Search results for: nonlinear systems
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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublicationWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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On homotopy Conley index for multivalued flows in Hilbert spaces
PublicationPodano aproksymacyjną definicję indeksu homotopijnego, otrzymując naturalne związki z podobnymi niezmiennikami. Zbadano własności tego niezmiennika i zastosowano do badania gradientowych potoków wykazując pewne geometryczne własności zbiorów niezmienniczych
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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Fixed point indices of iterations of planar homeomorphisms.
PublicationW pracy bada się postać indeksów iteracji lokalnych homeomorfizmów płaszczyzny.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Open Research DataThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Open Research DataPresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Nonlinear high temperature impedance of 35P2O5-30Fe2O3-27.5Nb2O5-7.5TiO2 glass
Open Research DataThe nonlinear high temperature impedance of iron- phosphate glasses doped with niobium oxide was measured. Glass samples of the composition of 35P2O5-30Fe2O3-27.5Nb2O5-7.5TiO2 (in %mol) were prepared by the conventional melt quenching technique. Appropriate amounts of reagents ((NH4)2HPO4 (≥99.9%, POCH), Fe2O3 (≥99.9%, POCH), Nb2O5 (≥99.9%, PLUKA AG)...
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Nonlinear impedance of 50(2Bi2O3-V2O5)-50SrB4O7 glass-ceramic heat-treated at 813 K measured with impedance spectroscopy method at high temperature region
Open Research DataNonlinear electrcial properties of 50(2Bi2O3-V2O5)-50SrB4O7 glass-ceramic heat treated at 813 K was measured by impedance spectroscopy method.
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Nonlinear impedance of 5(2Bi2O3-V2O5)-95SrB4O7 glass measured with impedance spectroscopy method at high temperature region
Open Research DataThe nonlinear electrcial properties of 5(2Bi2O3-V2O5)-95SrB4O7 glass was measured by impedance spectroscopy method.
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Moment resistance of I-section end-plate roof girder splices; a case study
PublicationThis article deals with the problem of determining the resistance of end-plate connections. A nonlinear FEM model of the joint was constructed in order to predict its carrying capacity. A standard code procedure was done as well. The analyses have been done to assess atypical end-plate joints designed and constructed as a part of roof structures.
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Determination of the Theoretical and Actual Working Volume of a Hydraulic Motor—Part II (The Method Based on the Characteristics of Effective Absorbency of the Motor)
Publication: In this article, the second method of determination of the theoretical and actual working volume of a hydraulic motor is described. The proposed new method is based on the characteristics of effective absorbency of the motor. The effective absorbency has been defined as the ratio of flow rate in a motor to the rotational speed of the motor’s shaft. It has been shown that the effective absorbency is a nonlinear function of the...
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An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
PublicationAn isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero...
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A Model-Based Improved Control of Dissolved Oxygen Concentration in Sequencing Wastewater Batch Reactor
PublicationBiochemical processes at wastewater treatment plant are complex, nonlinear, time varying and multivariable. Moreover, relationships between processes are very strong. One of the most important issues is exerting proper control over dissolved oxygen levels during nitrification phase. This parameter has a very large impact on activity of microorganisms in activated sludge and on quality of pollution removal processes. Oxygen is supplied...
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Globalisation and world economic poverty: The significance of hidden dimensions
PublicationThe aim of our research is to examine how individual dimensions of globalization affect economic poverty in the World. for this, regression models are estimated with FGT0 or FGT1 poverty measures as dependent variables and KOF indices of globalization as despendent variables. The poverty indices are estimated for 119 countries' income didtributions assuming log-normality and using Gini estimates from the WID2 database and GDP/capita...
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About definition of modes and magnetosonic heating in a plasma’s flow: Especial cases of perpendicular and nearly perpendicular wave vector and magnetic field
PublicationDynamics of hydrodynamic perturbations in a plasma depend strongly on an angle between the wave vector and equilibrium straight magnetic field. The case of perpendicular propagation is especial. There are only two (fast) magnetosonic modes since two (slow) ones degenerate into the stationary one with zero speed of propagation. This demands individual definition of wave modes by the links of hydrodynamic relations. These links are...
