Roughness and dynamics of a contact line of a viscous fluid on a disordered substrate

We have studied the roughness and the dynamics of the contact line of a viscous liquid on a disordered substrate. We have used photolithographic techniques to obtain a controlled disorder with a correlation length ξ = 10μm. Liquids with different viscosity were used: water and aqueous glycerol solution. We have found that the roughness W of the contact line depends neither on the viscosity nor on the velocity v of the contact line for v in the range 0.2-20μm/s. W is found to scale with the length L of the line as L ^ζ with a roughness exponent ζ = 0.51±0.03. This value is similar to the one obtained with superfluid helium. In the present experiment, we have checked that the motion of the contact line is actually overdamped, so that the phenomenological equation first proposed by Ertas and Kardar should be relevant. However, our measurement of ζ is in disagreement with the predicted value ζ = 0.39. We have also analyzed the avalanche-like motion of the contact line. We find that the size distribution does not follow a power law dependence. Received 18 April 2002     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Table-top kHz hard X-ray source with ultrashort pulse duration for time-resolved X-ray diffraction

The interaction of ultrashort laser pulses with solid state targets is studied concerning the production of short X-ray pulses with photon energies up to about 10 keV. The influence of various parameters such as pulse energy, repetition rate of the laser system, focusing conditions, the application of prepulses, and the chirp of the laser pulses on the efficiency of this highly nonlinear process is examined. In order to increase the X-ray flux, the laser pulse energy is increased by a 2nd multipass amplifier from 750 μJ to 5 mJ. By applying up to 4 mJ of the pulse energy a X-ray flux of 4×10¹⁰ Fe K _α photons/s or 2.75×10¹⁰ Cu K _α photons/s are generated. The energy conversion efficiency is therefore calculated to η _Fe≈1.4×10⁻⁵ and η _Cu≈1.0×10⁻⁵. The X-ray source size is determined to 15×25 μm². By focusing the produced X-rays using a toroidally bent crystal a quasi-monochromatic X-ray point source with a diameter of 56 μm×70μm is produced containing ≈10⁴ Fe K _α1 photons/s which permits the investigation of lattice dynamics on a picosecond or even sub-picosecond time scale. The lattice movement of a GaAs(111) crystal is shown as a typical application.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

Hydrodynamics and cell motion during the rounding of two dimensional hydra cell aggregates

Using a two dimensional experimental geometry, we study hydrodynamics and cell motion during the rounding-up of three kinds of hydra aggregates (ectodermal, endodermal and mixed). The relaxation of initially elongated aggregates toward a circular shape is exponential and the relaxation time is proportional to the aggregate size as expected from hydrodynamics laws. As for viscous liquids, aggregate rounding is driven by tissue surface tensions σ and resisted by tissue viscosity η. The ratio η/σ is the same for the three kinds of aggregates. With a reasonable value σ = 1 mN/m, we obtain an estimate larger than 10⁴ Pa s for the tissue viscosity. Cell motion during rounding is strongly cooperative and cell displacements exhibit some specific patterns in each aggregate. These results point out the role of adhesive bonds in the observed kinetics. Received 21 December 2001     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Molecular-orbital structure in neutron-rich Be and C isotopes

The structure of Be and C isotopes are investigated based on the molecular-orbit (MO) model. The low-lying states are characterized by several configurations of valence neutrons, which are constructed as combinations of basic orbits. In ¹⁰Be, all of the observed positive-parity bands and the negative-parity bands are described within the model. The second 0⁺ state of ¹⁰Be has a large α-α cluster structure, and this is characterized by a (1/2⁺ _σ)² configuration. An enlargement of the α-α distance due to two-valence neutrons along the α-α axis makes their wave function smooth and reduces the kinetic energy drastically. Furthermore, the contribution of the spin-orbit interaction due to coupling between the S _z = 0 and the S _z = 1 configurations, is important. In the ground state of ¹²Be, the calculated energy exhibits similar characteristics, that the remarkable α clustering and the contribution of the spin-orbit interaction make the binding of the state with (3/2^- _π)²(1/2⁺ _σ)² configuration properly stronger in comparison with the closed p-shell (3/2^- _π)²(1/2^- _π)² configuration. This is related to the breaking of the N = 8 (closed p-shell) neutron magic number. Also, the molecule-like structure of the C isotopes is investigated using a microscopic α+α+α+n+n+ ^{. . .} model. The combination of the valence neutrons in the π- and the σ-orbit is promising to stabilize the linear-chain state against the breathing and bending modes, and it is found that the excited states of ¹⁶C are the most promising candidates for such structure. Received: 1 May 2001 / Accepted: 4 December 2001     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

Search for narrow dibaryon resonances in neutral pion photoproduction from the deuteron

The reaction γd↦π⁰ X has been measured with TAPS at MAMI in the energy range E _γ = 140-300 MeV. Using the Glasgow tagging spectrometer a photon energy resolution of 0.8 MeV was achieved. The energy excitation functions of integral and differential total cross-sections show no structures of statistical significance > 2σ. Upper limits for the production of narrow isoscalar or isovector dibaryons with masses m? 2100 MeV/c² were deduced. They are in the range 2-5 μb averaged over the 0.8 MeV energy resolution. Received: 25 October 2000 / Accepted: 24 November 2000     

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self-interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one-loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/b ^d)N ^{2 - νd}≥1, where Δ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non-ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength Δ _c ∼ N ^{- γ} where the exponent γ ≈ 0.25 and does not depend from the solvent quality. Received 17 December 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: vilgis@mpip-mainz.mpg.de     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

High spin states above the α-decaying isomer in 211Po

Prompt and delayed γ-rays in nuclei of the ²⁰⁸Pb region produced in 450 MeV ⁷⁶Ge +²⁰⁸Pb collisions have been studied at GASP. Yrast states above the α-decaying isomer in ²¹¹Po have been located including a 0.25 μs 31/2⁻ isomer at 2135 keV and a 2 μs isomer at 4874 keV. Received: 22 September 1997     

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The ⁹Be and ⁹B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The ⁸Be (0 ⁺ , 2 ⁺ ) + n and ⁵He (3/2 ^- , 1/2 ^- ) + α (or mirror) channels are included by taking account of the unstable nature of ⁸Be and ⁵He. Spectroscopic properties of ⁹Be and ⁹B are analyzed. We show that the ⁵He + α configurations cannot be neglected to derive accurate results. The ⁹Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by ⁸Be + n channels at low energies, but ⁵He + α channels become important beyond E _γ≈ 4 MeV. Received: 7 September 2001 / Accepted: 19 November 2001     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Resonant coupling in the van der Waals interaction between an excited alkali atom and a dielectric surface: an experimental study via stepwise selective reflection spectroscopy

We present a detailed experimental study of the evaluation of the van der Waals (vW) atom-surface interaction for high-lying excited states of alkali-metal atoms (Cs and Rb), notably when they couple resonantly with a surface-polariton mode of the neighbouring dielectric surface. This report extends our initial observation [Phys. Rev. Lett. 83, 5467 (1999)] of a vW repulsion between Cs(6D_3/2) and a sapphire surface. The experiment is based upon FM selective reflection spectroscopy, on a transition reaching a high-lying state from a resonance level, that has been thermally pumped by an initial one-photon step. Along with a strong vW repulsion fitted with a blue lineshift, -160±25 kHz μm³ for Cs(6D_3/2) in front of a sapphire surface (with a perpendicular c-axis), we demonstrate a weaker vW repulsion (-32±5 kHz μm³) for Cs(6D_3/2) in front of a YAG surface, as due to a similar resonant coupling at 12 μm between a virtual atomic emission (6D_3/2-7P_1/2) and the surface polariton modes. A resonant behaviour of Rb(6D_5/2) in front of a sapphire surface exists also because of analogous decay channels in the 12 μm range. Finally, one demonstrates that fused silica, nonresonant for a virtual transition in the 12 μm range and hence weakly attracting for Cs(6D_3/2), exhibits a resonant behaviour for Cs(9S_1/2) as due to its surface polariton resonance in the 8-9 μm range. The limiting factors that affect both the accuracy of the theoretical prediction, and that of the fitting method applied to the experimental data, are discussed in the conclusion. Received 16 January 2003 / Received in final form 25 March 2003 Published online 5 May 2003     

Nuclear spins, magnetic moments and α-decay spectroscopy of long-lived isomeric states in 185Pb

Alpha-decay properties of the neutron-deficient isotope ¹⁸⁵Pb were studied at the PSB-ISOLDE (CERN) on-line mass separator using the resonance ionisation laser ion source (RILIS). The nuclei of interest were produced in a 1.4 GeV proton-induced spallation reaction of a uranium graphite target. In contrast to previous studies, two α-decaying isomeric states were identified in ¹⁸⁵Pb. The relative production of the isomers, monitored by their α-counting rates, could be significantly changed when a narrow-bandwidth laser at the RILIS setup was used to scan through the atomic hyperfine structure. Based on the atomic hyperfine structure measurements, along with the systematics for heavier odd-mass lead isotopes, the spin and the parity of these states were interpreted as 3/2^- and 13/2⁺ and their nuclear magnetic moments were deduced. The α-decay energy and half-life value for the I ^π = 13/2⁺ isomer are E _α = 6408(5) keV, T _1/2 = 4.3(2) s, respectively; while for the I ^π = 3/2^- isomer ( T _1/2 = 6.3(4) s) two α-decays with E _α1 = 6288(5) keV, I _α1 = 56(2)% and E _α2 = 6486(5) keV, I _α2 = 44(2)% were observed. By observing prompt α-γ coincidences new information on the low-lying states in the daughter isotope ¹⁸¹Hg was obtained. Received: 7 February 2002 / Accepted: 19 February 2002