scholarly journals Influence of the Moment in Mathematical Models for Open Systems

2021 ◽  
Vol 16 ◽  
pp. 250-260
Author(s):  
Evelina Prozorova
Keyword(s):  
Mathematical Models ◽  
Stress Tensor ◽  
Open Systems ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Collective Effects ◽  
Physical Parameters ◽  
Potential Flows ◽  
The Moment ◽  
Definition Of

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.

FREE VIBRATION OF AN ORTHOTROPIC HOLLOW BODY OF REVOLUTION

2005 ◽  
Vol 05 (02) ◽  
pp. 299-312
Author(s):  
D. REDEKOP
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Body Of Revolution ◽  
Orthotropic Cylinder ◽  
Dimensional Theory ◽  
Hollow Cylinders ◽  
Definition Of

A method is developed to determine the natural frequencies of vibration of an orthotropic hollow body of revolution of constant thickness but of arbitrary smooth meridian. Equations are derived using the linear three-dimensional theory of elasticity, and a numerical solution is obtained using the differential quadrature method. The geometric generality of the solution is attained by delaying definition of local geometric parameters until the solution stage. Validation is by comparison with previously published results, including results for a hollow orthotropic cylinder. Sample results are given for orthotropic hollow cylinders and spherical segments, and conclusions are drawn.

scholarly journals An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

1998 ◽  
Vol 09 (08) ◽  
pp. 1393-1404 ◽  
Author(s):  
D. J. Holdych ◽  
D. Rovas ◽  
J. G. Georgiadis ◽  
R. O. Buckius
Keyword(s):  
Multiphase Flow ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Effective Field ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Physical Parameters ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Definition Of

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

ПРИНЦИП ВОЗМОЖНЫХ ПЕРЕМЕЩЕНИЙ В МОМЕНТНОМЕМБРАННОЙ ДИНАМИЧЕСКОЙ ТЕОРИИ УПРУГИХ ТОНКИХ ОБОЛОЧЕК / The Principle of Possible Displacments in the Moment-Membrane Dynamic Theory of Elastic Thin Shells

2021 ◽  
pp. 10-19
Author(s):  
S. Sargsyan
Keyword(s):  
Boundary Value Problem ◽  
Dynamic Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Thin Shells ◽  
Moment Theory ◽  
Thin Region ◽  
Membrane Dynamic ◽  
Dimensional Boundary ◽  
The Moment

В работе излагается моментно-мембранная динамическая теория упругих тонких оболочек на основе метода гипотез, который соответствует качественной стороне результата интегрирования трехмерной граничной задачи моментной теории упругости в тонкой области оболочки. На основе принципа возможных перемещений трехмерной моментной динамической теории упругости с независимыми полями перемещений и вращений и основных соотношений моментномембранной динамической теории упругих тонких оболочек, устанавливается принцип возможных перемещений для моментномембранной динамической теории упругих тонких оболочек./ In the present paper the moment-membrane dynamic theory of elastic thin shells is presented based on the hypotheses method, which corresponds to the qualitative side of the result of integration of the three-dimensional boundary-value problem of the moment theory of elasticity in a thin region of the shell. On the basis of the principle of possible displacements of the threedimensional moment dynamic theory of elasticity with independent fields of displacements and rotations and the basic relations of the moment-membrane dynamic theory of elastic thin shells, the principle of possible displacements for the moment-membrane dynamic theory of elastic thin shells is established.

Conformation Control of DNA Molecules by Means Geometric and Physical Parameters

2019 ◽  
Vol 20 (9) ◽  
pp. 550-559
Author(s):  
A. A. Ilyukhin ◽  
D. V. Timoshenko
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interatomic Interaction ◽  
Theory Of Elasticity ◽  
Physical Parameters ◽  
Dimensional Problem ◽  
Dna Molecules ◽  
Conceptual Approach ◽  
Deformable Solid ◽  
One Dimensional

A conceptual approach to the problem of managing spatial configurations of DNA molecules is considered. The work is problematic in nature and is a synthesis of the authors’ research in the field of modeling the behavior and structure of DNA by the methods of the mechanics of a deformable solid. The subject of research in this paper is the question of the applicability of methods of control theory to a living object by the example of a DNA molecule. The paper considers both issues of controllability on examples of the influence of the parameters of a molecule on its configuration, and questions of observability and identification of parameters of a molecule, based on the visible configuration in the natural environment. A brief review of the authors’ results in terms of adaptation to the objects of research of existing and development of new mathematical models of deformable elastic objects with regard to their internal structure is given. The proposed approach is based on the concept of transition using known methods of molecular dynamics from a multi-element discrete medium to a continuum containing momentary stresses. To this end, in previous works, the authors obtained the dependence of the components of the strain tensors, force and moment stresses on various types of interatomic interaction potentials (LennardJones potential, Born-Meyer potential, etc.). The need to choose as the base model of a continuum containing momentary stresses is dictated by the peculiarities of the main object of study - nucleic acid molecules and biopolymers - which have several degrees of freedom of rotational motions. Also, as an example, we consider the case for which the reduction from the three-dimensional problem of the asymmetric theory of elasticity to a one-dimensional one was carried out by splitting the three-dimensional problem into a set of two-dimensional and one-dimensional problems. The kinematic parameters that are necessary to attract in order to obtain a closed system of equations of the one-dimensional moment theory of rods with the system of Kirchhoff’s differential equations are indicated. The remaining geometrical values are found from the relations defining them. The proposed approach is consistent with current trends in the field of molecular modeling in biophysics and physico-chemical biology, and it seems promising in solving the problems of controlling genetic and biochemical processes involving DNA.

