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91.
The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow. 相似文献
92.
M. Prochaska F. A. Probst W. Mathis 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(6):531-543
Emitter-coupled multivibrators play a decisive role in electrical engineering, especially for phase locked loops which are key-building blocks of analogue RF front-ends. Since multivibrators correspond to relaxation oscillators, in the following the modelling and analysis by the theory of singularly perturbed systems is presented. Models for fast and slow phenomena are derived, and the fast transients of emitter-coupled multivibrators are analysed for the first time. The results of our analysis lead to significant advantages for the design of electrical multivibrators. 相似文献
93.
94.
Mingxiang Chen Dominic P. Clemence 《Journal of Difference Equations and Applications》2013,19(12):1243-1256
This paper studies the stability properties of a nonstandard finite difference (NSFD) scheme used to simulate the dynamics of a mouse population model in hantavirus epidemics. It is shown that this difference scheme and the underlying system of differential equations have the same dynamics. The proof uses the fact that the total population obeys the logistic equation, as well as techniques from calculus, graphical analysis, and dynamical systems. 相似文献
95.
S. Y. Pilyugin 《Journal of Difference Equations and Applications》2013,19(3-4):271-282
We describe several generalizations of the classical notion of hyperbolicity for a sequence of linear mappings. It is shown that the following three statements are equivalent: (i) the corresponding linear non-homogeneous system has a bounded solution for any bounded nonhomogeneity, (ii) the sequence has a (C, λ)-structure, (iii) the sequence is piecewise hyperbolic with long enough intervals of hyperbolicity. 相似文献
96.
《Journal of Nonlinear Mathematical Physics》2013,20(3):311-338
We indicate how one can extend any dynamical system (namely, any system of nonlinearly coupled autonomous ordinary differential equations) so that the extended dynamical system thereby obtained is either isochronous or asymptotically isochronous or multi-periodic, namely its generic solutions are either completely periodic with a fixed period or tend asymptotically, in the remote future, to such completely periodic functions or are multi-periodic (or become multi-periodic only asymptotically, in the remote future). In all cases the scale of the periodicity can be arbitrarily assigned. Moreover, the solutions of the extended systems are generally well approximated by those of the original, unmodified, systems, up to a constant rescaling of the independent variable (time), as long as their evolution is considered over time intervals short with respect to the (arbitrarily assigned) periodicities characterizing the extended systems. Several examples are displayed. In some cases the general solution of these dynamical systems is also exhibited; in others, this is impossible inasmuch as the models being manufactured are extensions of dynamical systems displaying chaotic evolutions, such as, for instance, the well-known Lorenz model of 3 nonlinearly coupled ODEs. 相似文献
97.
In this paper we prove a conditional stability for the hexagonal anisotropic dynamical elastic systems with smooth coefficients satisfying some conditions. The proof is based on the localized Fourier–Gauss transformation and the three balls inequality for the associated elliptic system. 相似文献
98.
The class of rank 3 algebras includes the Jordan algebra of a symmetric bilinear form, the trace zero elements of a Jordan algebra of degree 3, pseudo-composition algebras, certain algebras that arise in the study of Riccati differential equations, as well as many other algebras. We investigate the representations of rank 3 algebras and show under some conditions on the eigenspaces of the left multiplication operator determined by an idempotent element that the finite-dimensional irreducible representations are all one-dimensional. 相似文献
99.
C.D. Roberts 《Progress in Particle and Nuclear Physics》2008,61(1):50-65
An overview of the theory and phenomenology of hadrons and QCD is provided from a Dyson-Schwinger equation viewpoint. Following a discussion of the definition and realization of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the UA(1) problem, and calculated masses of the lightest J=0,1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution. 相似文献
100.
Paritosh Mokhasi 《Physica D: Nonlinear Phenomena》2008,237(24):3197-3213
In this paper, the problem of approximating velocity fields at future and past times based on information available at the current time is addressed. A novel method called “episodic POD” is described and developed that enables us to achieve our objective. Application of episodic POD to an ensemble of flow data results in a set of spatio-temporal eigenfunctions and a set of coefficients associated with the eigenfunctions. From these eigenfunctions, we develop two models called the “forward model” and “inverse model” that enable us to approximate the velocity fields at future and past times, based on information provided at the current time. A second set of models, the forward and inverse sequential models are also developed that enable the dynamic update of approximated velocity fields when new information is made available, making these models more adept at on-line estimation. The various properties associated with these models are described in detail, and four different examples are used to validate the models and show the different properties associated with episodic POD. It is shown through numerical validation, that the episodic POD model has a form that is dynamically consistent with the original system. It is also shown that episodic POD outperforms linear Kalman filters in the presence of noise. 相似文献