A particular interaction-diffusion mussel-algae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layer containing algae as a food source is investigated employing weakly nonlinear diffusive instability analyses. The main results of these analyses can be represented by plots in the ratio of mussel motility to algae lateral diffusion versus the algae reservoir concentration dimensionless parameter space. Regions corresponding to bare sediment and mussel patterns consisting of rhombic or hexagonal arrays and isolated clusters of clumps or gaps, an intermediate labyrinthine state, and homogeneous distributions of low to high density may be identified in this parameter space. Then those Turing diffusive instability predictions are compared with both relevant field and laboratory experimental evidence and existing numerical simulations involving differential flow migrating band instabilities for the associated interaction-dispersion-advection mussel-algae model system as well as placed in the context of the results from some recent nonlinear pattern formation studies.

A mathematical model for forecasting the transmission of the COVID-19 outbreak is proposed to investigate the effects of quarantined and hospitalized individuals. We analyze the proposed model by considering the existence and the positivity of the solution. Then, the basic reproduction number (R0)—the expected number of secondary cases produced by a single infection in a completely susceptible population—is computed by using the next-generation matrix to carry out the stability of disease-free equilibrium and endemic equilibrium. The results show that the disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. Numerical simulations of the proposed model are illustrated. The sensitivity of the model parameters is considered in order to control the spread by intervention strategies. Numerical results confirm that the model is suitable for the outbreak that occurred in Thailand.

In this paper, we propose an impulsive mathematical model of bone formation and resorption accounting for the number of active osteoclastic cells, bone resorbing cells, and the number of active osteoblastic cells, bone forming cells, based on the effects of parathyroid hormone and calcitonin with impulsive estrogen supplement. The model is then analyzed theoretically in terms of its stability, permanence and oscillatory behavior. The conditions on the model parameters, for which the desirable behaviors of the solution of the system can be expected, are derived. Numerical simulations are also carried out in order to support our theoretical predictions. The results indicate that the frequency and dosage of the estrogen supplements are important since the behavior of the solution of the system depends on the frequency and dosage of the estrogen supplements.

This work presents a novel route for utilizing waste from power plants to create a new power source (solar cells). Bottom ash (BA) ceramic micro-particles were studied to improve an electrocatalytic activity in solar cell applications for the first time. In the counter electrodes (CE) of dye-sensitized solar cells (DSSC), bottom ash was mixed with PEDOT:PSS (PP) and polyvinylpyrrolidone (PVP) (BA/PP/PVP) in volume ratios of 3:7, 4:6, 5:5, and 6:4. We found that bottom ash has a significant impact in improving the electrocatalytic activity and DSSC efficiency of these cells. Moreover, the PP and PVP ratios have a high impact on solar cell performance. The BA/PP/PVP-(6:4) counter electrode attained a higher DSSC efficiency, 2.70%, compared to the other electrodes prepared under similar conditions and a Pt CE based DSSC (3.23%) at AM 1.5 (100 mWcm-2). The influences of bottom ash and PP/PVP ratios on film structure, electrocatalytic activity in reduction, redox reaction rate, and electron transport were characterized using scanning electron micros copy, cyclic voltammetry, Tafel, and, electrical impedance spectroscopy, respectively. The results show that low-cost BA/PP/PVP-(6:4) CE is a promising new alternative to Pt CEs in DSSCs.

No abstract