The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.

Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for Reduced Harmonic Distortion and Switching Loss

Novel switching sequences can be employed in spacevector-based pulsewidth modulation (PWM) of voltage source inverters. Differentswitching sequences are evaluated and compared in terms of inverter switching loss. A hybrid PWM technique named minimum switching loss PWM is proposed, which reduces the inverter switching loss compared to conventional space vector PWM (CSVPWM) and discontinuous PWM techniques at a given average switching frequency. Further, four space-vector-based hybrid PWM techniques are proposed that reduce line current distortion as well as switching loss in motor drives, compared to CSVPWM. Theoretical and experimental results are presented.

Instability of Coupled Longitudinal and Transverse Electromagnetic Modes of Wave‐Propagation in Bounded Streaming Plasmas

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k 2)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<0.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k3)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k2)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.

MECHANISMS AND EFFECTS OF MITOCHONDRIAL DNA INSTABILITY AND COPY NUMBER MANIPULATION

Defects in mitochondrial DNA (mtDNA) maintenance cause a range of human diseases, including autosomal dominant progressive external ophthalmoplegia (adPEO). This study aimed to clarify the molecular background of adPEO. We discovered that deoxynucleoside triphosphate (dNTP) metabolism plays a crucial in mtDNA maintenance and were thus prompted to search for therapeutic strategies based on the modulation of cellular dNTP pools or mtDNA copy number. Human mtDNA is a 16.6 kb circular molecule present in hundreds to thousands of copies per cell. mtDNA is compacted into nucleoprotein clusters called nucleoids. mtDNA maintenance diseases result from defects in nuclear encoded proteins that maintain the mtDNA. These syndromes typically afflict highly differentiated, post-mitotic tissues such as muscle and nerve, but virtually any organ can be affected. adPEO is a disease where mtDNA molecules with large-scale deletions accumulate in patients tissues, particularly in skeletal muscle. Mutations in five nuclear genes, encoding the proteins ANT1, Twinkle, POLG, POLG2 and OPA1, have previously been shown to cause adPEO. Here, we studied a large North American pedigree with adPEO, and identified a novel heterozygous mutation in the gene RRM2B, which encodes the p53R2 subunit of the enzyme ribonucleotide reductase (RNR). RNR is the rate-limiting enzyme in dNTP biosynthesis, and is required both for nuclear and mitochondrial DNA replication. The mutation results in the expression of a truncated form of p53R2, which is likely to compete with the wild-type allele. A change in enzyme function leads to defective mtDNA replication due to altered dNTP pools. Therefore, RRM2B is a novel adPEO disease gene. The importance of adequate dNTP pools and RNR function for mtDNA maintenance has been established in many organisms. In yeast, induction of RNR has previously been shown to increase mtDNA copy number, and to rescue the phenotype caused by mutations in the yeast mtDNA polymerase. To further study the role of RNR in mammalian mtDNA maintenance, we used mice that broadly overexpress the RNR subunits Rrm1, Rrm2 or p53R2. Active RNR is a heterotetramer consisting of two large subunits (Rrm1) and two small subunits (either Rrm2 or p53R2). We also created bitransgenic mice that overexpress Rrm1 together with either Rrm2 or p53R2. In contrast to the previous findings in yeast, bitransgenic RNR overexpression led to mtDNA depletion in mouse skeletal muscle, without mtDNA deletions or point mutations. The mtDNA depletion was associated with imbalanced dNTP pools. Furthermore, the mRNA expression levels of Rrm1 and p53R2 were found to correlate with mtDNA copy number in two independent mouse models, suggesting nuclear-mitochondrial cross talk with regard to mtDNA copy number. We conclude that tight regulation of RNR is needed to prevent harmful alterations in the dNTP pool balance, which can lead to disordered mtDNA maintenance. Increasing the copy number of wild-type mtDNA has been suggested as a strategy for treating PEO and other mitochondrial diseases. Only two proteins are known to cause a robust increase in mtDNA copy number when overexpressed in mice; the mitochondrial transcription factor A (TFAM), and the mitochondrial replicative helicase Twinkle. We studied the mechanisms by which Twinkle and TFAM elevate mtDNA levels, and showed that Twinkle specifically implements mtDNA synthesis. Furthermore, both Twinkle and TFAM were found to increase mtDNA content per nucleoid. Increased mtDNA content in mouse tissues correlated with an age-related accumulation of mtDNA deletions, depletion of mitochondrial transcripts, and progressive respiratory dysfunction. Simultaneous overexpression of Twinkle and TFAM led to a further increase in the mtDNA content of nucleoids, and aggravated the respiratory deficiency. These results suggested that high mtDNA levels have detrimental long-term effects in mice. These data have to be considered when developing and evaluating treatment strategies for elevating mtDNA copy number.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

A cost effective pipelined divider for double precision floating point number

he growth of high-performance application in computer graphics, signal processing and scientific computing is a key driver for high performance, fixed latency; pipelined floating point dividers. Solutions available in the literature use large lookup table for double precision floating point operations.In this paper, we propose a cost effective, fixed latency pipelined divider using modified Taylor-series expansion for double precision floating point operations. We reduce chip area by using a smaller lookup table. We show that the latency of the proposed divider is 49.4 times the latency of a full-adder. The proposed divider reduces chip area by about 81% than the pipelined divider in [9] which is based on modified Taylor-series.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

An Estimator Algorithm For Learning Automata With Changing Number Of Actions

In many problems of decision making under uncertainty the system has to acquire knowledge of its environment and learn the optimal decision through its experience. Such problems may also involve the system having to arrive at the globally optimal decision, when at each instant only a subset of the entire set of possible alternatives is available. These problems can be successfully modelled and analysed by learning automata. In this paper an estimator learning algorithm, which maintains estimates of the reward characteristics of the random environment, is presented for an automaton with changing number of actions. A learning automaton using the new scheme is shown to be e-optimal. The simulation results demonstrate the fast convergence properties of the new algorithm. The results of this study can be extended to the design of other types of estimator algorithms with good convergence properties.

Design of crosspoint-irredundant PLAs using minimal number of control inputs

The problem of determining a minimal number of control inputs for converting a programmable logic array (PLA) with undetectable faults to crosspoint-irredundant PLA for testing has been formulated as a nonstandard set covering problem. By representing subsets of sets as cubes, this problem has been reformulated as familiar problems. It is noted that this result has significance because a crosspoint-irredundant PLA can be converted to a completely testable PLA in a straightforward fashion, thus achieving very good fault coverage and easy testability.

Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.