The scale of homogeneity in the Las Campanas Redshift Survey

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/$h$) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/$h$, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data.Comment: 8 pages, 3 figures, accepted on Ap.J. Letter

Measuring the cosmological constant with redshift surveys

It has been proposed that the cosmological constant $\Lambda$ might be measured from geometric effects on large-scale structure. A positive vacuum density leads to correlation-function contours which are squashed in the radial direction when calculated assuming a matter-dominated model. We show that this effect will be somewhat harder to detect than previous calculations have suggested: the squashing factor is likely to be $<1.3$, given realistic constraints on the matter contribution to $\Omega$. Moreover, the geometrical distortion risks being confused with the redshift-space distortions caused by the peculiar velocities associated with the growth of galaxy clustering. These depend on the density and bias parameters via the combination $\beta\equiv \Omega^{0.6}/b$, and we show that the main practical effect of a geometrical flattening factor $F$ is to simulate gravitational instability with $\beta_{\rm eff}\simeq 0.5(F-1)$. Nevertheless, with datasets of sufficient size it is possible to distinguish the two effects; we discuss in detail how this should be done. New-generation redshift surveys of galaxies and quasars are potentially capable of detecting a non-zero vacuum density, if it exists at a cosmologically interesting level.Comment: MNRAS in press. 12 pages LaTeX including Postscript figures. Uses mn.sty and epsf.st

Semiconductor filled microstructured optical fibres with single mode guidance

Microstructured optical fibre (MOF) technology has generated new opportunities for the implementation of optical fibres with novel properties and functions [1]. It has been shown that silica MOFs make excellent 3D templates for semiconductor material deposition inside the capillary voids [2]. Recently a silicon MOF was designed and fabricated that had a high refractive index micron sized core, but yet only supported two guided modes [3]. This structure was realised via the complete filling of a hollow core photonic bandgap fibre (PBGF) with silicon so that the original air guiding PBGF was converted to a total internal reflection guiding fibre. Here, we extend the investigation by using a finite element method to model the optical properties of semiconductor filled MOFs of similar structures, with the aim to achieve broadband single mode guidance. Strategies to achieve single mode guidance both through the MOF template design and the selective filling of the voids of the original PBGF with semiconductor materials of different indices (silicon, silicon nitride, germanium) are proposed and investigated numerically. In particular, by selectively filling MOF templates with cladding rods that have a slightly raised index over that of the core, index guiding single mode operation can be observed in high index micron sized cores. Small index differences are achievable by controlling the nitrogen content in SiNx and an example of a single mode semiconductor MOF is shown in Figure 1, where the confinement loss of the fundamental mode is ~106 lower than the lowest order cladding mode

An upper bound for the representation dimension of group algebras with an elementary abelian Sylow pp-subgroup

Linckelmann showed in 2011 that a group algebra is separably equivalent to the group algebra of its Sylow p-subgroups. In this article we use this relationship, together with Mackey decomposition, to demonstrate that a group algebra of a group with an elementary abelian Sylow $p$-subgroup $P$, has representation dimension at most $|P|$

Decomposition algebras and axial algebras

We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field, thereby allowing repetition of eigenvalues; (2) They allow for decompositions that do not arise from multiplication by idempotents; (3) They admit a natural notion of homomorphisms, making them into a nice category. We exploit these facts to strengthen the connection between axial algebras and groups. In particular, we provide a definition of a universal Miyamoto group which makes this connection functorial under some mild assumptions. We illustrate our theory by explaining how representation theory and association schemes can help to build a decomposition algebra for a given (permutation) group. This construction leads to a large number of examples. We also take the opportunity to fix some terminology in this rapidly expanding subject.Comment: 23 page

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim

The DCU laser ion source

Laser ion sources are used to generate and deliver highly charged ions of various masses and energies. We present details on the design and basic parameters of the DCU laser ion source (LIS). The theoretical aspects of a high voltage (HV) linear LIS are presented and the main issues surrounding laser-plasma formation, ion extraction and modeling of beam transport in relation to the operation of a LIS are detailed. A range of laser power densities (I ∼ 108–1011 W cm−2) and fluences (F = 0.1–3.9 kJ cm−2) from a Q-switched ruby laser (full-width half-maximum pulse duration ∼ 35 ns, λ = 694 nm) were used to generate a copper plasma. In “basic operating mode,” laser generated plasma ions are electrostatically accelerated using a dc HV bias (5–18 kV). A traditional einzel electrostatic lens system is utilized to transport and collimate the extracted ion beam for detection via a Faraday cup. Peak currents of up to I ∼ 600 μA for Cu+ to Cu3+ ions were recorded. The maximum collected charge reached 94 pC (Cu2+). Hydrodynamic simulations and ion probe diagnostics were used to study the plasma plume within the extraction gap. The system measured performance and electrodynamic simulations indicated that the use of a short field-free (L = 48 mm) region results in rapid expansion of the injected ion beam in the drift tube. This severely limits the efficiency of the electrostatic lens system and consequently the sources performance. Simulations of ion beam dynamics in a “continuous einzel array” were performed and experimentally verified to counter the strong space-charge force present in the ion beam which results from plasma extraction close to the target surface. Ion beam acceleration and injection thus occur at “high pressure.” In “enhanced operating mode,” peak currents of 3.26 mA (Cu2+) were recorded. The collected currents of more highly charged ions (Cu4+–Cu6+) increased considerably in this mode of operation

An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution

We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model is designed so that it predicts a relation between the peculiar velocity and density contrast that agrees with the results of N-body simulations in the region where such a comparison can sensibly be made. Prior to turnaround, when the unmodified spherical collapse model is expect to be a good approximation, the predictions of the two models coincide almost exactly. The effects of a late time dominating dark energy component are also taken into account. The improved spherical collapse model is a useful tool when one requires a good approximation not just to the evolution of the density contrast but also its trajectory. Moreover, the analytical fitting formulae presented is simple enough to be used anywhere where the standard spherical collapse might be used but with the advantage that it includes a realistic model of the effects of virialisation.Comment: 6 pages, 3 figures. Matches the version in print at Astrophys.

Lensing effect on the relative orientation between the Cosmic Microwave Background ellipticities and the distant galaxies

The low redshift structures of the Universe act as lenses in a similar way on the Cosmic Microwave Background light and on the distant galaxies (say at redshift about unity). As a consequence, the CMB temperature distortions are expected to be statistically correlated with the galaxy shear, exhibiting a non-uniform distribution of the relative angle between the CMB and the galactic ellipticities. Investigating this effect we find that its amplitude is as high as a 10% excess of alignement between CMB and the galactic ellipticities relative to the uniform distribution. The relatively high signal-to-noise ratio we found should makes possible a detection with the planned CMB data sets, provided that a galaxy survey follow up can be done on a sufficiently large area. It would provide a complementary bias-independent constraint on the cosmological parameters.Comment: 7 pages, 3 figures; uses emulateapj.sty; submitted to Ap