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Methods of solving the Atkins equation determine shear angle with taking into consideration a modern fracture mechanics
PublicationIn the paper are presented methods of solving nonlinear Atkins equation . The Atkins equation describe shear angle with taking into account properties of material cutting. To solve Atkins equation has been used iterative methods: Newton method and simplified method of simple iteration. Method of simple iteration is presented in the form of Java application.
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On the synthesis of coupled-lossy resonator filters with unloaded quality factor control
PublicationA technique for fast synthesis of coupling matrix low-pass prototypes of generalized Chebyshev bandpass filters with lossy resonators is presented in this paper. The coupling matrix is found by solving a nonlinear least squares problem based on zeros and poles of filter's transfer functions. Additional constraints are introduced that allow one to control the level of unloaded quality factor of resonators.
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ON AXIALLY SYMMETRIC SHELL PROBLEMS WITH REINFORCED JUNCTIONS
PublicationWithin the framework of the six-parameter nonlinear resultant shell theory we consider the axially symmetric deformations of a cylindrical shell linked to a circular plate. The reinforcement in the junction of the shell and the plate is taken into account. Within the theory the full kinematics is considered. Here we analyzed the compatibility conditions along the junction and their in uence on the deformations and stressed state.
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Existence of unbounded solutions to parabolic equations with functional dependence
PublicationThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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Nonlinear impedance of 50(2Bi2O3-V2O5)-50SrB4O7 glass heat treated at 693 K measured with impedance spectroscopy method at high temperature region
Open Research DataThe nonlinear electrcial properties of 50(2Bi2O3-V2O5)-50SrB4O7 glass heat treated at 693 K was measured by impedance spectroscopy method.
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Nonlinear impedance of 50(2Bi2O3-V2O5)-50SrB4O7 glass heat treated two times measured with impedance spectroscopy method at high temperature region
Open Research DataThe nonlinear electrcial properties of 50(2Bi2O3-V2O5)-50SrB4O7 glass heat treated two times was measured by impedance spectroscopy method.
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Nonlinear impedance of 50(2Bi2O3-V2O5)-50SrB4O7 glass-ceramic heat-treated at 613 K measured with impedance spectroscopy method at high temperature region
Open Research DataNonlinear electrcial properties of 50(2Bi2O3-V2O5)-50SrB4O7 glass-ceramic heat treated at 613 K was measured by impedance spectroscopy method.
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Influence of the femoral offset on the muscles passive resistance in total hip arthroplasty
PublicationBackground Soft tissue tension is treated as a crucial factor influencing the post-THA dislocation. The femoral offset is regarded as one of the major parameters responsible for the stabilization of the prosthesis. It is unclear which soft tissue is mostly affected by the offset changes. Methods A finite element model of the hip was created. The model comprised muscles, bones, a stem, the acetabular component and a liner. The muscles...
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Robust Monitoring of Water Quality in Drinking Water Distribution System
PublicationThe paper develops a novel open loop set bounded observer for robust estimation of water quality in DWDS based on the advanced nonlinear quality dynamics model including disinfections by-products (DBPs). The observer utilises a cooperativeness of the quality dynamics model and is computationally efficient, hence applicable to on-line quality monitoring. The simulation results illustrate its good and sustainable performance.
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Speed sensorless asynchronous motor drive with inverter output lc filter
PublicationIn this paper a speed sensorless ac drive with inverter and output LC filter is proposed. A nonlinear, decoupled field oriented control algorithm with a flux and speed close-loop observer is used. In spite of using LC filter on the inverter output, the sensorless system works precisely. That result are obtained as a result of the appropriate estimation and control system use. The theory, simulation, and experimental results are...
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Stability of an Innovative Cold-Formed GEB Section
PublicationThis paper is focused on the numerical analysis and experimental test of stability of the cold-formed profile with an innovative GEB cross-section. For the shell model of the axially compressed member, the linear buckling analysis and the nonlinear static analysis were carried out. In the numerical research, the buckling load and the limit load for variable section heights were obtained. Some of the results were compared with the...
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MAGNETOACOUSTIC HEATING AND STREAMING IN A PLASMA WITH FINITE ELECTRICAL CONDUCTIVITY
PublicationNonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. Plasma is assumed to be an ideal gas with a finite electrical conductivity permeated by a magnetic filed orthogonal to the trajectories of gas particles. the excitation of non-wave modes in the filed of intense magnetoacoustic perturbations, i.e., magnetoaciustic heating and streaming, is discussed. The analysis includes a derivation if instantaneous...
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Modelling of Geared Multi-Rotor System
PublicationIn the paper the method of modelling a speed-varying geared rotor system is presented. The proposed approach enables us to obtain an accurate low-order lumped parameter representation of the investigated system. The final model consists of reduced modal models of an undamped beam/torsional shaft system as well as a spatially lumped model of other linear and nonlinear phenomena including gear mesh interaction.
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Numerical Analysis of Mice Carotid Arteries’ Response Emphasizing the Importance of Material Law Constants’ Validation
PublicationIn this paper, a detailed validation of the passive material properties of mice carotid arteries and constants of the Fung and Holzapfel hyperelastic material laws is conducted by means of static nonlinear FEM analyses. The response of the carotid arteries in an inflation test is studied here for the following mouse models: wild-type, mdx, sgcd−/−, Eln+/+, Eln+/−, Fbln5+/+, and Fbln5−/−. All FEM computations are conducted on models...
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An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
PublicationThis work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system,which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface...
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Comparison of tuning procedures based on evolutionary algorithm for multi-region fuzzy-logic PID controller for non-linear plant
PublicationThe paper presents a comparison of tuning procedures for a multi-region fuzzy-logic controller used for nonlinear process control. This controller is composed of local PID controllers and fuzzy-logic mechanism that aggregates local control signals. Three off-line tuning procedures are presented. The first one focuses on separate tuning of local PID controllers gains in the case when the parameters of membership functions of fuzzy-logic...
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Modal FEM Analysis of Ferrite Resonant Structures
PublicationThe finite-element method (FEM) is applied for modal analysis of ferrite-loaded spherical resonators. To improve the efficiency of the numerical calculations, the body-of-revolution (BOR) technique is utilized. Due to the frequency-dependent ferrite permeability, FEM leads to a nonlinear eigenvalue problem that is challenging to solve. To this end, Beyn’s method is proposed. The effectiveness of the proposed approach is confirmed...
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Application of data driven methods in diagnostic of selected process faults of nuclear power plant steam turbine
PublicationArticle presents a comparison of process anomaly detection in nuclear power plant steam turbine using combination of data driven methods. Three types of faults are considered: water hammering, fouling and thermocouple fault. As a virtual plant a nonlinear, dynamic, mathe- matical steam turbine model is used. Two approaches for fault detection using one class and two class classiers are tested and compared.
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A Novel Speed Observer for Doubly-Fed Induction Generator
PublicationThe purpose of this paper is to show a new state observer for doubly-fed generator. A proposed z-type observer algorithm based on mathematical model of doubly fed generator with additional variables treated as a disturbances has been used. A nonlinear multiscalar control method has been used to control active and reactive power of the generator. All analyses were verified by simulations and experiments tests.
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A note on simple bifurcation of equilibrium forms of an elastic rod on a deformable foundation
PublicationWe study bifurcation of equilibrium states of an elastic rod on a two-parameter Winkler foundation. In the article "Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation" [Nonlinear Anal., Real World Appl. 39 (2018) 451-463] the existence of simple bifurcation points was proved by the use of the Crandall-Rabinowitz theorem. In this paper we want to present an alternative proof of this fact based...
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Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force
PublicationIn this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the...
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Accurate simulation-driven modeling and design optimization of compact microwave structures
PublicationCost efficient design optimization of microwave structures requires availability of fast yet reliable replacement models so that multiple evaluations of the structure at hand can be executed in reasonable timeframe. Direct utilization of full-wave electromagnetic (EM) simulations is often prohibitive. On the other hand, accurate data-driven modeling normally requires a very large number of training points and it is virtually infeasible...
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Acoustic field and the entropy mode induced by it in a waveguide filled with some non-equilibrium gases
PublicationThe non-linear propagation of an acoustic beam in a rectangular waveguide is considered. The medium of sound propagation, is a gas where thermodynamically non-equilibrium processes take place: such as exothermic chemical reactions or excitation of vibrational degrees of a molecule’s freedom. The incident and reflected compounds of the acoustic field do not interact in the leading order in the case of periodic weakly nonlinear sound...
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Static and dynamic modelling blow- out type trauma of orbital wall
PublicationAuthors of the paper present initial results of finite element analysis of a blow-out type trauma of orbital wall. The research is liked with laboratory tests for the Young’s modulus of bones evaluation. In the finite element analysis the neighbourhood of orbital wall is modelled by triangle thin shell finite elements. In the paper results of nonlinear static and transient dynamic analysis (including damping) are compared. The...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Influence of thermal effects on mechanical properties of PVDF-coated fabric
PublicationThis paper describes the method of laboratory tests necessary for identification of temperature influence on mechanical properties of polyvinylidene fluoride-coated polyester fabric often used for tensile structures. Two nonlinear model descriptions are investigated. The first one is based on the piece-wise linear relations between stress and strain and the second one on the Murnaghan model of solid behavior. This paper is proposed...
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Experimental generation of complex noisy photonic entanglement
PublicationWe present an experimental scheme based on spontaneous parametric down-conversion to produce multiple-photon pairs in maximally entangled polarization states using an arrangement of two type-I nonlinear crystals. By introducing correlated polarization noise in the paths of the generated photons we prepare mixed-entangled states whose properties illustrate fundamental results obtained recently in quantum information theory, in particular those...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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State Observer for Doubly-fed Induction Generator
PublicationIn the paper a new state observer for doubly-fed generator has been proposed. In the new approach an extended mathematical model of the doubly fed generator is used to form equations of the introduced z type observer. Stability of the observer has been verified through poles placement analyses. The active and reactive powers of the generator are controlled by a nonlinear multiscalar control method. Simulation and experimental results...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Hierarchical dissolved oxygen control for activated sludge processes
PublicationA hierarchical controller for tracking the dissolved oxygen reference trajectory in activated sludge processes is proposed and investigated. The removal of nitrogen and phosphorous from wastewater is considered. Typically, an aeration system itself is a complicated hybrid nonlinear dynamical system with faster dynamics compared to the internal dynamics of the dissolved oxygen in a biological reactor. It is a common approach to...
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Enhancing seismic performance of steel buildings having semi-rigid connection with infill masonry walls considering soil type effects
PublicationUnpreventable constructional defects are the main issues in the case of steel Moment-Resisting Frames (MRFs) that mostly occur in the rigidities of beam-to-column connections. The present article aims to investigate the effects of different rigidities of structures and to propose Infill Masonry Walls (IMWs) as retrofitting strategy for the steel damaged buildings. A fault or failure to meet a certain consideration of the soil type...
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About Unusual Diffraction and Thermal Self-Action of Magnetosonic Beam
PublicationThe dynamics of slightly diverging two-dimensional beams whose direction forms a constant angle θ with the equilibrium straight magnetic strength is considered. The approximate dispersion relations and corresponding links which specify hydrodynamic perturbations in confined beams are derived. The study is dedicated to the diffraction of a magnetosonic beam and nonlinear thermal self-action of a beam in a thermoconducting gaseous plasma....