Richness-mass relation self-calibration for galaxy clusters

This work attains a threefold objective: first, we derived the richness-mass scaling in the local Universe from data of 53 clusters with individual measurements of mass. We found a 0.46+-0.12 slope and a 0.25+-0.03 dex scatter measuring richness with a previously developed method. Second, we showed on a real sample of 250 0.06<z<0.9 clusters, most of which are at z<0.3, with spectroscopic redshift that the colour of the red sequence allows us to measure the clusters' redshift to better than Delta z=0.02. Third, we computed the predicted prior of the richness-mass scaling to forecast the capabilities of future wide-field-area surveys of galaxy clusters to constrain cosmological parameters. We computed the uncertainty and the covariance matrix of the (evolving) richness-mass scaling of a PanStarrs 1+Euclid-like survey accounting for a large suite of sources of errors. We find that the richness-mass scaling parameters, which are the input ingredients of cosmological forecasts using cluster counts, can be determined 10^5 times better than estimated in previous works that did not use weak-lensing mass estimates. The better knowledge of the scaling parameters likely has a strong impact on the relative importance of the different probes used to constrain cosmological parameters. Richness-mass scaling parameters were recovered, but only if the cluster mass function and the weak-lensing redshift-dependent selection function were accounted for in the fitting of the mass-richness scaling. This emphasizes the limitations of often adopted simplifying assumptions, such as having a mass-complete redshift-independent sample. The fitting code used for computing the predicted prior, including the treatment of the mass function and of the weak-lensing selection function, is provided in the appendix. [Abridged]Comment: A&A, in pres

The fundamental solution of the unidirectional pulse propagation equation

The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.Comment: accepted to J. Math. Phy

Chaotic, staggered and polarized dynamics in opinion forming: the contrarian effect

We revisit the no tie breaking 2-state Galam contrarian model of opinion dynamics for update groups of size 3. While the initial model assumes a constant density of contrarians a for both opinions, it now depends for each opinion on its global support. Proportionate contrarians are thus found to indeed preserve the former case main results. However, restricting the contrarian behavior to only the current collective majority, makes the dynamics more complex with novel features. For a density a<a_c=1/9 of one-sided contrarians, a chaotic basin is found in the fifty-fifty region separated from two majority-minority point attractors, one on each side. For 1/9<a< 0.301 only the chaotic basin survives. In the range a>0.301 the chaotic basin disappears and the majority starts to alternate between the two opinions with a staggered flow towards two point attractors. We then study the effect of both, decoupling the local update time sequence from the contrarian behavior activation, and a smoothing of the majority rule. A status quo driven bias for contrarian activation is also considered. Introduction of unsettled agents driven in the debate on a contrarian basis is shown to only shrink the chaotic basin. The model may shed light to recent apparent contradictory elections with on the one hand very tied results like in US in 2000 and in Germany in 2002 and 2005, and on the other hand, a huge majority like in France in 2002.Comment: 17 pages, 10 figure

The clinical relevance of bifid and trifid mandibular canals

Item does not contain fulltextBACKGROUND: Bifid mandibular canals (BMC) and trifid mandibular canals (TMC) are variations on the normal anatomy with incidences ranging from 0.08% to 65.0%. Such aberrations have an important clinical impact. For example, an extra mandibular canal may explain inadequate anesthesia, especially when two mandibular foramina are involved. Furthermore, during mandibular surgery, a second, or even third, neurovascular bundle may be damaged causing paresthesia, neuroma development, or bleeding. CASE REPORT: Two cases are presented in this article. One patient had a BMC on both sites, and the other patient had a TMC on one site and a BMC on the other site. DISCUSSION: Initial screening for the presence of a BMC or TMC can be executed by conventional panoramic radiography. BMCs or TMCs are diagnosed, before executing mandibular surgery; additional CBCT scanning is indicated.1 maart 201

Cascaded self-compression of femtosecond pulses in filaments

Highly nonlinear wave propagation scenarios hold the potential to serve for energy concentration or pulse duration reduction of the input wave form, provided that a small range of input parameters be maintained. In particular when phenomena like rogue-wave formation or few-cycle optical pulses generation come into play, it becomes increasingly difficult to maintain control of the waveforms. Here we suggest an alternative approach towards the control of waveforms in a highly nonlinear system. Cascading pulse self-compression cycles at reduced nonlinearity limits the increase of input parameter sensitivity while still enabling an enhanced compression effect. This cascaded method is illustrated by experiments and in numerical simulations of the Nonlinear Schrödinger Equation, simulating the propagation of short optical pulses in a self-generated plasma

Iterated maps for clarinet-like systems

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.)

Averaging For Solitons With Nonlinearity Management

We develop an averaging method for solitons of the nonlinear Schr{\"o}dinger equation with periodically varying nonlinearity coefficient. This method is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed and experimentally realizable technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.Comment: 6 pages, 5 figures, in pres

Direct transition to high-dimensional chaos through a global bifurcation

In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori.The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.Comment: 7 page

Logarithmic periodicities in the bifurcations of type-I intermittent chaos

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.Comment: 4 pages, 6 figures, accepted for publication in PRL (2004