Computational mechanics of nonlinear response of shells

Energy Technology Data Exchange (ETDEWEB)

Kraetzig, W.B. (Bochum Univ. (Germany, F.R.). Inst. fuer Statik und Dynamik); Onate, E. (Universidad Politecnica de Cataluna, Barcelona (Spain). Escuela Tecnica Superior de Ingenieros de Caminos) (eds.)

1990-01-01

Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs.

Computational mechanics of nonlinear response of shells

International Nuclear Information System (INIS)

Kraetzig, W.B.; Onate, E.

1990-01-01

Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs

Variational principles of continuum mechanics I fundamentals

CERN Document Server

Berdichevskii, V L

2009-01-01

This is a concise and understandable book about variational principles of continuum mechanics. The book is accessible to applied mathematicians, physicists and engineers who have an interest in continuum mechanics.

Continuum mechanics of single-substance bodies

CERN Document Server

Eringen, A Cemal

1975-01-01

Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts-basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, k

Variational principles of continuum mechanics II applications

CERN Document Server

Berdichevsky, Victor L

2009-01-01

This concise and understandable book about variational principles of continuum mechanics presents the classical models. The book is accessible to applied mathematicians, physicists and engineers who have an interest in continuum mechanics.

Elementary Continuum Mechanics for Everyone - and Some More

DEFF Research Database (Denmark)

Byskov, Esben

Quite trivially, Continuum mechanics per se deals with the description of deformations of three-dimensional continua i.e. models whose properties are independent of scale in that the continuum does not possess a structure. Thus, continuum mechanics does not try to model the atomic structure...

Elementary Continuum Mechanics for Everyone - And Some More

DEFF Research Database (Denmark)

Byskov, Esben

Quite trivially, Continuum mechanics per se deals with the description of deformations of three-dimensional continua i.e. models whose properties are independent of scale in that the continuum does not possess a structure. Thus, continuum mechanics does not try to model the atomic structure...

Continuum Damage Mechanics A Continuum Mechanics Approach to the Analysis of Damage and Fracture

CERN Document Server

Murakami, Sumio

2012-01-01

Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry.  This, in turn, has caused more interest in continuum damage mechanics and its engineering applications.   This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook.   The book consists of two parts and an appendix.  Part I  is concerned with the foundation of continuum damage mechanics.  Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2.  In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application ...

Flat super-continuum generation based on normal dispersion nonlinear photonic crystal fibre

DEFF Research Database (Denmark)

Chow, K.K.; Takushima, Y.; Lin, C.

2006-01-01

Flat super-continuum generation spanning over the whole telecommunication band using a passively modelocked fibre laser source at 1550 nm together with a dispersion-flattened nonlinear photoinc crystal fibre is demonstrated. Since the pulses propagate in the normal dispersion regime of the fibre...

Generalized Continuum: from Voigt to the Modeling of Quasi-Brittle Materials

Directory of Open Access Journals (Sweden)

Jamile Salim Fuina

2010-12-01

Full Text Available This article discusses the use of the generalized continuum theories to incorporate the effects of the microstructure in the nonlinear finite element analysis of quasi-brittle materials and, thus, to solve mesh dependency problems. A description of the problem called numerically induced strain localization, often found in Finite Element Method material non-linear analysis, is presented. A brief historic about the Generalized Continuum Mechanics based models is presented, since the initial work of Voigt (1887 until the more recent studies. By analyzing these models, it is observed that the Cosserat and microstretch approaches are particular cases of a general formulation that describes the micromorphic continuum. After reporting attempts to incorporate the material microstructure in Classical Continuum Mechanics based models, the article shows the recent tendency of doing it according to assumptions of the Generalized Continuum Mechanics. Finally, it presents numerical results which enable to characterize this tendency as a promising way to solve the problem.

CISM-IUTAM International Summer School on Continuum Mechanics in Environmental Sciences and Geophysics

CERN Document Server

1993-01-01

Modern continuum mechanics is the topic of this book. After its introduction it will be applied to a few typical systems arising in the environmental sciences and in geophysics. In large lake/ocean dynamics peculiar effects of the rotation of the Earth will be analyzed in linear/nonlinear processes of a homogenous and inhomogenous water body. Strong thermomechanical coupling paired with nonlinear rheology affects the flow of large ice sheets (such as Antarctica and Greenland) and ice shelves. Its response to the climatic forcing in an environmental of greenhouse warming may significantly affect the life of future generations. The mechanical behavior of granular materials under quasistatic loadings requires non-classical mixture concepts and encounters generally complicated elastic-plastic-type constitutive behavior. Creeping flow of soils, consolidation processes and ground water flow are described by such theories. Rapid shearing flow of granular materials lead to constitutive relations for the stresses whic...

Nonlinear continua fundaments for the computational techniques

CERN Document Server

Dvorkin, Eduardo N

2005-01-01

Offers a presentation of Continuum Mechanics, oriented towards numerical applications in the nonlinear analysis of solids, structures and fluid mechanics. This book develops general curvilinear coordinator kinematics of the continuum deformation using general curvilinear coordinates.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

Energy Technology Data Exchange (ETDEWEB)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

Continuum mechanics for engineers

CERN Document Server

Mase, G Thomas; Mase, George E

2009-01-01

Continuum TheoryContinuum MechanicsStarting OverNotationEssential MathematicsScalars, Vectors and Cartesian TensorsTensor Algebra in Symbolic Notation - Summation ConventionIndicial NotationMatrices and DeterminantsTransformations of Cartesian TensorsPrincipal Values and Principal DirectionsTensor Fields, Tensor CalculusIntegral Theorems of Gauss and StokesStress PrinciplesBody and Surface Forces, Mass DensityCauchy Stress PrincipleThe Stress TensorForce and Moment Equilibrium; Stress Tensor SymmetryStress Transformation LawsPrincipal Stresses; Principal Stress DirectionsMaximum and Minimum Stress ValuesMohr's Circles For Stress Plane StressDeviator and Spherical Stress StatesOctahedral Shear StressKinematics of Deformation and MotionParticles, Configurations, Deformations and MotionMaterial and Spatial CoordinatesLangrangian and Eulerian DescriptionsThe Displacement FieldThe Material DerivativeDeformation Gradients, Finite Strain TensorsInfinitesimal Deformation TheoryCompatibility EquationsStretch RatiosRot...

Optical stealth transmission based on super-continuum generation in highly nonlinear fiber over WDM network.

Science.gov (United States)

Zhu, Huatao; Wang, Rong; Pu, Tao; Fang, Tao; Xiang, Peng; Zheng, Jilin; Chen, Dalei

2015-06-01

In this Letter, the optical stealth transmission carried by super-continuum spectrum optical pulses generated in highly nonlinear fiber is proposed and experimentally demonstrated. In the proposed transmission scheme, super-continuum signals are reshaped in the spectral domain through a wavelength-selective switch and are temporally spread by a chromatic dispersion device to achieve the same noise-like characteristic as the noise in optical networks, so that in both the time domain and the spectral domain, the stealth signals are hidden in public channel. Our experimental results show that compared with existing schemes where stealth channels are carried by amplified spontaneous emission noise, super-continuum signal can increase the transmission performance and robustness.

Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis

CERN Document Server

Laursen, Tod A

2003-01-01

This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

Science.gov (United States)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Temperature Dependences of Mechanisms Responsible for the Water-Vapor Continuum Absorption

Science.gov (United States)

Ma, Qiancheng

2014-01-01

The water-vapor continuum absorption plays an important role in the radiative balance in the Earth's atmosphere. It has been experimentally shown that for ambient atmospheric conditions, the continuum absorption scales quadratically with the H2O number density and has a strong, negative temperature dependence (T dependence). Over the years, there have been three different theoretical mechanisms postulated: far-wings of allowed transition lines, water dimers, and collision-induced absorption. The first mechanism proposed was the accumulation of absorptions from the far-wings of the strong allowed transition lines. Later, absorption by water dimers was proposed, and this mechanism provides a qualitative explanation for the continuum characters mentioned above. Despite the improvements in experimental data, at present there is no consensus on which mechanism is primarily responsible for the continuum absorption.

