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Testing the Isotropy Postulate at Deformation of V95 Aluminum Alloy along Two-Link Polygonal-Chain Trajectories Moscow Univ. Mech. Bull. Pub Date : 2023-12-21 V. G. Zubchaninov, V. I. Gultyaev, A. A. Alekseev, I. A. Savrasov
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Limit Reachability Region for Special Form of Third-Order Linear Oscillating System Moscow Univ. Mech. Bull. Pub Date : 2023-12-21 D. I. Bugrov
Abstract The problem under consideration is to find periodic trajectories lying on the boundary of the limit reachability region of a linear time-invariant third-order system with one controlling action bounded in absolute value. It is assumed that the characteristic equation of a homogeneous system has one negative real root and two complex conjugate roots, the real parts of all three roots are the
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Peculiarities of Behavior of Simplest Models of Nonlinear Elasticity Constructed Based on New Holonomic Tensor Measures Moscow Univ. Mech. Bull. Pub Date : 2023-12-21 E. S. Klimov, G. L. Brovko
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On the Variational Principle of Lagrange in the Micropolar Theory of Elasticity at Nonisothermal Processes Moscow Univ. Mech. Bull. Pub Date : 2023-11-13 A. V. Romanov
Abstract In this paper, a variational principle of Lagrange, the Ritz method, and piecewise polynomial serendipity shape functions are used to obtain a stiffness matrix and a system of linear algebraic equations in the micropolar theory of elasticity for anisotropic, isotropic, and centrally symmetric material in case of a nonisothermal process.
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Generalized Cesàro Formulas and Third-Order Compatibility Equations Moscow Univ. Mech. Bull. Pub Date : 2023-11-13 S. A. Lurie, P. A. Belov
Abstract We consider the classical problem of elasticity theory concerning the conditions of strain compatibility, which ensure the determination of a continuous field of displacements of an elastic body by the strain field. We construct generalized Cesàro representations that allow defining the displacement field through integrodifferential operators on the components of the strain tensor deviator
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Quasi-Self-Similar Solutions to Some Parabolic Problems in the Theory of Viscoplastic Flow Moscow Univ. Mech. Bull. Pub Date : 2023-11-13 V. A. Banko, D. V. Georgievskii
Abstract The initial-boundary value problems of acceleration from a state of rest of a two-constant viscoplastic medium (Bingham body) in a half-plane is investigated when the tangential stress is given at the boundary as a piecewise continuous monotonically nondecreasing function of time. As an additional condition at an unknown interface between a flow zone that increases with time in thickness and
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Equilibrium Point and Phase Portrait of a Model for Flow of Tixotropic Media Accounting for Structure Evolution Moscow Univ. Mech. Bull. Pub Date : 2023-11-13 A. V. Khokhlov
Abstract We continue the systematic analytical study of a nonlinear Maxwell-type constitutive equation for shear flow for thixotropic viscoelastic media accounting for interaction of deformation process and structure evolution, namely, the influence of the kinetics formation and breakage of chain cross-links, agglomerations of molecules and crystallites on viscosity and shear modulus and deformation
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Computing a Transfer Function of the Poincaré–Steklov Operator for a Functionally Graded Elastic Strip Moscow Univ. Mech. Bull. Pub Date : 2023-10-01
Abstract A boundary value problem is considered in a functionally graded elastic strip. A three-term asymptotic expansion of a transfer function is obtained for the Poincaré–Steklov operator that maps normal stresses to normal displacements on a part of the strip boundary. Padé approximations are determined for the obtained asymptotic series. An approach to computing the transfer function using the
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Displacement Discontinuity Method Taking into Account the Curvature of the Crack Moscow Univ. Mech. Bull. Pub Date : 2023-08-15 A. V. Zvyagin, D. D. Novov
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On Some Properties of the Kalman Filter in the Pedestrian Navigation Problem Moscow Univ. Mech. Bull. Pub Date : 2023-08-15 Yu. V. Bolotin, A. V. Bragin
