A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

AC conductivity of a quantum Hall line junction

We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter-or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (sigma) between the two edges is considered. Assuming that sigma is independent of the frequency omega, we derive expressions for the AC conductivity as a function of omega, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit (omega -> 0), and generalize those results for an interacting system. As a function of omega, the AC conductivity shows significant oscillations if sigma is small; the oscillations become less prominent as sigma increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.

Organized Nanostructures of Thermoresponsive Poly(N-isopropylacrylamide) Block Copolymers Obtained Through Controlled RAFT Polymerization

Kontrolloidut radikaalipolymerointimenetelmät, kuten RAFT-polymerointi, ovat moderni tapa valmistaa polymeerejä säädellysti. RAFT-polymeroinnilla polymeerien ketjunpituutta, moolimassajakaumaa, mikrorakennetta (taktisuus, järjestys), koostumusta ja funktionaalisuutta kyetään hallitsemaan. Siten menetelmällä voidaan valmistaa uudenlaisia polymeeriarkkitektuureja, kuten blokki- ja tähtipolymeerejä, sekä hybridimateriaaleja ja biokonjugaatteja. Polymeeristen rakennuspalikoiden itsejärjestyminen, missä huolellisesti syntetisoidut polymeerit järjestyvät halutulla tavalla nanoskaalassa, on suosittu tutkimuskohde materiaalitieteessä. On huomattava, että blokkipolymeerien itsejärjestyminen on vielä suhteellisen nuori tutkimusaihe. Tämän hetkiset polymeeriset nanomateriaalit ovat suhteellisen yksinkertaisia luonnon luomuksiin verrattuina, tarjoten jatkuvasti uusia mahdollisuuksia seuraavan sukupolven polymeereille. Tässä työssä RAFT-polymeroinnilla syntetisoitiin amfifiilisiä di- ja triblokkikopolymeerejä sekä tutkittiin niiden järjestymistä nanorakenteiksi. Kaikissa blokkikopolymeereissä käytettiin lämpöherkkää poly(N-isopropyyliakryyliamidia). Siten polymeerit ja tutkitut materiaalit reagoivat lämpötilanmuutokseen ympäristössä eli ovat ns. ympäristöherkkiä. Työssä tutkittiin taktisuuden kontrollointia N-isopropyyliakryyliamidin RAFT-polymeroinnissa. Polymeerin taktisuutta sekä ketjunpituutta ja blokkijärjestystä säätämällä voitiin hallita polymeerin itsejärjestymistä vesiliuoksessa. Amfifiiliset polymeerit järjestyivät laimeissa vesiliuoksissa erilaisiksi misellirakenteiksi, muodostaen ns. mikrosäiliöitä. Tällaisilla polymeereillä odotetaan olevan sovelluksia esim. lääkeainevapautuksessa. Amfifiilejä käytetään myös esimerkiksi apuaineina pinnoitteissa ja kosmetiikassa. Kiinteässä tilassa tutkitut triblokkikopolymeerit muodostivat teoreettisesti ennustettuja morfologioita. Lämpöherkän materiaalin hydrogeelit toimivat suodatinmembraanina nanokokoluokassa. RAFT-polymeroinnilla syntetisoituja polymeereja voidaan sellaisenaan käyttää kultananopartikkeleiden päällystämiseen. Kultananopartikkelit ovat erittäin kiinostavia mm. niiden stabiilisuuden ja ainutlaatuisten pintaominaisuuksien vuoksi. Kun amfifiilisiä polymeerejä kiinnitettiin kultapartikkelin pinnalle, sen liuos- ja optisia ominaisuuksia voitiin säädellä pH:n ja lämpötilan avulla. Tällaisilla kultananopartikkeleilla on sovelluksia mm. diagnostiikassa, sensoreina ja solukuvauksessa.

Congregation Ohabei Shalom Brookline, Massachusetts collection, undated, 1909-1991

Temple Ohabei Shalom was founded on February 26, 1843 by several Boston Jewish families, and is the first synagogue established in Massachusetts. After meeting in the homes of both a founding congregant and the first elected Rabbi, Abraham Saling, Ohabei Shalom dedicated its first building on Warren (now Warrenton) Street in Boston in 1852. In 1855, the German Jewish congregants left Ohabei Shalom and founded Congregation Adath Israel (now Temple Israel in Boston.) The Polish Jewish congregants maintained the name Ohabei Shalom and the cemetery land in East Boston. In 1858, East Prussian Jews also left the congregation, forming Die Israelitische Gemeinde Mishkan Israel (now Miskhan Tefila in Chestnut Hill, Massachusetts.) This collection contains flyers, programs and tickets for events as well as copies of bulletins and newsletters, such as Brotherhood Bulletin, Stars and Stripes, Temple Bulletin and Temple Tidings.

