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Quantum K-theory of incidence varieties

Xu, Weihong (Springer, 2024-06-01)

We prove a conjecture of Buch and Mihalcea in the case of the incidence variety X = Fl(1, n - 1; n) and determine the structure of its (T-equivariant) quantum K-theory ring. Our results are an interplay between geometry and combinatorics. The geometric side concerns Gromov-Witten varieties of 3-pointed genus 0 stable maps to X with markings sent to Schubert varieties, while on the combinatorial side are formulas for the (equivariant) quantum K-theory ring of X. We prove that the Gromov-Witten variety is rationally connected when one of the defining Schubert varieties is a divisor and another is a point. This implies that the (equivariant) K-theoretic Gromov-Witten invariants defined by two Schubert classes and a Schubert divisor class can be computed in the ordinary (equivariant) K-theory ring of X. We derive a positive Chevalley formula for the equivariant quantum K-theory ring of X and a positive closed formula for Littlewood-Richardson coefficients in the non-equivariant quantum K-theory ring of X. The Littlewood-Richardson rule in turn implies that non-empty Gromov-Witten varieties given by Schubert varieties in general position have arithmetic genus 0.

Controlled ion transport in the subsurface: A coupled advection-diffusion-electromigration system

Tang, Kunning; Bo, Zhenkai; Li, Zhe; Da Wang, Ying; McClure, James; Su, Hongli; Mostaghimi, Peyman; Armstrong, Ryan T. (AIP Publishing, 2024-06-01)

Ion transport within saturated porous media is an intricate process in which efficient ion delivery is desired in many engineering problems. However, controlling the behavior of ion transport proves challenging, as ion transport is influenced by a variety of driving mechanisms, which requires a systematic understanding. Herein, we study a coupled advection-diffusion-electromigration system for controlled ion transport within porous media using the scaling analysis. Using the Lattice-Boltzmann-Poisson method, we establish a transport regime classification based on an Advection Diffusion Index (ADI) and a novel Electrodiffusivity Index (EDI) for a two-dimensional (2D) microchannel model under various electric potentials, pressure gradients, and concentration conditions. The resulting transport regimes can be well controlled by changing the applied electric potential, the pressure field, and the injected ions concentration. Furthermore, we conduct numerical simulations in a synthetic 2D porous media and an x-ray microcomputed tomography sandstone image to validate the prevailing transport regime. The simulation results highlight that the defined transport regime observed in our simple micromodel domain is also observed in the synthetic two- and three-dimensional domains, but the boundary between each transport regime differs depending on the variation of the pore size within a given domain. Consequently, the proposed ADI and EDI emerge as dimensionless indicators for controlled ion transport. Overall, our proof-of-concept for ion transport control in porous media is demonstrated under advection-diffusion-electromigration transport, demonstrating the richness of transport regimes that can develop and provide future research directions for subsurface engineering applications.

Variability of Atomic Hydrogen Brightness in the Martian Exosphere: Insights From the Emirates Ultraviolet Spectrometer on Board Emirates Mars Mission

Susarla, R.; Deighan, J.; Chaffin, M. S.; Jain, S.; Lillis, R. J.; Chirakkil, K.; Brain, D.; Thiemann, E.; Eparvier, F.; Lootah, F.; Holsclaw, G.; Gacesa, M.; Fillingim, M. O.; El-Kork, N.; England, S.; Evans, J. S.; AlMazmi, H.; AlMatroushi, H. (American Geophysical Union, 2024-06-01)

The Emirates Mars Ultraviolet Spectrometer (EMUS), aboard the Emirates Mars Mission (EMM), has been conducting observations of ultraviolet emissions within the Martian exosphere. Taking advantage of the distinctive orbit of the EMM around Mars, EMUS utilizes a dedicated strafe observation strategy to scan the illuminated Martian exosphere at tangential altitudes ranging from 130 to over 20,000 km. To distinguish between emissions of Martian origin and those from the interplanetary background, EMUS conducts specialized background observations by looking away from the planet. This approach has allowed us to investigate the radial and seasonal variations in Martian coronal emission features at H Lyman-alpha, beta and gamma wavelengths. Our analysis supports the previous studies indicating that Martian exospheric hydrogen Lyman emission brightness attains its highest levels around the southern summer solstice and reaches its lowest levels when Mars is near aphelion. Additionally, a secondary peak emission at all altitudes is observed after perihelion during Martian Year (MY) 36, which can be attributed to a Class C dust storm. Our study establishes a strong correlation between solar flux and coronal brightness for these emissions, highlighting the impact of solar activity on the visibility of Martian corona. In addition, we have examined interannual variability and found that emission intensities in MY 37 surpassed those in MY 36, primarily due to increased solar activity. These observations help to understand potential seasonal patterns of exospheric hydrogen, which is driven by underlying mechanisms in the lower atmosphere and solar activity, eventually suggesting an impact on water loss in the Martian atmosphere. Atomic hydrogen primarily forms as a product when Martian water undergoes various photochemical reactions. These hydrogen atoms encircle Mars and become illuminated by solar radiation, leading to the creation of Martian hydrogen corona. The Emirates Mars Ultraviolet Spectrometer (EMUS), on the Emirates Mars Mission spacecraft, is currently studying the Martian atmosphere using the ultraviolet light emissions of different atoms and molecules on Mars. In this study, we have analyzed EMUS observations and determined that atomic hydrogen emission intensities increase during the Martian southern summer and decrease as Mars moves farther away from the Sun. Furthermore, we have compared the hydrogen brightness between two consecutive Martian years and have found that the hydrogen brightness is higher in the most recent year primarily due to increased solar radiation. These observations help us understand possible patterns that occur during different seasons on Mars and the mechanisms underlying water loss in the Martian atmosphere. We present the variability in Martian atomic hydrogen brightness from early Martian year (MY) 36 to the first quarter of MY 37 Martian exospheric H Ly-beta and gamma emissions reach their peak brightness during the southern summer of MY 36 Martian corona is much brighter at H Ly-beta wavelength in MY 37 compared to the previous year due to increased solar irradiance

Infection-induced increases to population size during cycles in a discrete-time epidemic model

Strube, Laura F.; Elgart, Shoshana; Childs, Lauren M. (Springer, 2024-06-01)

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.

Using hyperspectral signatures for predicting foliar nitrogen and calcium content of tissue cultured little-leaf mockorange (Philadelphus microphyllus A. Gray) shoots

Khajehyar, Razieh; Vahidi, Milad; Tripepi, Robert (Springer, 2024-06-01)

Determining foliar mineral status of tissue cultured shoots can be costly and time consuming, yet hyperspectral signatures might be useful for determining mineral contents of these shoots. In this study, hyperspectral signatures were acquired from tissue cultured little-leaf mockorange (Philadelphus microphillus) shoots to determine the feasibility of using this technology to predict foliar nitrogen and calcium contents. After using a spectroradiometer to take hyperspectral images for determining foliar N and Ca contents, the correlation between the hyperspectral bands, vegetation indices, and hyperspectral features were calculated from the spectra. Features with high correlations were selected to develop the models via different regression methods including linear, random forest (RF), and support vector machines. The results showed that non-linear regression models developed through machine learning techniques, including RF methods and support vector machines provided satisfactory prediction models with high R-2 values (%N by RF with R-2 = 0.72, and %Ca by RF with R-2 = 0.99), that can estimate nitrogen and calcium content of little-leaf mockorange shoots grown in vitro. Overall, the RF regression method provided the most accurate and satisfactory models for both foliar N and Ca estimation of little-leaf mockorange shoots grown in tissue culture.

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