Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.

Asymptotic behaviour and boundedness of linear systems with time varying coefficients

Motivated by developments in spacecraft dynamics, the asymptotic behaviour and boundedness of solution of a special class of time varying systems in which each term appears as the sum of a constant and a time varying part, are analysed in this paper. It is not possible to apply standard textbook results to such systems, which are originally in second order. Some of the existing results are reformulated. Four theorems which explore the relations between the asymptotic behaviour/boundedness of the constant coefficient system, obtained by equating the time varying terms to zero, to the corresponding behaviour of the time varying system, are developed. The results show the behaviour of the two systems to be intimately related, provided the solutions of the constant coefficient system approach zero are bounded for large values of time, and the time varying terms are suitably restrained. Two problems are tackled using these theorems.

Performance analysis of a slotted-ALOHA protocol on a capture channel with fading

We consider the slotted ALOHA protocol on a channel with a capture effect. There are M theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Effects of electron correlations in conjugated organic molecules and solids

The discrepancies between the non-interacting models and experimental results for conjugated systems is highlighted in this brief review. The interacting model hamiltonians correctly give the forbidden singlet state below the optical gap in polyenes and also explain both the nonvanishing optical gap in polyacetylenes and the vanishing optical gap in symmetric cyanine dyes. The negative spin densities in polyene radicals is also understood in terms of a correlated picture. The role of electron-electron interactions in other strongly correlated systems, such as polydiacetylene and mixed and segregated stack charge transfer solids, are also briefly discussed.

A note on the Berry phase for systems having one degree of freedom

A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.

Unconventional mechanism of stabilization of a tetragonal phase in the perovskite ferroelectric (PbTiO3)(1-x)(BiFeO3)(x)

Temperature-dependent x-ray powder-diffraction study of the tetragonal compositions of PbTiO3-BiFeO3 series has revealed that, unlike for all the known ferroelectric perovskites, the compositions exhibiting giant tetragonality is stabilized from the cubic phase via a complex transition pathway which involve (i) formation of minor monoclinic phase with a large pseudotetragonality along with an intermediate tetragonal phase (major) with a small tetragonality, (ii) gradual vanishing of the intermediate tetragonal phase and concomitant increase in the monoclinic regions, and finally (iii) gradual transformation of the monoclinic phase to the tetragonal phase with giant tetragonality.The system seems to adopt such a complex transition pathway to create amicrostructure with very large number of domains and interfaces for stress relief, which would not have been possible in case of a direct cubic-tetragonal transition.

Some recent results on the stability of linear time varying systems

Some theorems derived recently by the authors on the stability of multidimensional linear time varying systems are reported in this paper. To begin with, criteria based on Liapunov�s direct method are stated. These are followed by conditions on the asymptotic behaviour and boundedness of solutions. Finally,L 2 andL ? stabilities of these systems are discussed. In conclusion, mention is made of some of the problems in aerospace engineering to which these theorems have been applied.

Improving the phenomenology of Kl3 form factors with analyticity and unitarity

The shape of the vector and scalar K-l3 form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex t plane where zeros of the form factors are excluded. The results are useful for K-l3 data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

On measurement of top polarization as a probe of t(t)over-bar production mechanisms at the LHC

In this note we demonstrate the use of top polarization in the study of t (t) over bar resonances at the LHC, in the possible case where the dynamics implies a non-zero top polarization. As a probe of top polarization we construct an asymmetry in the decay-lepton azimuthal angle distribution (corresponding to the sign of cos phi(l)) in the laboratory. The asymmetry is non-vanishing even for a symmetric collider like the LHC, where a positive z axis is not uniquely defined. The angular distribution of the leptons has the advantage of being a faithful top-spin analyzer, unaffected by possible anomalous tbW couplings, to linear order. We study, for purposes of demonstration, the case of a Z' as might exist in the little Higgs models. We identify kinematic cuts which ensure that our asymmetry reflects the polarization in sign and magnitude. We investigate possibilities at the LHC with two energy options: root s = 14TeV and root s = 7TeV, as well as at the Tevatron. At the LHC the model predicts net top quark polarization of the order of a few per cent for M-Z' similar or equal to 1200GeV, being as high as 10% for a smaller mass of the Z' of 700GeV and for the largest allowed coupling in the model, the values being higher for the 7TeV option. These polarizations translate to a deviation from the standard-model value of azimuthal asymmetry of up to about 4% (7%) for 14 (7) TeV LHC, whereas for the Tevatron, values as high as 12% are attained. For the 14TeV LHC with an integrated luminosity of 10 fb(-1), these numbers translate into a 3 sigma sensitivity over a large part of the range 500 less than or similar to M-Z' less than or similar to 1500GeV.

New results on systems with second-class constraints

We show how, for large classes of systems with purely second-class constraints, further information can be obtained about the constraint algebra. In particular, a subset consisting of half the full set of constraints is shown to have vanishing mutual brackets. Some other constraint brackets are also shown to be zero. The class of systems for which our results hold includes examples from non-relativistic particle mechanics as well as relativistic field theory. The results are derived at the classical level for Poisson brackets, but in the absence of commutator anomalies the same results will hold for the commutators of the constraint operators in the corresponding quantised theories.

Hydrodynamics of the Renn-Lubensky twist grain boundary phase, and the decoupled lamellar phase

The long-wavelength hydrodynamics of the Renn-Lubensky twist grain boundary phase with grain boundary angle 2pialpha, alpha irrational, is studied. We find three propagating sound modes, with two of the three sound speeds vanishing for propagation orthogonal to the grains, and one vanishing for propagation parallel to the grains as well. In addition, we find that the viscosities eta1, eta2, eta4, and eta5 diverge like 1/Absolute value of omega as frequency omega --> 0, with the divergent parts DELTAeta(i) satisfying DELTAeta1DELTAeta4=(DELTAeta5)2, exactly. Our results should also apply to the predicted decoupled lamellar phase.

Thermomechanical behaviour of pin joints subjected to sheet loads

An important problem regarding pin joints in a thermal environment is addressed. The motivation emerges from structural safety requirements in nuclear and aerospace engineering. A two-dimensional model of a smooth, rigid misfit pin in a large isotropic sheet is considered as an abstraction. The sheet is subjected to a biaxial stress system and far-field unidirectional heat flow. The thermoelastic analysis is complex due to non-linear load-dependent contact and separation conditions at the pin-hole interface and the absence of existence and uniqueness theorems for the class of frictionless thermoelastic contact problems. Identification of relevant parameters and appropriate synthesis of thermal and mechanical variables enables the thermomechanical generalization of pin-joint behaviour. This paper then proceeds to explore the possibility of multiple solutions in such problems, especially interface contact configuration.

Waveform synthesis using Walsh functions International Journal of Electronics

A software and a microprocessor based hardware for waveform synthesis using Walsh functions are described. The software is based on Walsh function generation using Hadamard matrices and on the truncated Walsh series expansion for the waveform to be synthesized. The hardware employs six microprocessor controlled programmable Walsh function generators (PWFGs) for generating the first six non-vanishing terms of the truncated Walsh series. Improved approximation to a given waveform may be achieved by employing additional PWFGs.