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Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
An intuitively necessary requirement of models used to provide forecasts of a system's future is the existence of shadowing trajectories that are consistent with past observations of the system: given a system-model pair, do model…
We demonstrate that a scalar field is unable to reverse its direction of motion while continuously exchanging energy with another fluid. If the rate of transfer is modulated by the scalar's acceleration, the field can undergo a rapid…
Interacting dark energy models may play a crucial role in explaining several important observational issues in modern cosmology and also may provide a solution to current cosmological tensions. Since the phenomenology of the dark sector…
We discuss an instability in a large class of models where dark energy is coupled to matter. In these models the mass of the scalar field is much larger than the expansion rate of the Universe. We find models in which this instability is…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
In this study, we deviate from the traditional examination of the evolving universe through the scale factor and instead consider a parameter \(\chi_{ME}\), defined by the ratio of two competing energy densities: matter (DM) and dynamic…
The coincidence problems and other dynamical features of dark energy are studied in cosmological models with variable cosmological parameters and in models with the composite dark energy. It is found that many of the problems usually…
We compute the Bayesian evidences for one- and two-parameter models of evolving dark energy, and compare them to the evidence for a cosmological constant, using current data from Type Ia supernova, baryon acoustic oscillations, and the…
It has long been known that Newtonian dynamics applied to the visible matter in galaxies and clusters does not correctly describe the dynamics of those systems. While this is generally taken as evidence for dark matter it is in principle…
For physicists, recent developments in astrophysics and cosmology present exciting challenges. We are conducting "experiments" in energy regimes some of which will be probed by accelerators in the near future, and others which are…
This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence…
We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
In literature on stochastic thermodynamics it is stated that for a system connected to multiple thermal reservoirs, the transition rates between two energy levels equals the sum of transition rates corresponding to each thermal bath the…
We apply a new non-parametric Bayesian method for reconstructing the evolution history of the equation-of-state $w$ of dark energy, based on applying a correlated prior for $w(z)$, to a collection of cosmological data. We combine the latest…
Recent astrophysical observations, pertaining to either high-redshift supernovae or cosmic microwave background temperature fluctuations, as those measured recently by the WMAP satellite, provide us with data of unprecedented accuracy,…
Dynamic state estimation (DSE) accurately tracks the dynamics of a power system and provides the evolution of the system state in real-time. This paper focuses on the control and protection applications of DSE, comprehensively presenting…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…