Homogeneous Elements Research Articles

A novel personalized homogenous finite element model to predict the pull-out strength of cancellous bone screws

BackgroundOrthopedic surgeries often involve the insertion of bone screws for various fixation systems. The risk of postoperative screw loosening is usually assessed through experimental or finite element (FE) evaluations of the screw pull-out strength. FE simulations are based on either personalized complex but accurate heterogeneous modeling or non-personalized simple but relatively less accurate homogeneous modeling. This study aimed to develop and validate a novel personalized computed tomography (CT)-based homogeneous FE simulation approach to predict the pull-out force of cancellous bone screws.MethodsTwenty FE simulations of L1-L5 vertebral screw pull-out tests were conducted, i.e., 10 heterogeneous and 10 homogenous models. Screws were inserted into the lower-middle region of vertebrae. In our novel homogeneous model, the region around approximately twice the diameter of the screw was used as a bone material reference volume. Subsequently, the overall material property of this region was homogeneously attributed to the entire vertebra, and pull-out simulations were conducted.ResultsThe mean error of the predicted pull-out forces by our novel homogenous simulations was ~ 7.9% with respect to our heterogeneous model. When solely the cancellous bone was involved during the pull-out process (i.e., for L1, L2, and L3 vertebral bodies whose cortical bone in the inferior region is thin), the novel homogenous model yielded small mean error of < 6.0%. This error, however, increased to ~ 11% when the screw got involved to the cortical bone (for L4 and L5 vertebrae whose cortical bone in the inferior region is thick).ConclusionThe proposed personalized CT-based homogenous model was highly accurate in estimating the pull-out force especially when only the cancellous bone was involved with the screw.

Passivation of Deep‐Level Defects through Chemical Environment Regulation for Efficient CZTSSe Solar Cells Based on Active Selenium Adsorption–Desorption Process

AbstractInsufficient selenization and uneven distribution of elements caused by the poor diffusion and reaction activity of selenium clusters is one of the main issues limiting the efficiency of Cu2ZnSn(S,Se)4 (CZTSSe) solar cells. Here, this work designs a simple and feasible strategy to improve the activity of selenium (Se) by implementing high‐temperature treatment on graphite boxes loaded with Se pellets. The rapid adsorption/desorption characteristics of graphite on active gaseous small‐molecule selenium have successfully introduced hyperactive Se4, Se3, and Se2 into the selenization process. The results indicate that the adsorbed non‐toxic gaseous active Se3 and Se4 can quickly and uniformly diffuse into the precursor film at low temperatures, thereby inducing nucleation and grain growth at both surface and back interface simultaneously, which inhibits the upward migration and aggregation of cations, especially Cu, and promotes the homogenization of elements. The overall relatively Cu‐poor chemical environment suppresses the formation of CuZn defects and [2CuZn+SnZn] defect clusters, and also promotes the generation of favorable VCu. The band tail states and non‐radiative recombination are then optimized. Finally, the CZTSSe solar cells achieve a power conversion efficiency (PCE) of 14.5%, with VOC/VOCSQ of 67% being one of the highest in the literature.

Measured and predicted sound transmission through a laboratory concrete floor

The direct sound transmission through a simple, massive, homogeneous building element with and without lining is investigated experimentally and compared with analytical and empirical models from the literature. A 150 mm thick concrete floor and a 100 mm thick floating floor were measured in the floor transmission facility of the National Research Council Canada, i.e. without flanking sound transmission. In addition to the sound reduction index and the normalized impact sound pressure level, loss factors, radiation efficiencies, and mean squared velocities were recorded in the laboratory. The measured data is compared to established models of sound transmission. A focus is placed on the calculation model of ISO 12354-1 (Appendix B), which uses calculated radiation efficiencies and loss factors to predict the sound reduction index of heavy, homogeneous building elements. Some difficulties with the calculation model and the examples in the standard are discussed. In principle, the results in this study show that the calculation model of ISO 12354-1 gives good estimates when the correct input parameters are used. However, deviations between the calculated and the measured loss factors and radiation efficiencies have large effects on the accuracy of the estimates, particularly in the region around the coincidence frequency.

