Constant Surface Research Articles

Performance of loosely skirted square footing resting on reinforced sand under vertical concentric and eccentric loading

ABSTRACT The present study investigates the performance of loosely skirted square footing resting on multi-layered geo-grid reinforced medium dense sand under vertical concentric and eccentric loading through a series of laboratory model tests. The load eccentricity (e) is varied as 0, 0.1B, 0.15B, 0.2B (where B is the width of the footing). Parametric variations like depth of skirt (d = 1B, 1.5B, 2B), number of geo-grid layers (N; varies with variation of depth of skirt), spacing between horizontal reinforcements (Y = 0.25B,0.5B,0.75B,1B) have been investigated with a constant surface dimension D/B = 1(D is the top surface dimension of the skirt). The test results show that load intensity increases significantly with the increment of skirt depth and approaches the optimum value at d/B = 2 for a spacing of 0.25B for both the loading conditions. However this increment is less prominent for footing with only skirt and without reinforcements. Increment in number of horizontal reinforcements too showed an increase in bearing capacity and reduction in settlement. Effect of eccentricity on load intensity for both concentric and eccentric loading has been compared in the present experimental work. The improvement in bearing capacity and reduction in settlement of the footing has also been assessed in terms of bearing capacity ratio (BCR) and settlement reduction factors (SRF). Even while comparing the economic aspects, geogrid skirts prove to be a viable alternative to the conventional skirts

Spherical circles and constant angle surfaces

In this present paper, we obtain a general version of constant angle surfaces constructed concerning any direction in three dimensional Euclidean space. This constant angle surface is the special case of developable ruled surfaces whose direction is a spherical circle. Here, we obtain the constant angle surfaces by taking the circles (small circles) whose radius is less than the radius of the sphere, as the base curve. Also, the relationship between the isophote curve and this surface and its physical interpretation is mentioned. When we beam from a light source in a constant direction, the intensity of the light will be the same at every point on this constant angle surface. This study is very important in terms of associating optics, a branch of physics, with geometry, a branch of mathematics. Finally, we classify the singular points of these constant angle surfaces.

Symmetries of Vacuum Spacetimes with a Compact Cauchy Horizon of Constant Nonzero Surface Gravity

We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a nonzero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983 under the assumption on the surface gravity and generalises previous results due to Moncrief–Isenberg and Friedrich–Rácz–Wald, where the generators of the Cauchy horizon were closed or densely filled a 2-torus. Consequently, the maximal globally hyperbolic vacuum development of generic initial data cannot be extended across a compact Cauchy horizon with surface gravity that can be normalised to a nonzero constant. Our result supports, thereby, the validity of the strong cosmic censorship conjecture in the considered special case. The proof consists of two main steps. First, we show that the Killing equation can be solved up to infinite order at the Cauchy horizon. Second, by applying a recent result of the first author on wave equations with initial data on a compact Cauchy horizon, we show that this Killing vector field extends to the globally hyperbolic region.

Determination of constant diffusion coefficient for error function solution of diffusion equation using film-roll method

The error function solution of the diffusion equation with the constant surface concentration was derived by the heat kernel to determine the constant diffusion coefficient for diffusion satisfying the infinite dye-bath condition. For the sublimation diffusion of disperse dye in paste into PET film using the film-roll method, the constant surface concentration was determined from the concentration distribution, and the diffusion coefficients of each layer were obtained by the constant surface concentration from the error function solution. When comparing the diffusion coefficients between the layers and comparing the mean diffusion coefficients for different times at a specific temperature, the constant surface concentrations determined from the quadratic regression curves for concentration–distance plots were more appropriate than those determined from the steady-state concentration distributions, which was also confirmed by the plots of concentrations obtained from the error function solution. At a specific temperature, the average of the mean diffusion coefficients obtained by the constant surface concentration of the quadratic regression curve at three specific times matched well with the constant total-amount diffusion coefficient obtained by the slope of the linear regression line for the plot of total amount against square root of time, which was confirmed by their Arrhenius plots.

Ab initio supported study on the selective adsorption-induced microstructural difference of (Ti,Al)N/TiN and (Ti,Al)N/ZrN multilayers

Interface structure is essential for the mechanical properties of multilayers. Here, the effect of deposition process on the interface structure of arc-evaporated (Ti,Al)N/TiN and (Ti,Al)N/ZrN multilayers is studied by a combination of ab initio calculations and experiments. Based on x-ray diffractions and transmission electron microscope investigations, both multilayers with close modulation ratio and period reveal face centered cubic (fcc) structure with coherent interfaces. Nevertheless, thin (Ti,Zr)N layers are formed near the interfaces in (Ti,Al)N/ZrN multilayer, but are absent in (Ti,Al)N/TiN multilayer. Ab initio calculations suggest the selective absorption of Ti and Zr adatoms onto the surface of (Ti,Al)N/ZrN multilayer during deposition, which leads to the formation of (Ti,Zr)N-rich layers by interface. However, (Ti,Al)N/TiN multilayer is predicted to have almost constant surface adsorption of different adatoms.

