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.
The Simulation and Correction to the Brain Deformation Based on the Linear Elastic Model in IGS
Institute of Scientific and Technical Information of China (English)
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.
Linear models of income patterns in consumer demand for foods and evaluation of its elasticity
Directory of Open Access Journals (Sweden)
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.
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...
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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.
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...
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
International Nuclear Information System (INIS)
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.
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.
DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM
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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.
An enhanced finite volume method to model 2D linear elastic structures
CSIR Research Space (South Africa)
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...
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.
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.
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.
Directory of Open Access Journals (Sweden)
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.
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
Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses
International Nuclear Information System (INIS)
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.)
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
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.
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.
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.
International Nuclear Information System (INIS)
Streit, R.D.
1981-01-01
The failure evaluation of Pressurized Water Reactor (PWR) primary coolant loop pipe is often based on a plastic limit load criterion; i.e., failure occurs when the stress on the pipe section exceeds the material flow stress. However, in addition the piping system must be safe against crack propagation at stresses less than those leading to plastic instability. In this paper, elastic, elastic-plastic, and fully-plastic failure models are evaluated, and the requirements for piping integrity based on these models are compared. The model yielding the 'more' critical criteria for the given geometry and loading conditions defines the appropriate failure criterion. The pipe geometry and loading used in this study was choosen based on an evaluation of a guillotine break in a PWR primary coolant loop. It is assumed that the piping may contain cracks. Since a deep circumferential crack, can lead to a guillotine pipe break without prior leaking and thus without warning it is the focus of the failure model comparison study. The hot leg pipe, a 29 in. I.D. by 2.5 in. wall thickness stainless pipe, was modeled in this investigation. Cracks up to 90% through the wall were considered. The loads considered in this evaluation result from the internal pressure, dead weight, and seismic stresses. For the case considered, the internal pressure contributes the most to the failure loading. The maximum moment stress due to the dead weight and seismic moments are simply added to the pressure stress. Thus, with the circumferential crack geometry and uniform pressure stress, the problem is axisymmetric. It is analyzed using NIKE2D--an implicit, finite deformation, finite element code for analyzing two-dimensional elastic-plastic problems. (orig./GL)
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.
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.
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.
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.
A Linear Theory for Pretwisted Elastic Beams
DEFF Research Database (Denmark)
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...
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.
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.
On the use of elastic-plastic material characteristics for linear-elastic component assessments
International Nuclear Information System (INIS)
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)
Vectorized Matlab Codes for Linear Two-Dimensional Elasticity
Directory of Open Access Journals (Sweden)
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.
On the hyperbolicity condition in linear elasticity
Directory of Open Access Journals (Sweden)
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.
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
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.
Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass
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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.
Emergence of linear elasticity from the atomistic description of matter
Energy Technology Data Exchange (ETDEWEB)
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.
Emergence of linear elasticity from the atomistic description of matter
International Nuclear Information System (INIS)
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.
Non-linear elastic thermal stress analysis with phase changes
International Nuclear Information System (INIS)
Amada, S.; Yang, W.H.
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.)
Directory of Open Access Journals (Sweden)
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Modeling Pseudo-elastic Behavior of Springback
International Nuclear Information System (INIS)
Xia, Z. Cedric
2005-01-01
One of the principal foundations of mathematical theory of conventional plasticity for rate-independent metals is that there exists a well-defined yield surface in stress space for any material point under deformation. A material point can undergo further plastic deformation if the applied stresses are beyond current yield surface which is generally referred as 'plastic loading'. On the other hand, if the applied stress state falls within or on the yield surface, the metal will deform elastically only and is said to be undergoing 'elastic unloading'. Although it has been always recognized throughout the history of development of plasticity theory that there is indeed inelastic deformation accompanying elastic unloading, which leads to metal's hysteresis behavior, its effects were thought to be negligible and were largely ignored in the mathematical treatment.Recently there have been renewed interests in the study of unloading behavior of sheet metals upon large plastic deformation and its implications on springback prediction. Springback is essentially an elastic recovery process of a formed sheet metal blank when it is released from the forming dies. Its magnitude depends on the stress states and compliances of the deformed sheet metal if no further plastic loading occurs during the relaxation process. Therefore the accurate determination of material compliances during springback and its effective incorporation into simulation software are important aspects for springback calculation. Some of the studies suggest that the unloading curve might deviate from linearity, and suggestions were made that a reduced elastic modulus be used for springback simulation.The aim of this study is NOT to take a position on the debate of whether elastic moduli are changed during sheet metal forming process. Instead we propose an approach of modeling observed psuedoelastic behavior within the context of mathematical theory of plasticity, where elastic moduli are treated to be
Modeling elastic anisotropy in strained heteroepitaxy.
Dixit, Gopal Krishna; Ranganathan, Madhav
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.
Modeling elastic anisotropy in strained heteroepitaxy
Krishna Dixit, Gopal; Ranganathan, Madhav
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.
Remarks on orthotropic elastic models applied to wood
Directory of Open Access Journals (Sweden)
Nilson Tadeu Mascia
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.
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.
A reexamination of some puzzling results in linearized elasticity
Indian Academy of Sciences (India)
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 ...
Faraway, Julian J
2014-01-01
A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition.New to the Second EditionReorganiz
Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity
International Nuclear Information System (INIS)
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
Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium
International Nuclear Information System (INIS)
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
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.
Foundations of linear and generalized linear models
Agresti, Alan
2015-01-01
A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,
DEFF Research Database (Denmark)
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four of these cri......Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....
Extreme non-linear elasticity and transformation optics
DEFF Research Database (Denmark)
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...
A Membrane Model from Implicit Elasticity Theory
Freed, A. D.; Liao, J.; Einstein, D. R.
2014-01-01
A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079
DEFF Research Database (Denmark)
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....... of these criteria are widely used ones, while the remaining four are ones derived from the H-principle of mathematical modeling. Many examples from practice show that the criteria derived from the H-principle function better than the known and popular criteria for the number of components. We shall briefly review...
Modelling the elastic properties of cellulose nanopaper
DEFF Research Database (Denmark)
Mao, Rui; Goutianos, Stergios; Tu, Wei
2017-01-01
The elastic modulus of cellulose nanopaper was predicted using a two-dimensional (2D) micromechanical fibrous network model. The elastic modulus predicted by the network model was 12 GPa, which is well within the range of experimental data for cellulose nanopapers. The stress state in the network...
Non linear viscoelastic models
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2011-01-01
Viscoelastic eects are often present in loudspeaker suspensions, this can be seen in the displacement transfer function which often shows a frequency dependent value below the resonance frequency. In this paper nonlinear versions of the standard linear solid model (SLS) are investigated....... The simulations show that the nonlinear version of the Maxwell SLS model can result in a time dependent small signal stiness while the Kelvin Voight version does not....
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.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
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.
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.
A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.
International Nuclear Information System (INIS)
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
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.
Monahan, John F
2008-01-01
Preface Examples of the General Linear Model Introduction One-Sample Problem Simple Linear Regression Multiple Regression One-Way ANOVA First Discussion The Two-Way Nested Model Two-Way Crossed Model Analysis of Covariance Autoregression Discussion The Linear Least Squares Problem The Normal Equations The Geometry of Least Squares Reparameterization Gram-Schmidt Orthonormalization Estimability and Least Squares Estimators Assumptions for the Linear Mean Model Confounding, Identifiability, and Estimability Estimability and Least Squares Estimators F
Directory of Open Access Journals (Sweden)
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.
CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method
International Nuclear Information System (INIS)
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
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.
CONCERNING THE ELASTIC ORTHOTROPIC MODEL APPLIED TO WOOD ELASTIC PROPERTIES
Tadeu Mascia,Nilson
2003-01-01
Among the construction materials, wood reveals an orthotropic pattern, because of unique characteristics in its internal structure with three axes of wood biological directions (longitudinal, tangential and radial). elastic symmetry: longitudinal, tangential and radial, reveals an orthotropic pattern. The effect of grain angle orientation onin the elastic modulus constitutes the fundamental cause forof wood anisotropy. It is responsible for the greatest changes in the values of the constituti...
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.
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.
Campagnoli, Patrizia; Petris, Giovanni
2009-01-01
State space models have gained tremendous popularity in as disparate fields as engineering, economics, genetics and ecology. Introducing general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. It illustrates the fundamental steps needed to use dynamic linear models in practice, using R package.
Twist and Stretch of Helices Explained via the Kirchhoff-Love Rod Model of Elastic Filaments
Đuričković, Bojan; Goriely, Alain; Maddocks, John H.
2013-01-01
that within the context of the classic Kirchhoff-Love rod model of elastic filaments, both behaviors are possible, depending on the precise constitutive relations of the polymer. More generally, our analysis provides an effective linear response theory
Introduction to generalized linear models
Dobson, Annette J
2008-01-01
Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...
DEFF Research Database (Denmark)
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...
(Non) linear regression modelling
Cizek, P.; Gentle, J.E.; Hardle, W.K.; Mori, Y.
2012-01-01
We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1,…,Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1,…,Xp),p ∈ N, which explain or
Parameter Optimisation for the Behaviour of Elastic Models over Time
DEFF Research Database (Denmark)
Mosegaard, Jesper
2004-01-01
Optimisation of parameters for elastic models is essential for comparison or finding equivalent behaviour of elastic models when parameters cannot simply be transferred or converted. This is the case with a large range of commonly used elastic models. In this paper we present a general method tha...
Torsion of cracked nanorods using a nonlocal elasticity model
International Nuclear Information System (INIS)
Loya, J A; Aranda-Ruiz, J; Fernández-Sáez, J
2014-01-01
This paper presents a nonlocal cracked-rod model from which we have analysed the torsional vibrations of a carbon nanotube with a circumferential crack. Several types of boundary conditions, including the consideration of a buckyball at the end of the nanotube, have been studied. The nonlocal Eringen elasticity theory is used to formulate the problem. The cracked rod is modelled by dividing the cracked element into two segments connected by a torsional linear spring whose stiffness is related to the crack severity. The effect of the nonlocal small-scale parameter, crack severity, cracked section position, different boundary conditions and attached mass are examined in this work. (paper)
Compact solitary waves in linearly elastic chains with non-smooth on-site potential
Energy Technology Data Exchange (ETDEWEB)
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.
Four-dimensional Hooke's law can encompass linear elasticity and inertia
International Nuclear Information System (INIS)
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
Explorative methods in linear models
DEFF Research Database (Denmark)
Høskuldsson, Agnar
2004-01-01
The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....
Stepanova, Larisa; Bronnikov, Sergej
2018-03-01
The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. Two fracture criteria of traditional linear fracture mechanics (maximum tangential stress and minimum strain energy density criteria) are used. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.
Generalized, Linear, and Mixed Models
McCulloch, Charles E; Neuhaus, John M
2011-01-01
An accessible and self-contained introduction to statistical models-now in a modernized new editionGeneralized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed m
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.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
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.
A non-linear elastic constitutive framework for replicating plastic deformation in solids.
Energy Technology Data Exchange (ETDEWEB)
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.
Sparse Linear Identifiable Multivariate Modeling
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2011-01-01
and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable......In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully...
Czech Academy of Sciences Publication Activity Database
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
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Energy Technology Data Exchange (ETDEWEB)
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.
Macroscopic modelization of the cloud elasticity*
Directory of Open Access Journals (Sweden)
Etancelin J.-M.
2013-12-01
Full Text Available In order to achieve its promise of providing information technologies (IT on demand, cloud computing needs to rely on a mathematical model capable of directing IT on and off according to a demand pattern to provide a true elasticity. This article provides a first method to reach this goal using a “fluid type” partial differential equations model. On the one hand it examines the question of service time optimization for the simultaneous satisfaction of the cloud consumer and provider. On the other hand it tries to model a way to deliver resources according to the real time capacity of the cloud that depends on parameters such as burst requests and application timeouts. All these questions are illustrated via an implicit finite volume scheme.
Parameterized Linear Longitudinal Airship Model
Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph
2010-01-01
A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics
Elastic models application for thorax image registration
International Nuclear Information System (INIS)
Correa Prado, Lorena S; Diaz, E Andres Valdez; Romo, Raul
2007-01-01
This work consist of the implementation and evaluation of elastic alignment algorithms of biomedical images, which were taken at thorax level and simulated with the 4D NCAT digital phantom. Radial Basis Functions spatial transformations (RBF), a kind of spline, which allows carrying out not only global rigid deformations but also local elastic ones were applied, using a point-matching method. The applied functions were: Thin Plate Spline (TPS), Multiquadric (MQ) Gaussian and B-Spline, which were evaluated and compared by means of calculating the Target Registration Error and similarity measures between the registered images (the squared sum of intensity differences (SSD) and correlation coefficient (CC)). In order to value the user incurred error in the point-matching and segmentation tasks, two algorithms were also designed that calculate the Fiduciary Localization Error. TPS and MQ were demonstrated to have better performance than the others. It was proved RBF represent an adequate model for approximating the thorax deformable behaviour. Validation algorithms showed the user error was not significant
Towards an elastic model of wurtzite AlN nanowires
International Nuclear Information System (INIS)
Mitrushchenkov, A; Chambaud, G; Yvonnet, J; He, Q-C
2010-01-01
Starting with ab initio calculations of AlN wurtzite [0001] nanowires with diameters up to 4 nm, a finite element method is developed to deal with larger nanostructures/nanoparticles. The ab initio calculations show that the structure of the nanowires can be well represented by an internal part with AlN bulk elastic properties, and one atomic surface layer with its own elastic behavior. The proposed finite element method includes surface elements with their own elastic properties using surface elastic coefficients deduced from the ab initio calculations. The elastic properties obtained with the finite element model compare very well with those obtained with the full ab initio calculations.
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.
International Nuclear Information System (INIS)
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)
Decomposable log-linear models
DEFF Research Database (Denmark)
Eriksen, Poul Svante
can be characterized by a structured set of conditional independencies between some variables given some other variables. We term the new model class decomposable log-linear models, which is illustrated to be a much richer class than decomposable graphical models.It covers a wide range of non...... The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphicalmodels, which......-hierarchical models, models with structural zeroes, models described by quasi independence and models for level merging. Also, they have a very natural interpretation as they may be formulated by a structured set of conditional independencies between two events given some other event. In relation to contingency...
Linear and Generalized Linear Mixed Models and Their Applications
Jiang, Jiming
2007-01-01
This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested
The application of linear elastic fracture mechanics to thermally stressed welded components
International Nuclear Information System (INIS)
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)
International Nuclear Information System (INIS)
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
On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement
International Nuclear Information System (INIS)
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.
Elastic Network Model of a Nuclear Transport Complex
Ryan, Patrick; Liu, Wing K.; Lee, Dockjin; Seo, Sangjae; Kim, Young-Jin; Kim, Moon K.
2010-05-01
The structure of Kap95p was obtained from the Protein Data Bank (www.pdb.org) and analyzed RanGTP plays an important role in both nuclear protein import and export cycles. In the nucleus, RanGTP releases macromolecular cargoes from importins and conversely facilitates cargo binding to exportins. Although the crystal structure of the nuclear import complex formed by importin Kap95p and RanGTP was recently identified, its molecular mechanism still remains unclear. To understand the relationship between structure and function of a nuclear transport complex, a structure-based mechanical model of Kap95p:RanGTP complex is introduced. In this model, a protein structure is simply modeled as an elastic network in which a set of coarse-grained point masses are connected by linear springs representing biochemical interactions at atomic level. Harmonic normal mode analysis (NMA) and anharmonic elastic network interpolation (ENI) are performed to predict the modes of vibrations and a feasible pathway between locked and unlocked conformations of Kap95p, respectively. Simulation results imply that the binding of RanGTP to Kap95p induces the release of the cargo in the nucleus as well as prevents any new cargo from attaching to the Kap95p:RanGTP complex.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.
Folding models for elastic and inelastic scattering
International Nuclear Information System (INIS)
Satchler, G.R.
1982-01-01
The most widely used models are the optical model potential (OMP) for elastic scattering, and its generalization to non-spherical shapes, the deformed optical model potential (DOMP) for inelastic scattering. These models are simple and phenomenological; their parameters are adjusted so as to reproduce empirical data. Nonetheless, there are certain, not always well-defined, constraints to be imposed. The potential shapes and their parameter values must be reasonable and should vary in a smooth and systematic way with the masses of the colliding nuclei and their energy. One way of satisfying these constraints, without going back to a much more fundamental theory, is through the use of folding models. The basic justification for using potentials of the Woods-Saxon shape for nucleon-nucleus scattering, for example, is our knowledge that a nuclear density distribution is more-or-less constant in the nuclear interior with a diffuse surface. When this is folded with a short-range nucleon-nucleon interaction, the result is a similar shape with a more diffuse surface. Folding procedures allow us to incorporate many aspects of nuclear structure (although the nuclear size is one of the most important), as well as theoretical ideas about the effective interaction of two nucleons within nuclear matter. It also provides us with a means of linking information obtained from nuclear (hadronic) interactions with that from other sources, as well as correlating that from the use of different hadronic probes. Folding model potentials, single-folded potentials, and the double-folding model including applications to heavy-ion scattering are discussed
Multicollinearity in hierarchical linear models.
Yu, Han; Jiang, Shanhe; Land, Kenneth C
2015-09-01
This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model. Copyright © 2015 Elsevier Inc. All rights reserved.
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.
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.
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.
Modelling of the elastic behaviour of metallic powders
International Nuclear Information System (INIS)
Riera, M.D.; Prado, J.M.
1998-01-01
In this work the elastic behaviour of metal powders compacted to different densities is studied. The authors apply a model based on the experimental observation that the elastic volumetric strain and the hydrostatic component of the applied stress are exponentially related. While a complete analysis should include both the volumetric and deviatoric components of the elastic strain, we only present here the first one. (Author) 9 refs
International Nuclear Information System (INIS)
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
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
Energy Technology Data Exchange (ETDEWEB)
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.
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Multivariate covariance generalized linear models
DEFF Research Database (Denmark)
Bonat, W. H.; Jørgensen, Bent
2016-01-01
are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...
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
Proposed higher order continuum-based models for an elastic ...
African Journals Online (AJOL)
Three new variants of continuum-based models for an elastic subgrade are proposed. The subgrade is idealized as a homogenous, isotropic elastic layer of thickness H overlying a firm stratum. All components of the stress tensor in the subgrade are taken into account. Reasonable assumptions are made regarding the ...
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.
Unsteady Model for Transverse Fluid Elastic Instability of Heat Exchange Tube Bundle
Directory of Open Access Journals (Sweden)
Jun Liu
2014-01-01
Full Text Available From the viewpoint of practical application, based on the unsteady analytical model for transverse fluid elastic instability of tube array proposed by Yetisir and the linear attenuation function introduced by Li Ming, a new explicit model based on nonsteady state “streamtube” hypothesis is proposed and solved using complex number method. In the model, numerical integral is avoided and inappropriate aspects in Li Ming model are modified. Using the model, the fluid elastic instability analysis of a single flexible tube is made. The stability graphs for four typical types of tube array are plotted and contrasted with experimental results. It is found that the current explicit model is effective in the analysis of transverse fluid elastic instability of tube bundle.
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.
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...
International Nuclear Information System (INIS)
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
First-order system least squares for the pure traction problem in planar linear elasticity
Energy Technology Data Exchange (ETDEWEB)
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.
Nonabelian Gauged Linear Sigma Model
Institute of Scientific and Technical Information of China (English)
Yongbin RUAN
2017-01-01
The gauged linear sigma model (GLSM for short) is a 2d quantum field theory introduced by Witten twenty years ago.Since then,it has been investigated extensively in physics by Hori and others.Recently,an algebro-geometric theory (for both abelian and nonabelian GLSMs) was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications.The abelian GLSM was relatively better understood and is the focus of current mathematical investigation.In this article,the author would like to look over the horizon and consider the nonabelian GLSM.The nonabelian case possesses some new features unavailable to the abelian GLSM.To aid the future mathematical development,the author surveys some of the key problems inspired by physics in the nonabelian GLSM.
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.
Model-Based Reconstructive Elasticity Imaging Using Ultrasound
Directory of Open Access Journals (Sweden)
Salavat R. Aglyamov
2007-01-01
Full Text Available Elasticity imaging is a reconstructive imaging technique where tissue motion in response to mechanical excitation is measured using modern imaging systems, and the estimated displacements are then used to reconstruct the spatial distribution of Young's modulus. Here we present an ultrasound elasticity imaging method that utilizes the model-based technique for Young's modulus reconstruction. Based on the geometry of the imaged object, only one axial component of the strain tensor is used. The numerical implementation of the method is highly efficient because the reconstruction is based on an analytic solution of the forward elastic problem. The model-based approach is illustrated using two potential clinical applications: differentiation of liver hemangioma and staging of deep venous thrombosis. Overall, these studies demonstrate that model-based reconstructive elasticity imaging can be used in applications where the geometry of the object and the surrounding tissue is somewhat known and certain assumptions about the pathology can be made.
Nematic elastomers: from a microscopic model to macroscopic elasticity theory.
Xing, Xiangjun; Pfahl, Stephan; Mukhopadhyay, Swagatam; Goldbart, Paul M; Zippelius, Annette
2008-05-01
A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.
International Nuclear Information System (INIS)
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
CSIR Research Space (South Africa)
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...
A note on modeling road accident frequency: a flexible elasticity model.
Couto, António; Ferreira, Sara
2011-11-01
Count data models and their variants have been widely applied in accident modeling. The traditional log-linear function is used to represent the relationship between explanatory variables and the dependent variable (accident frequency). However, this function assumes constant elasticity for the estimation parameters, which is a limitation in the analysis of the effects of explanatory variables on accident risk. Although interaction effects between explanatory variables have been studied in the road safety context (where they are normally assessed by logistic regression), no one has yet examined the possibility of using a flexible function form allowing non-constant elasticity values. This paper seeks to explore the use of the translog function usually used in the economics context to allow the elasticity to vary with the values of other explanatory variables. Therefore, the objective of this study was to evaluate the application of the translog function to accident modeling and to compare the results with those of the traditional log-linear function negative binomial (NB) model. The results show that, in terms of goodness-of-fit statistics and residual analysis, the NB model with the translog function performs better than the traditional NB model. Additional evaluations in terms of predictive performance, hotspot identification and uncertainty associated with the estimated values were taken into account. Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. It is hoped that this novel accident modeling methodology will open the door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency. Copyright © 2011 Elsevier Ltd. All rights reserved.
Modelling of the Elasticity Modulus for Rock Using Genetic Expression Programming
Directory of Open Access Journals (Sweden)
Umit Atici
2016-01-01
Full Text Available In rock engineering projects, statically determined parameters are more reflective of actual load conditions than dynamic parameters. This study reports a new and efficient approach to the formulation of the static modulus of elasticity Es applying gene expression programming (GEP with nondestructive testing (NDT methods. The results obtained using GEP are compared with the results of multivariable linear regression analysis (MRA, univariate nonlinear regression analysis (URA, and the dynamic elasticity modulus (Ed. The GEP model was found to produce the most accurate calculation of Es. The proposed approach is a simple, nondestructive, and practical way to determine Es for anisotropic and heterogeneous rocks.
Effects of Host-rock Fracturing on Elastic-deformation Source Models of Volcano Deflation.
Holohan, Eoghan P; Sudhaus, Henriette; Walter, Thomas R; Schöpfer, Martin P J; Walsh, John J
2017-09-08
Volcanoes commonly inflate or deflate during episodes of unrest or eruption. Continuum mechanics models that assume linear elastic deformation of the Earth's crust are routinely used to invert the observed ground motions. The source(s) of deformation in such models are generally interpreted in terms of magma bodies or pathways, and thus form a basis for hazard assessment and mitigation. Using discontinuum mechanics models, we show how host-rock fracturing (i.e. non-elastic deformation) during drainage of a magma body can progressively change the shape and depth of an elastic-deformation source. We argue that this effect explains the marked spatio-temporal changes in source model attributes inferred for the March-April 2007 eruption of Piton de la Fournaise volcano, La Reunion. We find that pronounced deflation-related host-rock fracturing can: (1) yield inclined source model geometries for a horizontal magma body; (2) cause significant upward migration of an elastic-deformation source, leading to underestimation of the true magma body depth and potentially to a misinterpretation of ascending magma; and (3) at least partly explain underestimation by elastic-deformation sources of changes in sub-surface magma volume.
Multivariate generalized linear mixed models using R
Berridge, Damon Mark
2011-01-01
Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R. A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model...
International Nuclear Information System (INIS)
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)
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.
Nonlinear Modeling by Assembling Piecewise Linear Models
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Linear Logistic Test Modeling with R
Baghaei, Purya; Kubinger, Klaus D.
2015-01-01
The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…
A modal analysis of carbon nanotube using elastic network model
International Nuclear Information System (INIS)
Kim, Min Hyeok; Seo, Sang Jae; Lim, Byeong Soo; Choi, Jae Boong; Kim, Moon Ki; Liu, Wing Kam
2012-01-01
Although it is widely known that both size and chirality play significant roles in vibration behaviors of single walled carbon nanotubes (SWCNTs), there haven't been yet enough studies specifying the relationship between structure and vibration mode shape of SWCNTs. We have analyzed the chirality and length dependence of SWCNT by using normal mode analysis based elastic network model in which all interatomic interactions of the given SWCNTs structure are represented by a network of linear spring connections. As this method requires relatively short computation time compared to molecular dynamics simulation, we can efficiently analyze vibration behavior of SWCNTs. To ensure the relationship between SWCNT structure and its vibration mode shapes, we simulated more than one hundred SWCNTs having different types of chirality and length. Results indicated that the first two major mode shapes are bending and breathing. The minimum length of nanotube for maintaining the bending mode does not depend on chirality but on its diameter. Our simulations pointed out that there is a critical aspect ratio between diameter and length to determine vibration mode shapes, and it can be empirically formulated as a function of nanotube length and diameter. Therefore, uniformity control is the most important premise in order to utilize vibration features of SWCNTs. It is also expected that the obtained vibration aspect will play an important role in designing nanotube based devices such as resonators and sensors more accurately
Core seismic behaviour: linear and non-linear models
International Nuclear Information System (INIS)
Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.
1981-08-01
The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here
Simulating an elastic bipedal robot based on musculoskeletal modeling
Bortoletto, Roberto; Sartori, Massimo; He, Fuben; Pagello, Enrico
2012-01-01
Many of the processes involved into the synthesis of human motion have much in common with problems found in robotics research. This paper describes the modeling and the simulation of a novel bipedal robot based on series elastic actuators [1]. The robot model takes in- spiration from the human
Elastic properties of synthetic materials for soft tissue modeling
International Nuclear Information System (INIS)
Mansy, H A; Grahe, J R; Sandler, R H
2008-01-01
Mechanical models of soft tissue are useful for studying vibro-acoustic phenomena. They may be used for validating mathematical models and for testing new equipment and techniques. The objective of this study was to measure density and visco-elastic properties of synthetic materials that can be used to build such models. Samples of nine different materials were tested under dynamic (0.5 Hz) compressive loading conditions. The modulus of elasticity of the materials was varied, whenever possible, by adding a softener during manufacturing. The modulus was measured over a nine month period to quantify the effect of ageing and softener loss on material properties. Results showed that a wide range of the compression elasticity modulus (10 to 1400 kPa) and phase (3.5 0 -16.7 0 ) between stress and strain were possible. Some materials tended to exude softener over time, resulting in a weight loss and elastic properties change. While the weight loss under normal conditions was minimal in all materials (<3% over nine months), loss under accelerated weight-loss conditions can reach 59%. In the latter case an elasticity modulus increase of up to 500% was measured. Key advantages and limitations of candidate materials were identified and discussed
Composite Linear Models | Division of Cancer Prevention
By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty
Energy Technology Data Exchange (ETDEWEB)
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
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.
Directory of Open Access Journals (Sweden)
Yang Yu
2013-01-01
Full Text Available The structural scheme of mechanical elastic energy storage (MEES system served by permanent magnet synchronous motor (PMSM and bidirectional converters is designed. The aim of the research is to model and control the complex electromechanical system. The mechanical device of the complex system is considered as a node in generalized coordinate system, the terse nonlinear dynamic model of electromechanical coupling for the electromechanical system is constructed through Lagrange-Maxwell energy method, and the detailed deduction of the mathematical model is presented in the paper. The theory of direct feedback linearization (DFL is applied to decouple the nonlinear dynamic model and convert the developed model from nonlinear to linear. The optimal control theory is utilized to accomplish speed tracking control for the linearized system. The simulation results in three different cases show that the proposed nonlinear dynamic model of MEES system is correct; the designed algorithm has a better control performance in contrast with the conventional PI control.
Thermodynamic model for the elastic form factor in diffraction scattering of protons
International Nuclear Information System (INIS)
Grashin, A.F.; Evstratenko, A.S.; Lepeshkin, M.V.
1988-01-01
An explicit expression is obtained for the differential pp(p-bar)-scattering cross section in the diffraction-cone region by employing the thermodynamic model for the elastic form factor previously proposed in Ref. 4. Data for the energy region 16.3≤(s)/sup 1/2/ ≤546 GeV have been analyzed and significant deviations have been discovered from the commonly used approximations in the form of linear or quadratic exponentials
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Actuarial statistics with generalized linear mixed models
Antonio, K.; Beirlant, J.
2007-01-01
Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics
On model-independent analyses of elastic hadron scattering
International Nuclear Information System (INIS)
Avila, R.F.; Campos, S.D.; Menon, M.J.; Montanha, J.
2007-01-01
By means of an almost model-independent parametrization for the elastic hadron-hadron amplitude, as a function of the energy and the momentum transfer, we obtain good descriptions of the physical quantities that characterize elastic proton-proton and antiproton-proton scattering (total cross section, r parameter and differential cross section). The parametrization is inferred on empirical grounds and selected according to high energy theorems and limits from axiomatic quantum field theory. Based on the predictive character of the approach we present predictions for the above physical quantities at the Brookhaven RHIC, Fermilab Tevatron and CERN LHC energies. (author)
Modeling dynamic acousto-elastic testing experiments: validation and perspectives.
Gliozzi, A S; Scalerandi, M
2014-10-01
Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.
Elastic-plastic constitutive modeling of concrete
International Nuclear Information System (INIS)
Takahashi, Y.
1983-03-01
The need to understand concrete behavior under high temperatures in the nuclear industry has become rather accute. For this purpose, a constitutive model of concrete especially developed for this severe environment is indispensable. This report reviews the presently available constitutive models of concrete at standard-temperature conditions and considers their advantages and drawbacks. A rather simple but effective approach is selected to treat concrete behavior at high temperatures. Special emphasis is devoted to the modeling of concrete up to and including failure. The derived constitutive model is checked with biaxial and triaxial benchmark experimental results. Very good agreement is obtained
Elastic scattering of surface plasmon polaritons: Modeling and experiment
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Coello, V.
1998-01-01
excitation wavelengths (594 and 633 nm) and different metal (silver and gold) films. The near-field optical images obtained are related to the calculated SPP intensity distributions demonstrating that the model developed can be successfully used in studies of SPP elastic scattering, e.g., to design...
Polynomial constitutive model for shape memory and pseudo elasticity
International Nuclear Information System (INIS)
Savi, M.A.; Kouzak, Z.
1995-01-01
This paper reports an one-dimensional phenomenological constitutive model for shape memory and pseudo elasticity using a polynomial expression for the free energy which is based on the classical Devonshire theory. This study identifies the main characteristics of the classical theory and introduces a simple modification to obtain better results. (author). 9 refs., 6 figs
Global model for the lithospheric strength and effective elastic thickness
Tesauro, M.; Kaban, M.K.; Cloetingh, S.A.P.L.
2013-01-01
Global distribution of the strength and effective elastic thickness (Te) of the lithosphere are estimated using physical parameters from recent crustal and lithospheric models. For the Te estimation we apply a new approach, which provides a possibility to take into account variations of Young
A Smoothed Finite Element-Based Elasticity Model for Soft Bodies
Directory of Open Access Journals (Sweden)
Juan Zhang
2017-01-01
Full Text Available One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.
Vásquez Lavín, F. A.; Hernandez, J. I.; Ponce, R. D.; Orrego, S. A.
2017-07-01
During recent decades, water demand estimation has gained considerable attention from scholars. From an econometric perspective, the most used functional forms include log-log and linear specifications. Despite the advances in this field and the relevance for policymaking, little attention has been paid to the functional forms used in these estimations, and most authors have not provided justifications for their selection of functional forms. A discrete continuous choice model of the residential water demand is estimated using six functional forms (log-log, full-log, log-quadratic, semilog, linear, and Stone-Geary), and the expected consumption and price elasticity are evaluated. From a policy perspective, our results highlight the relevance of functional form selection for both the expected consumption and price elasticity.
Comparing linear probability model coefficients across groups
DEFF Research Database (Denmark)
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
Numerical modelling of elastic space tethers
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P. L.; Roberts, R. M.
2012-01-01
In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermo....... It is also shown that on the slow manifold the dynamics of the satellites are well-approximated by the finite dimensional slack-spring model....
An elastic-plastic contact model for line contact structures
Zhu, Haibin; Zhao, Yingtao; He, Zhifeng; Zhang, Ruinan; Ma, Shaopeng
2018-06-01
Although numerical simulation tools are now very powerful, the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications. For the line contact structures widely used in the engineering field, few analytical models are available for predicting the mechanical behaviour when the structures deform plastically, as the classic Hertz's theory would be invalid. Thus, the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism. A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained. The proposed model was verified through an actual line contact test and a corresponding numerical simulation. The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.
The elastic solid solution model for minerals at high pressures and temperatures
Myhill, R.
2018-02-01
Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order-disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function
Interactive Character Deformation Using Simplified Elastic Models
Luo, Z.
2016-01-01
This thesis describes the results of our research into realistic skin and model deformation methods aimed at the field of character deformation and animation. The main contributions lie in the properties of our deformation scheme. Our approach preserves the volume of the deformed object while
Spaghetti Bridges: Modeling Linear Relationships
Kroon, Cindy D.
2016-01-01
Mathematics and science are natural partners. One of many examples of this partnership occurs when scientific observations are made, thus providing data that can be used for mathematical modeling. Developing mathematical relationships elucidates such scientific principles. This activity describes a data-collection activity in which students employ…
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...
A micromechanics model of the elastic properties of human dentine
Energy Technology Data Exchange (ETDEWEB)
Kinney, J. H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Balooch, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Marshall, G. W. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry; Marshall, S. J. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry
1999-10-01
A generalized self-consistent model of cylindrical inclusions in a homogeneous and isotropic matrix phase was used to study the effects of tubule orientation on the elastic properties of dentin. Closed form expressions for the five independent elastic constants of dentin were derived in terms of tubule concentration, and the Young's moduli and Poisson ratios of peri- and intertubular dentin. An atomic force microscope (AFM) indentation technique determined the Young's moduli of the peri- and intertubular dentin as approximately 30 GPa and 15 GPa, respectively. Over the natural variation in tubule density found in dentin, there was only a slight variation in the axial and transverse shear moduli with position in the tooth, and there was no measurable effect of tubule orientation. We conclude that tubule orientation has no appreciable effect on the elastic behavior of normal dentin, and that the elastic properties of healthy dentin can be modeled as an isotropic continuum with a Young's modulus of approximately 16 GPa and a shear modulus of 6.2 GPa.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Extended Linear Models with Gaussian Priors
DEFF Research Database (Denmark)
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Linear mixed models for longitudinal data
Molenberghs, Geert
2000-01-01
This paperback edition is a reprint of the 2000 edition. This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Several variations to the conventional linear mixed model are discussed (a heterogeity model, conditional linear mixed models). This book will be of interest to applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia. The book is explanatory rather than mathematically rigorous. Most analyses were done with the MIXED procedure of the SAS software package, and many of its features are clearly elucidated. However, some other commerc...
Linear mixed models in sensometrics
DEFF Research Database (Denmark)
Kuznetsova, Alexandra
quality of decision making in Danish as well as international food companies and other companies using the same methods. The two open-source R packages lmerTest and SensMixed implement and support the methodological developments in the research papers as well as the ANOVA modelling part of the Consumer...... an open-source software tool ConsumerCheck was developed in this project and now is available for everyone. will represent a major step forward when concerns this important problem in modern consumer driven product development. Standard statistical software packages can be used for some of the purposes......Today’s companies and researchers gather large amounts of data of different kind. In consumer studies the objective is the collection of the data to better understand consumer acceptance of products. In such studies a number of persons (generally not trained) are selected in order to score products...
Modeling universal dynamics of cell spreading on elastic substrates.
Fan, Houfu; Li, Shaofan
2015-11-01
A three-dimensional (3D) multiscale moving contact line model is combined with a soft matter cell model to study the universal dynamics of cell spreading over elastic substrates. We have studied both the early stage and the late stage cell spreading by taking into account the actin tension effect. In this work, the cell is modeled as an active nematic droplet, and the substrate is modeled as a St. Venant Kirchhoff elastic medium. A complete 3D simulation of cell spreading has been carried out. The simulation results show that the spreading area versus spreading time at different stages obeys specific power laws, which is in good agreement with experimental data and theoretical prediction reported in the literature. Moreover, the simulation results show that the substrate elasticity may affect force dipole distribution inside the cell. The advantage of this approach is that it combines the hydrodynamics of actin retrograde flow with moving contact line model so that it can naturally include actin tension effect resulting from actin polymerization and actomyosin contraction, and thus it might be capable of simulating complex cellular scale phenomenon, such as cell spreading or even crawling.
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Statistical Tests for Mixed Linear Models
Khuri, André I; Sinha, Bimal K
2011-01-01
An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models a
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
Applying the elastic model for various nucleus-nucleus fusion
International Nuclear Information System (INIS)
HASSAN, G.S.; RAGAB, H.S.; SEDDEEK, M.K.
2000-01-01
The Elastic Model of two free parameters m,d given by Scalia has been used for wider energy regions to fit the available experimental data for potential barriers and cross sections. In order to generalize Scalia's formula in both sub- and above-barrier regions, we calculated m, d for pairs rather than those given by Scalia and compared the calculated cross sections with the experimental data. This makes a generalization of the Elastic Model in describing fusion process. On the other hand, Scalia's range of interacting systems was 24 ≤ A ≤194 where A is the compound nucleus mass number. Our extension of that model includes an example of the pairs of A larger than his final limit aiming to make it as a general formula for any type of reactants: light, intermediate or heavy systems. A significant point is the comparison of Elastic Model calculations with the well known methods studying complete fusion and compound nucleus formation, namely with the resultants of using Proximity potential with either Sharp or Smooth cut-off approximations
Phenomenological models of elastic nucleon scattering and predictions for LHC
Kundrat, V; Lokajicek, M; Prochazka, J
2011-01-01
The hitherto analyses of elastic collisions of charged nucleons involving common influence of Coulomb and hadronic scattering have been based practically on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model enabling to determine physical characteristics in impact parameter space seems to be more pertinent. The contemporary phenomenological models admit, of course, different distributions of collision processes in the impact parameter space and cannot give any definite answer. Nevertheless, some predictions for the planned LHC energy that have been given on their basis may be useful, as well as the possibility of determining the luminosity from elastic scattering. (C) 2010 Elsevier B.V. All rights reserved.
The elastic scattering between heavy ions using Glauber model
International Nuclear Information System (INIS)
Esmael, E.H.; El-Muhbad, SH.A.
2002-01-01
The differential cross sections of the elastic scattering of 1 2 C+ 12 C at energies 1016, 1449 and 2400 MeV and 1 6O +1 2C at energy 1503 MeV are calculated using high energy folding model. An analytical expression for the optical potential is derived. The effect of introducing imaginary phase and the dependence of the ratio of the real to imaginary parts of the forward nucleon-nucleon scattering amplitude on the square of momentum transfer are taken into consideration. Two different types of nuclear densities of the projectile and the target nuclei are considered. The considered systems of interaction are studied by using both modified Glauber I and modified Glauber II. The results show that the elastic scattering differential cross section for the considered interacting systems can be satisfactorily reproduced by this model
Elastic models: a comparative study applied to retinal images.
Karali, E; Lambropoulou, S; Koutsouris, D
2011-01-01
In this work various methods of parametric elastic models are compared, namely the classical snake, the gradient vector field snake (GVF snake) and the topology-adaptive snake (t-snake), as well as the method of self-affine mapping system as an alternative to elastic models. We also give a brief overview of the methods used. The self-affine mapping system is implemented using an adapting scheme and minimum distance as optimization criterion, which is more suitable for weak edges detection. All methods are applied to glaucomatic retinal images with the purpose of segmenting the optical disk. The methods are compared in terms of segmentation accuracy and speed, as these are derived from cross-correlation coefficients between real and algorithm extracted contours and segmentation time, respectively. As a result, the method of self-affine mapping system presents adequate segmentation time and segmentation accuracy, and significant independence from initialization.
Self-consistent Modeling of Elastic Anisotropy in Shale
Kanitpanyacharoen, W.; Wenk, H.; Matthies, S.; Vasin, R.
2012-12-01
Elastic anisotropy in clay-rich sedimentary rocks has increasingly received attention because of significance for prospecting of petroleum deposits, as well as seals in the context of nuclear waste and CO2 sequestration. The orientation of component minerals and pores/fractures is a critical factor that influences elastic anisotropy. In this study, we investigate lattice and shape preferred orientation (LPO and SPO) of three shales from the North Sea in UK, the Qusaiba Formation in Saudi Arabia, and the Officer Basin in Australia (referred to as N1, Qu3, and L1905, respectively) to calculate elastic properties and compare them with experimental results. Synchrotron hard X-ray diffraction and microtomography experiments were performed to quantify LPO, weight proportions, and three-dimensional SPO of constituent minerals and pores. Our preliminary results show that the degree of LPO and total amount of clays are highest in Qu3 (3.3-6.5 m.r.d and 74vol%), moderately high in N1 (2.4-5.6 m.r.d. and 70vol%), and lowest in L1905 (2.3-2.5 m.r.d. and 42vol%). In addition, porosity in Qu3 is as low as 2% while it is up to 6% in L1605 and 8% in N1, respectively. Based on this information and single crystal elastic properties of mineral components, we apply a self-consistent averaging method to calculate macroscopic elastic properties and corresponding seismic velocities for different shales. The elastic model is then compared with measured acoustic velocities on the same samples. The P-wave velocities measured from Qu3 (4.1-5.3 km/s, 26.3%Ani.) are faster than those obtained from L1905 (3.9-4.7 km/s, 18.6%Ani.) and N1 (3.6-4.3 km/s, 17.7%Ani.). By making adjustments for pore structure (aspect ratio) and single crystal elastic properties of clay minerals, a good agreement between our calculation and the ultrasonic measurement is obtained.
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
Global model for the lithospheric strength and effective elastic thickness
Magdala Tesauro; Mikhail Kaban; S. A. P. L. Cloetingh
2013-01-01
Global distribution of the strength and effective elastic thickness (Te) of the lithosphere are estimated using physical parameters from recent crustal and lithospheric models. For the Te estimation we apply a new approach, which provides a possibility to take into account variations of Young modulus (E) within the lithosphere. In view of the large uncertainties affecting strength estimates, we evaluate global strength and Te distributions for possible end-member ‘hard’ (HRM) and a ‘soft’ (SR...
Modeling digital switching circuits with linear algebra
Thornton, Mitchell A
2014-01-01
Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf
Updating Linear Schedules with Lowest Cost: a Linear Programming Model
Biruk, Sławomir; Jaśkowski, Piotr; Czarnigowska, Agata
2017-10-01
Many civil engineering projects involve sets of tasks repeated in a predefined sequence in a number of work areas along a particular route. A useful graphical representation of schedules of such projects is time-distance diagrams that clearly show what process is conducted at a particular point of time and in particular location. With repetitive tasks, the quality of project performance is conditioned by the ability of the planner to optimize workflow by synchronizing the works and resources, which usually means that resources are planned to be continuously utilized. However, construction processes are prone to risks, and a fully synchronized schedule may expire if a disturbance (bad weather, machine failure etc.) affects even one task. In such cases, works need to be rescheduled, and another optimal schedule should be built for the changed circumstances. This typically means that, to meet the fixed completion date, durations of operations have to be reduced. A number of measures are possible to achieve such reduction: working overtime, employing more resources or relocating resources from less to more critical tasks, but they all come at a considerable cost and affect the whole project. The paper investigates the problem of selecting the measures that reduce durations of tasks of a linear project so that the cost of these measures is kept to the minimum and proposes an algorithm that could be applied to find optimal solutions as the need to reschedule arises. Considering that civil engineering projects, such as road building, usually involve less process types than construction projects, the complexity of scheduling problems is lower, and precise optimization algorithms can be applied. Therefore, the authors put forward a linear programming model of the problem and illustrate its principle of operation with an example.
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
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
Estimation of parameters of constant elasticity of substitution production functional model
Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi
2017-11-01
Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.
Modelling Analysis of Forestry Input-Output Elasticity in China
Directory of Open Access Journals (Sweden)
Guofeng Wang
2016-01-01
Full Text Available Based on an extended economic model and space econometrics, this essay analyzed the spatial distributions and interdependent relationships of the production of forestry in China; also the input-output elasticity of forestry production were calculated. Results figure out there exists significant spatial correlation in forestry production in China. Spatial distribution is mainly manifested as spatial agglomeration. The output elasticity of labor force is equal to 0.6649, and that of capital is equal to 0.8412. The contribution of land is significantly negative. Labor and capital are the main determinants for the province-level forestry production in China. Thus, research on the province-level forestry production should not ignore the spatial effect. The policy-making process should take into consideration the effects between provinces on the production of forestry. This study provides some scientific technical support for forestry production.
Elastic instability model of rapid beak closure in hummingbirds.
Smith, M L; Yanega, G M; Ruina, A
2011-08-07
The hummingbird beak, specialized for feeding on floral nectars, is also uniquely adapted to eating flying insects. During insect capture the beak often appears to close at a rate that cannot be explained by direct muscular action alone. Here we show that the lower jaw of hummingbirds has a shape and compliance that allows for a controlled elastic snap. Furthermore, hummingbirds have the musculature needed to independently bend and twist the sides of the lower jaw. According to both our simple physical model and our elastic instability calculation, the jaw can be smoothly opened and then snapped closed through an appropriate sequence of bending and twisting actions by the muscles of the lower jaw. Copyright © 2011 Elsevier Ltd. All rights reserved.
A linear model of ductile plastic damage
International Nuclear Information System (INIS)
Lemaitre, J.
1983-01-01
A three-dimensional model of isotropic ductile plastic damage based on a continuum damage variable on the effective stress concept and on thermodynamics is derived. As shown by experiments on several metals and alloys, the model, integrated in the case of proportional loading, is linear with respect to the accumulated plastic strain and shows a large influence of stress triaxiality [fr
Ker, H. W.
2014-01-01
Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…
Faraway, Julian J
2005-01-01
Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway''s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author''s treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the ...
