
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR

April 29June
28, 2013
Thematic Program on the Mathematics of Oceans
Workshop
on Wave Interactions and Turbulence
May
20  24, 2013
Location:
May
2023: Fields Institute, Room 230 (map)
May 24: Bahen Centre, Room 1190 (map)


Organizing
Committee:
Walter Craig (McMaster), Sergei Kuksin (Ecole Polytechnique,
Palaiseau), Sergey Nazarenko (Warwick)
Efim
Pelinovsky(Russian Academy of Sciences), Catherine Sulem (Toronto)


To
be informed of start times and locations please subscribe to the Fields
mail list for information about the Thematic Program on the Mathematics
of Oceans.
Workshop Schedule
Monday, May 20
Fields Institute, Room 230

10:15  10:30 
Welcome and Introduction 
10:30  11:10 
Sergey Nazarenko, University
of Warwick
Theoretical challenges in Wave Turbulence 
11:15  11:55 
Dario Paolo Bambusi, Università
degli Studi di Milano
On the genaration and propagation of tsunamis 
12:10  14:20 
Lunch Break 
14:20  15:00 
Benno Rumpf, Southern Methodist
University
An instability of wave turbulence as the source of
radiating coherent pulses 
15:00  15:30 
Tea Break 
15:30  16:10 
Zaher Hani, New York University
Coherent frequency profiles for the periodic nonlinear
Schrodinger equation 
16:15  16:55 
Nicholas Kevlahan, McMaster
University
A Conservative Adaptive Wavelet Method for the
Rotating Shallow Water Equations on the Sphere 
Tuesday, May 21
Fields Institute, Room 230 
9:45  10:25 
Slim Ibrahim, University
of Victoria
Finitetime blowup for the inviscid Primitive equation 
10:25  10:45 
Tea Break 
10:45  11:25 
Paul Milewski, University
of Bath
NonlinearOpticslike Behaviour in Water Waves 
11:30  12:10 
Alex Korotkevich, University
of New Mexico
Inverse cascade of gravity waves in the presence
of condensate: numerical simulation. 
12:10  14:20 
Lunch Break 
14:20  15:00 
Antonio Córdoba,
Universita Autonoma  Madrid
Singular Integrals in Fluid Mechanics 
15:00  15:30 
Tea Break 
15:30  16:10 
Miguel Bustamante, University
College Dublin (presentation slides)
Which wave system is more turbulent: strongly
or weakly nonlinear?
"BigAmplitude" CharneyHasegawaMima simulation: video
"SmallAmplitude" CharneyHasegawaMima simulation: video
"MediumAmplitude" CharneyHasegawaMima simulation: video

16:15 
Reception 
Wednesday, May 22
Fields Institute, Room 230 
10:15  10:55 
Erwan Faou, ENS Cachan Bretagne
Upwind normal forms and nonlinear transport equations

10:55  11:15 
Tea Break 
11:15  11:55 
Baylor FoxKemper, Brown University
Surface Waves in Turbulent and Laminar Submesoscale
Flow 
12:00  12:40 
Peter Janssen, European Center for MediumRange Weather Forecasts
(presentation slides)
Effect of sea state on upperocean mixing

Thursday, May 23
Fields Institute, Room 230 
9:45  10:25 
Colm Connaughton, University of Warwick
(presentation slide)
Feedback of zonal flows on Rossby/driftwave turbulence
driven by small scale instability

10:25  10:45 
Tea Break 
10:45  11:25 
Benoît Grébert, Université
de Nantes
KAM theorem for multidimensional PDEs 
11:30  12:10 
Armen Shirikyan, Université de
CergyPontoise
Large deviations from a stationary measure
for a class of dissipative PDE's with random kicks 
12:10  14:20 
Lunch Break 
14:20  15:00 
Elena Kartashova, Johannes Kepler University
Time scales and structures of wave interaction 
15:00  15:30 
Tea Break 
15:30  16:10 
Massimiliano Berti, University Federico
II of Naples
KAM for quasilinear KdV equations 
16:15  16:55 
Sergio Rica, Universidad Adolfo Ibáñez
Observation of the condensation of classical waves 
Friday, May 24
Bahen Centre, Room 1190 
9:30  10:10 
Samir Hamdi, Laval University
Nonlinear interactions of water waves with river
ice 
10:15  10:55 
David Ambrose, Drexel University
Traveling and TimePeriodic Waves in Interfacial
Fluid Dynamics 
10:55  11:15 
Tea Break 
11:15  11:55 
Victor Shrira, Keele University
Towards probability distribution of wave heights
in the ocean from first principles 
12:00  12:40 
Eugene Wayne, Boston University (presentation
slide)
Metastability and the NavierStokes equations 
Speaker
& Affiliation

