3,569 research outputs found
Volume-preserving normal forms of Hopf-zero singularity
A practical method is described for computing the unique generator of the
algebra of first integrals associated with a large class of Hopf-zero
singularity. The set of all volume-preserving classical normal forms of this
singularity is introduced via a Lie algebra description. This is a maximal
vector space of classical normal forms with first integral; this is whence our
approach works. Systems with a non-zero condition on their quadratic parts are
considered. The algebra of all first integrals for any such system has a unique
(modulo scalar multiplication) generator. The infinite level volume-preserving
parametric normal forms of any non-degenerate perturbation within the Lie
algebra of any such system is computed, where it can have rich dynamics. The
associated unique generator of the algebra of first integrals are derived. The
symmetry group of the infinite level normal forms are also discussed. Some
necessary formulas are derived and applied to appropriately modified
R\"{o}ssler and generalized Kuramoto--Sivashinsky equations to demonstrate the
applicability of our theoretical results. An approach (introduced by Iooss and
Lombardi) is applied to find an optimal truncation for the first level normal
forms of these examples with exponentially small remainders. The numerically
suggested radius of convergence (for the first integral) associated with a
hypernormalization step is discussed for the truncated first level normal forms
of the examples. This is achieved by an efficient implementation of the results
using Maple
Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates
Depinning of two-dimensional liquid ridges and three-dimensional drops on an
inclined substrate is studied within the lubrication approximation. The
structures are pinned to wetting heterogeneities arising from variations of the
strength of the short-range polar contribution to the disjoining pressure. The
case of a periodic array of hydrophobic stripes transverse to the slope is
studied in detail using a combination of direct numerical simulation and
branch-following techniques. Under appropriate conditions the ridges may either
depin and slide downslope as the slope is increased, or first breakup into
drops via a transverse instability, prior to depinning. The different
transition scenarios are examined together with the stability properties of the
different possible states of the system.Comment: Physics synopsis link:
http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630
The cusp–Hopf bifurcation
The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a planar system. Bifurcation varieties and phase portraits are presented. The phenomena include all four cases that occur in the codimension-two fold-Hopf bifurcation, in addition to bistability involving equilibria, limit cycles or invariant tori, and a fold-heteroclinic bifurcation that leads to bursting oscillations. Uniqueness of the torus family is established locally. Numerical simulations confirm the prediction from the bifurcation analysis of bursting oscillations that are similar in appearance to those that occur in the electrical behavior of neurons and other physical systems
Female Mucopolysaccharidosis IIIA Mice Exhibit Hyperactivity and a Reduced Sense of Danger in the Open Field Test
Reliable behavioural tests in animal models of neurodegenerative diseases allow us to study the natural history of disease and evaluate the efficacy of novel therapies. Mucopolysaccharidosis IIIA (MPS IIIA or Sanfilippo A), is a severe, neurodegenerative lysosomal storage disorder caused by a deficiency in the heparan sulphate catabolising enzyme, sulfamidase. Undegraded heparan sulphate accumulates, resulting in lysosomal enlargement and cellular dysfunction. Patients suffer a progressive loss of motor and cognitive function with severe behavioural manifestations and premature death. There is currently no treatment. A spontaneously occurring mouse model of the disease has been described, that has approximately 3% of normal enzyme activity levels. Behavioural phenotyping of the MPS IIIA mouse has been previously reported, but the results are conflicting and variable, even after full backcrossing to the C57BL/6 background. Therefore we have independently backcrossed the MPS IIIA model onto the C57BL/6J background and evaluated the behaviour of male and female MPS IIIA mice at 4, 6 and 8 months of age using the open field test, elevated plus maze, inverted screen and horizontal bar crossing at the same circadian time point. Using a 60 minute open field, we have demonstrated that female MPS IIIA mice are hyperactive, have a longer path length, display rapid exploratory behaviour and spend less time immobile than WT mice. Female MPS IIIA mice also display a reduced sense of danger and spend more time in the centre of the open field. There were no significant differences found between male WT and MPS IIIA mice and no differences in neuromuscular strength were seen with either sex. The altered natural history of behaviour that we observe in the MPS IIIA mouse will allow more accurate evaluation of novel therapeutics for MPS IIIA and potentially other neurodegenerative disorders
An energy balance model for paleoclimate transitions
A new energy balance model (EBM) is presented and is used to study paleoclimate
transitions. While most previous EBMs only dealt with the globally averaged climate, this
new EBM has three variants: Arctic, Antarctic and tropical climates. The EBM incorporates
the greenhouse warming effects of both carbon dioxide and water vapour, and also includes
ice–albedo feedback and evapotranspiration. The main conclusion to be inferred from this
EBM is that the climate system may possess multiple equilibrium states, both warm and
frozen, which coexist mathematically. While the actual climate can exist in only one of
these states at any given time, the EBM suggests that climate can undergo transitions
between the states via mathematical saddle-node bifurcations. This paper proposes that
such bifurcations have actually occurred in Paleoclimate transitions. The EBM is applied
to the study of the Pliocene paradox, the glaciation of Antarctica and
the so-called warm, equable climate problem of both the mid-Cretaceous Period
and the Eocene Epoch. In all cases, the EBM is in qualitative agreement with the
geological record.</p
Symmetry-breaking transitions in networks of nonlinear circuit elements
We investigate a nonlinear circuit consisting of N tunnel diodes in series,
which shows close similarities to a semiconductor superlattice or to a neural
network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like
system. The tunnel diodes are coupled globally through a load resistor. We find
complex bifurcation scenarios with symmetry-breaking transitions that generate
multiple fixed points off the synchronization manifold. We show that multiply
degenerate zero-eigenvalue bifurcations occur, which lead to multistable
current branches, and that these bifurcations are also degenerate with a Hopf
bifurcation. These predicted scenarios of multiple branches and degenerate
bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file
Minimum error discrimination of Pauli channels
We solve the problem of discriminating with minimum error probability two
given Pauli channels. We show that, differently from the case of discrimination
between unitary transformations, the use of entanglement with an ancillary
system can strictly improve the discrimination, and any maximally entangled
state allows to achieve the optimal discrimination. We also provide a simple
necessary and sufficient condition in terms of the structure of the channels
for which the ultimate minimum error probability can be achieved without
entanglement assistance. When such a condition is satisfied, the optimal input
state is simply an eigenstate of one of the Pauli matrices.Comment: 8 pages, no figure
Enhancing multiphoton rates with quantum memories
Single photons are a vital resource for optical quantum information
processing. Efficient and deterministic single photon sources do not yet exist,
however. To date, experimental demonstrations of quantum processing primitives
have been implemented using non-deterministic sources combined with heralding
and/or postselection. Unfortunately, even for eight photons, the data rates are
already so low as to make most experiments impracticable. It is well known that
quantum memories, capable of storing photons until they are needed, are a
potential solution to this `scaling catastrophe'. Here, we analyze in detail
the benefits of quantum memories for producing multiphoton states, showing how
the production rates can be enhanced by many orders of magnitude. We identify
the quantity as the most important figure of merit in this connection,
where and are the efficiency and time-bandwidth product of the
memories, respectively.Comment: Just over 4 pages, 2 figure
Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry
The effect of temporal modulation on traveling waves in the flows in two
distinct systems of rotating cylinders, both with broken azimuthal symmetry,
has been investigated. It is shown that by modulating the control parameter at
twice the critical frequency one can excite phase-locked standing waves and
standing-wave-like states which are not allowed when the system is rotationally
symmetric. We also show how previous theoretical results can be extended to
handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from
http://www.esam.nwu.edu/riecke/lit/lit.htm
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