Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter mu. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter epsilon, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting epsilon = 0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (epsilon << 1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter mu. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

A channel-aware, fast sub-channel to user assignment algorithm in OFDMA systems

Channel-aware assignment of sub-channels to users in the downlink of an OFDMA system demands extensive feedback of channel state information (CSI) to the base station. Since the feedback bandwidth is often very scarce, schemes that limit feedback are necessary. We develop a novel, low feedback splitting-based algorithm for assigning each sub-channel to its best user, i.e., the user with the highest gain for that sub-channel among all users. The key idea behind the algorithm is that, at any time, each user contends for the sub-channel on which it has the largest channel gain among the unallocated sub-channels. Unlike other existing schemes, the algorithm explicitly handles multiple access control aspects associated with the feedback of CSI. A tractable asymptotic analysis of a system with a large number of users helps design the algorithm. It yields 50% to 65% throughput gains compared to an asymptotically optimal one-bit feedback scheme, when the number of users is as small as 10 or as large as 1000. The algorithm is fast and distributed, and scales with the number of users.

Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional `orthotropy parameter' is defined and asymptotic expansions are found for the wavenumbers in in vacuo and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell-Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of E-x >> E-theta is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a `slightly orthotropic' shell (E-x approximate to E-theta) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem.

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Tradeoff of average power and average delay for a point-to-point link with fading

We consider a discrete time system with packets arriving randomly at rate lambda per slot to a fading point-to-point link, for which the transmitter can control the number of packets served in a slot by varying the transmit power. We provide an asymptotic characterization of the minimum average delay of the packets, when average transmitter power is a small positive quantity V more than the minimum average power required for queue stability. We show that the minimum average delay will grow either as log (1/V) or 1/V when V down arrow 0, for certain sets of values of lambda. These sets are determined by the distribution of fading gain, the maximum number of packets which can be transmitted in a slot, and the assumed transmit power function, as a function of the fading gain and the number of packets transmitted. We identify a case where the above behaviour of the tradeoff differs from that obtained from a previously considered model, in which the random queue length process is assumed to evolve on the non-negative real line.

Optimal design of timer-based, distributed selection with unknown number of nodes

The timer-based selection scheme is a popular, simple, and distributed scheme that is used to select the best node from a set of available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal timer mapping that maximizes the average success probability for the practical scenario in which the number of nodes in the system is unknown but only its probability distribution is known. We show that it has a special discrete structure, and present a recursive characterization to determine it. We benchmark its performance with ad hoc approaches proposed in the literature, and show that it delivers significant gains. New insights about the optimality of some ad hoc approaches are also developed.

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).

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.

Asymptotic expansions for the structural wavenumbers of isotropic and orthotropic fluid-filled circular cylindrical shells in the intermediate frequency range

We consider wavenumbers in in vacuo and fluid-filled isotropic and orthotropic shells. Using the Donnell-Mushtari (DM) theory we find compact and elegant asymptotic expansions for the wavenumbers in the intermediate frequency range, i.e., around the ring frequency. This frequency range corresponds to the frequencies where there is a rapid change in the values of bending wavenumbers and is found to exist in isotropic and orthotropic shells (in vacua and fluid-filled) for low circumferential orders n only. The same is first identified using the n=0 mode of an orthotropic shell. Following this, using the expression for the intermediate frequency, asymptotic expansions are found for other cases. Here, in order to get compact expansions we consider slight orthotropy (epsilon << 1) and light fluid loading (mu << 1). Thus, the orthotropy parameter epsilon and the fluid loading parameter mu are used as asymptotic parameters along with the non-dimensional thickness parameter beta. The methodology can be extended to any order of epsilon, only the expansions become unwieldy. The expansions are matched with the numerical solutions of the corresponding dispersion relation. The match is found to be good.

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.

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.

Asymptotically-good, multigroup decodable space-time block codes

For a family of Space-Time Block Codes (STBCs) C-1, C-2,..., with increasing number of transmit antennas N-i, with rates R-i complex symbols per channel use, i = 1, 2,..., we introduce the notion of asymptotic normalized rate which we define as lim(i ->infinity) R-i/N-i, and we say that a family of STBCs is asymptotically-good if its asymptotic normalized rate is non-zero, i. e., when the rate scales as a non-zero fraction of the number of transmit antennas. An STBC C is said to be g-group decodable, g >= 2, if the information symbols encoded by it can be partitioned into g groups, such that each group of symbols can be ML decoded independently of the others. In this paper we construct full-diversity g-group decodable codes with rates greater than one complex symbol per channel use for all g >= 2. Specifically, we construct delay-optimal, g-group decodable codes for number of transmit antennas N-t that are a multiple of g2left perpendicular(g-1/2)right perpendicular with rate N-t/g2(g-1) + g(2)-g/2N(t). Using these new codes as building blocks, we then construct non-delay-optimal g-group decodable codes with rate roughly g times that of the delay-optimal codes, for number of antennas N-t that are a multiple of 2left perpendicular(g-1/2)right perpendicular, with delay gN(t) and rate Nt/2(g-1) + g-1/2N(t). For each g >= 2, the new delay-optimal and non-delay- optimal families of STBCs are both asymptotically-good, with the latter family having the largest asymptotic normalized rates among all known families of multigroup decodable codes with delay T <= gN(t). Also, for g >= 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.

Optimal Timer-Based Best Node Selection for Wireless Systems with Unknown Number of Nodes

The distributed, low-feedback, timer scheme is used in several wireless systems to select the best node from the available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal metric-to-timer mappings for the practical scenario where the number of nodes is unknown. We consider two cases in which the probability distribution of the number of nodes is either known a priori or is unknown. In the first case, the optimal mapping maximizes the success probability averaged over the probability distribution. In the second case, a robust mapping maximizes the worst case average success probability over all possible probability distributions on the number of nodes. Results reveal that the proposed mappings deliver significant gains compared to the mappings considered in the literature.