Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel–Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.     

Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Properties of renormalization group flow in the neighborhood of Gaussian fixed point

We investigate the dynamics of the renormalization group transformation in the fermionic hierarchical model, given by the Lagrangian. We construct the invariant neighborhood of the Gaussian fixed point in the upper half-plane g > 0. We describe the subsets of the points of this neighborhood tending to the Gaussian fixed point under the iterations of the renormalization group transformation from the left and from the right.     

Exact solutions for the unsteady axial flow of Non-Newtonian fluids through a circular cylinder

The velocity field and the shear stress corresponding to the motion of a generalized Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent shear stress are established by means of the Laplace and finite Hankel transforms. The exact solutions, written under series form, can be easily specialized to give the similar solutions for generalized Maxwell and generalized second grade fluids as well as for ordinary Oldroyd-B, Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid are shown by graphical illustrations.     

The variable neighborhood search for the two machine flow shop problem with a passive prefetch

We consider the two machine flow shop scheduling problem with passive loading of the buffer on the second machine. To compute lower bounds for the global optimum, we present four integer linear programming formulations of the problem. Three local search methods with variable neighborhoods are developed for obtaining upper bounds. Some new large neighborhood is designed. Our methods use this neighborhood along with some other well-known neighborhoods. For computational experiments, we present a new class of test instances with known global optima. Computational results indicate a high efficiency of the proposed approach for the new class of instances as well as for other classes of instances of the problem.     

Controlling multiparticle system on the line. II. Periodic case

As in [A. Sarychev, Controlling multiparticle system on the line. I, J. Differential Equations 246 (12) (2009) 4772-4790] we consider classical system of interacting particles P₁,…,Pn on the line with only neighboring particles involved in interaction. On the contrast to [A. Sarychev, Controlling multiparticle system on the line. I, J. Differential Equations 246 (12) (2009) 4772-4790] now periodic boundary conditions are imposed onto the system, i.e. P₁ and Pn are considered neighboring. Periodic Toda lattice would be a typical example. We study possibility to control periodic multiparticle systems by means of forces applied to just few of its particles; mainly we study system controlled by single force. The free dynamics of multiparticle systems in periodic and nonperiodic case differ substantially. We see that also the controlled periodic multiparticle system does not mimic its nonperiodic counterpart.Main result established is global controllability by means of single controlling force of the multiparticle system with a generic potential of interaction. We study the nongeneric potentials for which controllability and accessibility properties may lack. Results are formulated and proven in Sections 2, 3.     

A boundary control problem for the blood flow in venous insufficiency. The general case

The purpose of this article is to introduce and study an optimal control problem with medical applications. When a vein loses its elasticity, phenomena such as stagnation and recirculation of the blood may appear; these phenomena produce medical complications. We propose an optimization model in order to diminish the negative consequences of the lack of vein elasticity. We extend a previous model involving the interaction between a viscous fluid and an elastic boundary to the case when both the fluid and the elastic medium occupy three dimensional domains. After establishing the existence and uniqueness of the solution for the coupled problem, we present a boundary control problem in order to determine an exterior compression that realizes a blood flow without recirculation. Since it is not possible to find such a compression directly, we consider a sequence of cost functionals and we study the corresponding optimal control problems. The existence and uniqueness of the optimal controls are proved and the optimality conditions that characterize the optimal controls are derived. Finally, we establish the relation between the control problem with physical meaning and the sequence of optimal controls already constructed.     

The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

The paper proves the nonexistence of the solution for the following Cauchy problem\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&\qquad \left(x,t\right)\in S_{T} ={\mathbb{R}}^N \times \left(0,T\right), \\u\left(x,\; 0\right)=\delta \left(x\right), &\qquad x\in {\mathbb{R}}^,\end{cases}\end{align*}under some conditions on \textit{m,p,q},$\lambda$, where $\delta $ is Dirac function.     

非牛顿多方渗流方程Cauchy问题的可解性

本文讨论非牛顿多方渗流方程初始迹为测度时Ｃａｕｃｈｙ问题的可解性（当ｍ（ｐ—１）＜１时）．     

Asymptotic behavior of quantum walks on the line

This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the ‘normalized’ position of the walk. When the position is in the support of the weak-limit distribution obtained by Konno (2005) [5], one observes, in addition to the limit distribution itself, an oscillating phenomenon in the leading term of the asymptotic formula. When the position lies outside of the support, one can establish an asymptotic formula of large deviation type. The rate function, which expresses the exponential decay rate, is explicitly given. Around the boundary of the support of the limit distribution (called the ‘wall’), the asymptotic formula is described in terms of the Airy function.     

The asymptotic behavior of solutions of ordinary differential equations in the degenerate case

We investigate the asymptotic behavior of the fundamental system of solutions of a homogeneous linear differential equation of high order on the semiaxis for large values of the argument in the case when the contributions of the coefficients to the asymptotic formulae are the same and one of them increases indefinitely together with the argument. We find the deficiency indices of the corresponding minimal operator.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 36–55, 1988.In conclusion the author expresses his deep gratitude to A. G. Kostyuchenko for a discussion of the results.     

Relationship between the asymptotic behavior of exponents of a multidimensional exponential series and the asymptotic behavior of its coefficients in a neighborhood of singular points

We study the relation of the asymptotic behavior of the coefficients of multidimensional exponential series to the asymptotic behavior of its sum by using theR-order of the growthp _QR (a ₁,...,a _n ) in an octantQ(a ₁,...,a _n ). Bryansk Pedagogical Institute, Bryansk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1193–1200, September, 1999.     

Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

A dynamical system is studied in the neighborhood of an invariant toroidal manifold for the most general relationship between the dimensionality of the phase space and the dimensionality of the manifold.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1399–1408, October, 1994.