Non-equilibrium distributions at finite noise intensities

We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are in good agreement with the results of numerical solution of the Fokker-Planck equation and Monte Carlo simulations.Comment: 4 pages, 3 figure

Structure of Stochastic Dynamics near Fixed Points

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition, but might have instead a divergence-free probability current. In the linear case the force can be split into two parts, one of which gives detailed balance with the diffusive motion, while the other induces cyclic motion on surfaces of constant cost function. Using the Jordan transformation for the force matrix, we find an explicit construction of the cost function. We discuss singularities of the transformation and their consequences for the stationary distribution. This Boltzmann-like distribution may be not unique, and nonlinear effects and boundary conditions may change the distribution and induce additional currents even in the neighborhood of a fixed point.Comment: 7 page

Energy-optimal steering of transitions through a fractal basin boundary.

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

Optimal fluctuations and the control of chaos.

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identied with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms

A synthesis of palynological data from the Lower Permian Cerro Pelado Formation (Parana Basin, Uruguay): A record of warmer climate stages during Gondwana glaciations

This paper presents a synthesis of the palynological record in the Cerro Pelado Formation deposits (Lower Permian, Paraná basin, Cerro Largo Department, north-eastern Uruguay) based on pre-existing data and new findings. The successions studied in this formation consist mainly of non-marine to glacial-marine mudstones and sandy mudstones. The palynological assemblages yielded by 32 samples collected from two outcrops and thirty borehole samples demonstrate that not significant floral changes took place through the considered stratigraphic range. The correlation of these assemblages with biostratigraphic palynozones, proposed previously for the Paraná/Chacoparaná Basin of Brazil, Argentina and Uruguay point to their Early Permian age. The most widespread spore genera in these assemblages are Punctatisporites, Lundbladispora, Vallatisporites and Granulatisporites. Among pollen grains, Caheniasaccites, Vittatina, Potonieisporites, Protohaploxypinus and Plicatipollenites are the most representative. Palynomorphs assigned to Chlorophyta, Prasinophyta, and acritarchs indicate the development of brackish to fresh water lacustrine environments. The results from the facies and palynological analyses suggest that these deposits were formed during interglacial or postglacial warmer climatic episodes. This fact would agree well with the proposal that Gondwana glaciations were characterized by discrete glacial phases (with multiple glacial lobe advance-retreat phases) alternating with warmer climatic episodes. These episodes could be recognized thanks to sub-glacial and melt water related continental deposits that would bear characteristic palynological assemblages, like the recorded in the Cerro Pelado Fm. successions

A synthesis of palynological data from the Lower Permian Cerro Pelado Formation (Paraná Basin, Uruguay): A record of warmer climate stages during Gondwana glaciations

This paper presents a synthesis of the palynological record in the Cerro Pelado Formation deposits (Lower Permian, Paraná basin, Cerro Largo Department, north eastern Uruguay) based on pre-existing data and new findings. The successions studied in this formation consist mainly of non-marine to glacial-marine mudstones and sandy mudstones. The palynological assemblages yielded by 32 samples collected from two outcrops and thirty borehole samples demonstrate that not significant floral changes took place through the considered stratigraphic range. The correlation of these assemblages with biostratigraphic palynozones, proposed previously for the Paraná/ Chacoparaná Basin of Brazil, Argentina and Uruguay point to their Early Permian age. The most widespread spore genera in these assemblages are Punctatisporites, Lundbladispora, Vallatisporites and Granulatisporites. Among pollen grains, Caheniasaccites, Vittatina, Potonieisporites, Protohaploxypinus and Plicatipollenites are the most representative. Palynomorphs assigned to Chlorophyta, Prasinophyta, and acritarchs indicate the development of brackish to fresh water lacustrine environments. The results from the facies and palynological analyses suggest that these deposits were formed during interglacial or postglacial warmer climatic episodes. This fact would agree well with the proposal that Gondwana glaciations were characterized by discrete glacial phases (with multiple glacial lobe advance-retreat phases) alternating with warmer climatic episodes. These episodes could be recognized thanks to sub-glacial and melt water related continental deposits that would bear characteristic palynological assemblages, like the recorded in the Cerro Pelado Fm. successions

Fast Monte Carlo simulations and singularities in the probability distributions of non-equilibrium systems

A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the asymptotically exact theory in the limit of extremely small noise intensity. Singularities of the non-equilibrium distributions are revealed by the simulations.Comment: 4 pages, 4 figure

Observation of nonlinear dynamics and transition to chaos in photonic integrated circuits

Photonic Integrated Circuit (PIC) technology has revolutionized the application and fabrication of optoelectronic devices. Most affected by this development is the field of telecommunications, where both active and passive photonic devices are key components in the optical networks. PIC based optical components are cheaper to fabricate than their stand-alone counter parts, multifunctional, low energy consumers and much smaller in size. These qualities make PICs very attractive from a mass-integration point of view and they are generally viewed as the successors of electronic ICs. In this work we demonstrate that the nonlinear dynamics exhibited by the PICs are stable, well-classifiable from a bifurcational theoretical point of view and reproducible from batch-to-batch

Exponentially fast Monte Carlo simulations for non equilibrium systems.

A new numerical technique is demonstrated and shown to reduce exponentially the time required for Monte Carlo simulations of non-equilibrium systems. The quasi stationary probability dis- tribution is computed for two model systems, and the results are compared with the asymptotically exact theory in the limit of extremely small noise intensity. Singularities of the non-equilibrium distributions are revealed by the simulations