The review exact (described by algebraic functions) solutions of a transonic set of Karman–Falkovitch equations is given. Self-similar solutions and two classes of the polynomial-parametrical solutions associated with self-similar at indexes n = 2 and n = 3 are considered. Connection with local exposition of singularities of transonic flows is specified , in particular in Laval nozzles.
A fluid-solid interaction problem of a pulsation of the human carotid bifurcation was solved using finite element method. Hyperelastic orthotropic wall model that accounts for the carotid histological structure and in-vivo vessel geometry obtained from the CT-imaging were utilized. In-vivo blood flow boundary conditions for the problem were determined using Doppler Ultrasound.
The equations of the one-dimensional theory of dynamics of a blood-groove in arterial systems of large blood vessels are formulated most. Analytic solution of the formulated system of equation and some variants of edge and contact conditions are proposed.
Let Λψ,p[0, 1)d be a near to L∞[0, 1)d Lorentz space. We find the function ψ˜ for which the multiple Vilenkin–Fourier of any f ∈ Λψ,p[0, 1)d converge to f in the norm of Lorentz space Λ ˜ [0, 1)d.
This research contains one of the world-class developed authorized approaches of computing gas-dynamic properties for pulse knocking engine with diffuser. Constructed mathematical model and computational experiment on it demonstrates that diffuser is increasing knocking engine efficiency.
In work the class of tasks of a nonlinear refraction of shock waves is examined. Research is reduced to the decision of regional tasks of refraction. For the decision of the received regional tasks the theory of interaction of shock waves in gas-liquids environments (biphasic), generalizing the theory of interaction in single-phase environments is constructed asymptotic. The numerical method of the decision of regional tasks for areas with significant gradients of parameters (areas of short waves) is constructed.
Vibratory bend of a thick plate-strip with arbitrary edge fixing is considered. The equations of 3D viscoelastic theory in displacements are accepted as governing equations. Boundary problem dimensions reduction is realized with spline-collocation method. 1D boundary problem is solved numerically using discrete orthogonalization method. New effects that cannot be explained with the classic Kirhgof theory are mentioned.
The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.
The investigation of deformation waves behavior in elastic shells is one of the important trends in the contemporary wave dynamics. There exist mathematical models of wave motions in infinitely long geometrically non-linear shells, containing viscous incompressible liquid, based on the related hydroelasticity problems, which are derived by the shell dynamics and viscous incompressible liquid equations in the form of generalized Korteweg – de Vries equations.
The new and known strapdown INS algorithms for high-precision estimation of the orientation parameters of a moving object (Rodrigues–Hamilton (Euler) parameters) in the inertial frame are nvestigated. The new algorithms are based upon using the classical Hamilton rotation quaternion, quaternion with zero scalar part, which is correlated to the classical rotation quaternion via the quaternion equivalent of Cayley formula, and also the new quaternion differential equation for the inertial orientation of a moving object.
