Stefano Olla
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View article: Multitime fields and hard rod scaling limits
Multitime fields and hard rod scaling limits Open
A Poisson line process is a random set of straight lines contained in the plane, as the image of the map $(x,v)\mapsto (x+vt)_{t\in\mathbb{R}}$, for each point $(x,v)$ of a Poisson process in the space-velocity plane. By associating a step…
View article: $β$-FPUT chains under time-periodic forcing
$β$-FPUT chains under time-periodic forcing Open
Recent works proved a hydrodynamic limit for periodically forced atom chains with harmonic interaction and pinning, together with momentum flip. When energy is the only conserved quantity, one would expect similar results in the anharmonic…
View article: Thermal boundary conditions in fractional superdiffusion of energy
Thermal boundary conditions in fractional superdiffusion of energy Open
We study heat conduction in a one-dimensional {finite}, unpinned chain of atoms perturbed by stochastic momentum exchange and coupled to Langevin heat baths at {possibly} distinct temperatures placed at the endpoints of the chain. While in…
View article: Macroscopic diffusive fluctuations for generalized hard rods dynamics
Macroscopic diffusive fluctuations for generalized hard rods dynamics Open
Accepted for the publication in Annals of Applied Probability
View article: Convergent Power Series for Anharmonic Chain with Periodic Forcing
Convergent Power Series for Anharmonic Chain with Periodic Forcing Open
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, prev…
View article: Heat flow in a periodically forced, unpinned thermostatted chain
Heat flow in a periodically forced, unpinned thermostatted chain Open
International audience
View article: Scaling limits of solitons in the box-ball system
Scaling limits of solitons in the box-ball system Open
We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and als…
View article: Heat equation from a deterministic dynamics
Heat equation from a deterministic dynamics Open
We derive the heat equation for the thermal energy under diffusive space-time scaling for a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic force acting like a magnetic field.
View article: On the behaviour of a periodically forced and thermostatted harmonic chain
On the behaviour of a periodically forced and thermostatted harmonic chain Open
We consider a chain consisting of $n+1$ pinned harmonic oscillators subjected on the right to a time dependent periodic force $\cF(t)$ while Langevin thermostats are attached at both endpoints of the chain. We show that for long times the …
View article: Macroscopic diffusive fluctuations for generalized hard rods dynamics
Macroscopic diffusive fluctuations for generalized hard rods dynamics Open
We study the fluctuations in equilibrium for a dynamics of rods with random length. This includes the classical hard rod elastic collisions, when rod lengths are constant and equal to a positive value. We prove that in the diffusive space-…
View article: Space-time fluctuations in a quasi-static limit
Space-time fluctuations in a quasi-static limit Open
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time fiel…
View article: On the conversion of work into heat: microscopic models and macroscopic equations
On the conversion of work into heat: microscopic models and macroscopic equations Open
We summarize and extend some of the results obtained recently for the microscopic and macroscopic behavior of a pinned harmonic chain, with random velocity flips at Poissonian times, acted on by a periodic force {at one end} and in contact…
View article: Diffusive Fluctuations in Hard Rods System
Diffusive Fluctuations in Hard Rods System Open
We examine the behaviour of density fluctuation in equilibrium under diffusive space-time scaling of a completely integrable dynamics of hard rods with variable length. This is the extended abstract of a talk given by S.Olla at the worksho…
View article: Heat flow in a periodically forced, thermostatted chain II
Heat flow in a periodically forced, thermostatted chain II Open
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamil…
View article: Heat flow in a periodically forced, thermostatted chain
Heat flow in a periodically forced, thermostatted chain Open
We investigate the properties of a harmonic chain in contact with a thermal bath at one end and subjected, at its other end, to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat …
View article: A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation
A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation Open
We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schrödinger equation that models the action of a heat bath at a given temperature. We prove that the corresponding canonical Gibbs distribution is the unique …
View article: Asymptotic Scattering by Poissonian Thermostats
Asymptotic Scattering by Poissonian Thermostats Open
We consider an infinite chain of coupled harmonic oscillators with a Poisson thermostat at the origin. In the high frequency limit, we establish the reflection-transmission-scattering coefficients for the wave energy scattered off the ther…
View article: Hydrodynamic limit for a chain with thermal and mechanical boundary forces
Hydrodynamic limit for a chain with thermal and mechanical boundary forces Open
We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a d…
View article: Quasi-static limit for a hyperbolic conservation law
Quasi-static limit for a hyperbolic conservation law Open
We study the quasi-static limit for the L∞ entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with the quas…