Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map

The breakup of shearless invariant tori with winding number $\omega=[0,1,11,1,1,...]$ (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders (folded-over invariant tori which are not graphs over the x-axis in $(x,y)$ phase space), whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.Comment: submitted to Chao

Molecular and Electronic Structure of Electroactive Self-Assembled Monolayers

Self-assembled monolayers (SAMs) containing electroactive functional groups are excellent model systems for the formation of electronic devices by self-assembly. In particular ferrocene-terminated alkanethiol SAMs have been extensively studied in the past. However, there are still open questions related with their electronic structure including the influence of the ferrocene group in the SAM-induced work function changes of the underlying metal. We have thus carried out a thorough experimental and theoretical investigation in order to determine the molecular and electronic structure of ferrocene-terminated alkanethiol SAMs on Au surfaces. In agreement with previous studies we found that the Fc-containing alkanethiol molecules adsorb forming a thiolate bond with the Au surface with a molecular geometry 30 degrees tilted with respect to the surface normal. Measured surface coverages indicate the formation of a compact monolayer. On the other hand, contrary with previous observations, we found that the ferrocene group has little influence on the observed work function decrease which is largely determined by the alkanethiol. Furthermore, the ferrocene moiety lies 14 Å above the metal surface covalently bonded to the alkanethiol SAM and its HOMO is located at -1.6 eV below the Fermi level. Our results provide new valuable insight into the molecular and electronic structure of electroactive SAMs which are of fundamental importance in the field of molecular electronics.Fil: Méndez de Leo, Lucila Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; ArgentinaFil: de la Llave, Ezequiel Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; ArgentinaFil: Scherlis Perel, Damian Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; ArgentinaFil: Williams, Federico Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentin

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

Regularity of critical invariant circles of the standard nontwist map

We study critical invariant circles of several noble rotation numbers at the edge of break-up for an area-preserving map of the cylinder, which violates the twist condition.These circles admit essentially unique parametrizations by rotational coordinates. We present a high accuracy computation of about 107 Fourier coefficients. This allows us to compute the regularity of the conjugating maps and to show that, to the extent of numerical precision, it only depends on the tail of the continued fraction expansion.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49075/2/non5_3_013.pd

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential

Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Families of Canonical Transformations by Hamilton-Jacobi-Poincar\'e equation. Application to Rotational and Orbital Motion

The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.Comment: 21 page

Toll-like receptor signaling adapter proteins govern spread of neuropathic pain and recovery following nerve injury in male mice.

BackgroundSpinal Toll-like receptors (TLRs) and signaling intermediaries have been implicated in persistent pain states. We examined the roles of two major TLR signaling pathways and selected TLRs in a mononeuropathic allodynia.MethodsL5 spinal nerve ligation (SNL) was performed in wild type (WT, C57BL/6) male and female mice and in male Tlr2-/-Tlr3-/-, Tlr4-/-, Tlr5-/-, Myd88-/-, Triflps2, Myd88/Triflps2, Tnf-/-, and Ifnar1-/- mice. We also examined L5 ligation in Tlr4-/- female mice. We examined tactile allodynia using von Frey hairs. Iba-1 (microglia) and GFAP (astrocytes) were assessed in spinal cords by immunostaining. Tactile thresholds were analyzed by 1- and 2-way ANOVA and the Bonferroni post hoc test was used.ResultsIn WT male and female mice, SNL lesions resulted in a persistent and robust ipsilateral, tactile allodynia. In males with TLR2, 3, 4, or 5 deficiencies, tactile allodynia was significantly, but incompletely, reversed (approximately 50%) as compared to WT. This effect was not seen in female Tlr4-/- mice. Increases in ipsilateral lumbar Iba-1 and GFAP were seen in mutant and WT mice. Mice deficient in MyD88, or MyD88 and TRIF, showed an approximately 50% reduction in withdrawal thresholds and reduced ipsilateral Iba-1. In contrast, TRIF and interferon receptor null mice developed a profound ipsilateral and contralateral tactile allodynia. In lumbar sections of the spinal cords, we observed a greater increase in Iba-1 immunoreactivity in the TRIF-signaling deficient mice as compared to WT, but no significant increase in GFAP. Removing MyD88 abrogated the contralateral allodynia in the TRIF signaling-deficient mice. Conversely, IFNβ, released downstream to TRIF signaling, administered intrathecally, temporarily reversed the tactile allodynia.ConclusionsThese observations suggest a critical role for the MyD88 pathway in initiating neuropathic pain, but a distinct role for the TRIF pathway and interferon in regulating neuropathic pain phenotypes in male mice

Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y