Stability numbers for an unsupported vertical circular excavation in c-phi soil

By using an axisymmetric lower bound finite element limit analysis formulation, the stability numbers (gamma H/C) for an unsupported vertical circular excavation in a cohesive-frictional soil have been generated. The numerical results are obtained for values of normalized excavation height (H/b) and friction angle (phi) greater than those considered previously in the literature. The results compare well with those available in literature. The stability numbers presented in this note would be beneficial from a design point of view. (C) 2011 Elsevier Ltd. All rights reserved.

Tractable theories for the synthesis of neural networks

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Vertical uplift capacity of a group of two coaxial anchors in a general c-phi soil

The vertical uplift resistance of a group of two horizontal coaxial strip anchors, embedded in a general c-phi soil (where c is the unit cohesion and phi is the soil friction angle), has been determined by using the lower bound finite element limit analysis. The variation of uplift factors F-c and F-gamma, due to the components of soil cohesion and unit weight, respectively, with changes in depth (H)/width (B) has been established for different values of vertical spacing (S)/B. As compared to a single isolated anchor, the group of two anchors provides a significantly greater magnitude of F-c for phi <= 20 degrees and with H/B >= 3. The magnitude of F-c becomes almost maximum when S/B is kept closer to 0.5H/B. On the other hand, with the same H/B, as compared to a single anchor, hardly any increase in F-gamma occurs for a group of two anchors.

Low-Delay, High-Rate Nonsquare Complex Orthogonal Designs

The maximal rate of a nonsquare complex orthogonal design for transmit antennas is 1/2 + 1/n if is even and 1/2 + 1/n+1 if is odd and the codes have been constructed for all by Liang (2003) and Lu et al. (2005) to achieve this rate. A lower bound on the decoding delay of maximal-rate complex orthogonal designs has been obtained by Adams et al. (2007) and it is observed that Liang's construction achieves the bound on delay for equal to 1 and 3 modulo 4 while Lu et al.'s construction achieves the bound for n = 0, 1, 3 mod 4. For n = 2 mod 4, Adams et al. (2010) have shown that the minimal decoding delay is twice the lower bound, in which case, both Liang's and Lu et al.'s construction achieve the minimum decoding delay. For large value of, it is observed that the rate is close to half and the decoding delay is very large. A class of rate-1/2 codes with low decoding delay for all has been constructed by Tarokh et al. (1999). In this paper, another class of rate-1/2 codes is constructed for all in which case the decoding delay is half the decoding delay of the rate-1/2 codes given by Tarokh et al. This is achieved by giving first a general construction of square real orthogonal designs which includes as special cases the well-known constructions of Adams, Lax, and Phillips and the construction of Geramita and Pullman, and then making use of it to obtain the desired rate-1/2 codes. For the case of nine transmit antennas, the proposed rate-1/2 code is shown to be of minimal delay. The proposed construction results in designs with zero entries which may have high peak-to-average power ratio and it is shown that by appropriate postmultiplication, a design with no zero entry can be obtained with no change in the code parameters.

Relay Selection for Geographical Forwarding in Sleep-Wake Cycling Wireless Sensor Networks

Our work is motivated by geographical forwarding of sporadic alarm packets to a base station in a wireless sensor network (WSN), where the nodes are sleep-wake cycling periodically and asynchronously. We seek to develop local forwarding algorithms that can be tuned so as to tradeoff the end-to-end delay against a total cost, such as the hop count or total energy. Our approach is to solve, at each forwarding node enroute to the sink, the local forwarding problem of minimizing one-hop waiting delay subject to a lower bound constraint on a suitable reward offered by the next-hop relay; the constraint serves to tune the tradeoff. The reward metric used for the local problem is based on the end-to-end total cost objective (for instance, when the total cost is hop count, we choose to use the progress toward sink made by a relay as the reward). The forwarding node, to begin with, is uncertain about the number of relays, their wake-up times, and the reward values, but knows the probability distributions of these quantities. At each relay wake-up instant, when a relay reveals its reward value, the forwarding node's problem is to forward the packet or to wait for further relays to wake-up. In terms of the operations research literature, our work can be considered as a variant of the asset selling problem. We formulate our local forwarding problem as a partially observable Markov decision process (POMDP) and obtain inner and outer bounds for the optimal policy. Motivated by the computational complexity involved in the policies derived out of these bounds, we formulate an alternate simplified model, the optimal policy for which is a simple threshold rule. We provide simulation results to compare the performance of the inner and outer bound policies against the simple policy, and also against the optimal policy when the source knows the exact number of relays. Observing the good performance and the ease of implementation of the simple policy, we apply it to our motivating problem, i.e., local geographical routing of sporadic alarm packets in a large WSN. We compare the end-to-end performance (i.e., average total delay and average total cost) obtained by the simple policy, when used for local geographical forwarding, against that obtained by the globally optimal forwarding algorithm proposed by Kim et al. 1].