Number of homogeneous components of counterexamples to the Dixmier conjecture

Assume that P and Q are elements of A 1 satisfying [ P , Q ] = 1 . The Dixmier Conjecture for A 1 says that they always generate A 1. We show that if P is a sum of not more than 4 homogeneous elements of A 1 then P and Q generate A 1, which generalizes the main result in [10].

On the effect of energy input on microstructure evolution and mechanical properties of laser beam powder bed fusion processed Ti-27Nb-6Ta biomedical alloy

Additive manufacturing of pre-alloyed Ti-27Nb-6Ta powder by laser beam powder bed fusion (PBF-LB/M) employing a wide range of processing parameters is reported. An in-depth microstructure analysis along the whole process chain from powder feedstock material to additively manufactured bulk structures was conducted employing scanning electron microscopy (SEM) as well as X-ray and high-energy synchrotron diffraction. It is shown that near-fully dense parts (≥ 99.96%) with β+α’’ dual-phase microstructure and very homogenous element distribution are obtained in a large process window. In particular, a considerable influence of the energy input during PBF-LB/M on the solidification microstructure, i.e. phase composition and texture, is found. With increasing energy per unit area (EA) values both an increase in the volume fraction of the bcc β-phase and more pronounced texture components are seen. Furthermore, the mechanical behavior was evaluated under monotonic tensile loading. The PBF-LB/M processed Ti-27Nb-6Ta structures feature good mechanical properties with ultimate tensile strength (UTS) and strain to failure values of up to 768 MPa and 33.8 %, respectively. Due to the strong impact of the energy input during additive manufacturing on the microstructure evolution, however, a significant inverse strength-ductility behavior is observed. While UTS clearly decreases with increasing EA values, strain to failure increases at the same time. The underlying relationships between processing (energy input), microstructure and mechanical properties are explored and rationalized.

Semisimple elements and the little Weyl group of real semisimple [formula omitted]-graded Lie algebras

We consider the semisimple orbits of a Vinberg θ-representation. First we take the complex numbers as base field. By a case by case analysis we show a technical result stating the equality of two sets of hyperplanes, one corresponding to the restricted roots of a Cartan subspace, the other corresponding to the complex reflections in the (little) Weyl group. The semisimple orbits have representatives in a finite number of sets that correspond to reflection subgroups of the (little) Weyl group. One of the consequences of our technical result is that the elements in a fixed such set all have the same stabilizer in the acting group. Secondly we study what happens when the base field is the real numbers. We look at Cartan subspaces and show that the real Cartan subspaces can be classified by the first Galois cohomology set of the normalizer of a fixed real Cartan subspace. In the real case the orbits can be classified using Galois cohomology. However, in order for that to work we need to know which orbits have a real representative. We show a theorem that characterizes the orbits of homogeneous semisimple elements that do have such a real representative. This closely follows and generalizes a theorem from [6].

Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings

In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous elements x,y∈R, then x2∈P or yn∈P, for some positive integer n. Many examples and properties of Gwsq-primary ideals are given. Among several results, we compare Gwsq-primary ideals and other classical graded ideals such as graded strongly quasi primary ideals, graded weakly primary ideals and graded weakly 2-prime ideals etc.

Unraveling impacts of polycrystalline microstructures on ionic conductivity of ceramic electrolytes by computational homogenization and machine learning

The ionic conductivity at the grain boundaries (GBs) in oxide ceramics is typically several orders of magnitude lower than that within the grain interior. This detrimental GB effect is the main bottleneck for designing high-performance ceramic electrolytes intended for use in solid-state lithium-ion batteries, fuel cells, and electrolyzer cells. The macroscopic ionic conductivity in oxide ceramics is essentially governed by the underlying polycrystalline microstructures where GBs and grain morphology go hand in hand. This provides the possibility to enhance the ion conductivity by microstructure engineering. To this end, a thorough understanding of microstructure–property correlation is highly desirable. In this work, we investigate numerous polycrystalline microstructure samples with varying grain and grain boundary features. Their macroscopic ionic conductivities are numerically evaluated by the finite element homogenization method, whereby the GB resistance is explicitly regarded. The influence of different microstructural features on the effective ionic conductivity is systematically studied. The microstructure–property relationships are revealed. Additionally, a graph neural network-based machine learning model is constructed and trained. It can accurately predict the effective ionic conductivity for a given polycrystalline microstructure. This work provides crucial quantitative guidelines for optimizing the ionic conducting performance of oxide ceramics by tailoring microstructures.