Studying the performance of phase change heat storage enhanced by ultrasonic energy

The ultrasonic wave could propagate in elastic media and bring ultrasonic flow which could effectively strengthen the convective heat transfer. Thus, various research works have been carried out on the enhancement effect for its potential future application. This work studied the influence of the acoustic flow effect on the melting process of phase change material. For the first, the influence of ultrasonic acting position on enhancement effect was examined. Then, the effectiveness of ultrasonic energy on enhancing heat storage process was discussed. The present work was also compared with other representative studies. The results show that when the side surface of the container is a constant temperature heating surface, the ultrasonic vibration surface at the bottom of the container has best melting performance of phase change heat storage. Then, a new evaluation method of heat transfer enhancement was proposed. The new method cannot only measure the improvement of melting performance, but also clearly measure the relationship between the improvement of melting performance and the consumption of ultrasonic energy. Finally, by contrast and analysis with representative studies, the development potential and further research direction of ultrasonic enhanced phase change heat storage are clarified. This work can provide reference for the further application of active heat transfer enhancement technology in the field of phase change heat storage.

Nuclear shapes are geometrically determined by the excess surface area of the nuclear lamina.

Introduction: Nuclei have characteristic shapes dependent on cell type, which are critical for proper cell function, and nuclei lose their distinct shapes in multiple diseases including cancer, laminopathies, and progeria. Nuclear shapes result from deformations of the sub-nuclear components-nuclear lamina and chromatin. How these structures respond to cytoskeletal forces to form the nuclear shape remains unresolved. Although the mechanisms regulating nuclear shape in human tissues are not fully understood, it is known that different nuclear shapes arise from cumulative nuclear deformations post-mitosis, ranging from the rounded morphologies that develop immediately after mitosis to the various nuclear shapes that roughly correspond to cell shape (e.g., elongated nuclei in elongated cells, flat nuclei in flat cells). Methods: We formulated a mathematical model to predict nuclear shapes of cells in various contexts under the geometric constraints of fixed cell volume, nuclear volume and lamina surface area. Nuclear shapes were predicted and compared to experiments for cells in various geometries, including isolated on a flat surface, on patterned rectangles and lines, within a monolayer, isolated in a well, or when the nucleus is impinging against a slender obstacle. Results and Discussion: The close agreement between predicted and experimental shapes demonstrates a simple geometric principle of nuclear shaping: the excess surface area of the nuclear lamina (relative to that of a sphere of the same volume) permits a wide range of highly deformed nuclear shapes under the constraints of constant surface area and constant volume. When the lamina is smooth (tensed), the nuclear shape can be predicted entirely from these geometric constraints alone for a given cell shape. This principle explains why flattened nuclear shapes in fully spread cells are insensitive to the magnitude of the cytoskeletal forces. Also, the surface tension in the nuclear lamina and nuclear pressure can be estimated from the predicted cell and nuclear shapes when the cell cortical tension is known, and the predictions are consistent with measured forces. These results show that excess surface area of the nuclear lamina is the key determinant of nuclear shapes. When the lamina is smooth (tensed), the nuclear shape can be determined purely by the geometric constraints of constant (but excess) nuclear surface area, nuclear volume, and cell volume, for a given cell adhesion footprint, independent of the magnitude of the cytoskeletal forces involved.

Analysis of the chosen thermal and flammability parameters of dried sewage dust

The hazardous sludge disposal process in the form of landfills requires the determination inter alia of the flammable and explosion properties of dried sewage sludge dust, which has the ability to ignite and spontaneously combust when stored in silos. At a constant furnace surface temperature, the minimum ignition temperature of the sludge dust layer with a layer thickness of 5 mm is 270 °C, and for a layer thickness of 12.5 mm it is 250 °C. Two selected fire extinguishing powders for Class A, B, C and D fires were used in the study to determine the possibility of reducing the susceptibility of dried wastewater to ignition from heated surface, self-ignition and explosion parameters. The most effective extinguishing powder was ABC Favorit, which increased the value of the minimum ignition temperature of the layer (5 mm thick) to 360 °C and the spontaneous ignition temperature of the sludge with this powder increased by 22 °C at 169.6 cm3 in comparison to the sludge without extinguishing powder, respectively. The lowest self-ignition temperature of 136 °C was recorded for the largest tested volume (169.6 cm3) for dried sewage dust without any fire extinguishing powders. The biggest values of pmax and (dp/dt)max dried sewage dust were recorded 4.8 bar and 113 bar/s respectively. By analysing the obtained test results, it can be assumed that dried sewage dust is a combustible material with properties similar to biomass.

Influence of elevated surface temperature on the formability in cold forming of aluminum alloy sheets

In recent decades, deep drawing has been widely used in the automotive industry for producing lightweight car body components of 5xxx and 6xxx aluminum alloys. Although sheets of these alloys are usually deep-drawn at room temperature, heat generated by friction and plastic deformation may locally increase the surface temperature of the drawing tools during the serial production of components. Therefore, this work investigates the influence of elevated surface temperatures of the tool on the formability of commercial hotmelt-lubricated 1.5 mm-thick EN AW-5182 and EN AW-6016-T4 sheets. Deep drawing experiments were performed at different constant surface temperatures between room temperature (RT) and 80 °C using a cross-shaped tool with open die. With increasing surface temperature, the maximum drawing depth – that was considered as indicator for the formability – decreased by about 21 % and 28 % for EN AW-6016-T4 and EN AW-5182, respectively. Tribological experiments performed using a pin-on-plate tribometer confirmed this trend. The results clearly showed that the coefficient of friction (COF) between the sheet and the tool significantly increase at elevated surface temperature; the most notable increase of the COF occurred between 40 °C and 60 °C.

An isothermal constant surface area horizontal helical coil under natural convection and radiative heat loss: A CFD study

This paper presents a numerical analysis of a horizontally oriented constant surface area isothermal helical coil under natural convection heat transfer and surface radiation. Numerical computationsare carried out in the laminar regime of Rayleigh number (104 ≤ Ra ≤ 108), surface emissivity (0 ≤ ε ≤ 1), and geometrical parameters of the helical-coil, like diameter of the coil (8 ≤ D/d ≤ 24), pitch (3 ≤ p/d ≤ 7.5), and coil height (40 ≤ H/d ≤ 60) to study the heat transfer characteristics. This study is used for effectively designing the helical coils, which are typically manufactured at an extremely high temperature. The numerical computation has been validated by comparing the average Nusselt number (Nu) with the previous experimental results. Temperature-dependent fluid properties are incorporated to achieve precise results over a wide range of temperatures. The effect of the geometrical parameters on the heat transfer characteristics has been depicted graphically in terms of average Nu, relative convection and radiation heat transfer rate, and the temperature profile. It is found that the relative contribution of radiative heat transfer is 87.8% at an emissivity of 0.9 and Ra of 10(Ali, 19944), whereas, for an emissivity of 0.1 and Ra of 10(Moawed, 20058), the relative contribution of radiation heat transfer is only 6.4%. Lastly, a correlation has been developed for the average Nu based on all the pertinent parameters which can be beneficial to the engineers in the industry and also academic researchers. The developed correlation has been used to predict the cooling curve of the helical coil in certain situations.

A test of invariance of dark matter halo surface density using multiwavelength mock galaxy catalogues

ABSTRACT A large number of observations have shown that the dark matter halo surface density, given by the product of halo core radius and core density, is nearly constant for a diverse suite of galaxies. Although this invariance of the halo surface density is violated at galaxy cluster and group scales, it is still an open question on whether the aforementioned constancy on galactic scales can be explained within Lambda cold dark matter (ΛCDM). For this purpose, we probe the variation of halo surface density as a function of mass using multiwavelength mock galaxy catalogues from ΛCDM simulations, where the adiabatic contraction of dark matter haloes in the presence of baryons has been taken into account. We find that these baryonified ΛCDM haloes were best fitted with a generalized Navarro–Frenk–White profile, and the halo surface density from these haloes has a degeneracy with respect to both the halo mass and the virial concentration. We find that the correlation with mass when averaged over concentration is consistent with a constant halo surface density. However, a power-law dependence as a function of halo mass also cannot be ruled out.

Viscoelastic boundary layer analysis of constant surface temperature plate embedded in saturated porous media

AbstractMathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field. Therefore, the present study is concerned with the effects of forced convection of the viscoelastic boundary layer on a horizontal plate embedded in saturated porous media subjected to constant surface temperature. The study explores the profiles of shear stress, velocity, temperature, and heat transfer coefficient. The governing equations in nondimensional forms are obtained by using a model of Darcy–Forchheimer–Brinkman and finally are solved numerically by using bvp4c with MATLAB package. The results of the numerical solution show an insignificant rise in the distribution of the velocity boundary layer and shear stress profile as the Darcy parameter is increased, while a decrease in the temperature and Nusselt numbers are found. On the other hand, as the viscoelastic parameter is increased, the Darcy parameter shows a reverse response. Finally, insignificant increases in profiles of boundary layer velocity, temperature, shear stress, and Nusselt number are observed at high values of the Forchheimer number.

Effect of geometric deviations on the strength of additively manufactured ultralight periodic shell-based lattices

Lightweight shell-based lattice structures with various multifunctional applications can be fabricated with limited manufacturing constraints, thanks to the advancements of additive manufacturing technologies. However, there is always a geometric deviation between the 3D digital model and the additively manufactured lattice structure. In some cases, the geometric deviations may be as small as the machine accuracy, but they would cause a significant decrease in the strength of the lattice. In other cases, the lattice may not be so sensitive to geometric deviations. The sensitivity of lattice structures to the geometric deviations depends on their constituent material, loading condition, relative density, and the geometry of the unit-cell. To understand this, buckling failure should be considered beside yielding. This paper presents a local failure analysis of the ultralight shell-based lattices and explores the effects of the aforementioned factors on their strength and failure mechanism under compression. The main finding of this research is that unlike the high-relative density lattices, which are not sensitive to geometric deviations, in the design of ultralight shell-based lattices (with relative densities lower than 26 %), beside the loading conditions, the constituent material and relative density should be considered, as well. For example, for a 10 % relative density lattice designed for a triaxial compressive macroscopic state of stress, if the base material is stainless steel, the minimal surface is the optimal unit-cells, while if it is made of pyrolytic carbon, a constant mean curvature surface with a certain value of mean curvature other than zero is optimal. However, for shell-based lattices with relative densities higher than 26 %, the geometric deviation does not influence the lattice strength and thus the optimal geometry can be designed without regard to the base material and relative density.

Theoretical and Numerical Constant Mean Curvature Surface and Liquid Entry Pressure Calculations for a Combined Pillar–Pore Structure

Modern microfabrication techniques have led to a growing interest in micropillars and pillar–pore structures. Therefore, in this paper a study of the liquid entry pressure of a hydrophobic pillar–pore structure and the corresponding liquid–gas interface shape for the pressurized liquid is presented. We theoretically analysed the constant mean curvature problem for the rotationally symmetric case and determined an analytical expression for the liquid entry pressure of a hydrophobic pillar–pore structure. Furthermore, the shape of the liquid–gas interface as well as a formula for the location of the minimum were derived. The results are useful for designing geometries with specific properties, such as preventing or facilitating liquid intrusion into rough structures. We compared these results to multiphase lattice Boltzmann simulations where equilibrium contact angles in the range of 157∘ to 102∘ were tested. In our further analysis, we compared theoretical findings from previous works to our lattice Boltzmann simulations. The presented cases can serve as a benchmark for the development and validation of numerical multiphase models.

120 Determining moisture content in equine arena footing on-farm

Arenas are important fixtures on equine farms as they provide constant surfaces for horses to work and train on. Water serves to help control dust issues and increase the shear strength of the footing. Some footing companies indicate an optimal moisture content for their product, but without a method to determine the moisture content, arena managers and owners rely on dust production to decide when to add more water, which is an unreliable method. Oven drying of soil/arena footing is a common method for determining moisture content in the research settings but is not a practical solution on farms. This study sought to compare 3 different methods for determining moisture content in arena footing: oven drying, microwave drying, and a FieldScout TDR 350 Soil Moisture Meter. The 3 methods were tested with 3 footing types: a straight sand footing, a sand and fiber mixture, and a sand with organic material mixture. The oven drying method consisted of drying 3 samples of at least 30 g in a 100C oven for 24hrs, the microwave method also used 3 samples of at least 30 g that were dried in a standard microwave oven until all water evaporated, and the TDR moisture content method utilized the average of 3 TDR measurements in the footing. Paired t-tests were used to compare the microwave and the TDR methods to the oven drying method for each footing type. Though the paired t-test analysis for the microwave drying method determined statistically significant differences for the sand with fiber (P < 0.001)and the sand (P < 0.001), nominally the difference in the moisture contents of the 3 footings are unlikely to have an impact in on-farm use as all were within 0.6% of the oven-dried moisture contents. In comparison, all of the paired t-tests determined statistically significant difference for the TDR method (sand with organic material P < 0.001, sand with fiber P < 0.001, and sand P = 0.003). The TDR determined moisture contents were at least 1.6% higher than the moisture contents determined with the oven drying method. Overall, the microwave drying method provides a viable on-farm solution for determining the moisture content of footing, provided that the footing material is microwave safe.

