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Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually…
In an increasingly interconnected world, understanding congestion-related phenomena in transportation and their underlying mechanisms is crucial for improving efficiency. As the transportation system becomes denser, different modes of…
Synchronization is ubiquitous in nature at various scales and fields. This phenomenon not only offers a window into the intrinsic harmony of complex systems, but also serves as a robust probe for many-body quantum systems. One such system…
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…
Stochastic orders are very useful tool to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system of used components performs better (worse) than a used coherent system with respect to…
Interface circuits are the key components that enable the hybrid integration of superconductor and semiconductor digital electronics. The design requirements of superconductor-semiconductor interface circuits vary depending on the…
Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an…
In sequential circuits, the current output may depend on both past and current inputs. However, certain kinds of sequential circuits do not refer to all of the past inputs to generate the current output; they only refer to a subset of past…
Distributed fault-tolerance can mask the effect of a limited number of permanent faults, while self-stabilization provides forward recovery after an arbitrary number of transient fault hit the system. FTSS protocols combine the best of both…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
We investigate chaos antisynchronization between two uni-directionally coupled multiple time delay power systems.The results are of certain importance to prevent power black-out in the entire power grid.
This paper presents a novel design of an electronic circuit that is equivalent to a mechanical discontinuous impact oscillator exhibiting hard impacts. The governing equations of the electronic circuit are derived to demonstrate its…
The paper proposes a novel general definition of coherency among power system devices of any type. The proposed approach is thus not limited to synchronous machines. With this aim, the paper shows that coherency can be formally based on the…
We study chaos synchronization between Josephson junctions governed by a central junction with a time delay and demonstrate with numerical simulations the possibility of high quality synchronization. The results are important for obtaining…
We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a…
The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same or the opposite state. Subspaces of the state space…