Integumentary organs exhibit diverse morphologies and functions. The complex mechanical property of the architecture is mainly contributed by the ingenious multiscale assembly of keratins. A cross-scale characterization on keratin integration in an integument system will help us understand the principles on how keratin-based bio-architecture are built and function in nature. In this study, we used feather as a model integument organ. We develop autofluorescence (AF) microscopy to study the characteristics of its keratin assemblies over a wide range of length scales. The AF intensity of each feather component, following the hierarchy from the rachis to barb to barbule, decreased with the physical dimension. By combining the analysis of AF signal and tensile testing, we can probe regional material density and the associated mechanical strength in a composite feather. We further demonstrated that the AF micro-images could resolve subtle variations in the defective keratin assembly in feathers from frizzled chicken variants with a mutation in -keratin 75. The distinction between AF patterns and the morphological features of feather components across different length scales indicated a synergetic interplay between material integration and complex morphogenesis during feather development. The work shows AF microscopy can serve as an easy and non-invasive approach to study multiscale keratin organizations and the associated bio-mechanical properties in diverse integumentary organs. This approach will facilitate our learning of many bio-inspired designs in diverse animal integumentary organs/appendages.

Blood stenosis is considered one of the most serious risks which face humanity nowadays. In addition, it is also one of the most apparent symptoms of COVID (19) (Corona Virus). Consequently, this research is shedding light on studying the blood flow in case of having blood clots and artery elasticity in the presence of stenosis during studying the flow. Hematopoiesis requires a model of the yield stress fluid, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). Navier stokes equation is used to simulate this subject in a mathematical way. The elasticity on the stenosis arterial walls is simulated by Rubinow & Keller model [24] and Mazumdar model [25]. The results reveal exciting behaviors that, in turn, require adequate study of non-Newtonian fluid flow phenomena, especially the results showed that the increase in the parameters related to the elasticity of the walls facilitating the flow of blood through the stenosis area. In addition, a comparison between two elasticity models (Rubinow & Keller model and Mazumdar model) is considered. Further, for normal artery without stenosis, our results are the same as those obtained by Vajravelu et.al [22].

Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model are directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia.

Lockdown procedures have been proven successful in mitigating the spread of the viruses in this COVID-19 pandemic, but they also have devastating impact on the economy. We use a modified Susceptible-Infectious-Recovered-Deceased model with time dependent infection rate to simulate how the infection is spread under lockdown. The economic cost due to the loss of workforce and incurred medical expenses is evaluated with a simple model. We find the best strategy, meaning the smallest economic cost for the entire course of the pandemic, is to keep the strict lockdown as long as possible.

In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples.