Complex structures and the Elie Cartan approach to the theory of spinors

Each isometric complex structure on a 2$\ell$-dimensional euclidean space $E$ corresponds to an identification of the Clifford algebra of $E$ with the canonical anticommutation relation algebra for $\ell$ ( fermionic) degrees of freedom. The simple spinors in the terminology of E.~Cartan or the pure spinors in the one of C. Chevalley are the associated vacua. The corresponding states are the Fock states (i.e. pure free states), therefore, none of the above terminologies is very good.Comment: 10

A Fintech Approach Towards Resolving the Young Adult Home Ownership Challenge

Housing prices globally remain very expensive for young adults while financial instruments to obtain them become more complicated, demanding, and discouraging, especially in the modern post global financial crisis (2007–2017). The way people acquire homes haven’t change over the last 100 years, maintaining the three classic and dominant alternatives which is either thorough mortgages, cash payments, or combination of these. Young adults have been underserved by financial institutions and their products have not yet met young adults’ conditions. This research has been directed to utilize today’s technology and contribute with innovative financing solutions that can addresses the young adults’ needs. The proposed Fintech approach presents the architecture of a technology-based platform whereby Co-sharing agreements between real estate developers and young adults can be created. Such agreements can be integrated into the financial institutions processes to efficiently address and serve this significant target group by delivering creative innovative financing alternatives

Ultra-low phase noise all-optical microwave generation setup based on commercial devices

In this paper, we present a very simple design based on commercial devices for the all-optical generation of ultra-low phase noise microwave signals. A commercial, fibered femtosecond laser is locked to a laser that is stabilized to a commercial ULE Fabry-Perot cavity. The 10 GHz microwave signal extracted from the femtosecond laser output exhibits a single sideband phase noise $\mathcal{L}(f)=-104 \ \mathrm{dBc}/\mathrm{Hz}$ at 1 Hz Fourier frequency, at the level of the best value obtained with such "microwave photonics" laboratory experiments \cite{Fortier2011}. Close-to-the-carrier ultra-low phase noise microwave signals will now be available in laboratories outside the frequency metrology field, opening up new possibilities in various domains.Comment: 8 pages, 3 figures. To be published in Applied Optics, early posting version available at http://www.opticsinfobase.org/ao/upcoming_pdf.cfm?id=23114

Vibrational dynamics of confined granular material

By means of two-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. We use irregular polygonal grains allowing for strong variability of solid fraction. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude and the square of gravity. Interestingly, compaction occurs during the extension of the packing, followed by decompaction in the contraction phase. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency and then it declines in inverse proportion to frequency. The characteristic frequency is interpreted in terms of the time required for the relaxation of the packing through collective grain rearrangements between two equilibrium states

Damping rate of plasmons and photons in a degenerate nonrelativistic plasma

A calculation is presented of the plasmon and photon damping rates in a dense nonrelativistic plasma at zero temperature, following the resummation program of Braaten-Pisarski. At small soft momentum $k$, the damping is dominated by $3 \to 2$ scattering processes corresponding to double longitudinal Landau damping. The dampings are proportional to $(\alpha/v_{F})^{3/2} k^2/m$, where $v_{F}$ is the Fermi velocity.Comment: 9 pages, 2 figure

Spin glass behavior in an interacting gamma-Fe2O3 nanoparticle system

In this paper we investigate the superspin glass behavior of a concentrated assembly of interacting maghemite nanoparticles and compare it to that of canonical atomic spin glass systems. ac versus temperature and frequency measurements show evidence of a superspin glass transition taking place at low temperature. In order to fully characterize the superspin glass phase, the aging behavior of both the thermo-remanent magnetization (TRM) and ac susceptibility has been investigated. It is shown that the scaling laws obeyed by superspin glasses and atomic spin glasses are essentially the same, after subtraction of a superparamagnetic contribution from the superspin glass response functions. Finally, we discuss a possible origin of this superparamagnetic contribution in terms of dilute spin glass models

N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Force chains and contact network topology in packings of elongated particles

By means of contact dynamic simulations, we investigate the contact network topology and force chains in two-dimensional packings of elongated particles modeled by rounded-cap rectangles. The morphology of large packings of elongated particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and orientations of contacts between particles. We show that particle elongation affects force distributions and force/fabric anisotropy via various local structures allowed by steric exclusions and the requirement of force balance. As a result, the force distributions become increasingly broader as particles become more elongated. Interestingly, the weak force network transforms from a passive stabilizing agent with respect to strong force chains to an active force-transmitting network for the whole system. The strongest force chains are carried by side/side contacts oriented along the principal stress direction.Comment: Soumis a Physical Review