Geometry and Topology of Random 2-complexes

We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be aspherical; this implies that any aspherical subcomplex of a random 2-complex satisfies the Whitehead conjecture. We use inequalities for Cheeger constants and systoles of simplicial surfaces to analyse spheres and projective planes lying in random 2-complexes. Our proofs exploit the strong hyperbolicity property of random 2-complexes.Comment: 37 page

The asphericity of random 2-dimensional complexes

We study random 2-dimensional complexes in the Linial - Meshulam model and prove that for the probability parameter satisfying $$p\ll n^{-46/47}$$ a random 2-complex $Y$ contains several pairwise disjoint tetrahedra such that the 2-complex $Z$ obtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complex $Z$ satisfies the Whitehead conjecture, i.e. any subcomplex $Z'\subset Z$ is aspherical. This implies that $Y$ is homotopy equivalent to a wedge $Z\vee S^2\vee...\vee S^2$ where $Z$ is a 2-dimensional aspherical simplicial complex. We also show that under the assumptions $$c/n3$and$0<\epsilon<1/47$, the complex$Z$is genuinely 2-dimensional and in particular, it has sizable 2-dimensional homology; it follows that in the indicated range of the probability parameter$p$the cohomological dimension of the fundamental group$\pi_1(Y)$ of a random 2-complex equals 2.Comment: 11 pages, 2 figure

On Stability of Sampling-Reconstruction Models

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and quantify the robustness of a model with respect to them. We also use the theory of localized frames to study the frame algorithm for recovering the original signal from its samples.Comment: 26 page

Pull-back components of the space of foliations of codimension ≥2\ge2

We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on $\mathbb P^{n}$, $n\geq3$, $k\ge2$. They are associated to pull-back of dimension one foliations on $\mathbb P^{n-k+1}$ by non-linear rational maps

Reply to "Comment on 'Background Thermal Contributions in Testing the Unruh effect' "

Park et al's recent comment (hep-th/9605132) that for detectors with large energy gap in comparison with the temperature of the background thermal bath, the maximum excitation rate is obtained for some non-zero detector's velocity is correct but was previously discussed by ourselves elsewhere, and moreover does not affect in our paper above any mathematical formula, numerical result, and consequently our final conclusion that the background thermal bath does not contribute substantially in the depolarization of electrons at LEP.Comment: 4 pages, (REVTEX 3.0

MHD simulations of coronal supra-arcade downflows including anisotropic thermal conduction

Coronal supra-arcade downflows (SADs) are observed as dark trails descending towards hot turbulent fan shaped regions. Due to the large temperature values, and gradients in these fan regions the thermal conduction should be very efficient. While several models have been proposed to explain the triggering and the evolution of SADs, none of these scenarios address a systematic consideration of thermal conduction. Thus, we accomplish this task numerically simulating the evolution of SADs within this framework. That is, SADs are conceived as voided (subdense) cavities formed by non-linear waves triggered by downflowing bursty localized reconnection events in a perturbed hot fan. We generate a properly turbulent fan, obtained by a stirring force that permits control of the energy and vorticity input in the medium where SADs develop. We include anisotropic thermal conduction and consider plasma properties consistent with observations. Our aim is to study if it is possible to prevent SADs to vanish by thermal diffusion. We find that this will be the case, depending on the turbulence parameters. In particular, if the magnetic field lines are able to envelope the voided cavities, thermally isolating them from the hot environment. Velocity shear perturbations that are able to generate instabilities of the Kelvin-Helmholtz type help to produce magnetic islands, extending the life-time of SADs

3D MHD simulation of flare supra-arcade downflows in a turbulent current sheet medium

Supra-arcade downflows (SADs) are sunward, generally dark, plasma density depletions originated above posteruption flare arcades. In this paper using 3D MHD simulations we investigate if the SAD cavities can be produced by a direct combination of the tearing mode and Kelvin-Helmholtz instabilities leading to a turbulent current sheet (CS) medium or if the current sheet is merely the background where SADs are produced triggered by an impulsive deposition of energy. We find that to give account of the observational dark lane structures an addition of local energy, provided by a reconnection event, is required. We suggest that there may be a closed relation between characteristic SAD sizes and CS widths that must be satisfied to obtain an observable SAD.Comment: 12 pages, 10 figures. Accepted for publication in The Astrophysical Journa

Decaying Vacuum Cosmology and its Scalar Field Description

We discuss the cosmological consequences of an interacting model in the dark sector in which the $\Lambda$ component evolves as a truncated power series of the Hubble parameter. In order to constrain the free parameters of the model we carry out a joint statistical analysis involving observational data from current type Ia supernovae, recent estimates of the cosmic microwave background shift parameter and baryon acoustic oscillations measurements. Finally, we adopt a theoretical method to derive the coupled scalar field version for this non-equilibrium decaying vacuum accelerating cosmology.Comment: 5 pages, 2 figure

Dynamical and observational analysis of interacting models

We investigate the dynamical behaviour of a general class of interacting models in the dark sector in which the phenomenological coupling between cold dark matter and dark energy is a power law of the cosmic scale factor. From numerical simulations we show that, in this background, dark energy always dominates the current composition cosmic. This behaviour may alleviate substantially the coincidence problem. By using current type Ia supernovae, baryonic acoustic oscillations and cosmic microwave background data, we perform a joint statistical analysis and obtain constraints on free parameters of this class of model

The puzzling MgAl anticorrelation in globular-cluster red giants: primordial plus deep mixing scenario?

Star-to-star abundance variations of C, N, O, Na and Al in globular-cluster red giants have been recently supplemented by the finding that [Mg/Fe] is depleted in stars with extremely large [Al/Fe] (Shetrone 1996a). This and other new spectroscopic results allow us to test current models of stellar evolution and nucleosynthesis, as well as those of the formation and chemical enrichment of globular clusters. In an effort to explain self-consistently these observations we have considered two possibilities: (1) a deep mixing scenario which assumes that in red giants some kind of (extra)mixing transports products of nuclear reactions from the hydrogen burning shell (HBS) to the base of the convective envelope; and (2) a combination of primordial and deep mixing scenarios. It is shown that (1) cannot account for the anticorrelation of [Mg/Fe] vs. [Al/Fe] without additional ad hoc assumptions, among which we identify a strong but still undetected low energy resonance in the reaction 24Mg(p,gamma)25Al, and episodical increases of the HBS temperature up to the value T approx. 74x10^6 K. In (2) intermediate mass AGB stars are assumed to produce the decreased 24Mg and increased 25Mg initial abundances in some globular-cluster low mass stars and Al is synthesized at the expense of 25Mg in the HBS and transported to the surface of the red giant by extramixing. We discuss advantages and deficiencies of both scenarios and propose some observational tests.Comment: 22 pages, 8 figures included; submitted to A&