The Genesis of a Theorem in the Galois Theory of &amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;-Extensions of &amp;#8474; with Restricted Tame Ramification

This article traces the genesis of a theorem that gives for the first time examples of the Galois group &amp;lt;I&amp;gt;G&amp;lt;SUB&amp;gt;S&amp;lt;/SUB&amp;gt;&amp;lt;/I&amp;gt; of the maximal &amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;-extension of &amp;#8474;, unramified outside a finite set of primes not containing an odd &amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;, that are of cohomlogical dimension 2 if the primes in &amp;lt;I&amp;gt;S&amp;lt;/I&amp;gt; satisfy a certain linking condition. Because the ramification is tame the pro-&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;-group &amp;lt;I&amp;gt;G&amp;lt;SUB&amp;gt;S&amp;lt;/SUB&amp;gt;&amp;lt;/I&amp;gt; has all of its derived factors finite which is a strong finitenesss condition on &amp;lt;I&amp;gt;G&amp;lt;SUB&amp;gt;S&amp;lt;/SUB&amp;gt;&amp;lt;/I&amp;gt;. The paper starts with a question of Serre on one relator pro-&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;-groups and then a detour to discrete groups where the notion of strong freeness for a sequence of homogeneous Lie elements is given and a criterion for strong freeness is established. These notions are then carried over to pro-&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;-groups where the linking condtion on the primes of &amp;lt;I&amp;gt;S&amp;lt;/I&amp;gt; is translated into a cohomological criterion for a pro-p-group to have cohomological dimension 2. An analysis is given of the work of Koch where he gives a weaker criterion for a pro-p-group to have have cohomological dimension 2. A connecttion is made with this work of Koch and that of the author which would have been sufficient to prove the fact that &amp;lt;I&amp;gt;G&amp;lt;SUB&amp;gt;S&amp;lt;/SUB&amp;gt;&amp;lt;/I&amp;gt; was of cohomological dimension 2 for certain sets &amp;lt;I&amp;gt;S&amp;lt;/I&amp;gt; had it been applied to investigate whether the linking condition was true for certain sets &amp;lt;I&amp;gt;S&amp;lt;/I&amp;gt;. It is not known if the cohomological dimension of &amp;lt;I&amp;gt;G&amp;lt;SUB&amp;gt;S&amp;lt;/SUB&amp;gt;&amp;lt;/I&amp;gt; is 2 if &amp;lt;I&amp;gt;S&amp;lt;/I&amp;gt; does not satisfy this linking condition.

Development of a numerical and analytical methodology for analyzing hybrid laminates with multi-oriented piezoelectric and structural layers

Piezoelectric materials can generate an electrical response under mechanical stress, functioning as sensors. Conversely, applying an electrical field to these materials enables precise motion control, making them effective as actuators. Using a proposed methodology, this work focuses on evaluating the effective properties of hybrid multi-oriented composite laminates consisting of structural and piezoelectric layers driven by monoclinic constitutive equations. Square unit cell model was used to calculate all coefficients of the material tensor. The finite element (FE) homogenization method and periodic boundary conditions implemented by node-to-node constraint equations are used to study a representative volume element (RVE) modeled as three-layer unit cell in the mesoscale. The pre-processing, FE analysis, and post-processing are conducted in the FE package ABAQUSⓇ through Python scripts. The computational approach yields results that align closely with the analytical effective coefficients derived from the Asymptotic Homogenization Method (AHM), demonstrating the robustness and accuracy of the proposed methodology.

