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In this paper, the mathematical model of distribution of the injected compound in biological liquid flow has been described. It is considered that biological liquid contains a few phases such as water, peptides and cells. The injected compound (for example, photosensitizer) can interact with peptides and cells. At the time, viscosity of the biological liquid depends on pathology present in organism. The obtained distribution of the compound connects on changes of its fluorescence spectra which are registered during fluorescent diagnostics of tumors. It is obtained that the curves do not have monotonic nature. There is a sharp curves decline in the first few seconds after injection. Intensivity of curves rises after decreasing. It is especially pronounced for wavelength 590nm and 580nm (near the “transparency window” of biological tissues). Time of inflection point shifts from 8.4s to 6.9s for longer wavelength. However, difference between curves is little for different viscosity means of the biological liquid. Thus, additional pathology present in organism does not impact to the results of in vivo biomedical investigations.

An accretion flow around a black hole has a saddle type sonic point just outside the event horizon to guarantee that the flow enters the black hole supersonically. This feature exclusively present in the strong gravity limit makes its marks in every observation of black hole candidates. Another physical sonic point is present (as in a Bondi flow) even in weak gravity. Every aspect of spectral or temporal properties of every black hole can be understood using this transonic or advective flow having more than one saddle type points. This most well known and generalized solution with viscosity and radiative transfer has been verified by numerical simulations also. Spectra, computed for various combinations of the standard Keplerian, and advective sub-Keplerian components match accurately with those from satellite observations. Standing, oscillating and propagatory oscillating shocks are produced due to centrifugal barrier of the advective component. The post-shock region acts as the Compton cloud producing the power-law spectra. Jets and outflows are also produced from this post-shock region, commonly known as the CENtrifugal barrier supported BOundary Layer or CENBOL. In soft states, the CENBOL is cooled down by soft photons from the Keplerian disk, and thus the outflow is absent. Type-C and Type-B QPOs are generated respectively due to strong and weak resonance oscillations of the CENBOL. Away from resonance, oscillation may be triggered when Rankine-Hugoniot conditions are not satisfied and Type-A QPOs could be seen.

We use α prescription of viscosity and study steady state solutions of an accretion flow, in presence of dissipative shocks. The flow solutions depend on four initial parameters namely, ε_in, l_H, α and f. We study all such solutions possible and divide the parameter space into regions which allow the formation of such shock waves and which do not. Then, we follow a similar study in presence of outflows. From the analysis of the resultant parameter space, we find that the dissipative shocks can still form for the values of α as high as 0.27 in small regions of the flow parameter space in absence of outflows. This value reduces to 0.2 in presence of outflows. The typical values of αappear in the range 0.01 − 0.15. The values of α reported from numerical simulations are always lower than 0.1. This signifies that viscosity parameter in accretion flows is low enough to form dissipative shocks, both in presence and absence of outflows. This supports our claim that shocks could be omnipresent. It was also found that a dissipation factor of f ≻ 0.3 does not produce shocks in significant region of the flow parameter space and hence, these values are not physically relevant. Likewise, at the maximum, ∼ 13% of inflowing matter can be ejected as outflows at the CENBOL.

We discuss two aspects of the scenario in which dark matter possesses (fundamental or effective) viscosity: a) Large shear viscosity can induce the acceleration of the average expansion through the backreaction of fluctuations. b) Treating dark matter at large scales as an effectively viscous fluid provides an improved framework for the calculation of the matter power spectrum. We use intuition from the Wilsonian renormalization group in order to make this framework concrete, and review results that demonstrate that it improves the convergence of cosmological perturbation theory.