Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

Acoustic black holes for relativistic fluids

We derive a new acoustic black hole metric from the Abelian Higgs model. In the non-relativistic limit, while the Abelian Higgs model becomes the Ginzburg-Landau model, the metric reduces to an ordinary Unruh type. We investigate the possibility of using (type I and II) superconductors as the acoustic black holes. We propose to realize experimental acoustic black holes by using spiral vortices solutions from the Navier-stokes equation in the non-relativistic classical fluids.Comment: 16 pages. typos corrected, contents expande

On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons

The paper considers some typical problems for kinetic models evolving through pair-collisions at temperatures not far from absolute zero, which illustrate specific quantum behaviours. Based on these examples, a number of differences between quantum and classical Boltzmann theory is then discussed in more general terms.Comment: 25 pages, minor updates of previous versio

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Anomalous Enhancement of the Superconducting Transition Temperature in Electron-Doped Cuprate Heterostructures

The superconducting transition temperature $T_{c}$ of multilayers of electron-doped cuprates, composed of underdoped (or undoped) and overdoped La% $_{2-x}$Ce$_{x}$CuO$_{4}$ (LCCO) and Pr$_{2-x}$Ce$_{x}$CuO$_{4}$ (PCCO) thin films, is found to increase significantly with respect to the $T_{c}$ of the corresponding single-phase films. By investigating the critical current density of superlattices with different doping levels and layer thicknesses, we find that the $T_{c}$ enhancement is caused by a redistribution of charge over an anomalously large distance.Comment: 4 figures. To appear in PRB as a Rapid Communicatio

A Rotating-Tip-Based Mechanical Nano-Manufacturing Process: Nanomilling

We present a rotating-tip-based mechanical nanomanufacturing technique, referred to here as nanomilling. An atomic force microscopy (AFM) probe tip that is rotated at high speeds by out-of-phase motions of the axes of a three-axis piezoelectric actuator is used as the nanotool. By circumventing the high-compliance AFM beam and directly attaching the tip onto the piezoelectric actuator, a high-stiffness arrangement is realized. The feeding motions and depth prescription are provided by a nano-positioning stage. It is shown that nanomilling is capable of removing the material in the form of long curled chips, indicating shearing as the dominant material removal mechanism. Feature-size and shape control capabilities of the method are demonstrated

Performance Evaluation of the Global Airline Industry under the Impact of the COVID- 19 Pandemic: A Dynamic Network Data Envelopment Analysis Approach

This is the author accepted manuscript.The COVID-19 pandemic posed unprecedented challenges to the airline industry, necessitating a focus on maintaining high efficiency for profitability. This study assesses the efficiency of 26 international airlines from 2019 to 2022 using a dynamic network data envelopment analysis (DNDEA) methodology. The model accounts for the dynamic effect between two consecutive periods and incorporates an internal structure to evaluate airline performance across multiple dimensions. It enables the assessment of overall, period-specific, and stage-specific efficiencies. The findings reveal that while overall efficiency is moderately high on average, no airline achieved full efficiency during the pandemic. Efficiency decreased notably from 2019 to 2020, with a partial recovery but not a return to pre-pandemic levels by 2022. Operational performance remains satisfactory and stable, while service and financial performance exhibit lower efficiency, especially among low-cost airlines compared to full-service counterparts. Additionally, the study explores airlines' environmental impact by considering greenhouse gas emissions. Comparative analysis with a dynamic DEA model without internal structure highlights theoretical contributions, and the study offers managerial insights for airline leaders and policymakers

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the timereversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice, so it still holds in the presence of the Hubbard correlation. In contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice.Comment: 5 pages, 2 figure

Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately

Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equations

The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations provide promising tools to make the accelerate failure time models more attractive in practice. For semiparametric multivariate accelerated failure time models, we propose a generalized estimating equation approach to account for the multivariate dependence through working correlation structures. The marginal error distributions can be either identical as in sequential event settings or different as in parallel event settings. Some regression coefficients can be shared across margins as needed. The initial estimator is a rank-based estimator with Gehan's weight, but obtained from an induced smoothing approach with computation ease. The resulting estimator is consistent and asymptotically normal, with a variance estimated through a multiplier resampling method. In a simulation study, our estimator was up to three times as efficient as the initial estimator, especially with stronger multivariate dependence and heavier censoring percentage. Two real examples demonstrate the utility of the proposed method