Title
and Abstract 
David Ambrose
Drexel University

Traveling and TimePeriodic Waves in Interfacial
Fluid Dynamics
We will discuss issues related to timeperiodic and traveling waves
for the vortex sheet with surface tension and for the water wave with
surface tension. Results include computations of nontrivially timeperiodic
solutions for the full equations of motion for the vortex sheet with
surface tension, and computations and proof of existence of traveling
waves (which are trivially timeperiodic). The traveling waves to
be discussed include large amplitude waves, such as waves with multivalued
height. If time permits, computation and analysis for a simple model
system will be discussed.
This includes joint work with Jon Wilkening, Benjamin Akers, J. Douglas
Wright, Mark Kondrla, Michael Valle, and possibly C. Eugene Wayne.

Dario Paolo Bambusi
Università degli Studi di Milano

On the genaration and propagation of tsunamis
This lecture is spilt into two parts: in the first one I
will discuss a rough model for the formation of a tsunami and in the
second one I will present a deduction of a couple of KdV equations as
the normal form of the equations for the water wave problem.
In the first part I will model the earthquake creating a tsumani
by a boundary condition for the water wave problem and deduce the
characteristic of the generated wave. In the second part I will start
from the Hamiltonian formulation of the water wave problem, based
on the use of the Dirichlet Neumann operator, and use normal form
techniques to deduce an effective equation fo the propagation of the
waves. The effective equation will turn out to coincide with a couple
of independent KdV equations.

Massimiliano Berti
University Federico II of Naples

KAM for quasilinear KdV equations
We prove the existence and the stability of Cantor families
of quasiperiodic, small amplitude, solutions of quasilinear autonomous
Hamiltonian and reversible KdV equations. The proof is based on a NashMoser
scheme, the search of an approximate inverse for the linearized operators
and a Birkhoff normal form argument.

Miguel Bustamante
University College Dublin

Which wave system is more turbulent: strongly or weakly nonlinear?
In a turbulent nonlinear wave system, there is usually a
complex structure of energy transfers between modes of oscillations.
In systems of finite size whose governing equation has quadratic or
higher nonlinearity (e.g. planetary Rossby waves, water gravity/capillary
waves), the wavevectors that interact most efficiently appear in groups
of three (socalled triads). These groups tend to form “clusters”,
which are networks of triads connected via one and twocommonmode
connections.
The cluster representation of turbulent interactions is particularly
well suited for modelling turbulence theory and for comparison with
pseudospectral numerical simulations, due to the discreteness of
the wavevector spectrum in these approaches.
I will present two results that shed light on the actual physical
mechanisms that are responsible for energy transfer and cascades in
turbulence. First, the efficiency of transfers in turbulent cascades
is maximised at a nonlinearity level that is intermediate between
weakly nonlinear and fully nonlinear. This goes against the common
belief that high nonlinearity implies stronger turbulence. Second,
clusters formed by nonresonant triads are the rule more than the
exception.
(Work in collaboration with Brenda Quinn)

Colm Connaghton
University of Warwick

Feedback of zonal flows on
Rossby/driftwave turbulence driven by small scale instability
We demonstrate theoretically and numerically the zonalflow/wave
turbulence feedback mechanism in CharneyHasegawaMima turbulence
forced by a small scale instability. Zonal flows are generated by
a secondary modulational instability of the waves which are directly
driven by the primary instability. The shear generated by the zonal
flows then suppresses the small scale turbulence thereby arresting
the energy injection into the system. This process can be described
using nonlocal wave turbulence theory. Finally, the arrest of the
energy input results in saturation of the zonal flows at a level which
can be estimated from the theory and the system reaches stationarity
even without large scale damping.
(Joint work with S. Nazarenko and B. Quinn)

Antonio Córdoba
Universita Autonoma  Madrid 
Singular Integrals in Fluid Mechanics
Two examples will be discussed in order to illustrate how new estimates
for singular integrals help us to obtain blow up, in finite time,
for transport equations related to the QuasiGeostrophic system, but
also how some classical instruments of fluid dynamics can be used
to understand conical Fourier multipliers.

Erwan Faou
ENS Cachan Bretagne

Upwind normal forms and nonlinear transport equations
We consider equations of Vlasov type, with periodic boundary conditions
in space and small initial data. We introduce simple Hamiltonian nonlinear
transformations allowing to control the long time behavior of these
equations. We prove that the dynamics can be reduced to the free linear
equation with a modified initial data over very long times. As a consequence,
we obtain Landau damping results over polynomially long times with
respect to the size of the perturbation, for initial data with finite
regularity.
This is a joint work with Frédéric Rousset (Univ. Rennes
1).

Baylor FoxKemper
Brown University

Surface Waves in Turbulent and Laminar Submesoscale
Flow
Surface gravity waveswind waves and swellcan affect the upper
ocean in a number of ways. The CraikLeibovich Boussinesq (CLB) equations
are an asymptotic approximation to the fluid equations that filter
out the processes leading to surface gravity and sound waves, but
preserve the Stokes drift coupling between surface gravity waves and
flow. The CLB equations are amenable to Large Eddy Simulations of
Langmuir (wavedriven) Turbulence and analysis. I will present recent
work with my colleagues studying the effects of Stokes drift in the
CLB equations. Surprising and unsurprising results for laminar flow
balances, turbulent fluxes, and coupling between turbulence and submesoscale
flow will be discussed. Important remaining questions will be highlighted.

Benoît Grébert
Université de Nantes

KAM theorem for multidimensional PDEs
I will present a quick overview of the KAM results proved
in the context of nonlinear PDEs. In particular I will detail the recent
result that I have obtained in collaboration with H. Eliasson and S.
Kuksin for multidimensional PDEs and an application to the Beam equation
and the nonlinear wave equation.

Samir Hamdi
Laval University 
Nonlinear interactions of water waves with river ice
In the first part of our presentation we will discuss some
new analytical results regarding the dynamics of river ice wave motion
near a breaking front. We will present closed form analytical solutions
of ice velocity as a function of time for several values of the breaking
front speed and river bank resistance. The solutions are derived by
solving an Abel equation of the second kind analytically. Several photos
and videos will be presented to illustrate salient features of the dynamics
of river ice breakup waves.
In the second part we will present a nonlinear study of the interaction
of floating ice cover with shallow water waves. The ice cover is assumed
to be a relatively thin, uniform elastic plate. The nonlinear propagation
of waves is analyzed using a coupled system of three timedependent
and nonlinear partial differential equations(PDEs). These governing
equations describing fluid continuity, momentum, and icecover response
are reduced to a fifth order Kortewegde Vries equation (FKDV), which
is a well know evolutionary PDE. It is shown analytically that when
the time evolution and nonlinear wave steepening are balanced by wave
dispersion due to ice cover bending and inertia of the ice cover and
the axial force, the FKDV model equation predicts solitary waves which
propagate with a permanent shape and constant speed. Closedform cnoidal
solutions and solitary wave solutions are obtained for any order of
the nonlinear term and for any given values of the coefficients of the
cubic and quintic dispersive terms. Analytical expressions for three
conservation laws and for three invariants of motion that represent
the conservation of mass, momentum and energy for solitary wave solutions
are also derived.

Zaher Hani
New York University 
Coherent frequency profiles for the periodic nonlinear Schrodinger
equation
Inspired by the general paradigm of weak turbulence theory,
we consider the 2D cubic nonlinear Schrodinger equation with periodic
boundary conditions. In an appropriate "large box limit",
we derive a continuum equation on $\R^2$, whose solutions serve as approximate
profiles (or envelopes) for the frequency modes of the cubic NLS equation.
The derived equation turns out to satisfy many surprising symmetries
and conservation laws, as well as several families of explicit solutions.
(This is joint work with Erwan Faou (INRIA, France) and Pierre Germain
(Courant Institute, NYU)).

Slim Ibrahim
University of Victoria 
Finitetime blowup for the inviscid Primitive equation
The Primitive equations are of great use in weather prediction. In
large oceanic and atmospheric dynamic models, the viscous Primitive
equations can be derived from Boussinesq equations using the so called
hydrostatic balance approximation. In this talk we show that, contrarily
to the viscous case, for certain class of initial data the corresponding
smooth solutions of the inviscid primitive equations blow up in ?finite
time. The proof is based on a reduction of the equations to a 1D model.
More related results about the 1D model will also be discussed.
These are joint works with C. Cao, K. Nakanishi and E. S. Titi.

Peter A.E.M Janssen
European Center for MediumRange Weather Forecasts

Effect of sea state on upperocean mixing
I will briefly discuss sea state effects, such as StokesCoriolis
force and enhanced mixing by wave breaking on the evolution of the sea
surface temperature (SST). In particular I will give a 'simple' derivation
of the Stokes drift and I will point out the role of the waveinduced
surface drift. Furthermore, I will report work of a number of my collegues
who performed on simulations over a 30 year period. It was found that
such sea state effects may have a considerable impact on the mean SST
field.

Elena Kartashova
Johannes Kepler University

Time scales and structures of wave interaction
Presently two models for computing energy spectra in weakly
nonlinear dispersive media are known: kinetic wave turbulence theory,
using a statistical description of an energy cascade over a continuous
spectrum (Kcascade), and the Dmodel, describing resonant clusters
and energy cascades (Dcascade) in a deterministic way as interaction
of distinct modes.
In this talk we give an overview of these structures and their properties
and a list of criteria, which model of an energy cascade should be used
in the analysis of a given experiment, using water waves as an example.
Applying time scale analysis to weakly nonlinear wave systems modeled
by the focusing nonlinear Schrodinger equation, we demonstrate that
Kcascade and Dcascade are not competing processes but rather two processes
taking place at different time scales, at different characteristic levels
of nonlinearity and based on different physical mechanisms.
Applying those criteria to data known from various experiments with
water waves we find, that the energy cascades observed occurs at short
characteristic times compatible only with a Dcascade.

Nicholas Kevlahan
McMaster University 
A Conservative Adaptive Wavelet Method for the Rotating Shallow
Water Equations on the Sphere
The fundamental computational challenge for climate and weather
models is to efficiently and accurately resolve the vast range of space
and time scales that characterize atmosphere and ocean flows. Not only
do these scales span many orders of magnitude, the minimum dynamically
active scale is also highly intermittent in both time and space. In
this talk we introduce an innovative waveletbased approach to dynamically
adjust the local grid resolution to maintain a uniform specified error
tolerance. The wavelet multiscale method is used to make dynamically
adaptive the TRiSK model (Ringler et al. 2010) for the rotating shallow
water equations on the sphere. We have carefully designed the interscale
restriction and prolongation operators to retain the mimetic properties
that are the main strength of this model. The wavelet method is computationally
efficient and allows for straightforward parallelization using MPI.
We will show verification results from the suite of smooth test cases
proposed by Williamson (1991), and a more recent nonlinear test case
suggested by Galewsky (2004): an unstable midlatitude zonal jet. To
investigate the ability of the method to handle boundary layers in ocean
flows, we will also show an example of flow past an island using penalized
boundary conditions. This adaptive "dynamical core" serves
as the foundation on which to build a complete climate or weather model.

Kostya Khanin
University of Toronto 

Alex Korotkevich
University of New Mexico

Inverse cascade of gravity waves in the presence of condensate:
numerical simulation.
We performed simulation of the isotropic turbulence of gravity
waves with the pumping narrow in frequency domain. Observed formation
of the inverse cascade and condensate in low frequencies. Currently
observed slopes of the inverse cascade are close to n_k ~ k^{3.15},
which differ significantly from theoretically predicted n_k ~ k^{23/6}
~ k^{3.83}. In order to investigate the origin of this discrepancy,
the dispersion relation for gravity waves was measured directly. Simple
qualitative explanation of the results has been given.

Paul Milewski
University of Bath 
NonlinearOpticslike Behaviour in Water Waves
A sufficiently high intensity beam of light in a medium whose
refractive index is intensity dependent (such as air or water) will
exhibit self focussing until higher order effects, noise, or plasma
generation come into play. The crosssectional profile of the focussed
beam depends on the initial profile. It turns out that a very similar
phenomenon occurs in a patch of capillarygravity water waves until
nonlinearity arrests the focussing and the patch breaks up into a complex
set of localised structures. The connection between the two problems
is the focussing 2+1 NLS equation. Whilst water under normal conditions
may be too viscous for the phenomena to be observed, computations suggest
that the behaviour should be observable in mercury.

