The Spirit Is Willing: Nonlinearity, Bifurcations, and Mental Control

In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior. In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics. We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem. In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes.     

Infrared and Raman spectroscopic investigation of Eu3+-doped mono and Di-urethanesil hybrid siliceous materials

The general features of two series of sol-gel derived materials, designatedurethanesils (Ut), have been investigated by infrared and Raman spectroscopies with the goal of elucidating the chemical environment of the Eu³⁺ cations. The host frameworks of the two families of ormolytes studied have been represented by m-Ut(350) and d-Ut(300), where m stands for mono, d stands for di, 350 and 300 are the average molecular weights of the organic precursors (poly(ethylene glycol) methyl ether, PEGME, and poly(ethylene glycol), PEG, respectively). The hybrid matrix of the mono-xerogels is composed by a siliceous backbone bonded by means of urethane linkages (-NHC (=O)O-) to pendant methyl end capped oligopolymer chains with approximately 7 oxyethylene units, whereas that of the di-xerogels is based on a siliceous network grafted through urethane groups to both ends of poly(oxyethylene) segments containing about 6 (OCH₂CH₂) repeat units. Both classes of materials have been doped with europium triflate (Eu(CF₃SO₃)₃). The doped samples have been identified by m-Ut(350)_nEu(CF₃SO₃)₃ and d-Ut(300)_nEu(CF₃SO₃), where n is the molar ratio of (OCH₂CH₂) repeat units per Eu³⁺ ion. Materials with n ranging from ∞ to 5 have been analyzed. The spectral data obtained provide evidence that the cations begin to coordinate to the ether oxygen atoms of the oligopolymer chains at n=40 in the mono-urethanesils and at n=10 in the di-urethanesils. In mono-urethanesils samples with n>40 and in di-urethanesils materials with n>10, the Eu³⁺ coordinate exclusively to the carbonyl oxygen atoms of the urethane linkages. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Global Optimal Image Reconstruction from Blurred Noisy Data by a Bayesian Approach

In this paper, a procedure is presented which allows the optimal reconstruction of images from blurred noisy data. The procedure relies on a general Bayesian approach, which makes proper use of all the available information. Special attention is devoted to the informative content of the edges; thus, a preprocessing phase is included, with the aim of estimating the jump sizes in the gray level. The optimization phase follows; existence and uniqueness of the solution is secured. The procedure is tested against simple simulated data and real data.     

Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Γ-type-invariants associated toPU(2)-bundles and the differentiable structure of Barlow's surface

Supported by a Heisenberg-scholarship of the DFG     

Equivalence of Toda-Hopf invariants

In this paper it is shown that various existing constructions of ‘Hopf invariant’ are equivalent to each other. In consequence one gets that the oneToda-Hopf invariant enjoys various properties. Both authors supported in part by the NSF.     

TR-LII for sizing of carbon particles forming at room temperature

Time-resolved laser-induced incandescence (TR-LII) was applied for the determination of particle sizes during carbon-particle formation from supersaturated atomic carbon vapor that was generated by laser photolysis of carbon suboxide (C₃O₂) at room temperature. Thus, the solid carbon particles were formed under hydrogen-free conditions. The TR-LII technique was used for in situ size measurement of growing carbon particles and samples of final particles were analyzed by transmission electron microscopy (TEM). It was found that the particles grow to a final size of 4–12 nm within 0.02–1 ms. The properties of the obtained particles depend on the initial conditions in the reaction volume, i.e. concentration of carbon suboxide, pressure and type of gas diluter, photolysis wavelength, and laser pulse energy. The comparison of TR-LII and TEM particle sizing results yields information about the effective thermal energy accommodation coefficients for He, Ar, CO, and C₃O₂ molecules on carbon particles. PACS 61.46.Df; 07.60.-j; 78.70.-g     

Numerical Analysis and Simulation Analysis for Space‐Time Data

Spatio temporal dynamics of the positive column of a dc neon glow discharge is studied and investigated experimentally and theoretically. Spatio temporal analysis by means of biorthogonal decomposition method (BOD) gives insights into the mechanism of irregularity and can be employed for characterization of spatio‐ temporal complexity. In the weak nonlinear region, the wave dynamics is approximated by an amplitude equation of the Ginzburg‐Landau equation (CGLE) with complex coefficients and an additional integral term based on a fluid model. In the present work we deal with irregular spatio‐temporal data. A comparison between the numerical analysis of the experimental data and simulation results are studied. A good agreement between the dynamical behaviour for experimental space‐time data and theoretical simulation space‐time results was obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)