Some Characterizations of Translation Surface Generated by Spherical Indicatrices of Timelike Curves in Minkowski 3-space

In this paper, we study translation surfaces generated by spherical indicatrices of timelike curves in Minkowski 3-space and find necessary and sufficient conditions for the translation surfaces to be flat or minimal. Further, we obtain necessary and sufficient conditions for generating curves of the translation surfaces to be geodesic, asymptotic line and line of curvature. Finally for such translation surfaces we obtain the axis when they are constant angle surfaces.

MATERIAL TRANSFER DURING THE COMBUSTION OF TARFAYA OIL SHALE OR JERADA COAL (MOROCCO), SIMULATION AND DIFFUSION LAWS

The study of the oxidation or combustion of oil shale or coal is important because it is the basis of the exploitation process to obtain the energy to be converted This exploitation involves several physical phenomena such as heat transfer, matter transfer and others. The laws of matter transfer have been adopted The respective combustion of two national energy materials (Morocco), namely the Z4 layer of oil shale from the Tarfaya deposit and the coal from Jerada, was the subject of this study in an isothermal regime. First, we were interested in mentioning the average temperatures remarkable for this combustion which turned out to be slightly different, then we started a study of the combustion of parallelepipeds with variable dimensions of the two previous materials and we presented a simulated theoretical model by comparing it with the experimental results. This simulated model allowed us to discuss the reactivity of the two energetic materials. Combustion was followed in an isothermal regime using a muffle furnace from 400°C to 800°C for fine-grained samples (&lt; 0.5 mm) and for grains. The noticeable loss of mass for oil shale at 500°C, and for coal at 600°C in the first instance. These remarkable temperatures were used to study the effect of parallelepiped dimensions, which have constant height (z = 2 mm) and square side surfaces (x = y = 2, 4, 6, 8, 10 mm). Several results and interpretations were noted when comparing the combustion of coal and oil shale.

Anisotropic compact stars in complexity formalism and isotropic stars made of anisotropic fluid under minimal geometric deformation (MGD) context in f(mathscr {T}) gravity-theory

In this paper, we present an anisotropic solution for static and spherically symmetric self-gravitating systems by demanding the vanishing of the complexity factor (Herrera in Phys Rev D 97:044010, 2018) along with the isotropization technique through the gravitational decoupling (GD) approach (Ovalle in Phys Rev D 95:104019, 2017) in f(mathscr {T})-gravity theory. We begin by implementing gravitational decoupling via MGD scheme as the generating mechanism to obtain anisotropic solutions describing physically realizable static, spherical self-gravitating systems. We adopt the Krori–Barua ansatz and present two new classes of stellar solutions: the minimally deformed anisotropic solution with a vanishing complexity factor and the isotropic solution via gravitational decoupling. We demonstrate that both classes of solutions obey conditions of regularity, causality and stability. An interesting feature is the switch in trends of some of the thermodynamical quantities such as effective density, radial and transverse stresses at some finite radius, r=r_*, depending on different values of the decoupling constant beta . We show that gravitational decoupling via the vanishing complexity factor enhances the stability of the stellar fluid surrounding the core’s central areas. By analyzing the effect of the decoupling constant beta on the M-Y_{TF} plots, (where Y_{TF} denotes the complexity factor) derived from both solutions, we find that a small contribution from the complexity factor leads to the prediction of lower maximum mass of a self-gravitating compact star via gravitational decoupling in f(mathscr {T})-gravity compared to their pure f(mathscr {T})-gravity counterparts. Furthermore, we have also determined the impact of decoupling constant beta and surface density on predicted radii via M{-}R for some known compact objects.

Standard-state entropies and their impact on the potential-dependent apparent activation energy in electrocatalysis

The apparent activation energy, Eapp, is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials. Recently, the electrocatalysis community adopted the concept of Eapp and combined it with the Butler-Volmer theory. Certain observations though, such as potential-dependent fluctuations of Eapp, are yet surprising because they conflict with the proposed linear decrease in Eapp with increasing overpotential. The most common explanation for this finding refers to coverage changes upon alterations in the temperature or the applied electrode potential. In the present contribution, it is demonstrated that the modulation of surface coverages cannot entirely explain potential-dependent oscillations of Eapp, and rather the impact of entropic contributions of the transition states has been overlooked so far. In the case of a nearly constant surface coverage, these entropic contributions can be extracted by a dedicated combination of Tafel plots and temperature-dependent experiments.

Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces

Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces