Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Extension of Darken's Quadratic Formalism to Dilute Multicomponent Solutions

Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.

A kinetic study of liquid-phase catalytic oxidation of styrene to benzaldehyde with Wilkinson complex

Liquid-phase homogeneous catalytic oxidation of styrene with Wilkinson complex by molecular oxygen in toluene medium gave selectively benzaldehyde and formaldehyde as the primary products. Higher temperatures and styrene conversions eventually led to acid formation due to co-oxidation of aldehyde.A reaction induction period and an initiation period, typical of free-radical reactions, characterized the oxidation process. The effects of temperature and catalyst and styrene concentrations on the conversion of styrene to benzaldehyde and acid formation have been studied. The optimum reaction parameters have been determined as a styrene-to-solvent mole ratio of 0.5, a catalyst-to-styrene mole ratio of 5.0 X lo4, and a reaction temperature of 75 "C. A reaction scheme based upon free-radical mechanism yielded a pseudo-first-order model which agreed well with the observed kinetic data in the absence of co-oxidation of aldehyde. A second-order model was found to fit the experimental data better in the case of aldehyde conversion to acid.

FTIR-spektroskopia kasviuutteiden analysoinnissa

FTIR-spektroskopia (Fourier-muunnosinfrapunaspektroskopia) on nopea analyysimenetelmä. Fourier-laitteissa interferometrin käyttäminen mahdollistaa koko infrapunataajuusalueen mittaamisen muutamassa sekunnissa. ATR-liitännäisellä varustetun FTIR-spektrometrin käyttö ei edellytä juuri näytteen valmistusta ja siksi menetelmä on käytössä myös helppo. ATR-liitännäinen mahdollistaa myös monien erilaisten näytteiden analysoinnin. Infrapunaspektrin mittaaminen onnistuu myös sellaisista näytteistä, joille perinteisiä näytteenvalmistusmenetelmiä ei voida käyttää. FTIR-spektroskopian avulla saatu tieto yhdistetään usein tilastollisiin monimuuttuja-analyyseihin. Klusterianalyysin avulla voidaan spektreistä saatu tieto ryhmitellä samanlaisuuteen perustuen. Hierarkkisessa klusterianalyysissa objektien välinen samanlaisuus määritetään laskemalla niiden välinen etäisyys. Pääkomponenttianalyysin avulla vähennetään datan ulotteisuutta ja luodaan uusia korreloimattomia pääkomponentteja. Pääkomponenttien tulee säilyttää mahdollisimman suuri määrä alkuperäisen datan variaatiosta. FTIR-spektroskopian ja monimuuttujamenetelmien sovellusmahdollisuuksia on tutkittu paljon. Elintarviketeollisuudessa sen soveltuvuutta esimerkiksi laadun valvontaan on tutkittu. Menetelmää on käytetty myös haihtuvien öljyjen kemiallisten koostumusten tunnistukseen sekä öljykasvien kemotyyppien havaitsemiseen. Tässä tutkimuksessa arvioitiin menetelmän käyttöä suoputken uutenäytteiden luokittelussa. Tutkimuksessa suoputken eri kasvinosien uutenäytteiden FTIR-spektrejä vertailtiin valikoiduista puhdasaineista mitattuihin FTIR-spektreihin. Puhdasaineiden FTIR-spektreistä tunnistettiin niiden tyypilliset absorptiovyöhykkeet. Furanokumariinien spektrien intensiivisten vyöhykkeiden aaltolukualueet valittiin monimuuttuja-analyyseihin. Monimuuttuja-analyysit tehtiin myös IR-spektrin sormenjälkialueelta aaltolukualueelta 1785-725 cm-1. Uutenäytteitä pyrittiin luokittelemaan niiden keräyspaikan ja kumariinipitoisuuden mukaan. Keräyspaikan mukaan ryhmittymistä oli havaittavissa, mikä selittyi vyöhykkeiden aaltolukualueiden mukaan tehdyissä analyyseissa pääosin kumariinipitoisuuksilla. Näissä analyyseissa uutenäytteet pääosin ryhmittyivät ja erottuivat kokonaiskumariinipitoisuuksien mukaan. Myös aaltolukualueen 1785-725 cm-1 analyyseissa havaittiin keräyspaikan mukaan ryhmittymistä, mitä kumariinipitoisuudet eivät kuitenkaan selittäneet. Näihin ryhmittymisiin vaikuttivat mahdollisesti muiden yhdisteiden samanlaiset pitoisuudet näytteissä. Analyyseissa käytettiin myös muita aaltolukualueita, mutta tulokset eivät juuri poikenneet aiemmista. 2. kertaluvun derivaattaspektrien monimuuttuja-analyysit sormenjälkialueelta eivät myöskään muuttaneet tuloksia havaittavasti. Jatkotutkimuksissa nyt käytettyä menetelmää on mahdollista edelleen kehittää esimerkiksi tutkimalla monimuuttuja-analyyseissa 2. kertaluvun derivaattaspektreistä suppeampia, tarkkaan valittuja aaltolukualueita.

