Newton's method and Baker domains

We show that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic functions without Baker domains. We also show that there exists an entire function f with exactly one zero for which the complement of the immediate attracting basin has at least two components and contains no invariant Baker domains of N. The second result answers a question of J. Rueckert and D. Schleicher while the first one gives a partial answer to a question of X. Buff.Comment: 6 page

Finite Size Effects in Fluid Interfaces

It is shown that finite size effects in the free energy of a rough interface of the 3D Ising and three--state Potts models are well described by the capillary wave model at {\em two--loop} order. The agreement between theoretical predictions and Monte Carlo simulations strongly supports the idea of the universality of this description of order--order interfaces in 3D statistical systems above the roughening temperature.Comment: 3 pages, uuencoded .ps file, figures included. (Proceeding of Lattice '93

The Statistical Mechanical Theory of Transport Processes. III. The Coefficients of Shear and Bulk Viscosity of Liquids

A molecular theory of the coefficients of shear and bulk viscosity of monatomic liquids is developed on the basis of the general theory of transport processes presented in the first article of this series. With the use of the Lennard-Jones potential and a reasonable analytic approximation to the experimental radial distribution function, calculations of the coefficients of shear and bulk viscosity of liquid argon at 89°K have been carried out. The theory leads explicitly to ratios of the coefficients to the friction constant of the theory of Brownian motion. With a preliminary estimate of the friction constant, a value of the shear viscosity of liquid argon in moderately good agreement with experiment is obtained

Profile and width of rough interfaces

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.Comment: 18 pages, 4 Postscript figures, LaTeX2e, formulation of sec.3.2 improved, 1 reference adde

Pre-dewetting transition on a hydrophobic wall: Statics and dynamics

For one-component fluids, we predict a pre-dewetting phase transition between a thin and thick low-density layer in liquid on a wall repelling the fluid. This is the case of a hydrophobic wall for water. A pre-dewetting line starts from the coexistence curve and ends at a surface critical point in the phase diagram. We calculate this line numerically using the van der Waals model and analytically using the free energy expansion up to the quartic order. We also examine the pre-dewetting dynamics of a layer created on a hydrophobic spot on a heterogeneous wall. It is from a thin to thick layer during decompression and from a thick to thin layer during compression. Upon the transition, a liquid region above the film is cooled for decompression and heated for compression due to latent heat convection and a small pressure pulse is emitted from the film into the liquid.Comment: 14 pages, 17 figure

Investigating trial design variability in trials of disease-modifying therapies in Parkinson’s disease: a scoping review protocol

\ua9 Author(s) (or their employer(s)) 2023. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.Introduction Parkinson’s disease (PD) is a debilitating neurological disorder for which the identification of disease-modifying interventions represents a major unmet need. Diverse trial designs have attempted to mitigate challenges of population heterogeneity, efficacious symptomatic therapy and lack of outcome measures that are objective and sensitive to change in a disease modification setting. It is not clear whether consensus is emerging regarding trial design choices. Here, we report the protocol of a scoping review that will provide a contemporary update on trial design variability for disease-modifying interventions in PD. Methods and analysis The Population, Intervention, Comparator, Outcome and Study design (PICOS) framework will be used to structure the review, inform study selection and analysis. The databases MEDLINE, Web of Science, Cochrane and the trial registry ClinicalTrials.gov will be systematically searched to identify published studies and registry entries in English. Two independent reviewers will screen study titles, abstracts and full text for eligibility, with disagreements being resolved through discussion or by a third reviewer where necessary. Data on general study information, eligibility criteria, outcome measures, trial design, retention and statistically significant findings will be extracted into a standardised form. Extracted data will be presented in a descriptive analysis. We will report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Scoping Review extension. Ethics and dissemination This work will provide an overview of variation and emerging trends in trial design choices for disease-modifying trials of PD. Due to the nature of this study, there are no ethical or safety considerations. We plan to publish our findings in a peer-reviewed journal

Molecular Dynamics Study of the Nematic-Isotropic Interface

We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit, however, the spectrum becomes isotropic and compares well with the predictions of a simple capillary wave theory.Comment: to appear in Phys. Rev.

Surface layering of liquids: The role of surface tension

Recent measurements show that the free surfaces of liquid metals and alloys are always layered, regardless of composition and surface tension; a result supported by three decades of simulations and theory. Recent theoretical work claims, however, that at low enough temperatures the free surfaces of all liquids should become layered, unless preempted by bulk freezing. Using x-ray reflectivity and diffuse scattering measurements we show that there is no observable surface-induced layering in water at T=298 K, thus highlighting a fundamental difference between dielectric and metallic liquids. The implications of this result for the question in the title are discussed.Comment: 5 pages, 4 figures, to appear in Phys. Rev. B. 69 (2004