An Adaptive Conditional Zero-Forcing Decoder With Full-Diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

Channel training signal design for reciprocal multiple antenna systems with beamforming

Fast and efficient channel estimation is key to achieving high data rate performance in mobile and vehicular communication systems, where the channel is fast time-varying. To this end, this work proposes and optimizes channel-dependent training schemes for reciprocal Multiple-Input Multiple-Output (MIMO) channels with beamforming (BF) at the transmitter and receiver. First, assuming that Channel State Information (CSI) is available at the receiver, a channel-dependent Reverse Channel Training (RCT) signal is proposed that enables efficient estimation of the BF vector at the transmitter with a minimum training duration of only one symbol. In contrast, conventional orthogonal training requires a minimum training duration equal to the number of receive antennas. A tight approximation to the capacity lower bound on the system is derived, which is used as a performance metric to optimize the parameters of the RCT. Next, assuming that CSI is available at the transmitter, a channel-dependent forward-link training signal is proposed and its power and duration are optimized with respect to an approximate capacity lower bound. Monte Carlo simulations illustrate the significant performance improvement offered by the proposed channel-dependent training schemes over the existing channel-agnostic orthogonal training schemes.

Bearing capacity of piles in soft clay underlaid by cohesive frictional soil

By using the axisymmetric quasi-lower bound finite-element limit analysis, the bearing capacity factors N-c(p) and N-gamma q(p) have been computed for axially loaded piles, with the shaft embedded in a fully cohesive soil medium and the tip placed over cohesive frictional soil strata. The results were obtained for various combinations of L/D, phi(l), and c(l)/c(u); the subscripts l and u refer to lower and upper soil strata, respectively. The factors N-c(p) and N-gamma q(p) increase continuously with increases in L/D and phi(l); the rate of increase of N-c(p) and N-gamma q(p) with L/D, however, decreases with an increase in L/D. For c(l)/c(u) > 100, the factor N-c(p) hardly depends on L/D.

Minimum uncertainty and entanglement

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

MINIMUM UNCERTAINTY AND ENTANGLEMENT

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (gamma H/c) which is plotted as a function of horizontal seismic earth pressure coefficient (k (h)) for different combinations of H/D and I center dot; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) k (h) is the earthquake acceleration coefficient and (4) gamma, c and I center dot define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in k (h). With an inclusion of k (h), the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.

Horizontal pullout capacity of a group of two vertical plate anchors in clay

The horizontal pullout capacity of a group of two vertical strip plate anchors, placed along the same vertical plane, in a fully cohesive soil has been computed by using the lower bound finite element limit analysis. The effect of spacing between the plate anchors on the magnitude of total group failure load (P-uT) has been evaluated. An increase of soil cohesion with depth has also been incorporated in the analysis. For a weightless medium, the total pullout resistance of the group becomes maximum corresponding to a certain optimum spacing between the anchor plates which has been found to vary generally between 0.5B and B; where B is the width of the anchor plate. As compared to a single plate anchor, the increase in the pullout resistance for a group of two anchors becomes greater at a higher embedment ratio. The effect of soil unit weight has also been analyzed. It is noted that the interference effect on the pullout resistance increases further with an increase in the unit weight of soil mass.

Seismic Bearing Capacity of Foundations on Cohesionless Slopes

By applying the lower bound theorem of limit analysis in conjunction with finite elements and nonlinear optimization, the bearing capacity factor N has been computed for a rough strip footing by incorporating pseudostatic horizontal seismic body forces. As compared with different existing approaches, the present analysis is more rigorous, because it does not require an assumption of either the failure mechanism or the variation of the ratio of the shear to the normal stress along the footing-soil interface. The magnitude of N decreases considerably with an increase in the horizontal seismic acceleration coefficient (kh). With an increase in kh, a continuous spread in the extent of the plastic zone toward the direction of the horizontal seismic body force is noted. The results obtained from this paper have been found to compare well with the solutions reported in the literature. (C) 2013 American Society of Civil Engineers.

Bearing Capacity of Foundations with Inclined Groundwater Seepage

The ultimate bearing capacity of strip foundations in the presence of inclined groundwater flow, considering both upward and downward flow directions, has been determined by using the lower bound finite-element limit analysis. A numerical solution has been generated for both smooth and rough footings placed on frictional soils. A correction factor (f gamma), which needs to be multiplied with the N gamma-term, has been computed to account for groundwater seepage. The variation of f gamma has been obtained as a function of the hydraulic gradient (i) for various inclinations of groundwater flow. For a given magnitude of i, there exists a certain critical inclination of the flow for which the value of f gamma is minimized. With an upward flow, for all flow inclinations, the magnitude of f gamma always reduces with an increase in the value of i. An example has also been provided to illustrate the application of the obtained results when designing foundations in the presence of groundwater seepage.

Power-Controlled Reverse Channel Training in a Multiuser TDD-MIMO Spatial Multiplexing System With CSIR

This paper considers the design of a power-controlled reverse channel training (RCT) scheme for spatial multiplexing (SM)-based data transmission along the dominant modes of the channel in a time-division duplex (TDD) multiple-input and multiple-output (MIMO) system, when channel knowledge is available at the receiver. A channel-dependent power-controlled RCT scheme is proposed, using which the transmitter estimates the beamforming (BF) vectors required for the forward-link SM data transmission. Tight approximate expressions for 1) the mean square error (MSE) in the estimate of the BF vectors, and 2) a capacity lower bound (CLB) for an SM system, are derived and used to optimize the parameters of the training sequence. Moreover, an extension of the channel-dependent training scheme and the data rate analysis to a multiuser scenario with M user terminals is presented. For the single-mode BF system, a closed-form expression for an upper bound on the average sum data rate is derived, which is shown to scale as ((L-c - L-B,L- tau)/L-c) log logM asymptotically in M, where L-c and L-B,L- tau are the channel coherence time and training duration, respectively. The significant performance gain offered by the proposed training sequence over the conventional constant-power orthogonal RCT sequence is demonstrated using Monte Carlo simulations.