Histone Deacetylases Regulate Multicellular Development in the Social Amoeba Dictyostelium discoideum

Epigenetic modifications of histones regulate gene expression and lead to the establishment and maintenance of cellular phenotypes during development. Histone acetylation depends on a balance between the activities of histone acetyltransferases and histone deacetylases (HDACs) and influences transcriptional regulation. In this study, we analyse the roles of HDACs during growth and development of one of the cellular slime moulds, the social amoeba Dictyostelium discoideum. The inhibition of HDAC activity by trichostatin A results in histone hyperacetylation and a delay in cell aggregation and differentiation. Cyclic AMP oscillations are normal in starved amoebae treated with trichostatin A but the expression of a subset of cAMP-regulated genes is delayed. Bioinformatic analysis indicates that there are four genes encoding putative HDACs in D. discoideum. Using biochemical, genetic and developmental approaches, we demonstrate that one of these four genes, hdaB, is dispensable for growth and development under laboratory conditions. A knockout of the hdaB gene results in a social context-dependent phenotype: hdaB- cells develop normally but sporulate less efficiently than the wild type in chimeras. We infer that HDAC activity is important for regulating the timing of gene expression during the development of D. discoideum and for defining aspects of the phenotype that mediate social behaviour in genetically heterogeneous groups.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Instability of Combustion

THE following equations governing the phenomenon of intrinsic instability of combustion, leading to low frequency oscillations in a rocket motor using a single liquid propellant, were derived and investigated by L. Crocco.

Dark matter dominance at all radii in the superthin galaxy UGC 7321

We model the shape and density profile of the dark matter halo of the low surface brightness, superthin galaxy UGC 7321, using the observed rotation curve and the H i scale height data as simultaneous constraints. We treat the galaxy as a gravitationally coupled system of stars and gas, responding to the gravitational potential of the dark matter halo. An isothermal halo of spherical shape with a core density in the range of View the MathML source and a core radius between 2.5 and 2.9 kpc, gives the best fit to the observations for a range of realistic gas parameters assumed. We find that the best-fit core radius is only slightly higher than the stellar disc scale length (2.1 kpc), unlike the case of the high surface brightness galaxies where the halo core radius is typically 3–4 times the disc scale length of the stars. Thus our model shows that the dark matter halo dominates the dynamics of the low surface brightness, superthin galaxy UGC 7321 at all radii, including the inner parts of the galaxy.

Every face on Vanity Fair’s Hollywood covers 1995-2008

‘Every face on Vanity Fair’s Hollywood covers 1995-2008’ renders an ethnographic-like study of Hollywood celebrity as a cinematic experience. Viewers are presented with constantly mutating portraits that violently twist and shear into other faces, while an immersive soundscape echoes the turbulent painterly surface. Through technical processes of scaling, looping and image morphing; the work explores a positive affectual response to the seductive power of celebrity imagery. Conceptually, given Vanity Fair magazine’s prestigious stature, the work also performs an ethnographic-mapping of the popularity of Hollywood stars over time, while at the same time creating in-between, ‘mutant’ versions of their visages. The installation explores the potential for fan-based responses to pop culture to lead to artworks that enable a more critical response to the subjective and intersubjective dynamics of celebrity portraiture. Questions are raised about how these cultural forms impact pop culture fans, and their role in the mapping of culture and social experience.

Intensity Oscillation in the Corona as Observed during the Total Solar Eclipse of 29 March 2006

We obtained the images of the eastern part of the solar corona in the Fe xiv 530.3 nm (green) and Fe x 637.4 nm (red) coronal emission lines during the total solar eclipse of 29 March 2006 at Manavgat, Antalya, Turkey. The images were obtained using a 35 cm Meade telescope equipped with a Peltier-cooled 2k x 2k CCD and 0.3 nm pass-band interference filters at the rates of 2.95 s (exposure times of 100 ms) and 2.0 s (exposure times of 300 ms) in the Fe xiv and Fe x emission lines,respectively. The analysis of the data indicates intensity variations at some locations with period of strongest power around 27 s for the green line and 20 s for the red line. These results confirm earlier findings of variations in the continuum intensity with periods in the range of 5 to 56 s by Singh et al. (Solar Phys. 170, 235, 1997). The wavelet analysis has been used to identify significant intensity oscillations at all pixels within our field of view. Significant oscillations with high probability estimates were detected for some locations only. These locations seem to follow the boundary of an active region and in the neighborhood, rather than within the loops themselves. These intensity oscillations may be caused by fast magneto-sonic waves in the solar corona and partly account for heating of the plasma in the corona.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Slow pressure modes in thin accretion discs

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber m = 1. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate through WKB analysis and numerical solution of the eigenvalue problem - that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrodinger like equation. The analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power-law discs, albeit for physically uninteresting values of the power-law index beta and barotropic index gamma.

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

Effect of pulse profile variations on measurement of eccentricity in orbits of Cen X-3 and SMC X-1

It has long been argued that better timing precision allowed by satellites like Rossi X-ray Timing Explorer (RXTE) will allow us to measure the orbital eccentricity and the angle of periastron of some of the bright persistent high-mass X-ray binaries (HMXBs) and hence a possible measurement of apsidal motion in these system. Measuring the rate of apsidal motion allows one to estimate the apsidal motion constant of the mass losing companion star and hence allows for the direct testing of the stellar structure models for these giant stars present in the HMXBs. In the present paper, we use the archival RXTE data of two bright persistent sources, namely Cen X-3 and SMC X-1, to measure the very small orbital eccentricity and the angle of periastron. We find that the small variations in the pulse profiles of these sources, rather than the intrinsic time resolution provided by RXTE, limit the accuracy with which we can measure arrival time of the pulses from these sources. This influences the accuracy with which one can measure the orbital parameters, especially the very small eccentricity and the angle of periastron in these sources. The observations of SMC X-1 in the year 2000 were taken during the high-flux state of the source and we could determine the orbital eccentricity and omega using this data set.