The relaxation of macroscopic non-equilibrium disturbances is governed by the same laws as the regression of spontaneous microscopic fluctuations in an equilibrium system.  This universal statement is the heart of the Onsager Regression Hypothesis [1] and also one of the main driving forces of the scientific legacy of Aleksandar Donev, who, unfortunately, left this world recently.  “Fluctuations” and “Dynamics of Non-Equilibrium Variables” are, therefore, intimately bound and also to their acronym (DoNEV). The theory of fluctuations is universally applicable and crosses many disciplines in physics. At scales smaller than a micron, fluctuations are ubiquitous and an ineluctable source of motion. Understanding fluctuations is thus necessary to properly model nanoscopic systems. Going further, following Onsager,  fluctuations become a substantial source of information in an expert’s hands [2,3,4]. The fluctuation-dissipation balance relates the short-time correlation of the variables with “their” Green function (mobility tensor or propagator [5]) which is the very solution of the equations of motion for the average dynamics.  A fluctuation can only be understood in relation to the average of the particular thermo-dynamic variable (or level of description). This connects DoNEV with coarse-graining and the multiscale paradigm: i.e. the transfer of information across scales. Following Mori and Zwanzig [6,7], such information encompasses entropy gradients, transport coefficients, and molecular viscoelasticity, where time matters [7]. Fluctuations are usually fast and come from very different physical mechanisms [4,8,9], resulting in diverse computational challenges. For instance, some fluctuations may impose severe limits to the time-step (e.g. sound) [8]. Another key challenge in the art of simulating DoNEV is to adiabatically eliminate irrelevant fluctuations of a problem by adding rigid constraints in the form of Lagrangian multipliers [8,10].

This first DoNEV workshop will focus on theoretical and computational aspects of fluctuating (hydro)dynamics and gather (and expand) a community which collects a broad range of expertise: applied mathematics, soft matter statistical physics, high-performance computing and, importantly, provide connection with experiments.

From the methodological standpoint, the workshop will focus on grid-based methods to solve stochastic partial differential equations [8,9] including spectral methods [11,12,13] and methods based on Green functions (e.g. Stokesian Brownian dynamics [14, 15]). Also Eulerian-Lagrangian schemes based on the Immersed Boundary (IB) method [16, 17] and variants [12,44,18,19]. The IB method can be broadly applied: to flexible [19], rigid structures [19,20,45] or fibers [21,22], compressible particles in ultrasound fields, [23], reaction-diffusion [24,25], electrophoresis [26,27,28], heated nanoparticles [25]. Finally, we will consider how to connect these mesoscopic scales with the underlying atomistic or molecular descriptions, using molecular dynamics (LAMMPS) -- by either equilibrium or nonequilibrium simulations. Despite the broad thematic scope, all these topics share theoretical framework and computational methodologies.

To connect with experimental systems and applications,  we will start by tracing and building on Donev’s works  [https://cims.nyu.edu/~donev/Publications.html] on electrolytes (continuum [30] or discrete settings [31]), deformable interface dynamics [32], active matter [33,34], reactive Brownian dynamics, reactive liquid mixtures [38], doubly periodic [35] and open geometries, slender bodies, including twisting and bending [37], suspensions of actin and other bio-polymers [36], integral methods [22]. And then explore further extensions to magnetic nanoparticles [39,40], electro and dielectrophoresis [41], fluid-solid friction and lubrication forces, optic-matter interaction [42] and thermophoretic forces [43].

General topics include (but are not limited to):

• Computational challenges on the mesoscale - from dozens of nanometers to microns
• Fluctuating hydrodynamics
• Immersed boundary methods for multiphysics
• Fundamental aspects of stochastic equations, including memory
• Soft matter in general: membranes, polymers, colloids, etc.
• Lubrication of soft and fluctuating interfaces

Program outline:

This alternative-format event will combine a standard workshop with an advanced school.

Days 1&2 will focus on tutorial lectures with hands-on training. The topics include fluctuating hydrodynamics, methods for colloidal suspensions, Mori-Zwanzig operators, linear response, Green-Kubo, and fluctuation spectra.

Days 3-5 will be the core workshop and focus on research talks.