Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model

A Bus Route Model (BRM) can be defined on a one-dimensional lattice, where buses are represented by "particles" that are driven forward from one site to the next with each site representing a bus stop. We replace the random sequential updating rules in an earlier BRM by parallel updating rules. In order to elucidate the connection between the BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg (NaSch) model, we propose two alternative extensions of the NaSch model with space-/time-dependent hopping rates. Approximating the BRMPU as a generalization of the NaSch model, we calculate analytically the steady-state distribution of the {\it time headways} (TH) which are defined as the time intervals between the departures (or arrivals) of two successive particles (i.e., buses) recorded by a detector placed at a fixed site (i.e., bus stop) on the model route. We compare these TH distributions with the corresponding results of our computer simulations of the BRMPU, as well as with the data from the simulation of the two extended NaSch models. We also investigate interesting kinetic properties exhibited by the BRMPU during its time evolution from random initial states towards its steady-states.Comment: Accepted for publication in EPJ

A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough.Comment: 5 pages, PostScript forma

Stress-driven instability in growing multilayer films

We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system recursively in terms of that of the old states of the buried layers. In turn, we use the result for the elastic state to derive the morphological evolution equation of surface profile to first order of perturbations, with the solution explicitly expressed by the growth conditions and material parameters of all the deposited layers. We apply these results to two kinds of multilayer structures. One is the alternating tensile/compressive multilayer structure, for which we determine the effective stability properties, including the effect of varying surface mobility in different layers, its interplay with the global misfit of the multilayer film, and the influence of asymmetric structure of compressive and tensile layers on the system stability. The nature of the asymmetry properties found in stability diagrams is in agreement with experimental observations. The other multilayer structure that we study is one composed of stacked strained/spacer layers. We also calculate the kinetic critical thickness for the onset of morphological instability and obtain its reduction and saturation as number of deposited layers increases, which is consistent with recent experimental results. Compared to the single-layer film growth, the behavior of kinetic critical thickness shows deviations for upper strained layers.Comment: 27 pages, 11 figures; Phys. Rev. B, in pres

Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations.Comment: 26 pages, 13 eps figure

Global, regional, and national cancer incidence, mortality, years of life lost, years lived with disability, and disability-Adjusted life-years for 29 cancer groups, 1990 to 2017 : A systematic analysis for the global burden of disease study

Importance: Cancer and other noncommunicable diseases (NCDs) are now widely recognized as a threat to global development. The latest United Nations high-level meeting on NCDs reaffirmed this observation and also highlighted the slow progress in meeting the 2011 Political Declaration on the Prevention and Control of Noncommunicable Diseases and the third Sustainable Development Goal. Lack of situational analyses, priority setting, and budgeting have been identified as major obstacles in achieving these goals. All of these have in common that they require information on the local cancer epidemiology. The Global Burden of Disease (GBD) study is uniquely poised to provide these crucial data. Objective: To describe cancer burden for 29 cancer groups in 195 countries from 1990 through 2017 to provide data needed for cancer control planning. Evidence Review: We used the GBD study estimation methods to describe cancer incidence, mortality, years lived with disability, years of life lost, and disability-Adjusted life-years (DALYs). Results are presented at the national level as well as by Socio-demographic Index (SDI), a composite indicator of income, educational attainment, and total fertility rate. We also analyzed the influence of the epidemiological vs the demographic transition on cancer incidence. Findings: In 2017, there were 24.5 million incident cancer cases worldwide (16.8 million without nonmelanoma skin cancer [NMSC]) and 9.6 million cancer deaths. The majority of cancer DALYs came from years of life lost (97%), and only 3% came from years lived with disability. The odds of developing cancer were the lowest in the low SDI quintile (1 in 7) and the highest in the high SDI quintile (1 in 2) for both sexes. In 2017, the most common incident cancers in men were NMSC (4.3 million incident cases); tracheal, bronchus, and lung (TBL) cancer (1.5 million incident cases); and prostate cancer (1.3 million incident cases). The most common causes of cancer deaths and DALYs for men were TBL cancer (1.3 million deaths and 28.4 million DALYs), liver cancer (572000 deaths and 15.2 million DALYs), and stomach cancer (542000 deaths and 12.2 million DALYs). For women in 2017, the most common incident cancers were NMSC (3.3 million incident cases), breast cancer (1.9 million incident cases), and colorectal cancer (819000 incident cases). The leading causes of cancer deaths and DALYs for women were breast cancer (601000 deaths and 17.4 million DALYs), TBL cancer (596000 deaths and 12.6 million DALYs), and colorectal cancer (414000 deaths and 8.3 million DALYs). Conclusions and Relevance: The national epidemiological profiles of cancer burden in the GBD study show large heterogeneities, which are a reflection of different exposures to risk factors, economic settings, lifestyles, and access to care and screening. The GBD study can be used by policy makers and other stakeholders to develop and improve national and local cancer control in order to achieve the global targets and improve equity in cancer care. © 2019 American Medical Association. All rights reserved.Peer reviewe

Elastic properties of homopolymer-homopolymer interfaces containing diblock copolymers

We study the elastic properties of homopolymer/homopolymer interfaces containing diblock copolymers by means of a theory of Gaussian fluctuations. The interfacial tension and the bending rigidity of the interface in the two-phase coexistence region are calculated from the power spectrum of capillary modes. Our theory shows that in the limiting case of a pure binary homopolymer mixture, while the interfacial tension increases monotonically with increasing χN (where χ is the Flory-Huggins parameter and N is the homopolymer molecular weight) the bending rigidity does not. The bending rigidity increases rapidly at first for small values of χN, but then decreases with further increase of χN. In the presence of diblock copolymers, the interfacial tension always decreases with increasing diblock copolymer volume fraction at a given χN. However, the bending rigidity can show either a decrease or an increase depending on χN and the ratio γ between the molecular weights of a diblock copolymer and that of a homopolymer. Our results for the surface pressure and the bending rigidity are further compared with results based on scaling arguments of wet polymer brushes. © 1998 American Institute of Physics

Molecular beam epitaxy in the presence of phase separation

Experiments have shown that phase separation during the growth of solid films by molecular beam epitaxy (MBE) is a phenomenon seen in a variety of systems. We study a MBE process where two types of particles are deposited simultaneously, and where the interatomic potential energy leads to phase separation. From a microscopic point of view, we describe the system with a solid-on-solid model augmented by an Ising model to represent the phase separation. Monte Carlo simulations of this model show that for low deposition rates, a lamellar pattern emerges in the bulk, with a modulation parallel to the growth plane. We show how the temperature and the deposition rate can be used to tailor the wavelength of the modulation. The effects of the phase separation on the surface morphology create a modulation consisting of steps or grooves at the interface between surface domains, which can be seen in the height-height correlation function and in the surface width. The temperature dependence of the surface width at fixed deposition rate is also presented. © 1997 The American Physical Society