An SIS epidemic reaction-diffusion model with saturated incidence rate and spontaneous infection is considered. We establish the existence of endemic equilibrium by using a fixed point theorem. We mainly investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium. Our analysis shows that the spontaneous infection can enhance persistence of infectious disease.

In this study, we investigate the sum-type singular nonlinear fractional q-integro-differential $m$-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo $q$-derivative, Riemann-Liouville fractional $q$-integral and the means of a fixed point theorem on a real Banach space $(\mathcal{X}, \|.\|)$ which has a partially order by using a cone $P \subset \mathcal{X}$. The proofs are based on solving the operator equation $\mathcal{O}_1 x + \mathcal{O}_2 x = x $ such that the operator $\mathcal{O}_1$, $\mathcal{O}_2$ are $r$-convex, sub-homogeneous, respectively and define on cone $P$. As applications, we provide an example illustrating the primary effects.

We study properties of a piecewise deterministic Markov process modeling the changes in concentration of specific antibodies.The evolution of densities of the process is described by a stochastic semigroup. The long-time behaviour of this semigroup is studied. In particular we prove theorems on its asymptotic stability.

In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense, and its physical meaning is clear. Based on the image spaces of Riemann-Liouville fractional integral operators on Lp([a, b]) space discussed in our previous work, after a step by step deduction, three kinds of Galerkin spectral formulations are proposed, the final obtained corresponding scheme of which shows to be well-conditioned—the condition number of the stiff matrix can be reduced from O(N2α) to O(Nα), where N is the degree of the polynomials used in the approximation. Another point is that the obtained schemes can also be applied successfully to approximate fractional Laplacian with generalized homogeneous boundary conditions, whose fractional order α ∈ (0, 2), not only having to be limited to α ∈ (1, 2). Several numerical experiments demonstrate the effectiveness of the derived schemes. Besides, based on the numerical results, we can observe the behavior of mean first exit time, an interesting quantity that can provide us with a further understanding about the mechanism of abnormal diffusion.

Environmental DNA (eDNA) is used for monitoring the occurrence of freshwater organisms. Various studies show a relation between the amount of eDNA detected and target organism abundance, thus providing a potential proxy for reconstructing population densities. However, environmental factors such as water temperature and microbial activity are known to affect the amount of eDNA present as well In this study, we use controlled aquarium experiments using Gammarus pulex L. (Amphipoda) to investigate the relationship between the amount of detectable eDNA through time, pH, and levels of organic material. We found eDNA to degrade faster when organic material was added to the aquarium water, but that pH had no significant effect. We infer that eDNA contained inside cells and mitochondria is extra resilient against degradation, though this may not reflect actual presence of target species. These results indicate that, although estimation of population density might be possible using eDNA, measured eDNA concentration could, in the future, be corrected for local environmental conditions in order to ensure accurate comparisons.

1. Terrestrial plant populations located at the margins of species’ distributions often display reduced sexual reproduction and an increased reliance on asexual reproduction. One hypothesis to explain this phenomenon is that the decline is associated with environmental effects on the energetic costs to produce reproductive organs. 2. In order to clarify the changing processes of sexual reproduction along an altitudinal gradient, we investigated the sexual reproductive parameters, such as the number of sporophytes and gametangia, in Racomitrium lanuginosum, a dioicous moss found on Mt. Fuji. Matured sporophytes were present only below 3000 m, and the number of sporophytes per shoot tended to be lower at higher altitudes. 3. The numbers of male inflorescences per shoot and antheridia per inflorescence and shoot significantly decreased with increasing altitude. In contrast, the numbers of female inflorescences per shoot and archegonia per inflorescence and shoot varied little across altitudes. 4. Synthesis. Our results suggest that the success of sexual reproduction in R. lanuginosum is restricted at higher altitudes on Mt. Fuji by decreases in male gametangia and the subsequent chance of fertilization. These differences between males and females may be caused by differences in the cost of production and development of gametangia, sensitivity to environmental stresses (low air temperature, shortened growth period, and environmental conditions in winter), and phenological patterns at higher altitudes.

Bubble formation from a downward-pointing capillary nozzle was investigated in this study. The experiments were conducted at gas flow rate of 40-5400 mL/h and inner nozzle radius of 0.030-0.255 mm. Experimental results show that microbubbles were formed continuously at moderate Weber number, which was not reported in pervious investigations with injecting gas through an upward-pointing capillary nozzle. High-speed visualization indicates that the formation of microbubbles arises from the convergence of the capillary waves induced by the partial coalescence of larger bubbles. A bubbling regime map is given to identify the critical conditions for the formation of microbubbles. In the present air-water experiments, the generated microbubbles are 20-170 μm in diameter. From experimental data, a scaling law for microbubble size is proposed as a function of Weber and Bond numbers.

Aim: Threats faced by narrowly distributed endemic plant species in the face of the Earth’s sixth mass extinction and climate change exposure are especially severe for taxa on islands. We investigated the current and projected distribution and range changes of Cochemiea halei, an island endemic cactus. This taxon is of conservation concern, currently listed as vulnerable on the International Union for the Conservation of Nature Red List and as a species of special concern under Mexican federal law. The goals of this study are to 1). identify the correlations between climate variables and current suitable habitat for C. halei; 2). determine if the species is a serpentine endemic or has a facultative relationship with ultramafic soils; 3). predict range changes of the species based on climate change scenarios. Location: The island archipelago in Bahía Magdalena on the Pacific coast, Baja California Sur, Mexico. Methods: We used temperature and precipitation variables at 30 arcsecond resolution and soil type, employing multiple species distribution modeling methods, to identify important climate and soil conditions driving current habitat suitability. The best model of current suitability is used to predict possible effects of four climate change scenarios based on best case to worst case representative concentration pathways, with projected climate data from two general circulation models, over two time periods. Main conclusions: The occurrence of the species is found to be strongly correlated with ultramafic soils. The most important climate predictor for habitat suitability is annual temperature range. The species is predicted to undergo range contractions from 21% to 53%, depending on the severity and duration of exposure to climate change. The broader implications for a wide range of narrowly adapted, threatened and endemic plant species indicate an urgent need for threat assessment based on habitat suitability and climate change modeling.

Bubble size distribution and bubble ellipticity were measured as a function of axial position in a vertically oriented semi-batch gas-liquid Taylor vortex reactor with varying gas flow rate and inner cylinder rotation speed producing axial Reynolds numbers in the range 23.8-119 and azimuthal Reynolds numbers up to 4.2×104. The mean bubble size increases monotonically with axial distance from the bottom of the reactor at the location of gas injection. The functional form of the growth of the mean bubble size with axial position depends upon the azimuthal Reynolds number. Specifically, when the azimuthal Reynolds number is less than 1.3×104, the mean bubble size increases linearly with axial distance from the bubble injection point. In contrast, for azimuthal Reynolds numbers greater than this critical value, the mean bubble size increases with axial distance in a sigmoidal manner.

Informative/Abstract:Estimating streamflow is time and labour intensive due to the necessity of developing a rating curve. The development of a rating curve involves acquiring at least thirty in-field measurements of streamflow across a wide range of flow levels, which can be costly and impractical in remote regions with limited seasonal access. Here we showcase an automated system which accurately estimates streamflow multiple times each day, greatly facilitating the development of rating curves for remote or seasonally inaccessible sites. The system uses an emerging technique referred to as particle image velocimetry (PIV) to track the movement of objects and flow structure features on the mobile water surface to generate velocity vector grids. Velocity grids were used to calculate streamflow and facilitate the development of a rating curve. This represents the first use of an automated PIV system to estimate streamflow in small streams (< 5 m wide) and the first system to automatically distribute particles for facilitated PIV analysis.Keywords: Particle Image Velocimetry, Streamflow Monitoring, Automated Systems, Particle TracerFunding: This research was funded through the Ministry of Natural Resources and Forestry, the Canada-Ontario Agreement Fund, and the Queen Elizabeth II Graduate Scholarship in Science and Technology.

A self-wiping co-rotating twin-screw extruder (TSE) is operated in a starved state where the screws are partially filled with resin. Understanding resin distribution on the screw surface is essential for the design, operation, and maintenance of the twin-screw extrusion process. In this study, the circumferential and axial distribution of pressure, temperature, and resin in a TSE are calculated using a novel method combining the mathematical formulation of Hele–Shaw flow, the finite element method, and a newly developed down-wind pressure update scheme. The experimental results were in good agreement with the measured results. This calculation method enables us to visualize, in detail, the resin distribution, pressure, and temperature for the entire axial and circumferential direction over the TSE.

