On the susceptibility function of piecewise expanding interval maps

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that Psi(z) is holomorphic in a disc of larger than one. Although Psi(1) is the formal derivative of the SRB measure of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5. In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for these examples.Comment: To appear Comm. Math. Phy

Eigenfunctions for smooth expanding circle maps

We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.Comment: 10 pages, 2 figure

Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

The Flow of a Viscous Compressible Fluid Through a Very Narrow Gap

The effect of compressibility on the pressure distribution in the narrow gap between a rotating cylinder and a plane in a viscous fluid was studied by Taylor and Saffman [1] during an investigation of the centripetal pump effect discovered by Reiner [2]

Planetary nebulae after common-envelope phases initiated by low-mass red giants

It is likely that at least some planetary nebulae are composed of matter which was ejected from a binary star system during common-envelope (CE) evolution. For these planetary nebulae the ionizing component is the hot and luminous remnant of a giant which had its envelope ejected by a companion in the process of spiralling-in to its current short-period orbit. A large fraction of CE phases which end with ejection of the envelope are thought to be initiated by low-mass red giants, giants with inert, degenerate helium cores. We discuss the possible end-of-CE structures of such stars and their subsequent evolution to investigate for which structures planetary nebulae are formed. We assume that a planetary nebula forms if the remnant reaches an effective temperature greater than 30 kK within 10^4 yr of ejecting its envelope. We assume that the composition profile is unchanged during the CE phase so that possible remnant structures are parametrized by the end-of-CE core mass, envelope mass and entropy profile. We find that planetary nebulae are expected in post-CE systems with core masses greater than about 0.3 solar masses if remnants end the CE phase in thermal equilibrium. We show that whether the remnant undergoes a pre-white dwarf plateau phase depends on the prescribed end-of-CE envelope mass. Thus, observing a young post-CE system would constrain the end-of CE envelope mass and post-CE evolution.Comment: Published in MNRAS. 12 pages, 12 figures. Minor changes to match published versio

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given

On Urabe's criteria of isochronicity

We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation $\ddot{x}+g(x)=0$. We show that apart from the harmonic oscillator there exists a large family of isochronous potentials which must all be non-polynomial and not symmetric (an even function of the coordinate x).Comment: 8 page

De-novo design of complementary (antisense) peptide mini-receptor inhibitor of interleukin 18 (IL-18).

Complementary (antisense) peptide mini-receptor inhibitors are complementary peptides designed to be receptor-surrogates that act by binding to selected surface features of biologically important proteins thereby inhibiting protein-cognate receptor interactions and subsequent biological effects. Previously, we described a complementary peptide mini-receptor inhibitor of interleukin-1beta (IL-1beta) that was designed to bind to an external surface loop (beta-bulge) of IL-1beta (Boraschi loop) clearly identified in the X-ray crystal structure of this cytokine. Here, we report the de-novo design and rational development of a complementary peptide mini-receptor inhibitor of cytokine interleukin-18 (IL-18), a protein for which there is no known X-ray crystal structure. Using sequence homology comparisons with IL-1beta, putative IL-18 surface loops are identified and used as a starting point for design, including a loop region 1 thought to be equivalent with the Boraschi loop of IL-1beta. Only loop region 1 complementary peptides are found to be promising leads as mini-receptor inhibitors of IL-18 but these are prevented from being properly successful owing to solubility problems. The application of "M-I pair mutagenesis" and inclusion of a C-terminal arginine residue are then sufficient to solve this problem and convert one lead peptide into a functional complementary peptide mini-receptor inhibitor of IL-18. This suggests that the biophysical and biological properties of complementary peptides can be improved in a rational and logical manner where appropriate, further strengthening the potential importance of complementary peptides as inhibitors of protein-protein interactions, even when X-ray crystal structural information is not readily available

Muon-Spin-Rotation Measurements of the Penetration Depth in the Infinite-Layer Electron-Doped Cuprate Superconductor Sr0.9La0.1CuO2

Muon spin rotation (mSR) measurements of the in-plane penetration depth lambda_ab have been performed in the electron-doped infinite layer high-Tc superconductor (HTS) Sr0.9La0.1CuO2. Absence of the magnetic rare-earth ions in this compound allowed to measure for the first time the absolute value of lambda_ab(0) in electron-doped HTS using mSR. We found lambda_ab(0)=116(2) nm. The zero-temperature depolarization rate sigma(0)?1/lambda_ab(0)^2=4.6(1) MHz is more than four times higher than expected from the Uemura line. Therefore this electron-doped HTS does not follow the Uemura relation found for hole-doped HTS.Comment: to be published in Physical Review Letter

Irrelevant Interactions without Composite Operators - A Remark on the Universality of Second Order Phase Transitions

We study the critical behaviour of symmetric $\phi^4_4$ theory including irrelevant terms of the form $\phi^{4+2n}/\Lambda_0^{2n}$ in the bare action, where $\Lambda_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for a spin system). The main technical tool is renormalization theory based on the flow equations of the renormalization group which permits to establish the required convergence statements in generality and rigour. As a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators. This is a technical simplification and seems preferable from the physical point of view. In this short note we restrict for simplicity to the symmetry class of the Ising model, i.e. one component $\phi^4_4$ theory. The method is general, however.Comment: 13 page