Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

We numerically investigate the characteristics of chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schr\"{o}dinger equation model. Completing previous investigations \cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak' and `strong chaos' dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $\Lambda$ decays in time $t$ as $\Lambda \propto t^{\alpha_{\Lambda}}$, with $\alpha_{\Lambda}$ being different from the $\alpha_{\Lambda}=-1$ value observed in cases of regular motion. In particular, $\alpha_{\Lambda}\approx -0.25$ (weak chaos) and $\alpha_{\Lambda}\approx -0.3$ (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $\Lambda$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.Comment: 11 pages, 10 figure

Computational efficiency of symplectic integration schemes: application to multidimensional disordered Klein–Gordon lattices

We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein–Gordon lattices with many degrees of freedom and investigate their numerical performance. For this purpose, we perform extensive numerical simulations by considering many different initial energy excitations and following the evolution of the created wave packets in the various dynamical regimes exhibited by these models. We compare the efficiency of the considered integrators by checking their ability to correctly reproduce several features of the wave packets propagation, like the characteristics of the created energy distribution and the time evolution of the systems’ maximum Lyapunov exponent estimator. Among the tested integrators the fourth order ABA864 scheme [S. Blanes et al., Appl. Numer. Math. 68, 58 (2013)] showed the best performance as it needed the least CPU time for capturing the correct dynamical behavior of all considered cases when a moderate accuracy in conserving the systems’ total energy value was required. Among the higher order schemes used to achieve a better accuracy in the energy conservation, the sixth order scheme s11ABA82_6 exhibited the best performance

Readiness of health facilities to manage individuals infected with COVID-19, Uganda, June 2021

Abstract Background The COVID-19 pandemic overwhelmed the capacity of health facilities globally, emphasizing the need for readiness to respond to rapid increases in cases. The first wave of COVID-19 in Uganda peaked in late 2020 and demonstrated challenges with facility readiness to manage cases. The second wave began in May 2021. In June 2021, we assessed the readiness of health facilities in Uganda to manage the second wave of COVID-19. Methods Referral hospitals managed severe COVID-19 patients, while lower-level health facilities screened, isolated, and managed mild cases. We assessed 17 of 20 referral hospitals in Uganda and 71 of 3,107 lower-level health facilities, selected using multistage sampling. We interviewed health facility heads in person about case management, coordination and communication and reporting, and preparation for the surge of COVID-19 during first and the start of the second waves of COVID-19, inspected COVID-19 treatment units (CTUs) and other service delivery points. We used an observational checklist to evaluate capacity in infection prevention, medicines, personal protective equipment (PPE), and CTU surge capacity. We used the “ReadyScore” criteria to classify readiness levels as > 80% (‘ready’), 40–80% (‘work to do’), and < 40% (‘not ready’) and tailored the assessments to the health facility level. Scores for the lower-level health facilities were weighted to approximate representativeness for their health facility type in Uganda. Results The median (interquartile range (IQR)) readiness scores were: 39% (IQR: 30, 51%) for all health facilities, 63% (IQR: 56, 75%) for referral hospitals, and 32% (IQR: 24, 37%) for lower-level facilities. Of 17 referral facilities, two (12%) were ‘ready’ and 15 (88%) were in the “work to do” category. Fourteen (82%) had an inadequate supply of medicines, 12 (71%) lacked adequate supply of oxygen, and 11 (65%) lacked space to expand their CTU. Fifty-five (77%) lower-level health facilities were “not ready,” and 16 (23%) were in the “work to do” category. Seventy (99%) lower-level health facilities lacked medicines, 65 (92%) lacked PPE, and 53 (73%) lacked an emergency plan for COVID-19. Conclusion Few health facilities were ready to manage the second wave of COVID-19 in Uganda during June 2021. Significant gaps existed for essential medicines, PPE, oxygen, and space to expand CTUs. The Uganda Ministry of Health utilized our findings to set up additional COVID-19 wards in hospitals and deliver medicines and PPE to referral hospitals. Adequate readiness for future waves of COVID-19 requires additional support and action in Uganda