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We study a linear stability of a resting state for flows of incompressible viscoelastic fluid in an infinite cylindrical channel under the influence of an external uniform magnetic field directed parallel to the cylinder axis (we use a generalized rheological Vinogradov–Pokrovski model as mathematical model) in a class of axisymmetric periodic along the axial variable flows. We establish that for some values of the parameters in the case of an absolute conductivity b m = 0 , the magnetic field can substantially lessen the real part of an exponent for perturbations of the radial velocity component, which is the main element of the instability development. For general case b m ≠ 0 , we justify the possibility of removing the instability based on the performed calculations. [ABSTRACT FROM AUTHOR]

We study the Lyapunov linear stability of the stationary state for flows of an incompressible viscoelastic polymer fluid in an infinite planar channel. As a model we choose the Vinogradov–Pokrovskii rheological model well-suited for describing the flow characteristics of linear polymer melts. We find the spectrum of the mixed problem and prove that the solution to the linearized mixed problem in the class of periodic perturbations of the variable changing along the channel side grows faster in time than the exponential with a linear exponent. In other words, the stationary state is linearly unstable. [ABSTRACT FROM AUTHOR]

We study a rheological Pokrovski‐Vinogradov model for the flows of solutions and melts of incompressible viscoelastic polymeric medium in case of a flow in an infinite plane channel with perforated walls. We prove the linear Lyapunov instability of the base solution with the constant flow rate in a perturbation class, periodic with respect to the variable, changing along the channel wall. [ABSTRACT FROM AUTHOR]

We study the linear stability of a resting state for a generalization of the basic rheological Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to the nonisothermal case under the influence of magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: for certain values of the conduction current which is given on the electrodes, i.e. on the channel boundaries, the problem has solutions whose amplitude grows exponentially (in the class of functions periodic along the channel). [ABSTRACT FROM AUTHOR]

We study a new rheological model describing flows of melts and solutions of incompressible viscoelastic polymeric media in an external uniform magnetic field in the presence of a temperature drop and a conduction current. We derive an asymptotic representation of the spectrum of the linear problem resulting from the linearization of the initial boundary value problem in an infinite plane channel about a Poiseuille-type flow. For this Poiseuille-type flow, we also determine the parameter domain of linear Lyapunov stability. [ABSTRACT FROM AUTHOR]

Studying the problem of a stationary supersonic van der Waals gas flow around an infinite plane wedge, we prove the local-in-time well-posedness of the generalized statement of the problem. [ABSTRACT FROM AUTHOR]

In this paper, we study a new rheological model (a modification of the well-known Pokrovskii-Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity in the variable that runs along the axis of the channel. [ABSTRACT FROM AUTHOR]

We study the classical problem for a flow of uniform inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, theoretically this problem has solutions of two types. Solutions of the first type correspond to a strong shock when the gas velocity behind the shock front is less than the sound speed whereas solutions of the second type correspond to the case of a weak shock when the gas velocity behind the shock front is greater than the sound speed. The shock fronts are attached to the wedge vertex. We consider the linear problem for a strong shock wave provided that the Lopatinski condition holds (in a weak sense) on the shock front and the initial data are compactly, i.e. supports of the initial data are separated from the coordinate axes. Under some additional conditions on the initial data we find a solution of the generalized problem. In contrast to the previously studied case when the uniform Lopatinski condition holds on the shock front, this solution contains plane waves. The stability of the found solution is thus justified on the linear level what gives a principle possibility to realize the flow regime containing a strong shock as time increases. [ABSTRACT FROM AUTHOR]

In this work we discuss an approach to the construction of the areas of two‐phase states for real gases, state equations for which are from the article by Fogelson and Likhachev in 2004 and formulate conditions that define absolute and neutral stability of the shock waves. [ABSTRACT FROM AUTHOR]

An asymptotic formula for the spectrum of a linearized problem of the stability of stationary flows of a polymer fluid with a space charge is obtained. [ABSTRACT FROM AUTHOR]

Experimental data on the self-organization of massive fractal granules with a total volume of up to 1.1 cm3 consisting of carbon nanofibers with transverse dimensions within 50–70 nm and a length of up to 1000 nm are presented. The fractal granules have a density of 1.3 g/cm3, an elastic modulus of 37.4 MPa, and a fractal dimension of D = 2.95. The resistivity of this material is about three orders of magnitude greater than the values typical of pyrolytic graphite. The surface layers in the fractal granule are characterized by a Seebeck coefficient of about S ∼ 24 μV/K, whereas the bulk regions have S ∼ 11 μV/K. [ABSTRACT FROM AUTHOR]