Growth limit of carbon onions – A continuum mechanical study

DEFF Research Database (Denmark)

Todt, Melanie; Bitsche, Robert; Hartmann, Markus A.

2014-01-01

of carbon onions and, thus, can be a reason for the limited size of such particles. The loss of stability is mainly evoked by van der Waals interactions between misfitting neighboring layers leading to self-equilibrating stress states in the layers due to mutual accommodation. The influence of the curvature......The growth of carbon onions is simulated using continuum mechanical shell models. With this models it is shown that, if a carbon onion has grown to a critical size, the formation of an additional layer leads to the occurrence of a structural instability. This instability inhibits further growth...... induced surface energy and its consequential stress state is investigated and found to be rather negligible. Furthermore, it is shown that the nonlinear character of the van der Waals interactions has to be considered to obtain maximum layer numbers comparable to experimental observations. The proposed...

Fundamentals of continuum mechanics – classical approaches and new trends

Science.gov (United States)

Altenbach, H.

2018-04-01

Continuum mechanics is a branch of mechanics that deals with the analysis of the mechanical behavior of materials modeled as a continuous manifold. Continuum mechanics models begin mostly by introducing of three-dimensional Euclidean space. The points within this region are defined as material points with prescribed properties. Each material point is characterized by a position vector which is continuous in time. Thus, the body changes in a way which is realistic, globally invertible at all times and orientation-preserving, so that the body cannot intersect itself and as transformations which produce mirror reflections are not possible in nature. For the mathematical formulation of the model it is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated. Finally, the kinematical relations, the balance equations, the constitutive and evolution equations and the boundary and/or initial conditions should be defined. If the physical fields are non-smooth jump conditions must be taken into account. The basic equations of continuum mechanics are presented following a short introduction. Additionally, some examples of solid deformable continua will be discussed within the presentation. Finally, advanced models of continuum mechanics will be introduced. The paper is dedicated to Alexander Manzhirov’s 60th birthday.

Introduction to continuum mechanics

CERN Document Server

Rubin, David; Lai, W Michael

1994-01-01

Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions. Through the addition of more advanced material (solution of classical elasticity problems, constitutive e

Nonlinear crack mechanics

International Nuclear Information System (INIS)

Khoroshun, L.P.

1995-01-01

The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

Variational principles of continuum mechanics. Vol. 1. Fundamentals

Energy Technology Data Exchange (ETDEWEB)

Berdichevsky, Victor L. [Wayne State Univ., Detroit, MI (United States). Dept. of Mechanical Engineering

2009-07-01

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky's work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. In this book, the first volume, the author covers the variational principles for systems with a finite number of degrees of freedom; the variational principles of thermodynamics; the basics of continuum mechanics; the variational principles for classical models of continuum mechanics, such as elastic and plastic bodies, and ideal and viscous fluids; and direct methods of calculus of variations. (orig.)

Frequency chirpings in Alfven continuum

Science.gov (United States)

Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

2017-10-01

We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Non-classical continuum mechanics a dictionary

CERN Document Server

Maugin, Gérard A

2017-01-01

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, every entry is followed by a cross-reference to other related subject entries in the dictionary.

A continuum mechanics-based musculo-mechanical model for esophageal transport

Science.gov (United States)

Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.

2017-11-01

In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE). To deal with the leakage of flow when the Lagrangian mesh becomes coarser than the fluid mesh, we employ adaptive interaction quadrature points to deal with Lagrangian-Eulerian interaction equations based on a previous work (Griffith and Luo [1]). In particular, we introduce a new anisotropic adaptive interaction quadrature rule. The new rule permits us to vary the interaction quadrature points not only at each time-step and element but also at different orientations per element. This helps to avoid the leakage issue without sacrificing the computational efficiency and accuracy in dealing with the interaction equations. For the material model, we extend our previous fiber-based model to a continuum-based model. We present formulations for general fiber-reinforced material models in the IB-FE framework. The new material model can handle non-linear elasticity and fiber-matrix interactions, and thus permits us to consider more realistic material behavior of biological tissues. To validate our method, we first study a case in which a three-dimensional short tube is dilated. Results on the pressure-displacement relationship and the stress distribution matches very well with those obtained from the implicit FE method. We remark that in our IB-FE case, the three-dimensional tube undergoes a very large deformation and the Lagrangian mesh-size becomes about 6 times of Eulerian mesh-size in the circumferential orientation. To validate the performance of the method in handling fiber-matrix material models, we perform a second study on dilating a long fiber-reinforced tube. Errors are small when we compare numerical solutions with analytical solutions. The technique is then applied to the problem of esophageal transport. We use two

