39,959 research outputs found
Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises
Nonlinear dynamical systems are sometimes under the influence of random
fluctuations. It is desirable to examine possible bifurcations for stochastic
dynamical systems when a parameter varies.
A computational analysis is conducted to investigate bifurcations of a simple
dynamical system under non-Gaussian {\alpha}-stable Levy motions, by examining
the changes in stationary probability density functions for the solution orbits
of this stochastic system. The stationary probability density functions are
obtained by numerically solving a non local Fokker-Planck equation. This allows
numerically investigating phenomenological bifurcation, or
P-bifurcation, for stochastic differential equations with non-Gaussian Levy
noises.Comment: priprin
Slow foliation of a slow-fast stochastic evolutionary system
This work is concerned with the dynamics of a slow-fast stochastic
evolutionary system quantified with a scale parameter. An invariant foliation
decomposes the state space into geometric regions of different dynamical
regimes, and thus helps understand dynamics. A slow invariant foliation is
established for this system. It is shown that the slow foliation converges to a
critical foliation (i.e., the scale parameter is zero) in probability
distribution, as the scale parameter tends to zero. The approximation of slow
foliation is also constructed with error estimate in distribution. Furthermore,
the geometric structure of the slow foliation is investigated: every fiber of
the slow foliation parallels each other, with the slow manifold as a special
fiber. In fact, when an arbitrarily chosen point of a fiber falls in the slow
manifold, the fiber must be the slow manifold itself
Highly Accurate Nystr\"{o}m Volume Integral Equation Method for the Maxwell equations for 3-D Scatters
In this paper, we develop highly accurate Nystr\"{o}m methods for the volume
integral equation (VIE) of the Maxwell equation for 3-D scatters. The method is
based on a formulation of the VIE equation where the Cauchy principal value of
the dyadic Green's function can be computed accurately for a finite size
exclusion volume with some explicit corrective integrals of removable
singularities. Then, an effective interpolated quadrature formula for tensor
product Gauss quadrature nodes in a cube is proposed to handle the
hyper-singularity of integrals of the dyadic Green's function. The proposed
high order Nystr\"{o}m VIE method is shown to have high accuracy and
demonstrates -convergence for computing the electromagnetic scattering of
cubes in
Cost and Effects of Pinning Control for Network Synchronization
In this paper, the problem of pinning control for synchronization of complex
dynamical networks is discussed. A cost function of the controlled network is
defined by the feedback gain and the coupling strength of the network. An
interesting result is that lower cost is achieved by the control scheme of
pinning nodes with smaller degrees. Some rigorous mathematical analysis is
presented for achieving lower cost in the synchronization of different
star-shaped networks. Numerical simulations on some non-regular complex
networks generated by the Barabasi-Albert model and various star-shaped
networks are shown for verification and illustration.Comment: 12 pages, 18 figure
X-ray afterglow of GRB 050712: Multiple energy injections into the external shock
As indicated by the observed X-ray flares, a great amount of energy could be
intermediately released from the postburst central engine of gamma-ray bursts
(GRBs). As a natural consequence, the GRB external shock could be energized
over and over. With such a multiple energy injection model, we explore the
unique X-ray afterglow light curve of GRB 050712, which exists four apparent
shallow decay plateaus. Together with three early X-ray flares, the central
engine of GRB 050712 is supposed to release energy at least seven times after
the burst. Furthermore we find that the energy released during four plateaus
are all on the same order of magnitude, but the luminosity decreases with time
significantly. These results may provide some interesting implications for the
GRB central engine.Comment: 7 pages, two figures, Research in Astronomy and Astrophysics (RAA),
2014, in pres
Thermal engineering in low-dimensional quantum devices: a tutorial review of nonequilibrium Green's function methods
Thermal engineering of quantum devices has attracted much attention since the
discovery of quantized thermal conductance of phonons. Although easily
submerged in numerous excitations in macro-systems, quantum behaviors of
phonons manifest in nanoscale low-dimensional systems even at room temperature.
