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BEGIN:VEVENT
SUMMARY:Jason Atnip (University of New South Wales (UNSW))
DTSTART:20200515T060000Z
DTEND:20200515T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/1
DESCRIPTION:Title: Thermodynamic formalism for random weighted covering systems
\nby Jason Atnip (University of New South Wales (UNSW)) as part of Sydney
Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Laing (Massey University)
DTSTART:20200522T040000Z
DTEND:20200522T050000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/2
DESCRIPTION:Title: Dynamics and stability of chimera states in two coupled populati
ons of oscillators\nby Carlo Laing (Massey University) as part of Sydn
ey Dynamics Group Seminar\n\n\nAbstract\nWe consider networks formed from
two populations of identical oscillators\, with uniform strength\nall-to-a
ll coupling within populations\, and also between populations\, with a dif
ferent strength. Such\nsystems are known to support chimera states in whic
h oscillators within one population are perfectly\nsynchronised while in t
he other the oscillators are incoherent\, and have a different mean freque
ncy\nfrom those in the synchronous population. Assuming that the oscillato
rs in the incoherent population\nalways lie on a closed smooth curve C\, w
e derive and analyse the dynamics of the shape of C and\nthe probability d
ensity on C\, for several different types of oscillators.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zachary Nicolaou (Northwestern University)
DTSTART:20200529T010000Z
DTEND:20200529T020000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/3
DESCRIPTION:Title: Critical switching in globally attractive chimeras\nby Zacha
ry Nicolaou (Northwestern University) as part of Sydney Dynamics Group Sem
inar\n\n\nAbstract\nWe report on a new type of chimera state that attracts
almost all initial conditions and exhibits power-law switching behavior i
n networks of coupled oscillators. Such switching chimeras consist of two
symmetric configurations\, which we refer to as subchimeras\, in which one
cluster is synchronized and the other is incoherent. Despite each subchim
era being linearly stable\, switching chimeras are extremely sensitive to
noise: Arbitrarily small noise triggers and sustains persistent switching
between the two symmetric subchimeras. The average switching frequency sca
les as a power law with the noise intensity\, which is in contrast with th
e exponential scaling observed in typical stochastic transitions. Rigorous
numerical analysis reveals that the power-law switching behavior originat
es from intermingled basins of attraction associated with the two subchime
ras\, which\, in turn\, are induced by chaos and symmetry in the system. T
he theoretical results are supported by experiments on coupled optoelectro
nic oscillators\, which demonstrate the generality and robustness of switc
hing chimeras.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reza Mohammadpour (IMPAN-Warsaw)
DTSTART:20200612T070000Z
DTEND:20200612T080000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/4
DESCRIPTION:Title: Lyapunov spectrum properties\nby Reza Mohammadpour (IMPAN-Wa
rsaw) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nIn this talk
we discuss ergodic optimization and multifractal behavior\nof Lyapunov ex
ponents for matrix cocycles. We show that the restricted\nvariational prin
ciple holds for generic cocycles over mixing subshifts of finite type\, \n
and the Lyapunov spectrum is equal to the closure of the set where \nthe e
ntropy spectrum is positive for such cocycles. Moreover\, we show both the
continuity of the entropy spectrum at the boundary of Lyapunov spectrum f
or such cocycles\, and the continuity of the lower joint spectral radius f
or linear cocycles under the assumption that linear cocycles satisfy a con
e condition. We consider a subadditive potential $\\Phi$. We obtain that f
or $t\\rightarrow \\infty$ any accumulation point of a family of equilibri
um states of $t\\Phi$ is a maximizing measure\, and that the Lyapunov expo
nent and entropy of equilibrium states for $t\\Phi$ converge in the limit
$t\\rightarrow \\infty$ to the maximum Lyapunov exponent and entropy of ma
ximizing measures.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Dewar (ANU)
DTSTART:20200605T060000Z
DTEND:20200605T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/5
DESCRIPTION:Title: Time-dependent relaxed magnetohydrodynamics -- inclusion of cros
s helicity constraint using phase-space action\nby Bob Dewar (ANU) as
part of Sydney Dynamics Group Seminar\n\n\nAbstract\nA phase-space version
of the ideal MHD Lagrangian is derived from first principles and shown to
give a relabeling transformation when a cross-helicity constraint is adde
d in Hamilton's Action Principle. A new formulation of time-dependent \\em
ph{Relaxed} Magnetohydrodynamics (RxMHD) is derived using microscopic cons
ervation of mass\, and macroscopic constraints on total magnetic helicity\
, cross helicity and entropy under variations of density\, pressure\, flui
d velocity\, and magnetic vector potential. This gives Euler--Lagrange eq
uations consistent with previous work on both ideal and relaxed MHD equili
bria with flow\, but generalizes the relaxation concept from statics to dy
namics. The application of the new dynamical formalism is illustrated for
short-wavelength linear waves\, and the interface connection conditions fo
r Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether $\\ve
c{E} + \\vec{u}\\cross\\vec{B} = 0$ should be a constraint is discussed.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Wormell (University of Sydney)
DTSTART:20200626T060000Z
DTEND:20200626T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/6
DESCRIPTION:Title: Spectral convergence of diffusion maps\nby Caroline Wormell
(University of Sydney) as part of Sydney Dynamics Group Seminar\n\n\nAbstr
act\nDiffusion maps is a manifold learning algorithm widely used for dimen
sionality reduction. Using a sample from a distribution\, it approximates
the eigenvalues and eigenfunctions of associated Laplace-Beltrami operator
s. Theoretical bounds on the approximation error are however generally muc
h weaker than the rates that are seen in practice. We present new approach
es to improve the error bounds in the model case where the distribution is
supported on a hypertorus. For the data sampling (variance) component of
the error we make spatially localised compact embedding estimates on certa
in Hardy spaces\; we study the deterministic (bias) component as a perturb
ation of the Laplace-Beltrami operator's associated PDE\, and apply releva
nt spectral stability results. These techniques enable long-standing point
wise error bounds to be matched for both the spectral data and the norm co
nvergence of the operator discretisation.\n \nWe also introduce an alterna
tive normalisation for diffusion maps based on Sinkhorn weights. This norm
alisation approximates a Langevin diffusion on the sample and yields a sym
metric operator approximation. We prove that it has better convergence com
pared with the standard normalisation on flat domains\, and present a high
ly efficient algorithm to compute the Sinkhorn weights.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Ravotti (Monash University)
DTSTART:20200703T060000Z
DTEND:20200703T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/7
DESCRIPTION:Title: Quantitative global-local mixing for accessible skew products\nby Davide Ravotti (Monash University) as part of Sydney Dynamics Group
Seminar\n\n\nAbstract\nSkew products\, or group extensions\, over hyperbol
ic diffeomorphisms are important examples of partially hyperbolic systems.
Dolgopyat showed that generic compact extensions of topologically mixing
Axiom A diffeomorphisms are rapidly mixing\, namely the decay of correlati
ons of smooth observables is faster than any given polynomial.\nIn this ta
lk\, we will consider the case of $\\mathbb{R}$-extensions. We will focus
on global-local mixing\, one of the possible notions of mixing for infinit
e measure preserving systems. We will present a quantitative mixing result
for skew products which satisfy an accessibility condition\; in particula
r\, we will relate the rate of decay of correlations to the ''low frequenc
y behaviour'' of the spectral measure associated to our global observables
.\nThis is a joint work with Paolo Giulietti and Andy Hammerlindl.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pfefferle (University of Western Australia)
DTSTART:20200731T060000Z
DTEND:20200731T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/8
DESCRIPTION:Title: What do spinning tops and flowing plasmas have in common?\nb
y David Pfefferle (University of Western Australia) as part of Sydney Dyna
mics Group Seminar\n\n\nAbstract\nAt a macroscopic level\, a plasma is sui
tably described by magneto-hydrodynamics (MHD) equations or extensions the
reof. The hotter a plasma\, the less resistive it is (the opposite of a me
tal)\, becoming an ideal conductor in the infinite temperature limit. Idea
l MHD equations are relevant to the modelling of magnetic confinement fusi
on plasmas\, the heliosphere\, solar flares\, accretion disks\, etc. They
feature several structural properties leading to important conservation la
ws\, in particular Alfvén's frozen-in theorem where the magnetic field is
dragged along the plasma fluid motion. It is interesting to interpret the
ideal MHD equations as the Euler-Poincaré equations obtained by reductio
n of geodesic motion on the Lie-Fréchet group of diffeomorphisms equipped
with a right-invariant Riemannian metric. The advantages of attaching a v
ariational problem to ideal MHD are theoretical (origins of relabelling sy
mmetry and conservation laws) and computational (hints for better discreti
sation schemes). In this talk\, we will review Euler-Poincaré reduction u
sing rigid body dynamics as an example\, we will apply the recipe to the
ideal MHD problem\, and discuss whether Multi-Region relaXed magnetohydrod
ynamics (MRxMHD) fits in this picture.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pfefferle (University of Western Australia (UWA))
DTSTART:20200821T060000Z
DTEND:20200821T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/9
DESCRIPTION:Title: Spinning tops and magneto-hydrodynamics: Part 2\nby David Pf
efferle (University of Western Australia (UWA)) as part of Sydney Dynamics
Group Seminar\n\n\nAbstract\nIn part 1\, we reviewed the constrained vari
ational problem originating from the Euler-Poincaré reduction of geodesic
s on Lie groups with left-invariant Riemannan metric and applied it to the
case of SO(3) to derive the well-known Euler equations of a free rigid bo
dy. In this talk\, we replicate those steps in the case of a semidirect pr
oduct between the Lie-Fréchet group of diffeomorphisms and the space of o
ne-forms on a domain of real space. Working at a formal level\, this infin
ite dimensional group is equipped with a right-invariant Riemannian metric
\, and out come incompressible ideal magneto-hydrodynamics equations from
the Euler-Poincaré reduction. Rather elegantly\, Alfvén's frozen-in flux
theorem is seen as a consequence of the semidirect product structure (whi
ch encodes advection)\, and relabelling symmetry is attributable to right-
invariance.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Gottwald (University of Sydney)
DTSTART:20200911T060000Z
DTEND:20200911T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/10
DESCRIPTION:Title: Supervised learning from noisy observations: Combining machine-
learning techniques with data assimilation\nby Georg Gottwald (Univers
ity of Sydney) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nDat
a-driven prediction and physics-agnostic machine-learning methods have att
racted increased interest in recent years achieving forecast horizons goin
g well beyond those to be expected for chaotic dynamical systems. In a se
parate strand of research data-assimilation has been successfully used to
optimally combine forecast models and their inherent uncertainty with inco
ming noisy observations. The key idea in our work here is to achieve incre
ased forecast capabilities by judiciously combining machine-learning algor
ithms and data assimilation. We combine the physics-agnostic data-driven a
pproach of random feature maps as a forecast model within an ensemble Kalm
an filter data assimilation procedure. The machine-learning model is learn
ed sequentially by incorporating incoming noisy observations. We show that
the obtained forecast model has remarkably good forecast skill while bein
g computationally cheap once trained. Going beyond the task of forecasting
\, we show that our method can be used to generate reliable ensembles for
probabilistic forecasting as well as to learn effective model closure in m
ulti-scale systems. \nThis is joint work with Sebastian Reich.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Priya Subramanian (Oxford)
DTSTART:20201009T050000Z
DTEND:20201009T060000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/11
DESCRIPTION:Title: Formation of complex spatial patterns in systems with two lengt
h scales\nby Priya Subramanian (Oxford) as part of Sydney Dynamics Gro
up Seminar\n\n\nAbstract\nPattern formation in many real world systems suc
h as neural-field models\, reaction-diffusion systems and fluid systems su
ch as the Faraday wave system have separation of scales leading to nonline
ar modal interactions. A general analysis of possible terms that can arise
via modal interactions is subject to both the choice of a lattice grid an
d the ratio between the two length scales $q$.\n \nIn the first half\, we
are motivated by the observance of different grid states and superlattice
states in experiments of the Faraday wave system. This leads us to conside
r a hexagonal lattice grid and identify families of amplitude equations fo
r different values of the ratio in the range 0Self-similarity in the Kepler-Heisenberg problem\nby Corey
Shanbrom (CSUS) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nTh
e Kepler-Heisenberg problem is that of determining the motion of a planet
around a sun in the Heisenberg group\, thought of as a three-dimensional s
ub-Riemannian manifold. The sub-Riemannian Hamiltonian provides the kineti
c energy\, and the gravitational potential is given by the fundamental sol
ution to the sub-Laplacian. The dynamics are at least partially integrable
\, possessing two first integrals as well as a dilational momentum which i
s conserved by orbits with zero energy. The system is known to admit close
