Time evolution of a fractal distribution: Particle concentrations in free-surface turbulence

Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating particles coagulate and form a fractal structure, a rare manifestation of a strange attractor observable in real space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions D_q(t) (q=1 to 6) of the floating particles starting with the uniform distribution D_q(0)=2 for Taylor Microscale Reynolds number Re_λ?160. Focus is on the time evolution of the correlation dimension D₂(t) as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.     

Universal nature of particle displacements close to glass and jamming transitions

We examine the structure of the distribution of single particle displacements (van Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical model that describes quantitatively numerical and experimental data in supercooled liquids, colloidal hard spheres, and granular materials. The tails of the distributions directly explain the decoupling between translational diffusion and structural relaxation observed in glassy materials.     

Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems

It is known that perturbation theory converges in fermionic field theory at weak coupling if the interaction and the covariance are summable and if certain determinants arising in the expansion can be bounded efficiently, e.g. if the covariance admits a Gram representation with a finite Gram constant. The covariances of the standard many–fermion systems do not fall into this class due to the slow decay of the covariance at large Matsubara frequency, giving rise to a UV problem in the integration over degrees of freedom with Matsubara frequencies larger than some Ω (usually the first step in a multiscale analysis). We show that these covariances do not have Gram representations on any separable Hilbert space. We then prove a general bound for determinants associated to chronological products which is stronger than the usual Gram bound and which applies to the many–fermion case. This allows us to prove convergence of the first integration step in a rather easy way, for a short–range interaction which can be arbitrarily strong, provided Ω is chosen large enough. Moreover, we give – for the first time – nonperturbative bounds on all scales for the case of scale decompositions of the propagator which do not impose cutoffs on the Matsubara frequency.     

Bestimmung der orthogonalitätstreuen Permutationen euklidischer Räume

Ohne Zusammenfassung     

Brillouin and ultrasonic study of the temperature dependence of the elastic constants in NaCN

The temperature dependence of the elastic constants of NaCN has been studied by propagation of ultrasonic waves at 15 MHz and by Brillouin scattering at 3 GHz over the temperature range from 287K to 355K. c₄₄ is observed to soften linearly with temperature as the order-disorder phase transition at 284K is approached from above. The other elastic constants also soften, except for c₁₂ which stiffens. Considerable dispersion is seen in the values of c₄₄ obtained ultrasonically and by Brillouin scattering. Measurements of the temperature dependence of the density are also reported.     

Widespread occurrence of polyhalogenated compounds in fat from kitchen hoods

Food and contaminated indoor environments are the most relevant sources of human exposure to polyhalogenated chemicals. This study analyzed for the first time fat residues in kitchen hoods for contaminations with polyhalogenated compounds. A wide range of contaminants was detected in all kitchen hoods (n?=?15) and most of them could be quantified. Between 0.2 and 18 μg polyhalogenated chemicals/g fat were detected, with chlorinated paraffins being the most relevant contaminant group. Aside from the chlorinated paraffins, each kitchen hood fat sample showed a distinct fingerprint. A wide range of old and current-use brominated flame retardants were also detected in the samples. In addition to these contaminants originating from their use in indoor equipment, residues of organochlorine pesticides and semi-volatile halogenated natural products verified that cooking of food, accompanied with the release of contaminants from the heated food, was another relevant source of contamination. Re-analyses of two samples after 3 months only resulted in small variations in contaminant pattern and concentrations. Therefore, fat from kitchen hoods is proposed as an easily accessible matrix to assess contamination of these hazardous polyhalogenated chemicals.

Biosensors based on gold nanoelectrode ensembles and screen printed electrodes

Gold nanowires were synthesized within polycarbonate membranes according to an electroless deposition method, obtaining nanoelectrode ensembles (NEEs) with special electrochemical features. NEEs were coupled with home-produced carbon graphite screen printed electrodes and the electrochemical properties of the original nanoelectrode ensemble on screen printed substrate (NEE/SPS) assembly has been tested for sensors application. Glucose oxidase has been used as model enzyme in order to verify the feasibility of disposable gold NEE/SPS biosensors. Finally, different immobilisation and electrochemical deposition techniques based on either self assembled monolayers of cysteamine (CYS) or amino-propyl-triethoxysilane (APTES) and conductive polyaniline (PANI) molecular wires were used. Spatial patterning of the enzyme on the polycarbonate surface and of PANI wires on gold nanoelectrodes was obtained. Possible direct electron transfer between the enzyme and the PANI modified gold nanoelectrodes has been evaluated.