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Fluids at the Nanoscale: From Continuum to Subcontinuum Transport
No full textNanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics, and condensed matter physics. This review is intended as a toolbox for fluids at the nanometer scale. After presenting the basic equations that govern fluid behavior in the continuum limit, we show how these equations break down and new properties emerge in molecular-scale confinement. A large number of analytical estimates and physical arguments are given to organize the results and different limits
Solving high-dimensional parabolic PDEs using the tensor train format
Get PDFHigh-dimensional partial differential equations
(PDEs) are ubiquitous in economics, science and
engineering. However, their numerical treatment
poses formidable challenges since traditional gridbased
methods tend to be frustrated by the curse of
dimensionality. In this paper, we argue that tensor
trains provide an appealing approximation framework
for parabolic PDEs: the combination of reformulations
in terms of backward stochastic differential
equations and regression-type methods
in the tensor format holds the promise of leveraging
latent low-rank structures enabling both compression
and efficient computation. Following this
paradigm, we develop novel iterative schemes, involving
either explicit and fast or implicit and
accurate updates. We demonstrate in a number
of examples that our methods achieve a favorable
trade-off between accuracy and computational efficiency
in comparison with state-of-the-art neural
network based approaches
Discrete approximation of dynamic phase-field fracture in visco-elastic materials
No full textAbstract: This contribution deals with the analysis of models for phase-field fracture in visco-elastic materials with dynamic effects. The evolution of damage is handled in two different ways: As a viscous evolution with a quadratic dissipation potential and as a rate-independent law with a positively 1-homogeneous dissipation potential. Both evolution laws encode a non-smooth constraint that ensures the unidirectionality of damage, so that the material cannot heal. Suitable notions of solutions are introduced in both settings. Existence of solutions is obtained using a discrete approximation scheme both in space and time. Based on the convexity properties of the energy functional and on the regularity of the displacements thanks to their viscous evolution, also improved regularity results with respect to time are obtained for the internal variable: It is shown that the damage variable is continuous in time with values in the state space that guarantees finite values of the energy functional
GENERIC framework for reactive fluid flows
Get PDFWe describe reactive fluid flows in terms of the formalism General Equation for Non-Equilibrium
Reversible-Irreversible Coupling also known as GENERIC. Together with the formalism, we present
the thermodynamical and mechanical foundations for the treatment of fluid flows using continuous
fields and present a clear relation and transformation between a Lagrangian and an Eulerian
formulation of the corresponding systems of partial differential equations. We bring the abstract
framework to life by providing many physically relevant examples for reactive compressive fluid
flows
Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench
No full textInferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods provide a promising alternative. In this work both methods are first applied to artificially generated data and second on a real world problem, by using data of an electric motor test bench. We show that both methods are able to infer the distribution of varying parameters with a Bayesian hierarchical approach. But the proposed ABC method is computationally much more efficient in order to achieve results with similar accuracy. We suggest to use summary statistics in order to reduce the dimension of the data which significantly increases the efficiency of the algorithm. Further the simulation model is replaced by a Polynomial Chaos Expansion (PCE) surrogate to speed up model evaluations. We proof consistency for the proposed surrogate-based ABC method with summary statistics under mild conditions on the (approximated) forward model.
David N. John, Livia Stohrer, Claudia Schillings, Michael Schick, Vincent Heuvelin
Thermodynamics and kinetics of aggregation of flexible peripheral membrane proteins
No full textBiomembrane remodeling is essential for cellular trafficking, with membrane-binding peripheral proteins playing a key role in it. Significant membrane remodeling as in endo- and exocytosis is often due to aggregates of many proteins with direct or membrane-mediated interactions. Understanding this process via computer simulations is extremely challenging: protein–membrane systems involve time and length scales that make atomistic simulations impractical, while most coarse-grained models fall short in resolving dynamics and physical effects of protein and membrane flexibility. Here, we develop a coarse-grained model of the bilayer membrane bestrewed with rotationally symmetric flexible proteins, parametrized to reflect local curvatures and lateral dynamics of proteins. We investigate the kinetics, equilibrium distributions, and the free energy landscape governing the formation and breakup of protein clusters on the surface of the membrane. We demonstrate how the flexibility of the proteins as well as their surface concentration play deciding roles in highly selective macroscopic aggregation behavior
Profiling of Sub-Lethal in Vitro Effects of Multi-Walled Carbon Nanotubes Reveals Changes in Chemokines and Chemokine Receptors
No full textEngineered nanomaterials are potentially very useful for a variety of applications, but studies are needed to ascertain whether these materials pose a risk to human health. Here, we studied three benchmark nanomaterials (Ag nanoparticles, TiO2 nanoparticles, and multi-walled carbon nanotubes, MWCNTs) procured from the nanomaterial repository at the Joint Research Centre of the European Commission. Having established a sub-lethal concentration of these materials using two human cell lines representative of the immune system and the lungs, respectively, we performed RNA sequencing of the macrophage-like cell line after exposure for 6, 12, and 24 h. Downstream analysis of the transcriptomics data revealed significant effects on chemokine signaling pathways. CCR2 was identified as the most significantly upregulated gene in MWCNT-exposed cells. Using multiplex assays to evaluate cytokine and chemokine secretion, we could show significant effects of MWCNTs on several chemokines, including CCL2, a ligand of CCR2. The results demonstrate the importance of evaluating sub-lethal concentrations of nanomaterials in relevant target cells
Shape of plutons in crustal shear zones: A tectono-magmatic guide based on analogue models
No full textPlutons in crustal shear zones may exploit inherited structures, interfere with strain localizing or be deformed passively. To constrain the relative timing of such tectono-magmatic relationships in natural settings is not always straight-forward. We here present sandbox-type analogue model experiments simulating magma emplacement into simple and transtensional crustal shear zones to test the diagnostic potential of pluton shape with respect to timing and setting. Observations based on surface deformation and intrusion shape exemplify the interplay between evolving and inherited tectonic structures and magma uprising. We observe markedly asymmetric intrusions in association with dikes reflecting the regional stresses, fault pattern and finite strain field. At the same time, the presence of an intrusion modifies the tectonic evolution, but only transiently, resulting in short-lived faults, reactivation and inversion. Diagnostic attributes include the pluton’s aspect ratio, its orientation and amplitude as well as dike association. Accordingly, syn-tectonic intrusions show the highest pluton amplitudes, but only intermediate elongation compared to other scenarios. They are oriented parallel to Riedel shears in simple shear, respectively to the compression direction in transtension. Post-tectonic intrusions are least elongated, have medium amplitudes and exploit Riedel shears. Pre-tectonic intrusions are characterized by lowest amplitudes but the highest aspect ratios and are parallel to the finite elongation direction. Intrusions in transtensional shear zones are generally of less elongate than those in simple shear zones. Experimental results are tested against observations from natural examples validating the diagnostic potential of pluton shape for the timing and the tectonic setting of the emplacement
Widening of Hydrous Shear Zones During Incipient Eclogitization of Metastable Dry and Rigid Lower Crust— Holsnøy, Western Norway
Get PDFThe partially eclogitized crustal rocks on Holsnøy in the Bergen Arcs, Norway, indicate
that eclogitization is caused by the interplay of brittle and ductile deformation promoted by fluid
infiltration and fluid-rock interaction. Eclogitization generated an interconnected network of millimeterto-
kilometer-wide hydrous eclogite-facies shear zones, which presumably caused transient weakening
of the mechanically strong lower crust. To decipher the development of those networks, we combine
detailed lithological and structural mapping of two key outcrops with numerical modeling. Both outcrops
are largely composed of preserved granulite with minor eclogite-facies shear zones, thus representing the
beginning phases of eclogitization and ductile deformation. We suggest that deformation promoted fluidrock
interaction and eclogitization, which gradually consumed the granulite until fluid-induced reactions
were no longer significant. The shear zones widen during progressive deformation. To identify the key
parameters that impact shear zone widening, we generated scale-independent numerical models, which
focus on different processes affecting the shear zone evolution: (i) rotation of the shear zones caused
by finite deformation, (ii) mechanical weakening due to a limited amount of available fluid, and (iii)
weakening and further hydration of the shear zones as a result of continuous and unlimited fluid supply.
A continuous diffusion-type fluid infiltration, with an effective diffusion coefficient around
2
10 16 m
s
D ,
coupled with deformation is prone to develop structures similar to the ones mapped in field. Our results
suggest that the shear zones formed under a continuous fluid supply, causing shear zone widening, rather
than localization, during progressive deformation
Γ-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems
No full textThe Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions