Multi-resolution simulation of DNA transport through large synthetic nanostructures

Modeling and simulation has become an invaluable partner in development of nanopore sensing systems. The key advantage of the nanopore sensing method --- the ability to rapidly detect individual biomolecules...

Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor–Green problem

The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor–Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which – by construction – rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to $8192^3$ (defined based on the $2{\rm \pi}$ -periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative $L^2$ -error of $0.27\,\%$ for the temporal evolution of the kinetic energy and $3.52\,\%$ for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.

From adaptive resolution to molecular dynamics of open systems

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method’s advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments. Graphic abstract

The Atlantic's freshwater budget under climate change in the Community Earth System Model with strongly eddying oceans

We investigate the freshwater budget of the Atlantic and Arctic oceans in coupled climate change simulations with the Community Earth System Model and compare a strongly eddying setup with 0.1∘ ocean grid spacing to a non-eddying 1∘ configuration typical of Coupled Model Intercomparison Project phase 6 (CMIP6) models. Details of this budget are important to understand the evolution of the Atlantic Meridional Overturning Circulation (AMOC) under climate change. We find that the slowdown of the AMOC in the year 2100 under the increasing CO2 concentrations of the Representative Concentration Pathway 8.5 (RCP8.5) scenario is almost identical between both simulations. Also, the surface freshwater fluxes are similar in their mean and trend under climate change in both simulations. While the basin-scale total freshwater transport is similar between the simulations, significant local differences exist. The high-ocean-resolution simulation exhibits significantly reduced ocean state biases, notably in the salt distribution, due to an improved circulation. Mesoscale eddies contribute considerably to the freshwater and salt transport, in particular at the boundaries of the subtropical and subpolar gyres. Both simulations start in the single equilibrium AMOC regime according to a commonly used AMOC stability indicator and evolve towards the multiple equilibrium regime under climate change, but only the high-resolution simulation enters it due to the reduced biases in the freshwater budget.