Mathematical Model Of Mechanism Research Articles

Modeling Of Chlorophyll a Content in Microalgae Cultures

The work focuses on mathematical modeling of light influence mechanisms on chlorophyll a content in microalgae biomass. The well-known qualitative models are based on concepts of synthesis and photodestructive oxidation of chlorophyll a, however the later for some microalgae species seems doubtful. We proposed an alternative approach to modeling the light-dependent chlorophyll a content in microalgae biomass. The basic model is based on generally accepted two-stage photoautotrophic growth of microalgae. At the first stage, during photosynthesis a reserve part of biomass is formed, from which the biosynthesis of cell structures occurs at the second stage. Three partial solutions of the basic system of equations describing the dependence of chlorophyll a content on the external light intensity are considered for various limiting conditions. Due to the equality of specific growth rates of formation of reserve and structural forms of biomass, the equations obtained can be used only for turbidostat cultures. Verification of the obtained equations for Arthrospira platensis allows us to estimate kinetic coefficients, the values of which are generally in good agreement with theoretically calculated ones. For approximate calculations, a simple equation is proposed that shows a good agreement with experimental data for Tetraselmis viridis (R2 = 0.98), Dunaliella tertiolecta (R2 = 0.92) and describes the results for Sceletonema costatum and Chlorella vulgaris (R2 = 0.8) quite well. Chlorophyll a refers to structural forms of biomass. The proportion of chlorophyll a in the structural biomass is about 2.5–3.5 %, it is a species-specific parameter.

Yeast ATM and ATR kinases use different mechanisms to spread histone H2A phosphorylation around a DNA double-strand break

One of the hallmarks of DNA damage is the rapid spreading of phosphorylated histone H2A (γ-H2AX) around a DNA double-strand break (DSB). In the budding yeast Saccharomyces cerevisiae, nearly all H2A isoforms can be phosphorylated, either by Mec1ATR or Tel1ATM checkpoint kinases. We induced a site-specific DSB with HO endonuclease at the MAT locus on chromosome III and monitored the formation of γ-H2AX by chromatin immunoprecipitation (ChIP)-qPCR in order to uncover the mechanisms by which Mec1ATR and Tel1ATM propagate histone modifications across chromatin. With either kinase, γ-H2AX spreads as far as ∼50 kb on both sides of the lesion within 1 h; but the kinetics and distribution of modification around the DSB are significantly different. The total accumulation of phosphorylation is reduced by about half when either of the two H2A genes is mutated to the nonphosphorylatable S129A allele. Mec1 activity is limited by the abundance of its ATRIP partner, Ddc2. Moreover, Mec1 is more efficient than Tel1 at phosphorylating chromatin in trans-at distant undamaged sites that are brought into physical proximity to the DSB. We compared experimental data to mathematical models of spreading mechanisms to determine whether the kinases search for target nucleosomes by primarily moving in three dimensions through the nucleoplasm or in one dimension along the chromatin. Bayesian model selection indicates that Mec1 primarily uses a three-dimensional diffusive mechanism, whereas Tel1 undergoes directed motion along the chromatin.

Capillary continuity in fractured porous media; part II: Evaluation of fracture capillary pressure in the presence of liquid bridges using a novel microfluidic approach

Fracture capillary pressure plays a major role in many aspects of fluid flow in fractured rocks, including physical interpretation, mathematical modeling, and simulation of various mechanisms. The 2D microfluidic devices are a ubiquitous tool to study the multiphase behavior of fractures. However, these devices still suffer from two essential limitations: 1) narrow-etched depth of the middle fracture, producing an undesirable effect on the fracture capillary pressure and 2) undesired deformation of the liquid bridge curvature. In this work, a novel technique is developed for fabricating microfluidic devices where the 2D domain is attached to a 3D open medium that is realistic enough to capture the essential physics underlying the mechanisms of multiphase flow and liquid bridge evolution in fractures.The developed “3D fracture-2D matrix” microfluidic device is utilized to study the mechanism of gas gravity drainage in fractured rocks and evaluate the available models that describe the fracture capillary pressure. The reasonable agreement between experimental results and theoretical calculations reveal that the Young-Laplace equation can be used as a framework for the fracture capillary pressure. This result is in contrast with the previous experimental results in the literature that rejected the validity of the Young-Laplace equation for evaluating fracture capillary pressure. Furthermore, the capillary bridge description is a key parameter in evaluating the fracture capillary pressure and estimating the recovery profile of matrix blocks through the capillary continuity phenomenon. The visual analysis shows that the circle approximation can describe the shape of the bridge and the dynamic bridge curvature is almost constant during the fracture desaturation under the gravity drainage mechanism. These findings can improve our understanding of fracture capillary pressure models that not only affect the ultimate recovery but also are required to design enhanced oil recovery in fractured reservoirs.