Abstract A pedestrian navigation system consisting of two foot-mounted strapdown inertial navigation systems (SINS)s is considered. The zero velocity conditions of the foot in the stance phase of a step and a limited distance between the feet are used for SINS corrections. The aim of the work is to study some consistency properties of the extended Kalman filter. It is shown that this consistency depends
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Constitutive Equations with Dissipative Stresses Moscow Univ. Mech. Bull. Pub Date : 2023-08-15 I. N. Molodtsov
Abstract A new class of constitutive equations for complex loading processes is obtained. It has three state functionals. A new method of mathematical modeling and mathematical principle is formulated. According to them, physically correct equations of state are changed by introducing gyroscopic terms that do not perform mechanical work. The constitutive equations of complex loading processes with
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On the Method for Identifying Inhomogeneous Fields of Residual Stresses Moscow Univ. Mech. Bull. Pub Date : 2023-08-15 E. B. Zavoychinskaya, A. S. Plotnikov
Abstract A numerical-analytical method for three-axial inhomogeneous elastic residual stress determination based on the data of the displacement optical measurement during the incremental hole drilling method is presented. The constitutive relations for the displacements as the three variable functions (in plane of the hole and along its depth) are represented by the Volterra integral operators. A
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On the Motion of Two Contacting Cylinders Interacting through Dry Friction Force Moscow Univ. Mech. Bull. Pub Date : 2023-06-22 E. E. Borisenko
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Stress Concentration Tensor of a Stretched Isotropic Plane Weakened by a Grid of Isotropic Inclusions Moscow Univ. Mech. Bull. Pub Date : 2023-06-22 I. F. Startsev
Abstract This work presents the construction of a solution to the plane doubly periodic loading problem for an infinite elastic isotropic plane with elliptical inclusions. The plane is under one of three loads: it is stretched in the direction of one of the inclusion axes or it has a pure shear at infinity. The concept of stress concentration tensor is considered and an example of its construction
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Necessary Existence Conditions for an Additional Integral in the Problem of Motion of a Rigid Body with a Fixed Point Bounded by the Surface of an Ellipsoid of Revolution in a Particle Flow Moscow Univ. Mech. Bull. Pub Date : 2023-06-22 M. M. Gadzhiev, A. S. Kuleshov
Abstract The problem of motion in a free molecular flow of particles of a rigid body with a fixed point bounded by the surface of an ellipsoid of revolution is considered. Necessary existence conditions for an additional analytic first integral independent of the energy integral are obtained in this problem.
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Free Oscillations of a Conical Shell Moscow Univ. Mech. Bull. Pub Date : 2023-06-22 S. D. Algazin, A. A. Sinitsyn
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On the Variational Principle of Lagrange of the Micropolar Elasticity Theory in the Case of Orthotropic Medium Moscow Univ. Mech. Bull. Pub Date : 2023-06-13 A. V. Romanov
Abstract In this paper, the variational principle of Lagrange, the Ritz method and piecewise polynomial serendipity shape functions are used to obtain the stiffness matrix and a system of linear algebraic equations in the micropolar theory of elasticity for orthotropic and centrally symmetric material.
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Dilution of Precision in the Problem of Estimating the Aircraft Velocity by Means of Three-Beam Lidar Measurements Moscow Univ. Mech. Bull. Pub Date : 2023-06-13 V. M. Zheleznov
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Calibration of an Accelerometer Unit under Restriction on Its Angular Positions in the Plane Case Moscow Univ. Mech. Bull. Pub Date : 2023-06-13 H. Yin, A. I. Matasov
Abstract The calibration problem for the accelerometer unit is considered under restrictions on its angular positions (for the plane case). The guaranteeing approach is applied to solve the problem. The solution is found in analytical form.