Classical Mechanics as Nonlinear Quantum Mechanics

International Nuclear Information System (INIS)

Nikolic, Hrvoje

2007-01-01

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics

Inelastic damage using continuum damage mechanics in composite plate reinforced by unidirectional fibers

Directory of Open Access Journals (Sweden)

Žmindák Milan

2018-01-01

Full Text Available It is well that a finite element method is very popular simulation method to predict the physical behavior of systems and structures. In the last years an increase of interest in a new type of numerical methods known as meshless methods was observed. The paper deals with application of radial basis functions on modelling of inelastic damage using continuum damage mechanics of layered plate composite structures reinforced with long unidirectional fibers. For numerical simulations of elastic-plastic damage of layered composite plates own computational programs were implemented in MATLAB programming language. We will use the Newton-Raphson method to solve nonlinear systems of equations. Evaluation damage during plasticity has been solved using return mapping algorithm. The results of elastic-plastic damage analysis of composite plate with unsymmetrical laminate stacking sequence are presented.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Continuum Mechanics using Mathematica® Fundamentals, Applications and Scientific Computing

CERN Document Server

Romano, Antonio; Marasco, Addolorata

2006-01-01

This book's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. The book covers essential principles and fundamental applications, and provides a solid basis for a deeper study of more challenging and specialized problems related to elasticity, fluid mechanics, plasticity, materials with memory, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes. Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and two appendices * Recent developments highlighted through coverage of more significant applications to areas such as porous media, electromagnetic fields, and phase transitions Continuum Mechanics using Mathematica® is aimed at advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering. It may ser...

Continuum damage mechanics method for fatigue growth of surface cracks

International Nuclear Information System (INIS)

Feng Xiqiao; He Shuyan

1997-01-01

With the background of leak-before-break (LBB) analysis of pressurized vessels and pipes in nuclear plants, the fatigue growth problem of either circumferential or longitudinal semi-elliptical surface cracks subjected to cyclic loading is studied by using a continuum damage mechanics method. The fatigue damage is described by a scalar damage variable. From the damage evolution equation at the crack tip, a crack growth equation similar to famous Paris' formula is derived, which shows the physical meaning of Paris' formula. Thereby, a continuum damage mechanics approach is developed to analyze the configuration evolution of surface cracks during fatigue growth

Nonlocal and nonlinear dispersion in a nonlinear Schrodinger-type equation: exotic solitons and short-wavelength instabilities

DEFF Research Database (Denmark)

Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus

2004-01-01

We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...

Antieigenvalue analysis for continuum mechanics, economics, and number theory

Directory of Open Access Journals (Sweden)

Gustafson Karl

2016-01-01

Full Text Available My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

Continuum mechanical and computational aspects of material behavior

Energy Technology Data Exchange (ETDEWEB)

Fried, Eliot; Gurtin, Morton E.

2000-02-10

The focus of the work is the application of continuum mechanics to materials science, specifically to the macroscopic characterization of material behavior at small length scales. The long-term goals are a continuum-mechanical framework for the study of materials that provides a basis for general theories and leads to boundary-value problems of physical relevance, and computational methods appropriate to these problems supplemented by physically meaningful regularizations to aid in their solution. Specific studies include the following: the development of a theory of polycrystalline plasticity that incorporates free energy associated with lattice mismatch between grains; the development of a theory of geometrically necessary dislocations within the context of finite-strain plasticity; the development of a gradient theory for single-crystal plasticity with geometrically necessary dislocations; simulations of dynamical fracture using a theory that allows for the kinking and branching of cracks; computation of segregation and compaction in flowing granular materials.

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

Dorfmann, Luis

2014-01-01

This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review

Directory of Open Access Journals (Sweden)

Zhi Yan

2017-01-01

Full Text Available Piezoelectric nanomaterials (PNs are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review.

Science.gov (United States)

Yan, Zhi; Jiang, Liying

2017-01-26

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Development of probabilistic fatigue curve for asphalt concrete based on viscoelastic continuum damage mechanics

Directory of Open Access Journals (Sweden)

Himanshu Sharma

2016-07-01

Full Text Available Due to its roots in fundamental thermodynamic framework, continuum damage approach is popular for modeling asphalt concrete behavior. Currently used continuum damage models use mixture averaged values for model parameters and assume deterministic damage process. On the other hand, significant scatter is found in fatigue data generated even under extremely controlled laboratory testing conditions. Thus, currently used continuum damage models fail to account the scatter observed in fatigue data. This paper illustrates a novel approach for probabilistic fatigue life prediction based on viscoelastic continuum damage approach. Several specimens were tested for their viscoelastic properties and damage properties under uniaxial mode of loading. The data thus generated were analyzed using viscoelastic continuum damage mechanics principles to predict fatigue life. Weibull (2 parameter, 3 parameter and lognormal distributions were fit to fatigue life predicted using viscoelastic continuum damage approach. It was observed that fatigue damage could be best-described using Weibull distribution when compared to lognormal distribution. Due to its flexibility, 3-parameter Weibull distribution was found to fit better than 2-parameter Weibull distribution. Further, significant differences were found between probabilistic fatigue curves developed in this research and traditional deterministic fatigue curve. The proposed methodology combines advantages of continuum damage mechanics as well as probabilistic approaches. These probabilistic fatigue curves can be conveniently used for reliability based pavement design. Keywords: Probabilistic fatigue curve, Continuum damage mechanics, Weibull distribution, Lognormal distribution

Gating mechanisms of mechanosensitive channels of large conductance, I: a continuum mechanics-based hierarchical framework.

Science.gov (United States)

Chen, Xi; Cui, Qiang; Tang, Yuye; Yoo, Jejoong; Yethiraj, Arun

2008-07-01

A hierarchical simulation framework that integrates information from molecular dynamics (MD) simulations into a continuum model is established to study the mechanical response of mechanosensitive channel of large-conductance (MscL) using the finite element method (FEM). The proposed MD-decorated FEM (MDeFEM) approach is used to explore the detailed gating mechanisms of the MscL in Escherichia coli embedded in a palmitoyloleoylphosphatidylethanolamine lipid bilayer. In Part I of this study, the framework of MDeFEM is established. The transmembrane and cytoplasmic helices are taken to be elastic rods, the loops are modeled as springs, and the lipid bilayer is approximated by a three-layer sheet. The mechanical properties of the continuum components, as well as their interactions, are derived from molecular simulations based on atomic force fields. In addition, analytical closed-form continuum model and elastic network model are established to complement the MDeFEM approach and to capture the most essential features of gating. In Part II of this study, the detailed gating mechanisms of E. coli-MscL under various types of loading are presented and compared with experiments, structural model, and all-atom simulations, as well as the analytical models established in Part I. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction.

Typology of nonlinear activity waves in a layered neural continuum.

Science.gov (United States)

Koch, Paul; Leisman, Gerry

2006-04-01

Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).

Sensitivity filtering from a continuum mechanics perspective

DEFF Research Database (Denmark)

Sigmund, Ole; Maute, Kurt

2012-01-01

In topology optimization filtering is a popular approach for preventing numerical instabilities. This short note shows that the well-known sensitivity filtering technique, that prevents checkerboards and ensures mesh-independent designs in density-based topology optimization, is equivalent to min...... to minimizing compliance for nonlocal elasticity problems known from continuum mechanics. Hence, the note resolves the long-standing quest for finding an explanation and physical motivation for the sensitivity filter....

On the physical origin for the geometric theory of continuum mechanics

International Nuclear Information System (INIS)

Guenther, H.

1984-01-01

It is explained, that the basic notion for a geometric picture of the continuum mechanics is a four dimensional material manifold. The four dimensional mechanical affinity is then the unified field for any defect distribution in the general time dependent case. The minimal number of geometric relations being valid for any continuum is formulated as a set of pure affine relations. The state variables of the theory are additional tensor fields as e.g. deformation defining a metric. A material with a well defined deformation has a Newton-Cartan structure. Only if defects are included into the dynamical determination by additional equilibrium conditions, the theory has a pseudo relativistic structure. (author)

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

On the continuum mechanics approach for the analysis of single walled carbon nanotubes

Science.gov (United States)

Chaudhry, M. S.; Czekanski, A.

2016-04-01

Today carbon nanotubes have found various applications in structural, thermal and almost every field of engineering. Carbon nanotubes provide great strength, stiffness resilience properties. Evaluating the structural behavior of nanoscale materials is an important task. In order to understand the materialistic behavior of nanotubes, atomistic models provide a basis for continuum mechanics modelling. Although the properties of bulk materials are consistent with the size and depends mainly on the material but the properties when we are in Nano-range, continuously change with the size. Such models start from the modelling of interatomic interaction. Modelling and simulation has advantage of cost saving when compared with the experiments. So in this project our aim is to use a continuum mechanics model of carbon nanotubes from atomistic perspective and analyses some structural behaviors of nanotubes. It is generally recognized that mechanical properties of nanotubes are dependent upon their structural details. The properties of nanotubes vary with the varying with the interatomic distance, angular orientation, radius of the tube and many such parameters. Based on such models one can analyses the variation of young's modulus, strength, deformation behavior, vibration behavior and thermal behavior. In this study some of the structural behaviors of the nanotubes are analyzed with the help of continuum mechanics models. Using the properties derived from the molecular mechanics model a Finite Element Analysis of carbon nanotubes is performed and results are verified. This study provides the insight on continuum mechanics modelling of nanotubes and hence the scope to study the effect of various parameters on some structural behavior of nanotubes.

On nonlocal modeling in continuum mechanics

Directory of Open Access Journals (Sweden)

Adam Martowicz

2018-01-01

Full Text Available The objective of the paper is to provide an overview of nonlocal formulations for models of elastic solids. The author presents the physical foundations for nonlocal theories of continuum mechanics, followed by various analytical and numerical techniques. The characteristics and range of practical applications for the presented approaches are discussed. The results of numerical simulations for the selected case studies are provided to demonstrate the properties of the described methods. The paper is illustrated with outcomes from peridynamic analyses. Fatigue and axial stretching were simulated to show the capabilities of the developed numerical tools.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

Science.gov (United States)

Bergan, Andrew C.; Leone, Frank A., Jr.

2016-01-01

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

Science.gov (United States)

Wang, John T.; Pineda, Evan J.; Ranatunga, Vipul; Smeltzer, Stanley S.

2015-01-01

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities: A numerical study

Science.gov (United States)

El Sayed, K.; Birkedal, D.; Lyssenko, V. G.; Hvam, J. M.

1997-01-01

We present a theoretical investigation of ultrafast transient four-wave mixing (FWM) of GaAs quantum wells for coherent excitation of excitons and a large number of continuum states. It is shown that in this case the line shape of the FWM signal is drastically altered due to an interaction-induced coupling of the exciton to all the excited continuum states. The signal is dominantly emitted at the spectral position of the exciton and decays, as a function of delay, on a time scale set by the duration of the laser pulse rather than by the intrinsic dephasing time. Nevertheless, the spectral width of the exciton line in the FWM spectrum and in the decay of the time-resolved FWM signal in real time are governed by the intrinsic excitonic dephasing rate. It is shown that for pulse durations of ~ 100 fs (for GaAs quantum wells) this behavior can be explained as the influence of the Coulomb exchange interaction, while for even shorter pulses this behavior is dominantly caused by nonlinear polarization decay.

Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

Science.gov (United States)

Duong, M. H.; Muntean, A.; Richardson, O. M.

2017-07-01

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

Stress, deformation, conservation, and rheology: a survey of key concepts in continuum mechanics

Science.gov (United States)

Major, J.J.