In the biopharmaceutical industry, Raman spectroscopy is now a proven PAT tool that enables in-line simultaneous monitoring of several CPPs and CQAs in real-time. However, as Raman monitoring requires multivariate modeling, variabilities unknown by models can impact the monitoring prediction accuracy. With the widespread use of Raman PAT tools, it is necessary to fix instrumental variability impacts, encountered for instance during a device replacement. In this work, we investigated the impact of instrumental variability between probes inside a multi-channel analyzer and between two analyzers, and explored solutions to correct them on model prediction errors in cell cultures. We found that the Kennard Stone Piecewise Direct Standardization (KS PDS) method enables to lower model prediction errors and that only one batch with the unknown device in the calibration dataset was sufficient to correct the prediction gap induced by instrumental variability. As a matter of fact, during device replacement a first cell culture monitoring can be performed with the KS PDS method. Then, the new data obtained can be inserted in the calibration dataset to integrate instrumental variability in the chemometric model. This methodology provides good multivariate calibration model prediction errors throughout the instrumental changes.

Seasonal suspended sediment transfer in glaciated catchments is responsive to meteorological, geomorphological, and glacio-fluvial conditions, and thus is a useful indicator of environmental system dynamics. Knowledge of multifaceted fluvial sediment-transfer processes is limited in the Arctic–a region sensitive to contemporary environmental change. For two glaciated sub-catchments at Lake Peters, northeast Brooks Range, Alaska, we conducted a two-year endeavor to monitor the hydrology and meteorology, and used the data to derive multiple-regression models of suspended sediment load. Statistical selection of the best models shows that incorporating meteorological or temporal explanatory variables improves performances of turbidity- and discharge-based sediment models. The resulting modeled specific suspended sediment yields to Lake Peters are: 33 (20-60) Mg km-2 yr-1 in 2015, and 79 (50-140) Mg km-2 yr-1 in 2016 (95% confidence band estimates). In contrast to previous studies in Arctic Alaska, fluvial suspended sediment transfer to Lake Peters was primarily influenced by rainfall, and secondarily influenced by temperature-driven melt processes associated with clockwise diurnal hysteresis. Despite different sub-catchment glacier coverage, specific yields were the same order of magnitude from the two primary inflows to Lake Peters, which are Carnivore Creek (128 km2; 10% glacier coverage) and Chamberlin Creek (8 km2; 23% glacier coverage). Seasonal to longer term sediment exhaustion and/or contrasting glacier dynamics may explain the lower than expected relative specific sediment yield from the more heavily glacierized Chamberlin Creek catchment. Absolute suspended sediment yield (Mg yr-1) from Carnivore Creek to Lake Peters was 28 times greater than from Chamberlin Creek, which we attribute to catchment size and sediment supply differences. Our results are useful for predicting changes in fluvial sediment transport in glaciated Arctic catchments.

Functional traits are becoming more common in the analysis of marine zooplankton community dynamics associated with environmental change. We use zooplankton groups with common functional properties to assess long-term trends in the zooplankton caused by certain environmental conditions in a highly eutrophicated gulf. Time series of zooplankton traits were collected since 1960 in the Gulf of Riga, Baltic Sea and were analysed using general additive model, principal component analysis, and multivariate model. One of the most significant changes was the considerable increase in the amount of the zooplankton functional groups (FGR) in coastal springtime communities, and dominance shifts from more complex to simpler organism groups – cladocerans and rotifers. The results also show that the functional trait organism complexity (body size) decreased considerably due to cladoceran and rotifer increase following elevated water temperature. Salinity and oxygen had negligible effects on the zooplankton community.

We present a numerical method for simulating 2D flow through a channel with deformable walls. The fluid is assumed to be incompressible and viscous. We consider the highly viscous regime, where fluid dynamics are described by the Stokes equations, and the less viscous regime described by the Navier-Stokes equations. The model is formulated as an immersed boundary problem, with the channel defined by compliant walls that are immersed in a larger computational fluid domain. The channel traverses through the computational domain, and the walls do not form a closed region. When the walls deviate from their equilibrium position, they exert singular forces on the underlying fluid. We compute the numerical solution to the model equations using the immersed interface method, which preserves sharp jumps in the solution and its derivatives. The immersed interface method typically requires a closed immersed interface, a condition that is not met by the present configuration. Thus, a contribution of the present work is the extension of the immersed interface method to immersed boundary problems with open interfaces. Numerical results indicate that this new method converges with second-order accuracy in both space and time, and can sharply capture discontinuities in the fluid solution.

