An analytical and numerical study of capillary menisci

В работе рассмотрены математические модели осесимметричных капиллярных менисков — лежащая и висящая капли, развернутый мениск, учитывающие размерную зависимость поверхностного натяжения. Доказаны теоремы существования и единственности решений задач, описывающих равновесные поверхности менисков. Разработаны и протестированы эффективные численные методы, предназначенные для приближенного расчета профилей менисков. На языке «Wolfram Language» написана компьютерная программа, с помощью которой проведены масштабные вычислительные эксперименты по выявлению степени и характера влияния параметров моделей на равновесную форму каждого из рассматриваемых менисков In the current paper we consider the mathematical models of axisymmetric capillary menisci — sessile and pendant drops, rolled out meniscus, taking into account the size dependence of surface tension. Existence and uniqueness theorems for solutions of problems describing equilibrium meniscus surfaces are proved. Effective numerical methods have been developed and tested for the approximate calculation of meniscus profiles. A computer program is written in the Wolfram Language, with the help of which large-scale computational experiments were carried out to reveal the degree and nature of the influence of the model parameters on the equilibrium shape of each type of menisci.

New historical records about the construction of the Arch of Ctesiphon and their impact on the history of structural engineering

A piece of historical research about the construction of the ancient Arch of Taq-iKisra, part of the imperial palace of the Sasanian Empire in the city of Ctesiphon, has been carried out. The information obtained, an analysis using graphic statics, the use of a physical model with hanging chains, and an ad hoc optimization program written in MATLAB have shown that the designer of this sixth century ad arch, a Byzantine named Farghán, was aware of the effects of the uneven distribution of loads and the differential settlements of the foundations on the equilibrium shape of structures working exclusively in compression and was able to control them. This discovery predates the earliest statement about the link between the shape of the catenary and that of an arch, by Robert Hooke, by eleven centuries and makes this building relevant not only because of its historical, archaeological, and architectural importance, but also because of its importance in the history of structural engineering. The building is currently in need of restoration to stop its collapse, and an awareness of the way it was designed could be of practical use for the definition of the intervention needed.

AN EFFICIENT IDENTIFICATION OF RED BLOOD CELL EQUILIBRIUM SHAPE USING NEURAL NETWORKS

This work of applied mathematics with interfaces in bio-physics focuses on the shape identification and numerical modelisation of a single red blood cell shape. The purpose of this work is to provide a quantitative method for interpreting experimental observations of the red blood cell shape under microscopy. In this paper we give a new formulation based on classical theory of geometric shape minimization which assumes that the curvature energy with additional constraints controls the shape of the red blood cell. To minimize this energy under volume and area constraints, we propose a new hybrid algorithm which combines Particle Swarm Optimization (PSO), Gravitational Search (GSA) and Neural Network Algorithm (NNA). The results obtained using this new algorithm agree well with the experimental results given by Evans et al. (8) especially for sphered and biconcave shapes.

Shape of dislocation line in stochastic shear stress field

The shape of the dislocation line in the stochastic shear stress field in the glide plane was studied using the method of discrete dislocation dynamics. Stochastic shear stresses can occur due to the distortion of the crystal lattice. Such distortion may exist, for example, in a solid solution. Different atoms in a solid solution induce atomic size misfit and elastic modulus misfit into crystal lattice. These misfits result in crystal lattice distortions which varies spatially. The distortions are the origin of internal stresses in the lattice. Such internal stress in certain location has stochastic value normally distributed. The particular case of such stresses is shear stress distribution in the glide plane. The special method was developed to model such stress distribution. The stochastic shear stress field results in movement of different segments of dislocation line to form its equilibrium shape. The important characteristic parameters of the equilibrium shape can be measured by numerical methods. This shape also includes a "long-wavelength" component that has a non-zero amplitude and was formed without thermal activation. The shape of the dislocation line determines to some extent the yield strength of the material. Thus, the study of dislocation line shape and modeling its formation in the field of stochastic shear stresses can help to determine the yield strength of multicomponent alloys, especially multi-principal element alloys. Keywords: dislocation, discrete dislocation dynamics, shear stresses.

Shape control of size-selected naked platinum nanocrystals

Controlled growth of far-from-equilibrium-shaped nanoparticles with size selection is essential for the exploration of their unique physical and chemical properties. Shape control by wet-chemistry preparation methods produces surfactant-covered surfaces with limited understanding due to the complexity of the processes involved. Here, we report the controlled production and transformation of octahedra to tetrahedra of size-selected platinum nanocrystals with clean surfaces in an inert gas environment. Molecular dynamics simulations of the growth reveal the key symmetry-breaking atomic mechanism for this autocatalytic shape transformation, confirming the experimental conditions required. In-situ heating experiments demonstrate the relative stability of both octahedral and tetrahedral Pt nanocrystals at least up to 700 °C and that the extended surface diffusion at higher temperature transforms the nanocrystals into equilibrium shape.

On the Role of Curved Membrane Nanodomains and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Comparative analysis of the effect of Ca and Mg-Al modification on the composite inclusions in S50C Die steel

At present, the effective ways to improve the cleanliness of S50C die steel are Ca or Mg-Al treatment processes. In order to explore the effect difference of two kinds of modification process of S50C killed steel, evaluate the industrial application prospect of the two processes, and clarify the modification mechanism. In this paper, the advantages of Mg-Al modification are demonstrated from the aspects of theoretical basis and actual sample modification effect. The thermodynamics and kinetics of inclusion precipitation, composition, morphology, and distribution are analyzed. The results show that: the precipitation temperature of MnS in S50C die steel is 1686 K, the corresponding solid-phase rate is 0.98. In Mg-Al modification, when the Al content is 332 ppm, the Mg content should be controlled below 14.1 ppm. When the Al content is higher than 0.02%, the Ca content should be controlled below 28.7 ppm. Kinetic calculations show that the equilibrium shape size of MnS is in the range of 0.3‑1.4 µm. Both modifications increase the nucleation rate of inclusions and control the shape and size of inclusions by pre-precipitation. Ca treatment is preventing the formation of large inclusions by forming calcium aluminate. Mg can provide more uniform nucleation sites and form smaller inclusions.

PREDICTION OF EQUILIBRIUM SCOUR HOLES USING OPTIMIZATION PROCEDURES

This paper presents an optimization procedure that finds the equilibrium scour depth under a pipeline. Even though much knowledge on scour is available for the most typical marine structures such as a vertical circular monopile of a horizontal pipelines the calculation of the scour depth complex and time-consuming as the transient solution is often modelled as well. In this paper we present a optimization procedure that combined with a computational fluid dynamics, and a model of the bed load finds the equilibrium shape of a scour hole. This can potentially speed up the calculation of the shape of the equilibrium scour hole with a factor of 100. However, it comes with a coast as we will not model the transition and the time scale of the scour hole development.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/LpKq9Twj7zo

Cohesive Channel Response to Watershed Urbanization: Insights from the Sand River, Aiken SC

Stream channel degradation is among the most widely documented symptoms of urban stream syndrome arising from watershed urbanization. Nevertheless, our present understanding of space and time scales associated with channel response to urbanization is poorly constrained and largely limited to assessments of non-cohesive systems. The purpose of this study is to assess the evolution of a cohesive, ephemeral river channel in response to watershed urbanization. The assessment of historical images document the stable, pre-urbanized channel conditions from 1870 to 1930. Historical assessments revealed a 131% increase in urbanized watershed area from 1930 to 1992, and a minimal increase in urbanized extent from 1992 to 2012. A 2012 lidar dataset was used to generate the modern long-channel profile, to reconstruct cross-channel profiles observed in 2002, and to estimate the volume flux of sediment removed from the channel from 1930 to 1992, and from 1992 to 2012. The long-channel profile reveals incision of up to 35 m in response to urbanization from 1930 to 1992. Cross-channel profiles reveal incision and widening of 2.5 and 3 m, respectively, from 2002 to 2012. Volume flux estimates indicate erosion rates of 9000 m3/yr during the first 62 years of the study period, and a flux of 4000 m3/yr after installation of stormwater control measures in 1992. Collectively, our findings highlight a cohesive channel that has undergone substantial incision and widening at a rate of ~0.20 m/yr since 1930, and the channel continues to adjust. Hence, we contend that the channel has not yet attained a new equilibrium “shape” at 82 years after peak land use change within the watershed, and that the channel will continue to adjust its shape until this new balance is achieved.