Curvature Dependence Research Articles

Surface element design of nanomaterials considering surface curvature dependence

Surface element design of nanomaterials considering surface curvature dependence

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Exploring the Properties of Curved Lipid Membranes: Comparative Analysis of Atomistic and Coarse-Grained Force Fields.

Curvature emerges as a fundamental membrane characteristic crucial for diverse biological processes, including vesicle formation, cell signaling, and membrane trafficking. Increasingly valuable insights into atomistic details governing curvature-dependent membrane properties are provided by computer simulations. Nevertheless, the underlying force field models are conventionally calibrated and tested in relation to experimentally derived parameters of planar bilayers, thereby leaving uncertainties concerning their consistency in reproducing curved lipid systems. In this study we compare the depiction of buckled phosphatidylcholine (POPC) and POPC-cholesterol membranes by four popular force field models. Aside from agreement with respect to general trends in curvature dependence of a number of parameters, we observe a few qualitative differences. Among the most prominent ones is the difference between atomistic and coarse grained force fields in their representation of relative compressibility of the polar headgroup region and hydrophobic lipid core. Through a number of downstream effects, this discrepancy can influence the way in which curvature modulates the behavior of membrane bound proteins depending on the adopted simulation model.

Geometry-induced friction at a soft interface

Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns are known to emerge. In this paper, we study the effect of geometry on the dynamical response of soft surfaces moving relative to each other. Using a simple experimental scheme, we measure friction between a highly bendable thin polymer sheet and a hydrogel substrate. At this soft and low-friction interface, we find a strong dependence of friction on the relative geometry of the two surfaces-a flat sheet experiences significantly larger friction on a spherical substrate than on flat or cylindrical substrate. We show that the stress developed in the sheet due to its geometrically incompatible confinement is responsible for the enhanced friction. This mechanism also leads to a transition in the nature of friction as the sheet radius is increased beyond a critical value. Our finding reveals a hitherto unnoticed mechanism based on an interplay between geometry and elasticity that may influence friction significantly in soft, biological, and nanoscale systems. In particular, it provokes us to reexamine our understanding of phenomena such as the curvature dependence of biological cell mobility.

Effects of liquid water injection on flame surface topology and propagation characteristics in spray flames: A direct numerical simulation analysis

The effects of water injection on flame surface topology and local flame propagation characteristics have been analyzed for statistically planar turbulent n-heptane spray flames with an overall (i.e., liquid + gaseous) equivalence ratio of unity using carrier-phase direct numerical simulations. Most fuel droplets have been found to evaporate as they approach the flame even though some droplets can survive until the burnt gas side is reached, whereas water droplets do not significantly evaporate ahead of the flame and the evaporation of water droplets starts to take place in the reaction zone and is completed within the burnt gas. However, the gaseous-phase combustion occurs predominantly in fuel–lean mode although the overall equivalence ratio remains equal to unity. The water injection has been found to suppress the fuel droplet-induced flame wrinkling of the progress variable isosurface under the laminar condition, and this effect is particularly strong for small water droplets. However, turbulence-induced flame wrinkling masks these effects, and thus, water injection does not have any significant impact on flame wrinkling for the turbulent cases considered here. The higher rate of evaporation and the associated high latent heat extraction for smaller water droplets induce stronger cooling effects, which weakens the effects of chemical reaction. This is reflected in the decrease in the mean values of density-weighted displacement speed with decreasing water droplet diameter. The weakening of flame wrinkling as a result of injection of small water droplets is explained through the curvature dependence of the density-weighted displacement speed. The combined influence of cooling induced by the latent heat extraction of water droplets and flame surface flattening leads to a decrease in volume-integrated burning rate with decreasing water droplet diameter in the laminar cases, whereas the cooling effects are primarily responsible for the drop in burning rate with decreasing water droplet diameter in the turbulent cases.

Cosmic strings arising in a self-dual Abelian Higgs model

In this note we construct self-dual cosmic strings from an Abelian Higgs model in two-dimension with a polynomial formation of the potential energy density. By integrating the Einstein equations, we obtain an equivalent form to the sources, which is a nonlinear elliptic equation with singularities and complicated exponential terms. We prove the existence of a solution governing strings in the broken symmetry category on the whole plane, and the multiple string solutions are valid under a sufficient condition imposed only on the total number of strings. The technique of upper–lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, a fixed-point theorem is used to study the properties of the nonlinear elliptic equation. Finally, we establish the sharp asymptotic estimate for the solutions at infinity and derive the dependence of the total gravitational curvature on the string number.

Experimental study of the effect of geodesic curvature on turbulent transport in magnetically confined plasma

An experimental study has demonstrated the impact of the geodesic curvature of the magnetic field line on turbulent ion-heat transport in magnetically confined plasma using the large helical device. Statistical analyses with corrected Akaike Information Criterion and multiple regression have revealed that the geodesic curvature indicates a dominant contribution to the ion-heat transport. Geodesic curvature dependence of the zonal-flow effect is evaluated by using a gyrokinetic-simulation-based reduced model. Then, the analysis implies a significant enhancement of the zonal-flow effect with a small geodesic curvature. These two independent analyses indicated the possibility of external zonal-flow control with the geodesic curvature of the magnetic field.

Intermediate morphology in the patterning of the crystalline Ge(001) surface induced by ion irradiation

We investigate the morphologies of the Ge(001) surface that are produced by bombardment with a normally incident, broad argon ion beam at sample temperatures above the recrystallization temperature. Two previously observed kinds of topographies are seen, i.e., patterns consisting of upright and inverted rectangular pyramids, as well as patterns composed of shallow, isotropic basins. In addition, we observe the formation of an unexpected third type of pattern for intermediate values of the temperature, ion energy, and ion flux. In this type of intermediate morphology, isolated peaks with rectangular cross-sections stand above a landscape of shallow, rounded basins. We also extend past theoretical work to include a second-order correction term that comes from the curvature dependence of the sputter yield. For a range of parameter values, the resulting continuum model of the surface dynamics produces patterns that are remarkably similar to the intermediate morphologies we observe in our experiments. The formation of the isolated peaks is the result of a term that is not ordinarily included in the equation of motion, a second-order correction to the curvature dependence of the sputter yield. Published by the American Physical Society 2024

Computing the influence of lipids and lipid complexes on membrane mechanics.

Methodology for extracting the spontaneous curvature, bending modulus, and neutral surface of a lipid bilayer is described. The "SPEX" method is a robust technique for computing the bilayer bending modulus while allowing for resolution of the spontaneous curvature of specific interacting lipids and complexes, and the dependence of spontaneous curvature on wavelength. The method is described referring to the publicly available MembraneAnalysis.jl software package.

Exploiting mechanisms for hierarchical branching structure of lung airway.

The lung airways exhibit distinct features with long, wide proximal branches and short, thin distal branches, crucial for optimal respiratory function. In this study, we investigated the mechanism behind this hierarchical structure through experiments and modeling, focusing on the regulation of branch length and width during the pseudoglandular stage. To evaluate the response of mouse lung epithelium to fibroblast growth factor 10 (FGF10), we monitored the activity of extracellular signal-regulated kinase (ERK). ERK activity exhibited an increase dependent on the curvature of the epithelial tissue, which gradually decreased with the progression of development. We then constructed a computational model that incorporates curvature-dependent growth to predict its impact on branch formation. It was demonstrated that branch length is determined by the curvature dependence of growth. Next, in exploring branch width regulation, we considered the effect of apical constriction, a mechanism we had previously proposed to be regulated by Wnt signaling. Analysis of a mathematical model representing apical constriction showed that branch width is determined by cell shape. Finally, we constructed an integrated computational model that includes curvature-dependent growth and cell shape controls, confirming their coordination in regulating branch formation. This study proposed that changes in the autonomous property of the epithelium may be responsible for the progressive branch morphology.

Abnormal condensation of water vapour at ambient temperature.

The homogeneous condensation of water vapor at ambient temperature is studied using molecular dynamics simulation. We reveal that there is a droplet size at the nanoscale where water droplets can be stabilized in the condensation process. Our simulations show that the growth of water droplets is dominated by collision and coagulation between small water droplets after nucleation. This process is found to be accompanied by exceptionally fast evaporation such that droplet growth is balanced by evaporation when water droplets grow to a critical size, approximately 12.5 Å in radius, reaching a stable size distribution. The extremely high evaporation rate is attributed to the curvature dependence of surface tension. Surface tension shows a significant decrease with decreasing droplet size below 20 Å, which causes the total free energy of nanoscaled water droplets to rise after collision and coagulation. Consequently, water droplets have to shrink via fast evaporation. The curvature dependence of surface tension is related to the dielectric ordering of water molecules near the surface of water droplets. Owing to fast evaporation, secondary condensation occurs, and many small water clusters form, ultimately exhibiting a bimodal distribution of water-droplet size.

Evolution of Flame Displacement Speed Within Flame Front in Different Regimes of Premixed Turbulent Combustion

A transport equation for the flame displacement speed evolution in premixed flames is derived from first principles, and the mean behaviours of the terms of this equation are analysed based on a Direct Numerical Simulation database of statistically planar turbulent premixed flames with a range of different Karlovitz numbers. It is found that the regime of combustion (or Karlovitz number) affects the statistical behaviour of the mean contributions of the terms of the displacement speed transport equation which are associated with the normal strain rate and curvature dependence of displacement speed. The contributions arising from molecular diffusion and flame curvature play leading order roles in all combustion regimes, whereas the terms arising from the flame normal straining and reactive scalar gradient become leading order contributors only for the flames with high Karlovitz number values representing the thin reaction zones regime. The mean behaviours of the terms of the displacement speed transport equation indicate that the effects arising from fluid-dynamic normal straining, reactive scalar gradient and flame curvature play key roles in the evolution of displacement speed. The mean characteristics of the various terms of the displacement speed transport equation are explained in detail and their qualitative behaviours can be expounded based on the behaviours of the corresponding terms in the case of 1D steady laminar premixed flames. This implies that the flamelet assumption has the potential to be utilised for the purpose of any future modelling of the unclosed terms of the displacement speed transport equation even in the thin reaction zones regime for moderate values of Karlovitz number.

Shape-driven confluent rigidity transition in curved biological tissues

Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those tissue-scale dynamics derive from local cell-level properties. Specifically, there has been little consideration of the interplay between local tissue geometry and cellular properties influencing larger-scale tissue behaviors. Here, we consider a simple two-dimensional computational vertex model for confluent tissue monolayers, which exhibits a rigidity phase transition controlled by the shape index (ratio of perimeter to square root area) of cells, on surfaces of constant curvature. We show that the critical point for the rigidity transition is a function of curvature such that positively curved systems are likely to be in a less rigid, more fluid, phase. Likewise, negatively curved systems (saddles) are likely to be in a more rigid, less fluid, phase. A phase diagram we generate for the curvature and shape index constitutes a testable prediction from the model. The curvature dependence is interesting because it suggests a natural explanation for more dynamic tissue remodeling and facile growth in regions of higher surface curvature. Conversely, we would predict stability at the base of saddle-shaped budding structures without invoking the need for biochemical or other physical differences. This concept has potential ramifications for our understanding of morphogenesis of budding and branching structures.

Simulated surface diffusion in nanoporous gold and its dependence on surface curvature

The morphological evolution of nanoporous gold is generally believed to be governed by surface diffusion. This work specifically explores the dependence of mass transport by surface diffusion on the curvature of a gold surface. The surface diffusivity is estimated by molecular dynamics simulations for a variety of surfaces of constant mean curvature, eliminating any chemical potential gradients and allowing the possible dependence of the surface diffusivity on mean curvature to be isolated. The apparent surface diffusivity is found to have an activation energy of ∼0.74 eV with a weak dependence on curvature, but is consistent with the values reported in the literature. The apparent concentration of mobile surface atoms is found to be highly variable, having an Arrhenius dependence on temperature with an activation energy that also has a weak curvature dependence. These activation energies depend on curvature in such a way that the rate of mass transport by surface diffusion is nearly independent of curvature, but with a higher activation energy of ∼1.01 eV. The curvature dependencies of the apparent surface diffusivity and concentration of mobile surface atoms is believed to be related to the expected lifetime of a mobile surface atom, and has the practical consequence that a simulation study that does not account for this finite lifetime could underestimate the activation energy for mass transport via surface diffusion by ∼0.27 eV.

Temperature- and curvature-dependent surface tensions and Tolman lengths for real fluids: A mesoscopic investigation

The curvature and temperature dependency of the liquid-vapor surface tension has a significant influence on the accurate prediction of the nanobubble/nanodrop nucleation process. In this work, a mesoscopic approach combining the pseudo-potential multiphase lattice Boltzmann method (LBM), the principle of dynamic similarity, and the van der Waals theory of corresponding states is adopted to quantitatively investigate the curvature and temperature dependency of the surface tension and Tolman length for real fluids (water and R134a). By Tolman length, we mean the distance from the surface of tension to the equimolar surface, which measures the extent by which the surface tension of a nanodrop/nanobubble deviates from the corresponding flat interface limit. We show that the Tolman lengths for flat liquid-vapor interfaces (δF) increase with the increase of temperature and are proportional to (1−Tr)−1.044. Equations for predicting surface tensions of water and R134a with effects of temperature and curvature radius taken into consideration are proposed. We demonstrate that the surface tensions increase while the Tolman lengths (δB) decrease with the increase of curvature for nanobubbles. For nanodroplets, however, the surface tensions decrease while the Tolman lengths (δD) increase with the increase of curvature. Effects of the equation of state for real fluids, which determines the interparticle interaction force in the pseudo-potential LBM, are also discussed. This mesoscopic approach can quantify the curvature dependency of liquid-vapor surface tensions for various real fluids in a wide temperature range with low computation costs, providing a new avenue for the accurate prediction of nucleation processes in micro-/nanoscale phase change heat transfer with applications to boiling, evaporation, and condensation.