LA-ICP-MS Analyses of Sulfides from Gold-Bearing Zones at the Perron Deposit, Abitibi Belt, Canada: Implications for Gold Remobilization through Metamorphism from Volcanogenic Mineralizations to Orogenic Quartz–Carbonate Veins

The Perron deposit, located in the northern part of the Archean Abitibi belt, bears some of the highest gold-grade mineralization for orogenic-vein-type deposits worldwide (High-Grade Zone: HGZ). More than 13 gold-bearing zones with different sulfide assemblages, hydrothermal alterations, and gold grades have been recently outlined, and they range from volcanogenic to orogenic in origin. In addition, seven zones are hosted in a restricted volume of ~1 km3, which is called the Eastern Gold Zone. Pyrite, sphalerite, pyrrhotite, and chalcopyrite—each from a different gold-bearing zone—were analyzed with LA-ICP-MS to decipher their genetic links, mineralizing processes, and temperature of formation. The temperatures calculated with the sphalerite GGIMFis thermometer range from 348 to 398 °C. All gold-bearing zones recorded volcanogenic hydrothermal inputs at different intensities, manifested by pyrrhotite. Pyrite was late-metamorphic and related to the orogenic gold system induced by the contact metamorphism of amphibolite facies. The pyrrhotite grains had very homogeneous trace element signatures in all zones, which is a characteristic of metamorphic recrystallization, exhibiting a loss of mobile elements (Au, Te, Bi, Tl, Sn, W, In) but high concentrations of Ni, Co, and As. Conversely, the pyrite was systematically enriched with all elements depleted from pyrrhotite, bearing five specific signatures of element enrichments: W, Tl, Sn, In-Cd-Zn, and Bi-Te-Au. For gold-rich zones (e.g., the HGZ), gold was linked to the Bi-Te-Au signature of pyrite, with Bi enrichment occurring at up to 72,000 times the background level in Archean shale pyrite. It was concluded that gold was transported, at least in part, as Bi-Te melts in the previously documented non-aqueous orogenic fluids, hence accounting for the very-high-grade gold content of the HGZ. Genetically, the metamorphism of primary gold-bearing volcanogenic mineralizations was the main source of gold during the overprinting of amphibolite (600 °C) in a metamorphically induced orogenic mineralizing event. A strong volcanogenic pre-enrichment is considered the main factor accounting for the gold endowment of the Eastern Gold Zone.

Enhanced humidity sensing properties of Ta2O5 and ITO doped rutile-TiO2 porous ceramics

In this study, we investigated the humidity sensing properties of TiO2-based ceramics doped with tantalum pentoxide (Ta2O5) and indium tin oxide (ITO). Pure TiO2, 1%Ta-doped TiO2 (1%TTO), 1%ITO-doped TiO2 (1%ISTO), and 1%(Ta2O5 + ITO) co-doped TiO2 (1%ISTTO) ceramic samples were obtained by sintering at 1200 °C for 3 h. The rutile phase was observed in all samples. The lattice parameters of the single and co-doped samples were larger than those of pure TiO2, confirming the substitution of dopants. Porosity was observed in all ceramics. The mean grain sizes of all doped samples were significantly reduced compared to undoped TiO2. A homogeneous element dispersion was observed in the 1%TTO and 1%ISTTO ceramics, while segregation particles of related In-rich elements was observed in the 1%ISTO ceramic. Giant dielectric properties were not achieved in any samples due to the porosity. Nevertheless, excluding the undoped TiO2, the dielectric properties of all porous ceramics varied significantly with changes in humidity. The 1%ISTTO ceramic demonstrated superior humidity sensing properties, including a low maximum hysteresis error of 3.6% at 102 Hz. In contrast, the 1% TTO and 1% ISTO ceramics showed higher maximum hysteresis errors of 7.2% and 19.8%, respectively. Notably, the response and recovery times were 7.05 ± 0.18 and 2.48 ± 0.39 min, respectively, with good repeatability. This improvement is likely due to the synergistic effect of oxygen vacancies and TaTi·\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Ta}}_{{{\ ext{Ti}}}}^{ \\cdot }$$\\end{document} defects on the surface, enhancing the humidity sensing properties of the 1% ISTTO ceramic, coupled with its optimal microstructure due to its lowest porosity and grain size.

