#### Sample records for linear elastic matrix

1. Introduction to linear elasticity

Gould, Phillip L

2013-01-01

Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also:  Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...

2. Uniqueness theorems in linear elasticity

Knops, Robin John

1971-01-01

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

3. Discriminative Elastic-Net Regularized Linear Regression.

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

4. Non-linear elastic deformations

Ogden, R W

1997-01-01

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

5. Integrodifferential relations in linear elasticity

Kostin, Georgy V

2012-01-01

This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.

6. Matrix algebra for linear models

Gruber, Marvin H J

2013-01-01

Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

7. Advances in biomimetic regeneration of elastic matrix structures

Sivaraman, Balakrishnan; Bashur, Chris A.

2012-01-01

Elastin is a vital component of the extracellular matrix, providing soft connective tissues with the property of elastic recoil following deformation and regulating the cellular response via biomechanical transduction to maintain tissue homeostasis. The limited ability of most adult cells to synthesize elastin precursors and assemble them into mature crosslinked structures has hindered the development of functional tissue-engineered constructs that exhibit the structure and biomechanics of normal native elastic tissues in the body. In diseased tissues, the chronic overexpression of proteolytic enzymes can cause significant matrix degradation, to further limit the accumulation and quality (e.g., fiber formation) of newly deposited elastic matrix. This review provides an overview of the role and importance of elastin and elastic matrix in soft tissues, the challenges to elastic matrix generation in vitro and to regenerative elastic matrix repair in vivo, current biomolecular strategies to enhance elastin deposition and matrix assembly, and the need to concurrently inhibit proteolytic matrix disruption for improving the quantity and quality of elastogenesis. The review further presents biomaterial-based options using scaffolds and nanocarriers for spatio-temporal control over the presentation and release of these biomolecules, to enable biomimetic assembly of clinically relevant native elastic matrix-like superstructures. Finally, this review provides an overview of recent advances and prospects for the application of these strategies to regenerating tissue-type specific elastic matrix structures and superstructures. PMID:23355960

8. Phase diagrams of ferroelectric nanocrystals strained by an elastic matrix

Nikitchenko, A. I.; Azovtsev, A. V.; Pertsev, N. A.

2018-01-01

Ferroelectric crystallites embedded into a dielectric matrix experience temperature-dependent elastic strains caused by differences in the thermal expansion of the crystallites and the matrix. Owing to the electrostriction, these lattice strains may affect polarization states of ferroelectric inclusions significantly, making them different from those of a stress-free bulk crystal. Here, using a nonlinear thermodynamic theory, we study the mechanical effect of elastic matrix on the phase states of embedded single-domain ferroelectric nanocrystals. Their equilibrium polarization states are determined by minimizing a special thermodynamic potential that describes the energetics of an ellipsoidal ferroelectric inclusion surrounded by a linear elastic medium. To demonstrate the stability ranges of such states for a given material combination, we construct a phase diagram, where the inclusion’s shape anisotropy and temperature are used as two parameters. The ‘shape-temperature’ phase diagrams are calculated numerically for PbTiO3 and BaTiO3 nanocrystals embedded into representative dielectric matrices generating tensile (silica glass) or compressive (potassium silicate glass) thermal stresses inside ferroelectric inclusions. The developed phase maps demonstrate that the joint effect of thermal stresses and matrix-induced elastic clamping of ferroelectric inclusions gives rise to several important features in the polarization behavior of PbTiO3 and BaTiO3 nanocrystals. In particular, the Curie temperature displays a nonmonotonic variation with the ellipsoid’s aspect ratio, being minimal for spherical inclusions. Furthermore, the diagrams show that the polarization orientation with respect to the ellipsoid’s symmetry axis is controlled by the shape anisotropy and the sign of thermal stresses. Under certain conditions, the mechanical inclusion-matrix interaction qualitatively alters the evolution of ferroelectric states on cooling, inducing a structural transition

9. Isogeometric BDDC deluxe preconditioners for linear elasticity

Pavarino, L. F.

2018-03-14

Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

10. Isogeometric BDDC deluxe preconditioners for linear elasticity

Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, Stefano

2018-01-01

Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

11. Matrix Tricks for Linear Statistical Models

Puntanen, Simo; Styan, George PH

2011-01-01

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

12. Description of elastic scattering in U-matrix method

Edneral, V.F.; Troshin, S.M.; Tyurin, N.E.; Khrustalev, O.A.

1975-01-01

The elastic pp-scattering has been analyzed using a generalized reaction matrix (the U-matrix). A good agreement has been reached with the experimental total cross sections for the (pp) reaction beginning with an energy of 30 GeV and for the dsub(t)(dt)(pp) for four ISR energies [ru

13. Non-linear theory of elasticity

Lurie, AI

2012-01-01

This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

14. Applied linear algebra and matrix analysis

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

15. A Linear Theory for Pretwisted Elastic Beams

Krenk, Steen

1983-01-01

contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...

16. Asymptotic expansions for high-contrast linear elasticity

Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

2015-01-01

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

17. Asymptotic expansions for high-contrast linear elasticity

Poveda, Leonardo A.

2015-03-01

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

18. Matrix elasticity regulates the optimal cardiac myocyte shape for contractility

McCain, Megan L.; Yuan, Hongyan; Pasqualini, Francesco S.; Campbell, Patrick H.

2014-01-01

Concentric hypertrophy is characterized by ventricular wall thickening, fibrosis, and decreased myocyte length-to-width aspect ratio. Ventricular thickening is considered compensatory because it reduces wall stress, but the functional consequences of cell shape remodeling in this pathological setting are unknown. We hypothesized that decreases in myocyte aspect ratio allow myocytes to maximize contractility when the extracellular matrix becomes stiffer due to conditions such as fibrosis. To test this, we engineered neonatal rat ventricular myocytes into rectangles mimicking the 2-D profiles of healthy and hypertrophied myocytes on hydrogels with moderate (13 kPa) and high (90 kPa) elastic moduli. Actin alignment was unaffected by matrix elasticity, but sarcomere content was typically higher on stiff gels. Microtubule polymerization was higher on stiff gels, implying increased intracellular elastic modulus. On moderate gels, myocytes with moderate aspect ratios (∼7:1) generated the most peak systolic work compared with other cell shapes. However, on stiffer gels, low aspect ratios (∼2:1) generated the most peak systolic work. To compare the relative contributions of intracellular vs. extracellular elasticity to contractility, we developed an analytical model and used our experimental data to fit unknown parameters. Our model predicted that matrix elasticity dominates over intracellular elasticity, suggesting that the extracellular matrix may potentially be a more effective therapeutic target than microtubules. Our data and model suggest that myocytes with lower aspect ratios have a functional advantage when the elasticity of the extracellular matrix decreases due to conditions such as fibrosis, highlighting the role of the extracellular matrix in cardiac disease. PMID:24682394

19. Non-linear theory of elasticity and optimal design

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

20. Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses

Sauer, G.

1998-01-01

Fatigue analysis requires that the maximum strain ranges be known. These strain ranges are generally computed from linear elastic analysis. The elastic strain ranges are enhanced by a factor K e to obtain the total elastic-plastic strain range. The reliability of the fatigue analysis depends on the quality of this factor. Formulae for calculating the K e factor are proposed. A beam is introduced as a computational model for determining the elastic-plastic strains. The beam is loaded by the elastic stresses of the real structure. The elastic-plastic strains of the beam are compared with the beam's elastic strains. This comparison furnishes explicit expressions for the K e factor. The K e factor is tested by means of seven examples. (orig.)

1. On the use of elastic-plastic material characteristics for linear-elastic component assessments

Kussmaul, K.; Silcher, H.; Eisele, U.

1995-01-01

In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)

2. Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

Jonas Koko

2007-01-01

Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

3. On the hyperbolicity condition in linear elasticity

Remigio Russo

1991-05-01

Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.

4. Energy in elastic fiber embedded in elastic matrix containing incident SH wave

Williams, James H., Jr.; Nagem, Raymond J.

1989-01-01

A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.

5. Comparison of matrix methods for elastic wave scattering problems

1983-01-01

This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error

6. Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix

O'Keeffe, Stephen G.

2013-11-01

We investigate the problem of an axially loaded, isotropic, slender cylinder embedded in a soft, isotropic, outer elastic matrix. The cylinder undergoes uniform axial growth, whilst both the cylinder and the surrounding elastic matrix are confined between two rigid plates, so that this growth results in axial compression of the cylinder. We use two different modelling approaches to estimate the critical axial growth (that is, the amount of axial growth the cylinder is able to sustain before it buckles) and buckling wavelength of the cylinder. The first approach treats the filament and surrounding matrix as a single 3-dimensional elastic body undergoing large deformations, whilst the second approach treats the filament as a planar, elastic rod embedded in an infinite elastic foundation. By comparing the results of these two approaches, we obtain an estimate of the foundation modulus parameter, which characterises the strength of the foundation, in terms of the geometric and material properties of the system. © 2013 Elsevier Ltd. All rights reserved.

7. Generation of discrete inelastic and elastic transfer matrix

Garcia, R.D.M.; Santina, M.D.

1985-01-01

A technique developed for the calculation of the isotropic and linearly anisotropic components components of elastic and discrete inelastic transfer matrices is presented in this work. The implementation of the technique is discussed in detail and numerical results obtained for some examples are compared with results reported in the literature or generated with the use of several processing codes. (author) [pt

8. Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

Puljiz, Mate; Menzel, Andreas M.

2017-05-01

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

9. A Lagrangian meshfree method applied to linear and nonlinear elasticity.

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

10. Non-linear elastic thermal stress analysis with phase changes

1978-01-01

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)

11. A Galerkin approximation for linear elastic shallow shells

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

12. Generating Nice Linear Systems for Matrix Gaussian Elimination

Homewood, L. James

2004-01-01

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

13. Linear elastic properties derivation from microstructures representative of transport parameters.

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

14. A reexamination of some puzzling results in linearized elasticity

University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA e-mail: jogc@mecheng.iisc.ernet.in; ..... ˆT (F) = C[ϵ] + o(∇u), where ϵ = [∇u+(∇u)T ]/2, and C = D ˆT (I) is the elasticity tensor, and one also linearizes the body force vector to get b = QT [ b∗ − ¨c. ] − ˙ × X − × ( × X) − 2 × v,. (5) where X is the position ...

15. Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

Wang, John T.

2010-01-01

The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

16. Generalised Assignment Matrix Methodology in Linear Programming

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

17. Linear matrix differential equations of higher-order and applications

Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

18. Matrix model and time-like linear dila ton matter

2004-01-01

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

19. Matrix preconditioning: a robust operation for optical linear algebra processors.

Ghosh, A; Paparao, P

1987-07-15

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

20. Compressor Surge Control Design Using Linear Matrix Inequality Approach

Uddin, Nur; Gravdahl, Jan Tommy

2017-01-01

A novel design for active compressor surge control system (ASCS) using linear matrix inequality (LMI) approach is presented and including a case study on piston-actuated active compressor surge control system (PAASCS). The non-linear system dynamics of the PAASCS is transformed into linear parameter varying (LPV) system dynamics. The system parameters are varying as a function of the compressor performance curve slope. A compressor surge stabilization problem is then formulated as a LMI probl...

1. Morphology and linear-elastic moduli of random network solids.

Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E

2011-06-17

The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

2. Emergence of linear elasticity from the atomistic description of matter

Cakir, Abdullah, E-mail: acakir@ntu.edu.sg [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Pica Ciamarra, Massimo [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli (Italy)

2016-08-07

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

3. Emergence of linear elasticity from the atomistic description of matter

Cakir, Abdullah; Pica Ciamarra, Massimo

2016-01-01

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

4. H∞ /H2 model reduction through dilated linear matrix inequalities

2012-01-01

This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arb......This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field... 5. A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson Harrod, Steven 2009-01-01 The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover... 6. Minimal solution of linear formed fuzzy matrix equations Maryam Mosleh 2012-10-01 Full Text Available In this paper according to the structured element method, the$mimes n$inconsistent fuzzy matrix equation$Ailde{X}=ilde{B},which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method. 7. Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations Garde, Henrik 2018-01-01 . For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method... 8. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel El-Gebeily, M.; Yushau, B. 2008-01-01 In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we… 9. The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space Parzen, G. 1997-01-01 It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. A set of equations is given from which the 12 elements of R can be computed form the one period transfer matrix. This set of equations also allows the linear parameters, the β i , α i , i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix 10. Non-linear waves in heterogeneous elastic rods via homogenization Quezada de Luna, Manuel 2012-03-01 We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved. 11. Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos Bin Wang 2015-01-01 Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results. 12. Mitochondrial function in engineered cardiac tissues is regulated by extracellular matrix elasticity and tissue alignment. Lyra-Leite, Davi M; Andres, Allen M; Petersen, Andrew P; Ariyasinghe, Nethika R; Cho, Nathan; Lee, Jezell A; Gottlieb, Roberta A; McCain, Megan L 2017-10-01 Mitochondria in cardiac myocytes are critical for generating ATP to meet the high metabolic demands associated with sarcomere shortening. Distinct remodeling of mitochondrial structure and function occur in cardiac myocytes in both developmental and pathological settings. However, the factors that underlie these changes are poorly understood. Because remodeling of tissue architecture and extracellular matrix (ECM) elasticity are also hallmarks of ventricular development and disease, we hypothesize that these environmental factors regulate mitochondrial function in cardiac myocytes. To test this, we developed a new procedure to transfer tunable polydimethylsiloxane disks microcontact-printed with fibronectin into cell culture microplates. We cultured Sprague-Dawley neonatal rat ventricular myocytes within the wells, which consistently formed tissues following the printed fibronectin, and measured oxygen consumption rate using a Seahorse extracellular flux analyzer. Our data indicate that parameters associated with baseline metabolism are predominantly regulated by ECM elasticity, whereas the ability of tissues to adapt to metabolic stress is regulated by both ECM elasticity and tissue alignment. Furthermore, bioenergetic health index, which reflects both the positive and negative aspects of oxygen consumption, was highest in aligned tissues on the most rigid substrate, suggesting that overall mitochondrial function is regulated by both ECM elasticity and tissue alignment. Our results demonstrate that mitochondrial function is regulated by both ECM elasticity and myofibril architecture in cardiac myocytes. This provides novel insight into how extracellular cues impact mitochondrial function in the context of cardiac development and disease. NEW & NOTEWORTHY A new methodology has been developed to measure O 2 consumption rates in engineered cardiac tissues with independent control over tissue alignment and matrix elasticity. This led to the findings that matrix 13. The influence of powder elasticity on the quality of pressed matrix bodies Heit, W.; Herrmann, F.J. 1976-01-01 The production of electrographite powder has dominating influence on the powder elasticity and the quality of pressed resin bonded bodies. The quality increases with increasing degree of graphitization and additionally depends strongly on the sequence of the process steps gruinding and graphitization. It could be shown that elasticity is the only property of the graphite powder correlating with the quality of pressed matrix bodies. (orig.) [de 14. Spatially patterned matrix elasticity directs stem cell fate Yang, Chun; DelRio, Frank W.; Ma, Hao; Killaars, Anouk R.; Basta, Lena P.; Kyburz, Kyle A.; Anseth, Kristi S. 2016-08-01 There is a growing appreciation for the functional role of matrix mechanics in regulating stem cell self-renewal and differentiation processes. However, it is largely unknown how subcellular, spatial mechanical variations in the local extracellular environment mediate intracellular signal transduction and direct cell fate. Here, the effect of spatial distribution, magnitude, and organization of subcellular matrix mechanical properties on human mesenchymal stem cell (hMSCs) function was investigated. Exploiting a photodegradation reaction, a hydrogel cell culture substrate was fabricated with regions of spatially varied and distinct mechanical properties, which were subsequently mapped and quantified by atomic force microscopy (AFM). The variations in the underlying matrix mechanics were found to regulate cellular adhesion and transcriptional events. Highly spread, elongated morphologies and higher Yes-associated protein (YAP) activation were observed in hMSCs seeded on hydrogels with higher concentrations of stiff regions in a dose-dependent manner. However, when the spatial organization of the mechanically stiff regions was altered from a regular to randomized pattern, lower levels of YAP activation with smaller and more rounded cell morphologies were induced in hMSCs. We infer from these results that irregular, disorganized variations in matrix mechanics, compared with regular patterns, appear to disrupt actin organization, and lead to different cell fates; this was verified by observations of lower alkaline phosphatase (ALP) activity and higher expression of CD105, a stem cell marker, in hMSCs in random versus regular patterns of mechanical properties. Collectively, this material platform has allowed innovative experiments to elucidate a novel spatial mechanical dosing mechanism that correlates to both the magnitude and organization of spatial stiffness. 15. Extreme non-linear elasticity and transformation optics Gersborg, Allan Roulund; Sigmund, Ole 2010-01-01 realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics... 16. A two-dimensional linear elasticity problem for anisotropic materials, solved with a parallelization code Mihai-Victor PRICOP 2010-09-01 Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code. 17. Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass Minh Hoang Nguyen 2016-12-01 Full Text Available This paper introduced a kind of cart and pole system. The pole in this system is not a solid beam but an elastic beam. The paper analyzed the dynamic equation of this complex system. Then, a linear feedback controller was designed to stabilize this model in order to keep the elastic beam balanced in the up-side position. The control results were proved to work well through simulation. 18. Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties Pepi, John W. 2017-08-01 Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes. 19. Linear models of income patterns in consumer demand for foods and evaluation of its elasticity Pavel Syrovátka 2005-01-01 Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions. 20. Linear Matrix Inequalities in Multirate Control over Networks Ángel Cuenca 2012-01-01 Full Text Available This paper faces two of the main drawbacks in networked control systems: bandwidth constraints and timevarying delays. The bandwidth limitations are solved by using multirate control techniques. The resultant multirate controller must ensure closed-loop stability in the presence of time-varying delays. Some stability conditions and a state feedback controller design are formulated in terms of linear matrix inequalities. The theoretical proposal is validated in two different experimental environments: a crane-based test-bed over Ethernet, and a maglev based platform over Profibus. 1. Fundamental Matrix for a Class of Point Delay Linear Systems Sen, M. de la; Alastruey, C. F. 1998-01-01 It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author) 2. Exact solution of some linear matrix equations using algebraic methods Djaferis, T. E.; Mitter, S. K. 1977-01-01 A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given. 3. A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation Diosady, Laslo T.; Murman, Scott M. 2018-01-01 A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases. 4. The Simulation and Correction to the Brain Deformation Based on the Linear Elastic Model in IGS MU Xiao-lan; SONG Zhi-jian 2004-01-01 @@ The brain deformation is a vital factor affecting the precision of the IGS and it becomes a hotspot to simulate and correct the brain deformation recently.The research organizations, which firstly resolved the brain deformation with the physical models, have the Image Processing and Analysis department of Yale University, Biomedical Modeling Lab of Vanderbilt University and so on. The former uses the linear elastic model; the latter uses the consolidation model.The linear elastic model only needs to drive the model using the surface displacement of exposed brain cortex,which is more convenient to be measured in the clinic. 5. Quantification of local and global elastic anisotropy in ultrafine grained gradient microstructures, produced by linear flow splitting Niehuesbernd, Jörn; Müller, Clemens; Pantleon, Wolfgang 2013-01-01 . Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process... 6. Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium Sofiyev, A.H.; Kuruoglu, N. 2013-01-01 In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. -- Highlights: • Nonlinear buckling of FGM conical shell surrounded by elastic medium is studied. • Pasternak foundation model is used to describe the shell–foundation interaction. • Nonlinear basic equations are derived. • Problem is solved by using Superposition and Galerkin methods. • Influences of various parameters on the nonlinear critical load are investigated 7. Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity Kao, B.G. 1979-11-01 Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials 8. Compact solitary waves in linearly elastic chains with non-smooth on-site potential Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milan (Italy); Gramchev, Todor [Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy); Walcher, Sebastian [Lehrstuhl A Mathematik, RWTH Aachen, 52056 Aachen (Germany) 2007-04-27 It was recently observed by Saccomandi and Sgura that one-dimensional chains with nonlinear elastic interaction and regular on-site potential can support compact solitary waves, i.e. travelling solitary waves with strictly compact support. In this paper, we show that the same applies to chains with linear elastic interaction and an on-site potential which is continuous but non-smooth at minima. Some different features arise; in particular, the speed of compact solitary waves is not uniquely fixed by the equation. We also discuss several generalizations of our findings. 9. Four-dimensional Hooke's law can encompass linear elasticity and inertia Antoci, S.; Mihich, L. 1999-01-01 The question is examined whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke law is found able to account for the inertia of matter; in the flat-space, slow-motion approximation the field equations for the displacement four-vector field ξ i can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity 10. Effects of matrix elasticity and cell density on human mesenchymal stem cells differentiation. Xue, Ruyue; Li, Julie Yi-Shuan; Yeh, Yiting; Yang, Li; Chien, Shu 2013-09-01 Human mesenchymal stem cells (hMSCs) can differentiate into various cell types, including osteogenic and chondrogenic cells. The matrix elasticity and cell seeding density are important factors in hMSCs differentiation. We cultured hMSCs at different seeding densities on polyacrylamide hydrogels with different stiffness corresponding to Young's moduli of 1.6 ± 0.3 and 40 ± 3.6 kPa. The promotion of osteogenic marker expression by hard gel is overridden by a high seeding density. Cell seeding density, however, did not influence the chondrogenic marker expressions induced by soft gel. These findings suggest that interplays between cell-matrix and cell-cell interactions contribute to hMSCs differentiation. The promotion of osteogenic differentiation on hard matrix was shown to be mediated through the Ras pathway. Inhibition of Ras (RasN17) significantly decreased ERK, Smad1/5/8 and AKT activation, and osteogenic markers expression. However, constitutively active Ras (RasV12) had little effect on osteogenic marker expression, suggesting that the Ras pathways are necessary but not sufficient for osteogenesis. Taken together, our results indicate that matrix elasticity and cell density are important microenvironmental cues driving hMSCs proliferation and differentiation. Copyright © 2013 Orthopaedic Research Society. 11. Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media. Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) 2017-08-01 Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius. 12. Covariance Matrix of a Double-Differential Doppler-Broadened Elastic Scattering Cross Section Arbanas, G.; Becker, B.; Dagan, R.; Dunn, M. E.; Larson, N. M.; Leal, L. C.; Williams, M. L. 2012-05-01 Legendre moments of a double-differential Doppler-broadened elastic neutron scattering cross section on 238U are computed near the 6.67 eV resonance at temperature T = 103 K up to angular order 14. A covariance matrix of these Legendre moments is computed as a functional of the covariance matrix of the elastic scattering cross section. A variance of double-differential Doppler-broadened elastic scattering cross section is computed from the covariance of Legendre moments. Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. 13. Generalized linear elastic fracture mechanics: an application to a crack touching the bimaterial interface Náhlík, Luboš; Šestáková, L.; Hutař, Pavel; Knésl, Zdeněk 2011-01-01 Roč. 452-453, - (2011), s. 445-448 ISSN 1013-9826 R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GA101/09/1821 Institutional research plan: CEZ:AV0Z20410507 Keywords : generalized stress intensity factor * bimaterial interface * composite materials * strain energy density factor * fracture criterion * generalized linear elastic fracture mechanics Subject RIV: JL - Materials Fatigue, Friction Mechanics 14. Extracellular matrix elasticity and topography: material-based cues that affect cell function via conserved mechanisms Janson, Isaac A.; Putnam, Andrew J. 2014-01-01 Chemical, mechanical, and topographic extracellular matrix (ECM) cues have been extensively studied for their influence on cell behavior. These ECM cues alter cell adhesion, cell shape, and cell migration, and activate signal transduction pathways to influence gene expression, proliferation, and differentiation. ECM elasticity and topography, in particular, have emerged as material properties of intense focus based on strong evidence these physical cue can partially dictate stem cell differentiation. Cells generate forces to pull on their adhesive contacts, and these tractional forces appear to be a common element of cells’ responses to both elasticity and topography. This review focuses on recently published work that links ECM topography and mechanics and their influence on differentiation and other cell behaviors, We also highlight signaling pathways typically implicated in mechanotransduction that are (or may be) shared by cells subjected to topographic cues. Finally, we conclude with a brief discussion of the potential implications of these commonalities for cell based therapies and biomaterial design. PMID:24910444 15. Price elasticity matrix of demand in power system considering demand response programs Qu, Xinyao; Hui, Hongxun; Yang, Shengchun; Li, Yaping; Ding, Yi 2018-02-01 The increasing renewable energy power generations have brought more intermittency and volatility to the electric power system. Demand-side resources can improve the consumption of renewable energy by demand response (DR), which becomes one of the important means to improve the reliability of power system. In price-based DR, the sensitivity analysis of customer’s power demand to the changing electricity prices is pivotal for setting reasonable prices and forecasting loads of power system. This paper studies the price elasticity matrix of demand (PEMD). An improved PEMD model is proposed based on elasticity effect weight, which can unify the rigid loads and flexible loads. Moreover, the structure of PEMD, which is decided by price policies and load types, and the calculation method of PEMD are also proposed. Several cases are studied to prove the effectiveness of this method. 16. Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States) 1996-12-31 Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included. 17. Mechanical analysis of single myocyte contraction in a 3-D elastic matrix. John Shaw Full Text Available Cardiac myocytes experience mechanical stress during each heartbeat. Excessive mechanical stresses under pathological conditions cause functional and structural remodeling that lead to heart diseases, yet the precise mechanisms are still incompletely understood. To study the cellular and molecular level mechanotransduction mechanisms, we developed a new 'cell-in-gel' experimental system to exert multiaxial (3-D stresses on a single myocyte during active contraction.Isolated myocytes are embedded in an elastic hydrogel to simulate the mechanical environment in myocardium (afterload. When electrically stimulated, the in-gel myocyte contracts while the matrix resists shortening and broadening of the cell, exerting normal and shear stresses on the cell. Here we provide a mechanical analysis, based on the Eshelby inclusion problem, of the 3-D strain and stress inside and outside the single myocyte during contraction in an elastic matrix.(1 The fractional shortening of the myocyte depends on the cell's geometric dimensions and the relative stiffness of the cell to the gel. A slender or softer cell has less fractional shortening. A myocyte of typical dimensions embedded in a gel of similar elastic stiffness can contract only 20% of its load-free value. (2 The longitudinal stress inside the cell is about 15 times the transverse stress level. (3 The traction on the cell surface is highly non-uniform, with a maximum near its ends, showing 'hot spots' at the location of intercalated disks. (4 The mechanical energy expenditure of the myocyte increases with the matrix stiffness in a monotonic and nonlinear manner.Our mechanical analyses provide analytic solutions that readily lend themselves to parametric studies. The resulting 3-D mapping of the strain and stress states serve to analyze and interpret ongoing cell-in-gel experiments, and the mathematical model provides an essential tool to decipher and quantify mechanotransduction mechanisms in cardiac 18. Co-effects of matrix low elasticity and aligned topography on stem cell neurogenic differentiation and rapid neurite outgrowth Yao, Shenglian; Liu, Xi; Yu, Shukui; Wang, Xiumei; Zhang, Shuming; Wu, Qiong; Sun, Xiaodan; Mao, Haiquan 2016-05-01 The development of novel biomaterials that deliver precise regulatory signals to direct stem cell fate for nerve regeneration is the focus of current intensive research efforts. In this study, a hierarchically aligned fibrillar fibrin hydrogel (AFG) that was fabricated through electrospinning and the concurrent molecular self-assembly process mimics both the soft and oriented features of nerve tissue, thus providing hybrid biophysical cues to instruct cell behavior in vitro and in vivo. The electrospun hydrogels were examined by scanning electron microscopy (SEM), polarized light microscopy, small angle X-ray scattering assay and atomic force microscopy (AFM), showing a hierarchically linear-ordered structure from the nanoscale to the macroscale with a soft elastic character (elasticity ~1 kPa). We found that this low elasticity and aligned topography of AFG exhibit co-effects on promoting the neurogenic differentiation of human umbilical cord mesenchymal stem cells (hUMSCs) in comparison to random fibrin hydrogel (RFG) and tissue culture plate (TCP) control after two week cell culture in growth medium lacking supplementation with soluble neurogenic induction factors. In addition, AFG also induces dorsal root ganglion (DRG) neurons to rapidly project numerous long neurite outgrowths longitudinally along the AFG fibers for a total neurite extension distance of 1.96 mm in three days in the absence of neurotrophic factor supplementation. Moreover, the AFG implanted in a rat T9 dorsal hemisection spinal cord injury model was found to promote endogenous neural cell fast migration and axonal invasion along AFG fibers, resulting in aligned tissue cables in vivo. Our results suggest that matrix stiffness and aligned topography may instruct stem cell neurogenic differentiation and rapid neurite outgrowth, providing great promise for biomaterial design for applications in nerve regeneration.The development of novel biomaterials that deliver precise regulatory signals to 19. Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach Akbarov, Surkay D 2015-01-01 This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. 20. Co-effects of matrix low elasticity and aligned topography on stem cell neurogenic differentiation and rapid neurite outgrowth. Yao, Shenglian; Liu, Xi; Yu, Shukui; Wang, Xiumei; Zhang, Shuming; Wu, Qiong; Sun, Xiaodan; Mao, Haiquan 2016-05-21 The development of novel biomaterials that deliver precise regulatory signals to direct stem cell fate for nerve regeneration is the focus of current intensive research efforts. In this study, a hierarchically aligned fibrillar fibrin hydrogel (AFG) that was fabricated through electrospinning and the concurrent molecular self-assembly process mimics both the soft and oriented features of nerve tissue, thus providing hybrid biophysical cues to instruct cell behavior in vitro and in vivo. The electrospun hydrogels were examined by scanning electron microscopy (SEM), polarized light microscopy, small angle X-ray scattering assay and atomic force microscopy (AFM), showing a hierarchically linear-ordered structure from the nanoscale to the macroscale with a soft elastic character (elasticity ∼1 kPa). We found that this low elasticity and aligned topography of AFG exhibit co-effects on promoting the neurogenic differentiation of human umbilical cord mesenchymal stem cells (hUMSCs) in comparison to random fibrin hydrogel (RFG) and tissue culture plate (TCP) control after two week cell culture in growth medium lacking supplementation with soluble neurogenic induction factors. In addition, AFG also induces dorsal root ganglion (DRG) neurons to rapidly project numerous long neurite outgrowths longitudinally along the AFG fibers for a total neurite extension distance of 1.96 mm in three days in the absence of neurotrophic factor supplementation. Moreover, the AFG implanted in a rat T9 dorsal hemisection spinal cord injury model was found to promote endogenous neural cell fast migration and axonal invasion along AFG fibers, resulting in aligned tissue cables in vivo. Our results suggest that matrix stiffness and aligned topography may instruct stem cell neurogenic differentiation and rapid neurite outgrowth, providing great promise for biomaterial design for applications in nerve regeneration. 1. Force sensing using 3D displacement measurements in linear elastic bodies Feng, Xinzeng; Hui, Chung-Yuen 2016-07-01 In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints. 2. Dynamic analysis of aircraft impact using the linear elastic finite element codes FINEL, SAP and STARDYNE Lundsager, P.; Krenk, S. 1975-08-01 The static and dynamic response of a cylindrical/ spherical containment to a Boeing 720 impact is computed using 3 different linear elastic computer codes: FINEL, SAP and STARDYNE. Stress and displacement fields are shown together with time histories for a point in the impact zone. The main conclusions from this study are: - In this case the maximum dynamic load factors for stress and displacements were close to 1, but a static analysis alone is not fully sufficient. - More realistic load time histories should be considered. - The main effects seem to be local. The present study does not indicate general collapse from elastic stresses alone. - Further study of material properties at high rates is needed. (author) 3. The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs. Sorokin, Sergey V 2011-03-01 Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America 4. New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity Spannenberg Jescica 2017-09-01 Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation. 5. Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads Donald Mark Santee 2006-01-01 Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion. 6. The application of linear elastic fracture mechanics to thermally stressed welded components Green, D. 1981-01-01 Linear Elastic Fracture Mechanics techniques are applied to components constructed from brittle materials and operating at low or ambient temperatures. It is argued that these techniques can justifiably be applied to components at high temperature provided that stresses are thermally induced, self-equilibrating and cyclic. Such loading conditions occur for example in an LMFBR and a simple welded detail containing a crevice is taken as an example. Theoretical and experimental estimates of crack growth in this component are compared and good agreement is shown. (author) 7. Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity Franca, L.P.; Stenberg, R. 1989-06-01 Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt 8. On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement Ikehata, M; Itou, H 2011-01-01 In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation. 9. Evaluation of linear polymerization shrinkage, flexural strength and modulus of elasticity of dental composites Gabriela Queiroz de Melo Monteiro 2010-03-01 Full Text Available Linear polymerization shrinkage (LPS, flexural strength (FS and modulus of elasticity (ME of 7 dental composites (Filtek Z350™, Filtek Z250™/3M ESPE; Grandio™, Polofil Supra™/VOCO; TPH Spectrum™, TPH3™, Esthet-X™/Denstply were measured. For the measurement of LPS, composites were applied to a cylindrical metallic mold and polymerized (n = 8. The gap formed at the resin/mold interface was observed using scanning electron microscopy (1500×. For FS and ME, specimens were prepared according to the ISO 4049 specifications (n = 10. Statistical analysis of the data was performed with one-way ANOVA and the Tukey test. TPH Spectrum presented significantly higher LPS values (29.45 µm. Grandio had significantly higher mean values for FS (141.07 MPa and ME (13.91 GPa. The relationship between modulus of elasticity and polymerization shrinkage is the main challenge for maintenance of the adhesive interface, thus composites presenting high shrinkage values, associated with a high modulus of elasticity tend to disrupt the adhesive interface under polymerization. 10. Non-linear elasticity of extracellular matrices enables contractile cells to communicate local position and orientation. Jessamine P Winer 2009-07-01 Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning. 11. Exploiting elastic anharmonicity in aluminum nitride matrix for phase-synchronous frequency reference generation Ghatge, Mayur; Tabrizian, Roozbeh 2018-03-01 A matrix of aluminum-nitride (AlN) waveguides is acoustically engineered to realize electrically isolated phase-synchronous frequency references through nonlinear wave-mixing. AlN rectangular waveguides are cross-coupled through a periodically perforated plate that is engineered to have a wide acoustic bandgap around a desirable frequency ( f1≈509 MHz). While the coupling plate isolates the matrix from resonant vibrations of individual waveguide constituents at f1, it is transparent to the third-order harmonic waves (3f1) that are generated through nonlinear wave-mixing. Therefore, large-signal excitation of the f1 mode in a constituent waveguide generates acoustic waves at 3f1 with an efficiency defined by elastic anharmonicity of the AlN film. The phase-synchronous propagation of the third harmonic through the matrix is amplified by a high quality-factor resonance mode at f2≈1529 MHz, which is sufficiently close to 3f1 (f2 ≅ 3f1). Such an architecture enables realization of frequency-multiplied and phase-synchronous, yet electrically and spectrally isolated, references for multi-band/carrier and spread-spectrum wireless communication systems. 12. The region of influence of significant defects and the mechanical vibrations of linear elastic solids Suarez Antola, R. 2004-12-01 The presence of cracks, voids or fields of pores, and their growth under applied forces or environmental actions, can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in machines and structures. A quite general expression for the square of modes proper frequency as a functional of displacement field, density field and elastic moduli fields is used as a starting point. The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields, introducing the concept of region of influence of each defect. This region of influence is derived from the relation between the stress field of flawed components in machines or structures, and the elastic energy released from a suitable reference state, due to the presence of significant defects in the above mentioned mechanical components. An approximate analytical expression is obtained, which relates the relative variation in the square of mode s proper frequency with position, size, shape and orientation of defects in mode displacement field. Some simple mathematical models of machine and structural elements with cracks or fields of pores are considered as examples. The connections between the relative lowering in the square of mode s proper frequency and the stress intensity factor of a defect are discussed : the concept of region of influence of a defect is used as a bridge between (low frequency and low amplitude) vibration dynamics and linear elastic fracture mechanics. Some limitations of the present approach are discussed as well as the possibility of applying the region of influence of defects to the damping of normal modes of vibration 13. Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection Hanks, Brantley R.; Skelton, Robert E. 1991-01-01 Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. 14. A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials Li, Chen; Liao, Yufei 2018-03-01 Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory. 15. Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints DeLuca, R. 2006-03-01 Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected. 16. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action Kim, Jin Kyu; Kim, Dong Keon 2016-01-01 A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics 17. Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26) Harris, John G. 2001-10-01 Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines 18. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of) 2016-09-15 A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics. 19. Printing Three-Dimensional Heterogeneities in the Elastic Modulus of an Elastomeric Matrix. Abdel Fattah, Abdel Rahman; Ghosh, Suvojit; Puri, Ishwar K 2016-05-04 We present a rapid and controllable method to create microscale heterogeneities in the 3D stiffness of a soft material by printing patterns with a ferrofluid ink. An ink droplet moved through a liquid polydimethylsiloxane (PDMS) volume using an externally applied magnetic field sheds clusters of magnetic nanoparticles (MNPs) in its wake. By varying the field spatiotemporally, a well-defined three-dimensional curvilinear feature is printed that contains MNP clusters. Subsequent cross-linking of the PDMS preserves the feature in place after the magnetic field is removed. Since the ferrofluid ink interferes with the cross-linking of PDMS, a 3D print containing ink density variations leads to corresponding spatial deviations in the elastic modulus of the matrix. The modulus is mapped in the experiments with atomic force microscopy. This rapid method to print 3D heterogeneities in soft matter promises the ability to mimic mechanical variations that occur in natural biomaterials. 20. Deposition of tropoelastin into the extracellular matrix requires a competent elastic fiber scaffold but not live cells. Kozel, Beth A; Ciliberto, Christopher H; Mecham, Robert P 2004-04-01 The initial steps of elastic fiber assembly were investigated using an in vitro assembly model in which purified recombinant tropoelastin (rbTE) was added to cultures of live or dead cells. The ability of tropoelastin to associate with preexisting elastic fibers or microfibrils in the extracellular matrix was then assessed by immunofluorescence microscopy using species-specific tropoelastin antibodies. Results show that rbTE can associate with elastic fiber components in the absence of live cells through a process that does not depend on crosslink formation. Time course studies show a transformation of the deposited protein from an initial globular appearance early in culture to a more fibrous structure as the matrix matures. Deposition required the C-terminal region of tropoelastin and correlated with the presence of preexisting elastic fibers or microfibrils. Association of exogenously added tropoelastin to the cellular extracellular matrix was inhibited by the addition of heparan sulfate but not chondroitin sulfate sugars. Together, these results suggest that the matrix elaborated by the cell is sufficient for the initial deposition of tropoelastin in the extracellular space and that elastin assembly may be influenced by the composition of sulfated proteoglycans in the matrix. 1. Response statistics of rotating shaft with non-linear elastic restoring forces by path integration Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael 2017-07-01 Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability. 2. Further results on "Robust MPC using Linear Matrix Inequalities" Lazar, M.; Heemels, W.P.M.H.; Munoz de la Pena, D.; Alamo, T. 2008-01-01 This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is 3. Elasticity theory and applications Saada, Adel S; Hartnett, James P; Hughes, William F 2013-01-01 Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ... 4. Extensions of linear-quadratic control, optimization and matrix theory Jacobson, David H 1977-01-01 In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat 5. Interpolation problem for the solutions of linear elasticity equations based on monogenic functions Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii 2017-11-01 Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis. 6. CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method Benzley, S.E.; Beisinger, Z.E. 1981-01-01 1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used 7. A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M. 2012-08-01 We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution. 8. Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials American Society for Testing and Materials. Philadelphia 2009-01-01 1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a... 9. Linear elastic obstacles: analysis of experimental results in the case of stress dependent pre-exponentials Surek, T.; Kuon, L.G.; Luton, M.J.; Jones, J.J. 1975-01-01 For the case of linear elastic obstacles, the analysis of experimental plastic flow data is shown to have a particularly simple form when the pre-exponential factor is a single-valued function of the modulus-reduced stress. The analysis permits the separation of the stress and temperature dependence of the strain rate into those of the pre-exponential factor and the activation free energy. As a consequence, the true values of the activation enthalpy, volume and entropy also are obtained. The approach is applied to four sets of experimental data, including Zr, and the results for the pre-exponential term are examined for self-consistency in view of the assumed functional dependence 10. First-order system least squares for the pure traction problem in planar linear elasticity Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S. 1996-12-31 This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit. 11. Fuzzy attitude control of solar sail via linear matrix inequalities Baculi, Joshua; Ayoubi, Mohammad A. 2017-09-01 This study presents a fuzzy tracking controller based on the Takagi-Sugeno (T-S) fuzzy model of the solar sail. First, the T-S fuzzy model is constructed by linearizing the existing nonlinear equations of motion of the solar sail. Then, the T-S fuzzy model is used to derive the state feedback controller gains for the Twin Parallel Distributed Compensation (TPDC) technique. The TPDC tracks and stabilizes the attitude of the solar sail to any desired state in the presence of parameter uncertainties and external disturbances while satisfying actuator constraints. The performance of the TPDC is compared to a PID controller that is tuned using the Ziegler-Nichols method. Numerical simulation shows the TPDC outperforms the PID controller when stabilizing the solar sail to a desired state. 12. On the hyperporous non-linear elasticity model for fusion-relevant pebble beds Di Maio, P.A.; Giammusso, R.; Vella, G. 2010-01-01 Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds. 13. Chosen interval methods for solving linear interval systems with special type of matrix Szyszka, Barbara 2013-10-01 The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic. 14. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis. Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping 2015-10-01 We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery. 15. A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier 2017-12-01 Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices. 16. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs Zuidwijk, Rob 2005-01-01 textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ... 17. Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems Adegas, Fabiano Daher; Stoustrup, Jakob 2015-01-01 the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd.... 18. A new technique for generating the isotropic and linearly anisotropic components of elastic and discrete inelastic transfer matrices Garcia, R.D.M. 1984-01-01 A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt 19. Some fundamental definitions of the elastic parameters for homogeneous isotropic linear elastic materials in pavement design and analysis De Beer, Morris 2008-07-01 Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture... 20. Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz 2015-10-01 In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods. 1. Linear models in matrix form a hands-on approach for the behavioral sciences Brown, Jonathon D 2014-01-01 This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum ... 2. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs R.A. Zuidwijk (Rob) 2005-01-01 textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an 3. Sensitivity of the elastic scattering matrix elements to the range of the inelastic potentials Rawitscher, G.H.; Rasoanaivo, R.Y. 1983-01-01 The solution to a system of coupled equations is examined with regard to the effect of the long range part of the inelastic potentials upon the elastic phase shifts. It is found that those parts of the inelastic potentials which occur beyond the range of the elastic to inelastic transition potentials affect the elastic phase shifts in only a minor way. The proof is given theoretically by means of a Green's function formulation which includes the long range part of the inelastic potentials perturbatively. When applied to the calculation of the effect of breakup on the deuteron-nucleus elastic scattering, the argument confirms the finding that errors in the long range part of the potentials in the breakup channels do not sensitively affect the elastic deuteron scattering cross section. This result explains why the elastic scattering is not very sensitive to the choice of the discretization procedure of the breakup space 4. Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry. Sherrit, Stewart; Masys, Tony J; Wiederick, Harvey D; Mukherjee, Binu K 2011-09-01 We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present the transform equations, in reduced matrix form, to other consistent material constant sets. We discuss the propagation of errors in going from one material data set to another and look at the limitations inherent in direct calculations of other useful coefficients from the data. 5. TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix Garbow, B. 1984-01-01 Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals 6. The detection of influential subsets in linear regression using an influence matrix Peña, Daniel; Yohai, Víctor J. 1991-01-01 This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue... 7. Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François 2014-01-01 Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper) 8. Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations. Kim, Dae-Hyeong; Song, Jizhou; Choi, Won Mook; Kim, Hoon-Sik; Kim, Rak-Hwan; Liu, Zhuangjian; Huang, Yonggang Y; Hwang, Keh-Chih; Zhang, Yong-wei; Rogers, John A 2008-12-02 Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics. 9. Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity. Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine 2015-08-01 Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved. 10. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M. 2017-04-01 This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods. 11. The structure of solutions of the matrix linear unilateral polynomial equation with two variables N. S. Dzhaliuk 2017-07-01 Full Text Available We investigate the structure of solutions of the matrix linear polynomial equationA(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices$A (\\lambda, B(\\lambda$\\ and \\$C(\\lambda$are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients$A(\\lambda$and$B(\\lambda.\$

12. Compressive Elasticity of Three-Dimensional Nanofiber Matrix Directs Mesenchymal Stem Cell Differentiation to Vascular Cells with Endothelial or Smooth Muscle Cell Markers

Wingate, Kathryn; Bonani, Walter; Tan, Yan; Bryant, Stephanie J.; Tan, Wei

2012-01-01

The importance of mesenchymal stem cell (MSC) in vascular regeneration is becoming increasingly recognized. However, few in vitro studies have been performed to identify the effects of environmental elasticity on the differentiation of MSC into vascular cell types. We utilized electrospinning and photopolymerization techniques to fabricate a 3D PEGdma nanofiber hydrogel matrix with a tunable elasticity for use as a cellular substrate. Compression testing demonstrated that the elastic modulus ...

13. Classification of the linear canonical transformation and its associated real symplectic matrix

Bastiaans, M.J.; Alieva, T.

2007-01-01

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

14. A simplified density matrix minimization for linear scaling self-consistent field theory

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

15. The Relationships between Weight Functions, Geometric Functions,and Compliance Functions in Linear Elastic Fracture Mechanics

Yuan, Rong [Univ. of California, Berkeley, CA (United States)

2007-01-01

Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight

16. Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

Wang, Wenjun; Li, Peng; Jin, Feng

2016-09-01

A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

17. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

Li, Deng-Feng

2016-01-01

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

18. Filamin A Mediates Wound Closure by Promoting Elastic Deformation and Maintenance of Tension in the Collagen Matrix

Mohammadi, Hamid; Pinto, Vanessa I.; Wang, Yongqiang; Hinz, Boris; Janmey, Paul A.; McCulloch, Christopher A.

2016-01-01

Cell-mediated remodeling and wound closure are critical for efficient wound healing, but the contribution of actin-binding proteins to contraction of the extracellular matrix is not defined. We examined the role of filamin A (FLNa), an actin filament cross-linking protein, in wound contraction and maintenance of matrix tension. Conditional deletion of FLNa in fibroblasts in mice was associated with ~ 4 day delay of full-thickness skin wound contraction compared with wild-type (WT) mice. We modeled the healing wound matrix using cultured fibroblasts plated on grid-supported collagen gels that create lateral boundaries, which are analogues to wound margins. In contrast to WT cells, FLNa knockdown (KD) cells could not completely maintain tension when matrix compaction was resisted by boundaries, which manifested as relaxed matrix tension. Similarly, WT cells on cross-linked collagen, which requires higher levels of sustained tension, exhibited approximately fivefold larger deformation fields and approximately twofold greater fiber alignment compared with FLNa KD cells. Maintenance of boundary-resisted tension markedly influenced the elongation of cell extensions: in WT cells, the number (~50%) and length (~300%) of cell extensions were greater than FLNa KD cells. We conclude that FLNa is required for wound contraction, in part by enabling elastic deformation and maintenance of tension in the matrix. PMID:26134946

19. Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation

Huebsch, Nathaniel; Lippens, Evi; Lee, Kangwon; Mehta, Manav; Koshy, Sandeep T.; Darnell, Max C.; Desai, Rajiv M.; Madl, Christopher M.; Xu, Maria; Zhao, Xuanhe; Chaudhuri, Ovijit; Verbeke, Catia; Kim, Woo Seob; Alim, Karen; Mammoto, Akiko; Ingber, Donald E.; Duda, Georg N.; Mooney, David J.

2015-12-01

The effectiveness of stem cell therapies has been hampered by cell death and limited control over fate. These problems can be partially circumvented by using macroporous biomaterials that improve the survival of transplanted stem cells and provide molecular cues to direct cell phenotype. Stem cell behaviour can also be controlled in vitro by manipulating the elasticity of both porous and non-porous materials, yet translation to therapeutic processes in vivo remains elusive. Here, by developing injectable, void-forming hydrogels that decouple pore formation from elasticity, we show that mesenchymal stem cell (MSC) osteogenesis in vitro, and cell deployment in vitro and in vivo, can be controlled by modifying, respectively, the hydrogel’s elastic modulus or its chemistry. When the hydrogels were used to transplant MSCs, the hydrogel’s elasticity regulated bone regeneration, with optimal bone formation at 60 kPa. Our findings show that biophysical cues can be harnessed to direct therapeutic stem cell behaviours in situ.

20. Elastic modulus of Al-Si/SiC metal matrix composites as a function of volume fraction

Santhosh Kumar, S; Rajasekharan, T [Powder Metallurgy Group, Defence Metallurgical Research Laboratory, Kanchanbagh PO, Hyderabad-500 058 (India); Seshu Bai, V [School of Physics, University of Hyderabad, Central University PO, Hyderabad-500 046 (India); Rajkumar, K V; Sharma, G K; Jayakumar, T, E-mail: dearsanthosh@gmail.co [Non-Destructive Evaluation Division, Indira Gandhi Center for Atomic Research, Kalpakkam, Chennai-603 102 (India)

2009-09-07

Aluminum alloy matrix composites have emerged as candidate materials for electronic packaging applications in the field of aerospace semiconductor electronics. Composites prepared by the pressureless infiltration technique with high volume fractions in the range 0.41-0.70 were studied using ultrasonic velocity measurements. For different volume fractions of SiC, the longitudinal velocity and shear velocity were found to be in the range of 7600-9300 m s{sup -1} and 4400-5500 m s{sup -1}, respectively. The elastic moduli of the composites were determined from ultrasonic velocities and were analysed as a function of the volume fraction of the reinforcement. The observed variation is discussed in the context of existing theoretical models for the effective elastic moduli of two-phase systems.

1. FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

N. A. Dudarenko

2014-09-01

Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.

2. Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

Darunee Hunwisai

2017-01-01

Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

3. A non-linear elastic constitutive framework for replicating plastic deformation in solids.

Roberts, Scott Alan; Schunk, Peter Randall

2014-02-01

Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

4. Advanced topics in linear algebra weaving matrix problems through the Weyr form

O'Meara, Kevin; Vinsonhaler, Charles

2011-01-01

The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the

5. Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

Charara, Ali; Keyes, David E.; Ltaief, Hatem

2017-01-01

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

6. Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

Charara, Ali

2017-03-06

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

7. Fatigue crack growth from a cracked elastic particle into a ductile matrix

Groh, S.; Olarnrithinun, S.; Curtin, W. A.; Needleman, A.; Deshpande, V. S.; Van der Giessen, E.

2008-01-01

The monotonic and cyclic crack growth rate of cracks is strongly influenced by the microstructure. Here, the growth of cracks emanating from pre-cracked micron-scale elastic particles and growing into single crystals is investigated, with a focus on the effects of (i) plastic confinement due to the

8. Aging linear viscoelasticity of matrix-inclusion composite materials featuring ellipsoidal inclusions

LAVERGNE, Francis; SAB, Karam; SANAHUJA, Julien; BORNERT, Michel; TOULEMONDE, Charles

2016-01-01

A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-a...

9. The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

Kim, Jeong Soo; Kim, Moon Kyum

2012-01-01

In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

10. A unified approach to fixed-order controller design via linear matrix inequalities

Iwasaki T.

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type B G C + ( B G C T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

11. A unified approach to fixed-order controller design via linear matrix inequalities

T. Iwasaki

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,-stabilization as a robust stabilization problem, and robust L∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type BGC+(BGCT+Q<0 for the unknown matrix G. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X∈1 and X−1∈2 where 1 and 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

12. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

Angela Mihai, L.; Goriely, Alain

2013-01-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

13. Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

Wu, J.-X.; Li, X.-F.; Tang, G.-J.

2012-01-01

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.

14. Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

Wu, J.-X. [School of Civil Engineering, Central South University, Changsha, Hunan 410075 (China); Li, X.-F., E-mail: xfli25@yahoo.com.cn [School of Civil Engineering, Central South University, Changsha, Hunan 410075 (China); Tang, G.-J. [College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha 410073 (China)

2012-02-15

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.

15. A method for accurate computation of elastic and discrete inelastic scattering transfer matrix

Garcia, R.D.M.; Santina, M.D.

1986-05-01

A method for accurate computation of elastic and discrete inelastic scattering transfer matrices is discussed. In particular, a partition scheme for the source energy range that avoids integration over intervals containing points where the integrand has discontinuous derivative is developed. Five-figure accurate numerical results are obtained for several test problems with the TRAMA program which incorporates the porposed method. A comparison with numerical results from existing processing codes is also presented. (author) [pt

16. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

17. An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

P. Bumroongsri

2014-01-01

Full Text Available An offline model predictive control (MPC algorithm for linear parameter varying (LPV systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

18. Particles geometry influence in the thermal stress level in an SiC reinforced aluminum matrix composite considering the material non-linear behavior

Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.

2009-01-01

An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)

19. Unified approach to numerical transfer matrix methods for disordered systems: applications to mixed crystals and to elasticity percolation

Lemieux, M.A.; Breton, P.; Tremblay, A.M.S.

1985-01-01

It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size analysis of critical exponents for the central force percolation universality class are presented

20. The ultra-structural organization of the elastic network in the intra- and inter-lamellar matrix of the intervertebral disc.

Tavakoli, J; Elliott, D M; Costi, J J

2017-08-01

The inter-lamellar matrix (ILM)-located between adjacent lamellae of the annulus fibrosus-consists of a complex structure of elastic fibers, while elastic fibers of the intra-lamellar region are aligned predominantly parallel to the collagen fibers. The organization of elastic fibers under low magnification, in both inter- and intra-lamellar regions, was studied by light microscopic analysis of histologically prepared samples; however, little is known about their ultrastructure. An ultrastructural visualization of elastic fibers in the inter-lamellar matrix is crucial for describing their contribution to structural integrity, as well as mechanical properties of the annulus fibrosus. The aims of this study were twofold: first, to present an ultrastructural analysis of the elastic fiber network in the ILM and intra-lamellar region, including cross section (CS) and in-plane (IP) lamellae, of the AF using Scanning Electron Microscopy (SEM) and second, to -compare the elastic fiber orientation between the ILM and intra-lamellar region. Four samples (lumbar sheep discs) from adjacent sections (30μm thickness) of anterior annulus were partially digested by a developed NaOH-sonication method for visualization of elastic fibers by SEM. Elastic fiber orientation and distribution were quantified relative to the tangential to circumferential reference axis. Visualization of the ILM under high magnification revealed a dense network of elastic fibers that has not been previously described. Within the ILM, elastic fibers form a complex network, consisting of different size and shape fibers, which differed to those located in the intra-lamellar region. For both regions, the majority of fibers were oriented near 0° with respect to tangential to circumferential (TCD) direction and two minor symmetrical orientations of approximately±45°. Statistically, the orientation of elastic fibers between the ILM and intra-lamellar region was not different (p=0.171). The present study used

1. Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)

2013-11-15

Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.

2. Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi

2013-01-01

Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation

3. T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-01-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders. -- Highlights: ► New superposition T-matrix code is applied to soot aerosols. ► Quasi-Rayleigh side-scattering peak in linear depolarization (LD) is explained. ► LD measurements can be used for morphological characterization of soot aerosols

4. Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

Tarp-Johansen, Niels Jacob; Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.......Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under......-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure...

5. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

Min Sun

2014-01-01

Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

6. Defects in Ceramic Matrix Composites and Their Impact on Elastic Properties (Postprint)

2013-07-01

SiC (CG Nicalon™) fiber, coated with boron nitride, in a matrix of sil- icon , nitrogen and carbon manufactured by multiple itera- tions of a polymer...For the dry fibers defect, Eq. (1) for E1d is modified to include the effect of the stress-discontinuity in the fibers direction utilizing a5

7. DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM

O. L. Shved

2014-01-01

Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.

8. Compressive elasticity of three-dimensional nanofiber matrix directs mesenchymal stem cell differentiation to vascular cells with endothelial or smooth muscle cell markers.

Wingate, K; Bonani, W; Tan, Y; Bryant, S J; Tan, W

2012-04-01

The importance of mesenchymal stem cells (MSC) in vascular regeneration is becoming increasingly recognized. However, few in vitro studies have been performed to identify the effects of environmental elasticity on the differentiation of MSC into vascular cell types. Electrospinning and photopolymerization techniques were used to fabricate a three-dimensional (3-D) polyethylene glycol dimethacrylate nanofiber hydrogel matrix with tunable elasticity for use as a cellular substrate. Compression testing demonstrated that the elastic modulus of the hydrated 3-D matrices ranged from 2 to 15 kPa, similar to the in vivo elasticity of the intima basement membrane and media layer. MSC seeded on rigid matrices (8-15 kPa) showed an increase in cell area compared with those seeded on soft matrices (2-5 kPa). Furthermore, the matrix elasticity guided the cells to express different vascular-specific phenotypes with high differentiation efficiency. Around 95% of MSC seeded on the 3-D matrices with an elasticity of 3 kPa showed Flk-1 endothelial markers within 24h, while only 20% of MSC seeded on the matrices with elasticity >8 kPa demonstrated Flk-1 marker. In contrast, ∼80% of MSC seeded on 3-D matrices with elasticity >8 kPa demonstrated smooth muscle α-actin marker within 24h, while fewer than 10% of MSC seeded on 3-D matrices with elasticity elasticity of the substrate could be a powerful tool for vascular tissue regeneration. Copyright Â© 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

9. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer-matrix composite.

Duan, Yuanyuan; Griggs, Jason A

2015-06-01

10. Geometric method for stability of non-linear elastic thin shells

Ivanova, Jordanka

2002-01-01

PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...

11. Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

12. Effect of oxidation at elevated temperature on elastic and interface properties of ceramic matrix composites

Brandstetter, J.; Glogar, Petr; Loidl, D.; Kromp, K.

2005-01-01

Roč. 290, - (2005), s. 340-343 ISSN 1013-9826. [International conference on fractography of advanced ceramics /2./. Stará Lesná, 03.10.2005-06.10.2005] R&D Projects: GA AV ČR(CZ) KSK2067107 Institutional research plan: CEZ:AV0Z30460519 Keywords : polysiloxane * ceramic matrix composite * shear modulus Subject RIV: JH - Ceramics, Fire-Resistant Materials and Glass Impact factor: 0.224, year: 2005

13. Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

14. New computational method for non-LTE, the linear response matrix

Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

1998-01-01

My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

15. Matrix effect study in the determination of linear alkylbenzene sulfonates in sewage sludge samples.

Cantarero, Samuel; Zafra-Gómez, Alberto; Ballesteros, Oscar; Navalón, Alberto; Vílchez, José L; Verge, Coral; De Ferrer, Juan A

2011-04-01

We propose a study of the matrix effect in the determination of linear alkylbenzene sulfonates (LAS) in sewage sludge samples. First, a rapid, selective and sensitive method is proposed. The method involves two stages: the extraction of the compound from the samples and analysis by liquid chromatography with fluorescence detection (LC-FLD). Three different techniques of extraction (microwave-assisted extraction, Soxhlet, and ultrasounds) were compared, and microwave-assisted extraction was selected as the best suited for our purpose. Microwave-assisted extraction allows reducing the extraction time (25 min compared with 12 h for conventional Soxhlet extraction) and solvent waste (25 ml of methanol compared with 200 ml for Soxhlet or more than 50 ml for the ultrasonic procedure). Absence of matrix effect was evaluated with two standards (2ØC(8:0) and 2ØC(16:0) ) that are not commercial; therefore, neither of them was detected in sewage sludge samples and they showed similar environmental behavior (adsorption and precipitation) to LAS (C(11:0) -C(13.0) ), which allow us to evaluate the matrix effect. Validation was carried out by a recovery assay, and the method was applied to samples from different sources; therefore, they had different compositions. Copyright © 2011 SETAC.

16. Investigation of Effects of Material Architecture on the Elastic Response of a Woven Ceramic Matrix Composite

Goldberg, Robert K.; Bonacuse, Peter J.; Mital, Subodh K.

2012-01-01

To develop methods for quantifying the effects of the microstructural variations of woven ceramic matrix composites on the effective properties and response of the material, a research program has been undertaken which is described in this paper. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, CVI SiC/SiC, composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents and collect relevant statistics such as within ply tow spacing. This information was then used to build two dimensional finite element models that approximated the observed section geometry. With the aid of geometrical models generated by the microstructural characterization process, finite element models were generated and analyses were performed to quantify the effects of the microstructure and its variation on the effective stiffness and areas of stress concentration of the material. The results indicated that the geometry and distribution of the porosity appear to have significant effects on the through-thickness modulus. Similarly, stress concentrations on the outer surface of the composite appear to correlate to regions where the transverse tows are separated by a critical amount.

17. Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

18. An enhanced finite volume method to model 2D linear elastic structures

Suliman, Ridhwaan

2014-04-01

Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...

19. A generic approach for a linear elastic fracture mechanics analysis of components containing residual stress

Lee, Hyeong Y.; Nikbin, Kamran M.; O'Dowd, Noel P.

2005-01-01

A review of through thickness transverse residual stress distribution measurements in a number of components, manufactured from a range of steels, has been carried out. Residual stresses introduced by welding and mechanical deformation have been considered. The geometries consisted of welded T-plate joints, pipe butt joints, tube-on-plate joints, tubular Y-joints and tubular T-joints as well as cold bent tubes and repair welds. In addition, the collected data cover a range of engineering steels including ferritic, austenitic, C-Mn and Cr-Mo steels. The methods used to measure the residual stresses also varied. These included neutron diffraction, X-ray diffraction and deep hole drilling techniques. Measured residual stress data, normalised by their respective yield stress have shown an inverse linear correlation versus the normalised depth of the region containing the residual stress (up to 0.5 of the component thickness). A simplified generic residual stress profile based on a linear fit to the data is proposed for the case of a transverse residual tensile stress field. Whereas the profiles in assessment procedures are case specific the proposed linear profile can be varied to produce a combination of membrane and bending stress distributions to give lower or higher levels of conservatism on stress intensity factors, depending on the amount of case specific data available or the degree of safety required

20. Pulsed-laser time-resolved thermal mirror technique in low-absorbance homogeneous linear elastic materials.

Lukasievicz, Gustavo V B; Astrath, Nelson G C; Malacarne, Luis C; Herculano, Leandro S; Zanuto, Vitor S; Baesso, Mauro L; Bialkowski, Stephen E

2013-10-01

A theoretical model for a time-resolved photothermal mirror technique using pulsed-laser excitation was developed for low absorption samples. Analytical solutions to the temperature and thermoelastic deformation equations are found for three characteristic pulse profiles and are compared to finite element analysis methods results for finite samples. An analytical expression for the intensity of the center of a continuous probe laser at the detector plane is derived using the Fresnel diffraction theory, which allows modeling of experimental results. Experiments are performed in optical glasses, and the models are fitted to the data. The parameters of the fit are in good agreement with previous literature data for absorption, thermal diffusion, and thermal expansion of the materials tested. The combined modeling and experimental techniques are shown to be useful for quantitative determination of the physical properties of low absorption homogeneous linear elastic material samples.

1. An anisotropic linear thermo-viscoelastic constitutive law - Elastic relaxation and thermal expansion creep in the time domain

Pettermann, Heinz E.; DeSimone, Antonio

2017-09-01

A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.

2. Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

3. On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

4. Ground states of linear rotor chains via the density matrix renormalization group

Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

5. Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Balasubramaniam, P.; Kalpana, M.; Rakkiyappan, R.

2012-01-01

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov—Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method. (interdisciplinary physics and related areas of science and technology)

6. Robust Model Predictive Control Using Linear Matrix Inequalities for the Treatment of Asymmetric Output Constraints

Mariana Santos Matos Cavalca

2012-01-01

Full Text Available One of the main advantages of predictive control approaches is the capability of dealing explicitly with constraints on the manipulated and output variables. However, if the predictive control formulation does not consider model uncertainties, then the constraint satisfaction may be compromised. A solution for this inconvenience is to use robust model predictive control (RMPC strategies based on linear matrix inequalities (LMIs. However, LMI-based RMPC formulations typically consider only symmetric constraints. This paper proposes a method based on pseudoreferences to treat asymmetric output constraints in integrating SISO systems. Such technique guarantees robust constraint satisfaction and convergence of the state to the desired equilibrium point. A case study using numerical simulation indicates that satisfactory results can be achieved.

7. Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry.

Patty, C H Lucas; Luo, David A; Snik, Frans; Ariese, Freek; Buma, Wybren Jan; Ten Kate, Inge Loes; van Spanning, Rob J M; Sparks, William B; Germer, Thomas A; Garab, Győző; Kudenov, Michael W

2018-06-01

Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650 nm to 710 nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization. Copyright © 2018 The Author(s). Published by Elsevier B.V. All rights reserved.

8. H-/H∞ structural damage detection filter design using an iterative linear matrix inequality approach

Chen, B; Nagarajaiah, S

2008-01-01

The existence of damage in different members of a structure can be posed as a fault detection problem. It is also necessary to isolate structural members in which damage exists, which can be posed as a fault isolation problem. It is also important to detect the time instants of occurrence of the faults/damage. The structural damage detection filter developed in this paper is a model-based fault detection and isolation (FDI) observer suitable for detecting and isolating structural damage. In systems, possible faults, disturbances and noise are coupled together. When system disturbances and sensor noise cannot be decoupled from faults/damage, the detection filter needs to be designed to be robust to disturbances as well as sensitive to faults/damage. In this paper, a new H - /H ∞ and iterative linear matrix inequality (LMI) technique is developed and a new stabilizing FDI filter is proposed, which bounds the H ∞ norm of the transfer function from disturbances to the output residual and simultaneously does not degrade the component of the output residual due to damage. The reduced-order error dynamic system is adopted to form bilinear matrix inequalities (BMIs), then an iterative LMI algorithm is developed to solve the BMIs. The numerical example and experimental verification demonstrate that the proposed algorithm can successfully detect and isolate structural damage in the presence of measurement noise

9. Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

10. T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-07-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

11. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

2010-01-01

and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...

12. P-S & S-P Elastic Wave Conversions from Linear Arrays of Oriented Microcracks

Jiang, L.; Modiriasari, A.; Bobet, A.; Pyrak-Nolte, L. J.

2017-12-01

Natural and induced processes can produce oriented mechanical discontinuities such as en echelon cracks, fractures and faults. Previous research has shown that compressional to shear (P-S) wave conversions occur at normal incidence to a fracture because of cross-coupling fracture compliances (Nakagawa et al., 2000). Here, experiments and computer simulation are presented to demonstrate the link among cross-coupling stiffness, microcrack orientation and energy partitioning among P, S, and P-S/S-P waves. A FormLabs 2 3D printer was used to fabricate 7 samples (50 mm x 50 mm x 100 mm) with linear arrays of microcracks oriented at 0, 15, 30, 45, 60, 75, and 900 with a print resolution of 0.025 mm. The microcracks were elliptical in cross-sections (2 mm long by 1 mm wide), through the 50 mm thickness of sample, and spaced 3 mm (center-to-center for adjacent cracks). A 25 mm length of each sample contained no microcracks to act as a reference material. Broadband transducers (0.2-1.5 MHz) were used to transmit and receive P and polarized S wave signals that were propagated at normal incidence to the linear array of microcracks. P-wave amplitude increased, while S-wave amplitude remained relatively constant, as the microcrack orientation increased from 0o to 90o. At normal incidence, P-S and S-P wave conversions emerged and increased in amplitude as the crack inclination increased from 00 to 450. From 450 to 900, the amplitude of these converted modes decreased. Between negative and positive crack angles, the P-to-S and S-to-P waves were 1800 phase reversed. The observed energy partitioning matched the computed compliances obtained from numerical simulations with ABAQUS. The cross-coupling compliance for cracks inclined at 450 was found to be the smallest magnitude. 3D printing enabled the study of microstructural effects on macro-scale wave measurements. Information on the orientation of microcracks or even en echelon fractures and faults is contained in P-S conversions

13. Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix --- The full report.

Ben Gharbia , Ibtihel; Gilbert , Jean Charles

2012-01-01

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q)=0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may...

14. LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

Dongarra, J.J.

1979-01-01

1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

15. Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEMin Nearly Incompressible Linear Elasticity

Dörsek, Philipp; Melenk, Jens M.

2017-01-01

We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...

16. THE STRESS-STRAIN STATE OF ELASTIC HALF-SPACE FROM RUNNING LINEAR LOAD ACTING ON THE LIMITED AND UNLIMITED EXTENT OVER ITS SURFACE

2009-02-01

Full Text Available The article shows the result of solving the problem of stress-strain state of an elastic half-space because of the load action that uniformly distributed over the line, with the use of untraditional linear dependence of deformations on stressed state that is different from the generalized Hooke’s law.

17. Linear and nonlinear response matrix and its application to the SIS18 synchrotron

Parfenova, Angelina

2008-01-01

This Thesis is dedicated to the numerical as well as the experimental study of beam dynamics in circular accelerators. The experimental part was undertaken in the SIS18 synchrotron. The detailed description of the experiments contained in this work can be considered as a starting point for future experiments and machine development. The work has the following structure. In Chapter 2 an overview of the GSI and FAIR accelerator facilities, and a general description of the SIS18 instrumentation related to the study of this work are given. The expected SIS18 performance in view of the upgrade program for FAIR project are outlined. The main beam dynamics issues connected with the purpose of this work are discussed. Chapter 3 is devoted to the study of linear beam dynamics in the SIS18. The resonance beam loss measurements were carried out with residual gas profile monitor in the SIS18 (Chapter 4). In the frame of this work a novel technique 'nonlinear tune response matrix method' to identify strengths, polarities and locations of nonlinear errors in circular accelerators is developed (Chapter 5). In the method the feed down effect of the nonlinear components at level of linear tune response to the closed-orbit change is explored. The closed-orbit change is introduced by varying correction steerers. The tune values are retrieved from the spectrum of coherent betatron oscillations excited by a fast kick. The theoretical background, the robustness of the method and numerical examples for the SIS18 using numerical library MICROMAP are presented. The technique to measure lattice nonlinearities was experimentally validated in the SIS18 where two normal as well as two skew sextupolar errors of the order of natural errors were reconstructed with a tolerant precision. It was shown how this technique can be applied to reconstruct sextupolar nonlinear errors in the complete machine. In Chapter 6 the main results and the conclusions of this work are outlined. (orig.)

18. Linear reversible second-order cellular automata and their first-order matrix equivalents

Macfarlane, A J

2004-01-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..

19. Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

Zulfatman; Marzuki, Mohammad; Alif Mardiyah, Nur

2017-04-01

Two-link flexible manipulator is a manipulator robot which at least one of its arms is made of lightweight material and not rigid. Flexible robot manipulator has some advantages over the rigid robot manipulator, such as lighter, requires less power and costs, and to result greater payload. However, suitable control algorithm to maintain the two-link flexible robot manipulator in accurate positioning is very challenging. In this study, sliding mode control (SMC) was employed as robust control algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are sliding on a sliding surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during sliding on the sliding surface. Stability of the control algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of control input (SSCI) indexes respectively 25.4% and 19.4%.

20. Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

Yoneoka, Daisuke; Henmi, Masayuki

2017-06-01

Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

1. Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity

Amir R. Ali

2017-01-01

Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.

2. Comparison between isotropic linear-elastic law and isotropic hyperelastic law in the finite element modeling of the brachial plexus.

Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P

2017-12-01

Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS ® from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

3. The interfascicular matrix enables fascicle sliding and recovery in tendon, and behaves more elastically in energy storing tendons.

Thorpe, Chavaunne T; Godinho, Marta S C; Riley, Graham P; Birch, Helen L; Clegg, Peter D; Screen, Hazel R C

2015-12-01

4. An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

Shao Hai-Jian; Cai Guo-Liang; Wang Hao-Xiang

2010-01-01

In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications

5. Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

Lee, Kyo-Beum; Blaabjerg, Frede

2004-01-01

This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

6. Comparison of Damage Models for Predicting the Non-Linear Response of Laminates Under Matrix Dominated Loading Conditions

Schuecker, Clara; Davila, Carlos G.; Rose, Cheryl A.

2010-01-01

Five models for matrix damage in fiber reinforced laminates are evaluated for matrix-dominated loading conditions under plane stress and are compared both qualitatively and quantitatively. The emphasis of this study is on a comparison of the response of embedded plies subjected to a homogeneous stress state. Three of the models are specifically designed for modeling the non-linear response due to distributed matrix cracking under homogeneous loading, and also account for non-linear (shear) behavior prior to the onset of cracking. The remaining two models are localized damage models intended for predicting local failure at stress concentrations. The modeling approaches of distributed vs. localized cracking as well as the different formulations of damage initiation and damage progression are compared and discussed.

7. Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

Kim, Jong Sung; Kim, Yong Woo [Sunchon National University, Suncheon (Korea, Republic of)

2014-10-15

Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected.

8. Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

Kim, Jong Sung; Kim, Yong Woo

2014-01-01

Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected

9. Radiation safety assessment of treatment teletherapy linear accelerators using the method of the risk matrix

Dumenigo Gonzalez, Cruz; Vilaragut Llanes, Juan J.; Morales Lopez, Jorge L.

2009-01-01

Accidents in the world of radiation, demonstrating the need for deepen security assessments. This study evaluates the safety of the treatment of teletherapy linear accelerator (LINAC) at a hospital in Cuba, based on applying the method Risk Matrix. This method has been used for many years in conventional industry, is simple, easy to apply and is based on the equation General risk R = f * P * C (where: f frequency of occurrence of the initiating event, P probability of failure of all barriers and magnitude of the consequences C expected). We have evaluated 140 accident sequences that were identified during the analysis of the treatment process. It was identified that 5 sequences are associated with the level of risk is very low, 96 low-risk, high risk and 39 with no very high risk. All accident sequences associated with high risk (considered unacceptable), have an impact on patients, and no concerns workers and public, which reaffirms that major security problems are related to radiation protection of patients. 34 sequences accidental high risk are associated with human errors and failures only 5 to equipment (LINAC, TPS, TAC, etc.). demonstrating the importance of human error. It shows that 35 of the 39 high-risk accident sequences leading to serious or very serious consequences for patients, which would mean the death of one or more patients, making specific recommendations to reduce risk in these cases. The findings of this work and regulators allow users to refine their programs quality assurance and inspection and suggest the hospital management, prioritize material resources according to criteria of irrigation management. (author)

10. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Nahed S. Hussein

2014-01-01

Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

11. Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

Zhe Zhang

2010-09-01

Full Text Available With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.In the framework of mixed model equations, a new best linear unbiased prediction (BLUP method including a trait-specific relationship matrix (TA was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP and BLUP with realized relationship matrix (GBLUP. It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.

12. ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

2017-11-01

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

13. Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom

Náprstek, Jiří; Pospíšil, Stanislav

2012-01-01

Roč. 111, č. 1 (2012), s. 1-13 ISSN 0167-6105 R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902 Institutional support: RVO:68378297 Keywords : aero-elastic system * self-excited vibration * instability * aero-elastic derivatives Subject RIV: JN - Civil Engineering Impact factor: 1.342, year: 2012

14. Speed-Sensorless DTC-SVM for Matrix Converter Drives With Simple Non-Linearity Compensation

Lee, Kyo-Beum; Blaabjerg, Frede; Yoon, Tae-Woong

2005-01-01

This paper presents a new method to improve sensorless performance of matrix converter drives using a parameter estimation scheme. To improve low-speed sensorless performance, the non-Iinearities of a matrix converter drive such as commutation delays, turn-on and turn-off times of switching devic...... method is applied for high performance induction motor drives using a 3 kW matrix converter system without a speed sensor. Experimental results are shown to illustrate the feasibility of the proposed strategy....

15. Investigation of translaminar fracture in fibrereinforced composite laminates---applicability of linear elastic fracture mechanics and cohesive-zone model

Hou, Fang

With the extensive application of fiber-reinforced composite laminates in industry, research on the fracture mechanisms of this type of materials have drawn more and more attentions. A variety of fracture theories and models have been developed. Among them, the linear elastic fracture mechanics (LEFM) and cohesive-zone model (CZM) are two widely-accepted fracture models, which have already shown applicability in the fracture analysis of fiber-reinforced composite laminates. However, there remain challenges which prevent further applications of the two fracture models, such as the experimental measurement of fracture resistance. This dissertation primarily focused on the study of the applicability of LEFM and CZM for the fracture analysis of translaminar fracture in fibre-reinforced composite laminates. The research for each fracture model consisted of two sections: the analytical characterization of crack-tip fields and the experimental measurement of fracture resistance parameters. In the study of LEFM, an experimental investigation based on full-field crack-tip displacement measurements was carried out as a way to characterize the subcritical and steady-state crack advances in translaminar fracture of fiber-reinforced composite laminates. Here, the fiber-reinforced composite laminates were approximated as anisotropic solids. The experimental investigation relied on the LEFM theory with a modification with respect to the material anisotropy. Firstly, the full-field crack-tip displacement fields were measured by Digital Image Correlation (DIC). Then two methods, separately based on the stress intensity approach and the energy approach, were developed to measure the crack-tip field parameters from crack-tip displacement fields. The studied crack-tip field parameters included the stress intensity factor, energy release rate and effective crack length. Moreover, the crack-growth resistance curves (R-curves) were constructed with the measured crack-tip field parameters

16. Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

Wu, Wei; Cui, Bao-Tong

2007-07-01

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

17. Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

18. Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

19. vSmartMOM: A vector matrix operator method-based radiative transfer model linearized with respect to aerosol properties

Sanghavi, Suniti; Davis, Anthony B.; Eldering, Annmarie

2014-01-01

In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions. We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (60°), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function. We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector [I,Q,U,V] as well as the more practical use of only [I,Q,U]. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes

20. On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

Bai, Z.-Z.; Rozložník, Miroslav

2015-01-01

Roč. 53, č. 4 (2015), s. 1716-1737 ISSN 0036-1429 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : matrix splitting * stationary iteration method * backward error * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.899, year: 2015

1. Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

2. Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

Pan, Guangming; Wang, Shaochen; Zhou, Wang

2017-10-01

In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.

3. H{infinity} Filtering for Dynamic Compensation of Self-Powered Neutron Detectors - A Linear Matrix Inequality Based Method -

Park, M.G.; Kim, Y.H.; Cha, K.H.; Kim, M.K. [Korea Electric Power Research Institute, Taejon (Korea)

1999-07-01

A method is described to develop and H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for both continuous- and discrete-time models. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency. (author). 15 refs., 4 figs., 3 tabs.

4. Matrix Operations for Engineers and Scientists An Essential Guide in Linear Algebra

Jeffrey, Alan

2010-01-01

Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful. According to the author the best way to understand the theory of matrices is by working simple exercises designe...

5. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

6. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

7. Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics

Lucchetti, Liana; Fraccia, Tommaso P.; Ciciulla, Fabrizio; Bellini, Tommaso

2017-01-01

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced bi...

8. Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J

2012-07-01

Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.

9. Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso

2017-07-10

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

10. Contractive maps on normed linear spaces and their applications to nonlinear matrix equations.

Reurings, M.C.B.

2017-01-01

In this paper the author gives necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space. These conditions are already well known for maps on intervals in R. Using the conditions and Banach's fixed point theorem a fixed point theorem can be

11. Preconditioner Updates for Solving Sequences of Linear Systems in Matrix-Free Environment

Duintjer Tebbens, Jurjen; Tůma, Miroslav

2010-01-01

Roč. 17, č. 6 (2010), s. 997-1019 ISSN 1070-5325 R&D Projects: GA AV ČR IAA100300802; GA AV ČR KJB100300703 Grant - others:GA AV ČR(CZ) M100300902 Institutional research plan: CEZ:AV0Z10300504 Source of funding: I - inštitucionálna podpora na rozvoj VO Keywords : preconditioned iterative methods * matrix-free environment * factorization updates * inexact Newton-Krylov methods * incomplete factorizations Subject RIV: BA - General Mathematics Impact factor: 1.163, year: 2010

12. A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

Liu, Tao; Huang, Jie

2017-04-17

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

13. Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

14. H{sub 2}/H{infinity} control of flexible structures through linear matrix inequalities with pole placement

Lopes, Jean C. [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil)

2009-07-01

The objective of this work is to apply the H2/H{infinity} control technique using linear matrix inequalities and pole placement constraints to the flexible structures control problem. The H2/H{infinity}control is a technique to design a controller with mixed features of the H2 and H{infinity} control formulations, such as, optimal dynamical performance and robust performance. The Linear Matrix Inequalities allow formulating the problem as a convex optimization problem, and additional constraints can be included such as the pole placement. The pole placement requirement comes from the necessity of adjusting the transient response of the plant and ensuring a specific behavior in terms of speed and damping responses. The mathematical model used for this study is related to a flexible beam, with an applied disturbance and an actuator in different positions. The state-space matrices of the structure were obtained using the finite element method with the Euler-Bernoulli formulation of beams. The results showed that the pole placement constraints can improve the performance of the controller H2/H{infinity}. The Matlab was used for the computational implementation. (author)

15. A comparative study of Kalman filter and Linear Matrix Inequality based H infinity filter for SPND delay compensation

Tamboli, P.K.; Duttagupta, Siddhartha P.; Roy, Kallol

2016-01-01

Highlights: • Derivation for delay compensation algorithm using recursive Kalman filter. • Derivation for delay compensation algorithm using Linear Matrix Inequality based H infinity filter. • Process modeling suitable for delay compensation. • Dynamic tuning of the delay compensation algorithm for both Kalman and H infinity filter. • Simulations and trade-off curve for Kalman and H infinity filter. - Abstract: This paper deals with delay compensation of vanadium Self Powered Neutron Detectors (SPNDs) using Linear Matrix Inequality (LMI) based H-infinity filtering method and compares the results with Kalman filtering method. The entire study is established upon the framework of neutron flux estimation in large core Pressurized Heavy Water Reactor (PHWR) in which delayed SPNDs such as vanadium SPNDs are used as in-core flux monitoring detectors. The use of vanadium SPNDs are limited to 3-D flux mapping despite of providing better Signal to Noise Ratio as compared to other prompt SPNDs, due to their small prompt component in the signal. The use of an appropriate delay compensation technique has been always considered to be an effective strategy to build a prompt and accurate estimate of the neutron flux. We also indicate the noise-response trade-off curve for both the techniques. Since all the delay compensation algorithms always suffer from noise amplification, we propose an efficient adaptive parameter tuning technique for improving performance of the filtering algorithm against noise in the measurement.

16. Comparison of linear-elastic-plastic, and fully plastic failure models in the assessment of piping integrity

Streit, R.D.

1981-01-01

17. Linear cascade calculations of matrix due to neutron-induced nuclear reactions

Avila, Ricardo E

2000-01-01

A method is developed to calculate the total number of displacements created by energetic particles resulting from neutron-induced nuclear reactions. The method is specifically conceived to calculate the damage in lithium ceramics by the 6L i(n, α)T reaction. The damage created by any particle is related to that caused by atoms from the matrix recoiling after collision with the primary particle. An integral equation for that self-damage is solved by interactions, using the magic stopping powers of Ziegler, Biersack and Littmark. A projectile-substrate dependent Kinchin-Pease model is proposed, giving and analytic approximation to the total damage as a function of the initial particle energy (au)

18. Some fundamental definitions of the elastic parameters for homogenous isotropic linear materials in road design and analysis

De Beer, Morris

2008-07-01

Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

19. Linear data mining the Wichita clinical matrix suggests sleep and allostatic load involvement in chronic fatigue syndrome.

Gurbaxani, Brian M; Jones, James F; Goertzel, Benjamin N; Maloney, Elizabeth M

2006-04-01

To provide a mathematical introduction to the Wichita (KS, USA) clinical dataset, which is all of the nongenetic data (no microarray or single nucleotide polymorphism data) from the 2-day clinical evaluation, and show the preliminary findings and limitations, of popular, matrix algebra-based data mining techniques. An initial matrix of 440 variables by 227 human subjects was reduced to 183 variables by 164 subjects. Variables were excluded that strongly correlated with chronic fatigue syndrome (CFS) case classification by design (for example, the multidimensional fatigue inventory [MFI] data), that were otherwise self reporting in nature and also tended to correlate strongly with CFS classification, or were sparse or nonvarying between case and control. Subjects were excluded if they did not clearly fall into well-defined CFS classifications, had comorbid depression with melancholic features, or other medical or psychiatric exclusions. The popular data mining techniques, principle components analysis (PCA) and linear discriminant analysis (LDA), were used to determine how well the data separated into groups. Two different feature selection methods helped identify the most discriminating parameters. Although purely biological features (variables) were found to separate CFS cases from controls, including many allostatic load and sleep-related variables, most parameters were not statistically significant individually. However, biological correlates of CFS, such as heart rate and heart rate variability, require further investigation. Feature selection of a limited number of variables from the purely biological dataset produced better separation between groups than a PCA of the entire dataset. Feature selection highlighted the importance of many of the allostatic load variables studied in more detail by Maloney and colleagues in this issue [1] , as well as some sleep-related variables. Nonetheless, matrix linear algebra-based data mining approaches appeared to be of

20. Automatic Offline Formulation of Robust Model Predictive Control Based on Linear Matrix Inequalities Method

Longge Zhang

2013-01-01

Full Text Available Two automatic robust model predictive control strategies are presented for uncertain polytopic linear plants with input and output constraints. A sequence of nested geometric proportion asymptotically stable ellipsoids and controllers is constructed offline first. Then the feedback controllers are automatically selected with the receding horizon online in the first strategy. Finally, a modified automatic offline robust MPC approach is constructed to improve the closed system's performance. The new proposed strategies not only reduce the conservatism but also decrease the online computation. Numerical examples are given to illustrate their effectiveness.

1. Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity.

Moussaoui, Ahmed; Bouziane, Touria

2016-01-01

The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are: •The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.•The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.•The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).

2. Electron re-scattering from aligned linear molecules using the R-matrix method

Harvey, A G; Tennyson, J

2009-01-01

Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron-molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H 2 and CO 2 . Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H 2 these cross sections show significant angular structure which, particularly for a scattering angle of 90 deg., are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO 2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.

3. Non linear thermal behaviour induced by damage of ceramic matrix composite

El-Yagoubi, J.

2011-10-01

In this work the relationship between the evolution of damage and the loss of thermal properties of Ceramic Matrix Composites is investigated by a multi-scale approach. Research are conducted both experimentally and theoretically. The implemented approach is to consider two significant scales (micro and meso) where different damage mechanisms are operating and then assess the effect on the effective thermal properties by homogenization techniques. Particular attention has been given to the development of a thorough experimental work combining various characterization tools (mechanical, thermal and microstructural). At the two aforementioned scales, an experimental setup was designed to perform thermal measurements on CMC under tensile test. Thermal diffusivity of mini-composites is estimated using Lock-in thermography. Also, transverse diffusivity mapping as well as global in-plane diffusivity of woven CMC are determined by suitable rear face flash methods. The evolution of damage is then derived from acoustic emission activity along with postmortem microstructural observations. Experimental results are systematically compared to simulations. At microscale, a micromechanical-based model is used to simulate the loss of thermal conductivity of a mini-composite under tensile test. At mesoscale, a multi-scale Finite Element Model is proposed to compute the effect of damage on thermal properties of woven CMC. (author) [fr

4. Linear reversible second-order cellular automata and their first-order matrix equivalents

Macfarlane, A. J.

2004-11-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, &{\\in}Z_2;) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first &2^M; times, M =0, 1, 2,\\ldots.

5. Q-Matrix Optimization Based on the Linear Logistic Test Model.

Ma, Lin; Green, Kelly E

This study explored optimization of item-attribute matrices with the linear logistic test model (Fischer, 1973), with optimal models explaining more variance in item difficulty due to identified item attributes. Data were 8th-grade mathematics test item responses of two TIMSS 2007 booklets. The study investigated three categories of attributes (content, cognitive process, and comprehensive cognitive process) at two grain levels (larger, smaller) and also compared results with random attribute matrices. The proposed attributes accounted for most of the variance in item difficulty for two assessment booklets (81% and 65%). The variance explained by the content attributes was very small (13% to 31%), less than variance explained by the comprehensive cognitive process attributes which explained much more variance than the content and cognitive process attributes. The variances explained by the grain level were similar to each other. However, the attributes did not predict the item difficulties of two assessment booklets equally.

6. Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

Majumdar, S.; Kwasny, R.

1985-01-01

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

7. An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models.

Riviere, Marie-Karelle; Ueckert, Sebastian; Mentré, France

2016-10-01

Non-linear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. In recent years, estimation algorithms for NLMEMs have transitioned from linearization toward more exact higher-order methods. Optimal design, on the other hand, has mainly relied on first-order (FO) linearization to calculate the FIM. Although efficient in general, FO cannot be applied to complex non-linear models and with difficulty in studies with discrete data. We propose an approach to evaluate the expected FIM in NLMEMs for both discrete and continuous outcomes. We used Markov Chain Monte Carlo (MCMC) to integrate the derivatives of the log-likelihood over the random effects, and Monte Carlo to evaluate its expectation w.r.t. the observations. Our method was implemented in R using Stan, which efficiently draws MCMC samples and calculates partial derivatives of the log-likelihood. Evaluated on several examples, our approach showed good performance with relative standard errors (RSEs) close to those obtained by simulations. We studied the influence of the number of MC and MCMC samples and computed the uncertainty of the FIM evaluation. We also compared our approach to Adaptive Gaussian Quadrature, Laplace approximation, and FO. Our method is available in R-package MIXFIM and can be used to evaluate the FIM, its determinant with confidence intervals (CIs), and RSEs with CIs. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

8. Linear and nonlinear intraband optical properties of ZnO quantum dots embedded in SiO2 matrix

Deepti Maikhuri

2012-03-01

Full Text Available In this work we investigate some optical properties of semiconductor ZnO spherical quantum dot embedded in an amorphous SiO2 dielectric matrix. Using the framework of effective mass approximation, we have studied intraband S-P, and P-D transitions in a singly charged spherical ZnO quantum dot. The optical properties are investigated in terms of the linear and nonlinear photoabsorption coefficient, the change in refractive index, and the third order nonlinear susceptibility and oscillator strengths. Using the parabolic confinement potential of electron in the dot these parameters are studied with the variation of the dot size, and the energy and intensity of incident radiation. The photoionization cross sections are also obtained for the different dot radii from the initial ground state of the dot. It is found that dot size, confinement potential, and incident radiation intensity affects intraband optical properties of the dot significantly.

9. Two-step algorithm of generalized PAPA method applied to linear programming solution of dynamic matrix control

Shimizu, Yoshiaki

1991-01-01

In recent complicated nuclear systems, there are increasing demands for developing highly advanced procedures for various problems-solvings. Among them keen interests have been paid on man-machine communications to improve both safety and economy factors. Many optimization methods have been good enough to elaborate on these points. In this preliminary note, we will concern with application of linear programming (LP) for this purpose. First we will present a new superior version of the generalized PAPA method (GEPAPA) to solve LP problems. We will then examine its effectiveness when applied to derive dynamic matrix control (DMC) as the LP solution. The approach is to aim at the above goal through a quality control of process that will appear in the system. (author)

10. Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

11. Structure of 14C via elastic and inelastic neutron scattering from 13C: Measurement, R-matrix analysis, and shell model calculations

Resler, D.A.

1987-03-01

The specific purpose of this work is to provide a better understanding of the 14 C level structure; the general purpose is to provide the details for using shell model calculations in R-matrix analyses. Using the TOF facilities of the Ohio University Accelerator Laboratory, the elastic and first 3 inelastic differential scattering cross sections for 13 C + n were measured at 69 energies for 4.5 ≤ E/sub n/ ≤ 11 MeV. A multiple scattering code was developed which provided a simulation of the experimental scattering process allowing accurate corrections to the small inelastic data. The integrated 13 C(n,α) 10 Be cross section is estimated. The sequential 2n-decay of 14 C states populated by 13 C + n was observed. A shell model code was developed. Normal and nonnormal parity calculations were made for the lithium isotopes using a new two-body interaction. The results for 5 Li predict the 2s/sub 1/2/ and 1d/sub 5/2/ single-particle states to be located below the 3/2 + state. Similar calculations were made for 13 C, 13 N, and 14 C. Results for 13 C and 13 N show for E/sub x/ 7 Li and 14 C, 2 h-barω calculations were done. Shell model calculations generated the R-matrix parameters for the elastic and first 3 inelastic channels of 13 C + n. After adjusting some energies, the predicted structure generally agrees with experiment for E/sub n/ 13 C + n data were refit to replace R 0 background terms by more realistic broad states and to get better agreement with model calculations. R-matrix fitting of the full data set produced new 14 C level information. For E/sub n/ > 4 MeV (E/sub x/ > 12 MeV), 5 states are given definite J/sup π/ assignments; 3, tentative assignments. 122 refs., 91 figs., 30 tabs

12. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

Angela Mihai, L.

2013-03-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

13. Efficient multiple-trait association and estimation of genetic correlation using the matrix-variate linear mixed model.

Furlotte, Nicholas A; Eskin, Eleazar

2015-05-01

Multiple-trait association mapping, in which multiple traits are used simultaneously in the identification of genetic variants affecting those traits, has recently attracted interest. One class of approaches for this problem builds on classical variance component methodology, utilizing a multitrait version of a linear mixed model. These approaches both increase power and provide insights into the genetic architecture of multiple traits. In particular, it is possible to estimate the genetic correlation, which is a measure of the portion of the total correlation between traits that is due to additive genetic effects. Unfortunately, the practical utility of these methods is limited since they are computationally intractable for large sample sizes. In this article, we introduce a reformulation of the multiple-trait association mapping approach by defining the matrix-variate linear mixed model. Our approach reduces the computational time necessary to perform maximum-likelihood inference in a multiple-trait model by utilizing a data transformation. By utilizing a well-studied human cohort, we show that our approach provides more than a 10-fold speedup, making multiple-trait association feasible in a large population cohort on the genome-wide scale. We take advantage of the efficiency of our approach to analyze gene expression data. By decomposing gene coexpression into a genetic and environmental component, we show that our method provides fundamental insights into the nature of coexpressed genes. An implementation of this method is available at http://genetics.cs.ucla.edu/mvLMM. Copyright © 2015 by the Genetics Society of America.

14. The second-order S-matrix element for the elastic scattering of photons by K-shell bound electrons: the nonrelativistic limit

Costescu, A [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Spanulescu, S [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Stoica, C [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania)

2007-08-14

The right expressions of the nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green's function method. Our analytical result does not have the spurious poles that occur in the old nonrelativistic result with retardation (Gavrila and Costescu 1970 Phys. Rev. A 2 1752). Starting from the expression of the second-order S-matrix element for the case of the elastic scattering of photons by K-shell bound electrons, we obtain the correct nonrelativistic Rayleigh angular distribution (valid for photon energies {omega} up to {alpha}Zm) by removing the relativistic higher order terms in {alpha}Z and {omega}/m. The imaginary part of the Rayleigh amplitudes is obtained for any scattering angles in a closed form in terms of elementary functions. Thereby a simple formula for the exact nonrelativistic photoeffect total cross-section is obtained via the optical theorem, giving significantly better predictions than Fischer's nonrelativistic photoeffect formula. Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel et al (Phys. Rev. 1980 A 22 1970), and with experimental results, a fairly good agreement within 10% is found for the angular distribution of Rayleigh scattering for photon energies up to 200 keV and both below and above the first resonance.

15. Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

16. Factorizable S-matrix for SO(D)/SO(2) circle times SO(D - 2) non-linear σ models with fermions

Abdalla, E.; Lima-Santos, A.

1988-01-01

The authors compute the exact S matrix for the non-linear sigma model with symmetry SO(D)/SO(2) circle times SO(D-2) coupled to fermions in a minimal or supersymmetric way. The model has some relevance in string theory with non-zero external curvature

17. Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Shahriar Dastjerdi

2016-06-01

Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.

18. MRI-based, wireless determination of the transfer function of a linear implant: Introduction of the transfer matrix.

Tokaya, Janot P; Raaijmakers, Alexander J E; Luijten, Peter R; van den Berg, Cornelis A T

2018-04-24

We introduce the transfer matrix (TM) that makes MR-based wireless determination of transfer functions (TFs) possible. TFs are implant specific measures for RF-safety assessment of linear implants. The TF relates an incident tangential electric field on an implant to a scattered electric field at its tip that generally governs local heating. The TM extends this concept and relates an incident tangential electric field to a current distribution in the implant therewith characterizing the RF response along the entire implant. The TM is exploited to measure TFs with MRI without hardware alterations. A model of rightward and leftward propagating attenuated waves undergoing multiple reflections is used to derive an analytical expression for the TM. This allows parameterization of the TM of generic implants, e.g., (partially) insulated single wires, in a homogeneous medium in a few unknowns that simultaneously describe the TF. These unknowns can be determined with MRI making it possible to measure the TM and, therefore, also the TF. The TM is able to predict an induced current due to an incident electric field and can be accurately parameterized with a limited number of unknowns. Using this description the TF is determined accurately (with a Pearson correlation coefficient R ≥ 0.9 between measurements and simulations) from MRI acquisitions. The TM enables measuring of TFs with MRI of the tested generic implant models. The MR-based method does not need hardware alterations and is wireless hence making TF determination in more realistic scenarios conceivable. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

19. Evaluation of Interlaminar Stresses in Composite Laminates with a Bolt-Filled Hole Using a Linear Elastic Traction-Separation Description

Yong Cao

2017-01-01

20. Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

V. Y. Zaitsev

2017-09-01

Full Text Available Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 % of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks. Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 % portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.

1. Linear algebra

Shilov, Georgi E

1977-01-01

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

2. Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems.

Langenbucher, Frieder

2005-01-01

A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

3. COVAR: Computer Program for Multifactor Relative Risks and Tests of Hypotheses Using a Variance-Covariance Matrix from Linear and Log-Linear Regression

Leif E. Peterson

1997-11-01

Full Text Available A computer program for multifactor relative risks, confidence limits, and tests of hypotheses using regression coefficients and a variance-covariance matrix obtained from a previous additive or multiplicative regression analysis is described in detail. Data used by the program can be stored and input from an external disk-file or entered via the keyboard. The output contains a list of the input data, point estimates of single or joint effects, confidence intervals and tests of hypotheses based on a minimum modified chi-square statistic. Availability of the program is also discussed.

4. Fracture toughness in metal matrix composites

Perez Ipiña J.E.

2000-01-01

Full Text Available Evaluations of the fracture toughness in metal matrix composites (Duralcan reinforced with 15% of Al(20(3 and SiC are presented in this work. The application of Elastic Plastic Fracture Mechanics is discussed and the obtained values are compared with the ones obtained by means of Linear Elastic Fracture Mechanics. Results show that J IC derived K JC values are higher than the corresponding values obtained by direct application of the linear elastic methodology. The effect of a heat treatment on the material fracture toughness was also evaluated in which the analyzed approaches showed, not only different toughness values, but also opposite tendencies. A second comparison of the J IC and K JC values obtained in this work with toughness values reported in the literature is presented and discussed.

5. Linearized inversion of two components seismic data; Inversion linearisee de donnees sismiques a deux composantes

Lebrun, D.

1997-05-22

The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.

6. Continuum mechanics elasticity, plasticity, viscoelasticity

Dill, Ellis H

2006-01-01

FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...

7. Elastic properties of Cs2HgBr4 and Cs2CdBr4 crystals

Kityk, A.V.; Zadorozhna, A.V.; Shchur, Y.I.; Martynyuk-Lototska, Y.I.; Burak, Y.; Vlokh, O.G.

1998-01-01

Using ultrasonic velocity measurements, all components of the elastic constant matrix C ij , elastic compliances matrix S ij , and linear compressibility constants matrix K ij of orthorhombic Cs 2 HgBr 4 and Cs 2 CdBr 4 crystals have been determined over a wide temperature range, including the region of the phase transition from the normal to the incommensurate phase. Results obtained are considered within the framework of the phenomenological theory. Preliminary analysis of the acoustical properties at room temperature clearly indicates that both crystals are relatively important materials for acousto-optical applications. Copyright (1998) CSIRO Australia

8. Measurement of angular scattering function and degree of linear polarization of bentonite clay particles embedded in cylindrical epoxy matrix

A. Gogoi

2011-09-01

Full Text Available Scattering properties of bentonite clay particles were investigated at 543.5 nm incident laser wavelength by using a designed and fabricated light scattering setup. The scattering samples were held in front of a laser beam by using a transparent cylindrical thermosetting epoxy matrix.

9. Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

10. Determination of Spearman Correlation Coefficient (r to Evaluate the Linear Association of Dermal Collagen and Elastic Fibers in the Perspectives of Skin Injury

Naveen Kumar

2018-01-01

Full Text Available Background. Difference in scar formation at different sites, in different directions at the same site, but with changes in the elasticity of skin with age, sex, and race or in some pathological conditions, is well known to clinicians. The inappropriate collagen syntheses and delayed or lack of epithelialization are known to induce scar formation with negligible elasticity at the site of damage. Changes in the elasticity of scars may be due to an unequal distribution of dermal collagen (C and elastic (E fibers. Materials and Methods. Spearman correlation coefficients (r of collagen and elastic fibers in horizontal (H and in vertical (V directions (variables CV, CH, EV, and EH were measured from the respective quantitative fraction data in 320 skin samples from 32 human cadavers collected at five selected sites over extremities. Results. Spearman’s correlation analysis revealed the statistically significant (p<0.01 strong positive correlation between CH and CV in all the areas, that is, shoulder joint area (r=0.66, wrist (r=0.75, forearm (r=0.75, and thigh (r=0.80, except at the ankle (r=0.26, p=0.14 region. Similarly, positive correlation between EH and EV has been observed at the forearm (r=0.65, moderate and thigh (r=0.42, low regions. However, a significant moderate negative correlation was observed between CV and EV at the forearm (r=-0.51 and between CH and EH at the thigh region (r=-0.65. Conclusion. Significant differences of correlations of collagen and elastic fibers in different directions from different areas of extremities were noted. This may be one of the possible anatomical reasons of scar behavior in different areas and different directions of the same area.

11. Determination of Spearman Correlation Coefficient (r) to Evaluate the Linear Association of Dermal Collagen and Elastic Fibers in the Perspectives of Skin Injury.

2018-01-01

Difference in scar formation at different sites, in different directions at the same site, but with changes in the elasticity of skin with age, sex, and race or in some pathological conditions, is well known to clinicians. The inappropriate collagen syntheses and delayed or lack of epithelialization are known to induce scar formation with negligible elasticity at the site of damage. Changes in the elasticity of scars may be due to an unequal distribution of dermal collagen (C) and elastic (E) fibers. Spearman correlation coefficients ( r ) of collagen and elastic fibers in horizontal (H) and in vertical (V) directions (variables CV, CH, EV, and EH) were measured from the respective quantitative fraction data in 320 skin samples from 32 human cadavers collected at five selected sites over extremities. Spearman's correlation analysis revealed the statistically significant ( p < 0.01) strong positive correlation between C H and C V in all the areas, that is, shoulder joint area ( r = 0.66), wrist ( r = 0.75), forearm ( r = 0.75), and thigh ( r = 0.80), except at the ankle ( r = 0.26, p = 0.14) region. Similarly, positive correlation between E H and E V has been observed at the forearm ( r = 0.65, moderate) and thigh ( r = 0.42, low) regions. However, a significant moderate negative correlation was observed between C V and E V at the forearm ( r = -0.51) and between C H and E H at the thigh region ( r = -0.65). Significant differences of correlations of collagen and elastic fibers in different directions from different areas of extremities were noted. This may be one of the possible anatomical reasons of scar behavior in different areas and different directions of the same area.

