Peeling Bifurcations of Toroidal Chaotic Attractors

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium

We investigate, via computer simulations, the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables $M$ describing the system are the (empirical) particle density f=\{f(\un{x},\un{v})\} and the total energy $E$. We find that $S(f_t,E)$ is monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of $S(M_t) = S(M_{X_t})$ should hold generally for ``typical'' (the overwhelming majority of) initial microstates (phase-points) $X_0$ belonging to the initial macrostate $M_0$, satisfying $M_{X_0} = M_0$. This is a direct consequence of Liouville's theorem when $M_t$ evolves autonomously.Comment: 8 pages, 5 figures. Submitted to PR

From a kinetic equation to a diffusion under an anomalous scaling

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, and Y(t) is an additive functional of K(t). We prove that under an anomalous rescaling Y converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately rescaled solution of the Boltzmann equation converges to a diffusion equation

Sampling rare fluctuations of height in the Oslo ricepile model

We have studied large deviations of the height of the pile from its mean value in the Oslo ricepile model. We sampled these very rare events with probabilities of order $10^{-100}$ by Monte Carlo simulations using importance sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf 73}, 021303, 2006] that in steady state of the Oslo ricepile model, the probability of large negative height fluctuations $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha$ held fixed, and $\kappa > 0$.Comment: 7 pages, 8 figure

Chaotic properties of quantum many-body systems in the thermodynamic limit

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.Comment: 4 pages RevTeX, 4 postscript figures included with psfig; Completely restructured version with new results on mixing properties added

Expanding direction of the period doubling operator

We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a ``Perron-Frobenius type operator'', to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced operator. The proof is constructive. One can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point

Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbour two-dimensional lattice system with spin variables taking values in -1,0,+1. We consider large but finite volume, small fixed magnetic field h and chemical potential "lambda" in the limit of zero temperature; we analyze the first excursion from the metastable -1 configuration to the stable +1 configuration. We compute the asymptotic behaviour of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the line h=2*lambda is crossed.Comment: 96 pages, 44 tex-figures, 7 postscript figure

Klamath Tribal response to the pandemic of COVID-19 among Klamath Tribal Community in Oregon, USA

Introduction Socially-disadvantaged populations are more at risk of contracting COVID-19 than those with access to better medical facilities. We looked at responses of Klamath Tribes in Oregon, USA to mitigate spread of COVID-19 in a community with a higher incidence of obesity, diabetes and coronary heart disease, compared to the general US population. This study reports on Klamath Tribes response to COVID-19 March -September 2020. Methods Klamath Tribes Tribal Health and Family Services established a COVID-19 Incident Management Team (IMT), instituting creative programs including a Walk-In Testing Center, implementing strict infection control protocols and regular sharing of information on the pandemic and prevalence of COVID-19 amongst Klamath Tribes. All COVID-19 tests were documented with positive cases isolated and people with high risk exposures quarantined and provided with wrap-around medical and social services until recovered or past quarantine time period. Results A total of 888 (12%) tribal members were tested for COVID1-19 between March to September 2020; 50 were found positive for COVID-19, giving a test positivity rate of 5.6% (Male – 6.3%; Female – 5.2%). No deaths have been reported amongst the local Klamath Tribes and other American Indians/Alaska Native (AI/AN) population served by the tribe. Conclusion Despite the fact that structural inequities including income disparities have shaped racial and ethnic impact of epidemics around the world, the timely response, establishment of partnerships and proactive control of the epidemic resulted in minimal impact among the Klamath Tribal and other AI/AN populations served by the tribal facilities

Subclinical infection of macaques and baboons with a baboon simarterivirus

Simarteriviruses (Arteriviridae: Simarterivirinae) are commonly found at high titers in the blood of African monkeys but do not cause overt disease in these hosts. In contrast, simarteriviruses cause severe disease in Asian macaques upon accidental or experimental transmission. Here, we sought to better understand the host-dependent drivers of simarterivirus pathogenesis by infecting olive baboons (n = 4) and rhesus monkeys (n = 4) with the simarterivirus Southwest baboon virus 1 (SWBV-1). Surprisingly, none of the animals in our study showed signs of disease following SWBV-1 inoculation. Three animals (two rhesus monkeys and one olive baboon) became infected and sustained high levels of SWBV-1 viremia for the duration of the study. The course of SWBV-1 infection was highly predictable: plasma viremia peaked between 1 × 107 and 1 × 108 vRNA copies/mL at 3–10 days post-inoculation, which was followed by a relative nadir and then establishment of a stable set-point between 1 × 106 and 1 × 107 vRNA copies/mL for the remainder of the study (56 days). We characterized cellular and antibody responses to SWBV-1 infection in these animals, demonstrating that macaques and baboons mount similar responses to SWBV-1 infection, yet these responses are ineffective at clearing SWBV-1 infection. SWBV-1 sequencing revealed the accumulation of non-synonymous mutations in a region of the genome that corresponds to an immunodominant epitope in the simarterivirus major envelope glycoprotein GP5, which likely contribute to viral persistence by enabling escape from host antibodies