Combined dual-exposure test and DFT investigations into effects of interstitial hydrogen on oxide film of Alloy 600 in high temperature water

The influence of interstitial hydrogen (Hi) in the oxide film of Alloy 600 was investigated using in-situ H charging via dual-exposure test and DFT calculations. H charging modified the oxide film by reducing the oxide particles in the outer oxide layer and transforming the inner oxide film from an uneven thickness and element distribution to a thicker oxide film with a homogenous element distribution. DFT calculations revealed that Hi enhanced the Cr-O interaction while facilitating electron loss in Ni. Additionally, Hi obviously enhanced O diffusion along the Ni-Cr surface, promoting the initial oxidation stage of the Ni-Cr surface.

High-speed shearing: An ultra-fast internal energy accumulation method for nucleation of SnZnO in photocatalysis

Zinc oxide (ZnO) nanoparticles and their derivatives, appreciated for their cost-effectiveness, simplicity in synthesis, and versatile applications, have garnered considerable attention. However, unraveling the nucleation and growth mechanisms of ZnO nanoparticles remains a formidable challenge. By comparing the magnetic stirring synthesis (MSS) and high-speed shearing (HSS) methods, we conducted time-dependent calculations of pressure and velocity at various positions in the solution. Under the powerful shearing force, which is the key route to accumulate internal energy (Ein), molecules could achieve at most 174 eV Ein in HSS instead of 0.81 eV Ein in MSS. Molecules could obtain enough energy for nucleation in just 1.03 μs. HSS, utilizing a high-speed rotor for robust shear forces, not only modifies nucleation patterns but also facilitates effective mixing in multi-element systems. SnxZn1−xO1+x nanoparticles prepared through HSS display uniform size, markedly reduced agglomeration, homogeneous element distribution, and a more pronounced bandgap change, causing a decrease in photocatalytic activity to the original 11.2 %.

Multiscale modeling and thermal conductivity evaluation of nano-reinforced composite materials with pore defect

The performance of resin-based composite materials often exhibits diversity due to the designability of various components. Thermal conductivity, an important thermal parameter of the composite, plays a significant role in thermal-chemical reactions, thermal stress analysis, temperature conduction, etc. However, it is relatively difficult to experimentally explore the thermal conduction mechanism of hybrid composite materials, mainly due to the relatively difficult control of various components. Therefore, this paper proposes a sequentially coupled cross-scale numerical method to characterize the thermal conductivity of nano-reinforced composite materials with pores by a multiscale periodic Representative Volume Element model generated by an improved Random Sequential Absorption algorithm. Firstly, periodic temperature boundary conditions are described, and the thermal conductivity performances of nano-reinforced matrix and composite with pores are investigated based on the finite element homogenization theory. Then, the proposed modes are validated and grid sensitivity analysis is conducted, indicating that the optimal grid sizes for the RVE models are 1.9 nm for the nano-reinforced matrix and 0.14 μm for the composite with pores based on a comprehensive comparison of four pore characterization methods, respectively. Furthermore, the study explored the effect of multiple parameters including nanoparticle content, pore content, and pore shape on thermal conductivity. Numerical findings reveal that the thermal conductivity of the nanocomposite matrix exhibits a linear increase with higher particle content. Specifically, compared to 0 % particle content, the thermal conductivity rises by 141.92 % at 12 % particle content. While the composite material's transverse thermal conductivity is sensitive to porosity content, it is less influenced by pore shape. The method proposed in this paper provides an effective approach for studying the thermal conduction of nano-reinforced composite materials with pores, and the research findings also offer theoretical guidance for process engineers.

Comparison of Continuous and Discrete Modeling Strategies for the Structural Assessment of a Masonry Vault Under Dynamic Seismic Loading

ABSTRACT To begin, the paper introduces methodologies employing both homogeneous continuous Finite Element Method (FEM) and block-by-block Discrete Element Method (DEM) to model masonry behaviors. In the continuous approach, the masonry is modeled as an anisotropic damageable material (homogeneous or not). In contrast, the block-based approach represents rigid blocks interacting through contact joints governed by frictional cohesive behaviors. The DEM framework allows for significant displacements, rotations, and complete detachments of blocks, aspects often overlooked in traditional FEM models. The primary application of this research involves the seismic assessment of a masonry cross vault. Notably, the numerical results exhibit the approach’s capability to provide realistic predictions of failure mechanisms, crucial for retrofitting efforts. This includes an accurate representation of the actual cracking pattern, accounting for significant displacements. The numerical implementation is accessible through the open-source LMGC90 software. Comparative analyses are then carried out, focusing on the strengths and weaknesses of FEM macro-modeling (continuous homogeneous description) and DEM utilizing rigid blocks.