Generalized mechanical-mathematical model for optimization of two-bearing shafts of minimal material consumption

A universal theory of solving the original problems of applied mechanics was developed to determine the rational geometric parameters of two-bearing three-stage shafts of the smallest volume with two nozzles, covering three modifications of the design under consideration. The optimization process model is brought to the calculation algorithm and is illustrated by a characteristic numerical example. Keywords: optimization, strength condition, minimum volume, extremum, objective function. klm221@mail.ru

Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate

The tower clocks designed and built in Europe starting from the end of the 13th century employed the “verge and foliot escapement” mechanism. This mechanism provided a relatively low accuracy of time measurement. The introduction of the pendulum into the clock mechanism by Christiaan Huygens in 1658–1673 improved the accuracy by about 30 times. The improvement is attributed to the isochronicity of small linear vibrations of a mathematical pendulum. We develop a mathematical model of both mechanisms. Using scaling arguments, we show that the introduction of the pendulum resulted in accuracy improvement by approximately π/μ ≈ 30 times, where μ ≈ 0.1 is the coefficient of friction. Several historic clocks are discussed, as well as the implications of both mechanisms to the history of science and technology.

Multiple limit-cycles shimmy characteristics of dual-axle steering mechanism considering the wheel alignment parameters

In this study, a nine degree of freedom mathematical model of dual-axle steering mechanism considering the wheel alignment parameters is established. Taking one multi-axle vehicle with dual-axle mechanism for example, the numerical method is used to analyze the effects of the wheel alignment parameters on multiple limit-cycles shimmy characteristics. The results show that the variation of the camber angle, the toe angle, and the caster angle will cause the maximum swing angles of first and second axle and the speed ranges of multiple limit-cycles shimmy to change. In addition, taking the caster angle as an example, the effects of matching of different wheel alignment parameters for the first and second axle on multiple limit-cycles shimmy characteristics were discussed. It is found that the effects which the caster angle of second axle having on multiple limit-cycles shimmy characteristics of dual-axle steering mechanism are much more greater than the caster angle of first axle's effects. This finding can provide theoretical guidance for suppressing multiple limit-cycles shimmy of the multi-axle vehicle with dual-axle steering mechanism.

Simulation and experimental study of mechanicalproperties of a compound water propulsion device

The traditional amphibious platform mostly adopts the displacement type boat shape vehicle body, equips the propulsion of two sets of water and land, which has the problems of the complex structure and low speed. Based on the bionic dynamical principle, this paper designed a wheel-blade hybrid propulsion amphibious platform to explore a new structure of amphibious platform with three functions: underwater diving, surface navigation and land driving. Some softwares were used to establish the numerical calculation model of wheel-blade compound propulsion mechanism, and the influence of different parameters on the driving performance was analyzed. The mathematical model of propulsion mechanism based on beam model is established and the impeller strength is checked.

THE MECHANISMS OF SMART MANAGEMENT FOR INDUSTRIAL ENTERPRISES

In this article you can find some mathematical models of the smart management mechanisms that can be used in the organizational system of management of production corporations. The following mechanisms can be used to improve the management effectiveness of this system: the resource-allocating mechanism (the mechanism of direct priorities, the reverse priorities, the competitive mechanism, the mechanism of open management); the mechanism of active expertise (the mechanism of averaging experts' opinions, mechanisms based on median schemes); the mechanism of domestic prices; cost-cutting pricing and taxation mechanisms; the supply chain optimization mechanism; the assortment selection mechanism; incentive mechanisms (incentives for individual results, collective results, and the brigade payment mechanism); integrated mechanisms.

Exon Definition Facilitates Reliable Control of Alternative Splicing in the RON Proto-Oncogene

Alternative splicing is a key step in eukaryotic gene expression that allows for the production of multiple transcript and protein isoforms from the same gene. Even though splicing is perturbed in many diseases, we currently lack insights into regulatory mechanisms promoting its precision and efficiency. We analyze high-throughput mutagenesis data obtained for an alternatively spliced exon in the proto-oncogene RON and determine the functional units that control this splicing event. Using mathematical modeling of distinct splicing mechanisms, we show that alternative splicing is based in RON on a so-called “exon definition” mechanism. Here, the recognition of the adjacent exons by the spliceosome is required for removal of an intron. We use our model to analyze the differences between the exon and intron definition scenarios and find that exon definition prevents the accumulation of deleterious, partially spliced retention products during alternative splicing regulation. Furthermore, it modularizes splicing control, as multiple regulatory inputs are integrated into a common net input, irrespective of the location and nature of the corresponding cis-regulatory elements in the pre-messenger RNA. Our analysis suggests that exon definition promotes robust and reliable splicing outcomes in RON splicing.

Brain energetics, mitochondria, and traumatic brain injury.

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

Signalling architectures can prevent cancer evolution

Cooperation between cells in multicellular organisms is preserved by an active regulation of growth through the control of cell division. Molecular signals used by cells for tissue growth are usually present during developmental stages, angiogenesis, wound healing and other processes. In this context, the use of molecular signals triggering cell division is a puzzle, because any molecule inducing and aiding growth can be exploited by a cancer cell, disrupting cellular cooperation. A significant difference is that normal cells in a multicellular organism have evolved in competition between high-level organisms to be altruistic, being able to send signals even if it is to their detriment. Conversely, cancer cells evolve their abuse over the cancer’s lifespan by out-competing their neighbours. A successful mutation leading to cancer must evolve to be adaptive, enabling a cancer cell to send a signal that results in higher chances to be selected. Using a mathematical model of such molecular signalling mechanism, this paper argues that a signal mechanism would be effective against abuse by cancer if it affects the cell that generates the signal as well as neighbouring cells that would receive a benefit without any cost, resulting in a selective disadvantage for a cancer signalling cell. We find that such molecular signalling mechanisms normally operate in cells as exemplified by growth factors. In scenarios of global and local competition between cells, we calculate how this process affects the fixation probability of a mutant cell generating such a signal, and find that this process can play a key role in limiting the emergence of cancer.

Modeling of deformation processes in rock massif in the vicinity of underground goafs considering the formation of discontinuity zones

ABSTRACT The construction of mechanical-mathematical model and numerical method for the deformation processes of rock massifs with goafs and underground structures is very complex and also important task in modern rock mechanics. In this study, the mechanical-mathematical model is developed for rock massif in vicinity of underground goafs considering the internal block-layered structure of the rock massif. A new constitutive model is introduced in this study to describe the negative Poisson's ratio for the lock-layered structure. Two types of defining equations systems for studying the state of a rock massif taking into account the block-layered structure are described. Finally, several examples are given using the present mechanical-mathematical model.

Структурный синтез семейства плоских восьмизвенных кинематических цепей рычажных механизмов с многократными шарнирами и наиболее сложным трехшарнирным звеном

Structural synthesis of closed kinematic chains to create various mechanisms is the first and most difficult stage of creative design of complex machines due to the large variance of possible structural solutions. In this paper, the authors examine the problem of structural synthesis of a family of eight-link kinematic chains with multiple joints of various types and the most complex three-joint link in order to create multi-loop multiple-joint mechanisms with one degree of freedom. To solve this problem, a synthesis technique is proposed based on the search for all integer solutions of a generalized structural mathematical model of plane linkage mechanisms and the identification of all structurally nonisomorphic kinematic chains using a two-column P-matrix. As the result of the structural synthesis, a family of eight-link multiple joint kinematic chains is obtained, which contains seven new kinematic structures. Examples of creating 1-DOF mechanisms with multiple joints based on the obtained new structures are presented. They confirm the effectiveness of using the structural synthesis procedure and analysis of complex mechanisms with multiple joints in various areas of modern engineering (precise guiding mechanisms, automatic lines, technological machines, robots, manipulators, etc.).

Mathematical model of a drive mechanism with a crank device of a crank press

The most important link in the forging equipment is a crank mechanism. Their significant drawback is the unbalanced inertia forces of the moving masses of the crank mechanism, which cause vibration. The analysis of the phenomena occurring in the mechanism and the assessment of the technological process are based on the theory of chains, which allows analytically analyzing the dynamic characteristics of systems with a large number of degrees of freedom, based on the analysis of one structural element. The study of the process of force interaction inevitably comes down to the construction of a mathematical model of mechanisms, the formative movement of which leads to its formation. One of the partial systems makes an irregular programmed motion, meaning the crank drive mechanism. In addition, unwanted vibrations caused by kinematic excitation are superimposed on this drive. According to numerous papers on this topic, significant dynamic errors arise due to vibration accelerations. One of the main tasks in reducing the vibration activity and, accordingly, the level of acoustic emission of the process under study is to ensure the required law of motion of the instrument. On this basis, the study of the stability of formative movements is of particular importance. This question is complicated by the fact that in the processing, there is a change in the process parameters and, consequently, in the characteristics of the friction coupling. The latter circumstance presupposes the evolution of the system under study, and therefore the need for process control.

