Single real-symbol decodable, high-rate, distributed space-time block codes

A scheme to apply the rate-1 real orthogonal designs (RODs) in relay networks with single real-symbol decodability of the symbols at the destination for any arbitrary number of relays is proposed. In the case where the relays do not have any information about the channel gains from the source to themselves, the best known distributed space time block codes (DSTBCs) for k relays with single real-symbol decodability offer an overall rate of complex symbols per channel use. The scheme proposed in this paper offers an overall rate of 2/2+k complex symbol per channel use, which is independent of the number of relays. Furthermore, in the scenario where the relays have partial channel information in the form of channel phase knowledge, the best known DSTBCs with single real-symbol decodability offer an overall rate of 1/3 complex symbols per channel use. In this paper, making use of RODs, a scheme which achieves the same overall rate of 1/3 complex symbols per channel use but with a decoding delay that is 50 percent of that of the best known DSTBCs, is presented. Simulation results of the symbol error rate performance for 10 relays, which show the superiority of the proposed scheme over the best known DSTBC for 10 relays with single real-symbol decodability, are provided.

Critical stress intensity factors for cracked hollow pipes under transient thermal loads

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.

Seismic horizontal pullout capacity of vertical anchors in sands

The problem of finding the horizontal pullout capacity of vertical anchors embedded in sands with the inclusion of pseudostatic horizontal earthquake body forces, was tackled in this note. The analysis was carried out using an upper bound limit analysis, with the consideration of two different collapse mechanisms: bilinear and composite logarithmic spiral rupture surfaces. The results are presented in nondimensional form to find the pullout resistance with changes in earthquake acceleration for different combinations of embedment ratio of the anchor (lambda), friction angle of the soil (phi), and the anchor-soil interface wall friction angle (delta). The pullout resistance decreases quite substantially with increases in the magnitude of the earthquake acceleration. For values of delta up to about 0.25-0.5phi, the bilinear and composite logarithmic spiral rupture surfaces gave almost identical answers, whereas for higher values of delta, the choice of the logarithmic spiral provides significantly smaller pullout resistance. The results compare favorably with the existing theoretical data.

Vertical thermal structure of the atmosphere during active and weak phases of convection over the north Bay of Bengal: Observation and model results

Owing to the lack of atmospheric vertical profile data with sufficient accuracy and vertical resolution, the response of the deep atmosphere to passage of monsoon systems over the Bay of Bengal. had not been satisfactorily elucidated. Under the Indian Climate Research Programme, a special observational programme called 'Bay of Bengal Monsoon Experiment' (BOBMEX), was conducted during July-August 1999. The present study is based on the high-resolution radiosondes launched during BOBMEX in the north Bay. Clear changes in the vertical thermal structure of the atmosphere between active and weak phases of convection have been observed. The atmosphere cooled below 6 km height and became warmer between 6 and 13 km height. The warmest layer was located between 8 and 10 km height, and the coldest layer was found just below 5 km height. The largest fluctuations in the humidity field occurred in the mid-troposphere. The observed changes between active and weak phases of convection are compared with the results from an atmospheric general circulation model, which is similar to that used at the National Centre for Medium Range Weather Forecasting, New Delhi. The model is not able to capture realistically some important features of the temperature and humidity profiles in the lower troposphere and in the boundary layer during the active and weak spells.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the-cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Interference Alignment as a Tool in Network Coding as Applied to Distributed Storage

In this paper, we outline an approach to the task of designing network codes in a non-multicast setting. Our approach makes use of the concept of interference alignment. As an example, we consider the distributed storage problem where the data is stored across the network in n nodes and where a data collector can recover the data by connecting to any k of the n nodes and where furthermore, upon failure of a node, a new node can replicate the data stored in the failed node while minimizing the repair bandwidth.

Comparative Analysis of Pilot-Assisted Distributed Cophasing Approaches in Wireless Sensor Networks

This paper compares and analyzes the performance of distributed cophasing techniques for uplink transmission over wireless sensor networks. We focus on a time-division duplexing approach, and exploit the channel reciprocity to reduce the channel feedback requirement. We consider periodic broadcast of known pilot symbols by the fusion center (FC), and maximum likelihood estimation of the channel by the sensor nodes for the subsequent uplink cophasing transmission. We assume carrier and phase synchronization across the participating nodes for analytical tractability. We study binary signaling over frequency-flat fading channels, and quantify the system performance such as the expected gains in the received signal-to-noise ratio (SNR) and the average probability of error at the FC, as a function of the number of sensor nodes and the pilot overhead. Our results show that a modest amount of accumulated pilot SNR is sufficient to realize a large fraction of the maximum possible beamforming gain. We also investigate the performance gains obtained by censoring transmission at the sensors based on the estimated channel state, and the benefits obtained by using maximum ratio transmission (MRT) and truncated channel inversion (TCI) at the sensors in addition to cophasing transmission. Simulation results corroborate the theoretical expressions and show the relative performance benefits offered by the various schemes.

Explicit Codes Uniformly Reducing Repair Bandwidth in Distributed Storage

A distributed storage setting is considered where a file of size B is to be stored across n storage nodes. A data collector should be able to reconstruct the entire data by downloading the symbols stored in any k nodes. When a node fails, it is replaced by a new node by downloading data from some of the existing nodes. The amount of download is termed as repair bandwidth. One way to implement such a system is to store one fragment of an (n, k) MDS code in each node, in which case the repair bandwidth is B. Since repair of a failed node consumes network bandwidth, codes reducing repair bandwidth are of great interest. Most of the recent work in this area focuses on reducing the repair bandwidth of a set of k nodes which store the data in uncoded form, while the reduction in the repair bandwidth of the remaining nodes is only marginal. In this paper, we present an explicit code which reduces the repair bandwidth for all the nodes to approximately B/2. To the best of our knowledge, this is the first explicit code which reduces the repair bandwidth of all the nodes for all feasible values of the system parameters.

Explicit and Optimal Codes for Distributed Storage

In the distributed storage coding problem we consider, data is stored across n nodes in a network, each capable of storing � symbols. It is required that the complete data can be reconstructed by downloading data from any k nodes. There is also the key additional requirement that a failed node be regenerated by connecting to any d nodes and downloading �symbols from each of them. Our goal is to minimize the repair bandwidth d�. In this paper we provide explicit constructions for several parameter sets of interest.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.