Schedule
- Tuesday,
December 5
- Wednesday,
December 6
Abstracts
- Patrice Abry, SiSypH:
Signals, Systems and Physics, a brief tour and Mutiscale anisotropic
scale-free texture analysis for the Historic Photographic Paper
Challenge
This talk will start by providing a brief
overview of the research activities of the statistical signal/image
processing team, SiSYPh, at the Physics Dept. at Ecole Normale
Supérieure de Lyon.
Then, it will be shown how and why the developed anisotropic multiscale
scale-free/multifractal texture analysis framework can be successfully
applied to the classification of a large database of historic art
photography papers, assembled by the MoMA (NYC).
Future challenges in multifractal texture analysis will also be
envisaged.
- Mokhtar Adda-Bedia, Origami Mechanics
Over the past thirty years, the ancient art of
paper folding, or origami, has evolved into an interdisciplinary
scientific field. Origami offers the possibility for new metamaterials
whose overall mechanical properties can be programmed by acting locally
on each crease. Origami metamaterials show for example auxetic
behaviour (negative Poisson ratio) and multistability, the latter
allowing reprogrammable configurations and deployable structures.
Starting from a thin plate and knowing the properties of the material
and the folding procedure, one would like to determine the shape taken
by the structure at rest and its mechanical response. During this talk,
we review some recent experimental and theoretical developments on the
physics and mechanics of origami-based metamaterials.
- Nathalie Aubrun, A theoretical computer science approach to
entropy
Subshifts of finite types (SFTs) are sets of
colorings of \(\mathbf{Z}^d\)
which avoid some finite family of patterns. SFTs are thus defined by
local interactions, and can thus model many real-world phenomena. These
objects are of particular interest in statistical mechanics, ergodic
theory and computability theory. In this talk we will focus on entropy
of these systems, which measures the asymptotic growth of the number of
allowed finite patterns. The entropy of one-dimensional SFTs can be
easily computed from the graph representation of the subshift and its
largest eigenvalue, and the possible values are algebraically
characterized. In higher dimension, entropy of SFTs becomes
uncomputable. We are nevertheless able to characterize the possible
values, but very few examples of SFTs are known to have a close formula
for entropy.
Slides
- Stefano Baroni, What I cannot compute, I do not understand: fathoming atomic heat transport from the struggle to simulate it
Modern simulation methods based on
electronic-structure theory have long be deemed unfit to compute heat
transport coefficients within the Green-Kubo formalism. This is so
because the quantum-mechanical energy density from which the heat flux
is derived is inherently ill defined, thus allegedly hampering the use
of the Green-Kubo formulism. Every property that can be measured can
also be computed, at least in principle: if it cannot, it's that the
underlying theory is still incomplete. Steered by this conviction, we
have derived an expression for the adiabatic energy flux from
density-functional theory, which allows thermal transport to be
simulated using ab initio equilibrium molecular dynamics. The resulting
thermal conductivity is shown to be unaffected by the ill-determinacy
of quantum mechanical energy densities and currents, by virtue of a
hitherto unrecognized gauge invariance principle of thermal transport.
In order to turn this new theory into a practical simulation tool,
further insight is also needed into the statistical properties of
finite time series, which I will also discuss if time allows. A few
representative applications to thermal transport in elemental and
molecular fluids will be presented.
- Marco Bertola, The
role of Riemann—Hilbert techniques in integrable systems,
geometry, spectral problems and stochastic point processes
A Riemann-Hilbert problem (RHP) is a particular type of boundary
value problem for a matrix valued function on the complex plane (or
other Riemann surface). It is the analytic tool, for example, to find
holomorphic sections of vector bundles, the typical example being the
Birkhoff factorization theorem on the Riemann Sphere. There is a
surprisingly wide plethora of problems that can be framed within
the theory of RHPs; it includes the inverse spectral problem for
integrable wave equations (KdV, mKdV, NLS, AKNS, and, to some extent,
KP), the theory of occupation numbers for certain stochastic point
fields, the theory of Painlevé equations and even the analysis of
the spectral properties of certain inverse problems in tomography.
Special techniques have been developed in the late '90 to study
asymptotic behaviours of solutions of RHPs and this allows rigorous and
very (extremely, in fact) detailed asymptotic analysis of nonlinear
waves, be it in the long-time or small-dispersion regimes; for example
results of "universality" of behaviour of solution near the caustic
curve of the zero-dispersion approximation can be approached (if not
outright solved) by such techniques. A "tau" function can be associated
to the deformation space of any RHP; in special cases it becomes a
Fredholm determinant, in others it takes the meaning of generating
function of intersection numbers of characteristic classes on moduli
spaces. In this talk I will try to give an overview of these topics to
showcase the breadth and reach of the method, as well as my
collaborators' research and my own.
Slides
- Giovanni Bussi, Using molecular simulations and NMR experiments to predict RNA structural dynamics
Ribonucleic acid (RNA) is acquiring a large importance in cell
biology, as more functions that it accomplishes are discovered.
However, experimental characterization of RNAs dynamical behavior at
atomistic level is difficult. Molecular simulations at atomistic
detail, in combination with state-of-the-art free-energy techniques and
advanced analysis protocols, could in principle bridge the gap
providing an unparalleled perspective on the mechanism and dynamics of
RNA folding and conformational transitions. However, current empirical
force fields used to model RNA are not yet accurate enough to predict
structural dynamics in agreement with solution phase experiments. I
will here show how the maximum entropy principle can be used to
optimally combine molecular simulations and experimental data. A
framework to model experimental errors will also be introduced.
Applications of our approach to the determination of RNA structural
dynamics will be presented, ranging from short oligonucleotide to
larger biologically relevant non-coding RNAs.
- Pasquale Calabrese, Entanglement and thermodynamics in non-equilibrium isolated quantum systems
Entanglement and entropy are key concepts standing at the
foundations of quantum and statistical mechanics. In the last decade
the study of quantum quenches revealed that these two concepts are
intricately intertwined. Although the unitary time evolution ensuing
from a pure initial state maintains the system globally at zero
entropy, at long time after the quench local properties are captured by
an appropriate statistical ensemble with non zero thermodynamic
entropy, which can be interpreted as the entanglement accumulated
during the dynamics. Therefore, understanding the post-quench
entanglement evolution unveils how thermodynamics emerges in isolated
quantum systems. An exact computation of the entanglement dynamics has
been provided only for non-interacting systems, and it was believed to
be unfeasible for genuinely interacting models. In this talk I show
that the standard quasiparticle picture of the entanglement evolution,
complemented with integrability-based knowledge of the asymptotic
state, leads to a complete analytical understanding of the entanglement
dynamics in the space-time scaling limit.
- Sergio Ciliberto, Two new critical effects
We describe two new effects that appear close to
the demixing critical point of two binary mixtures.
The first one is a surprising phenomenon consisting in a oscillating
phase transition which appears
in a binary mixture (PMMA-Octanone) when this is enlightened by a
strongly focused infrared laser beam. The dynamical properties of the
oscillations are produced by a competition between various effects: the
local accumulation of PMMA produced by the laser beam, thermophoresis,
and nonlinear diffusion. We show that the main properties of this kind
of oscillations can be reproduced in the Landau theory for a binary
mixture in which a local driving mechanism, simulating the laser beam,
is introduced.
The second effect that we describe is the observation of a
temperature-controlled synchronization of two Brownian-particles in a
binary mixture \((C_{12}E_5-H_2O)\) close to
the critical point of the demixing transition. The two beads are
trapped by two optical tweezers whose distance is periodically
modulated. We notice that the motion synchronization of the two beads
appears when the critical temperature is approached. In contrast, when
the fluid is far from its critical temperature, the displacements of
the two beads are uncorrelated. Small changes in temperature can
radically change the global dynamics of the system. We show that the
synchronisation is induced by the critical Casimir forces. Finally, we
present the measure of the energy transfers inside the system produced
by the critical interaction.
- Guido De Philippis, Spectral Optimisation problems with
perimeter penalisation
Aim of the talk is to present some old and new
results on
existence and regularity for optimal shapes of spectral optimisation
problems under perimeter constraint. A particular focus will be given
to the case in which the considered perimeter is anisotropic, a case
which (surprisingly) seems to present several additional difficulties.
The talk is based on joint works with B. Velichkov, M.
Pierre, J. Lamboley, M. Marini and J. Hirsch.
- Michele Fabrizio, A small taste of strong correlations
In the talk, I shall overview our activity on correlated electron
systems by presenting two works that attempt to explain theoretically
two intriguing results, one numerical and the other experimental.
The first is a puzzling outcome of numerical renormalization group
applied to a two-channel Kondo model (2CK) with superconducting
channels. Specifically, it was found that when the superconducting gap
\(\Delta\to0\), one does not recover the known spectrum of the 2CK at
\(\Delta=0\). We explain this result both qualitatively, by CFT
arguments, and quantitatively, by extending the scaling approach by
Anderson and Yuval to the case of gaped conduction baths.
The second work concerns a remarkable pump-probe experiment on
\(K_3C_{60}\), a molecular conductor that becomes superconducting below
Tc= 20K. The sample is shot by an ultrashort laser pulse and the
optical response is probed in time. When the laser frequency hits a
mid-infrared absorption peak, a transient superconducting response is
observed up to 200K, ten times higher than Tc. To explain this
phenomenon, we first propose that the absorption peak is due to a
spin-triplet molecular exciton. We next show that these excitons act as
an entropy sink for quasiparticles, which thus cool down meanwhile the
light pulse brings up the exciton population.
Slides
- Étienne Ghys, The three body problem
Three massive objects in space attract each other
according to Newton’s gravitation law. Can one describe the dynamics of
these objects in the long run ? This question is far too difficult,
even Today. However, this problem has been a source of a huge quantity
of new concepts in dynamical systems, symplectic geometry, topology,
and ergodic theory, which are some of the main themes of research in
the «geometry team» of UMPA. Starting from this example, I will try to
describe some developments and, perhaps more importantly, some open
questions.
- Alice Guionnet, Random tilings and Random matrices
I will survey how to study fluctuations in highly
correlated systems such as random tilings and random matrices.
Slides
- Vincent Pilloni, Zeta functions
Given a system of polynomial equations with
integral coefficients, one can try to compute the set of solutions over
finite fields, the field of rational number and more generally number
fields. The Zeta function of the system of equations packages the
information and makes it possible to formulate some deep conjectural
correspondence with functional analysis and representation theory
(Langlands).
- Andrea Romanino, Fundamental physics at SISSA
A brief introduction to the Physics Area of SISSA, focusing on
the research in theoretical particle physics, astrophysics, and
astroparticle physics.
- Gianluigi Rozza, Galerkin-RB-POD Reduced Order Methods:
state of the art and perspectives with focus on parametric
Computational Fluid Dynamics
In this talk, we provide the state of the art of
Reduced Order
Methods (ROM) for parametric Partial Differential Equations (PDEs), and
we focus on some perspectives in their current trends and developments,
with a special interest in parametric problems arising in Computational
Fluid Dynamics (CFD). Systems modelled by PDEs are depending by several
complex parameters in need of being reduced, even before the
computational phase in a pre-processing step, in order to reduce
parameter space. Efficient parametrizations (random inputs, geometry,
physics) are very important to be able to properly address an
offline-online decoupling of the computational procedures and to allow
competitive computational performances. Current ROM developments in CFD
include: a better use of stable high fidelity methods, considering also
spectral element method, to enhance the quality of the reduced model
too; more efficient sampling techniques to reduce the number of the
basis functions, retained as snapshots, as well as the dimension of
online systems; the improvements of the certification of accuracy based
on residual based error bounds and of the stability factors, as well as
the the guarantee of the stability of the approximation with proper
space enrichments. For nonlinear systems, also the investigation on
bifurcations of parametric solutions are crucial and they may be
obtained thanks to a reduced eigenvalue analysis of the linearised
operator. All the previous aspects are very important in CFD problems
to be able to focus in real time on complex parametric industrial and
biomedical flow problems, or even in a control flow setting, and to
couple viscous flows -velocity, pressure, as well as thermal field -
with a structural field or a porous medium, thus requiring also an
efficient reduced parametric treatment of interfaces between different
physics. Model flow problems will focus on few benchmark cases in a
time-dependent framework, as well as on simple fluid-structure
interaction problems. Further examples of applications will be
delivered concerning shape optimisation applied to industrial problems.
Slides
- Henning Samtleben, String compactifications and exceptional
geometry
Generalised and exceptional geometry have emerged
over recent years as powerful tools for the description and the
analysis of string compactifications. In particular, they yield
manifestly duality covariant formulations of supergravity theories. I
review recent constructions and applications.
Slides
- Denis Serre, Hilbert metric, singular elliptic PDEs and
gas dynamics
We consider a boundary-value problem for a rather
singular elliptic PDE. The data is a bounded convex planar domain. This
BVP occurs in several situations, among which the Riemann problem for a
Chaplygin gas, or the parametric case of complete minimal surfaces in
negative ambiant curvature. Because the PDE fails to be uniformly
elliptic, it is classical that we need to establish an a priori
estimate in Lipschitz norm. This task turns out to be quite simple when
using the Hilbert metric.
Slides
- Sandro Sorella
- Cédric Vaillant, Epigenomics in 3D: modeling the dynamic
coupling between epigenome and chromatin organization
Cellular differentiation occurs during the
development of multicellular organisms and leads to the formation of
many different tissues where gene expression is modulated without
modification of the genetic information. These modulations are in part
encoded by chromatin-associated proteins or biochemical tags that are
set down at the chromatin level directly on DNA or on histone tails.
These markers are directly or indirectly involved in the local
organization and structure of the chromatin fiber, and therefore may
modulate the accessibility of DNA to transcription factors or enzymatic
complexes, playing a fundamental role in the transcriptional regulation
of gene expression. Statistical analysis of the repartition of this
epigenomic information along the chromosomes have shown that genomes of
higher eukaryotes are linearly partitioned into domains of functionally
distinct chromatin states. In particular, experimental evidence has
shown that the pattern of chromatin markers along chromosomes is
strongly correlated with the 3D chromatin organization inside the
nucleus. This suggests a coupling between epigenomic information and
large-scale chromatin structure. Recently, using polymer physics and
numerical simulations, we showed that attractive interactions between
loci of the same chromatin state might be the driving forces of the
folding of chromatin inside the nucleus [1]. In this study, we assumed
that the epigenomic information pre-exists to the 3D organization.
However, increasing number of experimental results suggests that
chromatin marks are themselves highly dynamic during cell cycle or
developmental stages and that 3D organization of chromatin might play a
key role in the stabilization and function of chromatin markers. We
will describe our efforts to better understand the crosstalk between
the epigenome and the 3D organization by introducing an original
theoretical framework, the so-called "Living Chromatin model" (LC
model) where the dynamics of chromatin markers deposition along
chromosomes will be coupled to the 3D folding of the chromatin fiber.
As a main outcome, we show how the spatial folding of chromatin can
indeed strongly influence the establishment and the maintenance of
extended epigenomic domains. We discuss the implications of these
results in various biological systems like the formation and dynamics
of topologically-associated domains in drosophila or the establishment
of dosage compensation in worm and mammals.
Slides
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