Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. %such as Ising-type models. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the specific relative entropy between the exact and approximate coarse-grained equilibrium measures. Subsequently we carry out a cluster expansion around this first-and often inadequate-approximation and obtain more accurate coarse-graining schemes. The cluster expansions yield also sharp a posteriori error estimates for the coarse-grained approximations that can be used for the construction of adaptive coarse-graining methods. We present a number of numerical examples that demonstrate that the coarse-graining schemes developed here allow for accurate predictions of critical behavior and hysteresis in systems with intermediate and long-range interactions. We also present examples where they substantially improve predictions of earlier coarse-graining schemes for short-range interactions.Comment: 37 pages, 8 figure

Ab-initio calculation of all-optical time-resolved calorimetry of nanosized systems: Evidence of nanosecond-decoupling of electron and phonon temperatures

The thermal dynamics induced by ultrashort laser pulses in nanoscale systems, i.e. all-optical time-resolved nanocalorimetry is theoretically investigated from 300 to 1.5 K. We report ab-initio calculations describing the temperature dependence of the electron-phonon interactions for Cu nanodisks supported on Si. The electrons and phonons temperatures are found to decouple on the ns time scale at 10 K, which is two orders of magnitude in excess with respect to that found for standard low-temperature transport experiments. By accounting for the physics behind our results we suggest an alternative route for overhauling the present knowledge of the electron-phonon decoupling mechanism in nanoscale systems by replacing the mK temperature requirements of conventional experiments with experiments in the time-domain.Comment: 5 pages, 3 figures. Accepted on Physical Review B

A hierarchical view on material formation during pulsed-laser synthesis of nanoparticles in liquid

Pulsed-laser assisted nanoparticle synthesis in liquids (PLAL) is a versatile tool for nanoparticle synthesis. However, fundamental aspects of structure formation during PLAL are presently poorly understood. We analyse the spatio-temporal kinetics during PLAL by means of fast X-ray radiography (XR) and scanning small-angle X-ray scattering (SAXS), which permits us to probe the process on length scales from nanometers to millimeters with microsecond temporal resolution. We find that the global structural evolution, such as the dynamics of the vapor bubble can be correlated to the locus and evolution of silver nanoparticles. The bubble plays an important role in particle formation, as it confines the primary particles and redeposits them to the substrate. Agglomeration takes place for the confined particles in the second bubble. Additionally, upon the collapse of the second bubble a jet of confined material is ejected perpendicularly to the surface. We hypothesize that these kinetics influence the final particle size distribution and determine the quality of the resulting colloids, such as polydispersity and modality through the interplay between particle cloud compression and particle release into the liquid

Singular and regular solutions of a non-linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.Comment: 16 page

Microscopic View on Short-Range Wetting at the Free Surface of the Binary Metallic Liquid Gallium-Bismuth: An X-ray Reflectivity and Square Gradient Theory Study

We present an x-ray reflectivity study of wetting at the free surface of the binary liquid metal gallium-bismuth (Ga-Bi) in the region where the bulk phase separates into Bi-rich and Ga-rich liquid phases. The measurements reveal the evolution of the microscopic structure of wetting films of the Bi-rich, low-surface-tension phase along different paths in the bulk phase diagram. A balance between the surface potential preferring the Bi-rich phase and the gravitational potential which favors the Ga-rich phase at the surface pins the interface of the two demixed liquid metallic phases close to the free surface. This enables us to resolve it on an Angstrom level and to apply a mean-field, square gradient model extended by thermally activated capillary waves as dominant thermal fluctuations. The sole free parameter of the gradient model, i.e. the so-called influence parameter, $\kappa$, is determined from our measurements. Relying on a calculation of the liquid/liquid interfacial tension that makes it possible to distinguish between intrinsic and capillary wave contributions to the interfacial structure we estimate that fluctuations affect the observed short-range, complete wetting phenomena only marginally. A critical wetting transition that should be sensitive to thermal fluctuations seems to be absent in this binary metallic alloy.Comment: RevTex4, twocolumn, 15 pages, 10 figure