EHD instability of a cylindrical interface separating two couple-stress fluids.

This article is an attempt at examining the axi-symmetric and asymmetric streaming flows described by the CSF framework. A liquid that has microfibers implanted in it, like a fiber-reinforced composite substance, is so-called CSF. It is a system that consists of an endless vertical cylindrical interface that separates the two CSF structure. The CSFs are increasingly growing significant in modern manufacturing and technology, necessitating greater research into these fluids. An axial EF acts over the cylindrical contact in addition to the influence of CSF. The VPT is employed for the sake of convenience to minimize mathematical complexity. Combining the elementary linear equations of motion and the proper linear related BCs is the major procedure of the linear technique. A collection of physically dimensionless numbers is produced using a non-dimensional process. Subsequently, the requirements for hypothetical linear stability are developed. With the aid of the Gaster's theorem, the MS is applied in computing the dispersion relationships. After carefully examining a variety of effects on the stability investigation of the system at issue, it has been shown that the system is more unstable when a porous material is present than it would be without one. The resulting axisymmetric disturbance situation is more unstable. The linear techniques are depicted throughout a number of graphs.

Harnack inequality and one-endedness of UST on reversible random graphs.

We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al. (Ann Probab 29(1):1-65, 2001). Furthermore, we make progress towards a conjecture of Aldous and Lyons by proving that these conditions are fulfilled for strictly subdiffusive recurrent unimodular graphs. Finally, we discuss the behaviour of the random walk conditioned to never return to the origin, which is well defined as a consequence of our results.

Numerical and Experimental Study into Paper Compression Test.

The study aims to present the results of paper compression under an axial load. Different heights of samples subjected to compression were taken into account. The main goal of the analysis was to determine experimentally the maximum compression load. In addition, numerical models based on the finite element method (FEM) were validated to refer to empirical results. The performed numerical simulations were founded on Green-Lagrangian nonlinear equations for large displacements and strains. The progressive failure of the compressed orthotropic material after exceeding maximum stresses was based on Hill's anisotropy theory. Nonlinear calculations were conducted by using a typical Newton-Raphson algorithm for achieving a sequence convergence. The accuracy of the developed model was confirmed experimentally in compression tests. The technique of analysing the shape of the compressed paper sample on the basis of images recorded during the measurement was used. The obtained test results are directly applicable in practice, especially in the calculation of the mechanical properties of corrugated cardboard and in determining the load capacity of cardboard packaging. Knowing the maximum compressive stress that packaging paper can withstand allows packaging to be properly designed and its strength assessed in the context of the transport and storage of goods.

Corrosion of Reinforced A630-420H Steel in Direct Contact with NaCl Solution.

The deterioration of reinforced concrete structures in marine environments presents multiple problems due to the premature degradation of reinforced steel. This work aimed to study the corrosion of reinforced A630-420H steel when exposed to a 0.5 M NaCl solution. Although this carbon steel is the most widely used material for reinforced concrete structures in Chile, there is limited research on its resistance to corrosion when in contact with saline solutions. The electrochemical reactions and their roles in the corrosion rate were studied using linear sweep voltammetry, weight loss, scanning electron microscopy, and X-ray diffraction techniques. This analysis is unique as it used the superposition model based on mixed potential theory to determine the electrochemical and corrosion parameters. The outcomes of this study show that A630-420H steel has a higher corrosion rate than those of the other commercial carbon steels studied. This fact can be attributed to the competition between the cathodic oxygen reduction reaction and hydrogen evolution reaction, which also depends on the environmental conditions, exposure time, stabilization of the corrosion products layer, and presence of chloride ions. Additionally, the results under mechanical stress conditions show a brittle fracture of the corrosion product oriented longitudinally in the direction of the bend section, where the presence of pores and cracks were also observed. The corrosion products after corrosion were mainly composed of magnetite and lepidocrocite oxide phases, which is in concordance with the electrochemical results.

Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking.

We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

On the efficient evaluation of the azimuthal Fourier components of the Green's function for Helmholtz's equation in cylindrical coordinates.

In this paper, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large or complex. Furthermore, most state-of-the-art methods cannot be easily parallelized. In this paper, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as O(m), where m is the Fourier mode. Our algorithm's performance is independent of whether the wavenumber is real or complex. Furthermore, our algorithm is embarrassingly parallelizable.

Carrier mobility of one-dimensional vanadium selenide (V2Se9) monolayer and nanoribbon systems: DFT study.

