Switching dynamics of spatial solitary wave pixels

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching

[2.2](4,7)Isobenzofuranophanes - Synthesis, Characterisation and Reactivity

The isomeric Diels-Alder adducts 3, obtained by cycloaddition of tetraphenylcyclopentadienone to the 4,5:12,13-bis-(oxanorbornadieno)[2.2]paracyclophanes syn,syn- and anti,-syn-2[Note ][The stereochemical descriptors syn and anti refer to the orientation of the oxygen bridge in the oxabicyclo[2.2.1]heptadiene subunits with respect to the [2.2]paracyclophaneskeleton.], yield the unstable isobenzofuranophane 4 by consecutive extrusion of carbon monoxide and tetraphenylbenzene when heated to 180°C. The molecular ion of 4 was observed in the EI mass spectrum. The stable tetraphenyl-substituted analogue 10 was synthesized independently from the previously unknown 4,5,12,13-tetrabenzoyl[2.2]paracyclophane (9). UV/Vis as well as fluorescence spectra and an X-ray crystal structure analysis of 9 are reported

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

The Gap-Tooth Method in Particle Simulations

We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains (teeth) separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a closure-on-demand approach to solving hydrodynamics problems

Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

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

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures, compressed and encoded with uufiles, 170 k

The general classical solution of the superparticle

The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra \Cl(9,1). The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.Comment: 11 pages, REVTe

Substantia nigra activity level predicts trial-to-trial adjustments in cognitive control

Effective adaptation to the demands of a changing environment requires flexible cognitive control. The medial and the lateral frontal cortices are involved in such control processes, putatively in close interplay with the BG. In particular, dopaminergic projections from the midbrain (i.e., from the substantia nigra [SN] and the ventral tegmental area) have been proposed to play a pivotal role in modulating the activity in these areas for cognitive control purposes. In that dopaminergic involvement has been strongly implicated in reinforcement learning, these ideas suggest functional links between reinforcement learning, where the outcome of actions shapes behavior over time, and cognitive control in a more general context, where no direct reward is involved. Here, we provide evidence from functional MRI in humans that activity in the SN predicts systematic subsequent trial-to-trial RT prolongations that are thought to reflect cognitive control in a stop-signal paradigm. In particular, variations in the activity level of the SN in one trial predicted the degree of RT prolongation on the subsequent trial, consistent with a modulating output signal from the SN being involved in enhancing cognitive control. This link between SN activity and subsequent behavioral adjustments lends support to theoretical accounts that propose dopaminergic control signals that shape behavior both in the presence and in the absence of direct reward. This SN-based modulatory mechanism is presumably mediated via a wider network that determines response speed in this task, including frontal and parietal control regions, along with the BG and the associated subthalamic nucleus

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat