Statistical Mechanics has become in the last decades the standard tool
to study problems once considered to be out of the reach
and the scopes of Physics.
It has been in fact applied to the study of the complex behavior of
various kinds of systems of areas such as biological and sociological
sciences, finance, economy, theory of decisions, networks.
In particular several disciplines connected with Engineering are now
attracting more and more the interest of physicsts.
Granular matter is a remarkable example of these new disciplines.
The problem of understanding granular materials is widely recognized
as one of the main problems of engineering and industry. A
brief list of typical "granular" products comprehends: grains,
powders, sands, pills, seeds and similar particulate materials. More
generally, granular materials are a very large set of substances used
in the industry and in the everyday life: ceramics, fertilizers,
cosmetics, food products, paper, conductor pastes, resins,
electronics, polymers, suspensions, solid chemicals, construction
materials and so on. The international economic impact of particle
processing is substantial. The value added by manufacture that
involves particulate has been estimated to be a minimum of 80/100
billion/year, which is of the order of the US trade deficit with
Japan. The US Dept. of Commerce has estimated the total economic
impact of particulate products to be one trillion/year. Despite
economic impact, however, insufficient attention is paid to
difficulties associated with the processing of particles. An improved
understanding of micromechanics of granular media requires an
interdisciplinary approach involving both physicists and
engineers.
Mechanical engineers and geologists have studied Granular Matter for at least
two centuries and found several empirical laws describing its behavior.
Physicists have joined in more recently and
are interested in formulating general laws. For them granular matter is
a new type of condensed matter, showing two states: one fluid-like,
one solid-like. But there is not yet consensus on the description of these
two states. According to P.G. de Gennes Granular matter now is at the level
of solid-state physics in 1930.
Granular matter also represents an important paradigm for the study of
non-equilibrium stationary states. Due to the dissipative nature of the
interactions granular gases have to be considered as open systems
and therefore concepts from equilibrium thermodynamics cannot be applied,
at least in straightforward way.
The project we propose focuses on granular fluids.
We intend by granular fluid a large number of particles, whose
size is larger than a micron, colliding
with one another and losing a little energy in each collision.
Below one micron thermal agitation is important and Brownian motion
can be observed. Above one micron, thermal agitation is negligible.
However,if such a system is shaken to keep it in motion,
its dynamics resembles that of fluids, in that the grains move randomly.
One of the key differences between a granular material and a regular
fluid is that the grains of the former lose energy with each
collision, while the molecules of the latter do not. Even when the
inelasticity of the collisions is small, it can give rise to dramatic
effects, including the Maxwell Demon effect and
the phenomenon of granular clustering. Experiments and molecular dynamics
simulations alike show that granular gases in the
absence of gravity do not become homogeneous with time, but instead
form dense clusters of stationary particles surrounded by a lower
density region of more energetic particles. From a particulate point
of view, one can explain these clusters by noting that when a particle
enters a region of slightly higher density, it has more collisions,
loses more energy, and so is less able to leave that region, thus
increasing the local density and making it more likely for the next
particle to be captured.
Publications by
U. Marini Bettolo Marconi
Original papers
Statistical mechanics of granular gases in compartmentalized systems
Physical Review E 68, 031306 (2003) .
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Phys. Rev. Lett. 90, 064301 (2003)
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Complex fluid behavior of strongly asymmetric
binary mixtures. Thermodynamic properties
of a generalized Lin-Taylor model.
Molecular Physics 93, 501 (1998).
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Critical exponents in the Lin-Taylor model of asymmetrical
binary mixtures
Molecular Physics, 95 , 571 (1998).
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Driven low density granular mixtures
Phys. Rev. E 051304 (2002)
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Steady-state properties of a mean-field model of driven inelastic mixtures
Phys. Rev. E 66, 011301 (2002)
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Mean-field model of free-cooling inelastic mixtures
Phys. Rev. E 65, 051305 (2002)
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Cooling of a lattice granular fluid as an ordering process
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Driven granular gases with gravity
Groove instability in cellular solidification
Kinetic approach to granular gases
Phys. Rev. E 59, 5582-5595 (1999)
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Clustering and Non-Gaussian Behavior in Granular Matter
Interface pinning and slow ordering kinetics on infinitely ramified fractal
structures
Comment on Exact Results for the Lower Critical
Solution in the Asymmetric Model of an Interacting Binary Mixture
Soluble phase field model
Diffusion-controlled growth of a solid cylinder into its undercoded melt:
Instabilities and pattern formation studied with the phase-field model
Domain growth on self-similar structures
Growth kinetics in a phase field model with continuous symmetry
Growth in systems of vesicles and membranes
Phase-field model for dendritic growth in a channel
Diffusion Limited Growth in Systems with Continuous Symmetry
Complexity of the Minimum Energy Configurations
Effective action method for the Langevin equation
Deflated regime for pressurized ring polymers with long-range interactions
Ergodic properties of high-dimensional symplectic maps
Structure of the liquid-vapor interface:
A nonperturbative approach to the theory of interfacial fluctuations
Microscopic model for hysteresis and phase equilibria of fluids
confined between parallel plates
Critical adsorption and finite-geometry effects
Comment on Simple theory for the critical adsorption of a fluid
Capillary condensation versus prewetting
Transport of a heated granular gas in a washboard potential
J. Chem. Phys. 125, 204711 (2006)
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Nonequilibrium inertial dynamics of colloidal systems
J. Chem. Phys. 124, 164901 (2006)
Inelastic Takahashi hard-rod gas
J. Chem. Phys. 124, 044507 (2006)
The inelastic hard dimer gas: A nonspherical model for granular
matter
J. Chem. Phys. 122, 164505 (2005)
Inelastic hard rods in a periodic potential
J. Chem. Phys. 121, 5125 (2004)
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6. Fluid-like behavior of a one-dimensional granular gas
J. Chem. Phys. 120, 35 (2004)
Behavior of Granular Mixtures in Shaken Compartmentalized
Containers
Physica A 347, 411 (2005).
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Dynamic density functional theory of fluids
J. Chem. Phys. 110, 8032 (1999)
8. Pore-end effects on adsorption hysteresis in cylindrical and
slitlike pores
J. Chem. Phys. 97, 6942 (1992)
Hard-sphere mixtures near a hard wall
J. Chem. Phys. 90, 3704 (1989)
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Lennard-Jones fluids in cylindrical pores: Nonlocal theory and
computer simulation
J. Chem. Phys. 88, 6487 (1988)
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Phase equilibria and solvation forces for fluids confined between
parallel walls
J. Chem. Phys. 86, 7138 (1987)
Fluids in narrow pores: Adsorption, capillary condensation, and
critical points
J. Chem. Phys. 84, 2376 (1986)
O(N) model for charge density waves
Physica A Volume: 225, Issue: 3-4, April 1, 1996, pp. 281-293
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Novel Monte-Carlo lattice approach to rapid directional
solidification of binary alloys
Physica A Volume: 277, Issue: 1-2, March 1, 2000, pp. 35-46
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Fingering in slow combustion
Physica A Volume: 312, Issue: 3-4, September 15, 2002, pp. 381-391
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Interfacial dynamics in rapid solidification processes
Physica A Volume: 280, Issue: 1-2, May 15, 2000, pp. 148-154
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Janssen's law and stress fluctuations in confined dry granular materials
Physica A Volume: 280, Issue: 3-4, June 1, 2000, pp. 279-288
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Motion of a granular particle on a rough line
Europhys. Lett. 51 No 6 (15 September 2000) 685-690
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Influence of correlations on the velocity statistics of scalar granular
gases
Europhys. Lett. 58 No 1 (April 2002) 14-20
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Granular gases in compartmentalized systems
J. Phys.: Condens. Matter 17 No 24 (22 June 2005) S2641-S2656
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Dynamic density functional theory of fluids
J. Phys.: Condens. Matter 12 No 8A (28 February 2000) A413-A418
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A microscopic model for solidification
Europhys. Lett. 47 No 3 (1 August 1999) 338-344
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Europhys. Lett. 43 No 5 (1 September 1998) 552-557
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Time dependent Ginzburg - Landau model in the absence of
translational invariance. Non-conserved order parameter domain growth
J. Phys. A: Math. Gen. 30 No 4 (21 February 1997) 1069-1088
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Domain coarsening via heat diffusion: A numerical study with
the phase field model
Europhys. Lett. 36 No 6 (20 November 1996) 431-436
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On the antiferromagnetic phase in the Hubbard model
J. Phys. C: Solid State Phys. 15 No 26 (20 September 1982) L925-L928
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D. Paolotti, C. Cattuto, U. Marini Bettolo Marconi, A. Puglisi
Granular Matter 5, 75 (2003).
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Time dependent Ginzburg-Landau equation for an N-component model of
self-assembled fluids
Europhysics Letters 30, 349 (1995)
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Growth kinetics in the $\Phi^6$ N-component model.
Non conserved order parameter
Modern Physics Letters B, 8, 1115 (1994).
Growth Kinetics in the $\Phi ^6$ N-Component Model. Conserved Order Parameter
Modern Physics Letters B, {\bf 8}, 1125 (1994)
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Effective Action Method for Computing Next to
Leading Corrections of $O(N)$ Models
Physics Letters B 319 171, (1993)
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Application of simple models to the study of nonequilibrium
behavior of inelastic gases.
Phase Transitions, 77, 863 (2004)
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Kinetics Models of Inelastic Gases}
Math. Mod. Meth. Appl. S. 12, 965 (2002)
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Velocity fluctuations in cooling granular gases
in Lecture Notes in Physics ``Granular Gas Dynamics''
edited by T.Poeschel and N. Brilliantov, Springer (2003)
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Other Papers
J. M. Carmona, U. M. B. Marconi, J. J. Ruiz-Lorenzo, and A. Tarancon
Critical properties of the Ising model on Sierpinski fractals:
A finite-size scaling-analysis approach
Phys. Rev. B 58, 14387-14396 (1998)
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Exact two-particle effective interaction and superconductivity in
the two-level Hubbard model
Phys. Rev. B 39, 4277-4284 (1989)
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Variational approach to the phase diagram of rigid membranes
International Journal of Modern Physics B , 4615 (1993).
Novel scaling behavior of directed polymers:
disorder distribution with long tails
Journalof Statistical Physics 61, 885 (1990).
The magnetic critical exponent in the three
state three dimensional Potts model
Physics Letters 240 B, 419 (1990).
Monte Carlo simulations in fermionic systems:
the three band Hubbard model case
Physica A 171, 139 (1990).
Mode coupling theory of charge fluctuations spectrum
in a binary ionic liquid.
Il Nuovo Cimento 57B, 319 (1980).
Relativistic Theory of the binding energies of heavy
atomic ions
International Journal of Quantum Chemistry 20, 693 (1981).
On the failure of certain integral equations theories to
account for complete wetting at solid-fluid interfaces
Molecular Physics 50, 993 (1983).
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The structure of size asymmetric electrolytes at charged
surfaces
Chemical Physics Letters 107, 609 (1984).
Pairwise correlations at a fluid-fluid interface:
influence of a wetting film
Molecular Physics 54, 1357 (1985).
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The role of wetting films in capilllary condensation and
rise: influence of long-ranged forces
Chemical Physics Letters 114, 415 (1985).
Capillary condensation and adsorption in cylindrical
and slit-like pores
Faraday Transactions II,82, 1763 (1986).
Phase transitions in a confined lattice gas: prewetting
and capillary condensation
Physica A 141, 187 (1987).
Phase equilibria of fluid interfaces and
confined fluids
Molecular Physics 60, 573 (1987).
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Fluid mixtures in narrow cylindrical pores: Computer
simulation and Theory
International Journal of Thermophysics 9,
1051 (1988).
On the statistical mechanics of interfaces and
interfacial fluctuations
Physica A159, 221 (1989).
A model of Hysteresis in narrow pores
Europhysics Letters 8, 531 (1989).
Lennard-Jones Mixtures in a Cylindrical Pore.
A Comparison of Simulation and Density Functional Theory
Molecular Simulation 2, 393 (1989).
Phase diagram of the $Z(3)$ spin model in three
dimensions
Physics Letters B 217, 314 (1989).
Monte Carlo simulation and Variational study of the
phase diagram of the Potts three state model
Physica A 161, 284 (1989).
Renormalization Group study of the $d=3$, $q=3$
Potts model
Physics Letters
B 231, 157 (1989).
The crossover between complete wetting
and critical adsorption
Physica A 171, 69 (1991).
Structure effects and phase equilibria of Lennard-Jones
mixtures in a cylindrical pore. A non local density functional
theory
Molecular Physics 72 ,1081 (1991)
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La forza dei granelli}
Le Scienze, Agosto 2002
Simple Models for compartmentalized sand}
``Traffic and Granular flow 03'' S.P. Hoogendoorn, S.Luding, P.H. Bovy,
M. Schreckenberg, D.E. Wolf Editors, Springer 2005, p. 579.