Fractal Dimension of Disordered Submonolayers: Determination from He Scattering Data

We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms scattered from the surface, as a function of incidence energy. The (Minkowski) fractal dimension thus obtained is that of contours of constant electron density of the adatom system. Simulation results are presented, based on experimental data. A coverage dependent fractal dimension is found from a two-decade wide scaling regime.Comment: 12 pages, 4 figures, replaced with revised version. More info available at http://www.fh.huji.ac.il/~dani/ . Chem. Phys. Lett., in pres

A remedy for zero-point energy problems in classical trajectories. A combined semiclassical/clasical molecular dynamics algorithm

A new method is proposed for dealing with difficulties in molecular dynamics (MD) simulations caused by nonpreservation of zero-point energies (ZPE) in classical dynamics. Specifically addressed is a difficulty, for molecules held in weakly bound clusters, of energy flow from the initial ZPE of stiff molecular vibrations into soft cluster modes, causing unphysical dissociation or melting of the cluster. The remedy proposed is a classicallike MD algorithm, which treats the stiff modes by semiclassical Gaussian wave packets and the soft modes by classical dynamics, using the time-dependent self-consistent field (TDSCF) approach to couple the classical and the semiclassical modes. The resulting algorithm is very similar in form to classical MD, is computationally simple, stable, and appears free of unphysical effects. The method is illustrated by test applications to models of the clusters I2He and (HBr)2 in the ground states, which dissociate at the expense of their ZPE classically, but remain stable in the new method. @ 1992 American Institute of PhysicsThis research was supported by the Petroleum Research Fund, administered by the American Chemical Society (Grant No. 2966-AC6 to R.B.G.) and by the Institute for Surface and Interface Science at the University of California, Irvine.Peer Reviewe

He Scattering from Compact Clusters and from Diffusion-Limited Aggregates on Surfaces: Observable Signatures of Structure

The angular intensity distribution of He beams scattered from compact clusters and from diffusion limited aggregates, epitaxially grown on metal surfaces, is investigated theoretically. The purpose is twofold: to distinguish compact cluster structures from diffusion limited aggregates, and to find observable {\em signatures} that can characterize the compact clusters at the atomic level of detail. To simplify the collision dynamics, the study is carried out in the framework of the sudden approximation, which assumes that momentum changes perpendicular to the surface are large compared with momentum transfer due to surface corrugation. The diffusion limited aggregates on which the scattering calculations were done, were generated by kinetic Monte Carlo simulations. It is demonstrated, by focusing on the example of compact Pt Heptamers, that signatures of structure of compact clusters may indeed be extracted from the scattering distribution. These signatures enable both an experimental distinction between diffusion limited aggregates and compact clusters, and a determination of the cluster structure. The characteristics comprising the signatures are, to varying degrees, the Rainbow, Fraunhofer, specular and constructive interference peaks, all seen in the intensity distribution. It is also shown, how the distribution of adsorbate heights above the metal surface can be obtained by an analysis of the specular peak attenuation. The results contribute to establishing He scattering as a powerful tool in the investigation of surface disorder and epitaxial growth on surfaces, alongside with STM.Comment: 41 pages, 16 postscript figures. For more details see http://www.fh.huji.ac.il/~dan

Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and Sierpinski carpet as special cases. Also randomized versions of these fractals are treated. The general result is that the diffraction intensities obey a strict recursion relation, and become self-affine in the limit of large iteration number, with a self-affinity exponent related directly to the fractal dimension of the scattering object. Applications include neutron scattering, x-rays, optical diffraction, magnetic resonance imaging, electron diffraction, and He scattering, which all display the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at http://www.fh.huji.ac.il/~dani

Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

Constitutions and Policy Comparisons

Voters in democracies can learn from the experience of neighbouring states: about policy in a direct democracy (`policy experimentation'), about the quality of their politicians in a representative democracy (`yardstick competition'). Learning between states creates spillovers from policy choice, and also from constitutional choice. I model these spillovers in a simple principal-agent framework, and show that voter welfare may be maximized by a mixture of representative and direct democratic states. Because of this, empirical work examining voter welfare under direct democracy may need to be reinterpreted. Also, I show that the optimal mix of constitutions cannot always be achieved in a constitutional choice equilibrium involving many states. </jats:p

Spontaneous Magnetization of the O(3) Ferromagnet at Low Temperatures

We investigate the low-temperature behavior of ferromagnets with a spontaneously broken symmetry O(3) $\to$ O(2). The analysis is performed within the perspective of nonrelativistic effective Lagrangians, where the dynamics of the system is formulated in terms of Goldstone bosons. Unlike in a Lorentz-invariant framework (chiral perturbation theory), where loop graphs are suppressed by two powers of momentum, loops involving ferromagnetic spin waves are suppressed by three momentum powers. The leading coefficients of the low-temperature expansion for the partition function are calculated up to order $p^{10}$. In agreement with Dyson's pioneering microscopic analysis of the cubic ferromagnet, we find that, in the spontaneous magnetization, the magnon-magnon interaction starts manifesting itself only at order $T^4$. The striking difference with respect to the low-temperature properties of the O(3) antiferromagnet is discussed from a unified point of view, relying on the effective Lagrangian technique.Comment: 23 pages, 4 figure

Some aspects of the Liouville equation in mathematical physics and statistical mechanics

This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE)

Long Term Cyclic Pamidronate Reduces Bone Growth by Inhibiting Osteoclast Mediated Cartilage-to-Bone Turnover in the Mouse

Bisphosphonates, used to treat diseases exhibiting increased osteoclast activity, reduce longitudinal bone growth through an as yet undefined mechanism. Pamidronate, an aminobisphosphonate, was given weekly to mice at 0, 1.25, or 2.50 mg/kg/wk beginning at 4 weeks of age. At 12 weeks of age, humeral length, growth plate area, regional chondrocyte cell numbers, chondrocyte apoptosis, TRAP stained osteoclast number, and osteoclast function assessed by cathepsin K immunohistochemistry were quantified. Humeral length was decreased in pamidronate treated mice compared to vehicle control mice, and correlated with greater growth plate areas reflecting greater proliferative and hypertrophic chondrocyte cell numbers with fewer hypertrophic cells undergoing apoptosis. Pamidronate treatment increased TRAP stained osteoclast numbers yet decreased cathepsin K indicating that pamidronate repressed osteoclast maturation and function. The data suggest that long term cyclic pamidronate treatment impairs bone growth by inhibition of osteoclast maturation thereby reducing cartilage-to-bone turnover within the growth plate

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N [subscript G] is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε ε[subscript s] with slow internal dynamics. The cohesion strength ε[subscript s] of this freezing transition depends on N G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N [subscript G] . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi