Gradient and Generic systems in the space of fluxes, applied to reacting particle systems

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or Generic system in the space of fluxes. In a general setting we study how flux gradient or generic systems are related to gradient systems of concentrations. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well

Flux large deviations of independent and reacting particle systems, with implications for macroscopic fluctuation theory

We consider a system of independent particles on a finite state space, and prove a dynamic large-deviation principle for the empirical measure-empirical flux pair, taking the specific fluxes rather than net fluxes into account. We prove the large deviations under deterministic initial conditions, and under random initial conditions satisfying a large-deviation principle. We then show how to use this result to generalise a number of principles from Macroscopic Fluctuation Theory to the finite-space setting

Measurements of Penetration and Detoxification of PS II Herbicides in Whole Leaves by a Fluorometric Method

The effect of herbicides that inhibit the photosynthetic electron transport at the photosystem II acceptor side has been analyzed in whole plants by using a fluorometric method. The data reported indicate that the apparent variable fluorescence of the induction curve normalized to the control value provides reliable information about the penetration rate and metabolic detoxification of PS II herbicides in whole plants

Resonant plasmonic nanoparticles for multicolor second harmonic imaging

Nanoparticles capable of efficiently generating nonlinear optical signals, like second harmonic generation, are attracting a lot of attention as potential background-free and stable nano-probes for biological imaging. However, second harmonic nanoparticles of different species do not produce readily distinguishable optical signals, as the excitation laser mainly defines their second harmonic spectrum. This is in marked contrast to other fluorescent nano-probes like quantum dots that emit light at different colors depending on their sizes and materials. Here, we present the use of resonant plasmonic nanoparticles, combined with broadband phase-controlled laser pulses, as tunable sources of multicolor second harmonic generation. The resonant plasmonic nanoparticles strongly interact with the electromagnetic field of the incident light, enhancing the efficiency of nonlinear optical processes. Because the plasmon resonance in these structures is spectrally narrower than the laser bandwidth, the plasmonic nanoparticles imprint their fingerprints on the second harmonic spectrum. We show how nanoparticles of different sizes produce different colors in the second harmonic spectra even when excited with the same laser pulse. Using these resonant plasmonic nanoparticles as nano-probes is promising for multicolor second harmonic imaging while keeping all the advantages of nonlinear optical microscopy.Peer ReviewedPostprint (published version

From large deviations to Wasserstein gradient flows in multiple dimensions

We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma$-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof of Duong et al relies on regularity properties of optimal transport maps that are restricted to one dimension. In this note we present a new proof of the upper bound, thereby generalising the result of Adams et al to arbitrary dimensions

A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility

Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility leads to natural generalized symmetry conditions, which take the form of generalized gradient flows

Large deviations of jump process fluxes

We study a general class of systems of interacting particles that randomly interact to form new or different particles. In addition to the distribution of particles we consider the fluxes, defined as the rescaled number of jumps of each type that take place in a time interval. We prove a dynamic large deviations principle for the fluxes under general assumptions that include mass-action chemical kinetics. This result immediately implies a dynamic large deviations principle for the particle distribution

Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space

We study functions of bounded variation with values in a Banach or in a metric space. In finite dimensions, there are three well-known topologies; we argue that in infinite dimensions there is a natural fourth topology. We provide some insight into the structure of these four topologies. In particular, we study the meaning of convergence, duality and regularity for these topologies and provide some useful compactness criteria, also related to the classical Aubin–Lions theorem. After this we study the Bore