Element Length Research Articles

Wheeler-DeWitt canonical quantum gravity in hydrogenoid atoms according to de Broglie-Bohm and the geodesic hypothesis. Einstein’s Quantum Field Equation

We explore the geodesic hypothesis of orbital trajectories of the electrons in hydrogenoid atoms, in the frame of de Broglie-Bohm quantum theory. It is intended that the space-time can be curved, at very short distances, by the effect of the joint action of the energy content of the atomic system and the contribution of the electric and quantum potentials. The geodesic hypothesis would explain the non-lose of energy in the electron orbital trajectories. So we explore a conception where particles and waves interact in a closed system: the waves guide the particles and the particles generate the spacetime perturbation that acts as a wave, beyond the pilot-wave theory. We establish the equivalence, in a local neighborhood, between the electron trajectory of an hydrogenoid atom in the Minkowskian space where the de Broglie-Bohm can be cast with its movement in a Lorentzian manifold, according to the concept of metric tangent. Through the geodesic condition and the invariance of the elemental length, we establish a relationship between some components of the metrics. But as the particles in microphysics do not follow the Einstein’s field equation, we consider the 3+1 decomposition according to ADM and the quantization in the Wheeler De Witt theory and with a so-called quantum Einstein field equation, with a decomposition of spacetime into three-dimensional sheets of a spatial character. Then we derive from the moment-energy tensor a further equation between the components of the metrics. It opens the avenue to characterize the metric by an exact solution of the Einstein’s field equations.

Signature of viral fossils: a comparative genomics approach to understand the diversity of endogenous retroviruses in bats

Endogenous retroviruses (ERVs) are traces of past viral infections commonly found in vertebrate genomes. Many ERVs are tightly regulated by the host genomes and co-opted for various functions within the hosts. Bats are the only true volant mammals, with the smallest mammalian genomes and a high fraction of ERVs within the genomes. They are important hosts for various zoonotic viral pathogens and can effectively modulate their immune response to tolerate viral infections. Integrations of retroviruses have been implicated as one of the mechanisms by which bats have co-evolved strategies to combat viral infections. In this study, we investigated the diversity of ERVs in over 40 publicly available bat genomes to understand the distribution and the evolution of ERVs within bats. We observed all classes of ERVs within bat genomes including even the complex lenti retroviruses. Alpha and spuma retroviruses which are, generally considered rare in mammals, were common within bats. We observed a positive correlation between bat genome size and length of ERV elements. Interestingly, nearly 30% of the ERVs within bats are intact suggesting a recent origin or co-option by the host genome. Future studies focusing on comparative genomic and experimental data will be critical to understand the role of these ERVs in host genome evolution.

КРАЙОВІ ЕФЕКТИ В БАЛКАХ ІЗ КОМПОЗИТІВ

Beams made of composites are widely used in aircraft structures, various machines and mechanisms. The experience of operation and repair of such objects shows that when designing beams and spars, one must take into account such effects as the influence of thermal stresses and the additional contribution of Poisson's coefficients to the stressed state of beam elements both in the length direction and along the width beam elements. Scientific studies devoted to the assessment of the stress-strain state of load-bearing structures made of composites demonstrate the conclusions that the effects of thermal expansion (contraction) of heterogeneous connected elements and the influence of Poisson's ratios give significant increases in stress. The value of these increases can be up to dozens of percents of the base load (that is, without taking these effects into account).The paper proposes an engineering mathematical model that allows estimating the value of normal and shear stresses from thermal loading and Poisson stresses. An analysis of the distribution of these stresses along the length and width of the beam elements was carried out.When using the structural-technological solution of beams with sub-shoulders, the proposed method allows you to reasonably choose adhesive or binder for reliable connection of the cap with sub-shoulder, as well as more correctly justify the geometric dimensions of the beam elements. Also, this technique can be used to develop new structural and technological solutions for beams and other load-bearing elements (ribs, walls, webs, doublers, overlapping joints of composite parts).Another applied direction of using the developed methodology can be considered the development and optimization of existing technological processes for the production of parts and units of composites, in which the so-called hot polymerization of the binder (at elevated temperatures) is used. The method makes it possible to estimate the level of thermal stresses that occur during the manufacture of the unit.In general, the proposed technique makes it possible to understand the principles of additional stresses occurrence, to estimate their absolute values, and to increase the accuracy of estimating the stress-strain state of beam elements.

Quantifying the Vices and Virtues of Snakes and Ladders Through Time

Abstract The game of Gyan Chaupar or ‘Snakes and Ladders’ exists in many forms throughout history as a board game of varying size, structure, and game elements of snakes and ladders associated with various vices and virtues inscribed within the board. Three boards were analyzed via simulation in Python, including the 1998 Milton Bradley version, the 72-square Vaisnava board, and the 84-square Jaina board, with the goal of understanding the relationships between board design and associated behaviors and spiritual concepts. Game play on each board was simulated 100,000 times with variations that included individual removal of a snake or ladder, thereby quantifying the importance of that element towards achieving victory. Comparison of the weighted importance of each game element and associated vice and virtue permitted quantification of their importance for the game designer and their associated culture, with each game board component being assigned a contribution towards victory. Historical values inscribed within the class of Gyan Chaupar games were interpreted quantitatively via simulation allowing for comparison of different variations of the game and their associated cultures in different locations and time. The hypothesis that game element contribution towards victory could not be assessed by players a priori via element board length was supported by simulation data that identified many snakes and ladder game elements whose importance towards victory deviated significantly from proportionality with their game element length.

Bayesian Inference for the Calibration of Progressive Damage Model of Dovetail Specimens from Laminated Composite Fan Blade

Abstract Composite fan blades are the preferred alternative for the fan stage of most advanced high bypass ratio turbofan engines. The ability of the dovetail to safely bear this load is one of the key points of the multi-level “test pyramid” approach of compliance demonstration for special airworthiness regulation. Debonding between adjacent layers is the main damage mode of laminated composite fan blades. However, there is difficulty in measuring the as manufactured interlaminar mechanical properties used in finite element models. In this study, tensile loading was applied to simulate the interacting centrifugal force and capture mixed mode damage evolution. Structural responses and material damages were calibrated with measured tensile loads through Bayesian inversion. Posterior probability distributions of maximum interface tractions and contact stresses were solved using Markov chain Monte Carlo sampler. Results indicated the two bilinear cohesive material models had a capacity of predicting empirical means of longitudinal reaction forces as that in test considering additional discrepancy term (0.035 kN and 0.96 kN respectively), while they made an significant impact on the prediction of tensile load history especially when two delamination cracks initiated and propagated. Interface elements provided a higher matching quality in predicting loading history and capturing damage mechanism in association with in-plane progressive damage analysis. This calibrated parameter set could be functioned as benchmark in numerically determining the ultimate tensile load of dovetail elements and reducing the necessary number of physical tests at elemental length level.

Morpho-Anatomical Variations in Sisymbrium irio L. Plants Raised from Seeds Treated with γ Radiation.

This study determines the effect of γ irradiation on seed germination, growth, and morpho-anatomical traits of the Sisymbrium irio L. (London rocket) plant. Seeds irradiated with 2.5, 5, 10, 15, and 20 kGy of γ radiation showed a reduced germination percentage (13.68-56.84%) with reference to the control, showing an inverse relationship with radiation dose. Observations recorded at preflowering, flowering, and postflowering stages of plant growth showed a significant (P < 0.05%) dose-dependent decline in many growth parameters, such as root length, shoot length, shoot dry weight, number of leaves, and pods per plant, due to the radiation effect. However, root dry weight, leaf length, leaf dry weight, number of branches, and number of flowers per plant increased at the lowest dose (2.5 kGy) and then declined steadily with the increasing level of radiation. Likewise, several anatomical features (length of fibers and vessel elements, diameter of vessel elements, proportion of cortex, and vasculature in the stem) showed a consistent decrease with increasing γ irradiation in treated plants compared with the control. However, the pith area and the number of vessels per microscopic field decreased significantly with the lowest radiation dose (2.5 kGy) and then increased gradually with higher doses at each ontogenetic stage. The vulnerability factor in the control as well as treated plants increased with increasing plant age. In treated plants, vulnerability was higher under the effect of low-level radiation than in the control, but it showed an inverse relationship with the increasing level of radiation, thus being the lowest at 20 kGy radiation dose. Mesomorphy also showed an almost similar variation pattern with reference to the radiation dose.

Adaptive ray tracing in freeform gradient-index media using an index directional derivative.

Freeform gradient index (F-GRIN) media are increasingly used in optical systems. The existing ray tracing methods for F-GRIN have low calculation efficiency and require manual adjustment of step size, making the design process complex. To address this, we propose an adaptive ray tracing (ART) method for F-GRIN. ART obtains an initial step size based on an index directional derivative and the element's length. During the subsequent transmission process, the step size is adaptively adjusted. The accuracy and speed of ART were verified through multiple comparison tests. ART can reduce manual participation and significantly improve efficiency in the optical design of F-GRIN.

Evaluation of stresses on the surface of production columns equipped with sand filters when downing into a horizontal well

Relevance. The need to estimate the time of formation sand accumulation near the annulus of a horizontal well and the unit length of filter elements in the bottom of production strings and to determine the stresses on the surface of production strings equipped with sand filters when lowering into the well. Aim. Based on a study of the reasons for the continued flow of sand into wells equipped with anti-sand filters, to develop and propose measures related to the need to choose a reduction in the number of filters that provide the design flow rate of a horizontal well or a significant increase in the length of the filtering surface of the filters in order to reduce erosive wear of the wire winding. Objects. We are considering a well with a horizontal section, equipped with sand filters, the same size as the casing strings. It was assumed that the integrity of the surface of the filter elements would be preserved and the conditions for their destruction would be eliminated when lowering into the horizontal shaft. This presupposes the necessary efficient operation of the well throughout the entire operational period. The section of the first set of curvature and the forces arising during this are considered as wellas stability of a pipe string during possible stops. Centralizers are evenly located along the length of the column, then in some sections we will have a multi-span statically indeterminate beam, in each section of which a radial load acts. Methods. When studying the time of formation sand accumulation in the annular space of a horizontal well and a unit length of filter elements in the bottom of production strings, it is necessary at the first stage to determine the stresses on the surface of production strings equipped with sand filters when lowering into the well. Studying the assessment of the existence time of the transition period is of particular interest. This is, in other words, during what operational period there is a complete accumulation of formation sand in the annular space and the transition of formation drainage along the entire length of the horizontal wellbore to drainage of only zones adjacent to the filters. To calculate the fluid flow rate when the annular space of the horizontal well is completely filled with sand, the design values ​​of the AC4.8 formation parameters were used. The maximum value of depressions used in the calculations is assumed to be 1.5 MPa. Results. Consideration of situations that arise when filters are lowered into horizontal wells indicates that the outer surface of the filter elements is not protected from destruction as a result of contact stresses with the walls of the drilled wellbore. To protect against destruction and rubbing open gaps by clay-containing rocks, rigid centralizers should be installed along the edges of the filter elements, the maximum allowable distances between which should not exceed 4.0–4.5 m.

Comparison between experimental and numerical results for piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation

Abstract The bone formation is considered to be accompanied by the piezoelectric effects in bone. Therefore, the piezoelectric effect under ultrasound irradiation should be elucidated to realize the effective healing. Then, the piezoelectric properties in cancellous bone have been attempted to clarify by complementing experiments and simulations with each other. In this paper, the piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation were experimentally and numerically observed, and the effect of the trabecular orientation was investigated. The experimental observation was performed by the piezoelectric cell (PE-cell), which corresponds to an ultrasound receiver using the cancellous bone specimen as a piezoelectric element. The numerical observation was performed by the piezoelectric finite-difference time-domain (PE-FDTD) method, which is an elastic FDTD method with piezoelectric constitutive equations. In both the experimental and simulated results, the piezoelectric signal amplitude increased with the mean intercept lengths (MILs) of the trabecular elements and the pore spaces or the strength of the trabecular orientation. From the fact that the ultrasound propagation in water-saturated cancellous bone can depend on the trabecular orientation, it was considered that the ultrasound properties could be largely associated with the piezoelectric properties.

On finitely generated Engel branch groups

AbstractWe construct finitely generated Engel branch groups, answering a question of Fernández‐Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non‐nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case.

Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory

This paper presents an original finite element (FE) model that integrates the smeared crack band (SCB) approach and full layerwise plate theory (FLWT). The model enhances the computational efficiency of progressive failure analysis (PFA) of laminar composites in compression, by utilizing the layerwise approach which reduces a 3D model to a 2D one. The model distributes damage throughout the FE domain, with fracture mechanisms represented by material stiffness degradation controlled by damage variables (based on equivalent strains specifically defined for each failure mode). Mesh dependency issues are addressed by scaling fracture energy using a characteristic element length, and failure initiation and modes are determined using the 3D Hashin failure criterion.Accurately describing lamina response in fiber direction under compression requires linear-brittle softening with a stress plateau. The study showed that a model considering 30 % of residual stress accurately predicts maximum stress regardless of mesh refinement, demonstrating results’ minor dependence from the selected element size.The model accuracy has been confirmed by comparing the obtained results against experimental and benchmark data from the literature. The size effect study demonstrated a decrease in maximum stress of the open-hole laminates in compression with increasing specimen in-plane size. This trend is consistent with experimental and reference numerical observations, confirming the model accuracy and applicability even for relatively coarse meshes. Therefore, computational efficiency is improved, with preserved accuracy of conventional solid finite element models.

Shapovalov elements for U q ( s l ( N + 1 ) )

For a simple Lie algebra, Shapovalov elements give rise to highest weight vectors in Verma modules. The usual construction of these elements uses induction on the length of a certain Weyl group element. If g = s l ( N + 1 ) explicit expressions for Shapovalov elements were given in I. M. Musson [Explicit expressions for Shapovalov elements in type A, J. Algebra 623 (2023), 358–394]. Here we adapt the argument to the quantized enveloping algebra of g .

Stability analysis of sandwich double nanobeam-system with varying cross-section interconnected by Kerr-type three-parameter elastic layer

In this study, the endurable buckling load of the elastically connected parallel sandwich nano-beams with varying cross-sections is assessed. In this regard, a layered beam system consisting of two parallel axially loaded tapered sandwich nanobeams that are interconnected via a Kerr-type three-parameter elastic foundation is considered. The geometric properties are assumed to be changed exponentially along the length of the beam element. The governing equilibrium equations of the system are described by a set of three coupled homogeneous differential equations, which originates in the context of Eringen's non-local elasticity theory and Euler beam model. Then, the numerical differential quadrature technique is used to estimate the endurable axial critical loads. Eventually, a comprehensive parameterization research is performed to investigate the sensitivity of linear buckling resistance to tapering ratio, nonlocal parameter, stiffness of elastic connections, volume fraction exponent, and thickness ratio. The research work of the present study is novel, and the attained numerical outcomes can be used as benchmarks for future researches in this field.

Discrete Element Method Simulation of Particulate Material Fracture Behavior on a Stretchable Single Filter Fiber with Additional Gas Flow

This study presents a comprehensive discrete element method (DEM) simulation approach for the stretching of a filter fiber with a separated polydisperse particle structure on top. For a realistic interaction between the fiber surface and the particles, the original surface of the polymer fiber was projected onto the surface of the fiber cylinder using surface imaging technologies (atomic force microscopy (AFM) and white-light interferometry). In addition, the adhesive forces between particle–fiber and particle–particle contacts were calibrated in the DEM domain using values from self-conducted AFM measurements. Fiber stretching was implemented by the linear motion of small periodic fiber elements. Discretization problems were resolved through studying the stretching of a fiber segment at the size of 8 mm. A critical fiber element length was discovered to be ≈100 μm for minimizing discretization dependencies during the cracking of the particle structure. The number and density of particle–particle contacts within the particle loading on the fiber were obtained at two different elongation rates. Effects such as densification of the particulate structure and increased detachment due to additional air flow were demonstrated.

Mesh objective characteristic element length for higher-order finite beam elements

The use of fracture energy regularization techniques can effectively mitigate the mesh dependency of numerical solutions caused by the strain softening behavior of quasi-brittle materials. However, the successful regularization depends on the correct estimation of the crack bandwidth in Finite Element solutions. This paper aims to present an enhanced crack band formulation to overcome the strain localization instability especially for the higher-order elements developed in the framework of Carrera Unified Formulation (CUF). Besides, a modified Mazars damage method incorporating fracture energy regularization is employed to describe the nonlinear damage behavior of the concrete. To evaluate the efficiency of the proposed crack band formulation, three experimental concrete benchmarks are selected for the numerical damage analysis. By comparing numerical and experimental results, the proposed method can guarantee mesh objectivity despite varying finite element numbers and orders, indicating perseved fracture energy consumption within proposed higher-order beam models.

Crack Behavior of Eccentrically Braced Frame Type-V with Ground Granulated Blast Furnace Slag

To make the structure stronger and stiffer, which is more susceptible to earthquake forces, a special mechanism is required to improve the structure's lateral stability. EBF-V with a horizontal link beam is a brace that can enhance structural performance by providing good stiffness and ductility. On the other hand, GGBFS, as a partial OPC replacement material, was applied to contribute to using more environmentally friendly materials. Besides offering a smaller carbon footprint, GGBFS also positively improves the mechanical properties of concrete. Thus, this study focuses on investigating the crack propagation pattern of reinforced concrete braced frames combined with 20% GGBFS in EBF-V with three variations of link beam element lengths of 0 cm (CBF), 15 cm (EBF-V-) and 25 cm (EBF-V-25). As a result, the CBF specimen showed the best seismic performance. In EBF specimens, there is an increase in the collapse mechanism to be more ductile. The link beam plays a role in making the crack pattern more focused. EBF-V-15 performs well under seismic loading with large lateral capacity and ductility. The cracks in the frame are evenly distributed, dominated by fine cracks, and symmetrical on both sides. This validates that GGBFS plays a good role in improving the frame performance with its pore-filling effect and pozzolanic reaction.

Research on the recovery performance of SMA tendon and the active control effect of adaptive cable dome

Cable dome is a widely used cable-strut tensile structure, and whose form is controllable. The shape and internal force of the structure can be adjusted by adjusting the length of the cable elements to enhance its load-bearing capacity. Shape memory alloy (SMA), as a new type of intelligent material, has excellent driving performance and is widely used in aerospace engineering, biotechnology, and construction engineering. In order to achieve active control of cable elements in cable domes using SMA, this paper conducted uniaxial tensile tests on SMA wires. Based on the test results, this paper designs and manufactures a SMA tendon suitable for active control and establishes a recovery performance model specifically for SMA tendon. Subsequently, tests on recovery performance are conducted to delve into the recovery force and displacement of the steel tendon. Finally, the SMA tendon is connected in series with the steel wire rope to obtain the active control cable elements, which is used to replace the diagonal cable in the Levy cable dome. Apply full span load to the structure, conduct active control tests by heating SMA tendon, record cable stress and node displacement during the test, and compare the results with finite element results and control methods in literature to study the control effect of SMA tendon. The test results show that the SMA tendon has good recovery performance and can be used as the control device of the control cable elements in the cable dome structure. The control effect is stable and reliable. Adjusting length of the diagonal cable can achieve Levy cable dome structural shape adjustment and improve the relaxation phenomenon of the ridge cable.

