A predictive thermodynamic framework of cloud droplet activation for chemically unresolved aerosol mixtures, including surface tension, non-ideality, and bulk–surface partitioning

This work presents a thermodynamically consistent framework that enables self-contained, predictive Köhler calculations of droplet growth and activation with considerations of surface adsorption, surface tension reduction, and non-ideal water activity for chemically complex and unresolved surface-active aerosol mixtures. The common presence of surface-active species in atmospheric aerosols is now well-established. However, the impacts of different effects driven by surface activity, in particular bulk–surface partitioning and resulting bulk depletion and/or surface tension reduction, on aerosol hygroscopic growth and cloud droplet activation remain to be generally established. Because specific characterization of key properties, including water activity and surface tension, remains exceedingly challenging for finite-sized activating droplets, a self-contained and thermodynamically consistent model framework is needed to resolve the individual effects of surface activity during droplet growth and activation. Previous frameworks have achieved this for simple aerosol mixtures, comprising at most a few well-defined chemical species. However, atmospheric aerosol mixtures and more realistic laboratory systems are typically chemically more complex and not well-defined (unresolved). Therefore, frameworks which require specific knowledge of the concentrations of all chemical species in the mixture and their composition-dependent interactions cannot be applied. For mixtures which are unresolved or where specific interactions between components are unknown, analytical models based on retrofitting can be applied, or the mixture can be represented by a proxy compound or mixture with well-known properties. However, the surface activity effects evaluated by such models cannot be independently verified. The presented model couples Köhler theory with the Gibbs adsorption and Szyszkowski-type surface tension equations. Contrary to previous thermodynamic frameworks, it is formulated on a mass basis to obtain a quantitative description of composition-dependent properties for chemically unresolved mixtures. Application of the model is illustrated by calculating cloud condensation nuclei (CCN) activity of aerosol particles comprising Nordic aquatic fulvic acid (NAFA), a chemically unresolved and strongly surface-active model atmospheric humic-like substance (HULIS), and NaCl, with dry diameters of 30–230 nm and compositions spanning the full range of relative NAFA and NaCl mixing ratios. For comparison with the model presented, several other predictive Köhler frameworks, with simplified treatments of surface-active NAFA, are also applied. Effects of NAFA surface activity are gauged via a suite of properties evaluated for growing and activating droplets. The presented framework predicts a similar influence of surface activity of the chemically complex NAFA on CCN activation as was previously shown for single, strong surfactants. Comparison to experimental CCN data shows that NAFA bulk–surface partitioning is well-represented by Gibbs adsorption thermodynamics. Contrary to several recent studies, no evidence of significantly reduced droplet surface tension at the point of activation was found. Calculations with the presented thermodynamic model show that throughout droplet growth and activation, the finite amounts of NAFA in microscopic and submicron droplets are strongly depleted from the bulk, due to bulk–surface partitioning, because surface areas for a given bulk volume are very large. As a result, both the effective hygroscopicity and ability of NAFA to reduce droplet surface tension are significantly lower in finite-sized activating droplets than in macroscopic aqueous solutions of the same overall composition. The presented framework enables the influence of surface activity on CCN activation for other chemically complex and unresolved aerosol mixtures, including actual atmospheric samples, to be systematically explored. Thermodynamic input parameters can be independently constrained from measurements, instead of being either approximated by a proxy or determined by retrofitting, potentially confounding several mechanisms influenced by surface activity.

Classification of topological invariants related to corner states

We discuss some bulk-surface gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four things: (1) the definition of topological invariants, (2) a proof of their relation with corner states, (3) computations of K-groups and (4) a construction of explicit examples.

ENERGY LOSSES OF A POINT MAGNETIC DIPOLE DUE TO INTERACTION WITH A MAGNETIZED PLASMA CYLINDER

In this work, the excitation problem of bulk-surface helicons by a point magnetic dipole moving in a vacuum parallel to the element of magnetized solid-state plasma cylinder is theoretically studied. The external magnetic field is directed parallel to the cylinder axis. The problem is solved in the magnetostatic approximation. It is shown that hybrid modes of the magnetic type with large values of the azimuthal mode index and one field variation along the radius are most efficiently excited at nonrelativistic velocities of magnetic dipole.

Electrochemical Analysis of Nano- and Micro-Sized Pore Formed Ti–6Al–4V Alloys in Solution Containing Ca, P, Mn, and Si Ions via Plasma Eletrolytic Oxidation for Bio-Implant Materials

The purpose of this study was to investigate electrochemical analysis of nano- and micro-sized pore formed Ti–6Al–4V alloys in solution containing Ca, P, Mn and Si ions via plasma eletrolytic oxidation for bio-implant materials. The coatings were produced on Ti–6Al–4V alloy for dental implant using the plasma electrolytic oxidation (PEO) method in electrolytes with the various concentration of 0, 5, and 20% Mn and Si, respectively. Electrochemical potentiodynamic polarization and AC impedance behaviors were carried out in 0.9% NaCl solution at 36.5 ± 1 °C using potentiostat (Potentiostat, EG&G, 362) and electrochemical impedance spectroscope (EIS, EG&G, 1025). The potentiodynamic polarization test with a scan rate of 1.667 mV s-1 was carried out from –1500 mV to 2000 mV. The frequency range used for EIS was 102–105 Hz. The amplitude of AC signal was 10 mV and 5 points per decade was used. From the potentiodynamic polarization test, PEO treated alloy in electrolyte containing Ca, P, Mn, and Si show a lower corrosion potential than that on the bulk surface. In the case of Mn and Si doped surface, the corrosion resistance increase compared to non-doped surface with Mn and Si elements, and the current density was lower than that of the bulk surface. From the AC impedance test, in the case of Mn and Si doped surface, polarization resistance values were higher than other specimens, and nano- and micro-sized pores were covered with corrosion product consisted Mn and Si elements.

Bulk-surface coupling identifies the mechanistic connection between Min-protein patterns in vivo and in vitro

Self-organisation of Min proteins is responsible for the spatial control of cell division in Escherichia coli, and has been studied both in vivo and in vitro. Intriguingly, the protein patterns observed in these settings differ qualitatively and quantitatively. This puzzling dichotomy has not been resolved to date. Using reconstituted proteins in laterally wide microchambers with a well-controlled height, we experimentally show that the Min protein dynamics on the membrane crucially depend on the micro chamber height due to bulk concentration gradients orthogonal to the membrane. A theoretical analysis shows that in vitro patterns at low microchamber height are driven by the same lateral oscillation mode as pole-to-pole oscillations in vivo. At larger microchamber height, additional vertical oscillation modes set in, marking the transition to a qualitatively different in vitro regime. Our work reveals the qualitatively different mechanisms of mass transport that govern Min protein-patterns for different bulk heights and thus shows that Min patterns in cells are governed by a different mechanism than those in vitro.

Long time behavior and stable patterns in high-dimensional polarity models of asymmetric cell division

Asymmetric cell division is one of the fundamental processes to create cell diversity in the early stage of embryonic development. During this process, the polarity formation in the cell membrane has been considered as a key process by which the entire polarity formation in the cytosol is controlled, and it has been extensively studied in both experiments and mathematical models. Nonetheless, a mathematically rigorous analysis of the polarity formation in the asymmetric cell division has been little explored, particularly for bulk-surface models. In this article, we deal with polarity models proposed for describing the PAR polarity formation in the asymmetric cell division of a C. elegans embryo. Using a simpler but mathematically consistent model, we exhibit the long time behavior of the polarity formation of a bulk-surface cell. Moreover, we mathematically prove the existence of stable polarity solutions of the model equation in an arbitrary high-dimensional domain and analyse how the boundary position of polarity domain is determined. Our results propose that the existence and dynamics of the polarity in the asymmetric cell division can be understood universally in terms of basic mathematical structures.

An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries

The unfitted discontinuous Galerkin (UDG) method allows for conservative dG discretizations of partial differential equations (PDEs) based on cut cell meshes. It is hence particularly suitable for solving continuity equations on complex-shaped bulk domains. In this paper based on and extending the PhD thesis of the second author, we show how the method can be transferred to PDEs on curved surfaces. Motivated by a class of biological model problems comprising continuity equations on a static bulk domain and its surface, we propose a new UDG scheme for bulk-surface models. The method combines ideas of extending surface PDEs to higher-dimensional bulk domains with concepts of trace finite element methods. A particular focus is given to the necessary steps to retain discrete analogues to conservation laws of the discretized PDEs. A high degree of geometric flexibility is achieved by using a level set representation of the geometry. We present theoretical results to prove stability of the method and to investigate its conservation properties. Convergence is shown in an energy norm and numerical results show optimal convergence order in bulk/surface H 1 {H^{1}} - and L 2 {L^{2}} -norms.