An asymptotic relationship between coupling methods for stochastically modeled population processes

This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a computational framework by providing reductions in variance for different Monte Carlo estimators, thereby allowing for significantly more accurate results for a fixed amount of computational time. Common applications of the couplings include the estimation of parametric sensitivities via finite difference methods and the estimation of expectations via multi-level Monte Carlo algorithms. While a number of coupling strategies have been proposed for the models considered here, and a number of articles have experimentally compared the different strategies, to date there has been no mathematical analysis describing the connections between them. Such analyses are critical in order to determine the best use for each. In the current paper, we show a connection between the common reaction path (CRP) method and the split coupling (SC) method, which is termed coupled finite differences (CFD) in the parametric sensitivities literature. In particular, we show that the two couplings are both limits of a third coupling strategy we call the "local-CRP" coupling, with the split coupling method arising as a key parameter goes to infinity, and the common reaction path coupling arising as the same parameter goes to zero. The analysis helps explain why the split coupling method often provides a lower variance than does the common reaction path method, a fact previously shown experimentally.Comment: Edited Section 4.

Spectral Properties near the Mott Transition in the One-Dimensional Hubbard Model

Single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.Comment: 4 pages, 2 figure

Composition and structure of Pd nanoclusters in SiOx_x thin film

The nucleation, distribution, composition and structure of Pd nanocrystals in SiO$_2$ multilayers containing Ge, Si, and Pd are studied using High Resolution Transmission Electron Microscopy (HRTEM) and X-ray Photoelectron Spectroscopy (XPS), before and after heat treatment. The Pd nanocrystals in the as deposited sample seem to be capped by a layer of PdO$_x$. A 1-2 eV shift in binding energy was found for the Pd-3d XPS peak, due to initial state Pd to O charge transfer in this layer. The heat treatment results in a decomposition of PdO and Pd into pure Pd nanocrystals and SiO$_2$

Double-Exchange Model on Triangle Chain

We study ground state properties of the double-exchange model on triangle chain in the classical limit on $t_{2g}$ spins. The ground state is determined by a competition among the kinetic energy of the $e_g$ electron, the antiferromagnetic exchange energy between the $t_{2g}$ spins, and frustration due to a geometric structure of the lattice. The phase diagrams are obtained numerically for two kinds of the models which differ only in the transfer integral being real or complex. The properties of the states are understood from the viewpoint of the spin-induced Peierls instability. The results suggest the existence of a chiral glass phase which is characterized by a local spin chirality and a continuous degeneracy.Comment: 6 pages, 4 figure

Single-scattering properties of ellipsoidal dust aerosols constrained by measured dust shape distributions

Most global aerosol models approximate dust as spherical particles, whereas most remote sensing retrieval algorithms approximate dust as spheroidal particles with a shape distribution that conflicts with measurements. These inconsistent and inaccurate shape assumptions generate biases in dust single-scattering properties. Here, we obtain dust single-scattering properties by approximating dust as tri-axial ellipsoidal particles with observationally constrained shape distributions. We find that, relative to the ellipsoidal dust optics obtained here, the spherical dust optics used in most aerosol models underestimate dust single-scattering albedo, mass extinction efficiency, and asymmetry parameter for almost all dust sizes in both the shortwave and longwave spectra. We further find that the ellipsoidal dust optics are in substantially better agreement with observations of the scattering matrix and linear depolarization ratio than the spheroidal dust optics used in most retrieval algorithms. However, relative to observations, the ellipsoidal dust optics overestimate the lidar ratio by underestimating the backscattering intensity by a factor of ~2. This occurs largely because the computational method used to simulate ellipsoidal dust optics (i.e., the improved geometric optics method) underestimates the backscattering intensity by a factor of ~2 relative to other computational methods (e.g., the physical geometric optics method). We conclude that the ellipsoidal dust optics with observationally constrained shape distributions can help improve global aerosol models and possibly remote sensing retrieval algorithms that do not use the backscattering signal.</p

Star-shaped Local Density of States around Vortices in a Type II Superconductor

The electronic structure of vortices in a type II superconductor is analyzed within the quasi-classical Eilenberger framework. The possible origin of a sixfold ``star'' shape of the local density of states, observed by scanning tunneling microscope experiments on NbSe$_2$, is examined in the light of the three effects; the anisotropic pairing, the vortex lattice, and the anisotropic density of states at the Fermi surface. Outstanding features of split parallel rays of this star are well explained in terms of an anisotropic $s$-wave pairing. This reveals a rich internal electronic structure associated with a vortex core.Comment: 4 pages, REVTeX, 3 figures available upon reques