GiacomoGradenigo < TNTgroup

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---++ *Giacomo Gradenigo Home page*  

<br />     <img src="%ATTACHURLPATH%/img_0359.jpg"  alt="200"  width="400" />

Laboratoire Interdisciplinaire de Physique (LIPhy), Grenoble, FRANCE

---++ Research interests 

*SUPERCOOLED LIQUIDS AND THE GLASS TRANSITION*

 In this field my research activity has been devoted to the study of
amorphous order in supercooled liquids, mainly through numerical
simulations (papers [2-6] below) but also with analytical methods (paper [0-1]),
e.g. the study of istantonic solutions of a replica field theory. I am
a proficient programmer in C, the programming language that I used for
writing codes for the simulations of both lattice (spin models) and
off-lattice (liquids) models of glass-formers. My main contributions
to the field are the following. First I want to mention the numerical
measure, presented in [4], of the distribution of the overlap order
parameter, which is associated to the glass-transition, in the deeply
supercooled regime of a glass-forming liquid. The deeply supercooled
regime is when a viscous liquid is cooled far below its melting
temperature without cristallizing: a regime which is particularly
delicate to handle in numerical simulations. Our numerical results,
obtained for a realistic 3D glass-former, suggest the existence of a
transition at low temperatures from a low-overlap (liquid) phase to a
high-overlap (glassy) phase, in agreement with standard mean-field
predictions. The ``overlap'' is the order parameter which in the
field-theoretical formulation characterizes the glass
transition. Another relevant result that I have obtained in this field
was due to a collaboration with G. Biroli: by finding non-perturbative
solutions of the appropriate replica field-theory we clarified which
is the role of geometric confinement in systems which usually become
glassy by lowering the temperature. We obtained the results of [1]
working on a toy model where exact calculations are possible: this
notwidthstanding, we expect them to be particularly relevant for a
better understanding of the physics of glass-forming materials
confined in porous matrices. Working together with people expert in
the field of the glass transition I had indeed the chance to learn
several different methods, not only numerical. In the paper [0], which
is still in preparation, we approached the problem of the glass
transition in a lattice spin model by means of several
techniques. These techniques include the use of algorithms developed
to determine the solvability of constrained satisfaction problems, an
issue that is well know to be related to the problem of the glass
transition; also, we made use of the cavity method and the Belief
Propagation equations, which allows one to exactly calculate all
thermodynamic potentials for systems on random graph geometries.

[0] *The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model* <br />
S. Franz, G. Gradenigo, S. Spigler,  _in preparation_ . <br />

[1] *Confinement as a tool to probe amorphous order* <br />
  C. Cammarota, G. Gradenigo, G. Biroli
_Phys. Rev. Lett._ ( _Editor's suggestion_ )111, 107801 (2013).

[2] *Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry* <br />
  G. Gradenigo, R. Trozzo, A. Cavagna, T. Grigera, P. Verrocchio 
  J. Chem. Phys. 138, 12A509 (2013)

[3] *The ratchet effect in an ageing glass* <br />
Gradenigo G., Sarracino A., Villamaina D., Grigera T. S. and Puglisi A.
_J.Stat.Mech._  (2010) L12002. <br /> (http://iopscience.iop.org/1742-5468/2010/12/L12002?fromSearchPage=true)

[4] *Phase-Separation Perspective on Dynamic Heterogeneities in Glass-Forming Liquids* <br /> 
Cammarota C., Cavagna A., Giardina I., Gradenigo G., Grigera T.S., Parisi G. and Verrocchio P.
_PRL_, 105, 055703 (2010). <br /> (http://prl.aps.org/abstract/PRL/v105/i5/e055703)

[5] *Evidence for a spinodal limit of amorphous excitations in glassy systems* <br />
Cammarota C., Cavagna A., Gradenigo G., Grigera T.S. and Verrocchio P.  
_J.Stat.Mech._ (2009) L12002. <br /> (http://iopscience.iop.org/1742-5468/2009/12/L12002?fromSearchPage=true)

[6] *Numerical determination of the exponents controlling the relationship between time, length, and temperature in glass-forming liquids* <br />
Cammarota C., Cavagna A., Gradenigo G., Grigera T.S. and Verrocchio P.
_J.Chem.Phys._ 131, 194901 (2009). <br /> (http://jcp.aip.org/resource/1/jcpsa6/v131/i19/p194901_s1) <br /> <br /> 


*ANOMALOUS DIFFUSION*

The properties of the erratic motion of a tracer particle, like a
grain of dust within a glass of water, are well known when the
``environment'' is a homogeneous and equilibrium one: in this case one
finds the well-known Brownian motion characterized by a mean squared
displacement of the intruder increasing linearly with the
observational time, < X^2(t)> ~ t. In this situation
it is also well know that when the erratic motion of the tracer
particle is subjected to a small external field $\epsilon$ there is a
finite _drift_ in the direction of the field: <X(t)> ~\epsilon t.

What is more intriguing, and has been the object of several of my
publications [7,8,9,10], is the effect of an external perturbation in
the presence of anomalous diffusion: anomalous diffusion is when the
mean squared displacement of our tracer particles in the host medium
grows like <X^2(t)> ~t^{\nu}, with $\nu\neq 1$. 
Most often these are situations where the standard tools of
equilibrium statistical mechanics cannot be used and one must resort
on more general approaches, e.g. the study of the Master Equation
governing the process, which are well defined even in absence of an
equilibrium environment.

The more interesting result that I have obtained on this subject is
discussed in [7] and [8] and concerns the relation between the shape
of probability distributions of displacements in presence of an
external field and the exponent $\nu$ which characterize the
_anomaly_ in the diffusional properties. The models we studied
are the Continuous Time Random Walk model with trapping, which shows
subdiffusion ($\nu<1$), and the Levy Walk model, which shows
superdiffusion ($\nu>1$). The study of the interplay between the
action of an external field and anomalous diffusive properties is
quite of interest because anomalous diffusion is present in a large
class of systems, ranging from biological ones to inhomogeous
materials.


[7] *Scaling properties of field-induced superdiffusion in Continous Time Random Walks*  <br />
  R. Burioni, G. Gradenigo, A. Sarracino, A. Vezzani, A. Vulpiani,
  Theor. Phys. 62, 514 (2014). <br />
  
[8] *Rare events and scaling properties in field-induced anomalous dynamics* <br />
  R. Burioni, G. Gradenigo, A. Sarracino, A. Vezzani, A. Vulpiani,
  J. Stat. Mech. P09022 (2013). <br />

[9] *Einstein relation in superdiffusive systems* <br />
Gradenigo G., Sarracino A., Villamaina D. and Vulpiani A. <br /> 
_J.Stat.Mech._ (2012) L06001 <br />
(http://arxiv.org/abs/1205.6621=true)

[10] *On anomalous diffusion and the out of equilibrium response function in one-dimensional models* <br />
Villamaina D., Sarracino A., Gradenigo G., Puglisi A. and Vulpiani A. <br /> 
_J.Stat.Mech._ (2011) L01002. <br /> 
(http://iopscience.iop.org/1742-5468/2011/01/L01002?fromSearchPage=true) <br /> <br /> 



*FLUCTUATION THEOREM*

The most universal property that has been discovered in driven
stationary system is the Fluctuation Relation: this is a symmetry of
the probability distribution of the entropy produced per unit time,
$\sigma$, which reads as $\log[P(\sigma)/P(-\sigma)]=\sigma$. In
papers [7] and [9] of the list below I realized, in collaboration with
people in Rome, a detailed study of a toy model of a gas such that
exact results are available on $P(\sigma)$ and therefore the interplay
between the Fluctuation Relation and other phyisical properties of the
system can be discussed with remarkable precision.  The model of [7]
and [9] is a coarse-grained toy model of a gas where deterministic and
stochastic ingredients are coexisting. The model is characterized by
inelastic collisions among particles alternated by a deterministic
motion which, in presence of an external field, is ballistic: this is
the stochastic Lorentz gas. Due to the inelastic collisions and the
external field the system is ``out-of-equilibrium'': nevertheless, due
to the simplicity of the ingredients concourring in the description,
the related Boltzmann equation can be solved and the properties of the
system determined with accuracy. The Boltzmann equation is a very
general one for the probability of the microstates: it requires the
only assuption of ``molecular chaos'' and holds also for
out-of-equilibrium systems. The unknown of the Boltzmann equation is
indeed the probability distribution of microstates: the equation is
nonlinear and in general is not possible to solve it
exactly. Nevertheless, there are systems simple enough that the
equation becomes linear and can also be solved, like the one we
studied in [7],[9]. One of the properties which are more often studied
in systems like the stochastic Lorentz gas is the probability of very
unlikely events. While in an equilibrium system the average entropy
produced per unit time is zero, within an out-of-equilibrium system
this entropy is positive. Indeed one can assume as an equivalent
definition of being ``out-of-equilibrium'' that of having a positive
entropy production. We must then say that a positive entropy
production is an \emph{average} property of \emph{macroscopic}
systems. When a system is small, there can be rare fluctuations
leading to a \emph{negative} entropy production.  There is a branch of
the theory of probability that is called Large Deviation theory and
which is dealth with the study of these rare events. In [7] and [9] we
used the stochastic Lorentz gas as a benchmark to compare the
predictions of the Large Deviation theory on $P(\sigma)$ with the
symmetry properties of $P(\sigma)$ which correspond to the Fluctuation
Relation.

