Analysis of Nonlinear Noisy Integrate\&Fire Neuron Models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter

Archeops: an instrument for present and future cosmology

Archeops is a balloon-borne instrument dedicated to measure the cosmic microwave background (CMB) temperature anisotropies. It has, in the millimetre domain (from 143 to 545 GHz), a high angular resolution (about 10 arcminutes) in order to constrain high l multipoles, as well as a large sky coverage fraction (30%) in order to minimize the cosmic variance. It has linked, before WMAP, Cobe large angular scales to the first acoustic peak region. From its results, inflation motivated cosmologies are reinforced with a flat Universe (Omega_tot=1 within 3%). The dark energy density and the baryonic density are in very good agreement with other independent estimations based on supernovae measurements and big bang nucleosynthesis. Important results on galactic dust emission polarization and their implications for Planck are also addressed.Comment: 4 pages, 2 figures, to appear in Proceedings of the Multiwavelength Cosmology Conference, June 2003, Mykonos Island, Greec

Submillimetre point sources from the Archeops experiment: Very Cold Clumps in the Galactic Plane

Archeops is a balloon-borne experiment, mainly designed to measure the Cosmic Microwave Background (CMB) temperature anisotropies at high angular resolution (~ 12 arcminutes). By-products of the mission are shallow sensitivity maps over a large fraction of the sky (about 30 %) in the millimetre and submillimetre range at 143, 217, 353 and 545 GHz. From these maps, we produce a catalog of bright submillimetre point sources. We present in this paper the processing and analysis of the Archeops point sources. Redundancy across detectors is the key factor allowing to sort out glitches from genuine point sources in the 20 independent maps. We look at the properties of the most reliable point sources, totalling 304. Fluxes range from 1 to 10,000 Jy (at the frequencies covering 143 to 545 GHz). All sources are either planets (2) or of galactic origin. Longitude range is from 75 to 198 degrees. Some of the sources are associated with well-known Lynds Nebulae and HII compact regions in the galactic plane. A large fraction of the sources have an IRAS counterpart. Except for Jupiter, Saturn, the Crab and Cas A, all sources show a dust-emission-like modified blackbody emission spectrum. Temperatures cover a range from 7 to 27 K. For the coldest sources (T<10 K), a steep nu^beta emissivity law is found with a surprising beta ~ 3 to 4. An inverse relationship between T and beta is observed. The number density of sources at 353 GHz with flux brighter than 100 Jy is of the order of 1 per degree of Galactic longitude. These sources will provide a strong check for the calibration of the Planck HFI focal plane geometry as a complement to planets. These very cold sources observed by Archeops should be prime targets for mapping observations by the Akari and Herschel space missions and ground--based observatories.Comment: Version matching the published article (English improved). Published in Astron. Astrophys, 21 pages, 13 figures, 4 tables Full article (with complete tables) can be retrieved at http://www.archeops.org/Archeops_Publicatio

Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios like scattering of light in nonlinear Kerr media, or propagation of matter waves in disordered potentials.Comment: 4 pages, 3 figure

Temperature dependence in random matrix models with pairing condensates

We address a number of issues raised by a manuscript of Klein, Toublan, and Verbaarschot (hep-ph/0405180) in which the authors introduce a random matrix model for QCD with two colors, two flavors, and fermions in the fundamental representation. Their inclusion of temperature terms differs from the approach adopted in previous work on this problem (Phys. Rev. D 64, 074016 (2001).) We demonstrate that the two approaches are related by a transformation that leaves the thermodynamic potential invariant and which therefore has no effect on physical observables.Comment: 8 pages, revtex4. v2: typos corrected in reference

Geometry fluctuations in a two-dimensional quantum antiferromagnet

The paper considers the effects of random fluctuations of the local spin connectivities (fluctuations of the geometry) on ground state properties of a two-dimensional quantum antiferromagnet. We analyse the behavior of spins described by the Heisenberg model as a function of what we call phason flip disorder, following a terminology used for aperiodic systems. The calculations were carried out both within linear spin wave theory and using quantum Monte Carlo simulations. An "order by disorder" phenomenon is observed in this model, wherein antiferromagnetism is found to be enhanced by phason disorder. The value of the staggered order parameter increases with the number of defects, accompanied by an increase in the ground state energy of the system.Comment: 5 pages, 7 figures. Shortened and corrected version (as accepted for publication in Physical Review B

R\'enyi Entropies from Random Quenches in Atomic Hubbard and Spin Models

We present a scheme for measuring R\'enyi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO quantum simulators, and used to measure for instance area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.Comment: 5+9 page

Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores II. Simulated ALMA dust emission maps

First hydrostatic cores are predicted by theories of star formation, but their existence has never been demonstrated convincingly by (sub)millimeter observations. Furthermore, the multiplicity at the early phases of the star formation process is poorly constrained. The purpose of this paper is twofold. First, we seek to provide predictions of ALMA dust continuum emission maps from early Class 0 objects. Second, we show to what extent ALMA will be able to probe the fragmentation scale in these objects. Following our previous paper (Commer\c{c}on et al. 2012, hereafter paper I), we post-process three state-of-the-art radiation-magneto-hydrodynamic 3D adaptive mesh refinement calculations to compute the emanating dust emission maps. We then produce synthetic ALMA observations of the dust thermal continuum from first hydrostatic cores. We present the first synthetic ALMA observations of dust continuum emission from first hydrostatic cores. We analyze the results given by the different bands and configurations and we discuss for which combinations of the two the first hydrostatic cores would most likely be observed. We also show that observing dust continuum emission with ALMA will help in identifying the physical processes occurring within collapsing dense cores. If the magnetic field is playing a role, the emission pattern will show evidence of a pseudo-disk and even of a magnetically driven outflow, which pure hydrodynamical calculations cannot reproduce. The capabilities of ALMA will enable us to make significant progress towards understanding fragmentation at the early Class 0 stage and discovering first hydrostatic cores.Comment: 12 pages, 7 figures, accepted for publication in Astronomy and Astrophysic