This is a fundamental study addressing the articulation of knowledge from the context of the fourth industrial revolution (Industry 4.0). Industry 4.0 employs embedded systems (e.g., cyber-physical systems) to perform cognitive tasks. These systems cannot work without applying digitized knowledge. As a result, the digitization of knowledge-intensive activities (knowledge acquisition, representation, dissemination, utilization, and management) is critical for Industry 4.0. Before digitizing the knowledge and knowledge-intensive activities, a fundamental question arises: What is knowledge in Industry 4.0? This study answers this question. In doing so, this study first reviews the definitions of knowledge reported in the extant literature of epistemology, engineering design, manufacturing, organization science, information science, and education science. This study then defines that a piece of knowledge consists of three elements, namely, claim, provenance, and inference. Such a definition helps overcome the circularity and ambiguity in the definitions of knowledge reported so far. This definition results in four types of knowledge, namely, definitional, deductive, inductive, and creative knowledge. These types of knowledge are exemplified using some real-life scenarios relevant to engineering design and manufacturing. The exemplified pieces of knowledge are also represented by using knowledge graphs (concept maps) so that the contents can easily be digitized for human and machine learning. The outcomes of this study are the fundamentals based on which more sophisticated methods and tools can be developed to perform the cognitive tasks relevant to Industry 4.0.

The young water fraction (Fyw), the proportion of water younger than 2-3 months, was investigated in soil-, ground- and stream waters in the 0.56 Km2 sub-humid Mediterranean Can Vila catchment. Rain water was sampled at 5-mm rainfall intervals. Mobile soil water and groundwater were sampled fortnightly, using suction lysimeters and two shallow wells, respectively. Stream water was dynamically sampled at variable time intervals (30 minutes to 1 week), depending on flow. A total of 1,529 18O determinations obtained during 58 months were used. The usual hypothesis of rapid evapotranspiration of summer rainfall could not be maintained, leading to discard the use of an “effective precipitation” model. Soil mobile waters had Fyw up to 34%, while in ground and stream were strongly related to water table and discharge variations, respectively. In stream waters, due to the highly skewed flow duration curve, the flow-averaged young water fraction (F*yw) was 22.6%, whereas the time-averaged Fyw was 6.2%. Nevertheless, both F*yw and its exponential discharge sensitivity (Sd) showed relevant changes when different 12-month sampling periods were investigated. The availability of Sd and a detailed flow record allowed us to simulate the young water fraction that would be obtained with a virtual thorough sampling (F**yw). This showed that underestimation of F*yw is associated with missing the sampling of highest discharges and revealed underestimations of F*yw by 25% for the dynamic sampling and 66% for the weekly sampling. These results confirm that the young water fraction and its discharge sensitivity are metrics that depend more on precipitation forcing than on physiographic characteristics, so the comparisons between catchments should be based on mean annual values and inter-annual variability. They also support the dependence of the young water fraction on the sampling rate and show the advantages of flow-weighted F*yw. Water age investigations should be accompanied by the analysis of flow duration curves. In addition, the simulation of F**yw is proposed as a method for checking the adequacy of the sampling rate used.

In this article, a highly robust antenna is proposed for omnidirectional circular polarized communications in harsh environments at 2.45 GHz industrial, scientific, and medical frequency band. Circular polarization is realized by utilizing a combination of two magnetic and electric dipoles. The proposed antenna is based on a transparent structure and covered by a quarter wavelength thick layer of plexiglass to achieve desired robustness and visible light transparency.Meanwhile, because of the high transparency of the glass, it can integrate with solar cells to simultaneously propagate signals and harvest energy. The average gain and bandwidth of the antenna are 1.7 dBic and 300 MHz, respectively. The antenna’s axial ratio is achieved less than 3 dB within the bandwidth, showing circular polarization behavior. The proposed compact antenna is numerically and experimentally analyzed and the results have a great agreement. In another viewpoint, the structure delivers promising possibilities to improve the propagating and radiating properties, which bring in significant advantages for real-world multifunctional applications.