Regular and chaotic vibration in a piezoelectric energy harvester

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy

Understanding disease control: influence of epidemiological and economic factors

We present a local spread model of disease transmission on a regular network and compare different control options ranging from treating the whole population to local control in a well-defined neighborhood of an infectious individual. Comparison is based on a total cost of epidemic, including cost of palliative treatment of ill individuals and preventive cost aimed at vaccination or culling of susceptible individuals. Disease is characterized by pre- symptomatic phase which makes detection and control difficult. Three general strategies emerge, global preventive treatment, local treatment within a neighborhood of certain size and only palliative treatment with no prevention. The choice between the strategies depends on relative costs of palliative and preventive treatment. The details of the local strategy and in particular the size of the optimal treatment neighborhood weakly depends on disease infectivity but strongly depends on other epidemiological factors. The required extend of prevention is proportional to the size of the infection neighborhood, but this relationship depends on time till detection and time till treatment in a non-nonlinear (power) law. In addition, we show that the optimal size of control neighborhood is highly sensitive to the relative cost, particularly for inefficient detection and control application. These results have important consequences for design of prevention strategies aiming at emerging diseases for which parameters are not known in advance

A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts

Abstract. We present a Lagrangian convective transport scheme developed for Chemistry and Transport Models and ensemble trajectory simulations. Similar to existing schemes in other Lagrangian models, it is based on a statistical approach of calculating parcel displacements by convection. These schemes redistribute air parcels within a fixed time step by calculating probabilities for entrainment and the altitude of detrainment. Our scheme extends this approach by modelling vertical updraft velocities and the time that an air parcel spends inside the convective event, which is important for simulating the tropospheric chemistry of short-lived species, e.g. it determines the time available for heterogeneous processes on the surface of cloud droplets. Two different schemes for determining the vertical updraft velocities are introduced, which are based on constant or random convective area fraction profiles, respectively. SO2 is used as an example to show that there is a significant effect on species mixing ratios when modelling the time spent in convective updrafts compared to a nearly instantaneous redistribution of air parcels. The scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective parameterization, which can be obtained from meteorological analysis data or General Circulation Models. Validation runs driven by ECMWF ERA Interim reanalysis data are performed with the scheme implemented into the ATLAS Chemistry and Transport Model. These include long-term global trajectory simulations of Radon-222 that are compared to measurements, and runs testing mass conservation and the reproduction of the convective mass fluxes and detrainment rates of ERA Interim. Simulated vertical updraft velocities are validated by wind profiler measurements in Darwin. </jats:p

A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts (LaConTra v1.0)

We present a Lagrangian convective transport scheme developed for global chemistry and transport models, which considers the variable residence time that an air parcel spends in convection. This is particularly important for accurately simulating the tropospheric chemistry of short-lived species, e.g., for determining the time available for heterogeneous chemical processes on the surface of cloud droplets. In current Lagrangian convective transport schemes air parcels are stochastically redistributed within a fixed time step according to estimated probabilities for convective entrainment as well as the altitude of detrainment. We introduce a new scheme that extends this approach by modeling the variable time that an air parcel spends in convection by estimating vertical updraft velocities. Vertical updraft velocities are obtained by combining convective mass fluxes from meteorological analysis data with a parameterization of convective area fraction profiles. We implement two different parameterizations: a parameterization using an observed constant convective area fraction profile and a parameterization that uses randomly drawn profiles to allow for variability. Our scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective parameterization, which can be obtained from meteorological analysis data or from general circulation models. We study the effect of allowing for a variable time that an air parcel spends in convection by performing simulations in which our scheme is implemented into the trajectory module of the ATLAS chemistry and transport model and is driven by the ECMWF ERA-Interim reanalysis data. In particular, we show that the redistribution of air parcels in our scheme conserves the vertical mass distribution and that the scheme is able to reproduce the convective mass fluxes and detrainment rates of ERA-Interim. We further show that the estimated vertical updraft velocities of our scheme are able to reproduce wind profiler measurements performed in Darwin, Australia, for velocities larger than 0.6 m s−1. SO2 is used as an example to show that there is a significant effect on species mixing ratios when modeling the time spent in convective updrafts compared to a redistribution of air parcels in a fixed time step. Furthermore, we perform long-time global trajectory simulations of radon-222 and compare with aircraft measurements of radon activity

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models

Molecular and Physiological Properties Associated with Zebra Complex Disease in Potatoes and Its Relation with Candidatus Liberibacter Contents in Psyllid Vectors

Zebra complex (ZC) disease on potatoes is associated with Candidatus Liberibacter solanacearum (CLs), an α-proteobacterium that resides in the plant phloem and is transmitted by the potato psyllid Bactericera cockerelli (Šulc). The name ZC originates from the brown striping in fried chips of infected tubers, but the whole plants also exhibit a variety of morphological features and symptoms for which the physiological or molecular basis are not understood. We determined that compared to healthy plants, stems of ZC-plants accumulate starch and more than three-fold total protein, including gene expression regulatory factors (e.g. cyclophilin) and tuber storage proteins (e.g., patatins), indicating that ZC-affected stems are reprogrammed to exhibit tuber-like physiological properties. Furthermore, the total phenolic content in ZC potato stems was elevated two-fold, and amounts of polyphenol oxidase enzyme were also high, both serving to explain the ZC-hallmark rapid brown discoloration of air-exposed damaged tissue. Newly developed quantitative and/or conventional PCR demonstrated that the percentage of psyllids in laboratory colonies containing detectable levels of CLs and its titer could fluctuate over time with effects on colony prolificacy, but presumed reproduction-associated primary endosymbiont levels remained stable. Potato plants exposed in the laboratory to psyllid populations with relatively low-CLs content survived while exposure of plants to high-CLs psyllids rapidly culminated in a lethal collapse. In conclusion, we identified plant physiological biomarkers associated with the presence of ZC and/or CLs in the vegetative potato plant tissue and determined that the titer of CLs in the psyllid population directly affects the rate of disease development in plants

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors