Search results for "värähtelyt"
showing 5 items of 25 documents
Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture
2019
The Aizerman and Kalman conjectures played an important role in the theory of global stability for control systems and set two directions for its further development – the search and formulation of sufficient stability conditions, as well as the construction of counterexamples for these conjectures. From the computational perspective the latter problem is nontrivial, since the oscillations in counterexamples are hidden, i.e. their basin of attraction does not intersect with a small neighborhood of an equilibrium. Numerical calculation of initial data of such oscillations for their visualization is a challenging problem. Up to now all known counterexamples to the Kalman conjecture were const…
Acoustic wave tunneling across a vacuum gap between two piezoelectric crystals with arbitrary symmetry and orientation
2022
It is not widely appreciated that an acoustic wave can “jump” or “tunnel” across a vacuum gap between two piezoelectric solids, nor has the general case been formulated or studied in detail. Here, we remedy that situation, by presenting a general formalism and approach to study such an acoustic tunneling effect between two arbitrarily oriented anisotropic piezoelectric semi-infinite crystals. The approach allows one to solve for the reflection and transmission coefficients of all the partial-wave modes, and is amenable to practical numerical or even analytical implementation, as we demonstrate by a few chosen examples. The formalism can be used in the future for quantitative studies of the …
An analytical-numerical study of dynamic stability of an axially moving elastic web
2015
This paper is devoted to a dynamic stability analysis of an axially moving elastic web, modelled as a panel (a plate undergoing cylindrical deformation). The results are directly applicable also to the travelling beam. In accordance with the dynamic approach of stability analysis, the problem of harmonic vi- brations is investigated via the study of the dependences of the system’s nat- ural frequencies on the problem parameters. Analytical implicit expressions for the solution curves, with respect to problem parameters, are derived for ranges of the parameter space where the natural frequencies are real-valued, corresponding to stable vibrations. Both axially tensioned and non-tensioned tra…
Rhythmic Memory Consolidation in the Hippocampus
2022
Functions of the brain and body are oscillatory in nature and organized according to a logarithmic scale. Brain oscillations and bodily functions such as respiration and heartbeat appear nested within each other and coupled together either based on phase or based on phase and amplitude. This facilitates communication in wide-spread neuronal networks and probably also between the body and the brain. It is a widely accepted view, that nested electrophysiological brain oscillations involving the neocortex, thalamus, and the hippocampus form the basis of memory consolidation. This applies especially to declarative memories, that is, memories of life events, for example. Here, we present our vie…