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Numerical Modeling of Branched Cracks Moscow Univ. Mech. Bull. Pub Date : 2023-06-13 A. V. Zvyagin, A. S. Udalov
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Motion of an Anisotropic Magnetizable Elastomer in the Field of a Coil with Current Taking into Account the Interaction with Inclined Surface Moscow Univ. Mech. Bull. Pub Date : 2023-06-13 D. I. Merkulov, D. A. Pelevina, V. A. Turkov, V. A. Naletova
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Dynamic Tension of a Sheet Made of Rigid-Plastic Material Moscow Univ. Mech. Bull. Pub Date : 2023-02-28 I. M. Tsvetskov
Abstract The stress-strain state arising under dynamic stretching of a homogeneous sheet of an incompressible ideally rigid-plastic material, which obeys the Mises–Hencky criterion, is studied. The lateral boundary is stressfree and the longitudinal velocities are given at the ends. The possibility of thickening or thinning of the cross section along the length of the sheet is taken into account, which
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Neural Network Motion Control of a Spherical Robot in Planar Case Moscow Univ. Mech. Bull. Pub Date : 2023-02-28 N. V. Nor
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Atmospheric Vortex Excited by a Gasdynamic Instability Moscow Univ. Mech. Bull. Pub Date : 2023-02-28 V. Ya. Shkadov, A. N. Beloglazkin
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On the Instability with Probability One of Equilibrium of Ideal Incompressible Liquid Situated in a Vertical Cylinder under Its Random Coaxial Vibration Moscow Univ. Mech. Bull. Pub Date : 2023-02-28 I. L. Antonov
Abstract The paper concerns with the equilibrium of the ideal incompressible liquid situated in a moving cylindrical vertical vessel. It is proved that the equilibrium is unstable with probability one if the vessel movement is defined as the vertical random vibration. Random vibration is simulated by stationary Markov chain.
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A Solution to Heat Equation with Exacerbation and Stopped Heat Wave Moscow Univ. Mech. Bull. Pub Date : 2023-02-02 V. L. Natyaganov, Yu. D. Skobennikova
Abstract The generalization of Samarskii–Sobol’ solution in the mode of heat exacerbation and localization is obtained for a quasilinear heat equation in half-space. The analogy of this solution with summer heating of moisture-saturated soil in the permafrost zone is discussed.
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On Seismic Oscillations of Semi-Infinite Underground Pipeline Moscow Univ. Mech. Bull. Pub Date : 2023-02-02 M. Sh. Israilov, S. E. Nosov
Abstract Unsteady oscillations of a semi-infinite underground pipeline and elastic soil caused by the propagation of a longitudinal seismic wave along the pipeline are studied. The problem is not self-similar and its solution meets significant difficulties unlike the case of an infinite pipeline. It is shown that the formulation and consideration of this problem performed earlier by Rashidov are incorrect
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Anisotropic Scalar Constitutive Equations and Corresponding Models of Viscoplastic Flow Moscow Univ. Mech. Bull. Pub Date : 2023-02-02 D. V. Georgievskii
Abstract The tensor linear anisotropic constitutive relations of incompressible viscoplastic flow connecting the stress deviator and strain rates and the following scalar relation connecting the quadratic stress invariant and the hardening function are considered. In the case of a perfect plastic material, the latter relation is an anisotropic Mises–Hencky quadratic criterion of plasticity. The mutual
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Free Oscillations of an Orthotropic Conical Shell Moscow Univ. Mech. Bull. Pub Date : 2023-02-02 S. D. Algazin, I. A. Selivanov
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Nonlinear Model of Shear Flow of Thixotropic Viscoelastoplastic Continua Taking into Account the Evolution of the Structure and Its Analysis Moscow Univ. Mech. Bull. Pub Date : 2023-02-02 A. M. Stolin, A. V. Khokhlov
Abstract We formulate a nonlinear Maxwell-type constitutive equation for shear deformation of polymers in flow state or polymer viscoelastic melts and solutions which takes into account interaction of deformation process and structure evolution, namely, influence of the kinetics formation and breakage of chain cross-links, agglomerations of molecules and crystallites on viscosity and shear modulus
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Torsion of a Circular Solid Cylinder Made of Dilatant Material Moscow Univ. Mech. Bull. Pub Date : 2022-10-20 A. N. Sakharov, R. M. Izimov
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A Variational Principle of Lagrange of the Micropolar Theory of Elasticity in the Case of Transversely Isotropic Medium Moscow Univ. Mech. Bull. Pub Date : 2022-10-20 A. V. Romanov
Abstract In this paper, a variational principle of Lagrange in the micropolar theory of elasticity for transversely isotropic and centrally symmetric material is formulated. The Ritz method and piecewise-polynomial serendipity shape functions are used to obtain the components of the tensor-block stiffness matrix and a system of linear equations.
