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Актуальность исследования обусловлена широкой распространенностью проблемы предотвращения прорывов водных масс в подземные горные выработки, успешное решение которой во многом определяет эффективность и безопасность разработки месторождений. Цель: исследование взаимосвязи современных геодинамических движений с опасностью прорыва водных объектов в горные выработки при разработке месторождений в сложных гидрогеологических условиях. Объект: массив месторождений, находящиеся в сложных гидрогеологических условиях, а именно залегающих под мощной осадочной толщей, вмещающей несколько водоносных горизонтов. Методы: аналитический, спутниковое позиционирование двухчастотными геодезическими GPS приемниками, компьютерное моделирование векторного и тензорного деформационного поля. Результаты. На основании анализа произошедших аварийных ситуаций, связанных с прорывами вод на рудниках, их причин и способов предупреждения установлено, что одним из важнейших факторов, вызывающих прорыв водных объектов, являются современные геодинамические движения, формирующие неоднородное мозаичное напряженно-деформированное состояние в массиве пород, препятствующее сохранению целостности водозащитных массивов. Известные способы предотвращения опасности прорыва вод в горные выработки путем закладки выработанного пространства и поддержания налегающей толщи целиками при назначении и применении параметров очистных работ без учета формирования реального напряженно-деформированного состояния под влиянием геодинамических движений, как правило, сопровождаются авариями. В качестве рекомендаций по предупреждению прорывов вод в горные выработки представлен и апробирован метод изучения геодинамических движений и процессов деформирования, протекающих в массиве, на примере Еланского и Ёлкинского полиметаллических месторождений. Установлены векторы трендовых движения пунктов совместно с тектоническим строением исследуемого региона. Зафиксированы максимальные вертикальные поднятия и максимальные горизонтальные смещения. Результаты измерений обработаны и преобразованы в векторное и тензорное представление деформационного поля, где выделены главные компоненты тензора деформаций. Выводы. Исследуемый массив находится в умеренной зоне напряженно-деформированного состояния с характерной разнонаправленностью тензора деформаций, что приводит к развитию сдвиговых деформаций в массиве горных пород, отрицательно влияющих на устойчивость горных выработок, а также способствующих раскрытию естественных структурных нарушений массива горных пород и повышению его фильтрационных свойств. Повышение надежности применяемых способов предотвращения опасности прорывов вод в горные выработки требует проведения специальных исследований формирования реального напряженно-деформированного состояния и учета его параметров при проектировании и ведении очистных работ. 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 waterprotective 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.

Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper. First, for a periodic domain in ℝ3, and the coefficient of viscosity μ = 0, energy conservation is proved for u and F in certain Besov spaces. Furthermore, in the whole space ℝ3, it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed, that is, $$u \in B_{3,c(\mathbb{N})}^{{1 \over 3}}$$ , and $$F \in B_{3,\infty }^{{1 \over 3}}$$ . Finally, when μ > 0, in a periodic domain in ℝd again, a result independent of the spacial dimension is established. More precisely, it is shown that the energy is conserved for u ∈ Lr (0, T; Ls (Ω)) for any $${1 \over r} + {1 \over s} \leqslant {1 \over 2}$$ , with s ⩾ 4, and F ∈ Lm(0, T; Ln(Ω)) for any $${1 \over m} + {1 \over n} \leqslant {1 \over 2}$$ , with n ⩾ 4.

This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor $$\mathcal {D}(u)$$ D ( u ) to the 3D Navier–Stokes equations in Lorentz spaces. It is shown that a Leray–Hopf weak solution is regular on (0, T] provided that the norm $$\Vert \lambda _{2}^{+}\Vert _{L^{p,\infty }(0,T; L ^{q,\infty }(\mathbb {R}^{3}))} $$ ‖ λ 2 + ‖ L p , ∞ ( 0 , T ; L q , ∞ ( R 3 ) ) with $$ {2}/{p}+{3}/{q}=2$$ 2 / p + 3 / q = 2 $$( {3}/{2} ( 3 / 2 < q ≤ ∞ ) is small. This generalizes the corresponding works of Neustupa–Penel and Miller.

In this paper, we are concerned with the regularity of suitable weak solutions to the 3D Navier–Stokes equations in Lorentz spaces. We obtain $$\varepsilon $$ -regularity criteria in terms of either the velocity, the gradient of the velocity, the vorticity or deformation tensor in Lorentz spaces, which generalizes the corresponding results derived by Gustafson et al. (Commun Math Phys 273:161–176, 2007) in Lebesgue spaces. As applications, this allows us to extend recent results involving Leray’s blow up rate in time, and to show that the number of singular points of weak solutions belonging to $$ L^{p,\infty }(-1,0;L^{q,l}({\mathbb {R}}^{3})) $$ is finite, where the pair (p, q) satisfies $$ {2}/{p}+{3}/{q}=1$$ with $$3

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 W...

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.

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.

In this paper, we are concerned with the compressible viscoelastic flows in whole space \begin{document}$ \mathbb{R}^n $\end{document} with \begin{document}$ n\geq2 $\end{document} . We aim at extending the global existence in energy spaces (see [ 18 ] by Hu & Wang and [ 30 ] by Qian & Zhang) such that it holds in more general \begin{document}$ L^p $\end{document} critical spaces, which allows to the case of large highly oscillating initial velocity. Precisely, We define "two effective velocities" which are used to eliminate the coupling between the density, velocity and deformation tensor. Consequently, the global existence in the \begin{document}$ L^p $\end{document} critical framework is constructed by elementary energy approaches. In addition, the optimal time-decay estimates of strong solutions are firstly shown in the \begin{document}$ L^p $\end{document} framework, which improve recent decay efforts for compressible viscoelastic flows.

Shear bands are common in dense quasi-static granular flows. They can appear in the interior of the flowing material or at confining boundaries and are typically of the order of ten particle diameters in thickness. Deformation tends to be localized in shear bands separating non-deforming or weakly deforming regions. Dilatancy and sharp velocity variation are typical in these shear layers. Much work has been reported in the literature concerning the development of non-local quasi-static rheological models to predict the flow behaviour in shear layers. In a recent article, Dsouza & Nott (J. Fluid Mech., vol. 888, 2020, R3) derive a non-local extension to a classical plasticity model by postulating that some local quantities appearing in the yield function, which stipulates the relationship between different components of the stress for the material to undergo sustained yielding, and the flow rule which provides information on the rate of deformation tensor to within an arbitrary multiplicative constant, should be replaced by their local averages. They then obtain an explicit non-local model which does not involve new microstructural variables and they show that the model captures velocity and volume fraction fields in simple shear flows, although some model parameters must be fitted to achieve quantitative agreement. This article discusses the work of Dsouza & Nott (2020) and comments on work ahead for further testing and developing the model.

The strain intensity as well as the stress-strain state of grains has been experimentally estimated for aluminum sample in strip rolling. The level of correlation between the intensity of deformation and stress-strain state of individual grains in the sample has been calculated. An experimental two-dimensional function of its joint distribution has been constructed. The parameters of two-dimensional function of probability densities have been defined. A relative number of grains with deformation twice as high as the average deformation of the sample has been obtained. The results allow predicting the plasticity exhaustion in individual grains of the sample during rolling and can be used to estimate the likelihood of defects (micro pores and micro cracks) arising during the rolling of aluminum strips.

This paper develops a joint deformation tensor (JD), which considers all of the joint's mechanical and geometrical parameters that affect the deformability of the rock mass. The method based on JD (JD method) and an elastic deformation anisotropy index (EDAI) are deduced for estimating the spatial anisotropy deformation of a jointed rock mass. The numerical modeling and in situ true triaxial compressive experiments well verified the effectiveness of the EDAI and JD method for the rock mass containing one joint set, orthogonal joint sets or the rock mass containing any types of joint network with unity stiffness ratio.

Horizontal strains related to mining-induced subsidence may endanger infrastructure and surface users’ safety. While directional horizontal strains should be well determined, appropriate solutions for a complete assessment of the terrain surface deformation field are still required. As a result, the presented study examined a new method for calculating horizontal strain tensor based on the decomposition of satellite radar interferometry (InSAR) observations into vertical and azimuth look direction (ALD) displacements. Based on a geometric integral model, we tested our method on experimental data before applying it to an underground copper ore mine in Poland. In the case study, the displacement field was determined using the Multi-Temporal InSAR method on Sentinel-1 data. The model data relative error did not exceed 0.02 at σ = ±0.003. For the case study, land subsidence of up to −167 mm and ALD displacements ranging from −110 mm to +62 mm was obtained, whereas the extreme values of horizontal strains ranged from −0.52 mm/m to +0.36 mm/m at σ = ±0.050 mm/m. Our results demonstrate the high accuracy of the method in determining the horizontal strain tensor. As a result, the approach can broaden the assessment of the environmental impact of land subsidence worldwide.

In this paper, we are concerned with the local regularity of suitable weak solutions to the 3D Navier–Stokes equations and its generalized case with fractional power of the Laplacian ( − Δ ) α ( 3 / 4 ≤ α 1 ). In the first part, we derive some ϵ -regularity criteria in terms of the deformation tensor D ( u ) for the classical Navier–Stokes equations. In the second part, for the fractional case, we obtain some regularity conditions for suitable weak solutions including the velocity u , the gradient of the velocity ∇ u , the rotation tensor Ω ( u ) and the deformation tensor D ( u ) . This generalizes the results obtained by Gustafson et al. (2007).

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L ∞ ( 0 , T ; L 6 ) -norm of the density of particles and the L 1 ( 0 , T ; L ∞ ) -norm of the deformation tensor of velocity gradient.

Oxygen plays a critical role in human cell survival and proliferation; hence, it is an essential factor in cancer tumor propagation. In the literature, many studies have investigated the oxygen contribution to cell proliferation and tumor growth; however, lack of the studies considering the effect of blood oxygen solubility on the tumor growth is remarkably sensed among the literature. Accordingly, in this study, we investigated the effect of oxygen Bunsen solubility coefficient on the brain glioma growth, following continuum mechanics principles. A biomechanical simulation was conducted by assuming a compressible hyperelastic model of growth for spherical glioma tissue. Patient-specific MRI dataset was utilized to develop the geometry of the brain. An isotropic growth deformation tensor alongside oxygen and cell number concentration relations were applied to the simulation. The results demonstrated that the tumor maximum volume at the end of 90 days decreased from 1315.59 mm3 to 1236.43 mm3, as the increase of oxygen Bunsen solubility coefficient for 20 %. Thus, we concluded that the accessibility of oxygen with higher values of blood solubility lowers the risk of tumor sudden growth, which was verified in comparison to literature experiments.

We show that the covariant Raychaudhuri identity describing kinematic characteristics of space-time admits a representation involving a geometrical scalar $\xi$ which, depending on circumstances, might be related to, e.g., relativistic temperature or cosmological scalar field. With an appropriately chosen spacetime deformation tensor (fixing the symmetry of a problem under consideration), such scalarization opens a wide scope for physical applications. We consider few such applications including dynamics of cosmological (anti)scalar background, non-variational deduction of the field equations, scalar and black-hole thermodynamics and the reshaping of the Einstein equations into the Klein-Gordon equation in thermodynamic Killing space., Comment: Accepted in PRD

In this paper, we consider the short time strong solutions to the ideal compressible magnetohydrodynamic equations with initial vacuum, where the velocity field satisfies the Navier-slip condition. Inspired by Kato and Lax's idea, we use the contraction mapping argument to prove the local existence. Moreover, under the Navier-slip condition, we establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of L ∞ norm of the deformation tensor D ( u ) .

The objective of this paper is to develop a new unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues. The model assumes a simple continuum with a single velocity field. In contrast with many other formulations, evolution equations are proposed directly for a scalar measure of elastic dilatation and a tensorial measure of elastic distortional deformation. The evolution equation for elastic dilatation includes a rate of mass supply or removal that controls volumetric growth and causes the elastic dilatation to evolve towards its homeostatic value. Similarly, the evolution equation for elastic distortional deformation includes a rate of growth that causes the elastic distortional deformation tensor to evolve towards its homeostatic value. Specific forms for these inelastic rates of growth and the associated homeostatic values have been considered for volumetric, area and fiber growth processes, as well as for muscle activation. Since the rate of growth appears in the evolution equations and not a growth tensor it is possible to model the combined effects of multiple growth and muscle activation mechanisms simultaneously. Also, robust, strongly objective, numerical algorithms have been developed to integrate the evolution equations.

The response to stress delivered by a non-isochoric hollow cylinder is critical to its future life and integrity. The design of cylinders must emphasize durability; therefore, the knowledge of the yield stress of the constituent material is essential. The stress component of a pressurized compressible circular cylinder made of non-linearly elastic material was considered here and the yield stress was determined.

We consider the three-dimensional Boussinesq equations and obtain some regularity criteria via the velocity gradient (or the vorticity, or the deformation tensor) and the temperature gradient.

Tensor-based morphometry (TBM) studies encode the anatomical information in spatial deformations which are locally characterized by Jacobian matrices. Current methods perform voxel-wise statistical analysis on some features, such as the Jacobian determinant or the Cauchy---Green deformation tensor, which are not complete descriptors of the local deformation. This article introduces a right-invariant Riemannian distance on the GL+(n) group of Jacobian matrices making use of the complete geometrical information of the local deformation. A numerical recipe for the computation of the proposed distance is given. Additionally, experiments are performed on both a synthetic deformation study and a cross-sectional brain MRI study.

Methods originally developed to study the finite time blow-up problem of the regular solutions of the three dimensional incompressible Euler equations are used to investigate the regular solutions of the Camassa–Holm equation. We obtain results on the relative behaviors of the momentum density, the deformation tensor and the nonlocal term along the trajectories. In terms of these behaviors, we get new types of asymptotic properties of global solutions, blow-up criterion and blow-up time estimate for local solutions. More precisely, certain ratios of the quantities are shown to be vaguely monotonic along the trajectories of global solutions. Finite time blow-up of the accumulated momentum density is necessary and sufficient for the finite time blow-up of the solution. An upper estimate of the blow-up time and a blow-up criterion are given in terms of the initial short time trajectorial behaviors of the deformation tensor and the nonlocal term.

An adaptive meshless method based on the multi-scale Reproducing Kernel Particle Method (RKPM) for analysis of nonlinear elasto-plastic deformation is proposed in this research. In the proposed method, the equivalent strain, stress, and the second invariant of the Cauchy–Green deformation tensor are decomposed into two scale components, viz., high- and low-scale components by deriving them from the multi-scale decomposed displacement. Through combining the high-scale components of strain and the stress update algorithm, the equivalent stress is decomposed into two scale components. An adaptive algorithm is proposed to locate the high gradient region and enrich the nodes in the region to improve the computational accuracy of RKPM. Using the algorithm, the high-scale components of strain and stress and the second invariant of the Cauchy–Green deformation tensor are normalized and used as criteria to implement the adaptive analysis. To verify the validity of the proposed adaptive meshless method in nonlinear elasto-plastic deformation, four case studies are calculated by the multi-scale RKPM. The patch test results show that the used multi-scale RKPM is reliable in analysis of the regular and irregular nodal distribution. The results of other three cases show that the proposed adaptive algorithm can not only locate the high gradient region well, but also improve the computational accuracy in analysis of the nonlinear elasto-plastic deformation.

This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global existence of the solution for small initial data. Second, we derive the sharp time decay of the solution in $L^{2}-$norm. Finally, the sharp time decay of the solution of higher order Sobolev norms is obtained., Comment: 13 pages

In this paper, we study the regularity criterion of smooth solution to the Oldroyd model in $R^n(n=2,3)$. Firstly, we establish a regularity criterion in terms of the $BMO$ norm of the gradient of columns of the deformation tensor in two space dimensions; secondly, we obtain a Beale-Kato-Majda-type criterion in terms of vorticity with the $BMO$ norm in two and three space dimensions.

The crystal chemistry of many AB2O6 compounds is summarized in family trees comparing the crystal symmetry of several structures in group-subgroup relations. In this second part of a series the largest family derived from a hexagonally close packed arrangement of anions is described. On reducing the symmetry, different choices of octahedral sites for A and B cations and voids lead to four branches – the Rosiaite-, the ZnTa2O6-, the columbite- and the rutile-branch. We trace the reasons for the specific distribution patterns of the cations in the individual compounds by comparing long range contributions, i.e. the Madelung Part of Lattice Energy (MAPLE), and local effects represented by bond valence calculations according to I. D. Brown. Long range effects largely determine the choice of sites in the respective space groups, however, small local adjustments play a decisive role for the stability of a specific structural modification. Such mechanisms ultimately impose how the structure of an individual compound deviates from an ideally packed arrangement. We discuss the difference between the ideal structures and the real examples given in the family tree by defining a sort of deformation tensor and a measure of similarity, and we describe and depict the anisotropic deformation by a strain tensor.

In this paper, we get a blow-up criterion for the strong solutions to the 3D viscous liquid–gas two-phase flow model with vacuum. More precisely, we prove that the bound of L t 1 L x ∞ norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions.

We consider a hyperbolic quasilinear fluid model, that arises from a delayed version for the constitutive law for the deformation tensor in the incompressible Navier-Stokes equation. We prove global existence of small solutions and asymptotic results in R and the half-space with slip boundary conditions. Futhermore we show that this relaxed system is close to the classical Navier-Stokes equation in the sense that for small times t the solutions converge in high Sobolev norms to the solution of the incompressible Navier-Stokes equation.

This paper studies the classical problem of extension, inflation, and circumferential shearing of an annular cylinder for a new class of compressible elastic bodies wherein the left Cauchy–Green deformation tensor is given as a function of the Cauchy stress tensor. We use a semi-inverse method to study the problem by assuming forms for both the deformation field and the stress field. Focusing our attention on to three specific constitutive relations and two geometries corresponding to thick and thin annular cylinders, we study the qualitative features of the governing differential equations. The models are chosen so that they exhibit qualitatively different response features, one of them displaying a limiting stretch. The classical assumption that the hoop and axial stresses are nearly constant through the thickness of the thin annular cylinder subjected to inflation holds for this class of elastic bodies too. However, for thick-walled annular cylinders subjected to inflation at constant length and for a class of models that exhibits limiting stretch we find that stress “boundary layers” form and that the radial stretch is not monotonic.

An analysis of symmetry changes upon the structural B2-ISS2 phase transition with subsequent martensitic transformations into the B19 and B19′ phases has been performed. An interrelation between the atomic displacements and the lattice deformation has been shown to exist. It has been established that the structures with longitudinal and transverse displacements have the same symmetry and can pass into one another via a twinning operation. A sequence of transformations of the tensor of lattice deformations consistent with the transformations of the atomic displacements has been obtained. It has been found that the operations that provide these transformations are the operations of twinning.

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases.

In the present paper, the local well-posedness of the incompressible viscoelastic fluid system in the whole space is proved under the following assumption on the initial data: the deformation tensor is Holder continuous and the velocity is Lp integrable, p > d, where d is the space dimension.

Equations of the mechanics of a saturated porous medium that account for the deformation tensor of the fluid and the initial state of the medium are derived. Emphasis is on the linearization and justification of the basic nonlinear equations of the theory. The relationship between the pressure (deformation) of the fluid and the thermodynamic and kinematic parameters of the medium is established. The solutions obtained are compared with Biot’s well-known classical results and analyzed

Problems in elasticity are described by relations between the displacement field u, the strain or deformation tensor e, and the stress tensor σ. In 2D elasticity and if volume forces are absent, one may also consider an elastic potential. We explain these settings for a domain Ω with finitely many holes. On such domains the problem for the displacement and the potential problem are not necessarily equivalent. We will also recall the relation between these quantities. We conclude the paper with the potential setting for some specific problems in semi-periodic domains with infinite many holes. Also the setting for non-smooth domains is addressed.

The average stretching direction, local rotation angular, and stretching ratio parameters of molecular trains were used to express the rheology deformation. Based on this micro geometrical deformation, the macro deformation of medium was expressed. Then, using intrinsic elasticity concept, the stress—strain relation was obtained. In this theoretic formulation, the response functions of extension ratio and rotation angular were used to express the rheology feature of medium. For medium composed by incompressible molecular trains, the local rotation angular divides rheology deformation into three kinds: viscoelastic deformation or elasticity enhancement, viscoplastic deformation or elasticity degenerate and constant elasticity range. These results explain the experimental features of rheology deformation well.

Formation of spatially non-uniform mechanical tension in a transparent solid due to the lattice ionization under the intensive ultrashort laser pulses action is predicted and theoretically described. Within the framework of the continual theory of elasticity the estimation of both average values of deformation tensor and its variations in solid dielectric with non-uniform random distribution of ions was carried out. It was shown that three possible types of medium modiflcation can arise in solid depending on its ionization degree and the thickness of ionized layer. Since the Coulomb flelds inside ionized layer can be non-uniform, all three types of structuring can arise in solid simultaneously. PACS numbers: 81.07.{b, 81.16.{c

The synthesis of K2BiF5 by a tribochemical reaction is reported. This compound crystallises in a K2SmF5-type arrangement with the lattice parameters a = 11.3862(2), b = 7.5480(1), c = 6.6008(1) Å and space group Pnma. The effect of substituting Bi into the K2SmF5-type structure is discussed in comparison with other compounds considering the effect of the lone-pair activity of Bi3+.

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A_3-lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe., 9 pages, 8 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

Wrinkle simulation can reflect the texture and simulation effect of clothes. In this paper, we realize a new cloth wrinkle enhancement method based on the coarse mesh simulation. Firstly, we extend the deformation tensor to generate the mesh vertex stretch tensor, so as to obtain one measuring factor for the three-dimensional cloth mesh vertex deformation. Then, we introduce a new method to extract the wrinkle baseline in the 2D mesh which is stretching from 3D coarse mesh and mapping it to 3D coarse mesh. Finally, we use the convolution surface as framework to simulate the wrinkle shape. We also propose and realize the wrinkle surface adjustment method. Experiment result proves the effectiveness of this method, namely this method can significantly improve the cloth wrinkle effect based on the coarse mesh simulation.

The Press-Schechter theory of the cosmological mass function and its modifications allow to constraint cosmological scenarios of the structure formation. Recently a few new models have been suggested that explored the influence of anisotropic collapse on the shape of the mass function. I discuss in more detail a particular model that assumes that a fluid particle becomes a part of a gravitationally bound halo when the smallest eigenvalue of the deformation tensor of the filtered initial density field reaches a certain threshold (like the filtered density contrast reaches the threshold in the Press-Schechter formalism). Choosing the smallest eigenvalue guarantees that the fluid particle in question experiences collapse along all three axes. The model shows a better agreement with the N-body simulations than the standard Press-Schechter model., Talk at 15th Florida Workshop in Nonlinear Astronomy and Physics "The Onset of Nonlinearity", 17-19 February 2000, Gainesville, FL (12 pages, 5 figures)

This work is concerned with the study of steady flows of an incompressible viscoelastic fluid of Oldroyd type, with viscosity depending on the second invariant of the rate of deformation tensor in an exterior domain. We establish a result of existence and uniqueness of strong solutions for sufficiently small data and give estimates relating these solutions to those of the corresponding generalized Newtonian fluid.

This work is concerned with the study of steady flows of an incompressible quasi-Newtonian fluid, with viscosity depending on the second invariant of the rate of deformation tensor, in bounded domains. We first establish a result of existence of measure-valued solutions. Next, we prove that under some natural monotonicity conditions, these solutions are weak.

The dependence of the glass transition on the local volumetric strain of each atom has been shown by Egami and others. The atomistic strain defined by the deformation tensor of the Voronoi polyhedra exhibits a different tendency from that of the total strain of the whole system. Even below the glass transition temperature, some percent of the atoms have strains that are already over the critical strain predicted by theory. In addition, the atomic deviatoric distortion has a non-zero value, while the total deviatoric distortion remains zero at the glass transition in the heat cycle. In this paper, the strain states at the glass transition, such as the volumetric strain and deviatoric distortion, are investigated for Cu and Zr based amorphous metals with three different compositions. We found that the local glass transition depends on the deviatoric distortion of atoms and, in these cases, starts at 600 K, a lower temperature, than that of the global glass transition at 1100 K.

In this paper, we will study the Oldroyd model describing fluids with viscoelastic properties. Global classical solutions for the two-dimensional incompressible Oldroyd model with small initial displacements are shown to exist via the incompressible limit. The main difficulty is the lack of the damping mechanism on the deformation tensor.

In the context of finite deformations, a purely kinematical treatment of Volterra dislocations is presented. These dislocations correspond to deformations that have a jump discontinuity across a singular surface in a fixed reference configuration of the continuum, but whose right Cauchy-Green deformation tensor field is continuous and has second partial derivatives that are continuous. Analytical and geometrical proofs of Weingarten's theorem for finite deformations are given. Tune-dependent Volterra dislocations are also considered.

A structure-based constitutive equation for rubberlike networks is proposed. It is obtained by combining the Langevin-statistics-based theory of Arruda and Boyce (AB) with a term based on the first invariant of the generalized deformation tensor which follows from some theoretical treatments of the constraint effect. The combined (ABGI) four-parameter strain–energy function has been found to give (with the exception of the very-low strain region) a very good description (deviations

In order to describe the transient stress growth for polymer melts, the empirical model proposed by Seo for the viscosity of steady-state flow is combined with a phenomenological viscoelastic model of a differential type (the White–Metzner model) along the lines proposed by Souvaliotis and Beris. The relaxation time is taken as a function of the invariant of the stress tensor (hence that of the configuration tensor) rather than that of the rate of the deformation tensor. Numerical results show a good correlation with experimental data. The model predictions approach steady-state values at long times after the startup. The nonlinear form of the model correlates very well with the experimental data over many decades of the deformation rate, both in shearing and elongational deformations. The proposed model is a simple one that can also describe the overshoot in the transient stress growth. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 510–515, 2003

This study presents results of numerical simulations of the flow of fibre suspensions in a Newtonian fluid through a 4:1 planar contraction. Two approaches are adopted to determine the fibre orientation. The first one uses orientation tensors defined as dyadic products of the orientation vector, while the second one is based on the fibre aligned assumption. An implicit time discretization scheme and a mixed finite element method based on the introduction of the rate of deformation tensor as an additional unknown are used to obtain the steady-state flow. The numerical technique we use allows us to examine the flow of fibre suspensions in both dilute and semi-dilute regimes at high values of the parameters controlling inertial and fibre effects. The predicted flow patterns and fibre orientation are discussed, and a systematic comparison between the predictions of the two approaches is presented. On presente dans cette etude les resultats de simulations numeriques de l'ecoulement de suspensions de fibres dans un fluide newtonien dans une contraction planaire 4:1. Deux approches sont adoptees pour determiner l'orientation des fibres. La premiere recourt aux tenseurs d'orientation definis comme des produits dyadiques du vecteur d'orientation, tandis que la seconde repose sur l'hypothese des fibres alignees. Pour obtenir l'ecoulement a l'etat permanent, on emploie un schema de discretisation du temps implicite et une methode d'elements finis mixte s'appuyant sur l'introduction de la vitesse du tenseur de deformation comme inconnue supplementaire. La technique numerique que nous utilisons permet d'examiner l'ecoulement des suspensions de fibres autant en regime dilue que semi-dilue a des valeurs elevees des parametres controlant les effets de l'inertie et des fibres. Les profils d'ecoulement et l'orientation des fibres predits sont etudies, et une comparaison systematique entre les predictions de ces deux approches est presentee.