Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn–Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require $O(10^5)$ model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only $O(10^2)$ model runs and can accommodate internal climate variability. The approach consists of three stages: (i) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (ii) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (iii) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate-emulate-sample (CES) approach in a perfect-model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties

Binary recovery via phase field regularization for first-arrival traveltime tomography

We propose a double obstacle phase field methodology for binary recovery of the slowness function of an Eikonal equation found in first-arrival traveltime tomography. We treat the inverse problem as an optimization problem with quadratic misfit functional added to a phase field relaxation of the perimeter penalization functional. Our approach yields solutions as we account for well posedness of the forward problem by choosing regular priors. We obtain a convergent finite difference and mixed finite element based discretization and a well defined descent scheme by accounting for the non-differentiability of the forward problem. We validate the phase field technique with a Γ—convergence result and numerically by conducting parameter studies for the scheme, and by applying it to a variety of test problems with different geometries, boundary conditions, and source—receiver locations

Reconciling Bayesian and Perimeter Regularization for Binary Inversion

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of total variation. On the other hand, sparse or noisy data often demand a probabilistic approach to the reconstruction of images, to enable uncertainty quantification; the Bayesian approach to inversion, which itself introduces a form of regularization, is a natural framework in which to carry this out. In this paper the link between Bayesian inversion methods and perimeter regularization is explored. In this paper two links are studied: (i) the maximum a posteriori objective function of a suitably chosen Bayesian phase-field approach is shown to be closely related to a least squares plus perimeter regularization objective; (ii) sample paths of a suitably chosen Bayesian level set formulation are shown to possess a finite perimeter and to have the ability to learn about the true perimeter

EnsembleKalmanProcesses.jl: derivative-free ensemble-based model calibration

EnsembleKalmanProcesses.jl is a Julia-based toolbox that can be used for a broad class of black-box gradient-free optimization problems. Specifically, the tools enable the optimization, or calibration, of parameters within a computer model in order to best match user-defined outputs of the model with available observed data (Kennedy & O’Hagan, 2001). Some of the tools can also approximately quantify parametric uncertainty (Huang, Huang, et al., 2022). Though the package is written in Julia (Bezanson et al., 2017), a read–write TOML-file interface is provided so that the tools can be applied to computer models implemented in any language. Furthermore, the calibration tools are non-intrusive, relying only on the ability of users to compute an output of their model given a parameter value. As the package name suggests, the tools are inspired by the well-established class of ensemble Kalman methods. Ensemble Kalman filters are currently one of the only practical ways to assimilate large volumes of observational data into models for operational weather forecasting (Evensen, 1994; Houtekamer & Mitchell, 1998, 2001). In the data assimilation setting, a computational weather model is integrated for a short time over a collection, or ensemble, of initial conditions, and the ensemble is updated frequently by a variety of atmospheric observations, allowing the forecasts to keep track of the real system. The workflow is similar for ensemble Kalman processes. Here, a computer code is run (in parallel) for an ensemble of different values of the parameters that require calibration, producing an ensemble of outputs. This ensemble of outputs is then compared to observed data, and the parameters are updated to a new set of values which reduce the output–data misfit. The process is iterated until a user-defined criterion of convergence is met. Optimality of the update is guaranteed for linear models and Gaussian uncertainties, but good performance is observed outside of these settings, see Schillings & Stuart (2017). Optimal values are selected from statistics of the final ensemble

Facultative Symbiont Infections Affect Aphid Reproduction

Some bacterial symbionts alter their hosts reproduction through various mechanisms that enhance their transmission in the host population. In addition to its obligatory symbiont Buchnera aphidicola, the pea aphid Acyrthosiphon pisum harbors several facultative symbionts influencing several aspects of host ecology. Aphids reproduce by cyclical parthenogenesis whereby clonal and sexual reproduction alternate within the annual life cycle. Many species, including the pea aphid, also show variation in their reproductive mode at the population level, with some lineages reproducing by cyclical parthenogenesis and others by permanent parthenogenesis. While the role of facultative symbionts has been well studied during the parthenogenetic phase of their aphid hosts, very little is known on their possible influence during the sexual phase. Here we investigated whether facultative symbionts modulate the capacity to produce sexual forms in various genetic backgrounds of the pea aphid with controlled symbiont composition and also in different aphid genotypes from natural populations with previously characterized infection status and reproductive mode. We found that most facultative symbionts exhibited detrimental effects on their hosts fitness under sex-inducing conditions in comparison with the reference lines. We also showed that the loss of sexual phase in permanently parthenogenetic lineages of A. pisum was not explained by facultative symbionts. Finally, we demonstrated that Spiroplasma infection annihilated the production of males in the host progeny by inducing a male-killing phenotype, an unexpected result for organisms such as aphids that reproduce primarily through clonal reproduction