Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

First-order hyperpolarizabilities and pKa of weak organic acids in protic solvents are lineraly related

Second-order nonlinearities (beta) of five weak organic acids in protic solvents have been measured by the double-quantum Rayleigh scattering (DRS) technique. beta is found to bear a linear relationship to the pK(a) of these compounds in those solvents. A direct implication of this observation is that the DRS technique can be used to determine the pK(a) of weak organic acids in any solvent.

First-order hyperpolarizabilities of octupolar aromatic molecules: symmetrically substituted triazines

The first hyperpolarizabilities of some symmetrically substituted triazines have been measured and compared with those of the corresponding symmetrically substituted benzenes. The octupolar triazines have higher quadratic polarizabilities than the corresponding octupolar benzenes. The triazine ring seems to be a better central acceptor than the benzene ring, but if it acts as a donor as in sym-triphenyl triazine, the nonlinearity improves further.

First-Order Hyperpolarizabilities of Sulfophthalein Dyes

In this paper we report the first hyperpolarizabilities (beta) of 12, sulfophthalein dyes. Since these dyes are ionic in nature, their second-order nonlinearities were measured by the hyper-Rayleigh scattering technique in solution. The measured beta values are large and highly solvent dependent. Inclusion of solvent polarity in ab initio estimates of static second-order polarizability does not fully account for the experimental beta values. Contributions from the dissociated forms of the dye in different solvents seem to play an important role in enhancing beta in these systems.

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

The recently evaluated two-pion contribution to the muon g - 2 and the phase of the pion electromagnetic form factor in the elastic region, known from pi pi scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t = 0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations, and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, < r(pi)(2)> = (0.435 +/- 0.005) fm(2) and F(-1.6 GeV2) = 0.243(-0.014)(+0.022), we obtain the allowed ranges 3.75 GeV-4 less than or similar to c less than or similar to 3.98 GeV-4 and 9.91 GeV-6 less than or similar to d less than or similar to 10.46 GeV-6 for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

Metamorphic-metasomatic fluids and Al, Si order/disorder of K-rich alkali feldspars from southern Indian high grade terrain

The structural state of K-feldspars in the quartzofeldspathic gneisses, charnockites, metapelites and pegmatites from the southern Kamataka, northern Tamil Nadu and southern Kerala high-grade regions of southern India has been characterized using petrographic and powder X-ray diffraction methods. The observed distribution pattern of structural state with a preponderance of disordered K-feldspar polymorphs in granulites compared to the ordered microclines in the amphibolite facies rocks is interpreted to reflect principally the varying H2O contents in the metamorphic-metasomatic fluids across metamorphic grade. The K-feldspars in the pegmatites of granitic derivation and in a pegmatite of inferred metamorphic origin also point to the important role of aqueous fluids in their structural state.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

Aryl monosulphides and symmetrical disulphides based second order nonlinear optical chromophores with transparency in the visible

A series of aryl monosulphides and disulphides have been synthesized and characterized. Their molecular hyperpolarizability (beta) has been measured in solution with the hyper-Rayleigh Scattering technique and also calculated by semiempirical AMI method. The trend in the observed and calculated values of first hyperpolarizability of these compounds has been found to be in good agreement. These compounds show moderate P values and excellent transparency in the visible region.

A token-based distributed algorithm for total order atomic broadcast

In this paper, we propose a new token-based distributed algorithm for total order atomic broadcast. We have shown that the proposed algorithm requires lesser number of messages compared to the algorithm where broadcast servers use unicasting to send messages to other broadcast servers. The traditional method of broadcasting requires 3(N - 1) messages to broadcast an application message, where N is the number of broadcast servers present in the system. In this algorithm, the maximum number of token messages required to broadcast an application message is 2N. For a heavily loaded system, the average number of token messages required to broadcast an application message reduces to 2, which is a substantial improvement over the traditional broadcasting approach.

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.