Vanadium selenide (V2Se9) is a true one-dimensional (1D) crystal composed of atomic nanochains bonded by van der Waals (vdW) interactions. Recent experiments revealed the mechanical exfoliation of newly synthesized V2Se9. In this study, we predicted the electronic and transport properties of V2Se9through computational analyses. We calculated the intrinsic carrier mobility of V2Se9monolayers (MLs) and nanoribbons (NRs) using density functional theory and deformation potential theory. We found that the electron mobility of the two-dimensional (2D) (010)-plane ML of V2Se9is highly anisotropic, reachingµ2D,ze=1327cm2V-1s-1across the chain direction. The electron mobility of 1D NR systems in a (010)-plane ML of V2Se9along the chain direction continuously increased as the thickness increased from 1-chain to 4-chain NR (width below 3 nm). Interestingly, the electron mobility of 1D 4-chain NR along the chain direction (µ1D,xe=775cm2V-1s-1) was higher than that of a 2D (010)-plane ML (µ2D,xe=567cm2V-1s-1). These results demonstrate the potential of vdW-1D crystal V2Se9as a new nanomaterial for ultranarrow (sub-3 nm width) optoelectronic devices with high electron mobility.

Active thermal cloaking and mimicking.

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.

Dynamical landscape and multistability of a climate model.

We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyse their interplay. First, drawing from the theory of quasi-potentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states and investigate the most likely transition trajectories as well as the expected transition times between them. Second, harnessing techniques from data science, and specifically manifold learning, we characterize the data landscape of the simulation output to find climate states and basin boundaries within a fully agnostic and unsupervised framework. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, a third intermediate stable state in one of the two versions of PLASIM, the climate model used in this study. The combination of our approaches allows to identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically change the topography of the dynamical landscape of Earth's climate.

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls.

Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume constraint. When the volume of the gas is forced away from its typical value, the system undergoes a phase transition of the third order separating two phases (pulled and pushed). We prove this result (i) for the eigenvalues of one-cut, off-critical random matrices (log-gas in dimension d = 1 ) with hard walls; (ii) in arbitrary dimension d ≥ 1 for a gas with Yukawa interaction (aka screened Coulomb gas) in a generic confining potential. The latter class includes systems with Coulomb (long range) and delta (zero range) repulsion as limiting cases. In both cases, we obtain an exact formula for the free energy of the constrained gas which explicitly exhibits a jump in the third derivative, and we identify the 'electrostatic pressure' as the order parameter of the transition. Part of these results were announced in Cunden et al. (J Phys A 51:35LT01, 2018).

Analysis of tangential contact boundary value problems using potential functions.

This paper presents an analysis technique of high-order contact potential problems and its application to an elastic settlement analysis of a shallow foundation system subjected to a combined traction boundary condition. Closed-form solutions of potential functions are derived for an elastic half-space subjected to bilinear tangential traction boundary conditions over rectangular surface regions. Using the principle of superposition, the present solutions provide a means to form an approximate and continuous solution of elastic contact problems with higher-order tangential boundary conditions. As an application example, an elastic settlement analysis of a rigid footing founded on a dense granular soil is performed under a tangential traction boundary condition prescribed in an analogy with the stress equilibrium states of static sandpiles. A generalized solution approach to combined normal and tangential traction boundary value problems is discussed in the context of foundation engineering.

The extinction problem for a distylous plant population with sporophytic self-incompatibility.

In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means absorption at one of the axes. Despite connections with some classical probabilistic models (standard two-type Galton-Watson process, two-urn model), exact formulae for the probabilities of absorption seem to be difficult to come by and one must therefore resort to good approximations. In order to meet this task, we develop potential-theoretic tools and provide various sub- and super-harmonic functions which, for large initial populations, provide bounds which in particular improve those that have appeared earlier in the literature.

Corrosion Behaviors of Q345R Steel at the Initial Stage in an Oxygen-Containing Aqueous Environment: Experiment and Modeling.

The ingress of oxygen into pressure vessels used in oil & gas production and transportation could easily result in serious corrosion. In this work, the corrosion behaviors of Q345R steel at the initial stage in 1 wt.% NaCl solution were investigated using electrochemical techniques. The effects of oxygen concentration, temperature and pH on corrosion behaviors were discussed. Simultaneously, a numerical model based on the mixed potential theory was proposed. The results show that the proposed model accords well with the experimental data in the pH range from 9.0 to 5.0. In this pH range, the oxygen reduction reaction, H⁺ reduction, water reduction, and iron oxidation can be quantitatively analyzed using this model. However, this model shows a disagreement with the experimental data at lower pH. This can be attributed to the fact that actual area of reaction on the electrode is much smaller than the preset area due to the block effect resulted from hydrogen bubbles adsorbed on the electrode surface.