d orbits of any rational rotation number\, which all lie within the fundam
ental zero energy integrable subsystem. Here\, we demonstrate that all zer
o energy orbits are self-similar.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Urbanski (UNT)
DTSTART:20201105T230000Z
DTEND:20201106T000000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/13
DESCRIPTION:Title: Random non-hyperbolic exponential maps\nby Mariusz Urbanski
(UNT) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Vaienti (Toulon)
DTSTART:20201028T070000Z
DTEND:20201028T080000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/14
DESCRIPTION:Title: On some recent applications of extreme value theory to dynamica
l systems\nby Sandro Vaienti (Toulon) as part of Sydney Dynamics Group
Seminar\n\n\nAbstract\nWe review a few applications of extreme value theo
ry to: \n \n(i) open systems\; \n \n(ii) give the distribution of observab
les defined along the temporal evolution of a\ndynamical system. \n \nApp
lications are given for the class of prevalent observables.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Montgomery (UC Santa Cruz)
DTSTART:20210312T030000Z
DTEND:20210312T040000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/15
DESCRIPTION:Title: Some open questions in the N-body problem\nby Richard Montg
omery (UC Santa Cruz) as part of Sydney Dynamics Group Seminar\n\n\nAbstra
ct\nThe classical N-body problem\, despite being 333 years old\, is alive
and well.\nI will begin with a pictorial survey of a few solution curves.
I then state ``the\nproblem’’ and describe between two and four open
questions within the problem and survey of recent progress on them.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Duignan (University of Colorado Boulder)
DTSTART:20210326T050000Z
DTEND:20210326T060000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/16
DESCRIPTION:Title: Integrability\, Normal Forms\, and Magnetic Axis Coordinates\nby Nathan Duignan (University of Colorado Boulder) as part of Sydney Dy
namics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Atnip (University of New South Wales)
DTSTART:20210423T053000Z
DTEND:20210423T063000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/17
DESCRIPTION:Title: Random Interval Maps with Holes\nby Jason Atnip (University
of New South Wales) as part of Sydney Dynamics Group Seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Hester (University of Sydney)
DTSTART:20210430T060000Z
DTEND:20210430T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/18
DESCRIPTION:Title: Modelling fluid-solid interactions\nby Eric Hester (Univers
ity of Sydney) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florica Cîrstea (University of Sydney)
DTSTART:20210513T060000Z
DTEND:20210513T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/19
DESCRIPTION:Title: Existence of singular solutions to elliptic equations with crit
ical Hardy--Sobolev growth\nby Florica Cîrstea (University of Sydney)
as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cecilia Gonzáles-Tokman (University of Queensland)
DTSTART:20210528T060000Z
DTEND:20210528T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/20
DESCRIPTION:Title: Lyapunov exponents for transfer operator cocycles of random int
erval maps\nby Cecilia Gonzáles-Tokman (University of Queensland) as
part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monique Chyba (University of Hawaii)
DTSTART:20210610T230000Z
DTEND:20210611T000000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/21
DESCRIPTION:Title: Epidemiological modeling\, and COVID-19 Heterogeneity in Island
s Chain Environment\nby Monique Chyba (University of Hawaii) as part o
f Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Jackman (CIMAT)
DTSTART:20210625T060000Z
DTEND:20210625T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/22
DESCRIPTION:Title: The geometry of (planar) Kepler orbits\nby Connor Jackman (
CIMAT) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Wang (University of Sydney)
DTSTART:20210813T060000Z
DTEND:20210813T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/23
DESCRIPTION:Title: When random initialisations help: a study of variational infere
nce for community detection\nby Rachel Wang (University of Sydney) as
part of Sydney Dynamics Group Seminar\n\n\nAbstract\nVariational approxima
tion has been widely used in large-scale Bayesian inference recently\, the
simplest kind of which involves imposing a mean field assumption to appro
ximate complicated latent structures. Despite the computational scalabili
ty of mean field\, theoretical studies of its loss function surface and th
e convergence behaviour of iterative updates for optimising the loss are f
ar from complete. In this paper\, we focus on the problem of community de
tection for a simple two-class Stochastic Blockmodel (SBM) with equal clas
s sizes. Using batch co-ordinate ascent (BCAVI) for updates\, we show dif
