349 research outputs found
Figures of the article Limits of Semigroups Depending on Parameters by J. K. Hale and G. Raugel , vol 1, 1 , 1-45, 1993
Figures of the article Limits of Semigroups Depending on Parameters by J. K. Hale and G. Raugel , vol 1, 1 , 1-45, 199
A general class of evolutionary equations
За допомогою спостережуваних величин та змінної стану динамічного процесу визначено загальне еволюційне рівняння, що узагальнює класичні звичайні диференціальні рівняння, диференціальні рівняння з частинними похідними та спадкові системи із запізненням і системи нейтрального типу. Наведено специфічні ілюстрації з використанням ліній трансмісії із зчепленням "найближчих сусідів" на межі та теорії теплопереносу у твердих тілах. Розглянуто також певну спектральну теорію для лінеаризації рівнянь.Using observable quantities and state variable of a dynamical process, a general evolutionary equation is defined which unifies classical ordinary differential equations, partial differential equations, and hereditary systems of retarded and neutral type. Specific illustrations are given using transmission lines nearest neighbor coupled at the boundary and the theory of heat transfer in solids. Some spectral theory for linearization of the equations also is discussed
Poisson-Nernst-Planck Systems for Narrow Tubular-like Membrane Channels
We study global dynamics of the Poisson-Nernst-Planck (PNP) system for flows
of two types of ions through a narrow tubular-like membrane channel. As the
radius of the cross-section of the three-dimensional tubular-like membrane
channel approaches zero, a one-dimensional limiting PNP system is derived. This
one-dimensional limiting system differs from previous studied one-dimensional
PNP systems in that it encodes the defining geometry of the three-dimensional
membrane channel. To justify this limiting process, we show that the global
attractors of the three-dimensional PNP systems are upper semi-continuous to
that of the limiting PNP system. We then examine the dynamics of the
one-dimensional limiting PNP system. For large Debye number, the steady-state
of the one-dimensional limiting PNP system is completed analyzed using the
geometric singular perturbation theory. For a special case, an entropy-type
Lyapunov functional is constructed to show the global, asymptotic stability of
the steady-state
Moving lattice kinks and pulses: an inverse method
We develop a general mapping from given kink or pulse shaped travelling-wave
solutions including their velocity to the equations of motion on
one-dimensional lattices which support these solutions. We apply this mapping -
by definition an inverse method - to acoustic solitons in chains with nonlinear
intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion
equations and to discrete nonlinear Schr\"odinger systems. Potential functions
can be found in at least a unique way provided the pulse shape is reflection
symmetric and pulse and kink shapes are at least functions. For kinks we
discuss the relation of our results to the problem of a Peierls-Nabarro
potential and continuous symmetries. We then generalize our method to higher
dimensional lattices for reaction-diffusion systems. We find that increasing
also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure
On Pole Assignment and Stabilizability of Neutral Type Systems
In this note we present a systematic approach to the stabilizability problem of linear infinite-dimensional dynamical systems whose infinitesimal generator has an infinite number of instable eigenvalues. We are interested in strong non-exponential stabilizability by a linear feed-back control. The study is based on our recent results on the Riesz basis property and a careful selection of the control laws which preserve this property. The investigation may be applied to wave equations and neutral type delay equations
Synchronization of coupled limit cycles
A unified approach for analyzing synchronization in coupled systems of
autonomous differential equations is presented in this work. Through a careful
analysis of the variational equation of the coupled system we establish a
sufficient condition for synchronization in terms of the geometric properties
of the local limit cycles and the coupling operator. This result applies to a
large class of differential equation models in physics and biology. The
stability analysis is complemented with a discussion of numerical simulations
of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte
Open strings in relativistic ion traps
Electromagnetic plane waves provide examples of time-dependent open string
backgrounds free of corrections. The solvable case of open strings in
a quadrupolar wave front, analogous to pp-waves for closed strings, is
discussed. In light-cone gauge, it leads to non-conformal boundary conditions
similar to those induced by tachyon condensates. A maximum electric gradient is
found, at which macroscopic strings with vanishing tension are pair-produced --
a non-relativistic analogue of the Born-Infeld critical electric field. Kinetic
instabilities of quadrupolar electric fields are cured by standard atomic
physics techniques, and do not interfere with the former dynamic instability. A
new example of non-conformal open-closed duality is found. Propagation of open
strings in time-dependent wave fronts is discussed.Comment: 43 pages, 11 figures, Latex2e, JHEP3.cls style; v2: one-loop
amplitude corrected, open-closed duality proved, refs added, miscellaneous
improvements, see historical note in fil
Dynamics of Simple Balancing Models with State Dependent Switching Control
Time-delayed control in a balancing problem may be a nonsmooth function for a
variety of reasons. In this paper we study a simple model of the control of an
inverted pendulum by either a connected movable cart or an applied torque for
which the control is turned off when the pendulum is located within certain
regions of phase space. Without applying a small angle approximation for
deviations about the vertical position, we see structurally stable periodic
orbits which may be attracting or repelling. Due to the nonsmooth nature of the
control, these periodic orbits are born in various discontinuity-induced
bifurcations. Also we show that a coincidence of switching events can produce
complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure
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