Mechanical-mathematical model of tractor wheel propulsor interaction with bearing surface

Mechanical-mathematical model of tractor wheel propulsor interaction with bearing surface

Study of tensile properties of plain-woven fabrics in all-directional using energy method, Part I: theoretical study

In the first part of this series, a new mechanical parameter, that is, “Comprehensive Tensile Modulus (CTM)” is introduced and modeled to show the tensile behavior of plain-woven fabrics in the initial linear elastic region of the force-elongation curve subjected to tensile load and extended it simultaneously in all directions. Considering the initial load-extension behavior of fabrics, a mathematical-mechanical model is presented to predict the CTM of fabrics in the initial linear elastic region using Castigliano’s theorem. Based on the generated model, the initial sample length, dimension of the load imposed region, the geometrical shape created in the plain-woven fabric sample during tensile, the structural specification of these fabrics such as yarns sett, yarns crimp in fabric and mechanical properties of yarns such as bending rigidity in both warp and weft yarns affect in the comprehensive tensile modulus of fabric. In order to verify the conformity and accuracy of the model, a preliminary test was conducted on the prepared samples based on a novel tensile test method developed to measure load-extension curve of the fabric samples under the proposed loading condition. A reasonable agreement was found between theoretical and experimental results.

A Mathematical Model of Regulatory Mechanisms of Hepatocytes and Hepatitis B

A Mathematical Model of Regulatory Mechanisms of Hepatocytes and Hepatitis B

Simulation of vehicle’s lateral dynamics using nonlinear model with real inputs

Basic understanding of vehicle’s lateral dynamics may be achieved by using relatively simple mathematical-mechanical models. However, these models are often linearized and do not take into account nonlinear phenomena in vehicle’s lateral dynamics and highly nonstationary nature of vehicle’s vibrations in real driving conditions. One form of nonlinear nonstationary model of vehicle’s lateral dynamics is developed in this paper. Simulations were conducted using experimentally recorded values of the steering wheel angle for generation of the front wheels steer angle, and vehicle longitudinal velocity as inputs to the model. Results of simulations of vehicle angular vibrations around the vertical axis, angular body side slip vibrations, tire slip angles, vehicle lateral acceleration wheel forces and inertial force are presented and discussed. Finally, conclusions regarding possible further use of the developed model were drown.

A New Data-driven Roll Force and Roll Torque Model Based on FEM and Hybrid PSO-ELM for Hot Strip Rolling

In this paper, a new Extreme Learning Machine (ELM) regression model of roll force and roll torque based on data-driven is proposed. The three-dimensional elastic-plastic finite element model (FEM) is established to solve the roll force and roll torque under different parameters (including rolling reduction rate, roll radius, rolling speed, average width of strip, entry temperature of strip). The regression model of ELM optimized by Particle Swarm Optimization (PSO) is established through using the datasets obtained by FEM. The PSO-ELM model prediction values of roll force and roll torque are compared with the single ELM and PSO-SVM model, and the error results of the prediction values are analyzed. The error results fully verify the feasibility and accuracy of the PSO-ELM model proposed. It is found that the new data-drive model of roll force and roll torque is simple in structure and it can make up for the deficiency of traditional mathematical mechanism model in dealing with nonlinear problems. The research result reveals that PSO-ELM method is suitable for parameters prediction and model optimization in strip rolling process.

Classification and analysis of constraint singularities for parallel mechanisms using differential manifolds

• Differential manifolds and their tangent spaces are used for motion modelling. • Motions of parallel mechanisms with different constraint singularities are modelled. • Constraint singularities of parallel mechanisms are classified into two kinds. • Singularities causing bifurcated motions, instantaneous DoFs are separated. • Two examples are given to verify the theoretical results. This paper presents investigations into classification and analysis of constraint singularities for parallel mechanisms. Parallel mechanisms (also called parallel manipulators or parallel robots) have wide applications in industry. The singularities tremendously affect their applications. Existing research works show that constraint singularity causes a mechanism to have instantaneous degree-of-freedoms (DoFs) or bifurcated finite motions. However, the intrinsic differences among the conditions under which the specific constraint singularities happen have not been discussed. This paper is focused on these topics by using differential manifolds as mathematical tools. Firstly, the general mathematical models of parallel mechanisms are formulated by respectively describing their finite motions and instantaneous motions in forms of differential manifolds and their tangent spaces. Then, parallel mechanisms having bifurcated finite motions and instantaneous DoFs are modelled accordingly, and the constraint singularities are thus classified into two kinds by considering their influences on motions of mechanisms in both finite and instantaneous motion levels. Finally, two examples are given to further illustrate the theoretical analysis. This paper lays foundations for mathematical modelling and applications of parallel mechanisms with constraint singularities.