ferent convergence behaviour with respect to different initialisations. W
hen the parameters are known or estimated within a reasonable range and he
ld fixed\, we characterise conditions under which an initialisation can co
nverge to\nthe ground truth. On the other hand\, when the parameters need
to be estimated iteratively\, a random initialisation will converge to an
uninformative local optimum.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hinke Osinga (University of Auckland)
DTSTART:20210827T050000Z
DTEND:20210827T060000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/24
DESCRIPTION:Title: Computing periodic travelling waves and their stability in a he
teroclinic-cycle model\nby Hinke Osinga (University of Auckland) as pa
rt of Sydney Dynamics Group Seminar\n\n\nAbstract\nHeteroclinic-cycle mode
ls are often used in ecology to describe cyclic dominant behaviour between
competing populations. This so-called intransitive\, or non-hierarchical
competition is thought to increase biodiversity\, because there is no sing
le ‘best’ competitor. We consider such models in the form of reaction-
diffusion PDEs\, which exhibit travelling waves in one spatial dimension a
nd spiral waves in two spatial dimensions. The model also has travelling f
ronts formed by heteroclinic connections between two equilibria in a movin
g frame of reference\; these fronts are unstable\, but we find that large-
wavelength traveling waves made up of three of these unstable travellings
fronts can be stable. This talk includes a software demonstration of how t
o compute the essential spectrum (and hence\, stability) of these large-wa
velength travelling waves with the software package AUTO. Our computationa
l approach for determining the stability boundary is based on the continua
tion scheme developed by Rademacher\, Sandstede and Scheel (Physica D 229:
166–83\, 2007). We highlight the enhancements implemented in our versio
n\, including the new idea of computing what we call `belts of instability
'\, which are indicators of the growth rate of unstable travelling waves.
Our results from the stability analysis are verified by direct simulation
and we also show how the computed growth rates accurately quantify the ins
tabilities of the travelling waves.\n\nThis is joint work with Cris Hasan
(UCCork) Alastair Rucklidge (Leeds) and Claire Postlethwaite (University o
f Auckland).\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfonso Sorrentino (University of Rome "Tor Vergata")
DTSTART:20210910T063000Z
DTEND:20210910T073000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/25
DESCRIPTION:Title: The Hamilton–Jacobi equation on networks: weak KAM and Aubry
–Mather theories\nby Alfonso Sorrentino (University of Rome "Tor Ver
gata") as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nOver the la
st years there has been an increasing interest in the study of the Hamilto
n–Jacobi Equation on networks and related questions. These problems\, in
fact\, involve a number of subtle theoretical issues and have a great imp
act in the applications in various fields\, for example to data transmissi
on\, traffic management problems\, etc… While locally — i.e.\, on each
branch of the network (arcs) —\, the study reduces to the analysis of 1
-dimensional problems\, the main difficulties arise in matching together t
he information converging at the juncture of two or more arcs\, and relati
ng the local analysis at a juncture with the global structure/topology of
the network.\nIn this talk I shall discuss several results related to the
global analysis of this problem\, obtained in collaboration with Antonio S
iconolfi (Univ. of Rome La Sapienza)\; more specifically\, we developed an
alogues of the so-called Weak KAM theory and Aubry–Mather theory in this
setting. The salient point of our approach is to associate to the network
an abstract graph\, encoding all of the information on the complexity of
the network\, and to relate the differential equation to a discrete functi
onal equation on the graph.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chunxi Jiao (University of Sydney)
DTSTART:20210924T060000Z
DTEND:20210924T070000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/26
DESCRIPTION:Title: Solution of a stochastic Landau-Lifshitz-Slonczewski equation\nby Chunxi Jiao (University of Sydney) as part of Sydney Dynamics Group
Seminar\n\n\nAbstract\nWe study a stochastic Landau-Lifshitz-Slonczewski
equation on the real line with one-dimensional noise. We show that there e
xists a pathwise unique solution to this equation for small noises and dis
cuss the regularity of the solution. The proof is based on a discrete appr
oximation followed by a quadratic interpolation with some uniform estimate
s\, and we adapt arguments in Brzeźniak\, Goldys and Jegaraj (2012) for c
onvergence results.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meagan Carney (University of Queensland)
DTSTART:20211105T050000Z
DTEND:20211105T060000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/27
DESCRIPTION:Title: Nonstationary extremal modeling in weather systems\nby Meag
an Carney (University of Queensland) as part of Sydney Dynamics Group Semi
nar\n\n\nAbstract\nExtremes in weather can often take the form of a hurric
ane\, flood\, or heat-wave. A better understanding of how large and freque
nt these events will be can influence evacuation procedures and inform pre
ventative measures. We briefly discuss modeling extremes of dynamical syst
ems in the classical i.i.d. setting. Classical results of extreme value th
eory extend naturally to dependent sequences provided the distribution of
the sequence is stationary. In recent years\, climate variability has caus
ed changes in the distribution of weather observations. For example\, we h
ave shown that the mean and standard deviation of summer temperature extre
mes in Texas and Germany is increasing over time. We finish by discussing
how machine learning techniques can allow us to obtain more accurate\, tim
e-dependent extremal models in these settings.\n\nEmail the organiser dire
ctly for the Zoom link.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Courtney Quinn (CSIRO (Hobart))
DTSTART:20211008T050000Z
DTEND:20211008T060000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/28
DESCRIPTION:Title: Dynamical analysis of data-driven reduced models for persistent
atmospheric states\nby Courtney Quinn (CSIRO (Hobart)) as part of Syd
ney Dynamics Group Seminar\n\n\nAbstract\nWhile clustering techniques are
highly useful in identifying regimes of large-dimensional data\, some meth
ods (such as FEM-BV-VAR) also produce time-dependent models for the corres
ponding regime dynamics. We investigate these reduced models in the conte
xt of climate regimes\, where the FEM-BV-VAR methodology is applied to atm
ospheric reanalysis data of different regions. To analyse the dynamics we
use a method for computing the covariant Lyapunov vectors (CLVs) over var
ious time windows\, where short windows produce a set of mixed singular ve
ctors (MSVs) and longer windows approximate the asymptotic CLVs. The growt
h rates and alignment of the resulting time-dependent vectors are then com
pared\, with a particular focus on indicators of transitions between the s
tates. We find that the window chosen to compute the vectors acts as a fil
ter\, with short windows capturing the dynamics of individual transitions
and long windows identifying low-frequency variability. We then compare t
he properties of MSVs to those of traditional singular vectors and relate
to their application in ensemble numerical weather prediction (NWP). We sh
ow that MSVs provide a systematic approach to generate initial forecast pe
rturbations projected onto relevant expanding directions in phase space fo
r typical NWP forecast lead-times.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrus Girlado (University of Auckland)
DTSTART:20211022T040000Z
DTEND:20211022T050000Z
DTSTAMP:20260404T111101Z
UID:SDGSeminar/29
DESCRIPTION:Title: Degenerate singular cycles and chaotic switching in the two-sit
e open Bose--Hubbard model\nby Andrus Girlado (University of Auckland)
as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nThe two-site open
Bose-Hubbard dimer model is a celebrated fundamental quantum optical mode
l that accounts for the dynamics of bosons at two lossy interacting sites.
Recently\, two coupled\, driven\, and lossy photonic crystal nanocavities
---which are optical devices that operate with only a few hundred photons
due to their extremely small size--- have been shown to realise this mode
l experimentally. Thus\, there is much interest in understanding the diffe
rent behaviours that such model exhibits for theoretical and practical pur
poses.\n\nThis talk will show the different dynamics in the semiclassical
approximation of this quantum optical system by presenting a comprehensive
bifurcation analysis. We characterised different transitions of chaotic a
ttractors in parameter plane by numerically computing tangency bifurcation
s between stable and unstable manifolds of saddle equilibria and periodic
orbits. By doing so\, we identify codimension-two degenerate singular cycl
es\, and their generalisations\, as responsible for the organisations of d
ifferent tangency and heteroclinic bifurcations between saddle equilibria
periodic orbits in parameter plane. Thus\, we provide a roadmap for observ
able chaotic dynamics in the semiclassical approximation of the two-site B
ose-Hubbard dimer model\, which connects novel results in bifurcation theo
ry with novel applications through numerical continuation techniques.\n\nE
mail the organisers for the Zoom link.\n
LOCATION:https://stable.researchseminars.org/talk/SDGSeminar/29/
END:VEVENT
END:VCALENDAR