Related papers: On reality of dynamical matrix
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
In this contribution the symmetry properties of the interacting boson model of Arima and Iachello are reviewed. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
To the reduct problems of decision system, the paper proposes the notion of dynamic core according to the dynamic reduct model. It describes various formal definitions of dynamic core, and discusses some properties about dynamic core. All…
This paper discusses some links properties of operators with the well- known physical concepts of hyperstability, passivity, energy dissipativeness and conservativeness with positive realness properties of the transfer functions in linear…
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
Strong dynamics constitutes one of the pillars of the standard model of particle interactions, and it accounts for the bulk of the visible matter in the universe. It is therefore a well posed question to ask if the rest of the universe can…
Anomalous features of models with nonlinear symmetry realization are addressed. It is shown that such models can have anomalous amplitudes breaking of its original symmetry realization. An illustrative example of a simple models with a…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
Force-constant and positional disorder have been introduced into diamond lattice models in an attempt to mimic the vibrational properties of a realistic amorphous silicon model. Neither type of disorder is sufficient on its own to mimic the…
To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to…
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…