Experimental studies of the characteristics of a resonant leader emitter with a single-pass amplifier

The results of experimental studies of the energy and spatial characteristics of the lidar transmitter, built according to the generator-amplifier scheme based on an organic dye with tube pumping, are presented. The choice of a single-pass traveling wave amplifier used in the experiments was determined by preserving the spectral purity of the radiation. When constructing a lidar emitter according to the generator-amplifier scheme under conditions of constant pumping density, the problem arises of choosing the ratio between the length of the active element of the generator and the length of the active medium of the traveling wave amplifier, which would ensure the maximum efficiency of the entire emitter. The main task of the work was the experimental verification of the results of theoretical studies of the narrow-band emitter of the resonant lidar in order to determine the factors affecting the choice of the ratio of the lengths of the active elements of the generator and the amplifier based on the organic dye rhodamine 6Zh with tube pumping with limited total length. The amount of effective radiated energy was used as the main criterion for evaluating the efficiency of the generator-amplifier system. The experimental results confirm the theoretical conclusions that there are optimal ratios of the lengths of the generator and the amplifier, at which the effective radiation energy is maximal. The limiting length of the amplifier and the energy of the emitter built according to the generator-amplifier circuit are limited by the increase in the intensity of the radiation amplified along the active element, as well as the increase in the intensity of the amplified noise.

A microscale modeling method for predicting the compressive behavior of 3D needled nonwoven fiber preforms

The through-thickness compressive mechanism of 3D needled nonwoven fiber preforms is complicated due to the complex fiber structure and enormous fiber-to-fiber contacts. This work developed a microscale modeling method to predict compressive behavior of carbon fiber nonwoven preforms. A newly-developed virtual fiber is proposed based on the generalized beam elements, for which the low bending stiffness of the fiber is calibrated by experimental data and decoupled from the high tensile stiffness. The feasibility of the proposed virtual fiber method is demonstrated through a simulation example of three-point bending of 6 k carbon fiber yarn. Influence of modeling parameters including amount of virtual fibers in the yarn and the element length of virtual fibers on the simulations is analyzed. High precision model of 3D needled preform is then generated using the proposed virtual fiber method. Through-thickness and axial compressive deformations of the preform are simulated. The predicted load–displacement curves agreed well with the experimental results.

GROUPING OF CLONES OF 4-YEAR-OLD Eucalyptus spp. FOR PULP AND PAPER

As in other countries, In Brazil, new genetic materials of Eucalyptus spp. and their hybrids are multiplied through cloning. These materials, currently in experimental trials, must undergo several stages to select the best ones for pulp and paper production. Therefore, new studies on wood quality are essential. Therefore, this study aimed to group 11 clones of Eucalyptus spp. wood, from a clonal plantation in the municipality of Palmital, São Paulo State, for the production of paper and cellulose. For this purpose, four trees of each clone of 4-year-old Eucalyptus spp. were collected. From each tree, a log of 1 m in length was taken from the base of the tree, for the study of the characterization of the basic density and cellular dimensions of the wood. The results showed that there were significant differences between clones for basic density, fiber length, vessel element length and fiber wall thickness. The Runkel ratio, wall fraction and stiffness coefficient did not show significant differences between the different genotypes. From the results obtained, we can conclude that clones can be differentiated only by basic density, fiber length, vessel element length and fiber wall thickness. The Runkel index, flexibility coefficient and wall fraction of Eucalyptus spp. were more efficient to group the clones into two groups.