Especially in nano transport devices, phonons move quasi-ballistically when the
transport length is smaller than their bulk mean free paths. It has been shown
that phonon nonequilibrium Green's function method (NEGF) is effective for the
investigation of nanoscale quantum transport of phonons. In this tutorial
review two aspects of thermal engineering of quantum devices are discussed
using NEGF methods. One covers transport properties of pure phonons; the other
concerns the caloritronic effects, which manipulate other degrees of freedom,
such as charge, spin, and valley, via the temperature gradient. For each part,
we outline basic theoretical formalisms first, then provide a survey on related
investigations on models or realistic materials. Particular attention is given
to phonon topologies and a generalized phonon NEGF method. Finally, we conclude
our review and summarize with an outlook.Comment: 52 pages, 10 figure
Optimal Perfect Distinguishability between Unitaries and Quantum Operations
We study optimal perfect distinguishability between a unitary and a general
quantum operation. In 2-dimensional case we provide a simple sufficient and
necessary condition for sequential perfect distinguishability and an analytical
formula of optimal query time. We extend the sequential condition to general
d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for
optimal sequential query time. In the process a new iterative method is given,
the most notable innovation of which is its independence to auxiliary systems
or entanglement. Following the idea, we further obtain an upper bound and a
lower bound of (entanglement-assisted) q-maximal fidelities between a unitary
and a quantum operation. Thus by the recursion in [1] an upper bound and a
lower bound for optimal general perfect discrimination are achieved. Finally
our lower bound result can be extended to the case of arbitrary two quantum
operations.Comment: 11 pages, 0 figures. Comments are welcom
Analysis and control of network synchronizability
In this paper, the investigation is first motivated by showing two examples
of simple regular symmetrical graphs, which have the same structural
parameters, such as average distance, degree distribution and node betweenness
centrality, but have very different synchronizabilities. This demonstrates the
complexity of the network synchronizability problem. For a given network with
identical node dynamics, it is further shown that two key factors influencing
the network synchronizability are the network inner linking matrix and the
eigenvalues of the network topological matrix. Several examples are then
provided to show that adding new edges to a network can either increase or
decrease the network synchronizability. In searching for conditions under which
the network synchronizability may be increased by adding edges, it is found
that for networks with disconnected complementary graphs, adding edges never
decreases their synchronizability. This implies that better understanding and
careful manipulation of the complementary graphs are important and useful for
enhancing the network synchronizability. Moreover, it is found that an
unbounded synchronized region is always easier to analyze than a bounded
synchronized region. Therefore, to effectively enhance the network
synchronizability, a design method is finally presented for the inner linking
matrix of rank 1 such that the resultant network has an unbounded synchronized
region, for the case where the synchronous state is an equilibrium point of the
network.Comment: 12 pages, 8 figure
Disconnected synchronized regions of complex dynamical networks
This paper addresses the synchronized region problem, which is reduced to a
matrix stability problem, for complex dynamical networks. For any natural
number , the existence of a network which has disconnected synchronized
regions is theoretically demonstrated. This shows the complexity in network
synchronization. Convexity characteristic of stability for matrix pencils is
further discussed. Smooth and generalized smooth Chua's circuit networks are
finally discussed as examples for illustration.Comment: 13 pages, 2 figure
Evolution systems of measures for stochastic flows
A new concept of {\em an evolution system of measures for stochastic flows}
is considered. It corresponds to the notion of an invariant measure for random
dynamical systems (or cocycles). The existence of evolution systems of measures
for asymptotically compact stochastic flows is obtained. For a white noise
stochastic flow, there exists a one to one correspondence between evolution
systems of measures for a stochastic flow \emph{and} evolution systems of
measures for the associated Markov transition semigroup. As an application, an
alternative approach for evolution systems of measures of 2D stochastic
Navier-Stokes equations with a time-periodic forcing term is presented.Comment: 14 page
- …