Spectral Efficiency of Channel-Aware Schedulers in Non-identical Composite Links with Interference

Accurate system planning and performance evaluation requires knowledge of the joint impact of scheduling, interference, and fading. However, current analyses either require costly numerical simulations or make simplifying assumptions that limit the applicability of the results. In this paper, we derive analytical expressions for the spectral efficiency of cellular systems that use either the channel-unaware but fair round robin scheduler or the greedy, channel-aware but unfair maximum signal to interference ratio scheduler. As is the case in real deployments, non-identical co-channel interference at each user, both Rayleigh fading and lognormal shadowing, and limited modulation constellation sizes are accounted for in the analysis. We show that using a simple moment generating function-based lognormal approximation technique and an accurate Gaussian-Q function approximation leads to results that match simulations well. These results are more accurate than erstwhile results that instead used the moment-matching Fenton-Wilkinson approximation method and bounds on the Q function. The spectral efficiency of cellular systems is strongly influenced by the channel scheduler and the small constellation size that is typically used in third generation cellular systems.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented. (C) 2011 Elsevier B.V. All rights reserved.

Length of near-wall plumes in turbulent convection

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers (10(5) < Ra < 10(11)) and at three Prandtl numbers (Pr = 0.7, 5.2, 602). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (L(p)/A), made dimensionless by the near-wall length scale in turbulent convection (Z(w)), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to L(p)H/A for a given fluid layer of height H. The increase in Pr has a weak influence in decreasing L(p)/A. These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

An Accurate Model for EESM and its Application to Analysis of CQI Feedback Schemes and Scheduling in LTE

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts-Chebyshev cognate theorem is extended to statically balanced four-bar linkages. (C) 2011 Elsevier Ltd. All rights reserved.

Laser‐Induced Turbulence

In a recent experiment on laser beam transmission through an absorbing gas, the critical Reynold's number for the flow, induced by the heating of the gas, to become turbulent was found to be less than 30, which is many orders of magnitude smaller than that for pure shear flow in pipes. It is shown here that a Rayleigh number is the more appropriate criterion to characterize the stability of flow in this situation, and its value estimated in two limiting cases is found to bracket the expected critical Rayleigh number for vertical concentric cylinders.

Electrical Breakdown of Gases Between Coaxial Cylindrical Electrodes in Crossed Electric and Magnetic Fields

Sparking potentials have been measured in nitrogen and dry air between coaxial cylindrical electrodes for values of n = R2/R1 = approximately 1 to 30 (R1 = inner electrode radius, R2 = outer electrode radius) in the presence of crossed uniform magnetic fields. The magnetic flux density was varied from 0 to 3000 Gauss. It has been shown that the minimum sparking potentials in the presence of the crossed magnetic field can be evaluated on the basis of the equivalent pressure concept when the secondary ionization coefficient does not vary appreciably with B/p (B = magnetic flux density, p = gas pressure). The values of secondary ionization coefficients �¿B in nitrogen in crossed fields calculated from measured values of sparking potentials and Townsend ionization coefficients taken from the literature, have been reported. The calculated values of collision frequencies in nitrogen from minimum sparking potentials in crossed fields are found to increase with increasing B/p at constant E/pe (pe = equivalent pressure). Studies on the similarity relationship in crossed fields has shown that the similarity theorem is obeyed in dry air for both polarities of the central electrode in crossed fields.

Implications of unitarity and analyticity for the D pi form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D -> pi/nu. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(alpha(2)(s)) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low-energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the D pi form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.

XXVI. The relation between thermo-optic and piezo-optic phenomena in crystals

It is pointed out that the change in refractive index with temperature of a crystal is different from what is calculated from the accompanying change in volume and the piezo-optic coefficients. The difference, which is a pure temperature effect, is explained as being due to the change in polarizability of the atoms produced by a change in the amplitude of vibration. The polarizability (α) can be expanded as a Taylor series in the changes of the distance (r) between the atoms and it is found that while the piezo-optic coefficient depends only on ∂α/∂r, the pure temperature effect is a function of ∂ 2 a/∂r 2. Making use of the experimental data, the values of a and its first two derivatives can be determined. These values are foundto be of the same order as those deduced from the intensities of Rayleigh and Raman scattering of light. The theory predicts that dn/dT should vary as the coefficient of cubical expansion at different temperatures and this is verified to be true. Finally, calculations are made of the thermo- and piezo-optic coefficients, considering the electrostatic interaction between the atoms. These do not adequately explain the observed facts, since no provision is made for the distortion of electron atmospheres around the atoms and the consequent changes in polarizability.

On the athermal nature of the beta to omega transformation

One characteristic feature of the athermal beta -> omega transformation is the short time scale of the transformation. So far, no clear understanding of this issue exists. Here we construct a model that includes contributions from a Landau sixth-order free energy density, kinetic energy due to displacement, and the Rayleigh dissipation function to account for the dissipation arising from the rapid movement of the parent product interface during rapid nucleation. We also include the contribution from omega-like fluctuations to local stress. The model shows that the transformation is complete on a time scale comparable to the velocity of sound. The estimated nucleation rate is several orders higher than that for diffusion-controlled transformations. The model predicts that the athermal omega phase is limited to a certain range of alloying composition. The estimated nucleation rate and the size of ``isothermal'' particles beyond 17% Nb are also consistent with experimental results. The model provides an explanation for the reprecipitation process of the omega particles in the ``cleared'' channels formed during deformation of omega-forming alloys. The model also predicts that acoustic emission should be detectable during the formation of the athermal phase. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Minimal Triangulations of Manifolds

Finding vertex-minimal triangulations of closed manifolds is a very difficult problem. Except for spheres and two series of manifolds, vertex-minimal triangulations are known for only few manifolds of dimension more than 2 (see the table given at the end of Section 5). In this article, we present a brief survey on the works done in last 30 years on the following:(i) Finding the minimal number of vertices required to triangulate a given pl manifold. (ii) Given positive integers n and d, construction of n-vertex triangulations of different d-dimensional pl manifolds. (iii) Classifications of all the triangulations of a given pl manifold with same number of vertices.In Section 1, we have given all the definitions which are required for the remaining part of this article. A reader can start from Section 2 and come back to Section 1 as and when required. In Section 2, we have presented a very brief history of triangulations of manifolds. In Section 3,we have presented examples of several vertex-minimal triangulations. In Section 4, we have presented some interesting results on triangulations of manifolds. In particular, we have stated the Lower Bound Theorem and the Upper Bound Theorem. In Section 5, we have stated several results on minimal triangulations without proofs. Proofs are available in the references mentioned there. We have also presented some open problems/conjectures in Sections 3 and 5.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.