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Peculiarities in Applying the Theory of Elastoplastic Processes at Complex Loading along Curvilinear Deformation Trajectories Moscow Univ. Mech. Bull. Pub Date : 2022-10-20 I. N. Molodtsov
Abstract The approach to mathematical modeling of complex loading processes is based on the two ideas given by A.A. Il’yushin. One of them is called the Il’yushin three-term formula and sets the type of the differential dependence that connects the stress and strain deviator vectors in two- or-three-dimensional complex loading processes The second idea determines the type of the five-dimensional deformation
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Linear Stability of Stratified Flow of Two Viscous Fluids Moscow Univ. Mech. Bull. Pub Date : 2022-10-20 O. A. Logvinov
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Friedrichs Inequalities and Sharpened Sufficient Stability Conditions of Plane-Parallel Flows Moscow Univ. Mech. Bull. Pub Date : 2022-09-06 D. V. Georgievskii
Abstract From the standpoint of the linearized stability theory, two eigenvalue problems for the Orr–Sommerfeld equation with two groups of boundary conditions having a certain mechanical meaning are considered. The stability parameter, which is a real part of the spectral parameter, is estimated on the basis of the integral relations method operating with quadratic functionals. The technique of the
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On the Stability of Special Modes of Gliding of a Finned Body Moscow Univ. Mech. Bull. Pub Date : 2022-09-06 Yu. M. Okunev, O. G. Privalova, V. A. Samsonov
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Transient Oscillations of an Underground Pipeline and Soil at Inclined Fall of a Seismic Wave Moscow Univ. Mech. Bull. Pub Date : 2022-09-06 M. Sh. Israilov
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On the Motion of a Rigid Body with a Fixed Point in a Flow of Particles Moscow Univ. Mech. Bull. Pub Date : 2022-09-06 M. M. Gadzhiev, A. S. Kuleshov
Abstract The problem of motion of a rigid body with a fixed point in a free molecular flow of particles is considered. It is shown that the equations of motion of this body generalize the classical Euler–Poisson equations of motion of a heavy rigid body with a fixed point, and they are represented in the form of the classical Euler–Poisson equations in the case when the surface of the body in a flow
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Variation of the Size of Reachable Region of Second-Order Linear System Moscow Univ. Mech. Bull. Pub Date : 2022-07-08 D. I. Bugrov, M. I. Bugrova
Abstract A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on
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Pulsed Control of a Dangerous Asteroid in the Domain of $$\mathbf{1:1}$$ Resonance Moscow Univ. Mech. Bull. Pub Date : 2022-07-08 V. A. Proshkin, A. S. Chura
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Trigger Factors and Ways of Provoking the Seismic and Volcanic Activity Moscow Univ. Mech. Bull. Pub Date : 2022-07-08 V. L. Natyaganov, Yu. D. Skobennikova
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Theory of Five-Dimensional Elastoplastic Processes of Moderate Curvature Moscow Univ. Mech. Bull. Pub Date : 2022-07-08 I. N. Molodtsov
Abstract A variant of the constitutive equations for describing complex loading processes with deformation trajectories of arbitrary geometry and dimension is considered. The vector constitutive equations and a new method of mathematical modeling the five-dimensional complex loading processes are obtained. This method is validated for two- and three-dimensional processes of constant curvature. The
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Relation of the Modern Theory of Disperse Systems with the Classical Filtration Theory Moscow Univ. Mech. Bull. Pub Date : 2022-06-09 Ya. D. Yankov
Abstract The article examines how the filtration theory should look from the point of view of the modern theory of disperse systems, which is a nontrivial generalization of the classical theory of Brownian motion.
