Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Onttojen puiden lahopuukovakuoriaiset — kolmen pyydystyypin vertailu

Vanhat ja ontot puut ovat tärkeä elinympäristö monelle lahopuusta riippuvaiselle eliölajille. Onttoihin puihin on erikoistunut suuri määrä myös vaarantuneita ja harvinaisia hyönteislajeja, jotka elävät puun onkalon seinämillä tai onkalon pohjalle kerääntyvässä orgaanisessa aineksessa, ns. mulmissa. Tutkimuksen tavoitteena oli selvittää, mikä kolmesta pyydystyypistä (ikkuna-, vuoka- ja kuoppapyydys) soveltuu parhaiten onttojen puiden lahopuukovakuoriaisten pyyntiin. Lisäksi tavoitteena oli kartoittaa hyönteisnäytteiden ensimmäiseen laboratoriokäsittelyyn vaadittua aikaa. Tutkimuksessa oli mukana vanhoja rungostaan onttoutuneita lehmuksia, tammia ja vaahteroita pääkaupunkiseudun puisto- ja kartanoalueilta. Puiden onkaloiden sisään aseteltiin ikkuna-, vuoka- ja kuoppapyydyksiä, kaksi kutakin tyyppiä ja ne tyhjennettiin kolmen viikon välein touko-heinäkuussa 2006. Pyydyksiä oli siis yhteensä 90 per pyyntijakso. Kun näytteistä eroteltiin halutut hyönteislahkot (mukaanlukien kovakuoriaiset) niiden käsittelyyn käytetty aika kirjattiin ylös. Aineistosta tunnistettiin yhteensä 3825 kovakuoriaisyksilöä ja 212 lajia, joista lahopuusta riippuvaisia oli yhteensä 3398 yksilöä ja 121 lajia. Ikkunapyydyksissä esiintyi yhteensä 1639 yksilöä ja 140 lajia, vuokapyydyksissä 1506 yksilöä ja 134 lajia, kuoppapyydyksissä 680 yksilöä ja 111 lajia. Näytteiden käsittelyaikojen keskiarvot olivat 48,3 minuuttia ikkunapyydykselle, 65,5 minuuttia vuokapyydykselle ja 34,1 kuoppapyydykselle. Lajistokoostumuksen huomioiva ?-diversiteetti erosi huomattavasti pyydysten välillä, se oli 36,5 % ikkuna- ja vuokapyydysten välillä, 13,1 % ikkuna- ja kuoppapyydysten välillä ja 14,2 % vuoka- ja kuoppapyydysten välillä. Ikkuna- ja vuokapyydysten välillä ei havaittu tilastollisesti merkitsevää eroa saproksyylilajien (p<0,05), -yksilöiden (p<0,05) tai käsittelyaikojen (p<0,05) keskiarvoissa. Ikkuna- ja vuokapyydyksillä saatiin keskimäärin selvästi enemmän saproksyylilajeja ja –yksilöitä kuoppapyydykseen verrattuna. Kuoppapyydyksellä saatiin kokonaisyksilömäärään verrattuna suhteellisesti vähemmän saproksyylejä (59 %) kuin ikkuna- (69 %) ja vuokapyydyksillä (71 %). Ikkunapyydykset olivat tehokkain pyydystyyppi vertailtaessa pyydysten keräämää saproksyyliyksilömäärää suhteessa aineiston käsittelyn vaatimaan aikaan. Tehokkuus (yksilöä minuutissa) ikkunapyydykselle oli 0,74, vuokapyydykselle 0,43 ja kuoppapyydykselle 0,21. Ikkunapyydyksiä ei ole aikaisemmin käytetty puun onkalon sisällä hyönteisiä pyydettäessä vaan ne ovat aikaisemmissa tutkimuksissa roikkuneet onkalon ulkopuolella. Ikkunapyydykset kuitenkin toimivat erinomaisesti myös onkaloiden sisällä. Ikkuna- sekä vuokapyydys toimivatkin selkeästi paremmin lahopuukovakuoriaisten pyynnissä verrattuna kuoppapyydykseen, jonka poisjättäminen olisi kuitenkin tuottanut huomattavasti lajiköyhemmän aineiston. Mahdollisimman monimuotoisen onttojen puiden lahopuukovakuoriaislajiston keräämiseksi tulisi käyttää ikkuna- tai vuokapyydyksiä yhdessä kuoppapyydysten kanssa.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Improved mechanical properties of polymer nanocomposites incorporating graphene-like BN: Dependence on the number of BN layers

The mechanical properties of composites of polymethylmethacrylate (PMMA) with two-dimensional graphene-like boron nitride (BN) have been investigated to explore the dependence of the properties on the number of BN layers. This study demonstrates that significantly improved mechanical properties are exhibited by the composite with the fewest number of BN layers. Thus, with incorporation of three BN layers, the hardness and elastic modulus of the composite showed an increase of 125% and 130%, respectively, relative to pure PMMA. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.

Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations. (C) 2010 Elsevier Ltd. All rights reserved.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Generalised one-dimensional burgers'equation in relativistic fluiddynamics

This work deals with the effects of weak nonlinearity and weak dissipation on a linear wave in relativistic gasdynamics. Using perturbation and asymptotic expansions, a relativistic analogue of generalised one-dimensional Burgers' equation of classical gasdynamics is derived to describe far-field description of the wave. Steady state solution is presented for strict one-dimensional case.

Five-level inverter scheme for an open-end winding induction machine with less number of switches

Higher level of inversion is achieved with a less number of switches in the proposed scheme. The scheme proposes a five-level inverter for an open-end winding induction motor which uses only two DC-link rectifiers of voltage rating of Vdc/4, a neutral-point clamped (NPC) three-level inverter and a two-level inverter. Even though the two-level inverter is connected to the high-voltage side, it is always in square-wave operation. Since the two-level inverter is not switching in a pulse width modulated fashion and the magnitude of switching transient is only half compared to the convention three-level NPC inverter, the switching losses and electromagnetic interference is not so high. The scheme is experimentally verified on a 2.5 kW induction machine.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.

Precipitation in small systems-I. stochastic analysis

Precipitation in small droplets involving emulsions, microemulsions or vesicles is important for Producing multicomponent ceramics and nanoparticles. Because of the random nature of nucleation and the small number of particles in a droplet, the use of a deterministic population balance equation for predicting the number density of particles may lead to erroneous results even for evaluating the mean behavior of such systems. A comparison between the predictions made through stochastic simulation and deterministic population balance involving small droplets has been made for two simple systems, one involving crystallization and the other a single-component precipitation. The two approaches have been found to yield quite different results under a variety of conditions. Contrary to expectation, the smallness of the population alone does not cause these deviations. Thus, if fluctuation in supersaturation is negligible, the population balance and simulation predictions concur. However, for large fluctuations in supersaturation, the predictions differ significantly, indicating the need to take the stochastic nature of the phenomenon into account. This paper describes the stochastic treatment of populations, which involves a sequence of so-called product density equations and forms an appropriate framework for handling small systems.

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024(3) collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr-M over a large range, namely 0.01 <= Pr-M <= 10. We obtain data for a wide variety of statistical measures, such as probability distribution functions (PDFs) of the moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterize intermittency, isosurfaces of quantities, such as the moduli of the vorticity and current density, and joint PDFs, such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from a larger intermittency in the magnetic field than in the velocity field, at large Pr-M, to a smaller intermittency in the magnetic field than in the velocity field, at low Pr-M. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr-M, multiscaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.