Modelling and Intelligent Control of an Elastic Link Robot Manipulator
Directory of Open Access Journals (Sweden)
Malik Loudini
2013-01-01
Full Text Available In this paper, precise control of the end-point position of a planar single-link elastic manipulator robot is discussed. The Timoshenko beam theory (TBT has been used to characterize the structural link elasticity including important damping mechanisms. A suitable nonlinear model is derived based on the Lagrangian assumed modes method. Elastic link manipulators are classified as systems possessing highly complex dynamics. In addition, the environment in which they operate may have a lot of disturbances. These give rise to special problems that may be solved using intelligent control techniques. The application of two advanced control strategies based on fuzzy set theory is investigated. The first closed-loop control scheme to be applied is the standard Proportional-Derivative (PD type fuzzy logic controller (FLC, also known as PD-type Mamdani's FLC (MPDFLC. Then, a genetic algorithm (GA is used to optimize the MPDFLC parameters with innovative tuning procedures. Both the MPDFLC and the GA optimized FLC (GAOFLC are implemented and tested to achieve a precise control of the manipulator end-point. The performances of the adopted closed-loop intelligent control strategies are examined via simulation experiments.
Ground Motion Models for Future Linear Colliders
International Nuclear Information System (INIS)
Seryi, Andrei
2000-01-01
Optimization of the parameters of a future linear collider requires comprehensive models of ground motion. Both general models of ground motion and specific models of the particular site and local conditions are essential. Existing models are not completely adequate, either because they are too general, or because they omit important peculiarities of ground motion. The model considered in this paper is based on recent ground motion measurements performed at SLAC and at other accelerator laboratories, as well as on historical data. The issues to be studied for the models to become more predictive are also discussed
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...
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.
Hybrid Simulation Modeling to Estimate U.S. Energy Elasticities
Baylin-Stern, Adam C.
This paper demonstrates how an U.S. application of CIMS, a technologically explicit and behaviourally realistic energy-economy simulation model which includes macro-economic feedbacks, can be used to derive estimates of elasticity of substitution (ESUB) and autonomous energy efficiency index (AEEI) parameters. The ability of economies to reduce greenhouse gas emissions depends on the potential for households and industry to decrease overall energy usage, and move from higher to lower emissions fuels. Energy economists commonly refer to ESUB estimates to understand the degree of responsiveness of various sectors of an economy, and use estimates to inform computable general equilibrium models used to study climate policies. Using CIMS, I have generated a set of future, 'pseudo-data' based on a series of simulations in which I vary energy and capital input prices over a wide range. I then used this data set to estimate the parameters for transcendental logarithmic production functions using regression techniques. From the production function parameter estimates, I calculated an array of elasticity of substitution values between input pairs. Additionally, this paper demonstrates how CIMS can be used to calculate price-independent changes in energy-efficiency in the form of the AEEI, by comparing energy consumption between technologically frozen and 'business as usual' simulations. The paper concludes with some ideas for model and methodological improvement, and how these might figure into future work in the estimation of ESUBs from CIMS. Keywords: Elasticity of substitution; hybrid energy-economy model; translog; autonomous energy efficiency index; rebound effect; fuel switching.
Twist and Stretch of Helices Explained via the Kirchhoff-Love Rod Model of Elastic Filaments
Đuričković, Bojan
2013-09-05
In various single-molecule experiments, a chiral polymer, such as DNA, is simultaneously pulled and twisted. We address an elementary but fundamental question raised by various authors: does the molecule overwind or unwind under tension? We show that within the context of the classic Kirchhoff-Love rod model of elastic filaments, both behaviors are possible, depending on the precise constitutive relations of the polymer. More generally, our analysis provides an effective linear response theory for helical structures that relates axial force and axial torque to axial translation and rotation. © 2013 American Physical Society.
Modelling female fertility traits in beef cattle using linear and non-linear models.
Naya, H; Peñagaricano, F; Urioste, J I
2017-06-01
Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2 linear models; h 2 > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Modelling point patterns with linear structures
DEFF Research Database (Denmark)
Møller, Jesper; Rasmussen, Jakob Gulddahl
2009-01-01
processes whose realizations contain such linear structures. Such a point process is constructed sequentially by placing one point at a time. The points are placed in such a way that new points are often placed close to previously placed points, and the points form roughly line shaped structures. We...... consider simulations of this model and compare with real data....
Modelling point patterns with linear structures
DEFF Research Database (Denmark)
Møller, Jesper; Rasmussen, Jakob Gulddahl
processes whose realizations contain such linear structures. Such a point process is constructed sequentially by placing one point at a time. The points are placed in such a way that new points are often placed close to previously placed points, and the points form roughly line shaped structures. We...... consider simulations of this model and compare with real data....
Optimal designs for linear mixture models
Mendieta, E.J.; Linssen, H.N.; Doornbos, R.
1975-01-01
In a recent paper Snee and Marquardt [8] considered designs for linear mixture models, where the components are subject to individual lower and/or upper bounds. When the number of components is large their algorithm XVERT yields designs far too extensive for practical purposes. The purpose of this
Optimal designs for linear mixture models
Mendieta, E.J.; Linssen, H.N.; Doornbos, R.
1975-01-01
In a recent paper Snee and Marquardt (1974) considered designs for linear mixture models, where the components are subject to individual lower and/or upper bounds. When the number of components is large their algorithm XVERT yields designs far too extensive for practical purposes. The purpose of
A 3D Orthotropic Elastic Continuum Damage Material Model
Energy Technology Data Exchange (ETDEWEB)
English, Shawn Allen [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brown, Arthur A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2013-08-01
A three dimensional orthotropic elastic constitutive model with continuum damage is implemented for polymer matrix composite lamina. Damage evolves based on a quadratic homogeneous function of thermodynamic forces in the orthotropic planes. A small strain formulation is used to assess damage. In order to account for large deformations, a Kirchhoff material formulation is implemented and coded for numerical simulation in Sandia’s Sierra Finite Element code suite. The theoretical formulation is described in detail. An example of material parameter determination is given and an example is presented.
Model of K+p elastic scattering at high energies
International Nuclear Information System (INIS)
Fazal-e-Aleem
1985-01-01
Very recent measurements of the angular distribution for K + p elastic scattering which show a structure near -t = 3.8(GeV/c) 2 , together with the total cross section and ratio of the real and imaginary parts of the scattering amplitude for 50 2 , have been fitted by using a simple Regge-pole model with phenomenological residue functions. The break in the slope near -t = 0.5 (GeV/c) 2 observed in the differential cross section has also been explained
The impact of ice I rheology on interior models of Ganymede: The elastic vs. the visco-elastic case
Steinbrügge, Gregor; Hussmann, Hauke; Sohl, Frank; Oberst, Jürgen
2015-04-01
Many investigations on key processes of icy satellites are driven by the rheological behavior of planetary ices. Future missions to Jupiter's icy moons (e.g. JUICE / Europa clipper) aimed at constraining the thickness of the outer ice shell using radio science and/or laser altimetry will have to address this problem. We investigate for the case of Ganymede under which conditions the ice I viscosity could be constrained by measuring the phase-lag of the tidal response using laser altimetry. In the absence of seismic data, interior structure models are constrained by the satellite's mean density and mean moment-of-inertia factor. One key observable to reduce the ambiguity of the corresponding structural models is the measurement of the dynamic response of the satellite's outer ice shells to tidal forces exerted by Jupiter and characterized by the body tide surface Love numbers h2 and k2. The Love number k2 measures the variation of the gravitational potential due to tidally induced internal redistribution of mass and can be inferred from radio science experiments. The Love number h2 is a measure for the tide-induced radial displacement of the satellite's surface. It is an advantage that Ganymede's surface displacement Love number h2 can be expected to be measured with a high accuracy using laser altimetry (Steinbrügge et al., 2014). However, the determination of the resulting ice thickness further depends on the possible existence of a liquid subsurface water ocean and on the tidally effective rheology of the outer ice shell (Moore and Schubert, 2003). Here, we distinguish between an elastic, visco-elastic or even fluid behavior in the sense of the Maxwell model and alternative rheological models. In the case of Ganymede the fluid case would imply high ice temperatures which are at odds with thermal equilibrium models calculated by Spohn and Schubert (2003). However the visco-elastic case is still possible. Laboratory measurements of ice I (e.g. Sotin et al., 1998
Linear factor copula models and their properties
Krupskii, Pavel; Genton, Marc G.
2018-01-01
We consider a special case of factor copula models with additive common factors and independent components. These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme‐value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme‐value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set.
Linear factor copula models and their properties
Krupskii, Pavel
2018-04-25
We consider a special case of factor copula models with additive common factors and independent components. These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme‐value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme‐value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set.
Diagnostics for Linear Models With Functional Responses
Xu, Hongquan; Shen, Qing
2005-01-01
Linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations. Residual analysis and diagnostics are considered for such models. Studentized residuals are defined and their properties are studied. Chi-square quantile-quantile plots are proposed to check the assumption of Gaussian error process and outliers. Jackknife residuals and an associated test are proposed to det...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Mesoscopic approach to modeling elastic-plastic polycrystalline material behaviour
International Nuclear Information System (INIS)
Kovac, M.; Cizelj, L.
2001-01-01
Extreme loadings during severe accident conditions might cause failure or rupture of the pressure boundary of a reactor coolant system. Reliable estimation of the extreme deformations can be crucial to determine the consequences of such an accident. One of important drawbacks of classical continuum mechanics is idealization of inhomogenous microstructure of materials. This paper discusses the mesoscopic approach to modeling the elastic-plastic behavior of a polycrystalline material. The main idea is to divide the continuum (e.g., polycrystalline aggregate) into a set of sub-continua (grains). The overall properties of the polycrystalline aggregate are therefore determined by the number of grains in the aggregate and properties of randomly shaped and oriented grains. The random grain structure is modeled with Voronoi tessellation and random orientations of crystal lattices are assumed. The elastic behavior of monocrystal grains is assumed to be anisotropic. Crystal plasticity is used to describe plastic response of monocrystal grains. Finite element method is used to obtain numerical solutions of strain and stress fields. The analysis is limited to two-dimensional models.(author)
A new model for elastic deuteron-deuteron scattering
International Nuclear Information System (INIS)
Etim, E.; Satta, L.
1988-01-01
Straightforward application of the Glauber multiple scattering theory is drammatically challenged by data on elastic deuteron-deuteron scattering. The challenge has been argued to be met by an improved representation of the ground state wave function of the deuteron as an admixture of S-and D-waves. In the light of the failure of the Glauber and geometrical picture models in general, to explain proton-proton and proton-antiproton scattering data up to and including collider energies and for all momentum transfers, this argument becomes less and less compelling and more and more unconvincing. A model inspired by unitarity and which produces substantial elastic scattering through a unitarity sum over a specific class of intermediate states is presented. The model fits not only deuteron-deuteron, but also proton-proton, proton-antiproton and αN -> αN (N =α, d, He 3 ) data for all energies and momentum transfers. No detailed knowledge of ground state wave functions is required
Constraints on equivalent elastic source models from near-source data
International Nuclear Information System (INIS)
Stump, B.
1993-01-01
A phenomenological based seismic source model is important in quantifying the important physical processes that affect the observed seismic radiation in the linear-elastic regime. Representations such as these were used to assess yield effects on seismic waves under a Threshold Test Ban Treaty and to help transport seismic coupling experience at one test site to another. These same characterizations in a non-proliferation environment find applications in understanding the generation of the different types of body and surface waves from nuclear explosions, single chemical explosions, arrays of chemical explosions used in mining, rock bursts and earthquakes. Seismologists typically begin with an equivalent elastic representation of the source which when convolved with the propagation path effects produces a seismogram. The Representation Theorem replaces the true source with an equivalent set of body forces, boundary conditions or initial conditions. An extension of this representation shows the equivalence of the body forces, boundary conditions and initial conditions and replaces the source with a set of force moments, the first degree moment tensor for a point source representation. The difficulty with this formulation, which can completely describe the observed waveforms when the propagation path effects are known, is in the physical interpretation of the actual physical processes acting in the source volume. Observational data from within the source region, where processes are often nonlinear, linked to numerical models of the important physical processes in this region are critical to a unique physical understanding of the equivalent elastic source function
Mathematical model predicts the elastic behavior of composite materials
Directory of Open Access Journals (Sweden)
Zoroastro de Miranda Boari
2005-03-01
Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.
Jiandong Yang; Mingjiang Wang; Chao Wang; Wencheng Guo
2015-01-01
On the basis of the state–space method (SSM), a novel linear mathematical model of the unsteady flow for the tailrace system with an open channel is proposed. This novel model is an elastic linearized model of water hammer. The validity of the model has been verified by several examples of numerical simulation, which are based on a finite difference technique. Then, the complete mathematical model for the hydro-turbine governing system of hydropower station with an open tailrace channel, whi...
Li, Dongna; Li, Xudong; Dai, Jianfeng
2018-06-01
In this paper, two kinds of transient models, the viscoelastic model and the linear elastic model, are established to analyze the curing deformation of the thermosetting resin composites, and are calculated by COMSOL Multiphysics software. The two models consider the complicated coupling between physical and chemical changes during curing process of the composites and the time-variant characteristic of material performance parameters. Subsequently, the two proposed models are implemented respectively in a three-dimensional composite laminate structure, and a simple and convenient method of local coordinate system is used to calculate the development of residual stresses, curing shrinkage and curing deformation for the composite laminate. Researches show that the temperature, degree of curing (DOC) and residual stresses during curing process are consistent with the study in literature, so the curing shrinkage and curing deformation obtained on these basis have a certain referential value. Compared the differences between the two numerical results, it indicates that the residual stress and deformation calculated by the viscoelastic model are more close to the reference value than the linear elastic model.
[From clinical judgment to linear regression model.
Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O
2013-01-01
When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.
International Nuclear Information System (INIS)
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
Directory of Open Access Journals (Sweden)
Isa Kolo
2016-01-01
Full Text Available A coupled elastic-plasticity-damage constitutive model, AK Model, is applied to predict fracture propagation in rocks. The quasi-brittle material model captures anisotropic effects and the distinct behavior of rocks in tension and compression. Calibration of the constitutive model is realized using experimental data for Carrara marble. Through the Weibull distribution function, heterogeneity effect is captured by spatially varying the elastic properties of the rock. Favorable comparison between model predictions and experiments for single-flawed specimens reveal that the AK Model is reliable and accurate for modelling fracture propagation in rocks.
Testing Parametric versus Semiparametric Modelling in Generalized Linear Models
Härdle, W.K.; Mammen, E.; Müller, M.D.
1996-01-01
We consider a generalized partially linear model E(Y|X,T) = G{X'b + m(T)} where G is a known function, b is an unknown parameter vector, and m is an unknown function.The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model: (i) m is linear, i.e.
Modeling of Volatility with Non-linear Time Series Model
Kim Song Yon; Kim Mun Chol
2013-01-01
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.
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.
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.
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.
Thresholding projection estimators in functional linear models
Cardot, Hervé; Johannes, Jan
2010-01-01
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squ...
Decomposed Implicit Models of Piecewise - Linear Networks
Directory of Open Access Journals (Sweden)
J. Brzobohaty
1992-05-01
Full Text Available The general matrix form of the implicit description of a piecewise-linear (PWL network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced.
A mathematical model for the deformation of the eyeball by an elastic band.
Keeling, Stephen L; Propst, Georg; Stadler, Georg; Wackernagel, Werner
2009-06-01
In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given.
Entropic elasticity in the generation of muscle Force - A theoretical model
DEFF Research Database (Denmark)
Nielsen, Bjørn Gilbert
2002-01-01
A novel simplified structural model of sarcomeric force production in striate muscle is presented. Using some simple assumptions regarding the distribution of myosin spring lengths at different sliding velocities it is possible to derive a very simple expression showing the main components...... of the experimentally observed force-velocity relationship of muscle: nonlinearity during contraction (Hill, 1938), maximal force production during stretching equal to two times the isometric force (Katz, 1939), yielding at high stretching velocity, slightly concave force-extension relationship during sudden length......-bridges are explored [linear, power function and worm-like chain (WLC) model based], and it is shown that the best results are obtained if the individual myosin-spring forces are modelled using a WLC model, thus hinting that entropic elasticity could be the main source of force in myosin undergoing the conformational...
From spiking neuron models to linear-nonlinear models.
Ostojic, Srdjan; Brunel, Nicolas
2011-01-20
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
DEFF Research Database (Denmark)
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...
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.
Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.
2014-01-01
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.
An elastic network model of HK97 capsid maturation.
Kim, Moon K; Jernigan, Robert L; Chirikjian, Gregory S
2003-08-01
The structure of the capsid of bacteriophage HK97 has been solved at various stages of maturity by crystallography and cryo-electron microscopy, and has been reported previously in the literature. Typically the capsid assembles through polymerization and maturation processes. Maturation is composed of proteolytic cleavages to the precursor capsid (called Prohead II), expansion triggered by DNA packaging (in which the largest conformational changes of the capsid appear), and covalent cross-links of neighboring subunits to create the mature capsid called Head II. We apply a coarse-grained elastic network interpolation (ENI) to generate a feasible pathway for conformational change from Prohead II to Head II. The icosahedral symmetry of the capsid structure offers a significant computational advantage because it is not necessary to consider the whole capsid structure but only an asymmetric unit consisting of one hexamer plus an additional subunit from an adjacent pentamer. We also analyze normal modes of the capsid structure using an elastic network model which is also subject to symmetry constraints. Using our model, we can visualize the smooth evolution of capsid expansion and revisit in more detail several interesting geometric changes recognized in early experimental works such as rigid body motion of two compact domains (A and P) with two refolding extensions (N-arm and E-loop) and track the approach of the two particular residues associated with isopeptide bonds that make hexagonal cross-links in Head II. The feasibility of the predicted pathway is also supported by the results of our normal mode analysis.
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
Vibrational characteristics of graphene sheets elucidated using an elastic network model.
Kim, Min Hyeok; Kim, Daejoong; Choi, Jae Boong; Kim, Moon Ki
2014-08-07
Recent studies of graphene have demonstrated its great potential for highly sensitive resonators. In order to capture the intrinsic vibrational characteristics of graphene, we propose an atomistic modeling method called the elastic network model (ENM), in which a graphene sheet is modeled as a mass-spring network of adjacent atoms connected by various linear springs with specific bond ratios. Normal mode analysis (NMA) reveals the various vibrational features of bi-layer graphene sheets (BLGSs) clamped at two edges. We also propose a coarse-graining (CG) method to extend our graphene study into the meso- and macroscales, at which experimental measurements and synthesis of graphene become practical. The simulation results show good agreement with experimental observations. Therefore, the proposed ENM approach will not only shed light on the theoretical study of graphene mechanics, but also play an important role in the design of highly-sensitive graphene-based resonators.
International Nuclear Information System (INIS)
Glasgow, B.B.; Wolfer, W.G.
1986-01-01
Crack growth can result in a breech of a pressure boundary causing coolant loss or in total structural failure. This paper discusses brittle and plastic failure in terms of a unified structural model called the Two Criteria model. The model takes into account the flow stress of the material as well as the fracture toughness. Our results indicate that for fusion reactor first wall structures, ferritic steel is better able to resist crack propagation and subsequent structural failure than 316 stainless steel under the same wall loadings and geometry
Linear accelerator modeling: development and application
International Nuclear Information System (INIS)
Jameson, R.A.; Jule, W.D.
1977-01-01
Most of the parameters of a modern linear accelerator can be selected by simulating the desired machine characteristics in a computer code and observing how the parameters affect the beam dynamics. The code PARMILA is used at LAMPF for the low-energy portion of linacs. Collections of particles can be traced with a free choice of input distributions in six-dimensional phase space. Random errors are often included in order to study the tolerances which should be imposed during manufacture or in operation. An outline is given of the modifications made to the model, the results of experiments which indicate the validity of the model, and the use of the model to optimize the longitudinal tuning of the Alvarez linac
Running vacuum cosmological models: linear scalar perturbations
Energy Technology Data Exchange (ETDEWEB)
Perico, E.L.D. [Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, CEP 05508-090, São Paulo, SP (Brazil); Tamayo, D.A., E-mail: elduartep@usp.br, E-mail: tamayo@if.usp.br [Departamento de Astronomia, Universidade de São Paulo, Rua do Matão 1226, CEP 05508-900, São Paulo, SP (Brazil)
2017-08-01
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.
Kundrát, Vojtech; Kaspar, Jan; Procházka, Jirí
2010-01-01
The standard description of common influence of both the Coulomb and hadronic elastic scattering in the proton - proton elastic collisions at high energies with the help of West and Yennie complete amplitude is shown to be theoretically inconsistent. The approach being based on the eikonal model amplitude removes these troubles. The preference of its applica- tion to the analysis of experimental data and in obtaining the predictions of contemporary models for proton - proton high energy elastic hadronic scattering are discussed.
Linear Parametric Model Checking of Timed Automata
DEFF Research Database (Denmark)
Hune, Tohmas Seidelin; Romijn, Judi; Stoelinga, Mariëlle
2001-01-01
We present an extension of the model checker Uppaal capable of synthesize linear parameter constraints for the correctness of parametric timed automata. The symbolic representation of the (parametric) state-space is shown to be correct. A second contribution of this paper is the identication...... of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is know to be undecidable. Also we present a number of lemmas enabling the verication eort to be reduced for L/U automata in some cases. We illustrate our approach...
An Elastic Plastic Contact Model with Strain Hardening for the LAMMPS Granular Package
Energy Technology Data Exchange (ETDEWEB)
Kuhr, Bryan [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Brake, Matthew Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Component Science and Mechanics; Lechman, Jeremy B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanoscale and Reactive Processes
2015-03-01
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-11-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
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...
Global model for the lithospheric strength and effective elastic thickness
Tesauro, Magdala; Kaban, Mikhail K.; Cloetingh, Sierd A. P. L.
2013-08-01
Global distribution of the strength and effective elastic thickness (Te) of the lithosphere are estimated using physical parameters from recent crustal and lithospheric models. For the Te estimation we apply a new approach, which provides a possibility to take into account variations of Young modulus (E) within the lithosphere. In view of the large uncertainties affecting strength estimates, we evaluate global strength and Te distributions for possible end-member 'hard' (HRM) and a 'soft' (SRM) rheology models of the continental crust. Temperature within the lithosphere has been estimated using a recent tomography model of Ritsema et al. (2011), which has much higher horizontal resolution than previous global models. Most of the strength is localized in the crust for the HRM and in the mantle for the SRM. These results contribute to the long debates on applicability of the "crème brulée" or "jelly-sandwich" model for the lithosphere structure. Changing from the SRM to HRM turns most of the continental areas from the totally decoupled mode to the fully coupled mode of the lithospheric layers. However, in the areas characterized by a high thermal regime and thick crust, the layers remain decoupled even for the HRM. At the same time, for the inner part of the cratons the lithospheric layers are coupled in both models. Therefore, rheological variations lead to large changes in the integrated strength and Te distribution in the regions characterized by intermediate thermal conditions. In these areas temperature uncertainties have a greater effect, since this parameter principally determines rheological behavior. Comparison of the Te estimates for both models with those determined from the flexural loading and spectral analysis shows that the 'hard' rheology is likely applicable for cratonic areas, whereas the 'soft' rheology is more representative for young orogens.
Atomistic modelling of diffusional phase transformations with elastic strain
International Nuclear Information System (INIS)
Mason, D R; Rudd, R E; Sutton, A P
2004-01-01
Phase transformations in 2xxx series aluminium alloys (Al-Cu-Mg) are investigated with an off-lattice atomistic kinetic Monte Carlo simulation incorporating the effects of strain around misfitting atoms and vacancies. Atomic interactions are modelled by Finnis-Sinclair potentials constructed for these simulations. Vacancy diffusion is modelled by comparing the energies of trial states, where the system is partially relaxed for each trial state. No special requirements are made about the description of atomic interactions, making our approach suitable for more fundamentally based models such as tight binding if sufficient computational resources are available. Only a limited precision is required for the energy of each trial state, determined by the value of k B T. Since the change in the relaxation displacement field caused by a vacancy hop decays as 1/r 3 , it is sufficient to determine the next move by relaxing only those atoms in a sphere of finite radius centred on the moving vacancy. However, once the next move has been selected, the entire system is relaxed. Simulations of the early stages of phase separation in Al-Cu with elastic relaxation show an enhanced rate of clustering compared to those performed on the same system with a rigid lattice
Aspects of general linear modelling of migration.
