Survival-Time Distribution for Inelastic Collapse

In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power-law in time, and that the exponent governing this decay is non-universal. An approximate calculation of the collapse-time exponent confirms this behaviour and shows how inelastic collapse can be viewed as a generalised persistence phenomenon.Comment: 4 pages, RevTe

Novae Ejecta as Colliding Shells

Following on our initial absorption-line analysis of fifteen novae spectra we present additional evidence for the existence of two distinct components of novae ejecta having different origins. As argued in Paper I one component is the rapidly expanding gas ejected from the outer layers of the white dwarf by the outburst. The second component is pre-existing outer, more slowly expanding circumbinary gas that represents ejecta from the secondary star or accretion disk. We present measurements of the emission-line widths that show them to be significantly narrower than the broad P Cygni profiles that immediately precede them. The emission profiles of novae in the nebular phase are distinctly rectangular, i.e., strongly suggestive of emission from a relatively thin, roughly spherical shell. We thus interpret novae spectral evolution in terms of the collision between the two components of ejecta, which converts the early absorption spectrum to an emission-line spectrum within weeks of the outburst. The narrow emission widths require the outer circumbinary gas to be much more massive than the white dwarf ejecta, thereby slowing the latter's expansion upon collision. The presence of a large reservoir of circumbinary gas at the time of outburst is suggestive that novae outbursts may sometime be triggered by collapse of gas onto the white dwarf, as occurs for dwarf novae, rather than steady mass transfer through the inner Lagrangian point.Comment: 12 pages, 3 figures; Revised manuscript; Accepted for publication in Astrophysics & Space Scienc

Observability and nonlinear filtering

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential

We report on the results of molecular dynamics simulation (MD) studies of the classical two-dimensional electron crystal in the presence disorder. Our study is motivated by recent experiments on this system in modulation doped semiconductor systems in very strong magnetic fields, where the magnetic length is much smaller than the average interelectron spacing $a_0$, as well as by recent studies of electrons on the surface of helium. We investigate the low temperature state of this system using a simulated annealing method. We find that the low temperature state of the system always has isolated dislocations, even at the weakest disorder levels investigated. We also find evidence for a transition from a hexatic glass to an isotropic glass as the disorder is increased. The former is characterized by quasi-long range orientational order, and the absence of disclination defects in the low temperature state, and the latter by short range orientational order and the presence of these defects. The threshold electric field is also studied as a function of the disorder strength, and is shown to have a characteristic signature of the transition. Finally, the qualitative behavior of the electron flow in the depinned state is shown to change continuously from an elastic flow to a channel-like, plastic flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for publication in Phys. Rev. B., HAF94MD

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Optimization of the high-throughput synthesis of multiblock copolymer nanoparticles in aqueous media: Via polymerization-induced self-assembly

Over the past fifteen years or so, polymerization-induced self-assembly (PISA) has become widely recognized as a powerful and versatile platform technology for the synthesis of a wide range of block copolymer nanoparticles of controlled size, shape and surface chemistry. In the present study, we report that PISA formulations are sufficiently robust to enable high-throughput experiments using a commercial synthesis robot (Chemspeed Autoplant A100). More specifically, we use reversible addition-fragmentation chain transfer (RAFT) aqueous emulsion polymerization of either n-butyl methacrylate and/or benzyl methacrylate to prepare various examples of methacrylic multiblock copolymer nanoparticles using a poly(methacrylic acid) stabilizer block. Adequate stirring is essential to generate sufficiently small monomer droplets for such heterogeneous polymerizations to proceed efficiently. Good reproducibility can be achieved under such conditions, with well-defined spherical morphologies being obtained at up to 45% w/w solids. GPC studies indicate high blocking efficiencies but relatively broad molecular weight distributions (Mw/Mn= 1.36-1.85), suggesting well-defined (albeit rather polydisperse) block copolymer chains. These preliminary studies provide a sound basis for high-throughput screening of RAFT-mediated PISA formulations, which is likely to be required for commercialization of this technology. Our results indicate that methacrylic PISA formulations enable the synthesis of diblock and triblock copolymer nanoparticles in high overall yield (94-99%) within 1-3 h at 70 °C. However, tetrablocks suffer from incomplete conversions (87-96% within 5 h) and hence most likely represent the upper limit for this approach

