Some remarks on the finiteness of soliton mass

Some subtleties regarding regularizations in computing the soliton energy of degenerate systems are discussed.

Influence of quantum confinement on the photoemission from superlattices of optoelectronic materials

We study the photoemission from quantum wire and quantum dot superlattices with graded interfaces of optoelectronic materials on the basis of newly formulated electron dispersion relations in the presence of external photo-excitation. Besides, the influence of a magnetic field on the photoemission from the aforementioned superlattices together with quantum well superlattices in the presence of a quantizing magnetic field has also been studied in this context. It has been observed taking into account HgTe/Hg1-xCdxTe and InxGa1-xAs/InP that the photoemission from these nanostructures increases with increasing photon energy in quantized steps and exhibits oscillatory dependences with the increase in carrier concentration. Besides, the photoemission decreases with increasing light intensity and wavelength, together with the fact that said emission decreases with increasing thickness exhibiting oscillatory spikes. The strong dependences of the photoemission on the light intensity reflects the direct signature of light waves on the carrier energy spectra. The content of this paper finds six applications in the fields of low dimensional systems in general. (C) 2010 Elsevier Ltd. All rights reserved.

Worst inputs and a bound on the highest peak statistics of a class of non-linear systems

A method is developed by which the input leading to the highest possible response in an interval of time can be determined for a class of non-linear systems. The input, if deterministic, is constrained to have a known finite energy (or norm) in the interval under consideration. In the case of random inputs, the energy is constrained to have a known probability distribution function. The approach has applications when a system has to be put to maximum advantage by getting the largest possible output or when a system has to be designed to the highest maximum response with only the input energy or the energy distribution known. The method is also useful in arriving at a bound on the highest peak distribution of the response, when the excitation is a known random process.As an illustration the Duffing oscillator has been analysed and some numerical results have also been presented.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

While the tradeoff between the amount of data stored and the repair bandwidth of an (n, k, d) regenerating code has been characterized under functional repair (FR), the case of exact repair (ER) remains unresolved. It is known that there do not exist ER codes which lie on the FR tradeoff at most of the points. The question as to whether one can asymptotically approach the FR tradeoff was settled recently by Tian who showed that in the (4, 3, 3) case, the ER region is bounded away from the FR region. The FR tradeoff serves as a trivial outer bound on the ER tradeoff. In this paper, we extend Tian's results by establishing an improved outer bound on the ER tradeoff which shows that the ER region is bounded away from the FR region, for any (n; k; d). Our approach is analytical and builds upon the framework introduced earlier by Shah et. al. Interestingly, a recently-constructed, layered regenerating code is shown to achieve a point on this outer bound for the (5, 4, 4) case. This represents the first-known instance of an optimal ER code that does not correspond to a point on the FR tradeoff.

Inner Bound on the GDOF of the K-User MIMO Gaussian Symmetric Interference Channel

The K-user multiple input multiple output (MIMO) Gaussian symmetric interference channel where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log INR/log SNR level. Several interesting conclusions are drawn from the derived bounds. It is shown that when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is found to be GDOF optimal in many cases. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance.

A Few Case Studies on the Correlation of Particle Network and Its Stability on the Ionic Conductivity of Solid-Liquid Composite Electrolytes

We discuss here the crucial role of the particle network and its stability on the long-range ion transport in solid liquid composite electrolytes. The solid liquid composite electrolytes chosen for the study here comprise nanometer sized silica (SiO2) particles having various surface chemical functionalities dispersed in nonaqueous lithium salt solutions, viz, lithium perchlorate (LiClO4) in two different polyethylene glycol based solvents. These systems constitute representative examples of an independent class of soft matter electrolytes known as ``soggy sand'' electrolytes, which have tremendous potential in diverse electrochemical devices. The oxide additive acts as a heterogeneous dopant creating free charge carriers and enhancing the local ion transport. For long-range transport, however, a stable spanning particle network is needed. Systematic experimental investigations here reveal that the spatial and time dependent characteristics of the particle network in the liquid solution are nontrivial. The network characteristics are predominantly determined by the chemical makeup of the electrolyte components and the chemical interactions between them. It is noteworthy that in this study the steady state macroscopic ionic conductivity and viscosity of the solid liquid composite electrolyte are observed to be greatly determined by the additive oxide surface chemical functionality, solvent chemical composition, and solvent dielectric constant.

The effect of particle size on performance of cathode materials of Li-ion batteries

Beginning with the ‘frog-leg experiment’ by Galvani (1786), followed by the demonstrations of Volta pile by Volta (1792) and lead-acid accumulator by Plante´ (1859), several battery chemistries have been developed and realized commercially. The development of lithium-ion rechargeable battery in the early 1990s is a breakthrough in the science and technology of batteries. Owing to its high energy density and high operating voltage, the Li-ion battery has become the battery of choice for various portable applications such as note-book computers, cellular telephones, camcorders, etc. Huge efforts are underway in succeeding the development of large size batteries for electric vehicle applications. The origin of lithium-ion battery lies in the discovery that Li+-ions can reversibly be intercalated into/de-intercalated from the Van der Walls gap between graphene sheets of carbon materials at a potential close to the Li/Li+ electrode. By employing carbon as the negative electrode material in rechargeable lithium-ion batteries, the problems associated with metallic lithium in rechargeable lithium batteries have been mitigated. Complimentary investigations on intercalation compounds based on transition metals have resulted in establishing LiCoO2 as the promising cathode material. By employing carbon and LiCoO2, respectively, as the negative and positive electrodes in a non-aqueous lithium-salt electrolyte,a Li-ion cell with a voltage value of about 3.5 V has resulted.Subsequent to commercialization of Li-ion batteries, a number of research activities concerning various aspects of the battery components began in several laboratories across the globe. Regarding the positive electrode materials, research priorities have been to develop different kinds of active materials concerning various aspects such as safety, high capacity, low cost, high stability with long cycle-life, environmental compatibility,understanding relationships between crystallographic and electrochemical properties. The present review discusses the published literature on different positive electrode materials of Li-ion batteries, with a focus on the effect of particle size on electrochemical performance.

Implications of a viscosity bound on black hole accretion

Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (eta) to entropy density (s) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach 10(12) K in certain hot flows. We find that in both the cases eta/s is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on eta/s and vice versa. Finally we speculate that the Shakura-Sunyaev viscosity parameter should decrease with increasing density and/or temperatures. (C) 2012 Elsevier B.V. All rights reserved.

Layered Tabu Search Algorithm for Large-MIMO Detection and a Lower Bound on ML Performance

In this paper, we are concerned with low-complexity detection in large multiple-input multiple-output (MIMO) systems with tens of transmit/receive antennas. Our new contributions in this paper are two-fold. First, we propose a low-complexity algorithm for large-MIMO detection based on a layered low-complexity local neighborhood search. Second, we obtain a lower bound on the maximum-likelihood (ML) bit error performance using the local neighborhood search. The advantages of the proposed ML lower bound are i) it is easily obtained for MIMO systems with large number of antennas because of the inherent low complexity of the search algorithm, ii) it is tight at moderate-to-high SNRs, and iii) it can be tightened at low SNRs by increasing the number of symbols in the neighborhood definition. Interestingly, the proposed detection algorithm based on the layered local search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher-order QAM. For e. g., in a 32 x 32 V-BLAST MIMO system, the proposed detection algorithm performs close to within 1.7 dB of the proposed ML lower bound at 10(-3) BER for 16-QAM (128 bps/Hz), and close to within 4.5 dB of the bound for 64-QAM (192 bps/Hz).

On the Successive Refinability of MIMO channels: DMT and codes

Diversity embedded space time codes are high rate codes that are designed such that they have a high diversity code embedded within them. A recent work by Diggavi and Tse characterizes the performance limits that can be achieved by diversity embedded space-time codes in terms of the achievable Diversity Multiplexing Tradeoff (DMT). In particular, they have shown that the trade off is successively refinable for rayleigh fading channels with one degree of freedom using superposition coding and Successive Interference Cancellation (SIC). However, for Multiple-Input Multiple-Output (MIMO) channels, the questions of successive refinability remains open. We consider MIMO Channels under superposition coding and SIC. We derive an upper bound on the successive refinement characteristics of the DMT. We then construct explicit space time codes that achieve the derived upper bound. These codes, constructed from cyclic division algebras, have minimal delay. Our results establish that when the channel has more than one degree of freedom, the DMT is not successive refinable using superposition coding and SIC. The channels considered in this work can have arbitrary fading statistics.

On the generalized degrees of freedom of the K-user symmetric MIMO Gaussian interference channel

This work derives inner and outer bounds on the generalized degrees of freedom (GDOF) of the K-user symmetric MIMO Gaussian interference channel. For the inner bound, an achievable GDOF is derived by employing a combination of treating interference as noise, zero-forcing at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, depending on the number of antennas and the INR/SNR level. An outer bound on the GDOF is derived, using a combination of the notion of cooperation and providing side information to the receivers. Several interesting conclusions are drawn from the bounds. For example, in terms of the achievable GDOF in the weak interference regime, when the number of transmit antennas (M) is equal to the number of receive antennas (N), treating interference as noise performs the same as the HK scheme and is GDOF optimal. For K >; N/M+1, a combination of the HK and IA schemes performs the best among the schemes considered. However, for N/M <; K ≤ N/M+1, the HK scheme is found to be GDOF optimal.

Bounds on the sum-rate capacity of the Gaussian MIMO X channel

We consider the MIMO X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. Both the transmitters and receivers are equipped with multiple antennas. First, we derive an upper bound on the sum-rate capacity of the MIMO XC under individual power constraint at each transmitter. The sum-rate capacity of the two-user multiple access channel (MAC) that results when receiver cooperation is assumed forms an upper bound on the sum-rate capacity of the MIMO XC. We tighten this bound by considering noise correlation between the receivers and deriving the worst noise covariance matrix. It is shown that the worst noise covariance matrix is a saddle-point of a zero-sum, two-player convex-concave game, which is solved through a primal-dual interior point method that solves the maximization and the minimization parts of the problem simultaneously. Next, we propose an achievable scheme which employs dirty paper coding at the transmitters and successive decoding at the receivers. We show that the derived upper bound is close to the achievable region of the proposed scheme at low to medium SNRs.

Outer Bounds on the Secrecy Rate of the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation

This paper derives outer bounds for the 2-user symmetric linear deterministic interference channel (SLDIC) with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. Five outer bounds are derived, under different assumptions of providing side information to receivers and partitioning the encoded message/output depending on the relative strength of the signal and the interference. The usefulness of these outer bounds is shown by comparing the bounds with the inner bound on the achievable secrecy rate derived by the authors in a previous work. Also, the outer bounds help to establish that sharing random bits through the cooperative link can achieve the optimal rate in the very high interference regime.