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  • Artikel  (15)
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  • Physik  (4)
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  • Artikel  (15)
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  • Springer  (15)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
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  • 2000-2004
  • 1995-1999  (15)
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  • Mathematik  (13)
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  • 1
    Digitale Medien
    Digitale Medien
    On the Bifurcation of Flows of a Heat-Conducting Fluid between Two Rotating Permeable Cylinders (1997)
    Springer
    Georgian mathematical journal 4 (1997), S. 567-578 
    Details
    ISSN: 1572-9176
    Schlagwort(e): Flow ; bifurcation ; perturbation ; axisymmetric flow ; permeable cylinders
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Sufficient conditions are found for the bifurcation of flow of a viscous heat-conducting fluid between two rotating permeable cylinders.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022159609975
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  • 2
    Digitale Medien
    Digitale Medien
    Spatial Patterns for reaction-diffusion systems with conditions described by inclusions (1997)
    Springer
    Applications of mathematics 42 (1997), S. 421-449 
    Details
    ISSN: 1572-9109
    Schlagwort(e): reaction-diffusion systems ; variational inequalities ; inclusions ; bifurcation ; stationary solutions ; spatial patterns
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022203129542
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  • 3
    Digitale Medien
    Digitale Medien
    Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities (1997)
    Springer
    Czechoslovak mathematical journal 47 (1997), S. 469-486 
    Details
    ISSN: 1572-9141
    Schlagwort(e): reaction-diffusion systems ; unilateral conditions ; bifurcation ; quasivariational inequalities ; spatial patterns
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022411501260
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  • 4
    Digitale Medien
    Digitale Medien
    Evolution of single elliptic vortex rings (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 17-25 
    Details
    ISSN: 1614-3116
    Schlagwort(e): elliptic vortex ring ; pseudo-spectral method ; bifurcation ; vortex reconnection
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The evolution of single elliptic vortex rings for initial aspect ratio (AR)=2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 643 grid points in a periodic cube. We find that there are three kinds of vortex motion asAR increases and bifurcation occurs at certainAR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02487827
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  • 5
    Digitale Medien
    Digitale Medien
    On the problem of the number of bifurcation solutions at singular point (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 969-973 
    Details
    ISSN: 1573-2754
    Schlagwort(e): homotopy ; continuation method ; bifurcation ; isolated singularity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Mathematik , Physik
    Notizen: Abstract In this paper, it is proved that the solutions of a nonlinear equation are isolated under the condition that the singular points are isolated. It shows that there must have and only have finite solutions branching from bifurcation point. This is important for the numerical analysis of bifurcation problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00189288
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  • 6
    Digitale Medien
    Digitale Medien
    Nonlinear stability analysis of a clamped rod carrying electric current (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 825-834 
    Details
    ISSN: 1573-2754
    Schlagwort(e): magnetoelasticity ; bifurcation ; limit point ; numerical method ; straight rod carrying electric current
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Mathematik , Physik
    Notizen: Abstract This paper is devoted to the analysis of the nonlinear stability of a clamped rod carrying electric current in the magnetic field which is produced by the current flowing in a pair of inifinitely long parallel rigid wires. The natural state of the rod is in the plane of the wires and is equidistant from them. Firstly under the assumption of spatial deformation, the governing equations of the problem are derived, and the linearized problem and critical currents are discussed. Secondly, it is proved that the buckled states of the rod are always in planes. Finally, the global responses of the bifurcation problem of the rod are computed numerically and the distributions of the deflections, axial forces and bending moments are obtained. The results show that the buckled states of the rod may be either supercritical or subcritical, depending on the distancz between the rod and the wires. Furthermore, it is found that there exists a limit point on the branch solution of the supercritical buckled state. This is distinctively different from the buckled state of the elastic compressive rods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00133340
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  • 7
    Digitale Medien
    Digitale Medien
    Conservation and bifurcation of an invariant torus of a vector field (1997)
    Springer
    Mathematical notes 61 (1997), S. 29-37 
    Details
    ISSN: 1573-8876
    Schlagwort(e): invariant tori ; quasiperiodic motion ; bifurcation ; noncritical matrices
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT m. The flow on the torusT m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02355005
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  • 8
    Digitale Medien
    Digitale Medien
    Saddle-point method and resurgent analysis (1997)
    Springer
    Mathematical notes 61 (1997), S. 227-241 
    Details
    ISSN: 1573-8876
    Schlagwort(e): resurgent functions ; saddle-point method ; resurgent equations ; alient derivatives ; Stokes lines ; bifurcation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The topological part of the theory of the parameter-dependent Laplace integral is known to consist of two stages. At the first stage, the integration contour is reduced to a sum of paths of steepest descent for some value of the parameter. At the second stage, this decomposition (and hence the asymptotic expansion of the integral) is continued to all other parameter values. In the present paper, the second stage is studied with the help of resurgent analysis techniques.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02355733
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  • 9
    Digitale Medien
    Digitale Medien
    Bifurcation, Bursting, and Spike Frequency Adaptation (1997)
    Springer
    Journal of computational neuroscience 4 (1997), S. 257-277 
    Details
    ISSN: 1573-6873
    Schlagwort(e): bifurcation ; bursting ; singular perturbation ; spike frequency adaptation ; stomatogastric ganglion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Medizin , Physik
    Notizen: Abstract Many neural systems display adaptive properties that occur on timescales that are slower than the time scales associated withrepetitive firing of action potentials or bursting oscillations. Spike frequency adaptation is the name givento processes thatreduce the frequency of rhythmic tonic firing of action potentials,sometimes leading to the termination of spiking and the cell becomingquiescent. This article examines these processes mathematically,within the context of singularly perturbed dynamical systems.We place emphasis on the lengths of successive interspikeintervals during adaptation. Two different bifurcation mechanisms insingularly perturbed systems that correspond to the termination offiring are distinguished by the rate at which interspike intervalsslow near the termination of firing. We compare theoreticalpredictions to measurement of spike frequency adaptation in a modelof the LP cell of the lobster stomatogastric ganglion.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008871803040
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  • 10
    Digitale Medien
    Digitale Medien
    Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 57-68 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Saddle form cable-suspended roofs ; truncated spectral model ; bifurcation ; chaos
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The purpose of this paper is to investigate the dynamic behaviour of saddle form cable-suspended roofs under vertical excitation action. The governing equations of this problem are system of nonlinear partial differential and integral equations. We first establish a spectral equation, and then consider a model with one coefficient, i.e., a perturbed Duffing equation. The analytical solution is derived for the Duffing equation. Successive approximation solutions can be obtained in likely way for each time to only one new unknown function of time. Numerical results are given for our analytical solution. By using the Melnikov method, it is shown that the spectral system has chaotic solutions and subharmonic solutions under determined parametric conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008241710683
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  • 11
    Digitale Medien
    Digitale Medien
    Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 263-274 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Parametric excitation ; nonlinear systems ; bifurcation ; bifurcation control ; stabilization ; nonlinear control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a parametrically excited Duffing system we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response and in order to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. Because the bifurcation of the system is characterized by its modulation equations, we first determine the order of the feedback gain so that the feedback modifies the modulation equations. By theoretically analyzing the modified modulation equations, we show that the unstable region of the trivial steady state can be shifted and the nonlinear character can be changed, by means of the bifurcation control with the above feedback. The shift of the unstable region permits the stabilization of the trivial steady state in the frequency response, and the suppression of the discontinuous bifurcation due to the change of the nonlinear character allows the elimination of the jump in the quasistationary force response. Furthermore, by performing numerical simulations, and by comparing the responses of the uncontrolled system and the controlled one, we clarify that the proposed bifurcation control is available for the stabilization of the trivial steady state in the frequency response and for the reduction of the jump in the nonstationary force response.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008270815516
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  • 12
    Digitale Medien
    Digitale Medien
    Three-to-One Internal Resonances in Hinged-Clamped Beams (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 129-154 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Three-to-one resonance ; internal resonance ; beam vibrations ; bifurcation ; crises
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The nonlinear planar response of a hinged-clamped beam to a primary excitation of either its first mode or its second mode is investigated. The analysis accounts for mid-plane stretching, a static axial load and a restraining spring at one end, and modal damping. For a range of axial loads, the second natural frequency is approximately three times the first natural frequency and hence the first and second modes may interact due to a three-to-one internal resonance. The method of multiple scales is used to attack directly the governing nonlinear partial-differential equation and derive two sets of four first-order nonlinear ordinary-differential equations describing the modulation of the amplitudes and phases of the first two modes in the case of primary resonance of either the first or the second mode. Periodic motions and periodically and chaotically modulated motions of the beam are determined by investigating the equilibrium and dynamic solutions of the modulation equations. For the case of primary resonance of the first mode, only two-mode solutions are possible, whereas for the case of primary resonance of the second mode, single- and two-mode solutions are possible. The two-mode equilibrium solutions of the modulation equations may undergo a supercritical or a subcritical Hopf bifurcation, depending on the magnitude of the axial load. A shooting technique is used to calculate limit cycles of the modulation equations and Floquet theory is used to ascertain their stability. The limit cycles correspond to periodically modulated motions of the beam. The limit cycles are found to undergo cyclic-fold bifurcations and period-doubling bifurcations, leading to chaos. The chaotic attractors may undergo boundary crises, resulting in the destruction of the chaotic attractors and their basins of attraction.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008229503164
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  • 13
    Digitale Medien
    Digitale Medien
    The Study of a Parametrically Excited Nonlinear Mechanical System with the Continuation Method (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 1-22 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Nonlinear ; bifurcation ; continuation method ; parametric resonance
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The dynamic behavior of a one-degree-of-freedom, parametrically excited nonlinear system is investigated. The Galerkin method is applied to the principal and fundamental parameteric resonance of the system. The continuation method is used to study the change of harmonic oscillation with respect to the variation of excitation frequency. The numerical stability analysis of the trivial solution is carried out and the stable and unstable regions of the trivial solution are given. They are found to agree with the results obtained by the analytical method of Galerkin. Periodic solutions are traced and the coexistence of multi-periodic solutions is observed With the change of excitation frequency the large amplitude periodic-2 oscillation is found to be in the same closed branch with the small amplitude periodic-2 solution. In addition, the bifurcation pattern of the trivial solution is found to change from subcritical Hopf bifurcation into supercritical Hopf bifurcation with the increase of excitation amplitude. Combined with the conventional numerical integration method, new complex dynamic behavior is detected.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008269317038
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  • 14
    Digitale Medien
    Digitale Medien
    Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 139-156 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Cables ; active control ; nonlinear oscillations ; bifurcation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008255409438
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  • 15
    Digitale Medien
    Digitale Medien
    Perturbation Methods for Bifurcation Analysis from Multiple Nonresonant Complex Eigenvalues (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 193-210 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Perturbation methods ; stability ; bifurcation ; codimension two ; periodic and quasi-periodic solutions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way, amplitude modulation equations equal to normal form equations available in literature. With a remarkable computational improvement, the description of the central manifold is avoided. The Lindstedt–Poincaré Method can also be employed if only steady-state solutions have to be determined. An application is illustrated for a mechanical system subjected to aerodynamic excitation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008201828000
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