Curvature Coefficients Research Articles

Effect of aggregate size on the slump and uniaxial compressive strength of concrete: a DEM study

The aggregate size and particle-size distribution (PSD) can change the packing density, slump, and strength of concrete. The micromechanical effects of aggregate size on the slump and strength remain unclear. The current numerical study examined concrete behavior using slump and uniaxial compressive strength (UCS) tests considering the aggregate size distribution using the discrete element method. The effect of the aggregate size on the packing density, UCS, and slump of the concrete was analyzed. To accomplish this, we evaluated how variations in the uniformity and curvature coefficients of the PSD, as well as the specific surface area of the samples, were affected by changes in aggregate size. Although the simulations were based on standard specimens from the laboratory, the results showed good agreement with the documented experimental results. Briefly, at a 40–60% fine aggregate content, the packing density and compressive strength of the concrete reached their peaks and caused a decrease in the height of the slump. The uniformity and curvature coefficients did not influence the slump height. The induced shear band could be tracked during the UCS tests and the crack angles could be measured. At the optimum fine content (40–60%), the shear bands were primarily localized and propagated through the samples having different fine contents.

Fracture performance and cracking mechanism of large-particle size hydraulic asphalt concrete at different temperatures

This study investigates the fracture properties of large-particle size hydraulic asphalt concrete (LPSHAC) at various temperatures using pre-cracked trabecular bending tests and digital image correlation (DIC). Results show that temperature significantly affects LPSHAC’s fracture properties, with the energy release rate and J-integral fracture toughness increasing initially and then decreasing as temperature rises. Horizontal strain better characterizes damage progression at higher temperatures. Crack curvature coefficients at 0 °C and 20 °C increased by 8.2 % and 30.1 % compared to that at −20 °C, while the aggregate fracture area ratio rose as the temperature decreased from 20 °C to −20 °C.

Effects of particle gradation and material proportions on the mechanical properties of crushed stone aggregates under cyclic loading

To enhance the service performance of the subgrade and optimize subgrade design, we conduct a comprehensive analysis of the impact of gradation on the mechanical properties of crushed stone aggregates, considering both macroscopic and microscopic perspectives. And this paper establishes intricate relationships between deformation parameters, fragmentation, and gradation within crushed stone aggregates, shedding light on the nuanced variations in microscopic mechanical properties across various gradations. The research outcomes underscore that the cumulative deformation and resilience modulus of crushed stone aggregate gradually stabilized after 1000 loadings. The curvature coefficients of gradations 3 and 4 were significantly smaller than those of gradations 1 and 2, which were 1.09 and 0.92, respectively. The gradations with smaller curvature coefficients had better uniformity and density. The addition of limestone increased the resilience modulus of aggregate, but also increased the cumulative deformation. The best effect was achieved when the ratio of quartz to limestone in the aggregate was 3:1. For the failure form of crushed stone aggregate, the failure form of gradation 1 with less fine particle content was mainly characterized by crushing, while the failure forms of gradations 2, 3, and 4 were mainly grinding. When limestone was added to the aggregate, the failure form was also mainly grinding. In addition, the crushing degree of crushed stone aggregate was closely related to the change in the distribution coefficient r. The smaller the change, the lower the crushing degree. The crushing degree was the smallest when gradation 4 and the ratio of quartz to limestone was 3:1, and the change values were 0.038 and 0.073, respectively. The simulation results further show that when the aggregate gradation is 4 or the limestone content is less than 50 %, the microcrack content decreases, while the microcracks and force chains are more uniformly distributed.

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2+1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge (B, S) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of Tc(μB,μS)=Tc(1−(κ2Bμ^B2+κ2Sμ^S2+2κ11BSμ^Bμ^S)) along different lines in the (μB,μS) plane. On lattices with fixed cutoff in units of temperature, aT=1/8, we find κ2B=0.015(1), κ2S=0.0124(5) and κ11BS=−0.0050(7). We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μs=0. We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, Tc(ms)=Tc(msphy)(1−0.097(2)(ms−msphys)/msphy+O((Δms)2). Published by the American Physical Society 2024

Locomotion analysis of a crawling wave robot in circular canal

In this paper, we analyze the locomotion of a wave robot crawling in a curved canal between rigid walls. We determine the conditions for crawling, considering the robot geometry, orientation, wall curvature, canal width, and friction coefficients. Initially, we present an analytical model of the different cases of crawling and conditions for advancement. We found four cases of crawling: one where the robot touches only the outer wall, two with one contact point each on the outer and inner walls, and a third where the robot has two contact points with the outer wall and one with the inner wall. Subsequently, we introduce a multibody numerical simulation, which accounts for sliding along the wall and over the ground surface. The simulation allows one to validate our analytical results and analyze the robot's behavior under different conditions. Finally, we present validating results of multiple experiments conducted with our SAW robot. This analysis encompasses all types of crawling robots with internal thrust mechanisms that are not based on contact with the side walls of the pipe or canal.

Morphometric and soil texture analysis of soil material from wasp nests Sceliphron destillatorium (Illiger, 1807) (Apoidea: Sphecidae)

Background. The article presents the data obtained as a result of our research on the nests of an aboriginal wasp species on the territory of Ukraine – Sceliphron destillatorium (Illiger, 1807) that belongs to the family Sphecidae. We collected 54 wasp nests in different regions: Zakarpattia (n = 4), Ivano-Frankivsk (n = 1), Rivne (n = 12) and Lviv (n = 35) Regions. The data are presented as a result of measuring the main morphometric parame­ters of nests (length, width of cells and mass of nests) which are typical of the species under study. The paper also reports the results of the soil texture analysis of the soil material of twelve wasp nests from four different places of “mass nesting” and compares the results with the control samples of the surrounding soils in the corresponding areas. The study aimed at investigating the structure of the nests of S. destillatorium wasps, determining the soil texture of the soil material of nests from different regions of Ukraine and comparing them. Material and Methods. The nests of Sceliphron destillatorium wasps were the object of the study. The morphometric parameters of nests were measured with an automatic digital caliper 0–150 mm and Axis A500 technical chemical scales. The soil texture analysis was performed by the pipette method. The potentiometric method was used to determine the pH of the soil material. In addition, the determination of the CO2 carbonates was carried out according to the volumetric method. Results. We have analysed 54 nests of S. destillatorium. 46 nests were found in “mass nesting places” (in some places several samples were found): in Lviv (3 sites) and Rivne Regions (1 site – Rivne Nature Reserve). The content of granulometric elements was determined in twelve wasp nests from these places and twelve control soil samples were taken around the places of “mass nesting” (three samples of surrounding soil from each location). In order to compare the particle size distribution of elements in all analysed samples (24), we drew cumulative curves and determined coefficients of uniformity and curvature. Conclusions. Nest weighing revealed considerable variations in the mass of the nests – from 10.06 to 222.56 g – depending on the number of cells in a nest. The size of the nests also varied. The number of cells in the nests varied from 2 to 37 (mean = 13; n = 54 nests). As a result of the soil texture analysis of the nest soil material, we determined the percentage of granulometric elements used by the wasps for the construction of their nests. It was found that fine sand was one of the predominant fractions in all twelve nests. The similar content of all five fractions of soil material of wasp nests from different areas indicates that the soil texture of the nests which were built by S. destillatorium probably does not depend on their geographical location.

Experimental study on vertical seepage of coarse-grained calcareous sand

Calcareous sand, a special geotechnical material employed as foundation fill in numerous reef constructions, exhibits susceptibility to seepage deformation in complex marine dynamic environments. Its permeability characteristics are notably distinct from conventional terrestrial soil, making the understanding of these properties critical for further applications. This study conducted vertical seepage tests on coarse-grained calcareous sand samples with varying coefficients of uniformity (Cu), coefficients of curvature (Cc), relative compactions (Dr), and soil skeletal structures. These tests utilized a custom-designed apparatus, supplemented with image binarization and particle image velocimetry techniques. Based on the results, the findings revealed a three-stage vertical seepage process: steady seepage, hydraulic adjustment, and seepage failure. The permeability coefficient k20 of the calcareous sand samples was observed to transition from a decreasing to an increasing trend with rising Cu and Cc values. Moreover, the k20 of tightly compacted and medium-tightly compacted samples exceeded that during the steady seepage stage upon entering the second stage, while the opposite holds true for relatively loose samples. The spatial organization of the sample skeleton had a considerable impact on its permeability, with coarse-grained calcareous sand imposing a greater constraint on fine particle migration compared to river sand.

Stationary trajectories in Minkowski spacetimes

We determine the conjugacy classes of the Poincaré group ISO+(n, 1) and apply this to classify the stationary trajectories of Minkowski spacetimes in terms of timelike Killing vectors. Stationary trajectories are the orbits of timelike Killing vectors and, equivalently, the solutions to Frenet–Serret equations with constant curvature coefficients. We extend the 3 + 1 Minkowski spacetime Frenet–Serret equations due to Letaw to Minkowski spacetimes of arbitrary dimension. We present the explicit families of stationary trajectories in 4 + 1 Minkowski spacetime.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part II. Nonstationary Hamiltonians

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text], orthogonal to [Formula: see text] and [Formula: see text] and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian.

Theoretical and numerical study on ceiling temperature distribution of fire in the SRRT with curvature considering train blocking

The slopping rack railway tunnel (SRRT) with curvature is applied to pass through mountainous areas due to the terrain. And the temperature distribution under train blocking in the SRRT with curvature is significantly different when a fire occurs, posing a great threat to personnel safety. The train blocking and two curvature types of C-shaped and S-shaped are considered, and the mathematical expressions for temperature distribution with coefficients of slope and curvature are derived. The effects of slope, curvature, and train blocking on ceiling temperature are investigated using numerical simulation, and the applicability of the mathematical expressions is demonstrated through fitting. The results show that the mathematical expression for ceiling temperature distribution is a piecewise function with a stepped-down descent. The temperature attenuation is separated into three stages for C-shaped, and four stages for S-shaped. The coefficients are approximately linear with slope and curvature radius respectively. The train blocking on the ceiling maximum temperature for C-shaped is of a stronger effect than for S-shaped, and the slope on the temperature at the train tail for C-shaped is of a weaker effect than for S-shaped.

Supervised intelligent prediction of shear strength of rockfill materials based on data driven and a case study

The rockfill materials (RFM) are emerging and regarded waste reuse product in construction and mining engineering. In this paper, six distinctive supervised machine learning (SML) models, namely artificial neural network (ANN), extreme learning machine (ELM), random forest (RF), relevance vector regression (RVR), support vector regression (SVR), and extreme gradient boosting (XGBoost), are adopted to predict the RFM shear strength using 165 data cases with 13 features. To improve model performance, an improved physics meta-heuristic algorithm, named snow ablation optimizer with Logistic mapping (LogSAO), is utilized to select the optimal hyperparameter combination of the proposed models. Four popular statistical indices, including coefficient of determination (R2), root mean squared error (RMSE), Willmott’s index (WI), and Scatter index (SI) are employed to quantify the model performance. The model evaluation results show that the LogSAO-SVR model is the best prediction model with the highest values of R2 and WI while the lowest values of RMSE and SI in both training and testing phases (0.9985, 0.0257, 0.9996, and 0.0380; 0.9802, 0.0812, 0.9950, and 0.1335). Normal stress (Ns) is the most important feature with the highest importance score of 0.925 in predicting the RFM shear strength. Interestingly, the negative contribution of Ns to the RFM shear strength prediction will be transformed into the positive contribution when coefficients of curvature (Cu) values are small. The validation results demonstrate that the predicted values of the proposed LogSAO-SVR model are highly consistent with the measured values from the direct shear tests based on a case study.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part I. Stationary Hamiltonians

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text], orthogonal to both [Formula: see text] and [Formula: see text]. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit [Formula: see text] and [Formula: see text] states under evolution by a quantum Heisenberg Hamiltonian.

Effect of particle size and gradation on compressive strength of MICP-treated calcareous sand

Calcareous sand is a type of biological sand deposited from the remains of marine organisms. Although widely used in coastal construction, the reinforcement of calcareous sand is necessary due to its natures of low bearing capacity and high compressibility. Aiming for this, an environmentally bio-grouting technique, microbially induced calcium carbonate precipitation (MICP) was applied to reinforce the calcareous sand. However, MICP treatment is in turn influenced by the properties of calcareous sand, such as particle size and gradation. To reveal the effects of particle size and gradation, the MICP-treated calcareous sands with various median sizes, uniformity coefficients or curvature coefficients, were conducted with the unconfined compressive strength (UCS) tests and a series of laboratory experiments. The results indicated that with the median size or uniformity coefficient increasing, the UCS of the MICP-treated specimens decreased; while with increasing curvature coefficient, the UCS exhibited a trend of increasing before decreasing. Further experiments reveal that particle size and gradation affect the MICP process mainly by changing the amounts and volume of pores. The current study demonstrates the respective effects of particle size and gradation on the treatment of MICP and provides a theoretical reference for reinforcing calcareous sand in marine engineering.

Hypersurfaces with mean curvature prescribed by an ambient function: Compactness results

We consider, in a first instance, the class of boundaries of sets with locally finite perimeter whose (weakly defined) mean curvature is gν, for a given continuous positive ambient function g, and where ν denotes the inner normal. It is well-known that taking limits in the sense of varifolds within this class is not possible in general, due to the appearance of “hidden boundaries”, that is, portions (of positive measure with even multiplicity) on which the (weakly defined) mean curvature vanishes, so that g does not prescribe the mean curvature in the limit. As a special instance of a more general result, we prove that locally uniform Lq-bounds on the (weakly defined) second fundamental form, for q>1, in addition to the customary locally uniform bounds on the perimeters, lead to a compact class of boundaries with mean curvature prescribed by g.The proof relies on treating the boundaries as oriented integral varifolds, in order to exploit their orientability feature (that is lost when treating them as (unoriented) varifolds). Specifically, it relies on the formulation and analysis of a weak notion of curvature coefficients for oriented integral varifolds (inspired by Hutchinson's work [7]).This framework gives (with no additional effort) a compactness result for oriented integral varifolds with curvature locally bounded in Lq with q>1 and with mean curvature prescribed by any g∈C0 (in fact, the function can vary with the varifold for which it prescribes the mean curvature, as long as there is locally uniform convergence of the prescribing functions). Our notions and statements are given in a Riemannian manifold, with the oriented varifolds that need not arise as boundaries (for instance, they could come from two-sided immersions).

Accurately Predicting Quartz Sand Thermal Conductivity Using Machine Learning and Grey-Box AI Models

The thermal conductivity of materials is a crucial property with diverse applications, particularly in engineering. Understanding soil thermal conductivity is crucial for designing efficient geothermal systems, predicting soil temperatures, and assessing soil contamination. This paper aimed to predict quartz sand thermal conductivity by using four mathematical models: multiple linear regression (MLR), artificial neural network (ANN), classification and regression random forest (CRRF), and genetic programming (GP). A grey-box AI method, GP, was used for the first time in this topic. Seven inputs affecting thermal conductivity were evaluated in the study, including sand porosity, degree of saturation, coefficient of uniformity, coefficient of curvature, mean particle size, and minimum and maximum void ratios. In predicting thermal conductivity, the MLR model performed poorly, with a coefficient of determination R2 = 0.737 and a mean absolute error MAE = 0.300. Both ANN models using the Levenberg–Marquardt algorithm and the Bayesian Regularization (BR) algorithm outperformed the MLR model with an accuracy of R2 = 0.916 and an error of MAE = 0.151. In addition, the CRRF model had the best accuracy of R2 = 0.993 and MAE = 0.045. In addition, GP showed acceptable performance in predicting sand thermal conductivity. The R2 and MAE values of GP were 0.986 and 0.063, respectively. This paper presents the best GP equation for evaluating other databases. Additionally, the porosity and saturation of the sand were found to have the greatest impact on the model results, while coefficients of curvature and uniformity had the least influence. Overall, the results of this study demonstrate that grey-box artificial intelligence models can be used to accurately predict quartz sand thermal conductivity.

Study on shear characteristics of calcareous sand with different particle size distribution

For the island and reef project formed by filling calcareous sand, the problems of wide particle size distribution (PSD) and complex mechanical properties have to be faced. Therefore, in order to provide basic mechanical parameters for the construction of the island and reef project, triaxial shear tests were carried out on calcareous sands with five different typical PSDs. The results showed that as particle gradation became narrower, the axial strain corresponding to the strain-softening point all showed a decreasing trend and their differences gradually decreased; the confining pressure has a significant impact on the volumetric deformation modulus of calcareous sand with a wide PSD. The cohesion of calcareous sand showed a positive correlation with non-uniformity and curvature coefficients, while the variation of an internal friction angle showed a parabolic law; the internal friction angle also changes in the parabola with the change of fine particle contents. Furthermore, by establishing the PFC3D discrete element model, it was found that the numerical simulation results were in good agreement with the test results, which verifies the feasibility of the numerical simulation and the rationality of the mesoscopic parameter calibration. It was discovered that the wider the particle gradation range, the greater the axial strain corresponding to the critical coordination number; the sample with a narrow gradation interval was more likely to present a rotating displacement field to form a penetrating shear band. This study can provide design parameters for stability analysis of high and steep slopes in calcareous sand sites.

EFFECTS OF COARSE AGGREGATES GRADINGS ON THE PROPERTIES OF CONCRETE

Coarse aggregates gradings have varying effects on the properties of concrete. Coarse aggregates of sizes 10mm, 20mm and 25mm were used for this study. Sieve analysis was conducted on these aggregates. Their coefficients of curvature (Cc) ranged between 1.01 and 1.19, while the coefficients of uniformity (Cu) ranged between 1.24 and 1.73, showing that they are all uniformly graded. 10mm and 25mm coarse aggregates were mixed in various proportions to produce five different concrete mixes (concrete C1, C2, C3, C4 and C5). Concrete C6 was produced with 100% 20mm and was used as a check. Slump test was performed for each mixture, C1 gave the highest slump height of 88mm. Compressive strengths of the cast concrete cubes were determined after 7- and 28-days curing periods. C4 gave maximum compressive strength of 26.33N/mm2 at 28 days. Increase in the percentages of 25mm aggregates resulted in higher compressive strength and decreased workability.

Compaction Quality Control of Coarse-grained Soils Using Dynamic Penetration Test Results through Correlation with Relative Compaction Percentages

In this study, in order to control the compaction quality of the coarse-grained soils used in sub-base and base layers of several road construction projects, the dynamic penetration test (DPT) has been conducted on 50 locations using both dynamic penetrometer of light (DPL) and dynamic penetrometer of medium (DPM). First, in order to obtain the results independently from the penetrometer type, the dynamic cone resistance (qd) values were calculated in each location based on hammer blows of both DPL and DPM. Next, the average values of qd obtained by both the penetrometers, were correlated with the percentages of relative compaction (RC) in the same location obtained by performing the sand cone test on location and modified proctor test in laboratory. Accordingly, it was extracted a power correlation between the qd values and RC percentages, with the determination coefficient (R2) of about 0.64. Then, for considering the effect of soil grains size using the median particle size (D50), a more accurate power correlation was obtained which as a result, the R2 value enhanced to 0.89. Furthermore, in order to consider the soil vertical stresses caused by depth of testing as well as obtaining a normalized relationship, the qd values were divided by the vertical stresses and correlated with the RC percentages. Afterwards, regarding the effect of soils grains size and also their gradation properties, this time by using the dimensionless coefficients of uniformity (Cu) and curvature (Cc), it was extracted an other normalized power correlation. The results showed that the R2 value enhanced from about 0.49 to 0.92.

Impact of Metal Work-Function on Current Rectification by Metal-Insulator-Metal Diodes

This article presents the experimental investigation of the effect of metal work-function on current rectification by metal–insulator–metal (MIM) diodes. Diverse MIM diode topologies that utilized various types of metal configurations were fabricated and subjected to DC electrical (J-V) characterization, and it was found that the work-function of the various metals impacts the symmetry and linearity of the diodes’ current–voltage curves, the amount of current the diodes can rectify, and their typical zero-bias curvature coefficients. The diodes whose both metal layers have the same work-function exhibits more linear and symmetrical current–voltage curves, with the curves becoming more non-linear and asymmetrical as the variation in work-function of the metals increase, impacting the applications where MIM diodes can be used.

Finding the grain size distribution that produces the densest arrangement in frictional sphere packings: Revisiting and rediscovering the century-old Fuller and Thompson distribution

By means of discrete-element methods, we investigate the joint effects of the grain size distribution (GSD) and contact friction on the structure of three-dimensional samples composed of spherical grains. Specifically, we compress these systems isotropically until jamming and then analyze their structure in terms of density, connectivity, coefficients of uniformity and curvature, and parameters of grading entropy. Our study focuses on power-law GSDs and particularly on the Fuller and Thompson distribution, proposed over a century ago. First, we show that, among the set of GSDs investigated, this particular distribution produces the densest and best-connected systems, falsifying a conjecture recently posed in the literature. Second, we find that the jamming packing fraction can be accurately predicted as a function of simple descriptors of the GSD, but among these descriptors the granular entropy concept proves to be the most useful. This allows for an alternative interpretation of both jamming and grading entropy concepts. Finally, we compare the Fuller and Thompson distribution with two well-known GSDs: that of the Apollonian sphere packing and that towards which granular systems evolve after intensive grain fracturing. Surprisingly, we find that these three GSDs are practically coincident in the limit of large size spans, despite having been introduced or discovered in different scientific contexts (i.e., engineering, mathematics, and earth sciences, respectively).