Optofluidic Platform Based on Liquid Crystals in X-Cut Lithium Niobate: Thresholdless All-Optical Response

In this study, we present a new configuration of the recently reported optofluidic platform exploiting liquid crystals reorientation in lithium niobate channels. In order to avoid the threshold behaviour observed in the optical control of the device, we propose microchannels realized in a x-cut crystal closed by a z-cut crystal on the top. In this way, the light-induced photovoltaic field is not uniform inside the liquid crystal layer and therefore the conditions for a thresholdless reorientation are realized. We performed simulations of the photovoltaic effect based on the well assessed model for Lithium Niobate, showing that not uniform orientation and value of the field should be expected inside the microchannel. In agreement with the re-orientational properties of nematic liquid crystals, experimental data confirm the expected thresholdless behaviour. The observed liquid crystal response exhibits two different regimes and the response time shows an unusual dependence on light intensity, both features indicating the presence of additional photo-induced fields appearing above a light intensity of 107 W/m2.

On symmetric intersecting families of vectors

A family of vectors in [k] n is said to be intersecting if any two of its elements agree on at least one coordinate. We prove, for fixed k ≥ 3, that the size of any intersecting subfamily of [k] n invariant under a transitive group of symmetries is o(k n ), which is in stark contrast to the case of the Boolean hypercube (where k = 2). Our main contribution addresses limitations of existing technology: while there are now methods, first appearing in work of Ellis and the third author, for using spectral machinery to tackle problems in extremal set theory involving symmetry, this machinery relies crucially on the interplay between up-sets, biased product measures, and threshold behaviour in the Boolean hypercube, features that are notably absent in the problem considered here. To circumvent these barriers, introducing ideas that seem of independent interest, we develop a variant of the sharp threshold machinery that applies at the level of products of posets.

Analysis on a diffusive SEI epidemic model with/without immigration of infected hosts

<p style='text-indent:20px;'>In this paper, we study a reaction-diffusion SEI epidemic model with/without immigration of infected hosts. Our results show that if there is no immigration for the infected (exposed) individuals, the model admits a threshold behaviour in terms of the basic reproduction number, and if the system includes the immigration, the disease always persists. In each case, we explore the global attractivity of the equilibrium via Lyapunov functions in the case of spatially homogeneous environment, and investigate the asymptotic behavior of the endemic equilibrium (when it exists) with respect to the small migration rate of the susceptible, exposed or infected population in the case of spatially heterogeneous environment. Our results suggest that the strategy of controlling the migration rate of population can not eradicate the disease, and the disease transmission risk will be underestimated if the immigration of infected hosts is ignored.</p>

Increasing groundwater CO2 in a mid-continent tallgrass prairie: Controlling factors

Alkalinity and groundwater CO2 have increased linearly from 1991–2017 at the Konza Prairie Biological Station (KPBS), a tallgrass prairie research site in northeastern Kansas. The projected increase in groundwater alkalinity (as HCO3-) and CO2 based on an earlier trend was confirmed in 2016, with predictions nearly equal to recent values (e.g., 408 ppm vs 410 ppm as HCO3-, respectively). Both the water balance and groundwater CO2 trends within the study watershed could be impacted by long-term changes in land use and climate: 1) encroachment of woody vegetation (1983–2012) as a result of the 4-year fire return interval, 2) re-introduction of bison (phased in, 1994–2006), 3) increases in air temperature, and 4) changes in precipitation patterns. If only linear processes are driving the observed water chemistry changes, then the linear increase in air temperature (1983–2017) that stimulates soil respiration may be the most likely factor enhancing groundwater HCO3- and CO2, as air temperature has risen ~1 to 1.4°C over 34 years. If groundwater chemistry is driven by more threshold behaviour, woody encroachment, which was linear but in three distinct phases, may drive groundwater chemistry. The ~2 to 3‰ decrease in the discontinuous δ13C data in the groundwater-dominated stream suggests enhanced inputs of microbially-respired labile carbon, CO2 sourced from C3 (woody vegetation), or a combination of the two.

A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential

The asymptotic and threshold behaviour of the eigenvalues of a perturbed difference operator inside a spectral gap is investigated. In particular, applications of the Titchmarsh-Weyl m-function theory as well as the Birman-Schwinger principle is performed to investigate the existence and behaviour of the eigenvalues of the operator H0+λWn inside the spectral gap of H0 in the limits λ↑∞ and λ↓0.