Related papers: Kinetic roughening, global quantities, and fluctua…
The fluctuation-dissipation theory is grounded on the Langevin condition expressing the local independence between the thermal force and the particle velocity history. Upon hydrodynamic grounds, it is reasonable to relax this condition in…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
The lectures examine several problems related to non-equilibrium fluctuations of interfaces and flux lines. The first two introduce the phenomenology of depinning, with particular emphasis on interfaces and contact lines. The role of the…
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to…
Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood.…
Macroscopic friction coefficients observed in experiments are the result of various types of complex multiscale interactions between sliding surfaces. Therefore, there are several ways to modify them depending on the physical phenomena…
We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…
We develop a theory for fluctuations and correlations in a gas evolving under ballistic annihilation dynamics. Starting from the hierarchy of equations governing the evolution of microscopic densities in phase space, we subsequently…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
We develop a global bifurcation theory for two classes of nonlinear elastic materials. It is supposed that they are subjected to anti-plane shear deformation and occupy an infinite cylinder in the reference configuration. Curves of…
Four quantities are fundamental in homogenization of elliptic systems in divergence form and in its applications: the field and the flux of the solution operator (applied to a general deterministic right-hand side), and the field and the…
We establish the local-to-global property of the synthetic curvature-dimension condition for essentially non-branching locally finite metric-measure spaces, extending the work [F. Cavalletti, E. Milman \textit{Invent. Math.} 226 (2021), no.…
The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic…
We study the universal nature of global fluctuations in the critical regime of the spherical model by evaluating the exact distribution of the magnetization and its absolute value in the thermodynamical limit, in the presence of a conjugate…
It has long been conjectured that, in three dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and experimental evidence show that such modes share the same mean…
By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
For the problem of Burgers turbulence with random gaussian forcing a similarity functional solution of Hopf equation is presented and compared with scaling arguments and replica Bethe-anzatz treatments. The corresponding field theory is…
In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with…