1,227 research outputs found
Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?
The paradox of destabilization of a conservative or non-conservative system
by small dissipation, or Ziegler's paradox (1952), has stimulated an ever
growing interest in the sensitivity of reversible and Hamiltonian systems with
respect to dissipative perturbations. Since the last decade it has been widely
accepted that dissipation-induced instabilities are closely related to
singularities arising on the stability boundary. What is less known is that the
first complete explanation of Ziegler's paradox by means of the Whitney
umbrella singularity dates back to 1956. We revisit this undeservedly forgotten
pioneering result by Oene Bottema that outstripped later findings for about
half a century. We discuss subsequent developments of the perturbation analysis
of dissipation-induced instabilities and applications over this period,
involving structural stability of matrices, Krein collision, Hamilton-Hopf
bifurcation and related bifurcations.Comment: 35 pages, 11 figure
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
We present a bifurcation analysis of a normal form for travelling waves in
one-dimensional excitable media. The normal form which has been recently
proposed on phenomenological grounds is given in form of a differential delay
equation. The normal form exhibits a symmetry preserving Hopf bifurcation which
may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry
breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf
bifurcation for the propagation of a single pulse in a ring by means of a
center manifold reduction, and for a wave train by means of a multiscale
analysis leading to a real Ginzburg-Landau equation as the corresponding
amplitude equation. Both, the center manifold reduction and the multiscale
analysis show that the Hopf bifurcation is always subcritical independent of
the parameters. This may have links to cardiac alternans which have so far been
believed to be stable oscillations emanating from a supercritical bifurcation.
We discuss the implications for cardiac alternans and revisit the instability
in some excitable media where the oscillations had been believed to be stable.
In particular, we show that our condition for the onset of the Hopf bifurcation
coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao
Developmental course of psychopathology in youths with and without intellectual disabilities
Background: We aimed to describe similarities and differences in the developmental course of psychopathology between children with and without intellectual disabilities (ID). Method: Multilevel growth curve analysis was used to analyse the developmental course of psychopathology, using the Child Behavior Checklist (CBCL), in two longitudinal multiple-birth-cohort samples of 6- to 18-year-old children with ID (N=978) and without ID (N=2,047) using three repeated measurements across a 6-year period. Results: Children with ID showed a higher level of problem behaviours across all ages compared to children without ID. A significant difference between the samples in the developmental courses was found for Aggressive Behaviour and Attention Problems, where children with ID showed a significantly larger decrease. Gender differences in the development of psychopathology were similar in both samples, except for Social Problems where males with ID showed a larger decrease in problem behaviour across time than females with ID and males and females without ID. Conclusion: Results indicate that children with ID continue to show a greater risk for psychopathology compared to typically developing children, although this higher risk is less pronounced at age 18 than it is at age 6 for Aggressive Behaviour. Contrary to our expectations, the developmental course of psychopathology in children with ID was quite similar from age 6 to 18 compared to children without ID. The normative developmental trajectories of psychopathology in children with ID, presented here, can serve as a yardstick against which development of childhood psychopathology can be detected as deviant. © 2007 The Authors Journal compilation © 2007 Association for Child and Adolescent Mental Health
Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
Time-resolved measurement techniques are opening a window on nonequilibrium
quantum phenomena that is radically different from the traditional picture in
the frequency domain. The simulation and interpretation of nonequilibrium
dynamics is a conspicuous challenge for theory. This paper presents a novel
approach to quantum many-body dynamics that is based on a Hamiltonian
formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of
equations of motion for reduced density matrices. These equations have an
underlying symplectic structure, and we write them in the form of the classical
Hamilton equations for canonically conjugate variables. Applying canonical
perturbation theory or the Krylov-Bogoliubov averaging method to the resulting
equations yields a systematic approximation scheme. The possibility of using
memory-dependent functional approximations to close the Hamilton equations at a
particular level of the hierarchy is discussed. The geometric structure of the
equations gives rise to reduced geometric phases that are observable even for
noncyclic evolutions of the many-body state. The formalism is applied to a
finite Hubbard chain which undergoes a quench in on-site interaction energy U.
Canonical perturbation theory, carried out to second order, fully captures the
nontrivial real-time dynamics of the model, including resonance phenomena and
the coupling of fast and slow variables.Comment: 17 pages, revise
An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise
Logistic growth models are recurrent in biology, epidemiology, market models,
and neural and social networks. They find important applications in many other
fields including laser modelling. In numerous realistic cases the growth rate
undergoes stochastic fluctuations and we consider a growth model with a
stochastic growth rate modelled via an asymmetric Markovian dichotomic noise.
We find an exact analytical solution for the probability distribution providing
a powerful tool with applications ranging from biology to astrophysics and
laser physics
Fetching marked items from an unsorted database in NMR ensemble computing
Searching a marked item or several marked items from an unsorted database is
a very difficult mathematical problem. Using classical computer, it requires
steps to find the target. Using a quantum computer, Grover's
algorithm uses steps. In NMR ensemble computing,
Brushweiler's algorithm uses steps. In this Letter, we propose an
algorithm that fetches marked items in an unsorted database directly. It
requires only a single query. It can find a single marked item or multiple
number of items.Comment: 4 pages and 1 figur
Evolutionary game theory in growing populations
Existing theoretical models of evolution focus on the relative fitness
advantages of different mutants in a population while the dynamic behavior of
the population size is mostly left unconsidered. We here present a generic
stochastic model which combines the growth dynamics of the population and its
internal evolution. Our model thereby accounts for the fact that both
evolutionary and growth dynamics are based on individual reproduction events
and hence are highly coupled and stochastic in nature. We exemplify our
approach by studying the dilemma of cooperation in growing populations and show
that genuinely stochastic events can ease the dilemma by leading to a transient
but robust increase in cooperationComment: 4 pages, 2 figures and 2 pages supplementary informatio
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