scholarly journals Influence of the Angular Momentum in Problems Continuum Mechanics

2021 ◽  
Vol 16 ◽  
pp. 1-8
Author(s):  
Evelina Prozorova
Keyword(s):  
Conservation Laws ◽  
Continuum Mechanics ◽  
Stokes Equations ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Potential Flows ◽  
Balance Of Forces ◽  
And Mathematics

- For continuum mechanics a model is proposed, that is built with consideration outside the integral term when deriving conservation laws using the Ostrogradsky-Gauss theorem. Performed analysis shows discrepancy between accepted classical conservation laws and classical theoretical mechanics and mathematics. As a result, the theory developed for potential flows was extended to flows with significant gradients of physical parameters. We have proposed a model that takes into account the joint implementation of the laws for balance of forces and angular momentums. It does not follow from the Boltzmann equation that the pressure in the Euler and Navier-Stokes equations is equal to one third of the sum the pressures on the corresponding coordinate axes. The vector definition of pressure is substantiated. It is shown that the symmetry condition for the stress tensor is one of the possible conditions for closing the problem. An example of solving the problem of the theory of elasticity is given

Application of high-resolution field-emission LVSEM, backscatter imaging, immunogold staining to definition of the spatial distributions of two human neutrophil adherence receptors

1993 ◽  
Vol 51 ◽  
pp. 36-37
Author(s):  
Robert D. Nelson ◽  
Sharon R. Hasslen ◽  
Stanley L. Erlandsen
Keyword(s):  
Cell Surface ◽  
Surface Membrane ◽  
Three Dimensional ◽  
Human Neutrophils ◽  
Spatial Distributions ◽  
Immunogold Staining ◽  
Functional Control ◽  
Neutrophil Adherence ◽  
Definition Of ◽  
Mode Of Attachment

Receptors are commonly defined in terms of number per cell, affinity for ligand, chemical structure, mode of attachment to the cell surface, and mechanism of signal transduction. We propose to show that knowledge of spatial distribution of receptors on the cell surface can provide additional clues to their function and components of functional control.L-selectin and Mac-1 denote two receptor populations on the neutrophil surface that mediate neutrophil-endothelial cell adherence interactions and provide for targeting of neutrophil recruitment to sites of inflammation. We have studied the spatial distributions of these receptors using LVSEM and backscatter imaging of isolated human neutrophils stained with mouse anti-receptor (primary) antibody and goat anti-mouse (secondary) antibody conjugated to 12 nm colloidal gold. This combination of techniques provides for three-dimensional analysis of the expression of these receptors on different surface membrane domains of the neutrophil: the ruffles and microvilli that project from the cell surface, and the cell body between these projecting structures.

scholarly journals Proposing 3D Thermal Technology for Heritage Building Energy Monitoring

2021 ◽  
Vol 13 (8) ◽  
pp. 1537
Author(s):  
Antonio Adán ◽  
Víctor Pérez ◽  
José-Luis Vivancos ◽  
Carolina Aparicio-Fernández ◽  
Samuel A. Prieto
Keyword(s):  
Computer Vision ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Building Energy ◽  
Energy Monitoring ◽  
3D Computer Vision ◽  
Building Monitoring ◽  
Heritage Buildings ◽  
Heritage Building ◽  
Definition Of

The energy monitoring of heritage buildings has, to date, been governed by methodologies and standards that have been defined in terms of sensors that record scalar magnitudes and that are placed in specific positions in the scene, thus recording only some of the values sampled in that space. In this paper, however, we present an alternative to the aforementioned technologies in the form of new sensors based on 3D computer vision that are able to record dense thermal information in a three-dimensional space. These thermal computer vision-based technologies (3D-TCV) entail a revision and updating of the current building energy monitoring methodologies. This paper provides a detailed definition of the most significant aspects of this new extended methodology and presents a case study showing the potential of 3D-TCV techniques and how they may complement current techniques. The results obtained lead us to believe that 3D computer vision can provide the field of building monitoring with a decisive boost, particularly in the case of heritage buildings.

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