systems with M-QAM. A novel ingredient in the algorithm that is responsible for achieving near-optimal performance at low complexities is the joint use of a randomized MCMC (R-MCMC) strategy coupled with a multiple restart strategy with an efficient restart criterion. Near-optimal detection performance is demonstrated for large number of BS antennas and users (e.g., 64, 128, 256 BS antennas/users).