Congdon, P
1992-01-01
"This paper investigates the application of general linear modelling principles to analysing migration flows between areas. Particular attention is paid to specifying the form of the regression and error components, and the nature of departures from Poisson randomness. Extensions to take account of spatial and temporal correlation are discussed as well as constrained estimation. The issue of specification bears on the testing of migration theories, and assessing the role migration plays in job and housing markets: the direction and significance of the effects of economic variates on migration depends on the specification of the statistical model. The application is in the context of migration in London and South East England in the 1970s and 1980s." excerpt
Directory of Open Access Journals (Sweden)
I. K. Badalakha
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.
Model Selection with the Linear Mixed Model for Longitudinal Data
Ryoo, Ji Hoon
2011-01-01
Model building or model selection with linear mixed models (LMMs) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are codependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multilevel or…
Modelling and Predicting Backstroke Start Performance Using Non-Linear and Linear Models.
de Jesus, Karla; Ayala, Helon V H; de Jesus, Kelly; Coelho, Leandro Dos S; Medeiros, Alexandre I A; Abraldes, José A; Vaz, Mário A P; Fernandes, Ricardo J; Vilas-Boas, João Paulo
2018-03-01
Our aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances.
Modeling of a light elastic beam by a system of rigid bodies
Directory of Open Access Journals (Sweden)
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. .
Elastic constants of stressed and unstressed materials in the phase-field crystal model
Wang, Zi-Le; Huang, Zhi-Feng; Liu, Zhirong
2018-04-01
A general procedure is developed to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase-field crystal (PFC) models. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.
Modeling patterns in data using linear and related models
International Nuclear Information System (INIS)
Engelhardt, M.E.
1996-06-01
This report considers the use of linear models for analyzing data related to reliability and safety issues of the type usually associated with nuclear power plants. The report discusses some of the general results of linear regression analysis, such as the model assumptions and properties of the estimators of the parameters. The results are motivated with examples of operational data. Results about the important case of a linear regression model with one covariate are covered in detail. This case includes analysis of time trends. The analysis is applied with two different sets of time trend data. Diagnostic procedures and tests for the adequacy of the model are discussed. Some related methods such as weighted regression and nonlinear models are also considered. A discussion of the general linear model is also included. Appendix A gives some basic SAS programs and outputs for some of the analyses discussed in the body of the report. Appendix B is a review of some of the matrix theoretic results which are useful in the development of linear models
International Nuclear Information System (INIS)
Wang Weihua
2011-01-01
We study the similarity and correlations between relaxations and plastic deformation in metallic glasses (MGs) and MG-forming liquids. It is shown that the microscope plastic events, the initiation and formation of shear bands, and the mechanical yield in MGs where the atomic sites are topologically unstable induced by applied stress, can be treated as the glass to supercooled liquid state transition induced by external shear stress. On the other hand, the glass transition, the primary and secondary relaxations, plastic deformation and yield can be attributed to the free volume increase induced flow, and the flow can be modeled as the activated hopping between the inherent states in the potential energy landscape. We then propose an extended elastic model to describe the flow based on the energy landscape theory. That is, the flow activation energy density is linear proportional to the instantaneous elastic moduli, and the activation energy density ρ E is determined to be a simple expression of ρ E =(10/11)G+(1/11)K. The model indicates that both shear and bulk moduli are critical parameters accounting for both the homogeneous and inhomogeneous flows in MGs and MG-forming liquids. The elastic model is experimentally certified. We show that the elastic perspectives offers a simple scenario for the flow in MGs and MG-forming liquids and are suggestive for understanding the glass transition, plastic deformation, and nature and characteristics of MGs
Building alternate protein structures using the elastic network model.
Yang, Qingyi; Sharp, Kim A
2009-02-15
We describe a method for efficiently generating ensembles of alternate, all-atom protein structures that (a) differ significantly from the starting structure, (b) have good stereochemistry (bonded geometry), and (c) have good steric properties (absence of atomic overlap). The method uses reconstruction from a series of backbone framework structures that are obtained from a modified elastic network model (ENM) by perturbation along low-frequency normal modes. To ensure good quality backbone frameworks, the single force parameter ENM is modified by introducing two more force parameters to characterize the interaction between the consecutive carbon alphas and those within the same secondary structure domain. The relative stiffness of the three parameters is parameterized to reproduce B-factors, while maintaining good bonded geometry. After parameterization, violations of experimental Calpha-Calpha distances and Calpha-Calpha-Calpha pseudo angles along the backbone are reduced to less than 1%. Simultaneously, the average B-factor correlation coefficient improves to R = 0.77. Two applications illustrate the potential of the approach. (1) 102,051 protein backbones spanning a conformational space of 15 A root mean square deviation were generated from 148 nonredundant proteins in the PDB database, and all-atom models with minimal bonded and nonbonded violations were produced from this ensemble of backbone structures using the SCWRL side chain building program. (2) Improved backbone templates for homology modeling. Fifteen query sequences were each modeled on two targets. For each of the 30 target frameworks, dozens of improved templates could be produced In all cases, improved full atom homology models resulted, of which 50% could be identified blind using the D-Fire statistical potential. (c) 2008 Wiley-Liss, Inc.
Electron Model of Linear-Field FFAG
Koscielniak, Shane R
2005-01-01
A fixed-field alternating-gradient accelerator (FFAG) that employs only linear-field elements ushers in a new regime in accelerator design and dynamics. The linear-field machine has the ability to compact an unprecedented range in momenta within a small component aperture. With a tune variation which results from the natural chromaticity, the beam crosses many strong, uncorrec-table, betatron resonances during acceleration. Further, relativistic particles in this machine exhibit a quasi-parabolic time-of-flight that cannot be addressed with a fixed-frequency rf system. This leads to a new concept of bucketless acceleration within a rotation manifold. With a large energy jump per cell, there is possibly strong synchro-betatron coupling. A few-MeV electron model has been proposed to demonstrate the feasibility of these untested acceleration features and to investigate them at length under a wide range of operating conditions. This paper presents a lattice optimized for a 1.3 GHz rf, initial technology choices f...
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
Generalized Linear Models in Vehicle Insurance
Directory of Open Access Journals (Sweden)
Silvie Kafková
2014-01-01
Full Text Available Actuaries in insurance companies try to find the best model for an estimation of insurance premium. It depends on many risk factors, e.g. the car characteristics and the profile of the driver. In this paper, an analysis of the portfolio of vehicle insurance data using a generalized linear model (GLM is performed. The main advantage of the approach presented in this article is that the GLMs are not limited by inflexible preconditions. Our aim is to predict the relation of annual claim frequency on given risk factors. Based on a large real-world sample of data from 57 410 vehicles, the present study proposed a classification analysis approach that addresses the selection of predictor variables. The models with different predictor variables are compared by analysis of deviance and Akaike information criterion (AIC. Based on this comparison, the model for the best estimate of annual claim frequency is chosen. All statistical calculations are computed in R environment, which contains stats package with the function for the estimation of parameters of GLM and the function for analysis of deviation.
A thermo-elastic model for soft rocks considering structure
International Nuclear Information System (INIS)
He, Z.; Zhang, S.; Teng, J.; Xiong, Y.
2017-01-01
In the fields of nuclear waste geological deposit, geothermal energy and deep mining, the effects of temperature on the mechanical behaviors of soft rocks cannot be neglected. Experimental data in the literature also showed that the structure of soft rocks cannot be ignored. Based on the super-loading yield surface and the concept of temperature-deduced equivalent stress, a thermo-elastoplastic model for soft rocks is proposed considering the structure. Compared to the super-loading yield surface, only one parameter is added, i.e. the linear thermal expansion coefficient. The predicted results and the comparisons with experimental data in the literature show that the proposed model is capable of simultaneously describing heat increase and heat decrease of soft rocks. A stronger initial structure leads to a greater strength of the soft rocks. Heat increase and heat decrease can be converted between each other due to the change of the initial structure of soft rocks. Furthermore, regardless of the heat increase or heat decrease, a larger linear thermal expansion coefficient or a greater temperature always leads to a much rapider degradation of the structure. The degradation trend will be more obvious for the coupled greater values of linear thermal expansion coefficient and temperature. Lastly, compared to heat decrease, the structure will degrade more easily in the case of heat increase. (authors)
Rajagopal, K. R.
2011-01-06
This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.
Hierarchical modeling and its numerical implementation for layered thin elastic structures
Energy Technology Data Exchange (ETDEWEB)
Cho, Jin-Rae [Hongik University, Sejong (Korea, Republic of)
2017-05-15
Thin elastic structures such as beam- and plate-like structures and laminates are characterized by the small thickness, which lead to classical plate and laminate theories in which the displacement fields through the thickness are assumed linear or higher-order polynomials. These classical theories are either insufficient to represent the complex stress variation through the thickness or may encounter the accuracy-computational cost dilemma. In order to overcome the inherent problem of classical theories, the concept of hierarchical modeling has been emerged. In the hierarchical modeling, the hierarchical models with different model levels are selected and combined within a structure domain, in order to make the modeling error be distributed as uniformly as possible throughout the problem domain. The purpose of current study is to explore the potential of hierarchical modeling for the effective numerical analysis of layered structures such as laminated composite. For this goal, the hierarchical models are constructed and the hierarchical modeling is implemented by selectively adjusting the level of hierarchical models. As well, the major characteristics of hierarchical models are investigated through the numerical experiments.
Nonlinear price impact from linear models
Patzelt, Felix; Bouchaud, Jean-Philippe
2017-12-01
The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.
Armington elasticities for energy policy modeling: Evidence from four European countries
International Nuclear Information System (INIS)
Welsch, Heinz
2008-01-01
Elasticities of substitution among imports and competing domestic production (Armington elasticities) play an important role in computable general equilibrium (CGE) assessments of energy and climate policy. This paper provides estimates of Armington elasticities for 15 commodity groups in four European countries. Since Armington elasticities are found to be rather low on average, researchers may want to reconsider the device of using high values of Armington elasticities in CGE models to avoid unrealistic competitiveness effects or emission leakage rates associated with energy or carbon taxes or other forms of energy-related regulation. Estimated elasticities tend to be higher in the case of machinery and other investment goods than in the case of primary products, ores and chemicals, as well as consumer goods
Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.
2009-01-01
This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
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
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2008-01-01
The postbuckling behavior and imperfection sensitivity of the Shanley-Hutchinson plastic model column introduced by Hutchinson in 1973 are examined. The study covers the initial, buckled state and the advanced postbuckling regime of the geometrically perfect realization as well as its sensitivity...... to geometric imperfections. In Section 1, which is concerned with the perfect structure, a new, simple explicit upper bound for all solutions to the problem is found when the tangent modulus at bifurcation vanishes compared to the linear elastic (unloading) modulus. The difference between the upper bound...... and the solution to an actual problem is determined by an asymptotic expansion involving hyperbolic trial functions (instead of polynomials) which fulfill general boundary conditions at bifurcation and infinity. The method provides an accurate estimate of the maximum load even if it occurs in an advanced...
MODELING OF RAILWAY TRACK OPERATION AS A SYSTEM OF QUASI-ELASTIC ORTHOTROPIC LAYERS
Directory of Open Access Journals (Sweden)
Sychev Vyacheslav Petrovich
2016-03-01
Full Text Available In this paper the authors give a solution to the problem of the impact of a rolling stock on the rail track on the basis of modeling a railway track as a multi-layered space, introducing each of the layers is a quasi-elastic orthotropic layer with cylindrical anisotropy in the polar coordinate system. The article describes wave equations, taking into account the rotational inertia of cross sectional and transverse shear strains. From the point of view of classical structural mechanics train path can be represented as a multilayer system comprising separate layers with different stiffness, lying on the foundation being the elastic-isotropic space. Winkler model provides that the basis is linearly deformable space, there are loads influencing its surface. These loads are transferred through a layered deformable half-space. This representation is used in this study as an initial approximation. For more accurate results of the deformation of a railway track because of rolling dynamic loads it is proposed to present a railway track in the form of a layered structure, where each element (assembled rails and sleepers, ballast section, the soil in the embankment, basement soils is modeled as a planar quasi-elastic orthotropic layer with cylindrical anisotropy. The equations describing the dynamic behaviour of flat element in a polar coordinate system are hyperbolic in nature and take into account the rotational inertia of the cross sectional and the transverse shear strains. This allows identifying the impact on the final characteristics of the blade wave effects, and oscillatory processes. In order to determine the unknown functions included in the constitutive equations it is proposed to use decomposition in power series in spatial coordinate and time. In order to determine the coefficients of ray series for the required functions, it is necessary to differentiate the defining wave equations k times on time, to take their difference on the different
Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
2013-01-01
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
From linear to generalized linear mixed models: A case study in repeated measures
Compared to traditional linear mixed models, generalized linear mixed models (GLMMs) can offer better correspondence between response variables and explanatory models, yielding more efficient estimates and tests in the analysis of data from designed experiments. Using proportion data from a designed...
Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods
Prior, Christopher
2014-03-11
© 2014, Springer Science+Business Media Dordrecht. We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.
Montoye, Alexander H K; Begum, Munni; Henning, Zachary; Pfeiffer, Karin A
2017-02-01
This study had three purposes, all related to evaluating energy expenditure (EE) prediction accuracy from body-worn accelerometers: (1) compare linear regression to linear mixed models, (2) compare linear models to artificial neural network models, and (3) compare accuracy of accelerometers placed on the hip, thigh, and wrists. Forty individuals performed 13 activities in a 90 min semi-structured, laboratory-based protocol. Participants wore accelerometers on the right hip, right thigh, and both wrists and a portable metabolic analyzer (EE criterion). Four EE prediction models were developed for each accelerometer: linear regression, linear mixed, and two ANN models. EE prediction accuracy was assessed using correlations, root mean square error (RMSE), and bias and was compared across models and accelerometers using repeated-measures analysis of variance. For all accelerometer placements, there were no significant differences for correlations or RMSE between linear regression and linear mixed models (correlations: r = 0.71-0.88, RMSE: 1.11-1.61 METs; p > 0.05). For the thigh-worn accelerometer, there were no differences in correlations or RMSE between linear and ANN models (ANN-correlations: r = 0.89, RMSE: 1.07-1.08 METs. Linear models-correlations: r = 0.88, RMSE: 1.10-1.11 METs; p > 0.05). Conversely, one ANN had higher correlations and lower RMSE than both linear models for the hip (ANN-correlation: r = 0.88, RMSE: 1.12 METs. Linear models-correlations: r = 0.86, RMSE: 1.18-1.19 METs; p linear models for the wrist-worn accelerometers (ANN-correlations: r = 0.82-0.84, RMSE: 1.26-1.32 METs. Linear models-correlations: r = 0.71-0.73, RMSE: 1.55-1.61 METs; p models offer a significant improvement in EE prediction accuracy over linear models. Conversely, linear models showed similar EE prediction accuracy to machine learning models for hip- and thigh
Directory of Open Access Journals (Sweden)
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.
Three-Dimensional Computer-Assisted Two-Layer Elastic Models of the Face.
Ueda, Koichi; Shigemura, Yuka; Otsuki, Yuki; Fuse, Asuka; Mitsuno, Daisuke
2017-11-01
To make three-dimensional computer-assisted elastic models for the face, we decided on five requirements: (1) an elastic texture like skin and subcutaneous tissue; (2) the ability to take pen marking for incisions; (3) the ability to be cut with a surgical knife; (4) the ability to keep stitches in place for a long time; and (5) a layered structure. After testing many elastic solvents, we have made realistic three-dimensional computer-assisted two-layer elastic models of the face and cleft lip from the computed tomographic and magnetic resonance imaging stereolithographic data. The surface layer is made of polyurethane and the inner layer is silicone. Using this elastic model, we taught residents and young doctors how to make several typical local flaps and to perform cheiloplasty. They could experience realistic simulated surgery and understand three-dimensional movement of the flaps.
A elastic-plastic model for pipe whip
International Nuclear Information System (INIS)
Maneschy, J.E.A.
1980-04-01
The dynamic behavior of a cantilever beam simulating a pipe after full rupture at a given cross-section is investigated. This problem, known as pipe whip, has to be analysed within the frame of plastic deformations. The physical model is represented by a cantilever, subjected to a step-load at the free end, and a support designed to absorb the maximum possible kinetic energy of the tube generated by suddenly applied force. The analysis is performed using the Bernoulli theory for straight beams, assuming for the moment-curvature relation a bi-linear law. (author)
A staggered-grid convolutional differentiator for elastic wave modelling
Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun
2015-11-01
The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.
Elastic models for the non-Arrhenius relaxation time of glass-forming liquids
DEFF Research Database (Denmark)
Dyre, Jeppe
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all equivalent in the Einstein approximation (where the short-time...... elastic properties are all determined by just one effective, temperature-dependent force constant). We finally discuss the connection between the elastic models and two well-established research fields of condensed-matter physics: point defects in crystals and solid-state diffusion....
Elastic models for the Non-Arrhenius Relaxation Time of Glass-Forming Liquids
DEFF Research Database (Denmark)
Dyre, J. C.
2006-01-01
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all equivalent in the Einstein approximation (where the short-time...... elastic properties are all determined by just one effective, temperature-dependent force constant). We finally discuss the connection between the elastic models and two well-established research fields of condensed-matter physics: point defects in crystals and solid-state diffusion....
Xia, Z. M.; Wang, C. G.; Tan, H. F.
2018-04-01
A pseudo-beam model with modified internal bending moment is presented to predict elastic properties of graphene, including the Young's modulus and Poisson's ratio. In order to overcome a drawback in existing molecular structural mechanics models, which only account for pure bending (constant bending moment), the presented model accounts for linear bending moments deduced from the balance equations. Based on this pseudo-beam model, an analytical prediction is accomplished to predict the Young's modulus and Poisson's ratio of graphene based on the equation of the strain energies by using Castigliano second theorem. Then, the elastic properties of graphene are calculated compared with results available in literature, which verifies the feasibility of the pseudo-beam model. Finally, the pseudo-beam model is utilized to study the twisting wrinkling characteristics of annular graphene. Due to modifications of the internal bending moment, the wrinkling behaviors of graphene sheet are predicted accurately. The obtained results show that the pseudo-beam model has a good ability to predict the elastic properties of graphene accurately, especially the out-of-plane deformation behavior.
Evaluating the double Poisson generalized linear model.
Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique
2013-10-01
The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
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.
Non-Conventional Thermodynamics and Models of Gradient Elasticity
Directory of Open Access Journals (Sweden)
Hans-Dieter Alber
2018-03-01
Full Text Available We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory.
Petri Nets as Models of Linear Logic
DEFF Research Database (Denmark)
Engberg, Uffe Henrik; Winskel, Glynn
1990-01-01
The chief purpose of this paper is to appraise the feasibility of Girad's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic...
Paprottka, P M; Zengel, P; Cyran, C C; Ingrisch, M; Nikolaou, K; Reiser, M F; Clevert, D A
2014-01-01
To evaluate the ultrasound tissue elasticity imaging by comparison to multimodality imaging using image fusion with Magnetic Resonance Imaging (MRI) and conventional grey scale imaging with additional elasticity-ultrasound in an experimental small-animal-squamous-cell carcinoma-model for the assessment of tissue morphology. Human hypopharynx carcinoma cells were subcutaneously injected into the left flank of 12 female athymic nude rats. After 10 days (SD ± 2) of subcutaneous tumor growth, sonographic grey scale including elasticity imaging and MRI measurements were performed using a high-end ultrasound system and a 3T MR. For image fusion the contrast-enhanced MRI DICOM data set was uploaded in the ultrasonic device which has a magnetic field generator, a linear array transducer (6-15 MHz) and a dedicated software package (GE Logic E9), that can detect transducers by means of a positioning system. Conventional grey scale and elasticity imaging were integrated in the image fusion examination. After successful registration and image fusion the registered MR-images were simultaneously shown with the respective ultrasound sectional plane. Data evaluation was performed using the digitally stored video sequence data sets by two experienced radiologist using a modified Tsukuba Elasticity score. The colors "red and green" are assigned for an area of soft tissue, "blue" indicates hard tissue. In all cases a successful image fusion and plan registration with MRI and ultrasound imaging including grey scale and elasticity imaging was possible. The mean tumor volume based on caliper measurements in 3 dimensions was ~323 mm3. 4/12 rats were evaluated with Score I, 5/12 rates were evaluated with Score II, 3/12 rates were evaluated with Score III. There was a close correlation in the fused MRI with existing small necrosis in the tumor. None of the scored II or III lesions was visible by conventional grey scale. The comparison of ultrasound tissue elasticity imaging enables a
Linear approximation model network and its formation via ...
Indian Academy of Sciences (India)
To overcome the deficiency of `local model network' (LMN) techniques, an alternative `linear approximation model' (LAM) network approach is proposed. Such a network models a nonlinear or practical system with multiple linear models fitted along operating trajectories, where individual models are simply networked ...
Static friction in elastic adhesive MEMS contacts, models and experiment
Tas, Niels Roelof; Gui, C.; Elwenspoek, Michael Curt
2000-01-01
Static friction in shearing mode can be expressed as the product of the shear strength of the interface and the real contact area. The influence of roughness on friction in elastic adhesive contact is analyzed. Special attention is paid to low loading conditions, in which the number of contact
Double folding model analysis of elastic scattering of halo nucleus ...
Indian Academy of Sciences (India)
carried out which provide valuable insight for improving our understanding of nuclear reactions. One of the interesting aspects is to understand the effect of the halo structure, on elastic scattering cross-sections at near-Coulomb barrier energies in reactions induced by neutron halo nuclei and weakly bound radioactive ...
Phenomenological models of elastic nucleon scattering and predictions for LHC
Czech Academy of Sciences Publication Activity Database
Kašpar, J.; Kundrát, Vojtěch; Lokajíček, Miloš; Procházka, J.
2010-01-01
Roč. 843, č. 1 (2010), s. 84-106 ISSN 0550-3213 R&D Projects: GA MŠk LA08015 Institutional research plan: CEZ:AV0Z10100502 Keywords : high energy elastic hadron scattering Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 4.642, year: 2010
Linear regression crash prediction models : issues and proposed solutions.
2010-05-01
The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...
Game Theory and its Relationship with Linear Programming Models ...
African Journals Online (AJOL)
Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.
Electricity consumption forecasting in Italy using linear regression models
Energy Technology Data Exchange (ETDEWEB)
Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio [DIAM, Seconda Universita degli Studi di Napoli, Via Roma 29, 81031 Aversa (CE) (Italy)
2009-09-15
The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of {+-}1% for the best case and {+-}11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)
Electricity consumption forecasting in Italy using linear regression models
International Nuclear Information System (INIS)
Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio
2009-01-01
The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of ±1% for the best case and ±11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)
Czech Academy of Sciences Publication Activity Database
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
Directory of Open Access Journals (Sweden)
Xin Gu
2017-01-01
Full Text Available The constitutive modeling and numerical implementation of a nonordinary state-based peridynamic (NOSB-PD model corresponding to the classical elastic model are presented. Besides, the numerical instability problem of the NOSB-PD model is analyzed, and a penalty method involving the hourglass force is proposed to control the instabilities. Further, two benchmark problems, the static elastic deformation of a simple supported beam and the elastic wave propagation in a two-dimensional rod, are discussed with the present method. It proves that the penalty instability control method is effective in suppressing the displacement oscillations and improving the accuracy of calculated stress fields with a proper hourglass force coefficient, and the NOSB-PD approach with instability control can analyze the problems of structure deformation and elastic wave propagation well.
Modelling Elastic Scattering and Light Transport in 3D Collagen Gel Constructs
National Research Council Canada - National Science Library
Bixio, L
2001-01-01
A model of elastic scattering and light propagation is presented, which can be used to obtain the scattering coefficient, the index of refraction and the distribution of the collagen fibrils in a gel...
A Note on the Identifiability of Generalized Linear Mixed Models
DEFF Research Database (Denmark)
Labouriau, Rodrigo
2014-01-01
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity...... conditions, and, therefore, is extensible to quasi-likelihood based generalized linear models. In particular, binomial and Poisson mixed models with dispersion parameter are identifiable when equipped with the standard parametrization...
Connolly, Joseph W.; Kopasakis, George; Lemon, Kimberly A.
2010-01-01
A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model
Experimental models of Elastic Structures: Tensile Buckling and Eshelby-like Forces
Misseroni, Diego
2013-01-01
Mechanical models have been invented, designed and realized to experimentally confirm unexpected behaviours theoretically predicted in elasticity: - instabilities and bifurcations occurring in structures under ‘tensile dead load’ and the influence of the constraint’s curvature; - the presence of an ‘Eshelby-like’ or ‘configurational’ force in structures with movable constraints. Furthermore, ‘classical’ features in elasticity have been substantied by testing small-scale models and ob...
14O+p elastic scattering in a microscopic cluster model
International Nuclear Information System (INIS)
Descouvemont, P.; Baye, D.; Leo, F.
2006-01-01
The 14O+p elastic scattering is analyzed in a fully microscopic cluster model. With the Resonating Group Method associated with the microscopic R-matrix theory, phase shifts and cross sections are calculated. Data on 16O+p are used to test the precision of the model. For the 14O+p elastic scattering, an excellent agreement is found with recent experimental data. Resonances properties in 15F are discussed
Linear control theory for gene network modeling.
Shin, Yong-Jun; Bleris, Leonidas
2010-09-16
Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.
LINEAR MODEL FOR NON ISOSCELES ABSORBERS.
Energy Technology Data Exchange (ETDEWEB)
BERG,J.S.
2003-05-12
Previous analyses have assumed that wedge absorbers are triangularly shaped with equal angles for the two faces. In this case, to linear order, the energy loss depends only on the position in the direction of the face tilt, and is independent of the incoming angle. One can instead construct an absorber with entrance and exit faces facing rather general directions. In this case, the energy loss can depend on both the position and the angle of the particle in question. This paper demonstrates that and computes the effect to linear order.
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.
Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.
Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad
2016-02-01
In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.
Energy Technology Data Exchange (ETDEWEB)
Lester, Brian T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
Energy Technology Data Exchange (ETDEWEB)
Lester, Brian [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...
Tried and True: Springing into Linear Models
Darling, Gerald
2012-01-01
In eighth grade, students usually learn about forces in science class and linear relationships in math class, crucial topics that form the foundation for further study in science and engineering. An activity that links these two fundamental concepts involves measuring the distance a spring stretches as a function of how much weight is suspended…
Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems
Directory of Open Access Journals (Sweden)
Bambang Riyanto
2005-11-01
Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.
A modified elastic foundation contact model for application in 3D models of the prosthetic knee.
Pérez-González, Antonio; Fenollosa-Esteve, Carlos; Sancho-Bru, Joaquín L; Sánchez-Marín, Francisco T; Vergara, Margarita; Rodríguez-Cervantes, Pablo J
2008-04-01
Different models have been used in the literature for the simulation of surface contact in biomechanical knee models. However, there is a lack of systematic comparisons of these models applied to the simulation of a common case, which will provide relevant information about their accuracy and suitability for application in models of the implanted knee. In this work a comparison of the Hertz model (HM), the elastic foundation model (EFM) and the finite element model (FEM) for the simulation of the elastic contact in a 3D model of the prosthetic knee is presented. From the results of this comparison it is found that although the nature of the EFM offers advantages when compared with that of the HM for its application to realistic prosthetic surfaces, and when compared with the FEM in CPU time, its predictions can differ from FEM in some circumstances. These differences are considerable if the comparison is performed for prescribed displacements, although they are less important for prescribed loads. To solve these problems a new modified elastic foundation model (mEFM) is proposed that maintains basically the simplicity of the original model while producing much more accurate results. In this paper it is shown that this new mEFM calculates pressure distribution and contact area with accuracy and short computation times for toroidal contacting surfaces. Although further work is needed to confirm its validity for more complex geometries the mEFM is envisaged as a good option for application in 3D knee models to predict prosthetic knee performance.
Ordinal Log-Linear Models for Contingency Tables
Directory of Open Access Journals (Sweden)
Brzezińska Justyna
2016-12-01
Full Text Available A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.
Recent Updates to the GEOS-5 Linear Model
Holdaway, Dan; Kim, Jong G.; Errico, Ron; Gelaro, Ronald; Mahajan, Rahul
2014-01-01
Global Modeling and Assimilation Office (GMAO) is close to having a working 4DVAR system and has developed a linearized version of GEOS-5.This talk outlines a series of improvements made to the linearized dynamics, physics and trajectory.Of particular interest is the development of linearized cloud microphysics, which provides the framework for 'all-sky' data assimilation.
Optical model theory of elastic electron- and positron-atom scattering at intermediate energies
International Nuclear Information System (INIS)
Joachain, C.J.
1977-01-01
It is stated that the basic idea of the optical model theory is to enable analysis of the elastic scattering of a particle from a complex target by replacing the complicated interactions between the beam and the target by an optical potential, or pseudopotential, in which the incident particle moves. Once the optical potential is determined the original many-body elastic scattering problem reduces to a one-body situation. The resulting optical potential is, however, a very complicated operator, and the formal expressions obtained from first principles for the optical potential can only be evaluated approximately in a few simple cases, such as high energy elastic hadron-nucleus scattering, for the the optical potential can be expressed in terms of two-body hadron-nucleon amplitudes, and the non-relativistic elastic scattering of fast charged particles by atoms. The elastic scattering of an electron or positron by a neutral atom at intermediate energies is here considered. Exchange effects between the projectile and the atomic electrons are considered; also absorption and polarisation effects. Applications of the full-wave optical model have so far only been made to the elastic scattering of fast electrons and positrons by atomic H, He, Ne, and Ar. Agreements of the optical model results with absolute measurements of differential cross sections for electron scattering are very good, an agreement that improves as the energy increases, but deteriorates quickly as the incident energy becomes lower than 50 eV for atomic H or 100 eV for He. For more complex atoms the optical model calculations also appear very encouraging. With regard to positron-atom elastic scattering the optical model results for positron-He scattering differ markedly at small angles from the corresponding electron-He values. It would be interesting to have experimental angular distributions of positron-atom elastic scattering in order to check predictions of the optical model theory. (U.K.)
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.
Han, Fei; Azdoud, Yan; Lubineau, Gilles
2014-01-01
We present two modeling approaches for predicting the macroscopic elastic properties of carbon nanotubes/polymer composites with thick interphase regions at the nanotube/matrix frontier. The first model is based on local continuum mechanics
Double generalized linear compound poisson models to insurance claims data
DEFF Research Database (Denmark)
Andersen, Daniel Arnfeldt; Bonat, Wagner Hugo
2017-01-01
This paper describes the specification, estimation and comparison of double generalized linear compound Poisson models based on the likelihood paradigm. The models are motivated by insurance applications, where the distribution of the response variable is composed by a degenerate distribution...... implementation and illustrate the application of double generalized linear compound Poisson models using a data set about car insurances....
Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis
Luo, Wen; Azen, Razia
2013-01-01
Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…
Thurstonian models for sensory discrimination tests as generalized linear models
DEFF Research Database (Denmark)
Brockhoff, Per B.; Christensen, Rune Haubo Bojesen
2010-01-01
as a so-called generalized linear model. The underlying sensory difference 6 becomes directly a parameter of the statistical model and the estimate d' and it's standard error becomes the "usual" output of the statistical analysis. The d' for the monadic A-NOT A method is shown to appear as a standard......Sensory discrimination tests such as the triangle, duo-trio, 2-AFC and 3-AFC tests produce binary data and the Thurstonian decision rule links the underlying sensory difference 6 to the observed number of correct responses. In this paper it is shown how each of these four situations can be viewed...
Linear control theory for gene network modeling.
Directory of Open Access Journals (Sweden)
Yong-Jun Shin
Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.
Forecasting Volatility of Dhaka Stock Exchange: Linear Vs Non-linear models
Directory of Open Access Journals (Sweden)
Masudul Islam
2012-10-01
Full Text Available Prior information about a financial market is very essential for investor to invest money on parches share from the stock market which can strengthen the economy. The study examines the relative ability of various models to forecast daily stock indexes future volatility. The forecasting models that employed from simple to relatively complex ARCH-class models. It is found that among linear models of stock indexes volatility, the moving average model ranks first using root mean square error, mean absolute percent error, Theil-U and Linex loss function criteria. We also examine five nonlinear models. These models are ARCH, GARCH, EGARCH, TGARCH and restricted GARCH models. We find that nonlinear models failed to dominate linear models utilizing different error measurement criteria and moving average model appears to be the best. Then we forecast the next two months future stock index price volatility by the best (moving average model.
Extension of non-linear beam models with deformable cross sections
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
Wang, Likun; Du, Zhijiang; Dong, Wei; Shen, Yi; Zhao, Guangyu
2018-03-19
To achieve strength augmentation, endurance enhancement, and human assistance in a functional autonomous exoskeleton, control precision, back drivability, low output impedance, and mechanical compactness are desired. In our previous work, two elastic modules were designed for human-robot interaction sensing and compliant control, respectively. According to the intrinsic sensing properties of the elastic module, in this paper, only one compact elastic module is applied to realize both purposes. Thus, the corresponding control strategy is required and evolving internal model control is proposed to address this issue. Moreover, the input signal to the controller is derived from the deflection of the compact elastic module. The human-robot interaction is considered as the disturbance which is approximated by the output error between the exoskeleton control plant and evolving forward learning model. Finally, to verify our proposed control scheme, several experiments are conducted with our robotic exoskeleton system. The experiment shows a satisfying result and promising application feasibility.
Directory of Open Access Journals (Sweden)
Likun Wang
2018-03-01
Full Text Available To achieve strength augmentation, endurance enhancement, and human assistance in a functional autonomous exoskeleton, control precision, back drivability, low output impedance, and mechanical compactness are desired. In our previous work, two elastic modules were designed for human–robot interaction sensing and compliant control, respectively. According to the intrinsic sensing properties of the elastic module, in this paper, only one compact elastic module is applied to realize both purposes. Thus, the corresponding control strategy is required and evolving internal model control is proposed to address this issue. Moreover, the input signal to the controller is derived from the deflection of the compact elastic module. The human–robot interaction is considered as the disturbance which is approximated by the output error between the exoskeleton control plant and evolving forward learning model. Finally, to verify our proposed control scheme, several experiments are conducted with our robotic exoskeleton system. The experiment shows a satisfying result and promising application feasibility.
Wang, Likun; Du, Zhijiang; Dong, Wei; Shen, Yi; Zhao, Guangyu
2018-01-01
To achieve strength augmentation, endurance enhancement, and human assistance in a functional autonomous exoskeleton, control precision, back drivability, low output impedance, and mechanical compactness are desired. In our previous work, two elastic modules were designed for human–robot interaction sensing and compliant control, respectively. According to the intrinsic sensing properties of the elastic module, in this paper, only one compact elastic module is applied to realize both purposes. Thus, the corresponding control strategy is required and evolving internal model control is proposed to address this issue. Moreover, the input signal to the controller is derived from the deflection of the compact elastic module. The human–robot interaction is considered as the disturbance which is approximated by the output error between the exoskeleton control plant and evolving forward learning model. Finally, to verify our proposed control scheme, several experiments are conducted with our robotic exoskeleton system. The experiment shows a satisfying result and promising application feasibility. PMID:29562684
How can cells sense the elasticity of a substrate? An analysis using a cell tensegrity model
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
Andersen, Per Kragh; Klein, John P.; Rosthøj, Susanne
2003-01-01
Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model......Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model...
International Nuclear Information System (INIS)
Fazio, C; Guastella, I; Tarantino, G
2007-01-01
In this paper, we describe a pedagogical approach to elastic body movement based on measurements of the contact times between a metallic rod and small bodies colliding with it and on modelling of the experimental results by using a microcomputer-based laboratory and simulation tools. The experiments and modelling activities have been built in the context of the laboratory of mechanical wave propagation of the two-year graduate teacher education programme of Palermo's University. Some considerations about observed modifications in trainee teachers' attitudes in utilizing experiments and modelling are discussed
Linear and non-linear autoregressive models for short-term wind speed forecasting
International Nuclear Information System (INIS)
Lydia, M.; Suresh Kumar, S.; Immanuel Selvakumar, A.; Edwin Prem Kumar, G.
2016-01-01
Highlights: • Models for wind speed prediction at 10-min intervals up to 1 h built on time-series wind speed data. • Four different multivariate models for wind speed built based on exogenous variables. • Non-linear models built using three data mining algorithms outperform the linear models. • Autoregressive models based on wind direction perform better than other models. - Abstract: Wind speed forecasting aids in estimating the energy produced from wind farms. The soaring energy demands of the world and minimal availability of conventional energy sources have significantly increased the role of non-conventional sources of energy like solar, wind, etc. Development of models for wind speed forecasting with higher reliability and greater accuracy is the need of the hour. In this paper, models for predicting wind speed at 10-min intervals up to 1 h have been built based on linear and non-linear autoregressive moving average models with and without external variables. The autoregressive moving average models based on wind direction and annual trends have been built using data obtained from Sotavento Galicia Plc. and autoregressive moving average models based on wind direction, wind shear and temperature have been built on data obtained from Centre for Wind Energy Technology, Chennai, India. While the parameters of the linear models are obtained using the Gauss–Newton algorithm, the non-linear autoregressive models are developed using three different data mining algorithms. The accuracy of the models has been measured using three performance metrics namely, the Mean Absolute Error, Root Mean Squared Error and Mean Absolute Percentage Error.
The modified Black-Scholes model via constant elasticity of variance for stock options valuation
Edeki, S. O.; Owoloko, E. A.; Ugbebor, O. O.
2016-02-01
In this paper, the classical Black-Scholes option pricing model is visited. We present a modified version of the Black-Scholes model via the application of the constant elasticity of variance model (CEVM); in this case, the volatility of the stock price is shown to be a non-constant function unlike the assumption of the classical Black-Scholes model.
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.
Applicability of linear and non-linear potential flow models on a Wavestar float
DEFF Research Database (Denmark)
Bozonnet, Pauline; Dupin, Victor; Tona, Paolino
2017-01-01
as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...
A linear model of population dynamics
Lushnikov, A. A.; Kagan, A. I.
2016-08-01
The Malthus process of population growth is reformulated in terms of the probability w(n,t) to find exactly n individuals at time t assuming that both the birth and the death rates are linear functions of the population size. The master equation for w(n,t) is solved exactly. It is shown that w(n,t) strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of w(n,t).
Directory of Open Access Journals (Sweden)
Darenskiy Alexander
2017-01-01
Full Text Available At present, the most common track model is the one in which rails are presented as bars of infinite length rested on continuous elastic foundation. However, some specialists consider the model to be rather ideal for railways in terms of track and the technical state of track. Calculation of track as a bar rested on numerous elastic supports with variable characteristics of stiffness under static loads has shown that application of methods of elastic foundation gives results understated by 17-24%. The study presents mathematic models of the vehicle/track dynamic system, and a design scheme of track presented as a bar on numerous elastic dissipative supports with non-linear characteristics, which is taken on the base of this system. The authors developed models and methods to define the reduced vertical stiffness of the track in the wheel/rail contact point, which considers rail elastic and geometric characteristics, stiffness of supports, distance between supports and distributed track mass. The value of stiffness is variable by time for each wheel at any time and various for the vehicle’s wheels. The mathematical model proposed has been implemented in Matlab software and will make it possible to conduct numerical research into the track/vehicle dynamics.
Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy.
Cleveland, Robin O; Sapozhnikov, Oleg A
2005-10-01
A time-domain finite-difference solution to the equations of linear elasticity was used to model the propagation of lithotripsy waves in kidney stones. The model was used to determine the loading on the stone (principal stresses and strains and maximum shear stresses and strains) due to the impact of lithotripsy shock waves. The simulations show that the peak loading induced in kidney stones is generated by constructive interference from shear waves launched from the outer edge of the stone with other waves in the stone. Notably the shear wave induced loads were significantly larger than the loads generated by the classic Hopkinson or spall effect. For simulations where the diameter of the focal spot of the lithotripter was smaller than that of the stone the loading decreased by more than 50%. The constructive interference was also sensitive to shock rise time and it was found that the peak tensile stress reduced by 30% as rise time increased from 25 to 150 ns. These results demonstrate that shear waves likely play a critical role in stone comminution and that lithotripters with large focal widths and short rise times should be effective at generating high stresses inside kidney stones.
Directory of Open Access Journals (Sweden)
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.
A test for the parameters of multiple linear regression models ...
African Journals Online (AJOL)
A test for the parameters of multiple linear regression models is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. The test is robust relative to the assumptions of homogeneity of variances and absence of serial correlation of the classical F-test. Under certain null and ...
Modeling Non-Linear Material Properties in Composite Materials
2016-06-28
Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Reliability modelling and simulation of switched linear system ...
African Journals Online (AJOL)
Reliability modelling and simulation of switched linear system control using temporal databases. ... design of fault-tolerant real-time switching systems control and modelling embedded micro-schedulers for complex systems maintenance.
Three-dimensional inverse modelling of damped elastic wave propagation in the Fourier domain
Petrov, Petr V.; Newman, Gregory A.
2014-09-01
3-D full waveform inversion (FWI) of seismic wavefields is routinely implemented with explicit time-stepping simulators. A clear advantage of explicit time stepping is the avoidance of solving large-scale implicit linear systems that arise with frequency domain formulations. However, FWI using explicit time stepping may require a very fine time step and (as a consequence) significant computational resources and run times. If the computational challenges of wavefield simulation can be effectively handled, an FWI scheme implemented within the frequency domain utilizing only a few frequencies, offers a cost effective alternative to FWI in the time domain. We have therefore implemented a 3-D FWI scheme for elastic wave propagation in the Fourier domain. To overcome the computational bottleneck in wavefield simulation, we have exploited an efficient Krylov iterative solver for the elastic wave equations approximated with second and fourth order finite differences. The solver does not exploit multilevel preconditioning for wavefield simulation, but is coupled efficiently to the inversion iteration workflow to reduce computational cost. The workflow is best described as a series of sequential inversion experiments, where in the case of seismic reflection acquisition geometries, the data has been laddered such that we first image highly damped data, followed by data where damping is systemically reduced. The key to our modelling approach is its ability to take advantage of solver efficiency when the elastic wavefields are damped. As the inversion experiment progresses, damping is significantly reduced, effectively simulating non-damped wavefields in the Fourier domain. While the cost of the forward simulation increases as damping is reduced, this is counterbalanced by the cost of the outer inversion iteration, which is reduced because of a better starting model obtained from the larger damped wavefield used in the previous inversion experiment. For cross-well data, it is
Multivariate statistical modelling based on generalized linear models
Fahrmeir, Ludwig
1994-01-01
This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of m...
Approximating chiral quark models with linear σ-models
International Nuclear Information System (INIS)
Broniowski, Wojciech; Golli, Bojan
2003-01-01
We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear σ-model contains, at the lowest level of the gradient-expanded meson action, an additional term of the form ((1)/(2))A(σ∂ μ σ+π∂ μ π) 2 . We investigate the dynamical consequences of this term and its relevance to the phenomenology of the soliton models of the nucleon. It is found that the inclusion of the new term allows for a more efficient approximation of the underlying quark theory, especially in those cases where dynamics allows for a large deviation of the chiral fields from the chiral circle, such as in quark models with non-local regulators. This is of practical importance, since the σ-models with valence quarks only are technically much easier to treat and simpler to solve than the quark models with the full-fledged Dirac sea
Biomechanics – Elastic Foundation Applied in Modelling of Calcaneal Nails
Directory of Open Access Journals (Sweden)
Sejda František
2015-12-01
Full Text Available This paper presents a strength analysis of a calcaneal nail (material Ti6Al4V and stainless steel which is used to treat complex heel fractures. The application focuses on a unique calcaneal nail, the C-NAIL, produced by Medin a.s. (Nové Město na Moravě, Czech Republic. The paper first presents an analysis of fracture types, treatment methods and loading of the calcaneus. It then presents an analysis of limit conditions and loading. Calculations (displacement and stress are performed for 6 and 7 fixing screws using FEM (Ansys Workbench 14 software. The calculation involves a new, original application of an elastic foundation, which effectively replaces the complex interaction of the calcaneal nail and the heel bone.
Elastic model of the traction behavior of two traction lubricants
Loewenthal, S. H.; Rohn, D. A.
1984-01-01
In the analysis of rolling-sliding concentrated contacts, such as gears, bearings and traction drives, the traction characteristics of the lubricant are of prime importance. The elastic shear modulus and limiting shear stress properties of the lubricant dictate the traction/slip characteristics and power loss associated with an EHD contact undergoing slip and/or spin. These properties can be deducted directly from the initial slope m and maximum traction coefficient micron of an experimental traction curve. In this investigation, correlation equations are presented to predict m and micron for two modern traction fluids based on the regression analysis of 334 separate traction disk machine experiments. The effects of contact pressure, temperature, surface velocity, ellipticity ratio are examined. Problems in deducing lubricant shear moduli from disk machine tests are discussed. Previously announced in STAR as N83-20116
Latent log-linear models for handwritten digit classification.
Deselaers, Thomas; Gass, Tobias; Heigold, Georg; Ney, Hermann
2012-06-01
We present latent log-linear models, an extension of log-linear models incorporating latent variables, and we propose two applications thereof: log-linear mixture models and image deformation-aware log-linear models. The resulting models are fully discriminative, can be trained efficiently, and the model complexity can be controlled. Log-linear mixture models offer additional flexibility within the log-linear modeling framework. Unlike previous approaches, the image deformation-aware model directly considers image deformations and allows for a discriminative training of the deformation parameters. Both are trained using alternating optimization. For certain variants, convergence to a stationary point is guaranteed and, in practice, even variants without this guarantee converge and find models that perform well. We tune the methods on the USPS data set and evaluate on the MNIST data set, demonstrating the generalization capabilities of our proposed models. Our models, although using significantly fewer parameters, are able to obtain competitive results with models proposed in the literature.
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...
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.
Directory of Open Access Journals (Sweden)
Jintao Song
2015-01-01
Full Text Available The foundation boundaries of numerical simulation models of hydraulic structures dominated by a vertical load are investigated. The method used is based on the stress formula for fundamental solutions to semi-infinite space body elastic mechanics under a vertical concentrated force. The limit method is introduced into the original formula, which is then partitioned and analyzed according to the direction of the depth extension of the foundation. The point load will be changed to a linear load with a length of 2a. Inverse proportion function assumptions are proposed at parameter a and depth l of the calculation points to solve the singularity questions of elastic stress in a semi-infinite space near the ground. Compared with the original formula, changing the point load to a linear load with a length of 2a is more reasonable. Finally, the boundary depth criterion of a hydraulic numerical simulation model is derived and applied to determine the depth boundary formula for gravity dam numerical simulations.
Linear Regression Models for Estimating True Subsurface ...
Indian Academy of Sciences (India)
47
The objective is to minimize the processing time and computer memory required. 10 to carry out inversion .... to the mainland by two long bridges. .... term. In this approach, the model converges when the squared sum of the differences. 143.
Detection of Natural Fractures from Observed Surface Seismic Data Based on a Linear-Slip Model
Chen, Huaizhen; Zhang, Guangzhi
2018-03-01
Natural fractures play an important role in migration of hydrocarbon fluids. Based on a rock physics effective model, the linear-slip model, which defines fracture parameters (fracture compliances) for quantitatively characterizing the effects of fractures on rock total compliance, we propose a method to detect natural fractures from observed seismic data via inversion for the fracture compliances. We first derive an approximate PP-wave reflection coefficient in terms of fracture compliances. Using the approximate reflection coefficient, we derive azimuthal elastic impedance as a function of fracture compliances. An inversion method to estimate fracture compliances from seismic data is presented based on a Bayesian framework and azimuthal elastic impedance, which is implemented in a two-step procedure: a least-squares inversion for azimuthal elastic impedance and an iterative inversion for fracture compliances. We apply the inversion method to synthetic and real data to verify its stability and reasonability. Synthetic tests confirm that the method can make a stable estimation of fracture compliances in the case of seismic data containing a moderate signal-to-noise ratio for Gaussian noise, and the test on real data reveals that reasonable fracture compliances are obtained using the proposed method.
Islam, M M
2013-01-01
We study high energy $\\small{\\rm{pp}}$ and $\\small{\\rm{\\bar {p}p}}$ elastic scattering in the TeV region based on an effective field theory model of the proton. We phenomenologically investigate the main processes underlying elastic scattering and quantitatively describe the measured elastic d$\\small{\\sigma}$/dt at energies 7.0 TeV (LHC $\\small{\\rm{pp}}$), 1.96 TeV (Tevatron $\\small{\\rm{\\bar {p}p}}$), and 0.630 TeV (SPS $\\small{\\rm{\\bar {p}p}}$). Finally, we give our prediction for $\\small{\\rm{pp}}$ elastic d$\\small{\\sigma}$/dt at 14 TeV that will be measured by the TOTEM Collaboration.
Energy Technology Data Exchange (ETDEWEB)
Hamed, Elham [University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, 1206 West Green Street, Urbana, IL 61801 (United States); Novitskaya, Ekaterina, E-mail: eevdokim@ucsd.edu [University of California, San Diego, Department of Mechanical and Aerospace Engineering, Materials Science and Engineering Program, 9500 Gilman Dr., La Jolla, CA 92093 (United States); Li, Jun; Jasiuk, Iwona [University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, 1206 West Green Street, Urbana, IL 61801 (United States); McKittrick, Joanna [University of California, San Diego, Department of Mechanical and Aerospace Engineering, Materials Science and Engineering Program, 9500 Gilman Dr., La Jolla, CA 92093 (United States)
2015-09-01
The elastic moduli of trabecular bone were modeled using an analytical multiscale approach. Trabecular bone was represented as a porous nanocomposite material with a hierarchical structure spanning from the collagen–mineral level to the trabecular architecture level. In parallel, compression testing was done on bovine femoral trabecular bone samples in two anatomical directions, parallel to the femoral neck axis and perpendicular to it, and the measured elastic moduli were compared with the corresponding theoretical results. To gain insights on the interaction of collagen and minerals at the nanoscale, bone samples were deproteinized or demineralized. After such processing, the treated samples remained as self-standing structures and were tested in compression. Micro-computed tomography was used to characterize the hierarchical structure of these three bone types and to quantify the amount of bone porosity. The obtained experimental data served as inputs to the multiscale model and guided us to represent bone as an interpenetrating composite material. Good agreement was found between the theory and experiments for the elastic moduli of the untreated, deproteinized, and demineralized trabecular bone. - Highlights: • A multiscale model was used to predict the elastic moduli of trabecular bone. • Samples included demineralized, deproteinized and untreated bone. • The model portrays bone as a porous, interpenetrating two phase composite. • The experimental elastic moduli for trabecular bone fell between theoretical bounds.
International Nuclear Information System (INIS)
Hamed, Elham; Novitskaya, Ekaterina; Li, Jun; Jasiuk, Iwona; McKittrick, Joanna
2015-01-01
The elastic moduli of trabecular bone were modeled using an analytical multiscale approach. Trabecular bone was represented as a porous nanocomposite material with a hierarchical structure spanning from the collagen–mineral level to the trabecular architecture level. In parallel, compression testing was done on bovine femoral trabecular bone samples in two anatomical directions, parallel to the femoral neck axis and perpendicular to it, and the measured elastic moduli were compared with the corresponding theoretical results. To gain insights on the interaction of collagen and minerals at the nanoscale, bone samples were deproteinized or demineralized. After such processing, the treated samples remained as self-standing structures and were tested in compression. Micro-computed tomography was used to characterize the hierarchical structure of these three bone types and to quantify the amount of bone porosity. The obtained experimental data served as inputs to the multiscale model and guided us to represent bone as an interpenetrating composite material. Good agreement was found between the theory and experiments for the elastic moduli of the untreated, deproteinized, and demineralized trabecular bone. - Highlights: • A multiscale model was used to predict the elastic moduli of trabecular bone. • Samples included demineralized, deproteinized and untreated bone. • The model portrays bone as a porous, interpenetrating two phase composite. • The experimental elastic moduli for trabecular bone fell between theoretical bounds
Energy Technology Data Exchange (ETDEWEB)
Pavese, Christian; Kim, Taeseong; Wang, Qi; Jonkman, Jason; Sprague, Michael A.
2016-08-01
This work presents a comparison of two beam codes for aero-servo-elastic frameworks: a new structural model for the aeroelastic code HAWC2 and a new nonlinear beam model, BeamDyn, for the aeroelastic modularization framework FAST v8. The main goal is to establish the suitability of the two approaches to model the structural behaviour of modern wind turbine blades in operation. Through a series of benchmarking structural cases of increasing complexity, the capability of the two codes to simulate highly nonlinear effects is investigated and analyzed. Results show that even though the geometrically exact beam theory can better model effects such as very large deflections, rotations, and structural couplings, an approach based on a multi-body formulation assembled through linear elements is capable of computing accurate solutions for typical nonlinear beam theory benchmarking cases.
International Nuclear Information System (INIS)
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
Contributions to micromechanical model of the non linear behavior of the Callovo-Oxfordian argillite
International Nuclear Information System (INIS)
Abou-Chakra Guery, A.
2007-12-01
This work is performed in the general context of the project of underground disposal of radioactive waste, undertaken by the French National Radioactive Waste Management Agency (ANDRA). Due to its strong density and weak permeability, the formation of Callovo-Oxfordian argillite is chosen as one of possible geological barriers to radionuclides. The objective of the study to develop and validate a non linear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modelled as a composite constituted of an elasto(visco)plastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill. The derived model is first compared to Finite Element calculations on unit cell. It is then validated and applied for the prediction of the macroscopic stress-strain responses of the argillite at different geological depths. Finally, the micromechanical model is implemented in a commercial finite element code (Abaqus) for the simulation of a vertical shaft of the underground laboratory. This allows predicting the distribution of damage state and plastic strains and characterizing the excavation damage zone (EDZ). (author)
Radius anomaly in the diffraction model for heavy-ion elastic scattering
Pandey, L. N.; Mukherjee, S. N.
1984-04-01
The elastic scattering of heavy ions, 20Ne on 208Pb, 20Ne on 235U, 84Kr on 208Pb, and 84Kr on 232Th, is examined within the framework of Frahn's diffraction model. An analysis of the experiment using the "quarter point recipe" of the expected Fresnel cross sections yields a larger radius for 208Pb than the radii for 235U and 232Th. It is shown that inclusion of the nuclear deformation in the model removes the above anomaly in the radii, and the assumption of smooth cutoff of the angular momentum simultaneously leads to a better fit to elastic scattering data, compared to those obtained by the earlier workers on the assumption of sharp cutoff. [NUCLEAR REACTIONS Elastic scattering, 20Ne+208Pb (161.2 MeV), 20Ne+235U (175 MeV), 84Kr+208Pb (500 MeV), 84Kr+232Th (500 MeV), diffraction model, nuclear deformation.
Random effect selection in generalised linear models
DEFF Research Database (Denmark)
Denwood, Matt; Houe, Hans; Forkman, Björn
We analysed abattoir recordings of meat inspection codes with possible relevance to onfarm animal welfare in cattle. Random effects logistic regression models were used to describe individual-level data obtained from 461,406 cattle slaughtered in Denmark. Our results demonstrate that the largest...
Model Order Reduction for Non Linear Mechanics
Pinillo, Rubén
2017-01-01
Context: Automotive industry is moving towards a new generation of cars. Main idea: Cars are furnished with radars, cameras, sensors, etc… providing useful information about the environment surrounding the car. Goals: Provide an efficient model for the radar input/output. Reducing computational costs by means of big data techniques.
Identification of Influential Points in a Linear Regression Model
Directory of Open Access Journals (Sweden)
Jan Grosz
2011-03-01
Full Text Available The article deals with the detection and identification of influential points in the linear regression model. Three methods of detection of outliers and leverage points are described. These procedures can also be used for one-sample (independentdatasets. This paper briefly describes theoretical aspects of several robust methods as well. Robust statistics is a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. A simulation model of the simple linear regression is presented.
Heterotic sigma models and non-linear strings
International Nuclear Information System (INIS)
Hull, C.M.
1986-01-01
The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)
Linear latent variable models: the lava-package
DEFF Research Database (Denmark)
Holst, Klaus Kähler; Budtz-Jørgensen, Esben
2013-01-01
are implemented including robust standard errors for clustered correlated data, multigroup analyses, non-linear parameter constraints, inference with incomplete data, maximum likelihood estimation with censored and binary observations, and instrumental variable estimators. In addition an extensive simulation......An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling complex hierarchical structures. Several advanced features...
On-line control models for the Stanford Linear Collider
International Nuclear Information System (INIS)
Sheppard, J.C.; Helm, R.H.; Lee, M.J.; Woodley, M.D.
1983-03-01
Models for computer control of the SLAC three-kilometer linear accelerator and damping rings have been developed as part of the control system for the Stanford Linear Collider. Some of these models have been tested experimentally and implemented in the control program for routine linac operations. This paper will describe the development and implementation of these models, as well as some of the operational results
Modelling elasticity in solids using active cubes - application to simulated operations
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1995-01-01
The paper describes an approach to elastic modelling of human tissue based on the use of 3D solid active models-active cubes (M. Bro-Nielsen, 1994)-and a shape description based on the metric tensor in a solid. Active cubes are used because they provide a natural parameterization of the surface a...
Fingerprint Matching by Thin-plate Spline Modelling of Elastic Deformations
Bazen, A.M.; Gerez, Sabih H.
2003-01-01
This paper presents a novel minutiae matching method that describes elastic distortions in fingerprints by means of a thin-plate spline model, which is estimated using a local and a global matching stage. After registration of the fingerprints according to the estimated model, the number of matching
Tuition Elasticity of the Demand for Higher Education among Current Students: A Pricing Model.
Bryan, Glenn A.; Whipple, Thomas W.
1995-01-01
A pricing model is offered, based on retention of current students, that colleges can use to determine appropriate tuition. A computer-based model that quantifies the relationship between tuition elasticity and projected net return to the college was developed and applied to determine an appropriate tuition rate for a small, private liberal arts…
International Nuclear Information System (INIS)
Mungan, M.; Coppersmith, S.; Vinokur, V.M.
1999-01-01
We analyze the strains near threshold in 1-d charge density wave models at zero temperature and strong pinning. We show that in these models local strains diverge near the depinning threshold and characterize the scaling behavior of the phenomenon. This helps quantify when the underlying elastic description breaks down and plastic effects have to be included
CSIR Research Space (South Africa)
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...
Generalized Linear Models with Applications in Engineering and the Sciences
Myers, Raymond H; Vining, G Geoffrey; Robinson, Timothy J
2012-01-01
Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities."-Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Ma
Modelling a linear PM motor including magnetic saturation
Polinder, H.; Slootweg, J.G.; Compter, J.C.; Hoeijmakers, M.J.
2002-01-01
The use of linear permanent-magnet (PM) actuators increases in a wide variety of applications because of the high force density, robustness and accuracy. The paper describes the modelling of a linear PM motor applied in, for example, wafer steppers, including magnetic saturation. This is important
Application of the simplex method of linear programming model to ...
African Journals Online (AJOL)
This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...
Smart Rotor Modeling: Aero-Servo-Elastic Modeling of a Smart Rotor with Adaptive Trailing Edge Flaps
DEFF Research Database (Denmark)
Bergami, Leonardo
the trailing edge flap deflection to actively reduce the fatigue loads on the structure. The performance of the smart rotor configuration and its control algorithms are finally quantified by aero-servo-elastic simulations of the smart rotor turbine operating in a standard turbulent wind field.......This book presents the formulation of an aero-servo-elastic model for a wind turbine rotor equipped with Adaptive Trailing Edge Flaps (ATEF), a smart rotor configuration. As the name suggests, an aero-servo-elastic model consists of three main components: an aerodynamic model, a structural model......, and a control model. The book first presents an engineering type of aerodynamic model that accounts for the dynamic effects of flap deflection. The aerodynamic model is implemented in a Blade Element Momentum framework, and coupled with a multi-body structural model in the aero-servoelastic simulation code HAWC...
Genetic parameters for racing records in trotters using linear and generalized linear models.
Suontama, M; van der Werf, J H J; Juga, J; Ojala, M
2012-09-01
Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success.
Contemporary models of elastic nucleon scattering and their predictions for LHC
Kaspar, Jan; Lokajicek, Milos
2009-01-01
The analyses of elastic collisions of charged nucleons have been based standardly on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model seems to be more pertinent as it enables to determine physical characteristics in impact parameter space. The contemporary phenomenological models cannot give, of course, any definite answer as the elastic collisions may be interpreted differently, as central or peripheral processes. Nevertheless, the predictions for the planned LHC energy have been given on their basis and the possibility of exact determination of luminosity has been considered.
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).
From Process Modeling to Elastic Property Prediction for Long-Fiber Injection-Molded Thermoplastics
International Nuclear Information System (INIS)
Nguyen, Ba Nghiep; Kunc, Vlastimil; Frame, Barbara J.; Phelps, Jay; Tucker III, Charles L.; Bapanapalli, Satish K.; Holbery, James D.; Smith, Mark T.
2007-01-01
This paper presents an experimental-modeling approach to predict the elastic properties of long-fiber injection-molded thermoplastics (LFTs). The approach accounts for fiber length and orientation distributions in LFTs. LFT samples were injection-molded for the study, and fiber length and orientation distributions were measured at different locations for use in the computation of the composite properties. The current fiber orientation model was assessed to determine its capability to predict fiber orientation in LFTs. Predicted fiber orientations for the studied LFT samples were also used in the calculation of the elastic properties of these samples, and the predicted overall moduli were then compared with the experimental results. The elastic property prediction was based on the Eshelby-Mori-Tanaka method combined with the orientation averaging technique. The predictions reasonably agree with the experimental LFT data
On the elastic properties of carbon nanotube-based composites: modelling and characterization
Thostenson, E T
2003-01-01
The exceptional mechanical and physical properties observed for carbon nanotubes has stimulated the development of nanotube-based composite materials, but critical challenges exist before we can exploit these extraordinary nanoscale properties in a macroscopic composite. At the nanoscale, the structure of the carbon nanotube strongly influences the overall properties of the composite. The focus of this research is to develop a fundamental understanding of the structure/size influence of carbon nanotubes on the elastic properties of nanotube-based composites. Towards this end, the nanoscale structure and elastic properties of a model composite system of aligned multi-walled carbon nanotubes embedded in a polystyrene matrix were characterized, and a micromechanical approach for modelling of short fibre composites was modified to account for the structure of the nanotube reinforcement to predict the elastic modulus of the nanocomposite as a function of the constituent properties, reinforcement geometry and nanot...
International Nuclear Information System (INIS)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao
2015-01-01
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Jakubska-Busse, Anna; Janowicz, Maciej; Ochnio, Luiza; Jackowska-Zduniak, Beata
2016-01-01
Static properties of leaves with parallel venation, with particular emphasis on the genus EpipactisZinn, 1757 (Orchidaceae, Neottieae) have been modelled with coupled quasi-parallel elastic “beams.” The non-linear theory of strongly bended beams have been employed. The resulting boundary-value problem has been solved numerically with the help of the finite-difference method. Possible dislocations resulting in additional Dirac-delta like forces have been take into account. Morphological simila...
Linear approximation model network and its formation via ...
Indian Academy of Sciences (India)
niques, an alternative `linear approximation model' (LAM) network approach is .... network is LPV, existing LTI theory is difficult to apply (Kailath 1980). ..... Beck J V, Arnold K J 1977 Parameter estimation in engineering and science (New York: ...
Sphaleron in a non-linear sigma model
International Nuclear Information System (INIS)
Sogo, Kiyoshi; Fujimoto, Yasushi.
1989-08-01
We present an exact classical saddle point solution in a non-linear sigma model. It has a topological charge 1/2 and mediates the vacuum transition. The quantum fluctuations and the transition rate are also examined. (author)
On D-branes from gauged linear sigma models
International Nuclear Information System (INIS)
Govindarajan, S.; Jayaraman, T.; Sarkar, T.
2001-01-01
We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi-Yau manifold, where we find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi-Yau manifolds with one Kaehler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalisations
Optimization for decision making linear and quadratic models
Murty, Katta G
2010-01-01
While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.
Study of linear induction motor characteristics : the Mosebach model
1976-05-31
This report covers the Mosebach theory of the double-sided linear induction motor, starting with the ideallized model and accompanying assumptions, and ending with relations for thrust, airgap power, and motor efficiency. Solutions of the magnetic in...
Study of linear induction motor characteristics : the Oberretl model
1975-05-30
The Oberretl theory of the double-sided linear induction motor (LIM) is examined, starting with the idealized model and accompanying assumptions, and ending with relations for predicted thrust, airgap power, and motor efficiency. The effect of varyin...
An elastic-visco-plastic damage model: from theory to application
International Nuclear Information System (INIS)
Wang, X.C.; Habraken, A.M.
1996-01-01
An energy-based two-variable damage theory is applied to Bodner's model. It gives an elastic-viscoplastic damage model. Some theoretical details are described in this paper. The parameters identification procedure is discussed and a complete set of parameters for an aluminium is presented. Numerical modelling of the laboratory tests are used to validate the model. An industrial aeronautic rod fabrication process is simulated and some numerical results are presented in this paper. (orig.)
Energy Technology Data Exchange (ETDEWEB)
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)
Optimization Research of Generation Investment Based on Linear Programming Model
Wu, Juan; Ge, Xueqian
Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.
Calculation of single chain cellulose elasticity using fully atomistic modeling
Xiawa Wu; Robert J. Moon; Ashlie Martini
2011-01-01
Cellulose nanocrystals, a potential base material for green nanocomposites, are ordered bundles of cellulose chains. The properties of these chains have been studied for many years using atomic-scale modeling. However, model predictions are difficult to interpret because of the significant dependence of predicted properties on model details. The goal of this study is...
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.
Generalized linear mixed models modern concepts, methods and applications
Stroup, Walter W
2012-01-01
PART I The Big PictureModeling BasicsWhat Is a Model?Two Model Forms: Model Equation and Probability DistributionTypes of Model EffectsWriting Models in Matrix FormSummary: Essential Elements for a Complete Statement of the ModelDesign MattersIntroductory Ideas for Translating Design and Objectives into ModelsDescribing ""Data Architecture"" to Facilitate Model SpecificationFrom Plot Plan to Linear PredictorDistribution MattersMore Complex Example: Multiple Factors with Different Units of ReplicationSetting the StageGoals for Inference with Models: OverviewBasic Tools of InferenceIssue I: Data
A comparison of linear tyre models for analysing shimmy
Besselink, I.J.M.; Maas, J.W.L.H.; Nijmeijer, H.
2011-01-01
A comparison is made between three linear, dynamic tyre models using low speed step responses and yaw oscillation tests. The match with the measurements improves with increasing complexity of the tyre model. Application of the different tyre models to a two degree of freedom trailing arm suspension
Unification of three linear models for the transient visual system
Brinker, den A.C.
1989-01-01
Three different linear filters are considered as a model describing the experimentally determined triphasic impulse responses of discs. These impulse responses arc associated with the transient visual system. Each model reveals a different feature of the system. Unification of the models is
A BEHAVIORAL-APPROACH TO LINEAR EXACT MODELING
ANTOULAS, AC; WILLEMS, JC
1993-01-01
The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both
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.
Linearized models for a new magnetic control in MAST
Energy Technology Data Exchange (ETDEWEB)
Artaserse, G., E-mail: giovanni.artaserse@enea.it [Associazione Euratom-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati (RM) (Italy); Maviglia, F.; Albanese, R. [Associazione Euratom-ENEA-CREATE sulla Fusione, Via Claudio 21, I-80125 Napoli (Italy); McArdle, G.J.; Pangione, L. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB (United Kingdom)
2013-10-15
Highlights: ► We applied linearized models for a new magnetic control on MAST tokamak. ► A suite of procedures, conceived to be machine independent, have been used. ► We carried out model-based simulations, taking into account eddy currents effects. ► Comparison with the EFIT flux maps and the experimental magnetic signals are shown. ► A current driven model for the dynamic simulations of the experimental data have been performed. -- Abstract: The aim of this work is to provide reliable linearized models for the design and assessment of a new magnetic control system for MAST (Mega Ampère Spherical Tokamak) using rtEFIT, which can easily be exported to MAST Upgrade. Linearized models for magnetic control have been obtained using the 2D axisymmetric finite element code CREATE L. MAST linearized models include equivalent 2D axisymmetric schematization of poloidal field (PF) coils, vacuum vessel, and other conducting structures. A plasmaless and a double null configuration have been chosen as benchmark cases for the comparison with experimental data and EFIT reconstructions. Good agreement has been found with the EFIT flux map and the experimental signals coming from magnetic probes with only few mismatches probably due to broken sensors. A suite of procedures (equipped with a user friendly interface to be run even remotely) to provide linearized models for magnetic control is now available on the MAST linux machines. A new current driven model has been used to obtain a state space model having the PF coil currents as inputs. Dynamic simulations of experimental data have been carried out using linearized models, including modelling of the effects of the passive structures, showing a fair agreement. The modelling activity has been useful also to reproduce accurately the interaction between plasma current and radial position control loops.
Linearized models for a new magnetic control in MAST
International Nuclear Information System (INIS)
Artaserse, G.; Maviglia, F.; Albanese, R.; McArdle, G.J.; Pangione, L.
2013-01-01
Highlights: ► We applied linearized models for a new magnetic control on MAST tokamak. ► A suite of procedures, conceived to be machine independent, have been used. ► We carried out model-based simulations, taking into account eddy currents effects. ► Comparison with the EFIT flux maps and the experimental magnetic signals are shown. ► A current driven model for the dynamic simulations of the experimental data have been performed. -- Abstract: The aim of this work is to provide reliable linearized models for the design and assessment of a new magnetic control system for MAST (Mega Ampère Spherical Tokamak) using rtEFIT, which can easily be exported to MAST Upgrade. Linearized models for magnetic control have been obtained using the 2D axisymmetric finite element code CREATE L. MAST linearized models include equivalent 2D axisymmetric schematization of poloidal field (PF) coils, vacuum vessel, and other conducting structures. A plasmaless and a double null configuration have been chosen as benchmark cases for the comparison with experimental data and EFIT reconstructions. Good agreement has been found with the EFIT flux map and the experimental signals coming from magnetic probes with only few mismatches probably due to broken sensors. A suite of procedures (equipped with a user friendly interface to be run even remotely) to provide linearized models for magnetic control is now available on the MAST linux machines. A new current driven model has been used to obtain a state space model having the PF coil currents as inputs. Dynamic simulations of experimental data have been carried out using linearized models, including modelling of the effects of the passive structures, showing a fair agreement. The modelling activity has been useful also to reproduce accurately the interaction between plasma current and radial position control loops
Modeling of Distributed Sensing of Elastic Waves by Fiber-Optic Interferometry
Directory of Open Access Journals (Sweden)
Just Agbodjan Prince
2016-09-01
Full Text Available This paper deals with the transduction of strain accompanying elastic waves in solids by firmly attached optical fibers. Stretching sections of optical fibers changes the time required by guided light to pass such sections. Exploiting interferometric techniques, highly sensitive fiber-optic strain transducers are feasible based on this fiber-intrinsic effect. The impact on the actual strain conversion of the fiber segment’s shape and size, as well as its inclination to the elastic wavefront is studied. FEM analyses show that severe distortions of the interferometric response occur when the attached fiber length spans a noticeable fraction of the elastic wavelength. Analytical models of strain transduction are presented for typical transducer shapes. They are used to compute input-output relationships for the transduction of narrow-band strain pulses as a function of the mechanical wavelength. The described approach applies to many transducers depending on the distributed interaction with the investigated object.
Mathematical Modeling of Contact Problems of Elasticity Theory with Continuous Unilateral Contact
Directory of Open Access Journals (Sweden)
I. V. Stankevich
2015-01-01
Full Text Available The work [1] presents the formulation and numerical solution of the problem concerning the unilateral discrete contact interaction of an elastic body and a rigid half-space. However, many parts and components of engineering structures have a pronounced continuous contact within a given surface [2, 3]. In this paper we consider a special case of this option of contact interaction when, the elastic body of finite size, subjected to external forces, is based on a rigid half-space. Contact occurs through a dedicated contact surface, which in general can change their sizes.Developed to solve this problem, a numerical algorithm is a further adaptation and development of the approaches described in [1]. The paper shows results of solving the model problem of the elasticity theory with and without taking friction into account. In the latter case, were additionally obtained numerical data characterizing the convergence of the solution.
Foreign trade elasticities in centre-periphery models of growth and development
Directory of Open Access Journals (Sweden)
Anthony Philip Thirlwall
1983-09-01
Full Text Available The Author looks at the difference in growth rates among countries and argues that they can be traced to the strength of the balance of payments position, determined largely by the propensity to export relative to the propensity to import. Relative growth performance, thus, can be understood by looking to income elasticities of demand for exports and imports. This insight into the process of income determination in open economies, found in Harrod as well as in the literature on economic development, is developed through so-called centre-periphery models of growth and development. However, their essential conclusions were already contained in the early classic papers. The author concentrates on three of them (prebisch, seers, kaldor to argue that a country’s growth rate relative to another’s can be approximated by the ratio of its income elasticity of demand for exports to its income elasticity of demand for imports.
On the the Contact Lens Problem: Modeling Rigid and Elastic Beams on Thin Films
Trinh, Philippe; Wilson, Stephen; Stone, Howard
2011-11-01
Generally, contact lenses are prescribed by the practitioner to fit each individual patient's eye, but these fitting-philosophies are based on empirical studies and a certain degree of trial-and-error. A badly fitted lens can cause a range of afflictions, which varies from mild dry-eye-discomfort, to more serious corneal diseases. Thus, at this heart of this problem, is the question of how a rigid or elastic plate interacts with the free-surface of a thin viscous film. In this talk, we present several mathematical models for the study of these plate-and-fluid problems. Asymptotic and numerical results are described, and we explain the role of elasticity, surface tension, viscosity, and pressure in determining the equilibrium solutions. Finally, we discuss the implications of our work on the contact lens problem, as well as on other coating processes which involve elastic substrates.
An orthogonality condition model treatment of elastic and inelastic (α, 12C) scattering
International Nuclear Information System (INIS)
Suzuki, Y.; Imanishi, B.
1981-02-01
Elastic and inelastic scattering of α-particles on the deformed nucleus 12 C are investigated in the range of incident α-particle energies of 9 to 11 MeV by using the coupled-channel method with orthogonality condition. A doubly folded potential generated by the shell model wave functions of the α-particle and the deformed nucleus 12 C is employed for the relative motion between the α-particle and 12 C. Good agreement between theory and experiment is obtained for the elastic and inelastic angular distributions and the resonance structures. It is found, from the Born series expansion of the T-matrix, that the orthogonality constraint stresses the effects of the channel-coupling between the elastic and inelastic processes, and it indicates that the DWBA does not work well in this system. (author)
On the dynamic Stability of a quadratic-cubic elastic model structure ...
African Journals Online (AJOL)
The main substance of this investigation is the determination of the dynamic buckling load of an imperfect quadratic-cubic elastic model structure , which ,in itself, is a Mathematical generalization of some of the many physical structures normally encountered in engineering practice and allied fields. The load function in ...
Verschoor, M.; Jalba, A.C.
2012-01-01
Elastically deformable models have found applications in various areas ranging from mechanical sciences and engineering to computer graphics. The method of Finite Elements has been the tool of choice for solving the underlying PDE, when accuracy and stability of the computations are more important
International Nuclear Information System (INIS)
Hummel, E.; Tjon, J.A.
1989-01-01
Using the one-boson-exchange model a relativistic covariant analysis is carried out of the elastic electromagnetic form factors of the deuteron including the ρπγ and ωεγ mesonic-exchange-current contributions. The theoretical predictions are compared with the recent experimental data at high momentum transfer
An application of the Dipole Pomeron model to the pion-proton elastic scattering
International Nuclear Information System (INIS)
Covolan, R.J.M.; Leite, E.E.; Montanha, J.; Soares, M.S.
1994-01-01
The Pomeron model is applied to the pion-proton elastic scattering aiming to describe the total and differential cross sections and the ρ ratio between the scattering amplitude real and imaginary parts. It is also discussed how far the present available experimental results lead to the necessity of adopting a (α 0 > 1) supercritical trajectory. (author). 3 refs., 4 figs
H∞ /H2 model reduction through dilated linear matrix inequalities
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
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...
Non-linear Growth Models in Mplus and SAS
Grimm, Kevin J.; Ram, Nilam
2013-01-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134
Variance Function Partially Linear Single-Index Models1.
Lian, Heng; Liang, Hua; Carroll, Raymond J
2015-01-01
We consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model. We do not insist that the variance function depend only upon the mean function, as happens in the classical generalized partially linear single index model. We develop efficient and practical estimation methods for the variance function and for the mean function. Asymptotic theory for the parametric and nonparametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to further illustrate the results, and is shown to be a case where the variance function does not depend upon the mean function.
Non-linear modeling of active biohybrid materials
Paetsch, C.
2013-11-01
Recent advances in engineered muscle tissue attached to a synthetic substrate motivate the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs. © 2013 Elsevier Ltd. All rights reserved.
Finite element modelling of elastic intraplate stresses due to ...
Indian Academy of Sciences (India)
Among a range of material parameters analysed, the model with a mechan- ically strong lower ..... curves marked by solid circles and diamonds cor- respond to two values of .... the Indian continental lithosphere: Role of diffusion creep;. Proc.
Excitation function of elastic $pp$ scattering from a unitarily extended Bialas-Bzdak model
Nemes, F.; Csanád, M.
2015-01-01
The Bialas-Bzdak model of elastic proton-proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic $pp$ scattering not only at the lower ISR energies but also at $\\sqrt{s}=$7~TeV in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of elastic proton-proton scattering is predicted for the future LHC energies of $\\sqrt{s}=$13, 14, 15~TeV and also to 28~TeV. A non-trivial, significantly non-exponential feature of the differential cross-section of elastic proton-proton scattering is analyzed and the excitation function of the non-exponential behavior is predicted. The excitation function of the shadow profiles is discussed and related to saturation at small ...
Full Dynamic Ball Bearing Model with Elastic Outer Ring for High Speed Applications
Directory of Open Access Journals (Sweden)
Christian Wagner
2017-06-01
Full Text Available Ball bearings are commonly used in high speed turbomachinery and have a critical influence on the rotordynamic behavior. Therefore, a simulation model of the bearing to predict the dynamic influence is essential. The presented model is a further step to develop an accurate and efficient characterization of the ball bearing’s rotor dynamic parameters such as stiffness and deflections as well as vibrational excitations induced by the discrete rolling elements. To make it applicable to high speed turbomachinery, the model considers centrifugal forces, gyroscopic effects and ball spinning. The consideration of an elastic outer ring makes the bearing model suitable for integrated lightweight bearing constructions used in modern aircraft turbines. In order to include transient rotordynamic behavior, the model is built as a full dynamic multibody simulation with time integration. To investigate the influence of the elasticity of the outer ring, a comparison with a rigid formulation for several rotational speeds and loads is presented.
Comparison between linear quadratic and early time dose models
International Nuclear Information System (INIS)
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
Phylogenetic mixtures and linear invariants for equal input models.
Casanellas, Marta; Steel, Mike
2017-04-01
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).
Non-linear calibration models for near infrared spectroscopy
DEFF Research Database (Denmark)
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-01-01
by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear...... models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS......-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration...
Estimation and variable selection for generalized additive partial linear models
Wang, Li
2011-08-01
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.
A 2D nonlinear multiring model for blood flow in large elastic arteries
Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves
2017-12-01
In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.
Phason elasticity and surface roughening
International Nuclear Information System (INIS)
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
Matrix model and time-like linear dila ton matter
International Nuclear Information System (INIS)
Takayanagi, Tadashi
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)
Vortices, semi-local vortices in gauged linear sigma model
International Nuclear Information System (INIS)
Kim, Namkwon
1998-11-01
We consider the static (2+1)D gauged linear sigma model. By analyzing the governing system of partial differential equations, we investigate various aspects of the model. We show the existence of energy finite vortices under a partially broken symmetry on R 2 with the necessary condition suggested by Y. Yang. We also introduce generalized semi-local vortices and show the existence of energy finite semi-local vortices under a certain condition. The vacuum manifold for the semi-local vortices turns out to be graded. Besides, with a special choice of a representation, we show that the O(3) sigma model of which target space is nonlinear is a singular limit of the gauged linear sigma model of which target space is linear. (author)
TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS
Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.
2017-01-01
Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971
Linear mixed models a practical guide using statistical software
West, Brady T; Galecki, Andrzej T
2006-01-01
Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM. The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on bo
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.
Validation of elastic cross section models for space radiation applications
Energy Technology Data Exchange (ETDEWEB)
Werneth, C.M., E-mail: charles.m.werneth@nasa.gov [NASA Langley Research Center (United States); Xu, X. [National Institute of Aerospace (United States); Norman, R.B. [NASA Langley Research Center (United States); Ford, W.P. [The University of Tennessee (United States); Maung, K.M. [The University of Southern Mississippi (United States)
2017-02-01
The space radiation field is composed of energetic particles that pose both acute and long-term risks for astronauts in low earth orbit and beyond. In order to estimate radiation risk to crew members, the fluence of particles and biological response to the radiation must be known at tissue sites. Given that the spectral fluence at the boundary of the shielding material is characterized, radiation transport algorithms may be used to find the fluence of particles inside the shield and body, and the radio-biological response is estimated from experiments and models. The fidelity of the radiation spectrum inside the shield and body depends on radiation transport algorithms and the accuracy of the nuclear cross sections. In a recent study, self-consistent nuclear models based on multiple scattering theory that include the option to study relativistic kinematics were developed for the prediction of nuclear cross sections for space radiation applications. The aim of the current work is to use uncertainty quantification to ascertain the validity of the models as compared to a nuclear reaction database and to identify components of the models that can be improved in future efforts.
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Optical linear algebra processors - Noise and error-source modeling
Casasent, D.; Ghosh, A.
1985-01-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
CONTRIBUTIONS TO THE FINITE ELEMENT MODELING OF LINEAR ULTRASONIC MOTORS
Directory of Open Access Journals (Sweden)
Oana CHIVU
2013-05-01
Full Text Available The present paper is concerned with the main modeling elements as produced by means of thefinite element method of linear ultrasonic motors. Hence, first the model is designed and then a modaland harmonic analysis are carried out in view of outlining the main outcomes
Linear and Nonlinear Career Models: Metaphors, Paradigms, and Ideologies.
Buzzanell, Patrice M.; Goldzwig, Steven R.
1991-01-01
Examines the linear or bureaucratic career models (dominant in career research, metaphors, paradigms, and ideologies) which maintain career myths of flexibility and individualized routes to success in organizations incapable of offering such versatility. Describes nonlinear career models which offer suggestive metaphors for re-visioning careers…
The effective Schroedinger equation of the optical model of composite nuclei elastic collisions
International Nuclear Information System (INIS)
Mondragon, A.; Hernandez, E.
1980-01-01
An effective hamiltonian for elastic collisions between composite nuclei is obtained from the Schroedinger equation of the complete many-body system and its fully antisymmetric wave functions by means of a projection operator technique. This effective hamiltonian, defined in such a way that it has to reproduce the scattering amplitude in full detail, including exchange effects, is explicitly Galilean invariant. The effective interaction operator is a function of the relative distance between the centers of mass of the colliding nuclei and the constants of the motion of the whole system. The interaction operator of the optical model is obtained next, requiring as usual, that it reproduces the average over the energy of the scattering amplitude and keeping the Galilean invariance. The resulting optical potential operator has some terms identical to those obtained in the Resonating Group Method, and others coming from the elimination of all non elastic channels and the delayed elastic scattering. This result makes the relation existing among the projection operator method to the Feshbach and the cluster model equations of motion for positive energies (RGM) explicit. The additional interaction terms due to the flux loss in the elastic channel are non-local, and non-hermitean operators expressed in terms of the transition amplitudes and the density of states of the compound nucleus in such a way that an approximate evaluation, in a systematic fashion, seems possible. Theangular momentum dependence of the optical potential operator is discussed in some detail. (author)
REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI
Directory of Open Access Journals (Sweden)
O. Burlayenko
2018-04-01
Full Text Available Using a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, computer algebra systems Redberry and Mathematica for working with high order tensors in the symbolic and explicit form were used, in light of the overly complex computation. In an isotropic medium, there are four independent fourth order elastic moduli. This is due to the presence of four invariants for an eighth-rank tensor in the three-dimensional space, that has symmetries over the pairs of indices. As an example, the moduli of elasticity of an isotropic medium corresponding to certain crystals of cubic system are given (LiF, NaCl, MgO, CaF2. From the obtained results it can be seen that the reduced isotropic crystal model can be most effectively applied to high-symmetry crystal systems.
Institute of Scientific and Technical Information of China (English)
Sarp Adali
2012-01-01
Equations governing the vibrations and buckling of multilayered orthotropic graphene sheets can be expressed as a system of n partial differential equations where n refers to the number of sheets.This description is based on the continuum model of the graphene sheets which can also take the small scale effects into account by employing a nonlocal theory.In the present article a variational principle is derived for the nonlocal elastic theory of rectangular graphene sheets embedded in an elastic medium and undergoing transverse vibrations.Moreover the graphene sheets are subject to biaxial compression.Rayleigh quotients are obtained for the frequencies of freely vibrating graphene sheets and for the buckling load. The influence of small scale effects on the frequencies and the buckling load can be observed qualiatively from the expressions of the Rayleigh quotients.Elastic medium is modeled as a combination of Winkler and Pasternak foundations acting on the top and bottom layers of the mutilayered nano-structure.Natural boundary conditions of the problem are derived using the variational principle formulated in the study.It is observed that free boundaries lead to coupled boundary conditions due to nonlocal theory used in the continuum formulation while the local (classical) elasticity theory leads to uncoupled boundary conditions.The mathematical methods used in the study involve calculus of variations and the semi-inverse method for deriving the variational integrals.
Directory of Open Access Journals (Sweden)
J. Javorova
2016-06-01
Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.
A fast mass spring model solver for high-resolution elastic objects
Zheng, Mianlun; Yuan, Zhiyong; Zhu, Weixu; Zhang, Guian
2017-03-01
Real-time simulation of elastic objects is of great importance for computer graphics and virtual reality applications. The fast mass spring model solver can achieve visually realistic simulation in an efficient way. Unfortunately, this method suffers from resolution limitations and lack of mechanical realism for a surface geometry model, which greatly restricts its application. To tackle these problems, in this paper we propose a fast mass spring model solver for high-resolution elastic objects. First, we project the complex surface geometry model into a set of uniform grid cells as cages through *cages mean value coordinate method to reflect its internal structure and mechanics properties. Then, we replace the original Cholesky decomposition method in the fast mass spring model solver with a conjugate gradient method, which can make the fast mass spring model solver more efficient for detailed surface geometry models. Finally, we propose a graphics processing unit accelerated parallel algorithm for the conjugate gradient method. Experimental results show that our method can realize efficient deformation simulation of 3D elastic objects with visual reality and physical fidelity, which has a great potential for applications in computer animation.
AeroPropulsoServoElasticity: Dynamic Modeling of the Variable Cycle Propulsion System
Kopasakis, George
2012-01-01
This presentation was made at the 2012 Fundamental Aeronautics Program Technical Conference and it covers research work for the Dynamic Modeling of the Variable cycle Propulsion System that was done under the Supersonics Project, in the area of AeroPropulsoServoElasticity. The presentation covers the objective for the propulsion system dynamic modeling work, followed by the work that has been done so far to model the variable Cycle Engine, modeling of the inlet, the nozzle, the modeling that has been done to model the affects of flow distortion, and finally presenting some concluding remarks and future plans.
π- -12C elastic scattering above the Δ resonance using diffraction model
International Nuclear Information System (INIS)
Arafah, M.R.
2008-01-01
Phenomenological analysis of the π - - 12 C elastic scattering differential cross-section at 400, 486, 500, 584, 663, 672 and 766 MeV is presented. The analysis is made in the diffraction model framework using recently proposed parameterization of the phase-shift function. Good description of the experimental data is achieved at all energies. Microscopic interpretation of the parameters of the phase-shift function is provided in terms of Helm's model density parameters. (author)
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
Energy Technology Data Exchange (ETDEWEB)
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
The thermo-elastic instability model of melting of alkali halides in the Debye approximation
Owens, Frank J.
2018-05-01
The Debye model of lattice vibrations of alkali halides is used to show that there is a temperature below the melting temperature where the vibrational pressure exceeds the electrostatic pressure. The onset temperature of this thermo-elastic instability scales as the melting temperature of NaCl, KCl, and KBr, suggesting its role in the melting of the alkali halides in agreement with a previous more rigorous model.
Discrete elastic model for two-dimensional melting.
Lansac, Yves; Glaser, Matthew A; Clark, Noel A
2006-04-01
We present a network model for the study of melting and liquid structure in two dimensions, the first in which the presence and energy of topological defects (dislocations and disclinations) and of geometrical defects (elemental voids) can be independently controlled. Interparticle interaction is via harmonic springs and control is achieved by Monte Carlo moves which springs can either be orientationally "flipped" between particles to generate topological defects, or can be "popped" in force-free shape, to generate geometrical defects. With the geometrical defects suppressed the transition to the liquid phase occurs via disclination unbinding, as described by the Kosterlitz-Thouless-Halperin-Nelson-Young model and found in soft potential two-dimensional (2D) systems, such as the dipole-dipole potential [H. H. von Grünberg, Phys. Rev. Lett. 93, 255703 (2004)]. By contrast, with topological defects suppressed, a disordering transition, the Glaser-Clark condensation of geometrical defects [M. A. Glaser and N. A. Clark, Adv. Chem. Phys. 83, 543 (1993); M. A. Glaser, (Springer-Verlag, Berlin, 1990), Vol. 52, p. 141], produces a state that accurately characterizes the local liquid structure and first-order melting observed in hard-potential 2D systems, such as hard disk and the Weeks-Chandler-Andersen (WCA) potentials (M. A. Glaser and co-workers, see above). Thus both the geometrical and topological defect systems play a role in melting. The present work introduces a system in which the relative roles of topological and geometrical defects and their interactions can be explored. We perform Monte Carlo simulations of this model in the isobaric-isothermal ensemble, and present the phase diagram as well as various thermodynamic, statistical, and structural quantities as a function of the relative populations of geometrical and topological defects. The model exhibits a rich phase behavior including hexagonal and square crystals, expanded crystal, dodecagonal quasicrystal
Low-energy limit of the extended Linear Sigma Model
Energy Technology Data Exchange (ETDEWEB)
Divotgey, Florian [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); Kovacs, Peter [Wigner Research Center for Physics, Hungarian Academy of Sciences, Institute for Particle and Nuclear Physics, Budapest (Hungary); GSI Helmholtzzentrum fuer Schwerionenforschung, ExtreMe Matter Institute, Darmstadt (Germany); Giacosa, Francesco [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); Jan-Kochanowski University, Institute of Physics, Kielce (Poland); Rischke, Dirk H. [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); University of Science and Technology of China, Interdisciplinary Center for Theoretical Study and Department of Modern Physics, Hefei, Anhui (China)
2018-01-15
The extended Linear Sigma Model is an effective hadronic model based on the linear realization of chiral symmetry SU(N{sub f}){sub L} x SU(N{sub f}){sub R}, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the extended Linear Sigma Model (eLSM) for N{sub f} = flavors by integrating out all fields except for the pions, the (pseudo-)Nambu-Goldstone bosons of chiral symmetry breaking. The resulting low-energy effective action is identical to Chiral Perturbation Theory (ChPT) after choosing a representative for the coset space generated by chiral symmetry breaking and expanding it in powers of (derivatives of) the pion fields. The tree-level values of the coupling constants of the effective low-energy action agree remarkably well with those of ChPT. (orig.)
Linear Power-Flow Models in Multiphase Distribution Networks: Preprint
Energy Technology Data Exchange (ETDEWEB)
Bernstein, Andrey; Dall' Anese, Emiliano
2017-05-26
This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- from advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.
A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys
International Nuclear Information System (INIS)
Jin Ke; Kou Yong; Zheng Xiaojing
2012-01-01
This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops. - Highlights: ► A general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials is proposed. ► Model is thermodynamically motivated and the reversible magnetic domain rotation and irreversible domain wall motion are taken. ► The predictions are in good accordance with the experimental data including both rods and films. ► Magnetostrictive alloys are sensitive to environment temperature and pre-stress or residual stress.
Skinfold creep under load of caliper. Linear visco- and poroelastic model simulations.
Nowak, Joanna; Nowak, Bartosz; Kaczmarek, Mariusz
2015-01-01
This paper addresses the diagnostic idea proposed in [11] to measure the parameter called rate of creep of axillary fold of tissue using modified Harpenden skinfold caliper in order to distinguish normal and edematous tissue. Our simulations are intended to help understanding the creep phenomenon and creep rate parameter as a sensitive indicator of edema existence. The parametric analysis shows the tissue behavior under the external load as well as its sensitivity to changes of crucial hydro-mechanical tissue parameters, e.g., permeability or stiffness. The linear viscoelastic and poroelastic models of normal (single phase) and oedematous tissue (twophase: swelled tissue with excess of interstitial fluid) implemented in COMSOL Multiphysics environment are used. Simulations are performed within the range of small strains for a simplified fold geometry, material characterization and boundary conditions. The predicted creep is the result of viscosity (viscoelastic model) or pore fluid displacement (poroelastic model) in tissue. The tissue deformations, interstitial fluid pressure as well as interstitial fluid velocity are discussed in parametric analysis with respect to elasticity modulus, relaxation time or permeability of tissue. The creep rate determined within the models of tissue is compared and referred to the diagnostic idea in [11]. The results obtained from the two linear models of subcutaneous tissue indicate that the form of creep curve and the creep rate are sensitive to material parameters which characterize the tissue. However, the adopted modelling assumptions point to a limited applicability of the creep rate as the discriminant of oedema.
Modelling and measurement of a moving magnet linear compressor performance
International Nuclear Information System (INIS)
Liang, Kun; Stone, Richard; Davies, Gareth; Dadd, Mike; Bailey, Paul
2014-01-01
A novel moving magnet linear compressor with clearance seals and flexure bearings has been designed and constructed. It is suitable for a refrigeration system with a compact heat exchanger, such as would be needed for CPU cooling. The performance of the compressor has been experimentally evaluated with nitrogen and a mathematical model has been developed to evaluate the performance of the linear compressor. The results from the compressor model and the measurements have been compared in terms of cylinder pressure, the ‘P–V’ loop, stroke, mass flow rate and shaft power. The cylinder pressure was not measured directly but was derived from the compressor dynamics and the motor magnetic force characteristics. The comparisons indicate that the compressor model is well validated and can be used to study the performance of this type of compressor, to help with design optimization and the identification of key parameters affecting the system transients. The electrical and thermodynamic losses were also investigated, particularly for the design point (stroke of 13 mm and pressure ratio of 3.0), since a full understanding of these can lead to an increase in compressor efficiency. - Highlights: • Model predictions of the performance of a novel moving magnet linear compressor. • Prototype linear compressor performance measurements using nitrogen. • Reconstruction of P–V loops using a model of the dynamics and electromagnetics. • Close agreement between the model and measurements for the P–V loops. • The design point motor efficiency was 74%, with potential improvements identified
The minimal linear σ model for the Goldstone Higgs
International Nuclear Information System (INIS)
Feruglio, F.; Gavela, M.B.; Kanshin, K.; Machado, P.A.N.; Rigolin, S.; Saa, S.
2016-01-01
In the context of the minimal SO(5) linear σ-model, a complete renormalizable Lagrangian -including gauge bosons and fermions- is considered, with the symmetry softly broken to SO(4). The scalar sector describes both the electroweak Higgs doublet and the singlet σ. Varying the σ mass would allow to sweep from the regime of perturbative ultraviolet completion to the non-linear one assumed in models in which the Higgs particle is a low-energy remnant of some strong dynamics. We analyze the phenomenological implications and constraints from precision observables and LHC data. Furthermore, we derive the d≤6 effective Lagrangian in the limit of heavy exotic fermions.
A variational formulation for linear models in coupled dynamic thermoelasticity
International Nuclear Information System (INIS)
Feijoo, R.A.; Moura, C.A. de.
1981-07-01
A variational formulation for linear models in coupled dynamic thermoelasticity which quite naturally motivates the design of a numerical scheme for the problem, is studied. When linked to regularization or penalization techniques, this algorithm may be applied to more general models, namely, the ones that consider non-linear constraints associated to variational inequalities. The basic postulates of Mechanics and Thermodynamics as well as some well-known mathematical techniques are described. A thorough description of the algorithm implementation with the finite-element method is also provided. Proofs for existence and uniqueness of solutions and for convergence of the approximations are presented, and some numerical results are exhibited. (Author) [pt
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...
Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables
Henson, Robert A.; Templin, Jonathan L.; Willse, John T.
2009-01-01
This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…
Functional linear models for association analysis of quantitative traits.
Fan, Ruzong; Wang, Yifan; Mills, James L; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao
2013-11-01
Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study. © 2013 WILEY
Metamodel-based inverse method for parameter identification: elastic-plastic damage model
Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb
2017-04-01
This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.
Practical likelihood analysis for spatial generalized linear mixed models
DEFF Research Database (Denmark)
Bonat, W. H.; Ribeiro, Paulo Justiniano
2016-01-01
We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The Rhizoctonia root rot and the Rongelap are......, respectively, examples of binomial and count datasets modeled by spatial generalized linear mixed models. Our results show that the Laplace approximation provides similar estimates to Markov Chain Monte Carlo likelihood, Monte Carlo expectation maximization, and modified Laplace approximation. Some advantages...... of Laplace approximation include the computation of the maximized log-likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning...
Stochastic modeling of mode interactions via linear parabolized stability equations
Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo
2017-11-01
Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.
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...
Khatri, Jaidev
This thesis examines themodeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used for all analyses. This model is based upon classical compressible flow and Euler-Bernouli structural concepts. Higher fidelity computational fluid dynamics and finite element methods are needed for more precise intermediate and final evaluations. The methods presented within this thesis were shown to be useful for guiding initial control relevant design. The model was used to examine the vehicle's static and dynamic characteristics over the vehicle's trimmable region. The vehicle has significant longitudinal coupling between the fuel equivalency ratio (FER) and the flight path angle (FPA). For control system design, a two-input two-output plant (FER - elevator to speed-FPA) with 11 states (including 3 flexible modes) was used. Velocity, FPA, and pitch were assumed to be available for feedback. Aerodynamic heat modeling and design for the assumed TPS was incorporated to original Bolender's model to study the change in static and dynamic properties. De-centralized control stability, feasibility and limitations issues were dealt with the change in TPS elasticity, mass and physical dimension. The impact of elasticity due to TPS mass, TPS physical dimension as well as prolonged heating was also analyzed to understand performance limitations of de-centralized control designed for nominal model.
Support minimized inversion of acoustic and elastic wave scattering
International Nuclear Information System (INIS)
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
Microscopic cluster model analysis of 14O+p elastic scattering
International Nuclear Information System (INIS)
Baye, D.; Descouvemont, P.; Leo, F.
2005-01-01
The 14 O+p elastic scattering is discussed in detail in a fully microscopic cluster model. The 14 O cluster is described by a closed p shell for protons and a closed p3/2 subshell for neutrons in the translation-invariant harmonic-oscillator model. The exchange and spin-orbit parameters of the effective forces are tuned on the energy levels of the 15 C mirror system. With the generator-coordinate and microscopic R-matrix methods, phase shifts and cross sections are calculated for the 14 O+p elastic scattering. An excellent agreement is found with recent experimental data. A comparison is performed with phenomenological R-matrix fits. Resonances properties in 15 F are discussed
Directory of Open Access Journals (Sweden)
M. A. Nosov
2007-01-01
Full Text Available During the 2003 Tokachi-Oki tsunamigenic earthquake the real-time JAMSTEC observatory obtained records which provided a unique opportunity to have a look deep inside the tsunami source. Considering water column as a compressible medium we processed the bottom pressure records in order to estimate amplitude, duration and velocity of bottom displacement. Spectral analysis of the records revealed a clear manifestation of the low-frequency elastic oscillations of water column. We also presented 3-D finite-difference numerical model developed in the framework of linear potential theory of ideal compressible fluid to better understand dynamical processes in the tsunami source. The model reproduces position of the main spectral maximum rather correctly. However, due to neglecting of crust elasticity and to lack of exact knowledge of spatiotemporal laws of bottom motion, there is an essential difference between in-situ observed and computed spectra.
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.
Linear modeling of possible mechanisms for parkinson tremor generation
Lohnberg, P.
1978-01-01
The power of Parkinson tremor is expressed in terms of possibly changed frequency response functions between relevant variables in the neuromuscular system. The derivation starts out from a linear loopless equivalent model of mechanisms for general tremor generation. Hypothetical changes in this
Current algebra of classical non-linear sigma models
International Nuclear Information System (INIS)
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
Mathematical modelling and linear stability analysis of laser fusion cutting
International Nuclear Information System (INIS)
Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich
2016-01-01
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Non Linear signa models probing the string structure
International Nuclear Information System (INIS)
Abdalla, E.
1987-01-01
The introduction of a term depending on the extrinsic curvature to the string action, and related non linear sigma models defined on a symmetric space SO(D)/SO(2) x SO(d-2) is descussed . Coupling to fermions are also treated. (author) [pt
Confidence Intervals for Assessing Heterogeneity in Generalized Linear Mixed Models
Wagler, Amy E.
2014-01-01
Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…
Penalized Estimation in Large-Scale Generalized Linear Array Models
DEFF Research Database (Denmark)
Lund, Adam; Vincent, Martin; Hansen, Niels Richard
2017-01-01
Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension...
Expressions for linearized perturbations in ideal-fluid cosmological models
International Nuclear Information System (INIS)
Ratra, B.
1988-01-01
We present closed-form solutions of the relativistic linear perturbation equations (in synchronous gauge) that govern the evolution of inhomogeneities in homogeneous, spatially flat, ideal-fluid, cosmological models. These expressions, which are valid for irregularities on any scale, allow one to analytically interpolate between the known approximate solutions which are valid at early times and at late times
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Plane answers to complex questions the theory of linear models
Christensen, Ronald
1987-01-01
This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...
A simulation model of a coordinated decentralized linear supply chain
Ashayeri, Jalal; Cannella, S.; Lopez Campos, M.; Miranda, P.A.
2015-01-01
This paper presents a simulation-based study of a coordinated, decentralized linear supply chain (SC) system. In the proposed model, any supply tier considers its successors as part of its inventory system and generates replenishment orders on the basis of its partners’ operational information. We
Mathematical modelling and linear stability analysis of laser fusion cutting
Energy Technology Data Exchange (ETDEWEB)
Hermanns, Torsten; Schulz, Wolfgang [RWTH Aachen University, Chair for Nonlinear Dynamics, Steinbachstr. 15, 52047 Aachen (Germany); Vossen, Georg [Niederrhein University of Applied Sciences, Chair for Applied Mathematics and Numerical Simulations, Reinarzstr.. 49, 47805 Krefeld (Germany); Thombansen, Ulrich [RWTH Aachen University, Chair for Laser Technology, Steinbachstr. 15, 52047 Aachen (Germany)
2016-06-08
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Performances Of Estimators Of Linear Models With Autocorrelated ...
African Journals Online (AJOL)
The performances of five estimators of linear models with Autocorrelated error terms are compared when the independent variable is autoregressive. The results reveal that the properties of the estimators when the sample size is finite is quite similar to the properties of the estimators when the sample size is infinite although ...
Performances of estimators of linear auto-correlated error model ...
African Journals Online (AJOL)
The performances of five estimators of linear models with autocorrelated disturbance terms are compared when the independent variable is exponential. The results reveal that for both small and large samples, the Ordinary Least Squares (OLS) compares favourably with the Generalized least Squares (GLS) estimators in ...
A non-linear dissipative model of magnetism
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2010-01-01
Roč. 89, č. 6 (2010), s. 67004 ISSN 1286-4854 R&D Projects: GA AV ČR IAA100400501 Institutional research plan: CEZ:AV0Z40400503 Keywords : non-linear dissipative model of magnetism * thermodynamics * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry http://epljournal.edpsciences.org/
Modeling and verifying non-linearities in heterodyne displacement interferometry
Cosijns, S.J.A.G.; Haitjema, H.; Schellekens, P.H.J.
2002-01-01
The non-linearities in a heterodyne laser interferometer system occurring from the phase measurement system of the interferometer andfrom non-ideal polarization effects of the optics are modeled into one analytical expression which includes the initial polarization state ofthe laser source, the
DEFF Research Database (Denmark)
Holst, René; Jørgensen, Bent
2015-01-01
The paper proposes a versatile class of multiplicative generalized linear longitudinal mixed models (GLLMM) with additive dispersion components, based on explicit modelling of the covariance structure. The class incorporates a longitudinal structure into the random effects models and retains...... a marginal as well as a conditional interpretation. The estimation procedure is based on a computationally efficient quasi-score method for the regression parameters combined with a REML-like bias-corrected Pearson estimating function for the dispersion and correlation parameters. This avoids...... the multidimensional integral of the conventional GLMM likelihood and allows an extension of the robust empirical sandwich estimator for use with both association and regression parameters. The method is applied to a set of otholit data, used for age determination of fish....
Identifiability Results for Several Classes of Linear Compartment Models.
Meshkat, Nicolette; Sullivant, Seth; Eisenberg, Marisa
2015-08-01
Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.
Kim, H. Alicia; Hardie, Robert; Yamakov, Vesselin; Park, Cheol
2015-01-01
This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.
Modeling and simulation of liquid diffusion through a porous finitely elastic solid
Zhao, Qiangsheng
2013-01-29
A new theory is proposed for the continuum modeling of liquid flow through a porous elastic solid. The solid and the voids are assumed to jointly constitute the macroscopic solid phase, while the liquid volume fraction is included as a separate state variable. A finite element implementation is employed to assess the predictive capacity of the proposed theory, with particular emphasis on the mechanical response of Nafion® membranes to the flow of water. © 2013 Springer-Verlag Berlin Heidelberg.
Geophysical models of heat and fluid flow in damageable poro-elastic continua
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš
2017-01-01
Roč. 29, č. 2 (2017), s. 625-646 ISSN 0935-1175 R&D Projects: GA ČR(CZ) GA16-03823S; GA ČR GA14-15264S Institutional support: RVO:61388998 Keywords : poro-elastic rocks * damage * biot model Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.529, year: 2016 https://link.springer.com/article/10.1007/s00161-016-0547-5
Cluster folding-model for quasi-elastic scattering of 23Na from 208Pb
International Nuclear Information System (INIS)
Kabir, A.; Johnson, R.C.; Tostevin, M.H.
1991-01-01
A cluster model of 23 Na is used to calculate the 23 Na-target interaction potentials by folding the cluster wavefunction with the cluster-target interaction potentials. Coupled channels calculations are carried out for the quasi-elastic scattering of polarized 23 Na from 208 Pb at 170 MeV and compared with recent experiments. Qualitative agreement with experiment is obtained when the interaction is adjusted by a single overall normalization constant. (author)
Finite element modeling of nanotube structures linear and non-linear models
Awang, Mokhtar; Muhammad, Ibrahim Dauda
2016-01-01
This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.
Modeling of demand response in electricity markets : effects of price elasticity
International Nuclear Information System (INIS)
Banda, E.C.; Tuan, L.A.
2007-01-01
A design mechanism for the optimal participation of customer load in electricity markets was presented. In particular, this paper presented a modified market model for the optimal procurement of interruptible loads participating in day-ahead electricity markets. The proposed model considers the effect of price elasticity and demand-response functions. The objective was to determine the role that price elasticity plays in electricity markets. The simulation model can help the Independent System Operator (ISO) identify customers offering the lowest price of interruptible loads and load flow patterns that avoid problems associated with transmission congestion and transmission losses. Various issues associated with procurement of demand-response offerings such as advance notification, locational aspect of load, and power factor of the loads, were considered. It was shown that demand response can mitigate price volatility by allowing the ISO to maintain operating reserves during peak load periods. It was noted that the potential benefits of the demand response program would be reduced when price elasticity of demand is taken into account. This would most likely occur in actual developed open electricity markets, such as Nordpool. This study was based on the CIGRE 32-bus system, which represents the Swedish high voltage power system. It was modified for this study to include a broad range of customer characteristics. 18 refs., 2 tabs., 14 figs
Kopasakis, George; Connolly, Joseph W.; Seiel, Jonathan
2016-01-01
A summary of the propulsion system modeling under NASA's High Speed Project (HSP) AeroPropulsoServoElasticity (APSE) task is provided with a focus on the propulsion system for the low-boom supersonic configuration developed by Lockheed Martin and referred to as the N+2 configuration. This summary includes details on the effort to date to develop computational models for the various propulsion system components. The objective of this paper is to summarize the model development effort in this task, while providing more detail in the modeling areas that have not been previously published. The purpose of the propulsion system modeling and the overall APSE effort is to develop an integrated dynamic vehicle model to conduct appropriate unsteady analysis of supersonic vehicle performance. This integrated APSE system model concept includes the propulsion system model, and the vehicle structural aerodynamics model. The development to date of such a preliminary integrated model will also be summarized in this report
Linear Dynamics Model for Steam Cooled Fast Power Reactors
Energy Technology Data Exchange (ETDEWEB)
Vollmer, H
1968-04-15
A linear analytical dynamic model is developed for steam cooled fast power reactors. All main components of such a plant are investigated on a general though relatively simple basis. The model is distributed in those parts concerning the core but lumped as to the external plant components. Coolant is considered as compressible and treated by the actual steam law. Combined use of analogue and digital computer seems most attractive.
Deterministic operations research models and methods in linear optimization
Rader, David J
2013-01-01
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations resear
One-loop dimensional reduction of the linear σ model
International Nuclear Information System (INIS)
Malbouisson, A.P.C.; Silva-Neto, M.B.; Svaiter, N.F.
1997-05-01
We perform the dimensional reduction of the linear σ model at one-loop level. The effective of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum instability of the model for large N. (author)
Artificial Neural Network versus Linear Models Forecasting Doha Stock Market
Yousif, Adil; Elfaki, Faiz
2017-12-01
The purpose of this study is to determine the instability of Doha stock market and develop forecasting models. Linear time series models are used and compared with a nonlinear Artificial Neural Network (ANN) namely Multilayer Perceptron (MLP) Technique. It aims to establish the best useful model based on daily and monthly data which are collected from Qatar exchange for the period starting from January 2007 to January 2015. Proposed models are for the general index of Qatar stock exchange and also for the usages in other several sectors. With the help of these models, Doha stock market index and other various sectors were predicted. The study was conducted by using various time series techniques to study and analyze data trend in producing appropriate results. After applying several models, such as: Quadratic trend model, double exponential smoothing model, and ARIMA, it was concluded that ARIMA (2,2) was the most suitable linear model for the daily general index. However, ANN model was found to be more accurate than time series models.
A linearized dispersion relation for orthorhombic pseudo-acoustic modeling
Song, Xiaolei; Alkhalifah, Tariq Ali
2012-01-01
Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen's parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.
Non-linear sigma model on the fuzzy supersphere
International Nuclear Information System (INIS)
Kurkcuoglu, Seckin
2004-01-01
In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)
Directory of Open Access Journals (Sweden)
Anna Jakubska-Busse
2016-06-01
Full Text Available Static properties of leaves with parallel venation, with particular emphasis on the genus EpipactisZinn, 1757 (Orchidaceae, Neottieae have been modelled with coupled quasi-parallel elastic “beams.” The non-linear theory of strongly bended beams have been employed. The resulting boundary-value problem has been solved numerically with the help of the finite-difference method. Possible dislocations resulting in additional Dirac-delta like forces have been take into account. Morphological similarity of the model and real leaves has been obtained. In particular, the concentrated forces have been shown to cause undulation in the leaves.
Optimal difference-based estimation for partially linear models
Zhou, Yuejin; Cheng, Yebin; Dai, Wenlin; Tong, Tiejun
2017-01-01
Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
Optimal difference-based estimation for partially linear models
Zhou, Yuejin
2017-12-16
Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
Impact of climate change on Taiwanese power market determined using linear complementarity model
International Nuclear Information System (INIS)
Tung, Ching-Pin; Tseng, Tze-Chi; Huang, An-Lei; Liu, Tzu-Ming; Hu, Ming-Che
2013-01-01
Highlights: ► Impact of climate change on average temperature is estimated. ► Temperature elasticity of demand is measured. ► Impact of climate change on Taiwanese power market determined. -- Abstract: The increase in the greenhouse gas concentration in the atmosphere causes significant changes in climate patterns. In turn, this climate change affects the environment, ecology, and human behavior. The emission of greenhouse gases from the power industry has been analyzed in many studies. However, the impact of climate change on the electricity market has received less attention. Hence, the purpose of this research is to determine the impact of climate change on the electricity market, and a case study involving the Taiwanese power market is conducted. First, the impact of climate change on temperature is estimated. Next, because electricity demand can be expressed as a function of temperature, the temperature elasticity of demand is measured. Then, a linear complementarity model is formulated to simulate the Taiwanese power market and climate change scenarios are discussed. Therefore, this paper establishes a simulation framework for calculating the impact of climate change on electricity demand change. In addition, the impact of climate change on the Taiwanese market is examined and presented.
Optimization of micro and nanoimprint de-embossing by elastic fracture modelling
Balla, Tobias; Spearing, Simon Mark
2013-01-01
A semi-analytical model is presented for the de-embossing phase of the nanoimprint patterning process. The model is based on established principles of elastic fracture mechanics as developed for fibre-bridged cracking in composites. De-embossing is idealized as a steady-state fracture process, which enables the energy change to be considered by reference to a unit cell of a cylindrical polymer post, de-embossing from an axisymmetric stamp. The model provides predictions of the achievable limi...
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.
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.
A penalized framework for distributed lag non-linear models.
Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G
2017-09-01
Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.
General mirror pairs for gauged linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Aspinwall, Paul S.; Plesser, M. Ronen [Departments of Mathematics and Physics, Duke University,Box 90320, Durham, NC 27708-0320 (United States)
2015-11-05
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
General mirror pairs for gauged linear sigma models
International Nuclear Information System (INIS)
Aspinwall, Paul S.; Plesser, M. Ronen
2015-01-01
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
Dollet, Benjamin; Jones, Siân A; Méheust, Yves; Cantat, Isabelle
2014-08-01
We study foam flow in an elementary model porous medium consisting of a convergent and a divergent channel positioned side by side and possessing a fixed joint porosity. Configurations of converging or diverging channels are ubiquitous at the pore scale in porous media, as all channels linking pores possess a converging and diverging part. The resulting flow kinematics imposes asymmetric bubble deformations in the two channels, which modulate foam-wall friction and strongly impact the flux distribution. We measure, as well as quantitatively predict, the ratio of the fluxes in the two channels as a function of the channel widths by modeling pressure drops of both viscous and capillary origins. This study reveals the crucial importance of boundary-induced bubble deformation on the mobility of a flowing foam, resulting in particular in flow irreversibility.
Modelling and simulation of multi-phase effects on X-ray elasticity constants
Freour, S; Guillen, R; François, M X
2003-01-01
This paper deals with the calculation of X-ray Elasticity Constants (XEC) of phases embedded in multi-phase polycrystals. A three scales (macroscopic, pseudo-macroscopic, mesoscopic) model based on the classical self-consistent formalism is developed in order to analyse multi-phase effects on XEC values. Simulations are performed for cubic or hexagonal crystallographic structure phases embedded in several two-phases materials. In fact, it is demonstrated that XEC vary with the macroscopic stiffness of the whole polycrystal. In consequence, the constants of one particular phase depend on the elastic behaviour and the volume fraction of all the phases constituting the material. Now, XEC play a leading role in pseudo-macroscopic stresses determination by X-Ray Diffraction (XRD) methods. In this work, a quantitative analysis of the multi-phase effects on stresses determination by XRD methods was performed. Numerical results will be compared and discussed. (Abstract Copyright [2003], Wiley Periodicals, Inc.)
The study of the elasticity of spider dragline silk with liquid crystal model
International Nuclear Information System (INIS)
Cui Linying; Liu Fei; Ouyang Zhongcan
2009-01-01
Spider dragline silk is an optimal biomaterial with a combination of high tensile strength and high elasticity, and it has long been suggested to belong to liquid crystalline materials. However, a satisfactory liquid crystal description for the mechanical properties of the dragline is still missing. To solve the long existing problem, we generalized the Maier-Saupe theory of nematics to construct a liquid crystal model of the deformation mechanism of the dragline silk. We show that the remarkable elasticity of the dragline can be understood as the isotropic-nematic phase transition of the chain network with the beginning of the transition corresponding to the yield point. The calculated curve fits well with the measurements and the yield point is obtained self-consistently within our framework. The present theory can also qualitatively account for the drop of stress in supercontracted spider silk. All these comprehensive agreements between theory and experiments strongly indicate the dragline to belong to liquid crystal materials.
Liu, Y.; Guo, Q.; Sun, Y.
2014-04-01
In map production and generalization, it is inevitable to arise some spatial conflicts, but the detection and resolution of these spatial conflicts still requires manual operation. It is become a bottleneck hindering the development of automated cartographic generalization. Displacement is the most useful contextual operator that is often used for resolving the conflicts arising between two or more map objects. Automated generalization researches have reported many approaches of displacement including sequential approaches and optimization approaches. As an excellent optimization approach on the basis of energy minimization principles, elastic beams model has been used in resolving displacement problem of roads and buildings for several times. However, to realize a complete displacement solution, techniques of conflict detection and spatial context analysis should be also take into consideration. So we proposed a complete solution of displacement based on the combined use of elastic beams model and constrained Delaunay triangulation (CDT) in this paper. The solution designed as a cyclic and iterative process containing two phases: detection phase and displacement phase. In detection phase, CDT of map is use to detect proximity conflicts, identify spatial relationships and structures, and construct auxiliary structure, so as to support the displacement phase on the basis of elastic beams. In addition, for the improvements of displacement algorithm, a method for adaptive parameters setting and a new iterative strategy are put forward. Finally, we implemented our solution on a testing map generalization platform, and successfully tested it against 2 hand-generated test datasets of roads and buildings respectively.