Power Spectrum of Velocity Fluctuations in the Universe

We investigate the power spectrum of velocity fluctuations in the universe, $V^2(k)$, starting from four different measures of velocity: (1) the power spectrum of velocity fluctuations from peculiar velocities of galaxies; (2) the rms peculiar velocity of galaxy clusters; (3) the power spectrum of velocity fluctuations from the power spectrum of density fluctuations in the galaxy distribution; (4) and the bulk velocity from peculiar velocities of galaxies. We show that measures (1) and (2) are not consistent with each other and either the power spectrum from peculiar velocities of galaxies is overestimated or the rms cluster peculiar velocity is underestimated. The amplitude of velocity fluctuations derived from the galaxy distribution (measure 3) depends on the parameter $\beta$. We estimate the parameter $\beta$ on the basis of measures (2) and (4). The power spectrum of velocity fluctuations from the galaxy distribution in the Stromlo-APM redshift survey is consistent with the observed rms cluster velocity and with the observed large-scale bulk flow when the parameter $\beta$ is in the range 0.4-0.5. In this case the value of the function $V(k)$ at wavelength $\lambda=120h^{-1}$Mpc is $\sim 350$ km s$^{-1}$ and the rms amplitude of the bulk flow at the radius $r=60h^{-1}$ Mpc is $\sim 340$ km s$^{-1}$. The velocity dispersion of galaxy systems originates mostly from the large-scale velocity fluctuations with wavelengths $\lambda >100h^{-1}$ Mpc.Comment: Astrophysical Journal, Vol. 493, in press: 23 pages, uses AAS Latex, and 14 separate postscript figure

Contrasting alterations to synaptic and intrinsic properties in upper-cervical superficial dorsal horn neurons following acute neck muscle inflammation

Background: Acute and chronic pain in axial structures, like the back and neck, are difficult to treat, and have incidence as high as 15%. Surprisingly, most preclinical work on pain mechanisms focuses on cutaneous structures in the limbs and animal models of axial pain are not widely available. Accordingly, we developed a mouse model of acute cervical muscle inflammation and assessed the functional properties of superficial dorsal horn (SDH) neurons.<p></p> Results: Male C57/Bl6 mice (P24-P40) were deeply anaesthetised (urethane 2.2?g/kg i.p) and the rectus capitis major muscle (RCM) injected with 40??l of 2% carrageenan. Sham animals received vehicle injection and controls remained anaesthetised for 2?hrs. Mice in each group were sacrificed at 2?hrs for analysis. c-Fos staining was used to determine the location of activated neurons. c-Fos labelling in carrageenan-injected mice was concentrated within ipsilateral (87% and 63% of labelled neurons in C1 and C2 segments, respectively) and contralateral laminae I - II with some expression in lateral lamina V. c-Fos expression remained below detectable levels in control and sham animals. In additional experiments, whole cell recordings were obtained from visualised SDH neurons in transverse slices in the ipsilateral C1 and C2 spinal segments. Resting membrane potential and input resistance were not altered. Mean spontaneous EPSC amplitude was reduced by ~20% in neurons from carrageenan-injected mice versus control and sham animals (20.63???1.05 vs. 24.64???0.91 and 25.87???1.32 pA, respectively). The amplitude (238???33 vs. 494???96 and 593???167 pA) and inactivation time constant (12.9???1.5 vs. 22.1???3.6 and 15.3???1.4?ms) of the rapid A type potassium current (IAr), the dominant subthreshold current in SDH neurons, were reduced in carrageenan-injected mice.<p></p> Conclusions: Excitatory synaptic drive onto, and important intrinsic properties (i.e., IAr) within SDH neurons are reduced two hours after acute muscle inflammation. We propose this time point represents an important transition period between peripheral and central sensitisation with reduced excitatory drive providing an initial neuroprotective mechanism during the early stages of the progression towards central sensitisation

Steps toward the power spectrum of matter. I.The mean spectrum of galaxies

We calculate the mean power spectrum of galaxies using published power spectra of galaxies and clusters of galaxies. On small scales we use the power spectrum derived from the 2-dimensional distribution of APM galaxies, on large scales we use power spectra derived from 3-dimensional data for galaxy and cluster samples. Spectra are reduced to real space and to the amplitude of the power spectrum of APM galaxies. Available data indicate the presence of two different populations in the nearby Universe. Clusters of galaxies sample a relatively large region in the Universe where rich, medium and poor superclusters are well represented. Their mean power spectrum has a spike on scale 120 h^{-1}Mpc, followed by an approximate power-law spectrum of index n = -1.9 towards small scales. The power spectrum found from LCRS and IRAS 1.2 Jy surveys is flatter around the maximum, which may represent regions of the Universe with medium-rich and poor superclusters.Comment: LaTex (sty files added), 35 pages, 5 PostScript figures and Table with mean power spectrum embedded, Astrophysical Journal (accepted

Measuring the galaxy power spectrum with future redshift surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.Comment: Major revisions for clarity. Matches accepted ApJ version. 23 pages, with 2 figs included. Color figure and links at http://www.sns.ias.edu/~max/galpower.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/galpower.html (faster from Europe) or from [email protected]

End Zone Reinforcement for Pretensioned Concrete Girders

In this study, a literature review was conducted to establish the background of current specifications and to evaluate the applicability of various theories and methods for design of end zone reinforcement. Analytical methods reviewed in this paper include finite element analysis, strut-and-tie modeling, and the Gergely-Sozen equivalent beam method. Previous experimental work combined with work conducted as part of this study was used to correlate between various theoretical and experimental results. This paper illustrates that no single theoretical method adequately represents the complex behavior at the end of a pretensioned concrete member. A general semi-empirical design procedure is proposed here. It is based on theoretical behavior and experimental observation. Standard reinforcement details are given. The proposed procedure could result in significant reduction in the amount of reinforcement while maintaining acceptable crack control at the member end. Application of the proposed procedure to highly pretensioned bridge girders is demonstrated

An Inversion Method for Measuring Beta in Large Redshift Surveys

A precision method for determining the value of Beta= Omega_m^{0.6}/b, where b is the galaxy bias parameter, is presented. In contrast to other existing techniques that focus on estimating this quantity by measuring distortions in the redshift space galaxy-galaxy correlation function or power spectrum, this method removes the distortions by reconstructing the real space density field and determining the value of Beta that results in a symmetric signal. To remove the distortions, the method modifies the amplitudes of a Fourier plane-wave expansion of the survey data parameterized by Beta. This technique is not dependent on the small-angle/plane-parallel approximation and can make full use of large redshift survey data. It has been tested using simulations with four different cosmologies and returns the value of Beta to +/- 0.031, over a factor of two improvement over existing techniques.Comment: 16 pages including 6 figures Submitted to The Astrophysical Journa