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Nanoparticle (drug particle) dispersion is an important phenomenon during nanodrug delivery in the bloodstream by using multifunctional carrier particles. The aim of this study is to understand the dispersion of drug particle (nanoparticle) transport during steady blood flow through a microvessel. A two-phase fluid model is considered to define blood flow through a microvessel. Plug and intermediate regions are defined by a non-Newtonian Herschel-Bulkley fluid model where the plug region appears due to the aggregation of red blood cells at the axis in the vessel. The peripheral (porous in nature) region is defined by the Newtonian fluids. The wall of the microvessel is considered to be permeable and characterized by the Darcy model. Stress-jump and velocity slip conditions are incorporated respectively at the interface of the intermediate and peripheral regions and at the inner surface of the microvessel. The effects of the rheological parameter, the pressure constant, the particle volume fraction, the stress jump constant, the slip constant, and the yield stress on the dispersion are analyzed and discussed. It is observed that the non-dimensional pressure gradient and the yield stress enhance the dispersion rate of the nanoparticle, while the opposite trends are observed for the velocity slip constant, the nanoparticle volume fraction, the rheological parameter, and the stress-jump constant. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimization problem of maximizing biogas production at steady state in a two-stage anaerobic digestion model, which was initially proposed in Bernard et al. (Biotechnol Bioeng 75(4):424-438, 2001). Nominal operating points, consisting of steady states where the involved microorganisms coexist, are usually referred to as desired operational conditions, in particular for maximizing biogas production. Nevertheless, we prove that under some conditions related to input substrate concentrations and microorganism biology, characterized by their growth functions, the optimal steady state can be the extinction of one of the two species. We provide some numerical examples of this situation. [ABSTRACT FROM AUTHOR]

In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler’s numbers. To our knowledge, the answer is still an open question. The key point is that the coefficients can be connected with Euler’s numbers, and then they can be explicitly given. The constrained of our approach is that the formula is not valid outside the convergence set. The idea of the proof consists to explore some analogies with logistic function and Euler’s numbers, and then to generalize them in the fractional case. [ABSTRACT FROM AUTHOR]

Oscillators are essential to fuel autonomous behaviours in molecular systems. Artificial oscillators built with programmable biological molecules such as DNA and RNA are generally easy to build and tune, and can serve as timers for biological computation and regulation. We describe a new artificial nucleic acid biochemical reaction network, and we demonstrate its capacity to exhibit oscillatory solutions. This network can be built in vitro using nucleic acids and three bacteriophage enzymes, and has the potential to be implemented in cells. Numerical simulations suggest that oscillations occur in a realistic range of reaction rates and concentrations. [ABSTRACT FROM AUTHOR]

Microwave tomography has shown potential to successfully reconstruct the dielectric properties of the human breast, thereby providing an alternative to other imaging modalities used in breast imaging applications. Considering the costly forward solution and complex iterative algorithms, computational complexity becomes a major bottleneck in practical applications of microwave tomography. In addition, the natural tendency of microwave inversion algorithms to reward high contrast breast tissue boundaries, such as the skin-adipose interface, usually leads to a very slow reconstruction of the internal tissue structure of human breast. This paper presents a multistage selective weighting method to improve the reconstruction quality of breast dielectric properties and minimize the computational cost of microwave breast tomography. In the proposed two stage approach, the skin layer is approximated using scaled microwave measurements in the first pass of the inversion algorithm; a numerical skin model is then constructed based on the estimated skin layer and the assumed dielectric properties of the skin tissue. In the second stage of the algorithm, the skin model is used as a priori information to reconstruct the internal tissue structure of the breast using a set of temporal scaling functions. The proposed method is evaluated on anatomically accurate MRI-derived breast phantoms and a comparison with the standard single-stage technique is presented. [ABSTRACT FROM AUTHOR]

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature. [ABSTRACT FROM AUTHOR]