Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Absorption characteristics of a quantum dot array induced intermediate band: implications for solar cell design

We present a theoretical study of the electronic and absorption properties of the intermediate band (IB) formed by a three dimensional structure of InAs/GaAs quantum dots (QDs) arranged in a periodic array. Analysis of the electronic and absorption structures suggests that the most promising design for an IB solar cell material, which will exhibit its own quasi-Fermi level, is to employ small QDs (~6–12 nm QD lateral size). The use of larger QDs leads to extension of the absorption spectra into a longer wavelength region but does not provide a separate IB in the forbidden energy gap

Chaotic dynamics of the planet in HD 196885 AB

Depending on the planetary orbit around the host star(s), a planet could orbit either one or both stars in a binary system as S-type or P-type, respectively. We have analysed the dynamics of the S-type planetary system in HD 196885 AB with an emphasis on a planet with a higher orbital inclination relative to the binary plane. The mean exponential growth factor of nearby orbits (MEGNO) maps are used as an indicator to determine regions of periodicity and chaos for the various choices of the planet's semimajor axis, eccentricity and inclination with respect to the previously determined observational uncertainties. We have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space which indicate a likely regime of the planet's inclination. In addition, we inspect the resonant angle to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a very large inclination. Also, we demonstrate the possible higher mass limit of the planet and improve upon the current dynamical model based on our analysis.Comment: 10 pages, 9 figures (Accepted for publication at MNRAS

Ideas for the Arcturus personal workstation

In order to achieve more effective use of interpersonal collaboration, management lifecycle activities, and dynamic retrieval of as well as for ordinary programming chores, it may be useful to take a fresh look at the devices we use to help us conduct our transactions with computers.This paper presents some new ideas for using large flatscreen displays and dedicated computers as personal workstations

Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers

We use a long, all-atom molecular dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine (DMPC) lipid bilayer. From the analysis of a 0.1 $\mu$s MD trajectory we find that the time evolution of the mean square displacement, [\delta{r}(t)]^2, of lipid atoms and molecules exhibits three well separated dynamical regions: (i) ballistic, with [\delta{r}(t)]^2 ~ t^2 for t < 10 fs; (ii) subdiffusive, with [\delta{r}(t)]^2 ~ t^{\beta} with \beta<1, for 10 ps < t < 10 ns; and (iii) Fickian diffusion, with [\delta{r}(t)]^2 ~ t for t > 30 ns. We propose a memory function approach for calculating [\delta{r}(t)]^2 over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamics structure factor measured in neutron scattering experiments.Comment: Submitted to Phys. Rev.

SN2012ab: A Peculiar Type IIn Supernova with Aspherical Circumstellar Material

We present photometry, spectra, and spectropolarimetry of supernova (SN) 2012ab, mostly obtained over the course of $\sim 300$ days after discovery. SN 2012ab was a Type IIn (SN IIn) event discovered near the nucleus of spiral galaxy 2MASXJ12224762+0536247. While its light curve resembles that of SN 1998S, its spectral evolution does not. We see indications of CSM interaction in the strong intermediate-width emission features, the high luminosity (peak at absolute magnitude $M=-19.5$), and the lack of broad absorption features in the spectrum. The H$\alpha$ emission undergoes a peculiar transition. At early times it shows a broad blue emission wing out to $-14{,}000$ km $\mathrm{s^{-1}}$ and a truncated red wing. Then at late times ($>$ 100$\,$days) it shows a truncated blue wing and a very broad red emission wing out to roughly $+20{,}000$ km $\mathrm{s^{-1}}$. This late-time broad red wing probably arises in the reverse shock. Spectra also show an asymmetric intermediate-width H$\alpha$ component with stronger emission on the red side at late times. The evolution of the asymmetric profiles requires a density structure in the distant CSM that is highly aspherical. Our spectropolarimetric data also suggest asphericity with a strong continuum polarization of $\sim 1-3$% and depolarization in the H$\alpha$ line, indicating asphericity in the CSM at a level comparable to that in other SNe IIn. We estimate a mass-loss rate of $\dot{M} = 0.050\, {\rm M}_{\odot}\,\mathrm{yr^{-1}}$ for $v_{\rm pre} = 100$$\,$km$\,$$\mathrm{s^{-1}}$ extending back at least 75$\,$yr prior to the SN. The strong departure from axisymmetry in the CSM of SN 2012ab may suggest that the progenitor was an eccentric binary system undergoing eruptive mass loss.Comment: 18 pages, 12 figure

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.Comment: 26 pages, 11 figures. To appear in J. Stat. Phy

Conditional expectations, traces, angles between spaces and Representations of the Hecke algebras

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more general, vector valued case. This method is used to analyze the traces of the Hecke operators. We construct representations of the Hecke algebra of a group $G$, relative to an almost normal subgroup $\Gamma$, into the von Neumann algebra of the group $G$, tensor matrices. The representations we obtain are a lifting of the Hecke operators to this larger algebra. By summing up the coefficients of the terms in the representation one obtains the classical Hecke operators. These representations were used in the scalar case in [Ra], to find an alternative representation of the Hecke operators on Maass forms, and hence to reformulate the Ramanujan Petersson conjectures as a problem on the angle (see e.g. A. Connes's paper [Co] on the generalization of CKM matrix) between two subalgebras of the von Neumann algebra of the group $G$: the image of the representation of the Hecke algebra and the algebra of the almost normal subgroup.Comment: This is print versio