Studies in nonlinear optical materials: structure of di-2-menthyl 2-(N,N'-dimethyl-2-imidazolidinylidene)malonate monohydrate

C28H48N2Oa.H2 O, Mr=494.7, orthorhombic,P2~2~2~, a = 7.634 (2), b = 11.370 (2), c=34. 167 (4) A, V = 2966 (2) A 3, Z = 4, D m = 1.095,D x -- 1. 108 g cm -3, Mo Kct, 2 -- 0.7107 ,/k, ~ =0.43 cm -~, F(000) = 1088.0, T= 293 K, R = 0.061 for 1578 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is negligible (1/100th of the urea standard). The observed low second-order nonlinear response has been attributed to the unfavourable packing of the molecules in the crystal lattice.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Constructions and situations : a constructivist reading of Hegel's System

The object of this work is Hegel's Logic, which comprises the first third of his philosophical System that also includes the Philosophy of Nature and the Philosophy of Spirit. The work is divided into two parts, where the first part investigates Hegel s Logic in itself or without an explicit reference to rest of Hegel's System. It is argued in the first part that Hegel's Logic contains a methodology for constructing examples of basic ontological categories. The starting point on which this construction is based is a structure Hegel calls Nothing, which I argue to be identical with an empty situation, that is, a situation with no objects in it. Examples of further categories are constructed, firstly, by making previous structures objects of new situations. This rule makes it possible for Hegel to introduce examples of ontological structures that contain objects as constituents. Secondly, Hegel takes also the very constructions he uses as constituents of further structures: thus, he is able to exemplify ontological categories involving causal relations. The final result of Hegel's Logic should then be a model of Hegel s Logic itself, or at least of its basic methods. The second part of the work focuses on the relation of Hegel's Logic to the other parts of Hegel's System. My interpretation tries to avoid, firstly, the extreme of taking Hegel's System as a grand metaphysical attempt to deduce what exists through abstract thinking, and secondly, the extreme of seeing Hegel's System as mere diluted Kantianism or a second-order investigation of theories concerning objects instead of actual objects. I suggest a third manner of reading Hegel's System, based on extending the constructivism of Hegel's Logic to the whole of his philosophical System. According to this interpretation, transitions between parts of Hegel's System should not be understood as proofs of any sort, but as constructions of one structure or its model from another structure. Hence, these transitions involve at least, and especially within the Philosophy of Nature, modelling of one type of object or phenomenon through characteristics of an object or phenomenon of another type, and in the best case, and especially within the Philosophy of Spirit, transformations of an object or phenomenon of one type into an object or phenomenon of another type. Thus, the transitions and descriptions within Hegel's System concern actual objects and not mere theories, but they still involve no fallacious deductions.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

NDDO-based CI methods for the prediction of electronic spectra and sum-over-states molecular hyperpolarization

NDDO-based (AM1) configuration interaction (CI) calculations have been used to calculate the wavelength and oscillator strengths of electronic absorptions in organic molecules and the results used in a sum-over-states treatment to calculate second-order-hyperpolarizabilities. The results for both spectra and hyperpolarizabilities are of acceptable quality as long as a suitable CI-expansion is used. We have found that using an active space of eight electrons in eight orbitals and including all single and pair-double excitations in the CI leads to results that agree well with experiment and that do not change significantly with increasing active space for most organic molecules. Calculated second-order hyperpolarizabilities using this type of CI within a sum-over-states calculation appear to be of useful accuracy.

Parametric instability of stochastic columns

Columns which have stochastically distributed Young's modulus and mass density and are subjected to deterministic periodic axial loadings are considered. The general case of a column supported on a Winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered. Material property fluctuations are modeled as independent one-dimensional univariate homogeneous real random fields in space. In addition to autocorrelation functions or their equivalent power spectral density functions, the input random fields are characterized by scale of fluctuations or variance functions for their second order properties. The foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables. The system equations of boundary frequencies are obtained using Bolotin's method for deterministic systems. Stochastic FEM is used to obtain the discrete system with random as well as periodic coefficients. Statistical properties of boundary frequencies are derived in terms of input parameter statistics. A complete covariance structure is obtained. The equations developed are illustrated using a numerical example employing a practical correlation structure.

Excitation and correlation of N-14 overtone transitions and measurement of heteronuclear dipolar coupling using DAPT

For studying systems containing nitrogen, limited use of N-14 NMR spectroscopy has been made because of the large quadrupolar interaction experienced by the N-14 nucleus and the absence of a central transition. To overcome the above problem, use of overtone spectroscopy has been suggested. Though this approach has limited applicability for powder samples due to second order quadrupole broadening, it is useful for studying oriented samples and single crystals. Here, we demonstrate the use of the recently proposed dipolar assisted polarization transfer (DAPT) pulse scheme for exciting the overtone transitions. The pulse sequence may also be utilized as a two-dimensional experiment to obtain H-1-N-14 dipolar couplings and H-1 chemical shifts. (C) 2010 Elsevier B.V. All rights reserved.

Physics-Based Thermal Conductivity Model for Metallic Single-Walled Carbon Nanotube Interconnects

In this letter, a closed-form analytical model for temperature-dependent longitudinal diffusive lattice thermal conductivity (kappa) of a metallic single-walled carbon nanotube (SWCNT) has been addressed. Based on the Debye theory, the second-order three-phonon Umklapp, mass difference (MD), and boundary scatterings have been incorporated to formulate. in both low-and high-temperature regimes. It is proposed that. at low temperature (T) follows the T-3 law and is independent of the second-order three-phonon Umklapp and MD scatterings. The form factor due to MD scattering also plays a key role in the significant variation of. in addition to the SWCNT length. The present diameter-independent model of. agrees well with the available experimental data on suspended intrinsic metallic SWCNTs over a wide range of temperature and can be carried forward for electrothermal analyses of CNT-based interconnects.

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/4 pi. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.

Chance constrained uncertain classification via robust optimization

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.