12. Elasticity problems in domains with nonsmooth boundaries

Esparza, David

2001-01-01

In the present work we study the behaviour of elastic stress fields in domains with non-regular boundaries. We consider three-dimensional problems in elastic media with thin conical defects (inclusions or cavities) and analyse the stress singularity at their vertices. To construct asymptotic expansions for the stress and displacement fields in terms of a small parameter ε related to the 'thickness' of the defect, we employ a technique based on the work by Kondrat'ev, Maz'ya, Nazarov and Plamenevskii. We first study the stress distribution in an elastic body with a thin conical notch. We derive an asymptotic representation for the stress singularity exponent by reducing the original problem to a spectral problem for a 9x9 matrix. The elements of this matrix are found to depend upon the geometry of the cross-section of the notch and the elastic properties of the medium. We specify the sets of eigenvalues and the corresponding eigenvectors for a circular, elliptical, 'triangular' and 'square' cross-section, and show that the strongest singularity is associated with the 'triangular' cross-section, and is generated by a non-axisymmetric load. We then analyse the stress distribution near a thin conical inclusion which is allowed to slide freely along its axis. We derive the representation for the stress singularity exponent for the case of a circular conical inclusion whose elastic properties differ from those of the medium. In the last chapter we study the stress distribution in the vicinity of a thin 'coated' conical inclusion. We show that a soft thin coating (perfectly bonded to the inclusion and the surrounding material) can be replaced by a so-called linear interface at which the normal displacement is discontinuous, and the stresses are proportional to the 'jump' in the normal displacement across the coating. We analyse the effect of the properties of the coating on the stress singularity exponent and compare the results with those for a perfectly bonded

13. Influence of food matrix on absorption of flavour compounds by linear low-density polyethylene: proteins and carbohydrates

Willige, van R.W.G.; Linssen, J.P.H.; Voragen, A.G.J.

2000-01-01

The influence of oil and food components in real food products on the absorption of four flavour compounds (limonene, decanal, linalool and ethyl 2-methyl butyrate) into linear low-density polyethylene (LLDPE) was studied using a large volume injection GC in vial extraction method. Model food

14. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

1987-01-01

The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

15. Collusion and the elasticity of demand

David Collie

2004-01-01

The analysis of collusion in infinitely repeated Cournot oligopoly games has generally assumed that demand is linear, but this note uses constant-elasticity demand functions to investigate how the elasticity of demand affects the sustainability of collusion.

16. Linear algebra

Liesen, Jörg

2015-01-01

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

17. Linear Models

Searle, Shayle R

2012-01-01

This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

18. Linear and Nonlinear Finite Elements.

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

19. Elastic properties

Ledbetter, H.M.

1983-01-01

This chapter investigates the following five aspects of engineering-material solid-state elastic constants: general properties, interrelationships, relationships to other physical properties, changes during cooling from ambient to near-zero temperature, and near-zero-temperature behavior. Topics considered include compressibility, bulk modulus, Young's modulus, shear modulus, Poisson's ratio, Hooke's law, elastic-constant measuring methods, thermodynamic potentials, higher-order energy terms, specific heat, thermal expansivity, magnetic materials, structural phase transitions, polymers, composites, textured aggregates, and other-phenomena correlations. Some of the conclusions concerning polycrystalline elastic properties and their temperature dependence are: elastic constants are physical, not mechanical, properties which relate thermodynamically to other physical properties such as specific heat and thermal expansivity; elastic constants at low temperatures are nearly temperature independent, as required by the third law of thermodynamics; and elastic constants can be used to study directional properties of materials, such as textured aggregates and composites

20. Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P

2007-01-01

In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures

1. Some Differential Geometric Relations in the Elastic Shell

Xiaoqin Shen

2016-01-01

Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.

2. A virtual surgical training system that simulates cutting of soft tissue using a modified pre-computed elastic model.

Toe, Kyaw Kyar; Huang, Weimin; Yang, Tao; Duan, Yuping; Zhou, Jiayin; Su, Yi; Teo, Soo-Kng; Kumar, Selvaraj Senthil; Lim, Calvin Chi-Wan; Chui, Chee Kong; Chang, Stephen

2015-08-01

This work presents a surgical training system that incorporates cutting operation of soft tissue simulated based on a modified pre-computed linear elastic model in the Simulation Open Framework Architecture (SOFA) environment. A precomputed linear elastic model used for the simulation of soft tissue deformation involves computing the compliance matrix a priori based on the topological information of the mesh. While this process may require a few minutes to several hours, based on the number of vertices in the mesh, it needs only to be computed once and allows real-time computation of the subsequent soft tissue deformation. However, as the compliance matrix is based on the initial topology of the mesh, it does not allow any topological changes during simulation, such as cutting or tearing of the mesh. This work proposes a way to modify the pre-computed data by correcting the topological connectivity in the compliance matrix, without re-computing the compliance matrix which is computationally expensive.

3. A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

4. Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

5. Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

Kozlowski, K.K.

2010-12-15

Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)

6. Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

Meer, R. van; Gritsenko, O. V.; Baerends, E. J.

2014-01-01

Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω α and oscillator strengths f α for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω α (R) curves along the bond dissociation coordinate R for the molecules LiH, Li 2 , and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate

7. Elastic plastic fracture mechanics

Simpson, L.A.

1978-07-01

The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)

8. Introduction of non-linear elasticity models for characterization of shape and deformation statistics: application to contractility assessment of isolated adult cardiocytes.

Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul

2011-08-22

We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.

9. Introduction of a priori information in the elastic linearized inversion of seismic data before stacking; Introduction d'informations a priori dans l'inversion linearisee elastique de donnees sismiques de surface avant sommation

Tonellot, Th.L.

2000-03-24

In this thesis, we propose a method which takes into account a priori information (geological, diagraphic and stratigraphic knowledge) in linearized pre-stack seismic data inversion. The approach is based on a formalism in which the a priori information is incorporated in an a priori model of elastic parameters - density, P and S impedances - and a model covariance operator which describes the uncertainties in the model. The first part of the thesis is dedicated to the study of this covariance operator and to the norm associated to its inverse. We have generalized the exponential covariance operator in order to describe the uncertainties in the a priori model elastic parameters and their correlations at each location. We give the analytical expression of the covariance operator inverse in 1-D, 2-D, and 3-D, and we discretized the associated norm with a finite element method. The second part is dedicated to synthetic and real examples. In a preliminary step, we have developed a pre-stack data well calibration method which allows the estimation of the source signal. The impact of different a priori information is then demonstrated on synthetic and real data. (author)

10. Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening

Roche, R.

1983-12-01

A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr

11. Quasi-stationary states of an electron with linearly dependent effective mass in an open nanostructure within transmission coefficient and S-matrix methods

Seti, Julia; Tkach, Mykola; Voitsekhivska, Oxana

2018-03-01

The exact solutions of the Schrödinger equation for a double-barrier open semiconductor plane nanostructure are obtained by using two different approaches, within the model of the rectangular potential profile and the continuous position-dependent effective mass of the electron. The transmission coefficient and scattering matrix are calculated for the double-barrier nanostructure. The resonance energies and resonance widths of the electron quasi-stationary states are analyzed as a function of the size of the near-interface region between wells and barriers, where the effective mass linearly depends on the coordinate. It is established that, in both methods, the increasing size affects in a qualitatively similar way the spectral characteristics of the states, shifting the resonance energies into the low- or high-energy region and increasing the resonance widths. It is shown that the relative difference of resonance energies and widths of a certain state, obtained in the model of position-dependent effective mass and in the widespread abrupt model in physically correct range of near-interface sizes, does not exceed 0.5% and 5%, respectively, independently of the other geometrical characteristics of the structure.

12. Computing Low-Rank Approximation of a Dense Matrix on Multicore CPUs with a GPU and Its Application to Solving a Hierarchically Semiseparable Linear System of Equations

Ichitaro Yamazaki

2015-01-01

of their low-rank properties. To compute a low-rank approximation of a dense matrix, in this paper, we study the performance of QR factorization with column pivoting or with restricted pivoting on multicore CPUs with a GPU. We first propose several techniques to reduce the postprocessing time, which is required for restricted pivoting, on a modern CPU. We then examine the potential of using a GPU to accelerate the factorization process with both column and restricted pivoting. Our performance results on two eight-core Intel Sandy Bridge CPUs with one NVIDIA Kepler GPU demonstrate that using the GPU, the factorization time can be reduced by a factor of more than two. In addition, to study the performance of our implementations in practice, we integrate them into a recently developed software StruMF which algebraically exploits such low-rank structures for solving a general sparse linear system of equations. Our performance results for solving Poisson's equations demonstrate that the proposed techniques can significantly reduce the preconditioner construction time of StruMF on the CPUs, and the construction time can be further reduced by 10%–50% using the GPU.

13. Zirconium elasticity modules

Vavra, G.

1978-01-01

Considered are the limit and the intermediate values of the Young modulus E, modulus of shear G and of linear modulus of compression K obtainable at various temperatures (4.2 to 1133 K) for single crystals of α-zirconium. Determined and presented are the corrected isotropic elasticity characteristics of E, G, K over the above range of temperatures of textured and non-textured α-Zr

14. Elastic Beanstalk

Vliet, Jurg; Wel, Steven; Dowd, Dara

2011-01-01

While it's always been possible to run Java applications on Amazon EC2, Amazon's Elastic Beanstalk makes the process easier-especially if you understand how it works beneath the surface. This concise, hands-on book not only walks you through Beanstalk for deploying and managing web applications in the cloud, you'll also learn how to use this AWS tool in other phases of development. Ideal if you're a developer familiar with Java applications or AWS, Elastic Beanstalk provides step-by-step instructions and numerous code samples for building cloud applications on Beanstalk that can handle lots

15. Blocky inversion of multichannel elastic impedance for elastic parameters

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

16. Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading

Stepanova, Larisa; Bronnikov, Sergej

2018-03-01

17. Features of the non-collinear one-phonon anomalous light scattering controlled by elastic waves with elevated linear losses: potentials for multi-frequency parallel spectrum analysis of radio-wave signals.

Shcherbakov, Alexandre S; Arellanes, Adan Omar

2017-12-01

During subsequent development of the recently proposed multi-frequency parallel spectrometer for precise spectrum analysis of wideband radio-wave signals, we study potentials of new acousto-optical cells exploiting selected crystalline materials at the limits of their capabilities. Characterizing these wide-aperture cells is non-trivial due to new features inherent in the chosen regime of an advanced non-collinear one-phonon anomalous light scattering by elastic waves with significantly elevated acoustic losses. These features can be observed simpler in uniaxial, tetragonal, and trigonal crystals possessing linear acoustic attenuation. We demonstrate that formerly studied additional degree of freedom, revealed initially for multi-phonon regimes of acousto-optical interaction, can be identified within the one-phonon geometry as well and exploited for designing new cells. We clarify the role of varying the central acoustic frequency and acoustic attenuation using the identified degree of freedom. Therewith, we are strongly restricted by a linear regime of acousto-optical interaction to avoid the origin of multi-phonon processes within carrying out a multi-frequency parallel spectrum analysis of radio-wave signals. Proof-of-principle experiments confirm the developed approaches and illustrate their applicability to innovative technique for an advanced spectrum analysis of wideband radio-wave signals with the improved resolution in an extended frequency range.

18. Wave chaos in acoustics and elasticity

Tanner, Gregor; Soendergaard, Niels

2007-01-01

Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics-both experimentally and from a theoretical/numerical point of view. (topical review)

19. Two-Sided Estimates of Thermo-elastic Characteristics of Dispersed Inclusion Composites

V. S. Zarubin

2015-01-01

Full Text Available The composites, dispersion-reinforced with inclusions from high-strength and high-modulus materials are widely used in technology. Nanostructure elements can perform the role of such inclusions as well. Possible applications of such composites in heat-stressed structures under heavy mechanical and thermal influences significantly depend on a complex of thermo-mechanical characteristics including the values of the moduli of elasticity and coefficient of linear thermal expansion. There are different approaches to construction of mathematical models that allow calculating dependences to estimate elastic characteristics of composites. Relation between thermoelastic properties of matrix and inclusions of the composite with its temperature coefficient of linear expansion is studied in less detail. Thus, attention has been insufficient in estimating a degree of reliability and a possible error of derived dependencies.A dual variation formulation of the problem of thermo-elasticity in a non-uniform solids simulating the properties and structure of the composite with dispersed inclusions, makes it possible to define two-sided limits of possible values of the volume elasticity modulus, shear modulus, and coefficient of linear thermal expansion of such composite. These limits allow us to estimate the maximum possible error, if to take a half-sum of the limit values of these parameters as the thermoelastic characteristics of the composite. Implementing this approach to find possible errors, arising when using one or another calculating dependency, improves reliability of predicted thermo-elastic characteristics as applied to existing and promising composites.

20. An analysis of hypercritical states in elastic and inelastic systems

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

1. Phase properties of elastic waves in systems constituted of adsorbed diatomic molecules on the (001) surface of a simple cubic crystal

Deymier, P. A.; Runge, K.

2018-03-01

A Green's function-based numerical method is developed to calculate the phase of scattered elastic waves in a harmonic model of diatomic molecules adsorbed on the (001) surface of a simple cubic crystal. The phase properties of scattered waves depend on the configuration of the molecules. The configurations of adsorbed molecules on the crystal surface such as parallel chain-like arrays coupled via kinks are used to demonstrate not only linear but also non-linear dependency of the phase on the number of kinks along the chains. Non-linear behavior arises for scattered waves with frequencies in the vicinity of a diatomic molecule resonance. In the non-linear regime, the variation in phase with the number of kinks is formulated mathematically as unitary matrix operations leading to an analogy between phase-based elastic unitary operations and quantum gates. The advantage of elastic based unitary operations is that they are easily realizable physically and measurable.

2. A linear programming manual

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

3. Elastic scattering

1991-01-01

With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees

4. Advanced linear algebra for engineers with Matlab

Dianat, Sohail A

2009-01-01

Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu

5. Elastic and piezoelectric fields around a quantum wire of zincblende heterostructures with interface elasticity effect

Ye, Wei; Liu, Yifei

2018-04-01

This work formulates the solutions to the elastic and piezoelectric fields around a quantum wire (QWR) with interface elasticity effect. Closed-form solutions to the piezoelectric potential field of zincblende QWR/matrix heterostructures grown along [111] crystallographic orientation are found and numerical results of InAs/InP heterostructures are provided as an example. The piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the QWR. Our results indicate that interface elasticity can significantly alter the elastic and piezoelectric fields near the interface. Additionally, when the elastic property of the QWR is considered to be anisotropic in contrary to the common isotropic assumption, piezoelectric potentials are found to be distinct near the interface, but the deviations are negligible at positions far away from the interface.

6. Matrix with Prescribed Eigenvectors

2011-01-01

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

7. Triangularization of a Matrix

Much of linear algebra is devoted to reducing a matrix (via similarity or unitary similarity) to another that has lots of zeros. The simplest such theorem is the Schur triangularization theorem. This says that every matrix is unitarily similar to an upper triangular matrix. Our aim here is to show that though it is very easy to prove it ...

8. Parallelism in matrix computations

Gallopoulos, Efstratios; Sameh, Ahmed H

2016-01-01

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

9. Positron interactions with water–total elastic, total inelastic, and elastic differential cross section measurements

Tattersall, Wade; Chiari, Luca; Machacek, J. R.; Anderson, Emma; Sullivan, James P.; White, Ron D.; Brunger, M. J.; Buckman, Stephen J.; Garcia, Gustavo; Blanco, Francisco

2014-01-01

Utilising a high-resolution, trap-based positron beam, we have measured both elastic and inelastic scattering of positrons from water vapour. The measurements comprise differential elastic, total elastic, and total inelastic (not including positronium formation) absolute cross sections. The energy range investigated is from 1 eV to 60 eV. Comparison with theory is made with both R-Matrix and distorted wave calculations, and with our own application of the Independent Atom Model for positron interactions

10. CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

11. Phason elasticity and surface roughening

Tang Leihan; Jaric, M.V.

1990-01-01

The phason elasticity of two-dimensional (2D) equilibrium quasicrystals is discussed in analogy with surface roughening phenomena. Taking a Penrose tiling model as an example, we show that the phason elastic energy is linear in the phason strain at zero temperature (T = 0), but becomes quadratic at any T > 0 and sufficiently small strain. Heuristic and real-space renormalization group arguments are given for the thermal roughening of the hyper-surface which represents quasicrystal tiling. Monte Carlo method is applied to illustrate the logarithmically diverging phason fluctuations and power-law diffraction intensities at T > 0. For three-dimensional systems, we present arguments which suggest a finite temperature transition between two quasicrystal phases, characterized by linear and quadratic phason elastic energy, respectively. (author). 17 refs, 12 figs

12. Elastic properties of spherically anisotropic piezoelectric composites

En-Bo, Wei; Guo-Qing, Gu; Ying-Ming, Poon

2010-01-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed. (condensed matter: structure, thermal and mechanical properties)

13. Rapid and sensitive determination of major polyphenolic components in Euphoria longana Lam. seeds using matrix solid-phase dispersion extraction and UHPLC with hybrid linear ion trap triple quadrupole mass spectrometry.

Rathore, Atul S; Sathiyanarayanan, L; Deshpande, Shreekant; Mahadik, Kakasaheb R

2016-11-01

A rapid and sensitive method for the extraction and determination of four major polyphenolic components in Euphoria longana Lam. seeds is presented for the first time based on matrix solid-phase dispersion extraction followed by ultra high performance liquid chromatography with hybrid triple quadrupole linear ion trap mass spectrometry. Matrix solid-phase dispersion method was designed for the extraction of Euphoria longana seed constituents and compared with microwave-assisted extraction and ultrasonic-assisted extraction methods. An Ultra high performance liquid chromatography with hybrid triple quadrupole linear ion-trap mass spectrometry method was developed for quantitative analysis in multiple-reaction monitoring mode in negative electrospray ionization. The chromatographic separation was accomplished using an ACQUITY UPLC BEH C 18 (2.1 mm × 50 mm, 1.7 μm) column with gradient elution of 0.1% aqueous formic acid and 0.1% formic acid in acetonitrile. The developed method was validated with acceptable linearity (r 2 > 0.999), precision (RSD ≤ 2.22%) and recovery (RSD ≤ 2.35%). The results indicated that matrix solid-phase dispersion produced comparable extraction efficiency compared with other methods nevertheless was more convenient and time-saving with reduced requirements on sample and solvent volumes. The proposed method is rapid and sensitive in providing a promising alternative for extraction and comprehensive determination of active components for quality control of Euphoria longana products. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

14. Non-linear dynamic response of reactor containment

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

15. The visco-elastic multilayer program VEROAD

Hopman, P.C.

1996-01-01

The mathematical principles and derivation of a linear visco-elastic multilayer computer program are described. The mathematical derivation is based on Fourier Transformation. The program is called VEROAD, which is an acronym for Visco-Elastic ROad Analysis Delft. The program allows calculation of

16. A Formalism for the Consistent Description of Non-Linear Elasticity of Anisotropic Media Formalisme pour une description cohérente de l'élasticité non linéaire des milieux anisotropes

Helbig K.

2006-12-01

Full Text Available The propagation of elastic waves is generally treated under four assumptions: - that the medium is isotropic,- that the medium is homogeneous, - that there is a one-to-one relationship between stress and strain, - that stresses are linearly related to strains (equivalently, that strains are linearly related to stresses. Real media generally violate at least some-and often all-of these assumptions. A valid theoretical description of wave propagation in real media thus depends on the qualitative and quantitative description of the relevant inhomogeneity, anisotropy, and non-linearity: one either has to assume (or show that the deviation from the assumption can - for the problem at hand - be neglected, or develop a theoretical description that is valid even under the deviation. While the effect of a single deviation from the ideal state is rather well understood, difficulties arise in the combination of several such deviations. Non-linear elasticity of anisotropic (triclinic rock samples has been reported, e. g. by P. Rasolofosaon and H. Yin at the 6th IWSA in Trondheim (Rasolofosaon and Yin, 1996. Non-linear anisotropic elasticity matters only for non-infinitesimalamplitudes, i. e. , at least in the vicinity of the source. How large this vicinity is depends on the accuracy of observation and interpretation one tries to maintain, on the source intensity, and on the level of non-linearity. This paper is concerned with the last aspect, i. e. , with the meaning of the numbers beyond the fact that they are the results of measurements. As a measure of the non-linearity of the material, one can use the strain level at which the effective stiffness tensor deviates significantly from the zero-strain stiffness tensor. Particularly useful for this evaluation is the eigensystem (six eigenstiffnesses and six eigenstrains of the stiffness tensor : the eigenstrains provide suitable strain typesfor the calculation of the effective stiffness tensor, and the

17. Microstructural evolution in inhomogeneous elastic media

Jou, H.J.; Leo, P.H.; Lowengrub, J.S.

1997-01-01

We simulate the diffusional evolution of microstructures produced by solid state diffusional transformations in elastically stressed binary alloys in two dimensions. The microstructure consists of arbitrarily shaped precipitates embedded coherently in an infinite matrix. The precipitate and matrix are taken to be elastically isotropic, although they may have different elastic constants (elastically inhomogeneous). Both far-field applied strains and mismatch strains between the phases are considered. The diffusion and elastic fields are calculated using the boundary integral method, together with a small scale preconditioner to remove ill-conditioning. The precipitate-matrix interfaces are tracked using a nonstiff time updating method. The numerical method is spectrally accurate and efficient. Simulations of a single precipitate indicate that precipitate shapes depend strongly on the mass flux into the system as well as on the elastic fields. Growing shapes (positive mass flux) are dendritic while equilibrium shapes (zero mass flux) are squarish. Simulations of multiparticle systems show complicated interactions between precipitate morphology and the overall development of microstructure (i.e., precipitate alignment, translation, merging, and coarsening). In both single and multiple particle simulations, the details of the microstructural evolution depend strongly o the elastic inhomogeneity, misfit strain, and applied fields. 57 refs., 24 figs

18. Nonlinear Elasticity

Fu, Y. B.; Ogden, R. W.

2001-05-01

This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

19. Matrices and linear transformations

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

20. Sonoelastography can be used to monitor the restoration of Achilles tendon elasticity after injury.

Gehmert, S; Jung, E M; Kügler, T; Klein, S; Gehmert, S; Zeitler, K; Loibl, M; Prantl, L

2012-12-01

The aim of the current study was to evaluate an ultrasound approach for depicting elastic recovery after stem cell application on injured Achilles tendons. A rabbit Achilles tendon injury model was used and randomized hind limbs received an extracellular matrix either with autologous mesenchymal stem cells (group 2, n = 6) or without (group 3, n = 6). The cells were harvested from the rabbits' nuchal fat body. Untreated Achilles tendons (group 1, n = 6) served as controls. Specimens were harvested after 8 weeks and analyzed longitudinally for elasticity using a high resolution 6-15 MHz matrix linear probe. For each tendon, real-time color-coded sonoelastography sequences were recorded for 20 seconds and 10 color histogram frames were obtained. Defined regions of interest (ROIs) were placed on the injury (n = 3) and on the adjacent uninjured tendon tissue (n = 3). In total, 180 measurements were obtained for semi-quantitative analysis. Repeated measures ANOVA demonstrated a higher elasticity for the stem cell-seeded matrix (group 2) in comparison to the unseeded matrix (group 3) (p tendon tissue treated with stem cell-seeded matrix (group 2) and the uninjured Achilles tendons (group 1) (p > 0.05). Moreover, no differences were found between the measurements at different points in time (p > 0.05). Our results indicate that autologous mesenchymal stem cell application successfully restores the mechanical properties of injured tendon tissue. Furthermore, sonoelastography makes it possible to monitor the elasticity of injured Achilles tendons. © Georg Thieme Verlag KG Stuttgart · New York.

1. CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

2. Computational Elastic Knots

Zhao, Xin

2013-01-01

Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects

3. Prediction of SO{sub 2} pollution incidents near a power station using partially linear models and an historical matrix of predictor-response vectors

Prada-Sanchez, J.M.; Febrero-Bande, M.; Gonzalez-Manteiga, W. [Universidad de Santiago de Compostela, Dept. de Estadistica e Investigacion Operativa, Santiago de Compostela (Spain); Costos-Yanez, T. [Universidad de Vigo, Dept. de Estadistica e Investigacion Operativa, Orense (Spain); Bermudez-Cela, J.L.; Lucas-Dominguez, T. [Laboratorio, Central Termica de As Pontes, La Coruna (Spain)

2000-07-01

Atmospheric SO{sub 2} concentrations at sampling stations near the fossil fuel fired power station at As Pontes (La Coruna, Spain) were predicted using a model for the corresponding time series consisting of a self-explicative term and a linear combination of exogenous variables. In a supplementary simulation study, models of this kind behaved better than the corresponding pure self-explicative or pure linear regression models. (Author)

4. Prediction of SO2 pollution incidents near a power station using partially linear models and an historical matrix of predictor-response vectors

Prada-Sanchez, J.M.; Febrero-Bande, M.; Gonzalez-Manteiga, W.; Costos-Yanez, T.; Bermudez-Cela, J.L.; Lucas-Dominguez, T.

2000-01-01

Atmospheric SO 2 concentrations at sampling stations near the fossil fuel fired power station at As Pontes (La Coruna, Spain) were predicted using a model for the corresponding time series consisting of a self-explicative term and a linear combination of exogenous variables. In a supplementary simulation study, models of this kind behaved better than the corresponding pure self-explicative or pure linear regression models. (Author)

5. Matrix completion by deep matrix factorization.

Fan, Jicong; Cheng, Jieyu

2018-02-01

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

6. Involutional ectropion and entropion: clinicopathologic correlation between horizontal eyelid laxity and eyelid extracellular matrix.

Damasceno, Renato Wendell; Osaki, Midori Hentona; Dantas, Paulo Elias Correa; Belfort, Rubens

2011-01-01

To investigate the clinicopathologic correlation between horizontal eyelid laxity and extracellular matrix components, such as collagen and elastic fibers, in involutional ectropion and entropion. Another goal was to compare the differences between involutional ectropion and entropion in regard to extracellular matrix content using computer-assisted morphometry. This clinicopathologic study included 20 consecutive patients with involutional ectropion (group 1) and 20 consecutive patients with involutional entropion (group 2). The pinch test was performed to measure horizontal eyelid laxity in both groups. Full-thickness eyelid biopsy specimens were examined by light microscopy and computer-assisted morphometry. The Mann-Whitney U test, the Pearson chi-square test, the Pearson correlation coefficient calculation, and a linear regression analysis were performed. All sections of specimens from patients in groups 1 and 2 revealed abnormal collagen and elastic fibers. The Pearson correlation coefficient revealed a significant negative correlation between horizontal eyelid laxity and extracellular matrix content in the eyelid skin, the pretarsal orbicularis oculi muscle, the perimeibomian tarsal stroma, and the intermeibomian tarsal stroma. Linear regression demonstrated that horizontal eyelid laxity is dependent upon extracellular matrix components in all eyelid regions. Collagen fiber content was significantly increased in specimens from patients in group 1 compared with specimens from patients in group 2. The present findings suggest that a reduction of collagen and elastic fibers may contribute to the development of excessive horizontal eyelid laxity in patients with involutional ectropion and entropion of the lower eyelid.

7. Elastic-plastic dynamic analysis of a reactor building

Umemura, Hajime; Tanaka, Hiroshi.

1976-01-01

The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)

8. Matrix of transmission in structural dynamics

Mukherjee, S.

1975-01-01

Within the last few years numerous papers have been published on the subject of matrix method in elasto-mechanics. 'Matrix of Transmission' is one of the methods in this field which has gained considerable attention in recent years. The basic philosophy adopted in this method is based on the idea of breaking up a complicated system into component parts with simple elastic and dynamic properties which can be readily expressed in matrix form. These component matrices are considered as building blocks, which are fitted together according to a set of predetermined rules which then provide the static and dynamic properties of the entire system. A common type of system occuring in engineering practice consists of a number of elements linked together end to end in the form of a chain. The 'Transfer Matrix' is ideally suited for such a system, because only successive multiplication is necessary to connect these elements together. The number of degrees of freedom and intermediate conditions present no difficulty. Although the 'Transfer Matrix' method is suitable for the treatment of branched and coupled systems its application to systems which do not have predominant chain topology is not effective. Apart from the requirement that the system be linearely elastic, no other restrictions are made. In this paper, it is intended to give a general outline and theoretical formulation of 'Transfer Matrix' and then its application to actual problems in structural dynamics related to seismic analysis. The natural frequencies of a freely vibrating elastic system can be found by applying proper end conditions. The end conditions will yield the frequency determinate to zero. By using a suitable numerical method, the natural frequencies and mode shapes are determined by making a frequency sweep within the range of interest. Results of an analysis of a typical nuclear building by this method show very close agreement with the results obtained by using ASKA and SAP IV program. Therefore

9. Theory of atom displacements induced by fast electron elastic scattering in solids

Cruz, C. M.; Pinera, I.; Abreu, Y.; Leyva, A.

2006-01-01

Present contribution deals with the theoretical description of the conditions favoring the occurrence of single fast electron elastic scattering in solids, leading to the displacement of atoms from their crystalline sites. Firstly, the Moliere-Bethe-Goudsmit-Saunderson theory of Multiple Electron Scattering is applied, determining the limiting angle θ l over which the single electron elastic scattering prevails over the multiple one, leading to the evaluation of the total macroscopic cross-section for single electron elastic scattering on the basis of the Mott-Rutherford differential cross-section. On the basis of single electron elastic scattering by atoms in the solid matrix, it was determined the relative number of Atom Displacements produced by the Gamma Radiation as a primary act, as well as the energy and linear momentum of the ejected atoms. The statistical distributions of single electron elastic scattering and of those inducing Atom Displacements at different electron initial energies in comparison with the others electron inelastic scattering channels are discussed, where the statistical sampling methods on the basis of the rejection one where applied simulating different practical situations. (Full text)

10. Controlling elastic waves with small phononic crystals containing rigid inclusions

Peng, Pai

2014-05-01

We show that a two-dimensional elastic phononic crystal comprising rigid cylinders in a solid matrix possesses a large complete band gap below a cut-off frequency. A mechanical model reveals that the band gap is induced by negative effective mass density, which is affirmed by an effective medium theory based on field averaging. We demonstrate, by two examples, that such elastic phononic crystals can be utilized to design small devices to control low-frequency elastic waves. One example is a waveguide made of a two-layer anisotropic elastic phononic crystal, which can guide and bend elastic waves with wavelengths much larger than the size of the waveguide. The other example is the enhanced elastic transmission of a single-layer elastic phononic crystal loaded with solid inclusions. The effective mass density and reciprocal of the modulus of the single-layer elastic phononic crystal are simultaneously near zero. © CopyrightEPLA, 2014.

11. Computational Elastic Knots

Zhao, Xin

2013-05-01

Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.

12. Elastic metamaterial beam with remotely tunable stiffness

Qian, Wei [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Yu, Zhengyue [School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Wang, Xiaole [School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Lai, Yun [College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Yellen, Benjamin B., E-mail: yellen@duke.edu [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)

2016-02-07

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ∼30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

13. Elastic metamaterial beam with remotely tunable stiffness

Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.

2016-02-01

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

14. Elastic properties of Cs{sub 2}HgBr{sub 4} and Cs{sub 2}CdBr{sub 4} crystals

Kityk, A.V.; Zadorozhna, A.V.; Shchur, Y.I.; Martynyuk-Lototska, Y.I.; Burak, Y.; Vlokh, O.G. [Institute of Physical Optics, Lvov (Ukraine)

1998-12-31

Using ultrasonic velocity measurements, all components of the elastic constant matrix C{sub ij} , elastic compliances matrix S{sub ij}, and linear compressibility constants matrix K{sub ij} of orthorhombic Cs{sub 2}HgBr{sub 4} and Cs{sub 2}CdBr{sub 4} crystals have been determined over a wide temperature range, including the region of the phase transition from the normal to the incommensurate phase. Results obtained are considered within the framework of the phenomenological theory. Preliminary analysis of the acoustical properties at room temperature clearly indicates that both crystals are relatively important materials for acousto-optical applications. Copyright (1998) CSIRO Australia 16 refs., 1 tab. 8 figs. The URL for the electronic version of this article is http://www.publish.csiro.au/journals/ajp/electronic.html

15. Elasticities and the link between demographic and evolutionary dynamics

Van Tienderen, P.H.

2000-01-01

Multivariate selection models and demographic matrix projections are closely related. The subtle differences among the parameters of both approaches (sensitivities, elasticities, selection differentials, and gradients) can be confusing. I suggest a hierarchical framework for analysis using

16. Extremal Overall Elastic Response of Polycrystalline Materials

Bendsøe, Martin P; Lipton, Robert

1996-01-01

Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...... values.We show that the extremal overall elastic response is alwaysachieved by a configuration consisting of a single properlyoriented crystal. This result is compared to results for isotropicpolycrystals....

17. Plane strain problem in microstretch elastic solid

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

College, Patti 143 416, India. 3Department of Mathematics, Guru Nanak Dev University, Amritsar 143 005, ... lem in microstretch elastic solid by employing the eigenvalue approach. 975. Page 2. 976. Rajneesh Kumar et al. 2. Basic equations ..... of the matrix A are characteristic roots of (29) assuming that real parts of qs.

18. Elastic Anisotropy of Basalt

Becker, K.; Shapiro, S.; Stanchits, S.; Dresen, G.; Kaselow, A.; Vinciguerra, S.

2005-12-01

Elastic properties of rocks are sensitive to changes of the in-situ stress and damage state. In particular, seismic velocities are strongly affected by stress-induced formation and deformation of cracks or shear-enhanced pore collapse. The effect of stress on seismic velocities as a result of pore space deformation in isotropic rock at isostatic compression may be expressed by the equation: A+K*P-B*exp (-D*P) (1), where P=Pc-Pp is the effective pressure, the pure difference between confining pressure and pore pressure. The parameter A, K, B and D describe material constants determined using experimental data. The physical meaning of the parameters is given by Shapiro (2003, in Geophysics Vol.68(Nr.2)). Parameter D is related to the stress sensitivity of the rock. A similar relation was derived by Shapiro and Kaselow (2005, in Geophysics in press) for weak anisotropic rocks under arbitrary load. They describe the stress dependent anisotropy in terms of Thomson's (1986, in Geophysics, Vol. 51(Nr.10)) anisotropy parameters ɛ and γ as a function of stress in the case of an initially isotropic rock: ɛ ∝ E2-E3, γ ∝ E3-E2 (2) with Ei=exp (D*Pi). The exponential terms Ei are controlled by the effective stress components Pi. To test this relation, we have conducted a series of triaxial compression tests on dry samples of initially isotropic Etnean Basalt in a servo-controlled MTS loading frame equipped with a pressure cell. Confining pressure was 60, 40 and 20 MPa. Samples were 5 cm in diameter and 10 cm in length. Elastic anisotropy was induced by axial compression of the samples through opening and growth of microcracks predominantly oriented parallel to the sample axis. Ultrasonic P- and S- wave velocities were monitored parallel and normal to the sample axis by an array of 20 piezoceramic transducers glued to the surface. Preamplified full waveform signals were stored in two 12 channel transient recorders. According to equation 2 the anisotropy parameters are

19. Dynamic elasticity measurement for prosthetic socket design.

Kim, Yujin; Kim, Junghoon; Son, Hyeryon; Choi, Youngjin

2017-07-01

The paper proposes a novel apparatus to measure the dynamic elasticity of human limb in order to help the design and fabrication of the personalized prosthetic socket. To take measurements of the dynamic elasticity, the desired force generated as an exponential chirp signal in which the frequency increases and amplitude is maintained according to time progress is applied to human limb and then the skin deformation is recorded, ultimately, to obtain the frequency response of its elasticity. It is referred to as a Dynamic Elasticity Measurement Apparatus (DEMA) in the paper. It has three core components such as linear motor to provide the desired force, loadcell to implement the force feedback control, and potentiometer to record the skin deformation. After measuring the force/deformation and calculating the dynamic elasticity of the limb, it is visualized as 3D color map model of the limb so that the entire dynamic elasticity can be shown at a glance according to the locations and frequencies. For the visualization, the dynamic elasticities measured at specific locations and frequencies are embodied using the color map into 3D limb model acquired by using 3D scanner. To demonstrate the effectiveness, the visualized dynamic elasticities are suggested as outcome of the proposed system, although we do not have any opportunity to apply the proposed system to the amputees. Ultimately, it is expected that the proposed system can be utilized to design and fabricate the personalized prosthetic socket in order for releasing the wearing pain caused by the conventional prosthetic socket.

20. Elastic least-squares reverse time migration

Feng, Zongcai

2017-03-08

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

1. Elastic least-squares reverse time migration

Feng, Zongcai; Schuster, Gerard T.

2017-01-01

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

2. A method for determination of X-ray elastic constants of materials showing non-linear sin2ψ diagrams and its application to Zn-Ni-alloy electroplate

Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.

1990-01-01

This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)

3. Perturbation analysis of nonlinear matrix population models

Hal Caswell

2008-03-01

Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

4. Matrix analysis

Bhatia, Rajendra

1997-01-01

A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu­ ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe­ matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to...

5. Elastic scattering and quasi-elastic transfers

Mermaz, M.C.

1978-01-01

Experiments are presented which it will be possible to carry out at GANIL on the elastic scattering of heavy ions: diffraction phenomena if the absorption is great, refraction phenomena if absorption is low. The determination of the optical parameters can be performed. The study of the quasi-elastic transfer reactions will make it possible to know the dynamics of the nuclear reactions, form exotic nuclei and study their energy excitation spectrum, and analyse the scattering and reaction cross sections [fr

6. Unified continuum damage model for matrix cracking in composite rotor blades

Pollayi, Hemaraju; Harursampath, Dineshkumar [Nonlinear Multifunctional Composites - Analysis and Design Lab (NMCAD Lab) Department of Aerospace Engineering Indian Institute of Science Bangalore - 560012, Karnataka (India)

2015-03-10

7. Unified continuum damage model for matrix cracking in composite rotor blades

Pollayi, Hemaraju; Harursampath, Dineshkumar

2015-01-01

8. Semidefinite linear complementarity problems

Eckhardt, U.

1978-04-01

Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

9. Efficient education policy: A second-order elasticity rule

Richter, Wolfram F.

2010-01-01

Assuming a two-period model with endogenous choices of labour, education, and saving, efficient education policy is characterized for a Ramsey-like scenario in which the government is constrained to use linear instruments. It is shown that education should be effectively subsidized if, and only if, the elasticity of the earnings function is increasing in education. The strength of second-best subsidization increases in the elasticity of the elasticity of the earnings function. This second-ord...

10. Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

2010-01-01

11. ElasticSearch cookbook

Paro, Alberto

2013-01-01

Written in an engaging, easy-to-follow style, the recipes will help you to extend the capabilities of ElasticSearch to manage your data effectively.If you are a developer who implements ElasticSearch in your web applications, manage data, or have decided to start using ElasticSearch, this book is ideal for you. This book assumes that you've got working knowledge of JSON and Java

Tapp, Kristopher

2005-01-01

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.

13. Uniqueness in inverse elastic scattering with finitely many incident waves

Elschner, Johannes; Yamamoto, Masahiro

2009-01-01

We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)

14. Support minimized inversion of acoustic and elastic wave scattering

Safaeinili, A.

1994-01-01

This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

15. Extremal Overall Elastic Response of Polycrystalline Materials

Bendsøe, Martin P; Lipton, Robert

1997-01-01

Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...

16. The theory of elastic waves and waveguides

Miklowitz, J

1984-01-01

The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. The studies of elastodynamic theory and its application to fundamental value problems should prepare the reader to tackle many physical problems of general interest in engineering and geophysics, and of particular interest in mechanics and seismology.

17. Multivariate Matrix-Exponential Distributions

2010-01-01

be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...

18. Modular Matrix Multiplication on a Linear Array.

1983-11-01

is fl(n2). 2 Case e Irl __ (see Figure 5.2) 2 2 ,1 Y, " X2v- ’ Y2 -. x= -- ~ Y4 "i; Yin Figure 5Ŗ At t--xi, either all Gk, such that IkEA , have n...nat and Image Proceuing, IEEE Transactions on Computers, Vol. C-31, No. 10 22 (October, 1982), pp. IO0oo09. [41 H.T. Kung, Let’s Design Algorithms for...VLSI Systems, Proc. Caltech Conf. on Very Large Scale Integration: Architecture, Design , Fabrication (January, 1979), pp. 65. 90. 151 H.T. Kung, and

19. Handbook of linear algebra

Hogben, Leslie

2013-01-01

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

20. Response of orthotropic micropolar elastic medium due to time ...

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

namic response of anisotropic continuum has received the attention of ... linear theory of micropolar elasticity and bending of orthotropic micropolar ... medium due to time harmonic concentrated load, the continuum is divided into two half-.

1. Free vibration analysis of elastically supported Timoshenko columns ...

, concen- trated mass ... linear equations of motion for transverse vibrations of a simply supported beam carrying con- centrated ... a cantilever Timoshenko beam with a rigid tip mass. Ferreira .... Figure 3. Free body diagram of elastic support.

2. Matrix theory

Franklin, Joel N

2003-01-01

Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.

3. ElasticSearch cookbook

Paro, Alberto

2015-01-01

If you are a developer who implements ElasticSearch in your web applications and want to sharpen your understanding of the core elements and applications, this is the book for you. It is assumed that you've got working knowledge of JSON and, if you want to extend ElasticSearch, of Java and related technologies.

4. Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

5. Elastic K-means using posterior probability.

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model.

6. Nonlinear dynamics between linear and impact limits

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

7. Remarks on orthotropic elastic models applied to wood

2006-09-01

Full Text Available Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal, R( radial and T(tangential are coincident with the Cartesian axes (x, y, z, is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young´s modulus and shear modulus, with fiber orientation are presented.

8. Effects of ionizing radiation on extracellular matrix

Mohamed, F. [School of Physics, University of Exeter, Exeter EX44QL (United Kingdom)], E-mail: f.mohamed@ex.ac.uk; Bradley, D.A. [Department of Physics, University of Surrey, Guildford GU72XH (United Kingdom); Winlove, C.P. [School of Physics, University of Exeter, Exeter EX44QL (United Kingdom)

2007-09-21

9. Effects of ionizing radiation on extracellular matrix

Mohamed, F.; Bradley, D.A.; Winlove, C.P.

2007-01-01

10. The elastic response of composite materials

Laws, N.

1980-01-01

The theory of linear elasticity is used to study the elastic response of composite materials. The main concern is the prediction of overall moduli. Some attention is paid to the problem of deciding upon when the idea of an overall modulus is meaningful. In addition it is shown how to calculate some rigorous bounds on the overall moduli, and some predictions of the self-consistent method are discussed. The paper mainly concentrates on isotropic dispersions of spheres, unidirectional fibre-reinforced materials and laminates. (author)

11. Two Propositions on the Application of Point Elasticities to Finite Price Changes.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

12. A generic approach for expanding homolog-targeted residue screening of sulfonamides using a fast matrix separation and class-specific fragmentation-dependent acquisition with a hybrid quadrupole-linear ion trap mass spectrometer

Huang Chunlin [Department of Biochemistry and Molecular Biology, School of Pharmacy and Life Science, University of South China, Hengyang 421001 (China); Guo Bin, E-mail: binnguo@126.com [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Wang Xiaoying [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Li Jie [Department of Biochemistry and Molecular Biology, School of Pharmacy and Life Science, University of South China, Hengyang 421001 (China); Zhu Weitao; Chen Bo [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China); Ouyang Shan [Food Inspection and Quarantine Center, Shenzhen Entry-Exit Inspection and Quarantine Bureau of the People' s Republic of China, Shenzhen 518067 (China); Yao Shouzhuo [Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha 410081 (China)

2012-08-06

Highlights: Black-Right-Pointing-Pointer Generic homolog-targeted screening approach for multi-residual sulfonamide analogs. Black-Right-Pointing-Pointer Single-tube extraction/partitioning-multifunction adsorption cleanup for direct injection. Black-Right-Pointing-Pointer Class-specific fragmentation for expanding coverage of N{sup 4}-acetyl and N-OH metabolites. Black-Right-Pointing-Pointer PreS-IDA-EPI in LC-QqLIT for simultaneous screening and confirmation of real samples. - Abstract: A generic and efficient homolog-targeted approach was used to expand screening and detection of target class of sulfonamides and structural analogs, based on a fast single-tube extraction/partitioning-multifunction adsorption cleanup (SEP/MAC) for class-specific fragmentation-dependent acquisition with a liquid chromatography-hybrid triple-quadrupole linear ion trap mass spectrometer (LC-QqLIT). By combining the two-stage process conducted in a single tube as one-pot protocol, the straightforward SEP/MAC procedure was optimized to offer clean extracts with reasonable recovery (71-109% with RSDs < 20%) and decreased matrix interferences (-9 to 19%) of multiresidual sulfonamide extraction from different tissue samples. The novel use of neutral loss scan of 66 Da (NLS) or precursor ion scanning of m/z 108 (PreS) in positive ion mode was found to achieve more comprehensive coverage of protonated molecular ions of a wide array of sulfonamides including N{sup 4}-acetyl and hydroxylamine metabolites plus their possible dimers. Moreover, the PreS-triggered automatically enhanced product ion spectral acquisition enabled simultaneous screening, profiling and confirmation of an unlimited number of analytes belonging to the sulfonamide class within a single analysis. The validation and application results of the generic SEP/MAC-based LC-QqLIT strategy consistently demonstrated favorable performances with acceptable accuracy (67-116%), precision (RSDs < 25%), and sensitivity (LOQs {<=} 7.5 ng

13. Viscous-elastic dynamics of power-law fluids within an elastic cylinder

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Klumpp, A. R.; Lawson, C. L.

1988-01-01

Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

15. Radii of Solvability and Unsolvability of Linear Systems

2016-01-01

Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

16. Statistical mechanics of elasticity

Weiner, JH

2012-01-01

Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.

17. Elasticity of energy consumption

Stam, M.

2004-01-01

Insight is given into the price elasticities of several energy carriers. Next, attention is paid to the impact of the discussion on changes of the Regulating Energy Levy (REB, abbreviated in Dutch) in the Netherlands [nl

18. A generic approach for expanding homolog-targeted residue screening of sulfonamides using a fast matrix separation and class-specific fragmentation-dependent acquisition with a hybrid quadrupole-linear ion trap mass spectrometer

Huang Chunlin; Guo Bin; Wang Xiaoying; Li Jie; Zhu Weitao; Chen Bo; Ouyang Shan; Yao Shouzhuo

2012-01-01

Highlights: ► Generic homolog-targeted screening approach for multi-residual sulfonamide analogs. ► Single-tube extraction/partitioning-multifunction adsorption cleanup for direct injection. ► Class-specific fragmentation for expanding coverage of N 4 -acetyl and N-OH metabolites. ► PreS–IDA–EPI in LC–QqLIT for simultaneous screening and confirmation of real samples. - Abstract: A generic and efficient homolog-targeted approach was used to expand screening and detection of target class of sulfonamides and structural analogs, based on a fast single-tube extraction/partitioning-multifunction adsorption cleanup (SEP/MAC) for class-specific fragmentation-dependent acquisition with a liquid chromatography–hybrid triple-quadrupole linear ion trap mass spectrometer (LC–QqLIT). By combining the two-stage process conducted in a single tube as one-pot protocol, the straightforward SEP/MAC procedure was optimized to offer clean extracts with reasonable recovery (71–109% with RSDs 4 -acetyl and hydroxylamine metabolites plus their possible dimers. Moreover, the PreS-triggered automatically enhanced product ion spectral acquisition enabled simultaneous screening, profiling and confirmation of an unlimited number of analytes belonging to the sulfonamide class within a single analysis. The validation and application results of the generic SEP/MAC-based LC–QqLIT strategy consistently demonstrated favorable performances with acceptable accuracy (67–116%), precision (RSDs −1 ) to meet the acceptance criteria for all the sulfonamide–tissue combinations. Thus, the integration of the matrix-independent SEP/MAC procedure and the multiparameter matching algorithm with the unit-resolution LC–QqLIT instrument can serve as a valuable semi-targeted discovery strategy for rapid screening and reliable quantitative/confirmatory analysis of real samples.

19. The development of an algebraic multigrid algorithm for symmetric positive definite linear systems

Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)

1996-12-31

An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.

20. Mastering ElasticSearch

Kuc, Rafal

2013-01-01

A practical tutorial that covers the difficult design, implementation, and management of search solutions.Mastering ElasticSearch is aimed at to intermediate users who want to extend their knowledge about ElasticSearch. The topics that are described in the book are detailed, but we assume that you already know the basics, like the query DSL or data indexing. Advanced users will also find this book useful, as the examples are getting deep into the internals where it is needed.

1. Variational linear algebraic equations method

Moiseiwitsch, B.L.

1982-01-01

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

2. Modeling Pseudo-elastic Behavior of Springback

Xia, Z. Cedric

2005-01-01

3. Computation of the lamina stacking sequence effect on elastic moduli of a plain-weave Nicalon/SiC laminated composite with a [0/30/60] lay-up

Zhao Wei; Yu Niann-i

1998-01-01

Estimation of the elastic modulus is important in engineering design. One difference between CFCCs (continuous fiber-reinforced ceramic-matrix composites), and CMCs (whisker, particulate, or short fiber-reinforced ceramic-matrix composites), is that the anisotropic behavior of CFCCs plays an important role in affecting their mechanical behavior. This feature may also contribute to the variation of elastic properties and strengths of CFCC. In this paper, a Fortran program is developed to quantify the lamina stacking sequence effect on the effective elastic moduli of the laminated CFCCs. The material for modeling is a plain-weave Nicalon fiber-reinforced silicon carbide (Nicalon/SiC) CFCCs. Results show that various stacking sequences within the CFCC (a [0/30/60] lay-up) will give different effective elastic moduli of the CFCCs. This trend leads to a variation of the slope of the linear portion on the flexural stress-strain curve, i.e., changing the position of the starting point of the non-linear portion, and the shape of the whole curve, which gives a different value of the peak stress in the curve. (orig.)

4. Modeling elastic anisotropy in strained heteroepitaxy.

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

5. Modeling elastic anisotropy in strained heteroepitaxy

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to facets on the surface.

6. The R-matrix theory

Descouvemont, P; Baye, D

2010-01-01

The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schroedinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.

7. Elementary matrix algebra

Hohn, Franz E

2012-01-01

This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

8. Nonlinear elastic waves in materials

Rushchitsky, Jeremiah J

2014-01-01

The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

9. Vascular elastic photoacoustic tomography in humans

Hai, Pengfei; Zhou, Yong; Liang, Jinyang; Li, Chiye; Wang, Lihong V.

2016-03-01

Quantification of vascular elasticity can help detect thrombosis and prevent life-threatening conditions such as acute myocardial infarction or stroke. Here, we propose vascular elastic photoacoustic tomography (VE-PAT) to measure vascular elasticity in humans. VE-PAT was developed by incorporating a linear-array-based photoacoustic computed tomography system with a customized compression stage. By measuring the deformation of blood vessels under uniaxial loading, VE-PAT was able to quantify the vascular compliance. We first demonstrated the feasibility of VE-PAT in blood vessel phantoms. In large vessel phantoms, VE-PAT detected a decrease in vascular compliance due to simulated thrombosis, which was validated by a standard compression test. In small blood vessel phantoms embedded 3 mm deep in gelatin, VE-PAT detected elasticity changes at depths that are difficult to image using other elasticity imaging techniques. We then applied VE-PAT to assess vascular compliance in a human subject and detected a decrease in vascular compliance when an occlusion occurred downstream from the measurement point, demonstrating the potential of VE-PAT in clinical applications such as detection of deep venous thrombosis.

10. Probing hysteretic elasticity in weakly nonlinear materials

Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS

2010-12-07

Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.

11. Introduction to computational linear algebra

Nassif, Nabil; Erhel, Jocelyne

2015-01-01

Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

12. Dynamic nonlinear elasticity in geo materials

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

13. Mechanics of Fluctuating Elastic Plates and Fiber Networks

Liang, Xiaojun

Lipid membranes and fiber networks in biological systems perform important mechanical functions at the cellular and tissue levels. In this thesis I delve into two detailed problems--thermal fluctuation of membranes and non-linear compression response of fiber networks. Typically, membrane fluctuations are analysed by decomposing into normal modes or by molecular simulations. In the first part of my thesis, I propose a new semi-analytic method to calculate the partition function of a membrane. The membrane is viewed as a fluctuating von Karman plate and discretized into triangular elements. Its energy is expressed as a function of nodal displacements, and then the partition function and co-variance matrix are computed using Gaussian integrals. I recover well-known results for the dependence of the projected area of a lipid bilayer membrane on the applied tension, and recent simulation results on the ependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications I use this technique to study a membrane with heterogeneity and different boundary conditions. I also use this technique to study solid membranes by taking account of the non-linear coupling of in-plane strains with out-of-plane deflections using a penalty energy, and apply it to graphene, an ultra-thin two-dimensional solid. The scaling of graphene fluctuations with membrane size is recovered. I am able to capture the dependence of the thermal expansion coefficient of graphene on temperature. Next, I study curvature mediated interactions between inclusions in membranes. I assume the inclusions to be rigid, and show that the elastic and entropic forces between them can compete to yield a local maximum in the free energy if the membrane bending modulus is small. If the spacing between the inclusions is less than this local maximum then the attractive entropic forces dominate and the separation between the inclusions will be determined by short range interactions; if the

14. Matrix transformations and sequence spaces

Nanda, S.

1983-06-01

In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

15. Equilibrium stability of a cylindrical body subject to the internal structure of the material and inelastic behaviour of the completely compressed matrix

Gotsev, D. V.; Perunov, N. S.; Sviridova, E. N.

2018-03-01

The mathematical model describing the stress-strain state of a cylindrical body under the uniform radial compression effect is constructed. The model of the material is the porous medium model. The compressed skeleton of the porous medium possesses hardening elastic-plastic properties. Deforming of the porous medium under the specified compressive loads is divided into two stages: elastic deforming of the porous medium and further elastic-plastic deforming of the material with completely compressed matrix. The analytical relations that define the fields of stress and displacement at each stage of the deforming are obtained. The influence of the porosity and other physical, mechanical and geometric parameters of the construction on the size of the plastic zone is evaluated. The question of the ground state equilibrium instability is investigated within the framework of the three-dimensional linearized relationships of the stability theory of deformed bodies.

16. Application of elasticity theory at Sandia Labortories

Davison, L.

1975-01-01

Examples are given of the application of linear elasticity theory to the solution of practical problems encountered at Sandia Laboratories. It is being applied to a very broad range of problems: those in one, two, and three spatial dimensions, some involving static and some dynamic response, to materials having isotropic and anisotropic symmetry, to homogeneous and inhomogeneous bodies, etc. Various extensions of the theory to include electric, magnetic and thermal effects, to account for material microstructure, for radiation and spall damage, chemical reactions, and other phenomena have been developed and/or applied. In some applications linear elasticity represents the physics of a problem well and is the theory of choice. In others the theory was used because it lent insight into a larger problem that was also attacked by means of other theories and/or experiment, and in some cases it serves as a part of a more encompassing theory

17. Modern Nondestructive Test Methods for Army Ceramic Matrix Composites

Strand, Douglas J

2008-01-01

.... Ceramic matrix composites (CMC) are potentially good high-temperature structural materials because of their low density, high elastic moduli, high strength, and for those with weak interfaces, surprisingly good damage tolerance...

18. Are rapid changes in brain elasticity possible?

Parker, K. J.

2017-09-01

Elastography of the brain is a topic of clinical and preclinical research, motivated by the potential for viscoelastic measures of the brain to provide sensitive indicators of pathological processes, and to assist in early diagnosis. To date, studies of the normal brain and of those with confirmed neurological disorders have reported a wide range of shear stiffness and shear wave speeds, even within similar categories. A range of factors including the shear wave frequency, and the age of the individual are thought to have a possible influence. However, it may be that short term dynamics within the brain may have an influence on the measured stiffness. This hypothesis is addressed quantitatively using the framework of the microchannel flow model, which derives the tissue stiffness, complex modulus, and shear wave speed as a function of the vascular and fluid network in combination with the elastic matrix that comprise the brain. Transformation rules are applied so that any changes in the fluid channels or the elastic matrix can be mapped to changes in observed elastic properties on a macroscopic scale. The results are preliminary but demonstrate that measureable, time varying changes in brain stiffness are possible simply by accounting for vasodynamic or electrochemical changes in the state of any region of the brain. The value of this preliminary exploration is to identify possible mechanisms and order-of-magnitude changes that may be testable in vivo by specialized protocols.

19. Stressed-deformed state of mountain rocks in elastic stage and between elasticity

Samedov A.M.

2017-12-01

destroy as a plastic material. In the elastic stage, the link between stress and strain is linear.

20. Linear methods in band theory

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

1. NONLINEAR SPECTRAL IMAGING OF ELASTIC CARTILAGE IN RABBIT EARS

JING CHEN

2013-07-01

Full Text Available Elastic cartilage in the rabbit external ear is an important animal model with attractive potential value for researching the physiological and pathological states of cartilages especially during wound healing. In this work, nonlinear optical microscopy based on two-photon excited fluorescence and second harmonic generation were employed for imaging and quantifying the intact elastic cartilage. The morphology and distribution of main components in elastic cartilage including cartilage cells, collagen and elastic fibers were clearly observed from the high-resolution two-dimensional nonlinear optical images. The areas of cell nuclei, a parameter related to the pathological changes of normal or abnormal elastic cartilage, can be easily quantified. Moreover, the three-dimensional structure of chondrocytes and matrix were displayed by constructing three-dimensional image of cartilage tissue. At last, the emission spectra from cartilage were obtained and analyzed. We found that the different ratio of collagen over elastic fibers can be used to locate the observed position in the elastic cartilage. The redox ratio based on the ratio of nicotinamide adenine dinucleotide (NADH over flavin adenine dinucleotide (FAD fluorescence can also be calculated to analyze the metabolic state of chondrocytes in different regions. Our results demonstrated that this technique has the potential to provide more accurate and comprehensive information for the physiological states of elastic cartilage.

2. Matrix calculus

Bodewig, E

1959-01-01

Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well

3. Linear Algebraic Method for Non-Linear Map Analysis

Yu, L.; Nash, B.

2009-01-01

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

4. Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

Wu, H. I.; Spence, R. D.; Sharpe, P. J.; Goeschl, J. D.

1985-01-01

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.

5. Elastic anisotropy of crystals

Christopher M. Kube

2016-09-01

Full Text Available An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.

6. Shells on elastic foundations

Das, Y.C.; Kedia, K.K.

1977-01-01

No realistic analytical work in the area of Shells on Elastic Foundations has been reported in the literature. Various foundation models have been proposed by several authors. These models involve one or more than one parameters to characterise the foundation medium. Some of these models cannot be used to derive the basic equations governing the behaviour of shells on elastic foundations. In the present work, starting from an elastic continuum hypothesis, a mathematical model for foundation has been derived in curvilinear orthogonal coordinates by the help of principle of virtual displacements, treating one of the virtual displacements as known to satisfy certain given conditions at its edge surfaces. In this model, several foundation parameters can be considered and it can also be used for layered medium of both finite and infinite thickness. (Auth.)

7. Software to compute elastostatic Green's functions for sources in 3D homogeneous elastic layers above a (visco)elastic halfspace

2012-12-01

We describe software, in development, to calculate elastostatic displacement Green's functions and their derivatives for point and polygonal dislocations in three-dimensional homogeneous elastic layers above an elastic or a viscoelastic halfspace. The steps to calculate a Green's function for a point source at depth zs are as follows. 1. A grid in wavenumber space is chosen. 2. A six-element complex rotated stress-displacement vector x is obtained at each grid point by solving a two-point boundary value problem (2P-BVP). If the halfspace is viscoelastic, the solution is inverse Laplace transformed. 3. For each receiver, x is propagated to the receiver depth zr (often zr = 0) and then, 4, inverse Fourier transformed, with the Fourier component corresponding to the receiver's horizontal position. 5. The six elements are linearly combined into displacements and their derivatives. The dominant work is in step 2. The grid is chosen to represent the wavenumber-space solution with as few points as possible. First, the wavenumber space is transformed to increase sampling density near 0 wavenumber. Second, a tensor-product grid of Chebyshev points of the first kind is constructed in each quadrant of the transformed wavenumber space. Moment-tensor-dependent symmetries further reduce work. The numerical solution of the 2P-BVP problem in step 2 involves solving a linear equation A x = b. Half of the elements of x are of geophysical interest; the subset depends on whether zr ≤ zs. Denote these \\hat x. As wavenumber k increases, \\hat x can become inaccurate in finite precision arithmetic for two reasons: 1. The condition number of A becomes too large. 2. The norm-wise relative error (NWRE) in \\hat x is large even though it is small in x. To address this problem, a number of researchers have used determinants to obtain x. This may be the best approach for 6-dimensional or smaller 2P-BVP, where the combinatorial increase in work is still moderate. But there is an alternative

8. In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

9. Anisotropic elastic plates

Hwu, Chyanbin

2010-01-01

As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only in plane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element a

10. Hybrid elastic solids

Lai, Yun

2011-06-26

Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays super anisotropy-in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications. © 2011 Macmillan Publishers Limited. All rights reserved.

11. Hybrid elastic solids

Lai, Yun; Wu, Ying; Sheng, Ping; Zhang, Zhaoqing

2011-01-01

Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays super anisotropy-in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications. © 2011 Macmillan Publishers Limited. All rights reserved.

12. The law of elasticity

Sergio Cesare Masin

2010-01-01

Full Text Available Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight-a cognitive law analogous to Hooke¿s law of elasticity. Participants also estimated the total imagined elongation of springs joined either in series or in parallel. This total elongation was longer for serial than for parallel springs, and increased proportionally to the number of serial springs and inversely proportionally to the number of parallel springs. The results suggest that participants integrated load weight with imagined elasticity rather than with spring length.

13. ElasticSearch server

Rogozinski, Marek

2014-01-01

This book is a detailed, practical, hands-on guide packed with real-life scenarios and examples which will show you how to implement an ElasticSearch search engine on your own websites.If you are a web developer or a user who wants to learn more about ElasticSearch, then this is the book for you. You do not need to know anything about ElastiSeach, Java, or Apache Lucene in order to use this book, though basic knowledge about databases and queries is required.

14. Elastic representation surfaces of unidirectional graphite/epoxy composites

Kriz, R.D.; Ledbetter, H.M.

1985-01-01

Unidirectional graphite/epoxy composites exhibit high elastic anisotropy and unusual geometrical features in their elastic-property polar diagrams. From the five-component transverse-isotropic elastic-stiffness tensor we compute and display representation surfaces for Young's modulus, torsional modulus, linear compressibility, and Poisson's ratios. Based on Christoffel-equation solutions, we describe some unusual elastic-wave-surface topological features. Musgrave considered in detail the differences between phase-velocity and group-velocity surfaces arising from high elastic anisotropy. For these composites, we find effects similar to, but more dramatic than, Musgrave's. Some new, unexpected results for graphite/epoxy include: a shear-wave velocity that exceeds a longitudinal velocity in the plane transverse to the fiber; a wave that changes polarization character from longitudinal to transverse as the propagation direction sweeps from the fiber axis to the perpendicular axis

15. Multi-scale imaging and elastic simulation of carbonates

Faisal, Titly Farhana; Awedalkarim, Ahmed; Jouini, Mohamed Soufiane; Jouiad, Mustapha; Chevalier, Sylvie; Sassi, Mohamed

2016-05-01

Digital Rock Physics (DRP) is an emerging technology that can be used to generate high quality, fast and cost effective special core analysis (SCAL) properties compared to conventional experimental techniques and modeling techniques. The primary workflow of DRP conssits of three elements: 1) image the rock sample using high resolution 3D scanning techniques (e.g. micro CT, FIB/SEM), 2) process and digitize the images by segmenting the pore and matrix phases 3) simulate the desired physical properties of the rocks such as elastic moduli and velocities of wave propagation. A Finite Element Method based algorithm, that discretizes the basic Hooke's Law equation of linear elasticity and solves it numerically using a fast conjugate gradient solver, developed by Garboczi and Day [1] is used for mechanical and elastic property simulations. This elastic algorithm works directly on the digital images by treating each pixel as an element. The images are assumed to have periodic constant-strain boundary condition. The bulk and shear moduli of the different phases are required inputs. For standard 1.5" diameter cores however the Micro-CT scanning reoslution (around 40 μm) does not reveal smaller micro- and nano- pores beyond the resolution. This results in an unresolved "microporous" phase, the moduli of which is uncertain. Knackstedt et al. [2] assigned effective elastic moduli to the microporous phase based on self-consistent theory (which gives good estimation of velocities for well cemented granular media). Jouini et al. [3] segmented the core plug CT scan image into three phases and assumed that micro porous phase is represented by a sub-extracted micro plug (which too was scanned using Micro-CT). Currently the elastic numerical simulations based on CT-images alone largely overpredict the bulk, shear and Young's modulus when compared to laboratory acoustic tests of the same rocks. For greater accuracy of numerical simulation prediction, better estimates of moduli inputs

16. Random linear codes in steganography

Kamil Kaczyński

2016-12-01

Full Text Available Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code. In parallel, it offers easy generation of parity check matrix. In this paper, the modification of LSB algorithm is presented. A random linear code [8, 2] was used as a base for algorithm modification. The implementation of the proposed algorithm, along with practical evaluation of algorithms’ parameters based on the test images was made.[b]Keywords:[/b] steganography, random linear codes, RLC, LSB

17. Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

Contreras, Andres A.; Le Maî tre, Olivier P.; Aquino, Wilkins; Knio, Omar

2016-01-01

of stiff inclusions embedded in a soft matrix, mimicking tumors in soft tissues. We rely on a polynomial chaos (PC) surrogate to accelerate the inference process. The PC surrogate predicts the dependence of the displacements field with the random elastic

18. A companion matrix for 2-D polynomials

Boudellioua, M.S.

1995-08-01

In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

19. Negative stiffness honeycombs as tunable elastic metamaterials

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

20. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

Rietbergen, van B.; Odgaard, A.; Kabel, J.; Huiskes, H.W.J.

1996-01-01

A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric

1. Fracton-Elasticity Duality

2018-05-01

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

2. The Law of Elasticity

Cocco, Alberto; Masin, Sergio Cesare

2010-01-01

Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight--a cognitive law analogous to Hooke's law of elasticity. Participants also estimated the total imagined elongation of springs joined…

3. Autonomic Vertical Elasticity of Docker Containers with ElasticDocker

Al-Dhuraibi , Yahya; Paraiso , Fawaz; Djarallah , Nabil; Merle , Philippe

2017-01-01

International audience; Elasticity is the key feature of cloud computing to scale computing resources according to application workloads timely. In the literature as well as in industrial products, much attention was given to the elasticity of virtual machines, but much less to the elasticity of containers. However, containers are the new trend for packaging and deploying microservices-based applications. Moreover, most of approaches focus on horizontal elasticity, fewer works address vertica...

4. Finite element historical deformation analysis in piecewise linear plasticity by mathematical programming

De Donato, O.; Parisi, M.A.

1977-01-01

When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)

5. Study of Wood Plastic Composites elastic behaviour using full field measurements

Graciaa A.

2010-06-01

Full Text Available In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC. A non-linear behaviour is shown. The modulus of elasticity (MOE is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE.

6. Study of Wood Plastic Composites elastic behaviour using full field measurements

Ben Mbarek, T.; Robert, L.; Hugot, F.; Orteu, J. J.; Sammouda, H.; Graciaa, A.; Charrier, B.

2010-06-01

In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC) with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC). A non-linear behaviour is shown. The modulus of elasticity (MOE) is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM) is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE).

7. Elastic properties of gamma-Pu by resonant ultrasound spectroscopy

Migliori, Albert [Los Alamos National Laboratory; Betts, J [Los Alamos National Laboratory; Trugman, A [Los Alamos National Laboratory; Mielke, C H [Los Alamos National Laboratory; Mitchell, J N [Los Alamos National Laboratory; Ramos, M [Los Alamos National Laboratory; Stroe, I [WORXESTER, MA

2009-01-01

Despite intense experimental and theoretical work on Pu, there is still little understanding of the strange properties of this metal. We used resonant ultrasound spectroscopy method to investigate the elastic properties of pure polycrystalline Pu at high temperatures. Shear and longitudinal elastic moduli of the {gamma}-phase of Pu were determined simultaneously and the bulk modulus was computed from them. A smooth linear and large decrease of all elastic moduli with increasing temperature was observed. We calculated the Poisson ratio and found that it increases from 0.242 at 519K to 0.252 at 571K.

8. A Reevaluation of Price Elasticities for Irrigation Water

Howitt, Richard E.; Watson, William D.; Adams, Richard M.

1980-08-01

The effectiveness of pricing systems in the allocation of irrigation water is linked with the price elasticity of demand of farmers for water. Using microeconomic theory, it is shown that omission of the elasticity of demand for the crop produced leads to an inelastic bias in the demand for irrigated water. Linear programing approaches omit the product elasticity of demand and are consequently biased, whereas quadratic programing approaches to estimating derived demands for irrigation water include product demand functions. The difference between the resulting estimates are empirically demonstrated for regional derived demand functions estimated from a model of California's agricultural industry.

9. Elastic Property Simulation of Nano-particle Reinforced Composites

He Jiawei

2016-01-01

Full Text Available A series of numerical micro-mechanical models for two kinds of particle (cylindrical and discal particle reinforced composites are developed to investigate the effect of microstructural parameters on the elastic properties of composites. The effects of both the degree of particle clustering and particle’s shape on the elastic mechanical properties of composites are investigated. In addition, single particle unit cell approximation is good enough for the analysis of the effect of averaged parameters when only linear elastic response is considered without considering the particle clustering in particle-reinforced composites.

10. A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber-Reinforced Composites

Melek Usal

2010-01-01

Full Text Available The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.

11. Hyperplasia of elastic tissue in hepatic schistosomal fibrosis

1991-12-01

Full Text Available Elastic tissue hyperplasia, revealed by means of histological, immunocytochemical and ultrastructural methods, appeared as a prominent change in surgical liver biopsies taken from 61 patients with schistosomal periportal and septal fibrosis. Such hyperplasia was absent in ecperimental murine schistosomiasis, including mice with "pipe-stem" fibrosis. Displaced connective tissue cells in periportal areas, such as smooth muscle cells, more frequently observed in human material, could be the site of excessive elastin synthesis, and could explain the differences observed in human and experimental materials. Elastic tissue, sometimes represented by its microfibrillar components, also appeared to be more condensed in areas of matrix (collagen degradation, suggesting a participation of this tissue in the remodelling of the extracellular matrix. By its rectratile properties elastic tissue hyperplasia in hepatic schistosomiasis can cause vascular narrowing and thus play a role in the pathogenesis of portal hypeertension.

12. Effect of reinforcement volume fraction on the density & elastic ...

Effect of reinforcement volume fraction on the density & elastic parameters of BMG's matrix composites. Wahiba Metiri 1, Fatiha Hadjoub1, 2 and Leila Touati Tliba 1. 1 Laboratoire des Semi-Conducteurs, Département de Physique, Faculté des Sciences, Université Badji-. Mokhtar, BP 12, Annaba -23000, Algeria.

13. The Growing Importance of Linear Algebra in Undergraduate Mathematics.

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

14. On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

Qiu, S.; Clausen, B.; Padula, S.A.; Noebe, R.D.; Vaidyanathan, R.

2011-01-01

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

15. On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

Qiu, S. [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States); Clausen, B. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Padula, S.A.; Noebe, R.D. [NASA Glenn Research Center, Cleveland, OH 44135 (United States); Vaidyanathan, R., E-mail: raj@mail.ucf.edu [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States)

2011-08-15

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

16. Elastic properties of uniaxial-fiber reinforced composites - General features

Datta, Subhendu; Ledbetter, Hassel; Lei, Ming

The salient features of the elastic properties of uniaxial-fiber-reinforced composites are examined by considering the complete set of elastic constants of composites comprising isotropic uniaxial fibers in an isotropic matrix. Such materials exhibit transverse-isotropic symmetry and five independent elastic constants in Voigt notation: C(11), C(33), C(44), C(66), and C(13). These C(ij) constants are calculated over the entire fiber-volume-fraction range 0.0-1.0, using a scattered-plane-wave ensemple-average model. Some practical elastic constants such as the principal Young moduli and the principal Poisson ratios are considered, and the behavior of these constants is discussed. Also presented are the results for the four principal sound velocities used to study uniaxial-fiber-reinforced composites: v(11), v(33), v(12), and v(13).

17. Linear gate

Suwono.

1978-01-01

A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)

18. How can cells sense the elasticity of a substrate? An analysis using a cell tensegrity model

G De Santis

2011-10-01

Full Text Available A eukaryotic cell attaches and spreads on substrates, whether it is the extracellular matrix naturally produced by the cell itself, or artificial materials, such as tissue-engineered scaffolds. Attachment and spreading require the cell to apply forces in the nN range to the substrate via adhesion sites, and these forces are balanced by the elastic response of the substrate. This mechanical interaction is one determinant of cell morphology and, ultimately, cell phenotype. In this paper we use a finite element model of a cell, with a tensegrity structure to model the cytoskeleton of actin filaments and microtubules, to explore the way cells sense the stiffness of the substrate and thereby adapt to it. To support the computational results, an analytical 1D model is developed for comparison. We find that (i the tensegrity hypothesis of the cytoskeleton is sufficient to explain the matrix-elasticity sensing, (ii cell sensitivity is not constant but has a bell-shaped distribution over the physiological matrix-elasticity range, and (iii the position of the sensitivity peak over the matrix-elasticity range depends on the cytoskeletal structure and in particular on the F-actin organisation. Our model suggests that F-actin reorganisation observed in mesenchymal stem cells (MSCs in response to change of matrix elasticity is a structural-remodelling process that shifts the sensitivity peak towards the new value of matrix elasticity. This finding discloses a potential regulatory role of scaffold stiffness for cell differentiation.

19. Thermodynamic analysis of elastic-plastic deformation

Lubarda, V.

1981-01-01

The complete set of constitutive equations which fully describes the behaviour of material in elastic-plastic deformation is derived on the basis of thermodynamic analysis of the deformation process. The analysis is done after the matrix decomposition of the deformation gradient is introduced into the structure of thermodynamics with internal state variables. The free energy function, is decomposed. Derive the expressions for the stress response, entropy and heat flux, and establish the evolution equation. Finally, we establish the thermodynamic restrictions of the deformation process. (Author) [pt

20. Linear Accelerators

Vretenar, M

2014-01-01

The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics

1. Designing interactively with elastic splines

Brander, David; Bærentzen, Jakob Andreas; Fisker, Ann-Sofie

2018-01-01

We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes neglig...... negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline....

2. Matrix thermalization

Craps, Ben; Evnin, Oleg; Nguyen, Kévin

2017-01-01

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

3. Matrix thermalization

Craps, Ben; Evnin, Oleg; Nguyen, Kévin

2017-02-01

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

4. Matrix thermalization

Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Nguyen, Kévin [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

2017-02-08

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

5. Approximation by planar elastic curves

Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

2016-01-01

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

6. Linearization Method and Linear Complexity

Tanaka, Hidema

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

7. Numerical Modeling and Experimental Study of Elastic-Plastic Behavior of Carbon Nanotubes Reinforced Nanocompsites of PA6/NBR Using a Microfinite Element Model

Mir Hamid Reza Ghoreishy

2014-12-01

Full Text Available A theoretical and experimental study was conducted on the mechanical behavior of nanocomposites based on PA6/NBR thermoplastic elastomer reinforced by single wall carbon nanotubes (SWNTs. The selected samples include 60 and 40% NBR with 0.5, 1.0 and 1.5% SWNT. The modeling methodology was based on the use of two-dimensional "representative volume elements" (RVE. The Abaqus/standard code was employed to carry out the non-linear finite element calculations. Plane stress elements were selected for discretization of the domain. Linear elastic and isotropic hardening elastic-plastic models were utilized to describe the mechanical behaviors of the carbon nanotubes and polymer matrix, respectively. The samples were simultaneously prepared using melt mixing method in a laboratory internal mixer. Different orientations including regular in both longitudinal and transverse directions and random were selected for the nanotubes in the matrix. Also, two structural forms including hollow and solid for the carbon nanotubes were chosen. The highest and lowest predicted moduli were obtained from models with regular orientation in longitudinal and transverse directions, respectively. On the other hand, comparison between the predicted elastic modulus and elastic-plastic behaviors of the samples with their corresponding experimental data revealed that the random orientation in conjunction with hollow structural form gives the best results. Moreover, the selected material model for the thermoplastic elastomer i.e., isotropic hardening can precisely describe the mechanical behavior in both tension and compression modes. It is also concluded that the main source of error in this modeling methodology can be attributed to the effects of interface between polymer and nanotubes and orientation in perpendicular directions.

8. DFT calculation for elastic constants of orthorhombic structure within WIEN2K code: A new package (ortho-elastic)

Reshak, Ali H.; Jamal, Morteza

2012-01-01

Highlights: ► A new package for calculating elastic constants of orthorhombic structure is released. ► The package called ortho-elastic. ► It is compatible with [FP-(L)APW+lo] method implemented in WIEN2k code. ► Several orthorhombic structure compounds were used to test the new package. ► Elastic constants calculated using this package show good agreement with experiment. - Abstract: A new package for calculating the elastic constants of orthorhombic structure is released. The package called ortho-elastic. The formalism of calculating the ortho-elastic constants is described in details. The package is compatible with the highly accurate all-electron full-potential (linearized) augmented plane-wave plus local orbital [FP-(L)APW+lo] method implemented in WIEN2k code. Several orthorhombic structure compounds were used to test the new package. We found that the calculated elastic constants using the new package show better agreement with the available experimental data than the previous theoretical results used different methods. In this package the second-order derivative E ″ (ε) of polynomial fit E=E(ε) of energy vs strains at zero strain (ε=0), used to calculate the orthorhombic elastic constants.

9. Elasticity in Elastics-An in-vitro study.

2014-04-01

Orthodontic tooth movement results from application of forces to teeth. Elastics in orthodontics have been used both intra-orally and extra- orally to a great effect. Their use, combined with good patient co-operation provides the clinician with the ability to correct both anteroposterior and vertical discrepancies. Force decay over a period of time is a major problem in the clinical usage of latex elastics and synthetic elastomers. This loss of force makes it difficult for the clinician to determine the actual force transmitted to the dentition. It's the intent of the clinician to maintain optimal force values over desired period of time. The majority of the orthodontic elastics on the market are latex elastics. Since the early 1990s, synthetic products have been offered in the market for latex-sensitive patients and are sold as nonlatex elastics. There is limited information on the risk that latex elastics may pose to patients. Some have estimated that 0.12-6% of the general population and 6.2% of dental professionals have hypersensitivity to latex protein. There are some reported cases of adverse reactions to latex in the orthodontic population but these are very limited to date. Although the risk is not yet clear, it would still be inadvisable to prescribe latex elastics to a patient with a known latex allergy. To compare the in-vitro performance of latex and non latex elastics. Samples of 0.25 inch, latex and non latex elastics (light, medium, heavy elastics) were obtained from three manufacturers (Forestadent, GAC, Glenroe) and a sample size of ten elastics per group was tested. The properties tested included cross sectional area, internal diameter, initial force generated by the elastics, breaking force and the force relaxation for the different types of elastics. Force relaxation testing involved stretching the elastics to three times marketed internal diameter (19.05 mm) and measuring force level at intervals over a period of 48 hours. The data were

10. Linear algebra

Said-Houari, Belkacem

2017-01-01

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

11. Modeling of rail track substructure linear elastic coupling

2015-09-30

Most analyses of rail dynamics neglect contribution of the soil, or treat it in a very simple manner such as using spring elements. This can cause accuracy issues in examining dynamics for passenger comfort, derailment, substructure analysis, or othe...

12. pp-elastic scattering

Aprile, E; Cantale, G; Degli-Agosti, S; Hausammann, R; Heer, E; Hess, R; Lechanoine-LeLuc, C; Leo, W; Morenzoni, S; Onel, Y [Geneva Univ. (Switzerland). Dept. de Physique Nucleaire et Corpusculaire

1983-01-01

The aim of the elastic pp experimental program at SIN was to measure enough spin dependent parameters in order to do a direct experimental reconstruction of the elastic scattering amplitudes at a few energies between 400 and 600 MeV and at several angles between 38/sup 0/ cm and 90/sup 0/ cm. This reconstruction was not possible until recently due to lack of experimental data. Information instead has come mainly from phase shift analysis (PSA). The only way to extract the elastic scattering amplitudes without any hypotheses except those of basic symmetries, is to measure a sufficient set of spin dependent parameters at a given angle and energy. With this in view, the authors have measured at 448, 494, 515, 536 and 579 MeV, the polarization, the spin correlation parameters Asub(00nn), Asub(00ss), Asub(00kk), Asub(00ks), the 2-spin parameters Dsub(n0n0), Ksub(n00n), Dsub(s'0s0), Dsub(s'0k0) and the 3-spin parameters Msub(s'0sn), Msub(s'0kn) between 34/sup 0/ cm and 118/sup 0/ cm. A few of these parameters have also been measured at 560 and 470 MeV and at a few energies below 448 MeV. The indices refer to the polarization orientation of the scattered, recoil, beam and target particle respectively.

13. Homogenized Elastic Properties of Graphene for Small Deformations

Jurica Sorić

2013-09-01

Full Text Available In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.

14. Matrix dimensions bias demographic inferences: implications for comparative plant demography.

Salguero-Gómez, Roberto; Plotkin, Joshua B

2010-12-01

While the wealth of projection matrices in plant demography permits comparative studies, variation in matrix dimensions complicates interspecific comparisons. Collapsing matrices to a common dimension may facilitate such comparisons but may also bias the inferred demographic parameters. Here we examine how matrix dimension affects inferred demographic elasticities and how different collapsing criteria perform. We analyzed 13 x 13 matrices representing nine plant species, collapsing these matrices (i) into even 7 x 7, 5 x 5, 4 x 4, and 3 x 3 matrices and (ii) into 5 x 5 matrices using different criteria. Stasis and fecundity elasticities increased when matrix dimension was reduced, whereas those of progression and retrogression decreased. We suggest a collapsing criterion that minimizes dissimilarities between the original- and collapsed-matrix elasticities and apply it to 66 plant species to study how life span and growth form influence the relationship between matrix dimension and elasticities. Our analysis demonstrates that (i) projection matrix dimension has significant effects on inferred demographic parameters, (ii) there are better-performing methods than previously suggested for standardizing matrix dimension, and (iii) herbaceous perennial projection matrices are particularly sensitive to changes in matrix dimensionality. For comparative demographic studies, we recommend normalizing matrices to a common dimension by collapsing higher classes and leaving the first few classes unaltered.

15. Elastic properties of Gum Metal

Kuramoto, Shigeru; Furuta, Tadahiko; Hwang, Junghwan; Nishino, Kazuaki; Saito, Takashi

2006-01-01

In situ X-ray diffraction measurements under tensile loading and dynamic mechanical analysis were performed to investigate the mechanisms of elastic deformation in Gum Metal. Tensile stress-strain curves for Gum Metal indicate that cold working substantially decreases the elastic modulus while increasing the yield strength, thereby confirming nonlinearity in the elastic range. The gradient of each curve decreased continuously to about one-third its original value near the elastic limit. As a result of this decrease in elastic modulus and nonlinearity, elastic deformability reaches 2.5% after cold working. Superelasticity is attributed to stress-induced martensitic transformations, although the large elastic deformation in Gum Metal is not accompanied by a phase transformation

16. Data-Driven Problems in Elasticity

Conti, S.; Müller, S.; Ortiz, M.

2018-01-01

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.

17. Diffraction by an immersed elastic wedge

Croisille, Jean-Pierre

1999-01-01

This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.

18. Linear algebra

Stoll, R R

1968-01-01

Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

19. Passive and active ventricular elastances of the left ventricle

Ng Eddie YK

2005-02-01

Full Text Available Abstract Background Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep and active (Ea elastance. By incorporating this concept in left ventricular (LV models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. Methods and Results Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as: ; Epis represented as: . Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. Conclusions Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea can be used to characterize the ventricle's contractile state, while passive elastance (Ep can represent a measure of resistance-to-filling.

20. Linear programming

Solow, Daniel

2014-01-01

This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

1. Linear algebra

Berberian, Sterling K

2014-01-01

Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

2. LINEAR ACCELERATOR

Christofilos, N.C.; Polk, I.J.

1959-02-17

Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.

3. Matrix inequalities

Zhan, Xingzhi

2002-01-01

The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

4. Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour

Ottosen, N. Saabye; Gunneskov, O.

1985-01-01

to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...

5. Form finding in elastic gridshells

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

6. Elastic limit and microplastic response of hardened steels

Zaccone, M.A. (McDonnell Douglas Aerospace Co., St. Louis, MO (United States)); Krauss, G. (Colorado School of Mines, Golden, CO (United States). Dept. of Metallurgical and Materials Engineering)

1993-10-01

Tempered martensite-retained austenite microstructures were produced by direct quenching a series of 41XX medium carbon steels, direct quenching and reheating a series of five 0.8C-Cr-Ni-Mo steels and intercritically austenitizing at various temperatures, and quenching a SAE 52100 steel. All specimens were tempered either at 150 C or at 200 C. Specimens were subjected to compression and tension testing in the microstrain regime to determine the elastic limits and microplastic response of the microstructures. The retained austenite and matrix carbon content of the intercritically austenized specimens were measured by X-ray diffraction and Mossbauer spectroscopy. The elastic limit of the microstructures decreases with increasing amounts of retained austenite. Refining of the austenite distribution increases the elastic limit. Low elastic limits are mainly due to low flow stresses in the austenite and not internal stresses. The elastic limit correlates with the largest austenite free-mean path by a Hall-Petch type equation. The elastic limit increases with decreasing intercritical austenitizing temperature in the SAE 52100 due to a lower carbon content in the matrix reducing the retained austenite levels and retained carbides that refine grain size and, therefore, the austenite distribution in quenched specimens. In the microplastic region, the strain is accommodated by successively smaller austenite regions until the flow strength matches that of the martensite. Reheating and quenching refines the microstructure and renders the austenite unstable in the microplastic regime, causing transformation of the austenite to martensite by a strain-induced mechanism. The transformation of austenite to martensite occurs by a stress-assisted mechanism in medium carbon steels. The low elastic limits in medium carbon steels were due to the inability of the strain from the stress-assisted transformation to balance the plastic strain accumulated in the austenite.

7. Modeling of a light elastic beam by a system of rigid bodies

Šalinić Slaviša

2004-01-01

Full Text Available This paper has shown that a light elastic beam, in the case of small elastic deformations, can be modeled by a kinematic chain without branching composed of rigid bodies which are connected by passive revolute or prismatic joints with corresponding springs in them. Elastic properties of the beam are modeled by the springs introduced. The potential energy of the elastic beam is expressed as a function of components of the vector of elastic displacement and the vector of elastic rotation calculated for the elastic centre of the beam, which results in the diagonal stiffness matrix of the beam. As the potential energy of the introduced system of bodies with springs is expressed in the function of relative joint displacements, the diagonal stiffness matrix is obtained. In addition, these two stiffness matrices are equal. The modeling process has been demonstrated on the example of an elastic beam rotating about a fixed vertical axis, with a rigid body whose mass is considerably larger than the beam mass fixed to its free end. Differential equations of motion have been formed for this mechanical system. The modeling technique described here aims at expanding of usage of well developed methods of dynamics of systems of rigid bodies to the analysis of systems with elastic bodies. .

8. Elastic wave excitation in centrosymmetric strontium titanate crystals

Yushin, N.K.; Sotnikov, A.V.

1980-01-01

The main experimental dependencies are measured and the excitation mechanism of elastic waves in centrosymmetric crystals is established. The surface generation of three-dimensional elastic waves of the 30 MHz frequency in strontium titanate crystals is observed and studied. Elastic wave excitation is observed in the 4 350 K temperature range. The efficiency of hysteresis excitation depends on the external electric field. The effect of light irradiation on the amplitude of excited elastic waves is observed. It is shown that escitation is connected with linearization of electrostriction by the constant electric field appearing in a near-surface crystal layer due to phenomena in the Schottky barrier and appearance of electretic near-electrode layers

9. Elastic unitarity of direct channel and Froissart saturation

Glushko, N.I.; Kobylinsky, N.A.

1982-01-01

The condition of elastic unitarity for direct channel continued analytically to high-energy range reveals a fast (upper the Froissart bound) rise of the amplitude between elastic and inelastic cuts in the case when the hadron scattering picture approaches the black disc limit. This fact is assumed as a basis for a new model of generating the Froissart saturation which describes well the main characteristics of NN, PIN and KN scattering. The model suggested is also compared witn the U-matrix approach

10. Elastic properties of rigid fiber-reinforced composites

Chen, J.; Thorpe, M. F.; Davis, L. C.

1995-05-01

We study the elastic properties of rigid fiber-reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson's ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital-image-based method and a finite element analysis to perform computer simulations which confirm our analytical predictions.

11. Elastic scattering of positronium: Application of the confined variational method

Zhang, Junyi

2012-08-01

We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.

12. Elastic scattering of positronium: Application of the confined variational method

Zhang, Junyi; Yan, Zong-Chao; Schwingenschlö gl, Udo

2012-01-01

We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.

13. Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

Mikhailov, SE

2006-01-01

Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

14. Mathematical foundations of elasticity

Marsden, Jerrold E

1994-01-01

This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con

15. Elastic and viscoplastic properties

Lebensohn, R.A.

2015-01-01

In this chapter, we review crystal elasticity and plasticity-based self-consistent theories and apply them to the determination of the effective response of polycrystalline aggregates. These mean-field formulations, which enable the prediction of the mechanical behaviour of polycrystalline aggregates based on the heterogeneous and/or directional properties of their constituent single crystal grains and phases, are ideal tools to establish relationships between microstructure and properties of these materials, ubiquitous among fuels and structural materials for nuclear systems. (author)

16. SIMULATION OFTHERMO-ELASTICS PROPERTIESOFTHERMALBARRIERCOATINGS

A.M.Ferouani M. Ferouani

2015-07-01

Full Text Available Thermal barrier coatings are used to protect different parts in compressors and turbines from heat. They are generally composed of two layers, one metallic layer providing resistance to heat corrosion and oxidation, and one thermally insulating ceramic layer. Two different techniques are industrially used. Plasma spray results in a lamellar structure granting a low thermal conductivity, but with a low thermal expansion compliance. Electron Beam Physical Vapour Deposition generates a columnar structure allowing a better accommodation of the thermal expansion stresses, entailing improved lifetime of the coating, but with a higher thermal conductivity. The aim of the paper presented here is to develop a procedure of analysis based on the micro structural observation for the prediction of the properties of new coatings in court of industrial development and to predict the effect of the posterior thermal treatment on the properties of the coatings carried out. For a given coating, one has to calculate linear elasticity and its evolution with the temperature as well as thermal expansion, aiming at predicting different parameters related to the in service deterioration.

17. Further linear algebra

Blyth, T S

2002-01-01

Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the ex...

18. Matrix Encryption Scheme

Abdelhakim Chillali

2017-05-01

Full Text Available In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. In this work, we proposed a new problem applicable to the public key cryptography, based on the Matrices, called “Matrix discrete logarithm problem”, it uses certain elements formed by matrices whose coefficients are elements in a finite field. We have constructed an abelian group and, for the cryptographic part in this unreliable group, we then perform the computation corresponding to the algebraic equations, Returning the encrypted result to a receiver. Upon receipt of the result, the receiver can retrieve the sender’s clear message by performing the inverse calculation.

19. Green's matrix for a second-order self-adjoint matrix differential operator

Sisman, Tahsin Cagri; Tekin, Bayram

2010-01-01

A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

20. Mathematical methods in elasticity imaging

Ammari, Habib; Garnier, Josselin; Kang, Hyeonbae; Lee, Hyundae; Wahab, Abdul

2015-01-01

This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic...

1. Elastic-plastic deformation of fiber composites with a tetragonal structure

Makarova, E.IU.; Svistkova, L.A. (Permskii Politekhnicheskii Institut, Perm (USSR))

1991-02-01

Results of numerical solutions are presented for elastic-plastic problems concerning arbitrary loading of unidirectional composites in the transverse plane. The nucleation and evolution of microplastic zones in the matrix and the effect of this process on the macroscopic characteristics of the composite are discussed. Attention is also given to the effect of the fiber shape on the elastic-plastic deformation of the matrix and to deformation paths realized in simple microdeformation processes. The discussion is illustrated by results obtained for a composite consisting of a VT1-0 titanium alloy matrix reinforced by Ti-Mo fibers.

2. Linear regression

Olive, David J

2017-01-01

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

3. Linear Colliders

Alcaraz, J.

2001-01-01

After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs

4. Linear algebra

Edwards, Harold M

1995-01-01

In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

5. Elastic emission polishing

Loewenthal, M.; Loseke, K.; Dow, T.A.; Scattergood, R.O.

1988-12-01

Elastic emission polishing, also called elastic emission machining (EEM), is a process where a stream of abrasive slurry is used to remove material from a substrate and produce damage free surfaces with controlled surface form. It is a noncontacting method utilizing a thick elasto-hydrodynamic film formed between a soft rotating ball and the workpiece to control the flow of the abrasive. An apparatus was built in the Center, which consists of a stationary spindle, a two-axis table for the workpiece, and a pump to circulate the working fluid. The process is controlled by a programmable computer numerical controller (CNC), which presently can operate the spindle speed and movement of the workpiece in one axis only. This apparatus has been used to determine material removal rates on different material samples as a function of time, utilizing zirconium oxide (ZrO{sub 2}) particles suspended in distilled water as the working fluid. By continuing a study of removal rates the process should become predictable, and thus create a new, effective, yet simple tool for ultra-precision mechanical machining of surfaces.

6. Heavy ion elastic scatterings

Mermaz, M.C.

1984-01-01

Diffraction and refraction play an important role in particle elastic scattering. The optical model treats correctly and simultaneously both phenomena but without disentangling them. Semi-classical discussions in terms of trajectories emphasize the refractive aspect due to the real part of the optical potential. The separation due to to R.C. Fuller of the quantal cross section into two components coming from opposite side of the target nucleus allows to understand better the refractive phenomenon and the origin of the observed oscillations in the elastic scattering angular distributions. We shall see that the real part of the potential is responsible of a Coulomb and a nuclear rainbow which allows to determine better the nuclear potential in the interior region near the nuclear surface since the volume absorption eliminates any effect of the real part of the potential for the internal partial scattering waves. Resonance phenomena seen in heavy ion scattering will be discussed in terms of optical model potential and Regge pole analysis. Compound nucleus resonances or quasi-molecular states can be indeed the more correct and fundamental alternative

7. Design guidance for elastic followup

Naugle, F.V.

1983-01-01

The basic mechanism of elastic followup is discussed in relation to piping design. It is shown how mechanistic insight gained from solutions for a two-bar problem can be used to identify dominant design parameters and to determine appropriate modifications where elastic followup is a potential problem. It is generally recognized that quantitative criteria are needed for elastic followup in the creep range where badly unbalanced lines can pose potential problems. Approaches for criteria development are discussed

8. Income Elasticity of Environmental Amenities

Daniel Miles; Andrés Pereyra; Máximo Rossi

2000-01-01

In this paper we are concerned with the estimation of income elasticities of environmental amenities. The novelty is the application of econometric methods that take into account the problem of measurement errors when estimating these elasticities, which are common in microeconomic data and are not usually considered in the applied literature related with this issue. Our aim is to discuss whether the measurement error has signi…cant e¤ects on the elasticities. Data from the Expenditure Budget...

9. A meta-analysis of the price elasticity of gasoline demand. A SUR approach

Brons, M.R.E.; Nijkamp, P.; Pels, E.; Rietveld, P.

2008-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

10. A Meta-analysis of the Price Elasticity of Gasoline Demand. A System of Equations Approach

Brons, Martijn; Nijkamp, Peter; Pels, Eric; Rietveld, Piet

2006-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

11. Density functional calculations of elastic properties of portlandite, Ca(OH)(2)

Laugesen, Jakob Lund

2005-01-01

The elastic constants of portlandite, Ca(OH)(2), are calculated by use of density functional theory. A lattice optimization of an infinite (periodic boundary conditions) lattice is performed on which strains are applied. The elastic constants are extracted by minimizing Hooke's law of linear...

12. Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

2017-01-01

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

13. Two-velocity elasticity theory and facet growth

Andreev, A. F.; Melnikovsky, L. A.

2002-01-01

We explain the linear growth of smooth solid helium facets by the presence of lattice point defects. To implement this task, the framework of very general two-velocity elasticity theory equations is developed. Boundary conditions for these equations for various surface types are derived. We also suggest additional experiments to justify the concept.

14. On Love's approximation for fluid-filled elastic tubes

Caroli, E.; Mainardi, F.

1980-01-01

A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)

15. Effect of interface/surface stress on the elastic wave band structure of two-dimensional phononic crystals

Liu, Wei; Chen, Jiwei; Liu, Yongquan; Su, Xianyue

2012-01-01

In the present Letter, the multiple scattering theory (MST) for calculating the elastic wave band structure of two-dimensional phononic crystals (PCs) is extended to include the interface/surface stress effect at the nanoscale. The interface/surface elasticity theory is employed to describe the nonclassical boundary conditions at the interface/surface and the elastic Mie scattering matrix embodying the interface/surface stress effect is derived. Using this extended MST, the authors investigate the interface/surface stress effect on the elastic wave band structure of two-dimensional PCs, which is demonstrated to be significant when the characteristic size reduces to nanometers. -- Highlights: ► Multiple scattering theory including the interface/surface stress effect. ► Interface/surface elasticity theory to describe the nonclassical boundary conditions. ► Elastic Mie scattering matrix embodying the interface/surface stress effect. ► Interface/surface stress effect would be significant at the nanoscale.

16. Analysis of elastic interactions of hadrons at high energies

Yuldashev, B.S.; Fazilova, Z.F.; Ismatov, E.I.; Kurmanbai, M.S.; Ajniyazova, G.T.; Tskhay, K.V.; Medeuova, A.B.

2004-01-01

Study of elastic interactions of hadrons at high energies if of great interest due to the fact that the amplitude of this process is the simplest, and at the same time, it is a fundamental object for theoretical and experimental researches. Study of this process allows one to have a quantitative check of various theories and models, and to make a critical selection. By using of fundamental property of theory - unitarity condition of scattering matrix - elastic scattering can be connected with inelastic reaction. Based on S-channel unitarity condition expressing elastic amplitude via inelastic overlapping function, to study the latter, as well as to describe the experimentally measured characteristics of hadron-nucleon interactions at high-energies, as well as for results prediction. By using experimental data on differential cross-section of elastic scattering of hadrons at various energies and by theoretical information on ratio of a real part and an imaginary part of scattering amplitude δ(t) the t-dependence of inelastic and elastic overlapping functions is studied. Influence of a zigzag form of differential cross-section of elastic pp(p) scattering on profile function and inelastic overlapping function to violation of geometric scaling was studied. In frames of the scaling the general expressions for s- and t-dependences of inelastic overlapping function are derived. Comparison of this function in three elastic scattering models was carried out. It was demonstrated that one would need to assume that hadrons become blacker at central part in order to correctly describe experimental angular distribution data. Dependence of differential cross-section on transfer momentum square for elastic hadrons scattering at energies of ISR and SPS in the model of inelastic overlapping function is studied. (author)

17. Analysis of elastic interactions of hadrons at high energies

Fazylov, M.I.; Yuldashev, B.S.; Azhniyazova, G.T.; Ismatov, E.I.; Sartbay, T.; Kurmanbay, M.S.; Tskhay, K.V.

2004-01-01

Full text: Study of elastic interactions of hadrons at high energies if of great interest due to the fact that the amplitude of this process is the simplest, and at the same time, it is a fundamental object for theoretical and experimental researches. Study of this process allows one to have a quantitative check of various theories and models, and to make a critical selection. By using of fundamental property of theory - unitarity condition of scattering matrix - elastic scattering can be connected with inelastic reaction. Based on S-channel unitarity condition expressing elastic amplitude via inelastic overlapping function, to study the latter, as well as to describe the experimentally measured characteristics of hadron-nucleon interactions at high-energies, as well as for results prediction. By using experimental data on differential cross-section of elastic scattering of hadrons at various energies and by theoretical information on ratio of a real part and an imaginary part of scattering amplitude δ(t) the t-dependence of inelastic and elastic overlapping functions is studied. Influence of a zigzag form of differential cross-section of elastic pp(p) scattering on profile function and inelastic overlapping function to violation of geometric scaling was studied. In frames of the scaling the general expressions for s- and t-dependences of inelastic overlapping function are derived. Comparison of this function in three elastic scattering models was carried out. It was demonstrated that one would need to assume that hadrons become blacker at central part in order to correctly describe experimental angular distribution data. Dependence of differential cross-section on transfer momentum square for elastic hadrons scattering at energies of ISR and SPS in the model of inelastic overlapping function is studied

18. Identification of elastic properties of composite plate

Kovalovs, A; Rucevskis, S

2011-01-01

Composite laminates are used extensively in the aerospace industry, especially for the fabrication of high-performance structures. The determination of stiffness parameters for complex materials, such as fibre-reinforced composites, is much more complicated than for isotropic materials. A conventional way is testing the coupon specimens, which are manufactured by technology similar to that used for the real, large structures. When such a method is used, the question arises of whether the material properties obtained from the coupon tests are the same as those in the large structure. Therefore, the determination of actual material properties for composite laminates using non-destructive evaluation techniques has been widely investigated. A number of various non-destructive evaluation techniques have been proposed for determining the material properties of composite laminates. In the present study, attention is focused on the identification of the elastic properties of laminated plate using vibration test data. The problem associated with vibration testing is converting the measured modal frequencies to elastic constants. A standard method for solving this problem is the use of a numerical-experimental model and optimization techniques. The identification functional represents the gap between the numerical model response and the experimental one. This gap should be minimized, taking into account the side constraints on the design variables (elastic constants). The minimization problem is solved by using non-linear mathematical programming techniques and sensitivity analysis. The results obtained were verified by comparing the experimentally measured eigenfrequencies with the numerical ones obtained by FEM at the point of optima

19. Impact loads on beams on elastic foundations