Hydrophobic Mismatch Controls the Mode of Membrane-Mediated Interactions of Transmembrane Peptides

Various cellular processes require the concerted cooperative action of proteins. The possibility for such synchronization implies the occurrence of specific long-range interactions between the involved protein participants. Bilayer lipid membranes can mediate protein–protein interactions via relatively long-range elastic deformations induced by the incorporated proteins. We considered the interactions between transmembrane peptides mediated by elastic deformations using the framework of the theory of elasticity of lipid membranes. An effective peptide shape was assumed to be cylindrical, hourglass-like, or barrel-like. The interaction potentials were obtained for membranes of different thicknesses and elastic rigidities. Cylindrically shaped peptides manifest almost neutral average interactions—they attract each other at short distances and repel at large ones, independently of membrane thickness or rigidity. The hourglass-like peptides repel each other in thin bilayers and strongly attract each other in thicker bilayers. On the contrary, the barrel-like peptides repel each other in thick bilayers and attract each other in thinner membranes. These results potentially provide possible mechanisms of control for the mode of protein–protein interactions in membrane domains with different bilayer thicknesses.

Determination of Thermomechanical Stresses in Elements of Vehicles’ Braking Systems

The main objective of the study was to develop a model and analyze the thermomechanical behavior of the hub material of the vehicle brake disk. The simulation strategy was based on the solution of the three-dimensional problem of the theory of elasticity for the case of effect of external loads and temperature fields on the metal structure element of the vehicle brakes. To solve this type of task of the theory of elasticity, the differential equations of the second order were used for the first time. Adaptation of the proposed model, completed in the article, has proved the correctness of use of these equations in modeling the thermomechanical processes with determination of stresses and displacements in unevenly heated rotary cylinders of the final length. The proposed method can be applied with high efficiency in stress strain state simulation of individual parts of vehicles.

Two-level mathematical models for determining the stress state and life plate with a hole

Modern trends in the development of mechanical engineering and other industries related to the production of materials and structures with a given set of physical, mechanical, and technological properties are aimed at reducing material consumption, energy consumption, increasing accuracy, reliability, and competitiveness of the manufactured product. Therefore, the creation of mathematical methods for assessing the stress state of structural elements based on the analysis of the elastic characteristics of a material, taking into account the peculiarities of its internal microstructure, is an actual task. The considered algorithm includes the following stages: identification of strength parameters using data obtained from images of the material microstructure; study of the stress-strain state of the model based on the variational-difference finite element method; formation of a system of linear algebraic equations for solving the problem of analyzing the elastic properties of a material using the plane problem of the theory of elasticity; construction of the material yield surface for a series of tests based on the strength criteria of composite materials, taking into account the different resistance of the material under tensile and compressive loads. Based on the developed mathematical model, the SSS and the yield surface of the plate with a hole are estimated. Structural analysis is performed at the macro and micro levels. The occurrence of plastic deformations at the micro-level can lead to the development of cracks and structural damage at the macro level. As a result of the study, the probability of plastic deformation in the plate is determined, and the critical zones of the model are established. The practical significance of the results obtained is to create an approach to assessing the mechanical properties of a material, such as elastic modulus, shear modulus, Poisson's ratio, and their probabilistic characteristics following the internal material structure. The proposed approach contributes to the expansion of knowledge about the material and allows to increase the valuable information obtained by modeling. To assess the probability of plastic deformations, the generated method uses the entire set of probabilistic characteristics of the yield surface.

The generalized stokes integral theorem for a covariant pseudotensor field

Ориентируемые континуумы играют важную роль в микрополярной теории упругости, все реализации которой возможны только в рамках псевдотензорного формализма и представления об ориентируемом многообразии. Особенно это касается теории микрополярных гемитропных упругих сред. В настоящей работе рассматриваются различные формулировки интегральной теоремы Стокса для асимметричного ковариантного пседотензорного поля, заданного веса. Тем самым достигается распространение известной интегральной формулы Стокса на случай псевдотензоров. Последнее обстоятельство позволяет использовать, указанное обобщение для микрополярных континуумов. Исследование существенно опирается на класс специальных координатных систем. Oriented continua play an important role in the micropolar theory of elasticity, all realizations of which are possible only within the framework of the pseudotensor formalism and the orientable manifold concept. This especially concerns the theory of micropolar hemitropic elastic media. In this paper, we consider various formulations of the Stokes integral theorem for an asymmetric covariant pseudotensor field of a given weight. This extends the well-known Stokes integral formula to the case of pseudotensors. The latter circumstance makes it possible to use the manifistated generalization for micropolar continua. The study relies heavily on the class of special coordinate systems.

Modeling of relative shear deformation zones before strong earthquakes in Kamchatka from 2018-2021

Представлено сравнительное моделирование зон относительных сдвиговых деформаций для четырех камчатских землетрясений с Mw ≥ 4.8, произошедших в период с декабря 2018 г. по март 2021 г., основанное на статической модели деформационного поля в рамках теории упругости. Земная кора рассмотрена как однородное изотропное упругое полупространство, в котором присутствуют различные источники напряжения, описывающие очаг землетрясения: точечный источник в виде единичной силы, точечный источник в виде комбинации девяти двойных сил, распределенный источник в виде прямоугольной площадки. We present a comparative modeling of the zones of relative shear deformation for four Kamchatka earthquakes Mw≥4.8 that occurred between December 2018 and March 2021. Modeling based on a static model of the deformation field in the framework of the theory of elasticity. The Earth’s crust is considered as a homogeneous isotropic elastic half-space, in which there are different sources of stress describing the source of the earthquake: a point source in the form of a single force, a point source in the form of a combination of nine double forces, a distributed source in the form of a rectangular area.

Behavior of solution of the elasticity problem for a radial inhomogeneous cylinder with small thickness

A non-axisymmetric problem of the theory of elasticity for a radial inhomogeneous cylinder of small thickness is studied. It is assumed that the elastic moduli are arbitrary positive piecewise continuous functions of a variable along the radius. Using the method of asymptotic integration of the equations of the theory of elasticity, based on three iterative processes, a qualitative analysis of the stress-strain state of a radial inhomogeneous cylinder is carried out. On the basis of the first iterative process of the method of asymptotic integration of the equations of the theory of elasticity, particular solutions of the equilibrium equations are constructed in the case when a smooth load is specified on the lateral surface of the cylinder. An algorithm for constructing partial solutions of the equilibrium equations for special types of loads, the lateral surface of which is loaded by forces polynomially dependent on the axial coordinate, is carried out. Homogeneous solutions are constructed, i.e., any solutions of the equilibrium equations that satisfy the condition of the absence of stresses on the lateral surfaces. It is shown that homogeneous solutions are composed of three types: penetrating solutions, solutions of the simple edge effect type, and boundary layer solutions. The nature of the stress-strain state is established. It is found that the penetrating solution and solutions having the character of the edge effect determine the internal stress-strain state of a radial inhomogeneous cylinder. Solutions that have the character of a boundary layer are localized at the ends of the cylinder and exponentially decrease with distance from the ends. These solutions are absent in applied shell theories. Based on the obtained asymptotic expansions of homogeneous solutions, it is possible to carry out estimates to determine the range of applicability of existing applied theories for cylindrical shells. Based on the constructed solutions, it is possible to propose a new refined applied theory.

Influence of the Moment in Mathematical Models for Open Systems

Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.