Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A(d)e(-lambda parallel to x parallel to alpha), lambda, alpha > 0, x is an element of R-d, d >= 2. Let d(n) be the longest edge length of the nearest-neighbor graph on these points. We show that (lambda(-1) log n)(1-1/alpha) d(n) - b(n) converges weakly to the Gumbel distribution, where b(n) similar to ((d - 1)/lambda alpha) log log n. We also prove the following strong law for the normalized nearest-neighbor distance (d) over tilde (n) = (lambda(-1) log n)(1-1/alpha) d(n)/log log n: (d - 1)/alpha lambda <= lim inf(n ->infinity) (d) over tilde (n) <= lim sup(n ->infinity) (d) over tilde (n) <= d/alpha lambda almost surely. Thus, the exponential rate of decay alpha = 1 is critical, in the sense that, for alpha > 1, d(n) -> 0, whereas, for alpha <= 1, d(n) -> infinity almost surely as n -> infinity.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Head-on infall of two compact objects: Third post-Newtonian energy flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails, and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

Reentrant insulator-metal transition in the half-filled Hubbard model

Using the d=infinity or local-approximation approach to the half-filled Hubbard model on a compressible lattice, we present a detailed study of the transport and structural properties near the paramagnetic metal-insulator transition. The results describe qualitatively most of the observed data in V2O3, including the metal-insulator-metal crossover [Kuwamoto et al., Phys. Rev. B 22, 2626 (1980)]. In addition, we discuss an interesting and intrinsic reentrance feature in the resistivity of the half-filled Hubbard model at high temperatures.

Saturation throughput analysis of an input queueing ATM switch with multiclass bursty traffic

In this paper we consider an N x N non-blocking, space division ATM switch with input cell queueing. At each input, the cell arrival process comprises geometrically distributed bursts of consecutive cells for the various outputs. Motivated by the fact that some input links may be connected to metropolitan area networks, and others directly to B-ISDN terminals, we study the situation where there are two classes of inputs with different values of mean burst length. We show that when inputs contend for an output, giving priority to an input with smaller expected burst length yields a saturation throughput larger than if the reverse priority is given. Further, giving priority to less bursty traffic can give better throughput than if all the inputs were occupied by this less bursty traffic. We derive the asymptotic (as N --> infinity) saturation throughputs for each priority class.

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Nonequilibrium phase transitions in a driven sandpile model

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope sigma(c), a parameter alpha, governing the local current-slope relation (beyond threshold), and j(in), the mean input current of sand. A non-equilibrium phase diagram is obtained in the alpha-j(in) plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.z

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Analytical solutions for heat transfer during cyclic melting and freezing of a phase change material used in electronic or electrical packaging

In this paper we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each subdomain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.