Surface tension of cavitation bubbles

We have studied homogeneous cavitation in liquid nitrogen and normal liquid helium. We monitor the fluid content in a large number of independent mesopores with an ink-bottle shape, either when the fluid in the pores is quenched to a constant pressure or submitted to a pressure decreasing at a controlled rate. For both fluids, we show that, close enough to their critical point, the cavitation pressure threshold is in good agreement with the Classical Nucleation Theory (CNT). In contrast, at lower temperatures, deviations are observed, consistent with a reduction of the surface tension for bubbles smaller than two nanometers in radius. For nitrogen, we could accurately measure the nucleation rate as a function of the liquid pressure down to the triple point, where the critical bubble radius is about one nanometer. We find that CNT still holds, provided that the curvature dependence of the surface tension is taken into account. Furthermore, we evaluate the first- and second-order corrections in curvature, which are in reasonable agreement with recent calculations for a Lennard-Jones fluid.

On the curvature dependence of gradient damage models: Control and opportunities

Curvature dependence of gradient damage models is an often undesired side effect. It originates from a change of the orientation of the non-local gradient term. The resulting curvature dependence then implicitly affects the loading behaviour, the predicted fracture energy and also the damage distribution. Two extended approaches are presented here for curvature control and applied to a micromorphic gradient damage model and to a phase-field model for fracture. Both allow for a better control of the crack path and consider the Hessian of the non-local damage field by means of an additional micromorphic field, since curvature is connected to second derivatives. The first approach is based on an additional curvature-dependent potential within the Helmholtz energy and automatically fulfils the second law of thermodynamics. The second approach modifies the micro forces of the balance law that is responsible for the curvature dependence directly. Unlike the first approach, it allows to eliminate the curvature dependence completely. However, thermodynamic consistency has to be checked explicitly.

Tautomerization reactions of thiobarbituric acid: A detailed kinetic study using combined canonical variational transition state theory and QTAIM approach

AbstractThe kinetics of tautomerization reactions of thiobarbituric acid were thoroughly investigated at the B3LYP/6‐311+G(3df,2p) level of theory and elevated temperatures from 260 to 1000 K. The kinetic parameters were determined by employing canonical variational transition state theory (CVT). The quantum tunneling effect was included by centrifugal‐dominant small‐curvature semiclassical adiabatic ground‐state approximation method. Intrinsic reaction coordinate (IRC) analysis was performed to certify a unique connection from an obtained transition state configuration to optimized structures of reactant and products. The reaction forces and reaction force constants were computed across the IRC of each reaction. Then, using extremums of reaction forces, each reaction was partitioned into three stages containing reactant, transition state, and product stages. The extent of reactions was followed along with three reaction stages. The dependence of kinetic parameters and curvature of Arrhenius plots on temperature were investigated and discussed in the framework of CVT. To further unveil the mechanism of the reactions, the quantum theory of atoms in molecules was employed. To do this aim, QTAIM descriptors on the bond critical point (BCP) of involved bonds including the density of electrons, Laplacian of the density of electrons, Lagrangian kinetic energy, potential energy, and energy density were computed and surveyed along with reaction extent through IRC.

Technology and equipment of roll straightening of sheet metal

The features of the editing technology, possible defects of sheet metal and piece blanks of complex configuration are presented. The main schemes and designs of sheet‑straightening machines are considered, as well as the main directions of improvement of LSM designs and editing technologies are highlighted. The analysis of the process of roll straightening is presented taking into account the phenomena occurring in a metal undergoing alternating loading with decreasing amplitude (interaction of elastic and plastic deformation, Bauschinger effect, etc.). The parabolic dependence of the residual curvature on the yield strength is noted. The obtained data were used in the design of the roll straightening complex and the technology of straightening sheet blanks of complex configuration.

Quasi-two-dimensional bacterial swimming around pillars: Enhanced trapping efficiency and curvature dependence.

Microswimmers exhibit more diverse behavior in quasi-two dimensions than in three dimensions. Such behavior remains elusive due to the analytical difficulty of dealing with two parallel solid boundaries. The existence of additional obstacles in quasi-two dimensional systems further complicates the analysis. Combining experiments and hydrodynamic simulations, we investigate how the spatial dimension affects the interactions between microswimmers and obstacles. We fabricated microscopic pillars in quasi-two dimensions by etching glass coverslips and observed bacterial swimming among the pillars. Bacteria got trapped around the circular pillars and the trapping efficiency increased as the quasi-two-dimensionality was increased or as the curvature of the pillars was decreased. Numerical simulations of the simplest situation of a confined squirmer showed anomalous increase of hydrodynamic attractions, establishing that the enhanced interaction is a universal property of quasi-two-dimensional microhydrodynamics. We also demonstrated that the local curvature of the obstacle controls the trapping efficiency by experiments with elliptic pillars.