Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons

Kaniadakis and Quarati (1994) proposed a Fokker--Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open question whether this equation has solutions exhibiting condensates in finite time. The main analytical challenge lies in the continuation of exploding solutions beyond their first blow-up time while having a linear diffusion term. We present a thoroughly validated time-implicit numerical scheme capable of simulating solutions for arbitrarily large time, and thus enabling a numerical study of the condensation process in the Kaniadakis--Quarati model. We show strong numerical evidence that above the critical mass rotationally symmetric solutions of the Kaniadakis--Quarati model in 3D form a condensate in finite time and converge in entropy to the unique minimiser of the natural entropy functional at an exponential rate. Our simulations further indicate that the spatial blow-up profile near the origin follows a universal power law and that transient condensates can occur for sufficiently concentrated initial data.Comment: To appear in Kinet. Relat. Model

Object-based selection of irrelevant features is not confined to the attended object

Attention to one feature of an object can bias the processing of unattended features of that object. Here we demonstrate with ERPs in visual search that this object-based bias for an irrelevant feature also appears in an unattended object when it shares that feature with the target object. Specifically, we show that the ERP response elicited by a distractor object in one visual field is modulated as a function of whether a task-irrelevant color of that distractor is also present in the target object that is presented in the opposite visual field. Importantly, we find this modulation to arise with a delay of approximately 80 msec relative to the N2pc-a component of the ERP response that reflects the focusing of attention onto the target. In a second experiment, we demonstrate that this modulation reflects enhanced neural processing in the unattended object. These observations together facilitate the surprising conclusion that the object-based selection of irrelevant features is spatially global even after attention has selected the target object

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Separable mechanisms underlying global feature-based attention

Feature-based attention is known to operate in a spatially global manner, in that the selection of attended features is not bound to the spatial focus of attention. Here we used electromagnetic recordings in human observers to characterize the spatiotemporal signature of such global selection of an orientation feature. Observers performed a simple orientation-discrimination task while ignoring task-irrelevant orientation probes outside the focus of attention. We observed that global feature-based selection, indexed by the brain response to unattended orientation probes, is composed of separable functional components. One such component reflects global selection based on the similarity of the probe with task-relevant orientation values ("template matching"), which is followed by a component reflecting selection based on the similarity of the probe with the orientation value under discrimination in the focus of attention ("discrimination matching"). Importantly, template matching occurs at similar to 150 ms after stimulus onset, similar to 80 ms before the onset of discrimination matching. Moreover, source activity underlying template matching and discrimination matching was found to originate from ventral extrastriate cortex, with the former being generated in more anterolateral and the latter in more posteromedial parts, suggesting template matching to occur in visual cortex higher up in the visual processing hierarchy than discrimination matching. We take these observations to indicate that the population-level signature of global feature-based selection reflects a sequence of hierarchically ordered operations in extrastriate visual cortex, in which the selection based on task relevance has temporal priority over the selection based on the sensory similarity between input representations

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S^3_{pq}. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.Comment: 6 page

Re-entrant Nematic Phase Established for Several Homologous Biaromatic Liquid Crystals by Investigation of Binary Mixed Systems

Several homologous series of biaromatic liquid crystals with structure type CnH2n+1O • C6H4 • M•C6H4-CN are investigated. By studying the phase transition temperatures in binary mixed systems a "re-entrant" nematic phase N(re) is established for all compounds exhibiting smectic A phases. The virtual transition temperatures N(re) - SA are found to decrease with increasing chain length of the alkyloxy group. The influence of the middle group M on the re-entrant behaviour can be attributed mainly to its dipole moment. The temperature range of the smectic A phase decreases when the middle group dipole moment is additive to that of the nitrile group. To summarize it can be said that the "re-entrant" behaviour of biaromatic liquid crystals is found to be very similar to that of triaromatic systems reported recently

Combined pitching and yawing motion of airplanes

This report treats the following problems: The beginning of the investigated motions is always a setting of the lateral controls, i.e., the rudder or the ailerons. Now, the first interesting question is how the motion would proceed if these settings were kept unchanged for some time; and particularly, what upward motion would set in, how soon, and for how long, since therein lie the dangers of yawing. Two different motions ensue with a high rate of turn and a steep down slope of flight path in both but a marked difference in angle of attack and consequently different character in the resultant aerodynamic forces: one, the "corkscrew" dive at normal angle, and the other, the "spin" at high angle