Navier-Stokes equations with imposed pressure and velocity fluxes

Boundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non-standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.     

多重经济增长路径,多重稳态解和分歧

该文给出一个具有可解内生生育率的Cass-Koopmans（C-K）经济增长模型．证明参数满足时，模型存在多重经济增长路径和多重稳态解；当时，经济增长路径和稳态解唯一，即描述模型的微分动力系统出现分歧．文中讨论了多重经济增长路径的几何形态、位置关系和主要结果的经济意义．     

多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

Rheology of oil-in-water emulsions

The effect of interfacial tension on the steady-flow and dynamic viscoelastic behavior of emulsions are studied experimentally. At very low inter-facial tensions and low volume fractions, the viscosity decreases with increasing shear rate and becomes constant at high shear rates. The high-shear-rate Newtonian viscosity is not affected by interfacial tension, but the transition from pseudoplastic to Newtonian flow shifts to lower shear rates as the interfacial tension decreases. At an interfacial tension of 5 × 10^–3 Nm^–1, the viscosity decreases, passes through a minimum, and then increases as the shear rate is increased. The dilatant behavior may be attributed to elastic responses of interfaces during collision of drops. At high volume fractions, the emulsions show remarkable elasticity resulting from the interfacial energy associated with deformation of liquid films. The modulus and viscosity are proportional to interfacial tension and inversely proportional to drop size.     

主动隔振中气动压力跟踪的预测控制研究

气动伺服系统的压力跟踪是主动隔振系统中的一个重要环节。本文根据气动伺服系统的特点，建立了系统压力工作点的模型，应用基于状态空间的预测控制方法对系统压力进行了轨迹跟踪控制。首先，提出了一种控制器切换的方法来消除压力跟踪过程中的稳态误差；其次，通过对预测控制算法的改进减小了滞后对闭环系统动态性能和稳定性的影响。实验表明，本文提出的方法有效地解决了主动隔振系统中的气动压力跟踪问题。     

On stability of stationary motion of a nonconservative nonholonomic rheonomic system

One considers, in this paper, the motion of a mechanical system in a nonstationary field of potential and positional forces, subject to the action of rheonomic holonomic and nonholonomic linear homogeneous constraints. Assuming that differential equations of motion of the system considered satisfy the conditions for the existence of Painlevé's integral of energy, formulated in [Painlevé, P., 1897. Leçons sur l'intégration des équations de la Mécanique, Paris] and [Appell, P., 1911. Traité de mécanique rationnelle, T. II, Dynamique des systémes – Mécanique analitique, Gauthier-Villars, Paris] and generalized in [Čović, V., Vesković, M., 2004. On stability of motion of a rheonomic system in the field of potential and positional forces, BAMM-1720/2004, No-2233, 93–100] and [Čović, V., Vesković, M., 2005. Hagedorn's theorem in some special cases of rheonomic systems. Mechanics Research Communications 32 (3), 265–280], the original mechanical system is substituted by an equivalent one whose Lagrangian function, nontransformed with respect to nonholonomic constraints, does not depend on time explicitly. Using the properties of the equivalent system, which, in contrast to the original one, moves in a stationary field of potential forces and in a nonstationary field of gyroscopic forces, the definition of cyclic coordinates is generalized, as well as sufficient conditions for the existence of (cyclic) first integrals, corresponding to coordinates mentioned and linear in velocities are established. Further, the conditions for the existence of steady motion of the system considered are found. In the case of existence of such a motion of the system, the Theorem of Routh's type on stability of that motion, based on the minimum of reduced potential for which it is shown that, in contrast to known cases (see, for example, [Gantmacher, F., 1975. Lectures in Analytical Mechanics. Mir Publisher, Moscow; Neimark, J., Fufaev, N., 1972. Dynamics of Nonholonomic Systems. Amer. Math. Soc., Providence, RI; Pars, L., 1962. An Introduction to Calculus of Variations. Heinemann, London; Karapetyan, A., Rumyantsev, V., 1983. Stability of conservative and dissipative systems. In: Itogi Nauki I Tekhniki: Obschaya Mekh., vol. 6, VINITI, Moscow, pp. 3–128 (in Russian)]), it includes the influence of the positional forces field, is formulated. Thus, the Routh's Theorem on stability of steady motion of a conservative mechanical system is extended to the case of a nonconservative system.     

Global dynamics of an age‐structured virus model with saturation effects

An infection‐age virus dynamics model for human immunodeficiency virus (or hepatitis B virus) infections with saturation effects of infection rate and immune response is investigated in this paper. It is shown that the global dynamics of the model is completely determined by two critical values R ₀, the basic reproductive number for viral infection, and R ₁, the viral reproductive number at the immune‐free infection steady state (R ₁<R ₀). If R ₀<1, the uninfected steady state E ⁰ is globally asymptotically stable; if R ₀>1 > R ₁, the immune‐free infected steady state E ^? is globally asymptotically stable; while if R ₁>1, the antibody immune infected steady state is globally asymptotically stable. Moreover, our results show that ignoring the saturation effects of antibody immune response or infection rate will result in an overestimate of the antibody immune reproductive number. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 153–159, January–February, 2005     

An analytical solution for steady flow of a Quemada fluid in a circular tube

An analytical solution is obtained for steady flow of Quemada-type fluids in a circular tube driven by a constant pressure gradient. Expressions are derived for velocity distribution and for volumetric flow rate as a function of pressure gradient or wall shear stress.     

On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.