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The expressions for specific energy, constitutive relations, equations of motion and equilibrium of the second strain tensor and velocity vector gradient theory for an arbitrary anisotropic bodies are given, from which corresponding relations of the second strain tensor and velocity vector gradient theory of elastic thin bodies are obtained, on the basis of which, using the method of orthogonal polynomials the corresponding relations in moments are derived. Constitutive relations for gradient bodies are written using tensor-block matrices. In addition, static boundary conditions and equations of motion and equilibrium of gradient theories are represented by differential tensor-block matrix operators, for which, in the case of homogeneous bodies, differential tensor-block matrix operators of cofactors are constructed, which make it possible to split the initial-boundary value problems of some gradient theories. Herewith static boundary conditions can be split only for a homogeneous body having a piecewise flat boundary, i.e., for each flat section of the boundary the static boundary conditions can be split. The system of equations in moments of the displacement vector of the 10th order approximation is obtained. In particular, for each moment of the displacement vector included in these systems of equations, an equation of higher order elliptic type is obtained separately, for which an analytical solution can be written using the Vekua method. [ABSTRACT FROM AUTHOR]

Copyright of GeSec: Revista de Gestao e Secretariado is the property of Sindicato das Secretarias e Secretarios do Estado de Sao Paulo (SINSESP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we study the forward asymptotically almost periodic (AAP-) mild solutions of Navier–Stokes equations on the real hyperbolic manifold M = H d (R) with dimension d ⩾ 2 . Using the dispersive and smoothing estimates for the Stokes equation, we invoke the Massera-type principle to prove the existence and uniqueness of the AAP- mild solution for the inhomogeneous Stokes equations in L p (Γ (T M))) space with 1 < p ⩽ d . Next, we establish the existence and uniqueness of the small AAP- mild solutions of the Navier–Stokes equations using the fixed point argument, and the results of inhomogeneous Stokes equations. The asymptotic behaviour (exponential decay and stability) of these small solutions is also related. This work, together with our recent work (Xuan et al. in J Math Anal Appl 517(1):1–19, 2023), provides a full existence and asymptotic behaviour of AAP- mild solutions of Navier–Stokes equations in L p (Γ (T M))) spaces for all p > 1 . [ABSTRACT FROM AUTHOR]

We review several mathematical models and concepts in developmental biology that have been established over the last decade. (1) Feedback vertex set: Ascidian embryos contain cells of seven types, and cell fate is controlled by ~100 interacting genes. The "feedback vertex set" of the directed graph of the gene regulatory network consists of a small number of genes. By experimentally manipulating them, we can differentiate cells into any cell type. (2) Tissue deformation: Describing morphological changes in tissues and relating them to gene expression and other cellular processes is key in understanding morphogenesis. Expansion and anisotropy of the tissue are described by a "deformation tensor" at each location. A study on chick limb bud formation revealed that both the volume growth rate and anisotropy in deformation differed significantly between locations and stages. (3) Mechanobiology: Forces operating on each cell may alter cell shape and gene expression, which may subsequently exert forces on their surroundings. Measurements of force, tissue shape, and gene expression help us understand autonomous tissue deformation. (4) Adaptive design of development: An optimal growth schedule in fluctuating environments explains the growth response to starvation in Drosophila larvae. Adaptive placement of morphogen sources makes development robust to noises. [ABSTRACT FROM AUTHOR]

The inviscid limit for the two-dimensional compressible viscoelastic equations in the half plane is considered under the no-slip boundary condition. When the initial deformation tensor is a perturbation of the identity matrix and the initial density is near a positive constant, we establish the uniform estimates of solutions to the compressible viscoelastic flows in the conormal Sobolev spaces. It is well-known that for the corresponding inviscid limit of the compressible Navier-Stokes equations with the no-slip boundary condition, one does not expect the uniform energy estimates of solutions due to the appearance of strong boundary layers. However, when the deformation tensor effect is taken into account, our results show that the deformation tensor plays an important role in the vanishing viscosity process and can surprisingly prevent the formation of strong boundary layers. As a result we are able to justify the inviscid limit of solutions for the compressible viscous flows under the no-slip boundary condition governed by the viscoelastic equations, based on the uniform conormal regularity estimates achieved in this paper. [ABSTRACT FROM AUTHOR]

