15,156 research outputs found
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
The Declining Share of Agricultural Employment in the People\u27s Republic of China: How Fast?
From 1962 to 2013, the People’s Republic of China’s (PRC’s) agricultural employment share declined from 82% to 31%. The transfer of workers out of low-productivity agriculture is a fundamental pillar of the PRC’s aspirations to progress and eventually become a high-income economy. We hypothesize that the drivers of this decline have been the increase in income per capita, industrial value added, foreign direct investment, and domestic credit. We use an Autoregressive Distributed Lag Model to test the strong exogeneity of the regressors so that we can use it for forecasting. Results indicate that the share of employment in agriculture in the PRC will decline to about 24% by 2020, the end of the 13th Five-Year Plan (2016–2020). We also estimate that the PRC’s employment share will reach 5%, the share observed in today’s rich economies, by 2042–2048
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements
Continuous-time birth-death-shift (BDS) processes are frequently used in
stochastic modeling, with many applications in ecology and epidemiology. In
particular, such processes can model evolutionary dynamics of transposable
elements - important genetic markers in molecular epidemiology. Estimation of
the effects of individual covariates on the birth, death, and shift rates of
the process can be accomplished by analyzing patient data, but inferring these
rates in a discretely and unevenly observed setting presents computational
challenges. We propose a mutli-type branching process approximation to BDS
processes and develop a corresponding expectation maximization (EM) algorithm,
where we use spectral techniques to reduce calculation of expected sufficient
statistics to low dimensional integration. These techniques yield an efficient
and robust optimization routine for inferring the rates of the BDS process, and
apply more broadly to multi-type branching processes where rates can depend on
many covariates. After rigorously testing our methodology in simulation
studies, we apply our method to study intrapatient time evolution of IS6110
transposable element, a frequently used element during estimation of
epidemiological clusters of Mycobacterium tuberculosis infections.Comment: 31 pages, 7 figures, 1 tabl
Multi-Brane Worlds and modification of gravity at large scales
We discuss the implications of multi-brane constructions involving
combinations of positive and negative tension brane and show how anomalously
light KK states emerge when negative tension ''-'' branes are sandwiched
between ''+'' branes. We present a detailed study of a ''+--+'' brane
assignment which interpolates between two models that have been previously
proposed in which gravity is modified at large scales due to the anomalously
light states. We show that it has the peculiar characteristic that gravity
changes from four dimensional (4D) to 5D at large distances and returns to 4D
at even larger scales. We also consider a crystalline universe which leads to a
similar structure for gravity. The problems associated with intermediate
negative tension branes are discussed and a possible resolution suggested.Comment: 28 pages, 6 figures,references adde
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