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Variation Principles of Moment-Membrane Theory of Shells Moscow Univ. Mech. Bull. Pub Date : 2022-06-09 S. H. Sargsyan
Abstract In the present paper assumptions are formulated, and, on the basis of the moment theory of elasticity with independent fields of displacements and rotations, general variation principle of Hu–Washizu type is established and basic equations with boundary conditions of the moment-membrane theory of shells are set out. For the moment-membrane theory of shells particular variation principles of
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Influence of Flow Velocity Variability on Pipeline Stability Boundaries Moscow Univ. Mech. Bull. Pub Date : 2022-06-09 V. P. Radin, V. P. Chirkov, O. V. Novikova, A. V. Shchugorev, V. N. Shchugorev
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Dynamic Model of Ship Wind Turbine with Transmission Moscow Univ. Mech. Bull. Pub Date : 2022-06-09 M. A. Garbuz
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Dynamics of Rigid Body with Viscous Filler: Qualitative Analysis Moscow Univ. Mech. Bull. Pub Date : 2022-03-04 A. V. Karapetyan
Abstract The problem of motion by inertia of a rigid body with an ellipsoidal cavity filled with a liquid in the presence of the internal friction is discussed. The global qualitative analysis of the system dynamics and the limiting motions is given.
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The Mathieu Equation near the Boundaries of the Second and Third Resonance Zones Moscow Univ. Mech. Bull. Pub Date : 2022-03-04 V. M. Budanov, L. F. Davudova
Abstract A second-order differential equation with periodic coefficients is considered. The reduction of this equation to a first-order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu equation describing the behavior of solutions near the boundaries of these zones.
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The Galvanic Correction of the Gaze Stabilization Neural Control: Part 1 Moscow Univ. Mech. Bull. Pub Date : 2022-03-04 V. A. Sadovnichii, V. V. Aleksandrov, T. B. Aleksandrova, I. S. Konovalenko, K. V. Tikhonova, N. E. Shulenina, E. Soto
Abstract The article shows a theoretical (part 1) improvement in the stabilization of the gaze in galvanic vestibular stimulation.
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On the Positive Definiteness of the Poincaré–Steklov Operator for Elastic Half-Plane Moscow Univ. Mech. Bull. Pub Date : 2022-03-04 A. A. Bobylev
Abstract The Poincaré–Steklov operator that maps normal stresses to normal displacements on a part of a half-plane boundary is studied. A boundary value problem is formulated to introduce the associated Poincaré–Steklov operator. An integral representation based on the solution to the Flamant problem for an elastic half-plane subjected to a concentrated normal force is given for the operator under
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Initial Alignment Method for a Strapdown Inertial Navigation System on a Swing Base Moscow Univ. Mech. Bull. Pub Date : 2022-02-11 G. O. Barantsev, A. A. Golovan, P. Yu. Kuznetsov
Abstract The article is devoted to deriving reference models for the problem of initial alignment of a strapdown inertial navigation system (INS) on a swing base. It is assumed that the system does not move relative to the Earth, but its body can make uncontrolled angular motions. The described models are based on the approximation of the readings of INS accelerometers from projections on the axes
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Rotation of Isosceles Tetrahedron in Central Newtonian Force Field: Staude Cone Moscow Univ. Mech. Bull. Pub Date : 2022-02-11 A. A. Burov, E. A. Nikonova
Abstract The Staude cone is considered in the problem of motion of a homogeneous isosceles tetrahedron in a central Newtonian force field. The nature of the Staude cone degeneracy is studied for the case when an isosceles tetrahedron is close to regular. It is shown how the Staude cone equations can be obtained within the framework of the Routh theory.
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Relationship between Theory of Incompressible Disperse Systems and Theory of Fluidization Moscow Univ. Mech. Bull. Pub Date : 2022-02-11 Ya. D. Yankov
Abstract This work proposes a mathematical model of dispersed systems with constant number densities of the dispersed and carrier phases (incompressible dispersed system). This model makes it possible to construct a physically meaningful and mathematically correct theory of the movement of bubbles in a boiling (fluidized) layer.
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Bifurcations in Dynamics of Chaplygin Ball Moscow Univ. Mech. Bull. Pub Date : 2022-02-11 Shamil Magomedov
Abstract The stationary motions of an inhomogeneous dynamically symmetric ball on an absolutely rough plane are studied in the special case of the center of mass passing the highest point. The system is analyzed numerically, and the existence of stable and unstable precessions is discovered. The results are presented in the form of bifurcation diagrams.
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On Short-Wave Instability of One-Dimensional Radiative-Convective Models of Atmosphere in Quasi-Hydrostatic Approximation Moscow Univ. Mech. Bull. Pub Date : 2021-11-02 Xu, X.
Abstract One-dimensional radiative-convective models are widely used for studying long-term climate and the influence of various processes (condensation of water vapor, motion of droplets, and their impacts on radiative fluxes, etc.) on the hydrodynamics of the atmosphere. However, long-term prediction of climate is difficult due to the properties of the systems of equations, i.e., a small short-wave
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On the Influence of Surface Forces on Diffusion in Solution at the Initial Section of Liquid Film Development Moscow Univ. Mech. Bull. Pub Date : 2021-11-02 Beloglazkin, A. N., Shkadov, V. Ya.
Abstract The flow of a film of a viscous liquid is considered. The liquid is a weak solution containing a gas phase and a volatile surfactant. The distribution of the latter in the layer is controlled by the diffusion in the liquid volume, the adsorption–desorption processes between the liquid volume and the adsorbed near-surface layer, and the evaporation from the surface into the boundary gaseous
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Bulgakov Problem for a Hyperbolic Equation and Robust Stability Moscow Univ. Mech. Bull. Pub Date : 2021-11-02 Zhermolenko, V. N., Temoltzi-Ávila, R.
Abstract An inhomogeneous wave equation with dissipation in the presence of an external uncertain perturbation is considered. The problem of finding solutions with the maximum possible amplitudes is investigated. A method for solving this problem based on the Fourier method of separating variables and the Bulgakov problem of the maximum deviation of solutions of second-order ordinary differential equations
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Controlled Transition in a Model of Biomass Dynamics of Root Hemiparasitic Plants Moscow Univ. Mech. Bull. Pub Date : 2021-11-02 Aleksandrov, V. V., Aleksandrova, T. B., Cruzado, L. L., Escamilla, R. J. A.
Abstract The article shows the possibility of solving the problem of the transition between periodic and point attractors in the bistable Rosenzweig–MacArthur model with modifications for the dynamics of root hemiparasitic plants and their hosts.
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Resonance in Multicomponent Linear Systems Moscow Univ. Mech. Bull. Pub Date : 2021-09-07 Lykov, A. A., Malyshev, V. A., Melikian, M. V.
Abstract We consider a system of many point particles with arbitrary quadratic interaction and a harmonic force acting on a single fixed particle. Necessary and sufficient conditions for resonance and uniform boundedness of trajectories are obtained; and for the case of resonance the late time asymptotics for energy maximum of the system is obtained as well.
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A Modification of the Hodgkin–Huxley Model and a Mathematical Interpretation of the Principal Neurophysiological ‘‘All-or-None’’ Law Moscow Univ. Mech. Bull. Pub Date : 2021-09-07 Aleksandrov, V. V., Aleksandrova, O. V., Kozik, I. A., Semenov, Yu. S.
Abstract The paper presents the results of simulation with the simplified modified Hodgkin–Huxley model of an afferent primary neuron in the presence of stochastic noise. The transition from the attraction domain of a point attractor like a stable focus to the attraction domain of a periodic attractor and the inverse transition to the attraction domain of the point attractor are considered. Some examples