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We study the signal percolation through heart-like biological system. Starting from an initial distribution of waiting and inactive cells with probabilities $p$ and $(1-p)$ respectively, the signal propagation is observed in terms of active cells. As the signal enters the system from one end, the number of arrival of active sites at the other end is studied and analysis of the system behaviour is made by varying a few important parameters of the system like $p_{switch}$ (switching probability from inactive to waiting) and $p_{act}$ (switching probability from waiting to active). In this connection, the non-regular heart rhythms are discussed. Fraction of paths percolating through the system shows a transition from $0$ to $1$ near $p=p_c$. Some other important quantities like tortuosity and cluster distribution are discussed. Several critical exponents have been obtained and compared the exponents of standard percolation., Comment: 11 pages, 10 figures, 4 tables, revtex4-2

In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number of detection $n$ and amount of shift $s$ vary. It is seen that the occupation probability at the initial position $x_D$ of the detector is enhanced when $n$ is small which is a quantum mechanical effect but decreases when $n$ is large. The ratio of occupation probabilities of our walk to that of an Infinite walk shows a scaling behavior of $\frac{x_D^2}{n^2}$. It shows a definite scaling behavior with amount of shifts $s$ also. The limiting behaviors of the walk are observed when $x_D$ is large, $n$ is large and $s$ is large and the walker for these cases approach the Infinite Walk, The Semi Infinite Walk and the Quenched Quantum Walk respectively., Comment: 11 pages, 10 figures, revtex4-2

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are developed based on this clause instead of random choice. We prove the existence and uniqueness of the solution to the model we consider. Theoretically, we state that when species coexist, one may drive the other to die out, and both species extinct, considering all possible rational values of parameters. These results highlight a comparative study between two harvesting coefficients. Finally, we solve the model using a backward-Euler, decoupled, and linearized time-stepping fully discrete algorithm and observe a match between the theoretical and numerical findings., Comment: 37 pages, 13 figures

Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic, experts need to know the impact of the vaccine efficacy rate's threshold and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer, Moderna, AstraZeneca, and Johnson and Johnson, which are being used rigorously to control the COVID-19 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if frequent vaccination is continued with the Pfizer vaccine. During this time, six waves will happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. The more effective a vaccine, the less people suffer from this malign infection. Although specific groups of people get prioritized initially, mass vaccination is needed to control the spread of the disease.

This paper demonstrates a numerical study of heat transfer in a square porous cavity filled with non-Newtonian power-law fluid. A Graphics Processing Unit (GPU) has been used to accelerate the numerical simulation, which uses the Multiple-Relaxation-Time (MRT) Lattice Boltzmann Method. A modified power-law model has been employed to characterize the flow of non-Newtonian fluids. The simulations have been conducted for the power-law index $n$ ranging from $(0.6 \leq n \leq 1.0)$, the Darcy number $Da$ ranging from $(10^{-3} \leq Da \leq 10^{-1})$ and the Rayleigh number $Ra$ ranging from $(10^3 \leq Ra \leq 10^5)$. Results show that the average Nusselt number ($\overline{Nu}$) decreases with an increase in the value of $n$ while $\overline{Nu}$ increases with an increase in the value of $Da$. Moreover, an increment in the value of $Ra$ leads to an increase in the average Nusselt number., Comment: Accepted Version, International Conference on Mechanical Engineering 2019 (ICME2019) 18-20 December, Dhaka, Bangladesh

We construct a simple example of an integrable function on the ring of integers of the $p$-adic field $\Q_p$ having an almost everywhere divergent Fourier series. On the other hand, we prove the pointwise convergence of the Fourier series of functions in $L^p(\D,w)$, $1

Let $S_n f$ be the $n$th partial sum of the Fourier series of a function $f$ in $L^1(\D)$, where $\D$ is the ring of integers of a local field $K$. For $1