Graded amalgamated algebras along an ideal defined by graded 1-absorbing-like conditions

Let [Formula: see text] be a group with identity and [Formula: see text] be a [Formula: see text]-graded commutative ring with nonzero identity. A proper graded ideal [Formula: see text] of [Formula: see text] is called a graded 1-absorbing prime ideal (respectively, graded 1-absorbing primary ideal) if whenever nonunit homogeneous elements [Formula: see text] with [Formula: see text], then [Formula: see text] or [Formula: see text] (respectively, [Formula: see text] or [Formula: see text], where [Formula: see text] is the graded radical of [Formula: see text]). The purpose of this paper is to study the transfer of some graded 1-absorbing-like properties to the graded amalgamated algebra along an ideal (denoted by [Formula: see text]). Our results provide new techniques for the construction of new original examples satisfying the above-mentioned properties.

A Novel Weak-Form Plane Frame Quadrature Element and its Application to Bridge Analysis

A novel weak-form plane frame quadrature element (WPFQE) is developed. A complex structure can be divided into several non-homogeneous (or homogeneous) elements with large size. The Chebyshev–Lobatto differential quadrature dealing with differentiation and the Gauss–Lobatto quadrature dealing with integration have the same integration points including the ends of each element. Based on the energy variational principle, the diagonal mass matrix and positive definite real symmetric stiffness matrix for the element can be obtained. The unknown quantities at the internal quadrature points of the element can be represented by those at the endpoints of the element based on the principle of static equal effect anterior to the development of global matrices, which significantly reduces the sizes of modified element matrices while maintaining sufficient accuracy, thereby obtaining the small-sized global matrices. Assembly of elements can be performed efficiently just as that in the finite element (FE) method. In the case study, the static and dynamic performances of a three-span high-pier rigid-frame bridge with variable cross-section are studied by applying the proposed method. The results indicate that the orders of structural matrices and calculation time obtained by the WPFQE method are much smaller than those of the FE method.

Effect of Temperature on the Corrosion Behavior of a Al2Cr5Cu5Fe53Ni35 Multi-Principal Element Alloy (MPEA) in Simulated Soil Environments

The effect of varying temperatures (15, 35, and 45 °C) on the corrosion behavior of a new single-phase distorted face-centered cubic (fcc) Al2Cr5Cu5Fe53Ni35 multi-principal element alloy (MPEA) was studied in simulated soil environments (NS4 solution). X-ray diffraction and electron backscattered diffraction were used to confirm the presence of a single phase throughout the microstructure. Electrochemical tests such as electrochemical impedance spectroscopy and linear polarization resistance were performed to evaluate the interfacial behavior and corrosion rate at various test conditions. Additionally, cyclic potentiodynamic polarization (CPP) tests were also carried out at the selected temperatures to study the pitting behavior of the MPEA. Surface characterization techniques such as X-ray photoelectron spectroscopy and scanning electron microscopy were used to identify the nature of the passive film formed in such complex materials as well as study the pitting characteristics after CPP testing. A stable passive film was found to be present all tested temperatures with the absence of preferential sites for pitting due to homogenous element distribution.

Старение и надежность: как вариации во времени интенсивности отказов влияют на форму кривых дожития стареющих организмов

The article considers the regularities of the theory of reliability, which determine the constancy of the shape of the curves of organisms’ survival. The assumption that the probability of natural death is determined by the probability of accidental failure of a part of a series of homogeneous elements (cells) allows to obtain, analytically and through numerical experiments, survival curves similar to those observed in nature. The use of com-puter modelling methods makes it possible to identify the survival curve parameters determined by the dynamics of the probability of failure of an individual element. The value of one of these parameters, namely the coordinates of the inflection point of human survival curves, indicates that, apparently, both in long-lived species in general and in humans specifically, the ageing promoting mechanism is the progressive deterioration of reliability - the dilapidation of the elements (cells) crucial for ageing.