The area of the Mandelbrot set

Summary We obtain upper bounds for the area of the Mandelbrot set. An effective procedure is given for computing the coefficients of the conformal mapping from the exterior of the unit circle onto the exterior of the Mandelbrot set. The upper bound is obtained by computing finitely many of these coefficient and applying Green's Theorem. The error in such calculations is estimated by deriving explicit formulas for infinitely many of the coefficients and comparing.Partially supported by a grant from the National Science Foundation     

Modulated periodic stokes waves in deep water

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem indicate that under suitable conditions modulated periodic Stokes waves evolve chaotically. Sensitive spectral evolution in the neighborhood of homoclinic manifolds of the unperturbed nonlinear Schrodinger equation is found.     

Origin of negative thermal expansion in cubic ZrW2O8 revealed by high pressure inelastic neutron scattering

Isotropic negative thermal expansion has been reported in cubic ZrW2O8 over a wide range of temperatures (0-1050 K). Here we report the direct experimental determination of the Grüneisen parameters of phonon modes as a function of their energy, averaged over the whole Brillouin zone, by means of high pressure inelastic neutron scattering measurements. We observe a pronounced softening of the phonon spectrum at P = 1.7 kbar compared to that at ambient pressure by about 0.1-0.2 meV for phonons of energy below 8 meV. This unusual phonon softening on compression, corresponding to large negative Grüneisen parameters, is able to account for the observed large negative thermal expansion.     

A large‐volume gas cell for high‐energy X‐ray reflectivity investigations of interfaces under pressure

A cell for the investigation of interfaces under pressure is presented. Given the pressure and temperature specifications of the cell, P≤ 100 bar and 253 K ≤T≤ 323 K, respectively, high‐energy X‐rays are required to penetrate the thick Al₂O₃ windows. The CH₄(gas)/H₂O(liquid) interface has been chosen to test the performance of the new device. The measured dynamic range of the high‐energy X‐ray reflectivity data exceeds 10^?8, thereby demonstrating the validity of the entire experimental set‐up.     

Fingerprints of amorphous icelike behavior in the vibrational density of states of protein hydration water

The low-frequency modes of protein hydration water are investigated by inelastic neutron scattering. Experiments on both protonated and fully deuterated maltose binding protein samples allow us to unambiguously single out the contribution from water. The low-energy vibrational density of states of hydration water at 100 K is similar to the density of states of high- and low-density amorphous ice, and quite different from that of simple forms of crystalline ice. This result can be related to the picture of hydration water mass density depending on the protein surface curvature, which supports its glassy behavior.     

How confinement affects the dynamics of c60 in carbon nanopeapods

The dynamics of confined systems is of major concern for both fundamental physics and applications. In this Letter, the dynamics of C60 fullerene molecules inside single walled carbon nanotubes is studied using inelastic neutron scattering. We identify the C60 vibrations and highlight their sensitivity to temperature. Moreover, a clear signature of rotational diffusion of the C60 is evidenced, which persists at lower temperature than in 3D bulk C60. It is discussed in terms of confinement and of reduced dimensionality of the C60 chain.