Stabilnost mikrovalnih i elektroničkih aktivnih elemenata: Analiza primjenom teorije dinamičkih sustava

The general problem of stability of microwave and RF devices and circuits in the presence of multi-frequency or broadband signals is addressed. The problem is formulated in terms of the system of nonlinear non-autonomous differential equations for generalized coordinates in the phase space that can be attributed to, e.g., amplitudes of electric currents in circuits with lumped elements or mode amplitudes of the electromagnetic field in the distributed systems. An approach to the stability analysis is proposed that allows predicting the appearance of various kinds of instabilities including the deterministically chaotic motion. The new criterion based on the analysis of Lyapunov exponents is discussed that establishes the relation between maximal stable amplitude of oscillations and the levels of nonlinearity and damping in the system. The examples of one- and two-mode oscillators have been considered in detail.Razmotren je općeniti problem stabilnosti mikrovalnih i radiofrekvencijskih aktivnih elemenata i sklopova u prisutnosti višefrekvencijskih ili širokopojasnih signala. Problem je formuliran kao sustav nelinearnih neautonomnih diferencijalnih jednadžbi u poopćenim koordinatama faznog prostora koje se mogu pridružiti npr. amplitudama električnih struja u sklopovima od elemenata s koncentriranim parametrima ili amplitudama modova elektromagnetskog polja u sustavima s raspodijeljenim parametrima. Predložena je analiza stabilnosti koja omogućava predviđanje različitih vrsta nestabilnosti uključujući determinističko kaotično gibanje. Razmotren je novi kriterij koji se osniva na analizi Ljapunovljevih eksponenata. Taj kriterij uspostavlja vezu između najveće stabilne amplitude oscilacija te razina nelinearnosti i prigušenja u sustavu. Podrobno su analizirani primjeri jednomodnog i dvomodnog oscilatora

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds)

Probabilistic estimation of uncertain temporal relations

A wide range of AI applications should manage time varying information, for example, temporal databases, reservation systems, keeping medical records, financial applications, planning. Many published research articles in the area of temporal representation and reasoning assume that temporal data is precise and certain, even though in reality this assumption is often false. In many situations there is a need to know the relation between two temporal intervals, as it is, for example, during query processing. Indeterminacy means that we do not know exactly when a particular event happened. When two temporal intervals are indeterminate it is in many cases impossible to derive a certain temporal relation between them.Keywords: Uncertain temporal relation, point, interval, probability

Stabilnost mikrovalnih i elektroničkih aktivnih elemenata: Analiza primjenom teorije dinamičkih sustava

The general problem of stability of microwave and RF devices and circuits in the presence of multi-frequency or broadband signals is addressed. The problem is formulated in terms of the system of nonlinear non-autonomous differential equations for generalized coordinates in the phase space that can be attributed to, e.g., amplitudes of electric currents in circuits with lumped elements or mode amplitudes of the electromagnetic field in the distributed systems. An approach to the stability analysis is proposed that allows predicting the appearance of various kinds of instabilities including the deterministically chaotic motion. The new criterion based on the analysis of Lyapunov exponents is discussed that establishes the relation between maximal stable amplitude of oscillations and the levels of nonlinearity and damping in the system. The examples of one- and two-mode oscillators have been considered in detail.Razmotren je općeniti problem stabilnosti mikrovalnih i radiofrekvencijskih aktivnih elemenata i sklopova u prisutnosti višefrekvencijskih ili širokopojasnih signala. Problem je formuliran kao sustav nelinearnih neautonomnih diferencijalnih jednadžbi u poopćenim koordinatama faznog prostora koje se mogu pridružiti npr. amplitudama električnih struja u sklopovima od elemenata s koncentriranim parametrima ili amplitudama modova elektromagnetskog polja u sustavima s raspodijeljenim parametrima. Predložena je analiza stabilnosti koja omogućava predviđanje različitih vrsta nestabilnosti uključujući determinističko kaotično gibanje. Razmotren je novi kriterij koji se osniva na analizi Ljapunovljevih eksponenata. Taj kriterij uspostavlja vezu između najveće stabilne amplitude oscilacija te razina nelinearnosti i prigušenja u sustavu. Podrobno su analizirani primjeri jednomodnog i dvomodnog oscilatora