Mass of Spiral Galaxies by Means of a Maximum Disc Model / Masa de galaxias espirales por medio de un modelo de disco máximo / Massa de galáxias espirais por meio de um modelo de disco máximo

Abstract Maximum disc mass models for a set of spiral galaxies from the Ursa Major Cluster are presented. We construct the models using the Hunther method and the particular solutions are chosen in such a way that the circular velocities are adjusted very accurately to the observed rotation curves of some specific spiral galaxies. Under the maximum disc hypothesis, we consider that the rotation curves of the analyzed galaxies can be modeled with only the contribution of the disc. This implies that it is not necessary to consider the contribution ot the dark matter halo in the inner part of the spiral. In this way, the models reproduce the global behavior of the rotation curves in the great majority of galaxies. Producing good adjustments to calculate the total mass of these galaxies, and yielding values of the order of 1O10 M ☉. Based on the vertical stability criterion presented by Viera & Ramos-caro (2016), we find that all the galaxies analyzed present a vertically stable behavior. On the other hand, from the analysis of the epicyclic frequency we find that all the models exhibit mainly a radial stable behaviour except at the edge of the disc.

Resumen Presentamos modelos de masa de disco máximo para un conjunto de galaxias espirales del Cluster Ursa Major. Los modelos se obtienen por medio del método de Hunter y las soluciones particulares se eligen de tal manera que las velocidades circulares se ajustan muy exactamente a las curvas de rotación observadas de algunas galaxias espirales específicas. Bajo la hipótesis del disco máximo, suponemos que la masa del disco es lo más grande posible, en consonancia con la curva de rotación de la galaxia. Por lo tanto, la contribución de la masa del halo de la materia oscura se considera insignificante en las partes internas de las espirales. Los modelos reproducen la estructura general de las curvas de rotación en la mayoría de las galaxias, proporcionando buenos ajustes para calcular la masa total de estas galaxias obteniendo valores del orden de 1010 M ☉. Basados en el criterio de estabilidad vertical presentado por Vieira and Ramos-Caro (2016), encontramos que todas las galaxias analizadas presentan un comportamiento verticalmente estable. Por otro lado, a partir del análisis de la frecuencia epicíclica se observa que todos los modelos presentaron mayormente un comportamiento estable radial excepto en el borde del disco.

Resumo Apresentamos modelos de massa de disco máximo para um conjunto de galáxias espirais do Cluster Ursa Major. Os modelos são obtidos por meio do método Hunter e as soluções particulares são escolhidas de tal forma que as velocidades circulares são ajustadas com muita precisão às curvas de rotação observadas de algumas galáxias espirais específicas. Sob a hipótese de disco máximo, supomos que a massa do disco é tão grande quanto possível, consistente com a curva de rotação da galáxia. A contribuição de massa do halo da matéria escura é, portanto, assumida como insignificante nas partes internas das espirais. Os modelos reproduzem a estrutura geral das curvas de rotação na maioria das galáxias, proporcionando bons ajustes para calcular a massa total dessas galáxias obtendo valores da ordem de 1010 M ☉. Com base no critério de estabilidade vertical apresentado por Vieira and Ramos-Caro (2016), descobrimos que todas as galáxias analisadas apresentam um comportamento verticalmente estável. Por outro lado, a partir da análise da frequência epicíclica, descobrimos que todos os modelos apresentaram principalmente um comportamento estável radial, exceto na borda do disco.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space.

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical 'saddle-shaped' traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions.

High-Mobility Transport Anisotropy in Few-Layer MoO3 and Its Origin.

The novel two-dimensional semiconductors with high carrier mobility and excellent stability are essential to the next-generation high-speed and low-power nanoelectronic devices. Because of the natural abundance, intrinsic gap, and chemical stability, metal oxides were also recently suggested as potential candidates for electronic materials. However, their carrier mobilities are typically on the order of tens of square centimeters per volt per second, much lower than that for commonly used silicon. By using first-principles calculations and deformation potential theory, we have predicted few-layer MoO3 as chemically stable wide-band-gap semiconductors with a considerably high acoustic-phonon-limited carrier mobility above 3000 cm2 V-1 s-1, which makes them promising candidates for both electron- and hole-transport applications. Moreover, we also find a large in-plane anisotropy of the carrier mobility with a ratio of about 20-30 in this unusual system. Further analysis indicates that, because of the unique charge density distribution of whole valence electrons and the states near the band edge, both the elastic modulus and deformation potential are strongly directionally dependent. Also, the predicted high-mobility transport anisotropy of few-layer MoO3 can be attributed to the synergistic effect of the anisotropy of the elastic modulus and deformation potential. Our results not only give an insightful understanding for the high carrier mobility observed in few-layer MoO3 systems but also reveal the importance of the carrier-transport direction to the device performance.

FAST UPDATING MULTIPOLE COULOMBIC POTENTIAL CALCULATION.

We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position. Errors are bounded even after a large number of such shifts, making it practical for use in Monte Carlo Markov chain methods in molecular dynamics, computational astrophysics, computational chemistry, and other applications. The method uses truncated multipole expansions of the potential energy functional and a tree decomposition of the computational domain to reduce the computational complexity. Computational costs scale logarithmically in the size of the problem. Scaling, accuracy, and efficiency are confirmed with numerical experiments. The new method outperforms a direct calculation for moderate problem sizes.

On the solution of the Helmholtz equation on regions with corners.

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.