Sergey Nazarenko
University of Warwick 
Theoretical challenges in Wave Turbulence
Wave Turbulence has a long an successful history and by now
it is well accepted as an effective approach for describing physical
phenomena across a wide range of applications from quantum to cosmological
scales. However, there remain few theoretical challenges concerning
rigorous justifications of the assumptions and techniques used in Wave
Turbulence, overcomming which would allow to establish Wave Turbulence
as a mathematical subject. In my talk I will describe an approach dealing
with miltimode statistics in Wave Turbulence one of the major goals
of which is to justify that the assumed statistical properties survive
over the nonlinear evolution time.

Sergio Rico
Universidad Adolfo Ibáñez 
Observation of the condensation of classical
waves 
Benno Rumpf
Southern Methodist University

An instability of wave turbulence as the source of radiating coherent
pulses
I discuss the recent finding that wave turbulence can be
unstable in certain (usually one dimensional) systems by an instability
that breaks spatial homogeneity. This triggers a turbulent transport
of energy by radiating pulses. The direct energy cascade is provided
by adiabatically evolving pulses, the inverse cascade is due to the
excitation of radiation. The spectrum is steeper than the KolmogorovZakharov
spectrum of wave turbulence.
B. Rumpf, A.C. Newell, V.E. Zakharov, PRL 103, 074502 (2009) A.C.
Newell, B. Rumpf, V.E. Zakharov, PRL 109, 194502 (2012) B. Rumpf,
A.C. Newell, PLA 377, 1260 (2013)

Armen Shirikyan
Université de CergyPontoise

Large deviations from a stationary measure for a class of dissipative
PDE's with random kicks
We study a class of dissipative PDE's perturbed by a random
kick force. It is well known that if the random perturbation is sufficiently
nondegenerate, then the Markov process associated with the problem
in question has a unique stationary distribution, which is exponentially
mixing. In addition, the strong law of large numbers and the central
limit theorem are true. We are now interested in probabilities of deviations
for the time average of continuous functionals from their spatial average
with respect to the stationary distribution. Our main result shows that
the occupation measures of solutions satisfy the LDP with a good rate
function. The proof is based on Kifer's criterium for LDP, a LyapunovSchmidt
type reduction, and a general result on longtime behaviour of generalised
Markov semigroups.
This is a joint work with V. Jaksic, V. Nersesyan, and C.A. Pillet.

Victor Shrira
Keele University

Towards probability distribution of wave heights in the ocean from
first principles
The ultimate aim of studies of random wind waves is to predict
probability density function of wave characteristics, primarily wave
height, at any given place and time. Within the framework of wave turbulence
paradigm the evolution of wave spectra is described by the kinetic (Hasselmann)
equation derived from first principles in the sixties and now routinely
employed in operational forecasting. In contrast, in present the probability
density function is found using some empirical formulae.
We study longterm nonlinear evolution of typical random wind waves
which are characterized by broadbanded spectra and quasiGaussian
statistics. We find the departure of wave statistics from Gaussianity
from first principles using higherorder statistical momenta (skewness
and kurtosis) as a measure of this departure. Nonzero values of kurtosis
mean an increase or decrease of extreme wave probability (compared
to that in a Gaussian sea), which is important for assessing the risk
of freak waves and other applications. The approach is as follows.
NonGaussianity of a weakly nonlinear random wave field has two components.
The first one is due to nonlinear wavewave interactions. We refer
to this component as `dynamic', since it is linked to wave field evolution.
The other component is due to bound harmonics. It is nonzero for
every wave field with finite amplitude, contributes both to skewness
and kurtosis of gravity water waves, and can be determined entirely
from the instantaneous spectrum of surface elevation. We calculate
the dynamic kurtosis by two different methods. First, by performing
a DNS simulation of windgenerated random wave fields, using a specially
designed algorithm, based on the Zakharov equation for water waves.
Second, using the integral formulae found by Janssen (2003). In all
generic situations, the contribution to kurtosis due to wave interactions
is shown to be small compared to the bound harmonics contribution.
This crucial observation enables us to determine higher momenta by
calculating the bound harmonics part directly from spectra using asymptotic
expressions. Thus, the departure of evolving wave fields from Gaussianity
is explicitly contained in the instantaneous wave spectra. This enables
us to broaden significantly the capability of the existing systems
for wave forecasting: in addition to simulation of spectra it becomes
possible to find also higher momenta and, hence, the probability density
function. We found that the contributions due to bound harmonics to
both skewness and kurtosis are significant for oceanic waves, and
nonzero kurtosis (typically in the range 0.10.3) implies a tangible
increase of freak wave probability.
For random wave fields generated by steady or slowly varying wind
and for swell the derived largetime asymptotics of skewness and kurtosis
predict power law decay of the moments. The exponents of these laws
are determined by the degree of homogeneity of the interaction coefficients.
For all selfsimilar regimes the kurtosis decays twice as fast as
the skewness. These formulae complement the known largetime asymptotics
for spectral evolution prescribed by the Hasselmann equation. The
results are verified by the DNS of random wave fields based on the
Zakharov equation. The predicted asymptotic behaviour is shown to
be very robust: it holds both for steady and gusty winds.
From observations very little is known about the higher moments of
sea waves statistics. For observational model of wave spectra (JONSWAP)
we derived simple formulae for skewness and kurtosis valid for a very
broad range of parameters.

Eugene Wayne
Boston University 
Metastability and the NavierStokes equations
The study of stable, or stationary, states of a physical
system is a well established field of applied mathematics. Less well
known or understood are ``metastable'' states. Such states are a signal
that multiple time scales are important in the problem  for instance,
one associated with the emergence of the metastable state, one associated
with the evolution along the family of such states, and one associated
with the emergence of the asymptotic states. I will describe a dynamical
systems based approach to metastable behavior in the twodimensional
NavierStokes equation.

Confirmed
Participants as of May 14, 2013
* to be confirmed
Full Name 
University/Affiliation 
Ambrose, David 
Drexel University 
Ayala, Diego 
McMaster University 
Bambusi, Dario Paolo 
Università degli Studi di Milano 
Berti, Massimiliano 
University Federico II of Naples 
Bustamante, Miguel 
University College Dublin 
Castaing, M. Richard 
Ecole Polytechnique 
Chabchoub, Amin 
Hamburg University of Technology 
Chabchoub, Amin 
Hamburg University of Technology 
Choi, Yeontaek 
National Inst. Math. Sciences, South Korea 
Connaughton, Colm 
University of Warwick 
Córdoba, Antonio 
Universita Autonoma  Madrid 
Craig, Walter 
McMaster University 
Dutykh, Denys 
University College Dublin 
Faou, Erwan 
ENS Cachan Bretagne 
Fedele, Francesco 
Georgia Institute of Technology 
FoxKemper, Baylor 
Brown University 
Fruman, Mark 
Goethe University Frankfurt 
Garcia, Carlos 
McMaster University 
Goncalves, Iury Angelo 
National Institute for Space Research 
Grébert, Benoît 
Université de Nantes 
Hani, Zaher 
New York University 
Hamdi, Samir 
Laval University 
Harper, Katie 
University of Warwick 
Henderson, Diane 
Pennsylvania State University 
Henry, Legena 
University of the West Indies 
Hoang, Tung 
University of Waterloo 
Ibrahim, Slim 
University of Victoria 
Jackson, Ken 
University of Toronto 
Janssen, Peter A.E.M 
European Center for MediumRange Weather Forecasts (ECMWF) 
Kartashova, Elena 
Johannes Kepler University 
Kevlahan, Nicholas 
McMaster University 
Korotkevich, Alexander 
University of New Mexico 
Kuksin, Sergei 
CNRS 
Lacave, Christophe 
l'université ParisDiderot (Paris 7) 
Lannes, David 
Ecole Normale Superieure  Paris 
Milewski, Paul 
University of Bath 
Nazarenko, Sergey 
University of Warwick 
Pelinovsky, Efim 
Russian Academy of Sciences 
Proment, Davide 
University of East Anglia 
Quinn, Brenda 
University College Dublin 
Restrepo, Juan 
University of Arizona 
Rica, Sergio 
Universidad Adolfo Ibáñez 
Rumpf, Benno 
Southern Methodist University 
Schober, Constance 
University of Central Florida 
Shrira, Victor 
Keele University 
Tataru, Daniel 
University of California, Berkeley 
Trichtchenko, Olga 
University of Washington 
Viotti, Claudio 
University college dublin 
Wayne, C. Eugene 
Boston University 
Yang, Chiru 
McMaster University 
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