Relevance of the study is conditioned by wide spread problem of prevention of water mass breakthroughs into underground mine workings, successful solution of which in many respects determines the efficiency and safety of exploration. The aim of the research is to study the interrelation of modern geodynamic movements with danger of water objects breakthrough into mine workings during development of deposits in difficult hydrogeological conditions. Object: massif of deposits in difficult hydrogeological conditions, located under a powerful sedimentary stratum containing several aquifers. Methods: analytical, satellite positioning with dual-frequency GPS geodetic receivers, computer simulation of vector and tensor deformation field. Results. Based on the analysis of occurred emergency situations related to water breakthroughs at the mines, their causes and methods of prevention, it was found that one of the most important factors causing a breakthrough of water bodies are modern geodynamic movements that form a heterogeneous mosaic stress-strain state in the rock mass, which prevents the preservation of the integrity of water-protective massifs. The known methods to prevent the danger of water breakthrough in the rock by laying the depleted space and maintaining the overlying thickness of the whole, the appointment and application of parameters of treatment works without taking into account the formation of real tensely-deformed state under the influence of modern geodynamic movements are usually accompanied by accidents. As recommendations for prevention of water breakthroughs into the mine workings the method of studying modern geodynamic movements and the stress-strain state formed by them was presented and tested on the example of the massif Elanskoe and Elkinskoe polymetallic deposits. The vectors of trend movements of points together with the tectonic structure of the investigated region are established. Maximum vertical rises and maximum horizontal displacements were fixed. The obtained results of measurements using mathematical apparatus of solid medium mechanics were transformed into vectorial and tensor representation of deformation field with selection of main components of deformation tensor. Conclusions. The studied array is located in the temperate zone of stress-strain state with a characteristic multi-directionality of the deformation tensor, which leads to the development of shear deformations in an array of rocks, adversely affecting the stability of rock workings, as well as contributing to the disclosure of natural structural disorders of the array of rocks and improvement of its filtration properties. Increase of reliability of applied methods for preventing the danger of water breakthroughs into mine workings demands carrying out of special researches of formation of a real tensely-deformed condition and consideration of its parameters at designing and conducting clearing works.

Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection. [ABSTRACT FROM AUTHOR]

The directions of primary strain lines of local deformation in Epicardial and Endocardial layers have been the subject of debate in recent years. Different methods led to different conclusions and a complete assessment of strain direction patterns in large and variable (in terms of pathology) cohorts of healthy and diseased patients is still lacking. Here, we use local deformation tensors in order to evaluate the angle of strain lines with respect to the horizontal circumferential direction in both Epi- and Endo-layers. We evaluated this on a large group of 193 subjects including 82 healthy control and 111 patients belonging to a great variety of pathological conditions. We found that Epicardial strain lines obliquely directed while those of Endocardium are almost circumferential. This result occurs irrespective of pathological condition. We propose that the geometric vinculum characterizing Endocardium and Epicardium in terms of different lever arm length and orientation of muscular fibers during contraction inescapably requires Endocardial strain lines to be circumferentially oriented and this is corroborated by experimental results. Further investigations on transmural structure of myocytes could couple results presented here in order to furnish additional experimental explanations.

Invariants for geodesic and F-planar mappings defined on a generalized Riemannian space are obtained in this paper. These invariants are generalizations of the Thomas projective parameter and the Weyl projective tensor. [ABSTRACT FROM AUTHOR]

Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection.

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work showcases a method to map the full deformation tensor in a single micro‐sized crystal. It is shown that measuring the position of two Bragg reflections in reciprocal space is sufficient to obtain the full deformation tensor, if the condition of incompressibility of the material is imposed. This method is used to reveal the surface tension induced deformation at the edges of an as‐grown single‐crystal VO2 microwire. All components of the deformation tensor of the microwire were measured down to an absolute value of 10−4 in an 8 × 14 µm projected area of the wire. With a beam‐defined spatial resolution of 150 × 150 nm, the measurement time was merely 2.5 h. [ABSTRACT FROM AUTHOR]