[11] *Fluctuation relations without uniform large deviations* <br />
  G. Gradenigo, A. Sarracino, A. Puglisi, H. Touchette, 
  J. Phys. A: Math. Theor. 46, 335002, (2013). <br />

[12] *Non-equilibrium fluctuations in a driven stochastic Lorenz gas* <br />
  G. Gradenigo, U. Marini Bettolo Marconi, A. Puglisi, and A. Sarracino,
  Phys. Rev. E 85, 031112 (2012). <br /> <br /> 



*GRANULAR FLUIDS*


Granular fluids are a paradigmatic example of systems which cannot be
described with the standard tools of stastistical mechanics, namely
with the Boltzmann distribution of microstates. A fluid, which can be
more or less dense, is said ``granular'' when its elementary
components, which are usually mesoscopic beads, have inelastic
collisions: this means that some energy is lost within every
collision. Clearly, in order to prevent all the energy present in the
system to be sucked away by the collisions, leaving the system in a
quiet death, the characterization of a granular gas is usually
provided also specifying the mechanism by which energy is supplied to
the systems. Such a mechanism could be a homogeneous driving of all
the particles, like the one discussed in several of my papers on that subject
[14,17-19], but may also act just across the boundaries of the
system. The continuous flux of energy across the system allows the
granular gas to approach a non-equilibrium stationary state (NESS)
where the distribution of microstates becomes time-independent and is
of course different from the Boltzmann one. Granular fluids display
several interesting phenomena that are totally absent in equilibrium
fluids and that I studied during my three year post-doc in the TNT group.

Among these it is worthwile to mention the behaviour of correlations,
i.e. of cooperativity, between the elementary degree of the system,
which differ remarkably with respect to equilibrium fluids. In
equilibrium systems it happens that scale-free correlations, namely
the simultaneous cooperation of all the degrees of freedom of the
system, can be found only in the vicinity of a phase transition. On
the contrary in granular gases and in other out-of-equilibrium systems
this high degree of cooperativity can be found even far from critical
points, and is just due to the ``out-of-equilibrium'' nature of the system.

The intriguing point abount correlations in granular fluids to which I
dedicated most of my work on granular system is the precise
characterization of how the range of correlations depend on the energy
injection mechanism exploited to keep the system in a stationary
state. This dependence of correlations on the energy injection
mechanism is the main point that I underlined in the study of the
correlations among the velocities of granular beads presented in
papers [14] and [17-19].  The study of correlations in granular
fluids, which has been carried on making use of the linearized
hydrodynamic equations with noise, yielded results in fair agreement
with the experimental results obtained within the same group, paper
[17]. Such a collaboration was for me very stimulating, because I had the opportunity to approach a physical
problem from all the point of view: analytical, numerical and
experimental. Working on granular fluids I achieved familiarity with
one of analytical approaches which are usually exploited to study
out-of-equilibrium systems: the study of hydrodynamic
equations. Hydrodynamics equations are coupled partial differential
equations which can be obtained from the Boltzmann equation
postulating that only few coarse-grained field like local density
$\rho(x)$, local velocity $v(x)$ and local temperature $T(x)$ are
relevant.  In a granular fluids the hydrodynamics equations, which
represent a corase-grained description fo the model, can be linearized
around the stationary solution, obtaining more simple and tractable
expressions [18], and provide a very useful tool to study the extent
of correlations and fluctuations within the system.


[13] *Brownian ratchet in a thermal bath driven by Coulomb friction* <br />
  A. Gnoli, A. Petri, F. Dalton, G. Gradenigo, G. Pontuale, A. Sarracino, A. Puglisi,
  Phys. Rev. Lett. 110, 120601 (2013).

[14] *Entropy production in non-equilibrium fluctuating hydrodynamics* <br />
Gradenigo G., Puglisi A., Sarracino A.<br /> 
_J.Chem.Phys._ 137, 014509 (2012) <br />
(http://jcp.aip.org/resource/1/jcpsa6/v137/i1/p014509_s1=true)

[15] *Out-of-equilibrium generalized fluctuation-dissipation relations* <br />
Gradenigo G., Puglisi A., Sarracino A., Villamaina D. and Vulpiani A. <br />
Chapter in the book: R.Klages, W.Just, C.Jarzynski (Eds.), Nonequilibrium Statistical Physics of Small Systems: 
Fluctuation Relations and Beyond <br /> (Wiley-VCH, Weinheim, 2012; ISBN 978-3-527-41094-1) <br />
(http://www.maths.qmul.ac.uk/~klages/smallsys/smallsys_rk.html=true)

[16] *Dynamics of a massive intruder in a homogeneously driven granular fluid* <br />
A. Puglisi, A. Sarracino, G. Gradenigo, D. Villamaina <br />
Comments: 6 pages, 2 figures, to be published on "Granular Matter" in a special issue in honor of the memory of Prof. Isaac Goldhirsch 

[17] *Structure factors in granular experiments with homogeneous fluidization* <br />
A. Puglisi, A. Gnoli, G. Gradenigo, A. Sarracino, D. Villamaina <br />
_J.Chem.Phys._  136, 014704 (2012) <br />
(http://jcp.aip.org/resource/1/jcpsa6/v136/i1/p014704_s1=true)

[18] *Fluctuating hydrodynamics and correlation lengths in a driven granular fluid* <br />
Gradenigo G., Sarracino A., Villamaina D. and Puglisi A.
_J.Stat.Mech._ (2011) P08017 <br />
(http://iopscience.iop.org/1742-5468/2011/08/P08017?fromSearchPage=true)

[19] *Growing non-equilibrium length in granular fluids: from experiment to fluctuating hydrodynamics* <br /> 
Gradenigo G., Sarracino A., Villamaina D. and Puglisi A.
_EPL_ 96 14004 (2011) <br /> 
(http://iopscience.iop.org/0295-5075/96/1/14004?fromSearchPage=true)

[20] *Irreversible dynamics of a massive intruder in dense granular fluids* <br />
Sarracino A., Villamaina D., Gradenigo G. and Puglisi A.
_EPL_ 92, 34001 (2010). <br /> (http://iopscience.iop.org/0295-5075/92/3/34001?fromSearchPage=true) <br /> <br />



*DYNAMICAL SYSTEMS* 


[21] *Fluctuations in partitioning systems with few degrees of freedom*  <br />
  L. Cerino, G. Gradenigo, A. Sarracino, D. Villamaina, A. Vulpiani, 
  accepted on Phys. Rev. E (2014).

[22] *A study of the Fermi-Pasta-Ulam problem in dimension two* <br />
  Benettin G. and Gradenigo G., _Chaos_,  18, 013112 (Mar 2008). <br />
  (http://chaos.aip.org/resource/1/chaoeh/v18/i1/p013112_s1)
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Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
pdf	idrodinamica-long.pdf	r1	manage	549.9 K	2011-06-06 - 13:39	GiacomoGradenigo	Numerical/Theoretical study of fluctuating hydrodynamics in a granular fluid coupled to an equilibrium thermostat
jpg	img_0359.jpg	r1	manage	3018.5 K	2011-06-06 - 14:08	GiacomoGradenigo
Topic revision: r12 - 2015-03-23 - GiacomoGradenigo