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This paper describes the results of intraoperational monitoring of hemodynamic parameters (velocity and pressure) in brain vessels, carried out within the framework of 50 neurosurgical operations using a Volcano ComboMap instrumental measuring system. It is established that the introduced parameter of specific load used during the neurosurgical operations is a significant parameter for the success of the operation.

This paper presents a variational approach to the solution of direct and inverse problems based on the joint use of mathematical models and monitoring data for processes of geophysical hydrothermodynamics. This approach is used to solve problems related to environmental protection. A variational principle with weak restrictions is formulated to account for uncertainties and errors in models and data. Inclusion of uncertainties makes it possible to construct direct non-iterative algorithms for sequential assimilation of data obtained by various observational systems. Criteria and functions for controlling the quality of the natural environment are introduced into the modeling system to solve inverse problems of environmental safety. The problem with data assimilation for the Novosibirsk agglomeration is considered.

A review of publications on the Rayleigh-Taylor instability arising due to high-velocity implosion of liners is presented. Papers that describe experimental testing and numerical simulation of the development and suppression of this instability are also considered.

Characteristics of a system of equations that describe three-dimensional motion of an incompressible viscoelastic Maxwell medium with the upper and lower convective derivatives and the rotational Jaumann derivative being used in the rheological relation are calculated. An initial-boundary-value problem is formulated for the system linearized in the vicinity of the quiescent state, and its unique solvability is established.

For the numerical simulation of aerodynamics problems, the Euler and Navier-Stokes equations written in integral form are used to construct an implicit finite-dimensional predictor-corrector scheme. At the predictor stage, the splitting of equations into physical processes and spatial directions is introduced, which makes it possible to reduce the solution of the original system to the solution of individual equations on fractional steps by the scalar sweep method and ensure the stability of the algorithm as a whole. The paper also describes the supersonic gas flows in a narrowing channel with regular and non-regular reflection of the compression shock from the symmetry plane and the numerical substantiation of the existence of pulsating flow with a supersonic flow past a cylinder with a needle.

This paper presents the observation results for the internal wave boron in the coastal region of the Sea of Japan with the use of vertical thermistor chains. The data obtained is interpreted by the mathematical models of shallow water in which the effect of nonlinearity and variance on the propagation of internal wave packages is taken into account. Within the framework of the theory of multilayer shallow water, the problem of transformation of a solitary wave into an internal boron is solved, and the possibility of recovery of a space-time picture of the flow during the passage of an internal boron in the section between adjacent experimental bottom stations is demonstrated.

Magnetohydrodynamic (MHD) flow of a viscous electroconductive incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector along the normal to the surface is specified on the upper disk, and the lower disk is non-conductive. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameter: the electric current density on the upper plate Y and the Batchelor number (the magnetic Prandtl number). It is assumed that the external source producing the axial magnetic field is absent. The problem is solved for the Batchelor number in the range of 0-2. Fluid flow is produced by electric current. It is shown that for small values of Y , the fluid velocity vector of the has only axial and radial components. The rate of motion increases with increasing Y , and at a critical value of Y , there is a bifurcation of a new stable flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism of the bifurcation of rotation in the MHD flow is found.

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar-turbulent transition initiated by distributed roughness of the plate surface at the Mach number M=2 is considered.

The problem of experimental modeling of discontinuity formation in a cavitating liquid layer under shock wave loading is considered. It is shown that the discontinuity takes the shape of a sphere segment and retains it up to the closure instant. The discontinuity surface becomes covered with a dynamically growing thin boundary layer consisting of bubbles, which transforms to a ring-shaped vortex bubble cluster at the instant of closure of the discontinuity emitting a secondary shock wave. Specific features of the structure of the cavitating flow discontinuity arising at loading intensities lower than 0.1 and 5 kJ are discussed.

The influence of a cylinder-shaped single roughness element on the laminar-turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone mode at the Mach number M=5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400-500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.