Solution and Solid-State Behavior of Amphiphilic ABA Triblock Copolymers of Poly(acrylic acid-stat-styrene)-block-poly(butyl acrylate)-block-poly(acrylic acid-stat-styrene)

A combination of statistical and triblock copolymer properties is explored to produce stable aqueous polymer dispersions suitable for the film formation. In order to perform an extensive structural characterization of the products in the dissolved, dispersed, and solid states, a wide range of symmetrical poly(acrylic acid-stat-styrene)x-block-poly(butyl acrylate)y-block-poly(acrylic acid-stat-styrene)x, poly(AA-st-St)x-b-PBAy-b-poly(AA-st-St)x, (x = 56, 108 and 140, y = 100–750; the AA:St molar ratio is 42:58) triblock copolymers were synthesized by reversible addition–fragmentation chain transfer (RAFT) solution polymerization using a bifunctional symmetrical RAFT agent. It is demonstrated that the amphiphilic statistical outer blocks can provide sufficient stabilization to largely hydrophobic particles in aqueous dispersions. Such a molecular design provides an advantage over copolymers composed only of homoblocks, as a simple variation of the statistical block component ratio provides an efficient way to control the hydrophilicity of the stabilizer block, which ultimately affects the copolymer morphology in solutions and solid films. It was found by small-angle X-ray scattering (SAXS) that the copolymers behaved as dissolved chains in methylethylketone (MEK) but self-assembled in water into stable and well-defined spherical particles that increased in size with the length of the hydrophobic PBA block. These particles possessed an additional particulate surface structure formed by the statistical copolymer stabilizer block, which self-folded through the hydrophobic interactions between the styrene units. SAXS and atomic force microscopy showed that the copolymer films cast from the MEK solutions formed structures predicted by self-consistent field theory for symmetrical triblock copolymers, while the aqueous dispersions formed structural morphologies similar to a close-packed spheres, as would be expected for copolymer particles trapped kinetically due to the restricted movement of the blocks in the initial aqueous dispersion. A strong correlation between the structural morphology and mechanical properties of the films was observed. It was found that the properties of the solvent cast films were highly dependent on the ratios of the hard [poly(AA-st-St)] and soft (PBA) blocks, while the aqueous cast films did not show such a dependence. The continuous phase of hard blocks, always formed in the case of the aqueous cast films, produced films with a higher elastic modulus and a lower extension-to-break in a comparison with the solvent-cast films

Coherent electron-phonon coupling and polaron-like transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.Comment: 21 pages, 8 figures, accepted for publication in Phys. Rev. B (to appear march 2001

Control of particle size in the self-assembly of amphiphilic statistical copolymers

A range of amphiphilic statistical copolymers is synthesized where the hydrophilic component is either methacrylic acid (MAA) or 2-(dimethylamino)ethyl methacrylate (DMAEMA) and the hydrophobic component comprises methyl, ethyl, butyl, hexyl, or 2-ethylhexyl methacrylate, which provide a broad range of partition coefficients (log P). Small-angle X-ray scattering studies confirm that these amphiphilic copolymers self-assemble to form well-defined spherical nanoparticles in an aqueous solution, with more hydrophobic copolymers forming larger nanoparticles. Varying the nature of the alkyl substituent also influenced self-assembly with more hydrophobic comonomers producing larger nanoparticles at a given copolymer composition. A model based on particle surface charge density (PSC model) is used to describe the relationship between copolymer composition and nanoparticle size. This model assumes that the hydrophilic monomer is preferentially located at the particle surface and provides a good fit to all of the experimental data. More specifically, a linear relationship is observed between the surface area fraction covered by the hydrophilic comonomer required to achieve stabilization and the log P value for the hydrophobic comonomer. Contrast variation small-angle neutron scattering is used to study the internal structure of these nanoparticles. This technique indicates partial phase separation within the nanoparticles, with about half of the available hydrophilic comonomer repeat units being located at the surface and hydrophobic comonomer-rich cores. This information enables a refined PSC model to be developed, which indicates the same relationship between the surface area fraction of the hydrophilic comonomer and the log P of the hydrophobic comonomer repeat units for the anionic (MAA) and cationic (DMAEMA) comonomer systems. This study demonstrates how nanoparticle size can be readily controlled and predicted using relatively ill-defined statistical copolymers, making such systems a viable attractive alternative to diblock copolymer nanoparticles for a range of industrial applications