2013-01-01

This chapter provides a brief survey of key concepts in continuum mechanics. It focuses on the fundamental physical concepts that underlie derivations of the mathematical formulations of stress, strain, hydraulic head, pore-fluid pressure, and conservation equations. It then shows how stresses are linked to strain and rates of distortion through some special cases of idealized material behaviors. The goal is to equip the reader with a physical understanding of key mathematical formulations that anchor continuum mechanics in order to better understand theoretical studies published in geomorphology.

Consequences of inelastic discrete-level neutron-collision mechanics for inelastic continuum scattering

Energy Technology Data Exchange (ETDEWEB)

Hoogenboom, J.E. (Technische Hogeschool Delft (Netherlands))

1983-01-01

From the collision mechanics of inelastic discrete-level scattering several properties are derived for the secondary-neutron energy distribution (SNED) for inelastic continuum scattering, when conceived as scattering with continuously-distributed inelastic levels. Using assumptions about the level density and neutron cross section the SNED can be calculated and some examples are shown. A formula is derived to calculate from a given inelastic continuum SNED a function, which is proportional to the level density and the neutron cross section. From this relation further conditions follow for the SNED. Representations for the inelastic continuum SNED currently in use do not, in general, satisfy most of the derived conditions.

Consequences of inelastic discrete-level neutron-collision mechanics for inelastic continuum scattering

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1983-01-01

From the collision mechanics of inelastic discrete-level scattering several properties are derived for the secondary-neutron energy distribution (SNED) for inelastic continuum scattering, when conceived as scattering with continuously-distributed inelastic levels. Using assumptions about the level density and neutron cross section the SNED can be calculated and some examples are shown. A formula is derived to calculate from a given inelastic continuum SNED a function, which is proportional to the level density and the neutron cross section. From this relation further conditions follow for the SNED. Representations for the inelastic continuum SNED currently in use do not, in general, satisfy most of the derived conditions. (author)

A Dual-Continuum Model for Brine Migration in Salt Associated with Heat-Generating Nuclear Waste: Fully Coupled Thermal-Hydro-Mechanical Analysis

Science.gov (United States)

Hu, M.; Rutqvist, J.

2017-12-01

The disposal of heat-generating nuclear waste in salt host rock establishes a thermal gradient around the waste package that may cause brine inclusions in the salt grains to migrate toward the waste package. In this study, a dual-continuum model is developed to analyze such a phenomenon. This model is based on the Finite Volume Method (FVM), and it is fully thermal-hydro-mechanical (THM) coupled. For fluid flow, the dual-continuum model considers flow in the interconnected pore space and also in the salt grains. The mass balance of salt and water in these two continua is separately established, and their coupling is represented by flux associated with brine migration. Together with energy balance, such a system produces a coupled TH model with strongly nonlinear features. For mechanical analysis, a new formulation is developed based on the Voronoi tessellated mesh. By relating each cell to several connected triangles, first-order approximation is constructed. The coupling between thermal and mechanical fields is only considered in terms of thermal expansion. And the coupling between the hydraulic and mechanical fields in terms of pore-volume effects is consistent with Biot's theory. Therefore, a fully coupled THM model is developed. Several demonstration examples are provided to verify the model. Last the new model is applied to analyze coupled THM behavior and the results are compared with experimental data.

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei

2016-01-04

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei; Lubineau, Gilles; Azdoud, Yan; Askari, Abe

2016-01-01

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

Self-Assessment Exercises in Continuum Mechanics with Autonomous Learning

Science.gov (United States)

Marcé-Nogué, Jordi; Gil, LLuís; Pérez, Marco A.; Sánchez, Montserrat

2013-01-01

The main objective of this work is to generate a set of exercises to improve the autonomous learning in "Continuum Mechanics" through a virtual platform. Students will have to resolve four exercises autonomously related to the subject developed in class and they will post the solutions on the virtual platform within a deadline. Students…

Visible continuum pulses based on enhanced dispersive wave generation for endogenous fluorescence imaging.

Science.gov (United States)

Cui, Quan; Chen, Zhongyun; Liu, Qian; Zhang, Zhihong; Luo, Qingming; Fu, Ling

2017-09-01

In this study, we demonstrate endogenous fluorescence imaging using visible continuum pulses based on 100-fs Ti:sapphire oscillator and a nonlinear photonic crystal fiber. Broadband (500-700 nm) and high-power (150 mW) continuum pulses are generated through enhanced dispersive wave generation by pumping femtosecond pulses at the anomalous dispersion region near zero-dispersion wavelength of high-nonlinear photonic crystal fibers. We also minimize the continuum pulse width by determining the proper fiber length. The visible-wavelength two-photon microscopy produces NADH and tryptophan images of mice tissues simultaneously. Our 500-700 nm continuum pulses support extending nonlinear microscopy to visible wavelength range that is inaccessible to 100-fs Ti:sapphire oscillators and other applications requiring visible laser pulses.

Single-ion nonlinear mechanical oscillator

International Nuclear Information System (INIS)

Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

2010-01-01

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

Hybrid continuum-coarse-grained modeling of erythrocytes

Science.gov (United States)

Lyu, Jinming; Chen, Paul G.; Boedec, Gwenn; Leonetti, Marc; Jaeger, Marc

2018-06-01

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE-POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum-coarse-grained model for the study of RBCs in fluid flows.

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Grey-box state-space identification of nonlinear mechanical vibrations

Science.gov (United States)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

International Conference on Differential Equations and Nonlinear Mechanics

CERN Document Server

2001-01-01

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Ae...

Polymer quantum mechanics and its continuum limit

International Nuclear Information System (INIS)

Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.

2007-01-01

A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

Nonlinear optomechanical measurement of mechanical motion

DEFF Research Database (Denmark)

Brawley, G.A.; Vanner, M R; Larsen, Peter Emil

2016-01-01

Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with oth......Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing...... with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator...... by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can...

Continuum Mechanics of Beam and Plate Flexure

DEFF Research Database (Denmark)

Jönsson, Jeppe

This text has been written and used during the spring of 1995 for a course on flexural mechanics of beams and plates at Aalborg University. The idea has been to concentrate on basic principles of the theories, which are of importance to the modern structural engineer. Today's structural engineer...... must be acquainted with the classic beam and plate theories, when reading manuals and using modern software tools such as the finite element method. Each chapter includes supplementary theory and derivations enabling consultation of the notes also at a later stage of study. A preliminary chapter...... introduces the modern notation used in textbooks and in research today. It further gives an introduction to three-dimensional continuum mechanics of elastic bodies and the related principles of virtual work. The ideas to give the students a basic understanding of the stresses and strains, the equilibrium...

Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

International Nuclear Information System (INIS)

Eriksson, A M; Midtvedt, D; Croy, A; Isacsson, A

2013-01-01

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings. (paper)

Continuum damage mechanics: Present state and future trends

International Nuclear Information System (INIS)

Chaboche, J.L.

1987-01-01

Continuum Damage Mechanics (CDM) has developed since the initial works of Kachanov and Rabotnov. The paper gives a review of its main features, of the present possibilities and of further developments. Several aspects are considered successively: damage definitions and measures, damage growth equations and anisotropy effects, and use of CDM for local approaches of fracture. Various materials, loading conditions and damaging processes are incorporated in the same general framework. Particular attention is given to the possible connections between different definitions of damage, especially between the CDM definition and the information obtained from material science. (orig.)

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

Science.gov (United States)

Lehoucq, R B; Sears, Mark P

2011-09-01

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Numerical Modelling and Damage Assessment of Rotary Wing Aircraft Cabin Door Using Continuum Damage Mechanics Model

Science.gov (United States)

Boyina, Gangadhara Rao T.; Rayavarapu, Vijaya Kumar; V. V., Subba Rao

2017-02-01

The prediction of ultimate strength remains the main challenge in the simulation of the mechanical response of composite structures. This paper examines continuum damage model to predict the strength and size effects for deformation and failure response of polymer composite laminates when subjected to complex state of stress. The paper also considers how the overall results of the exercise can be applied in design applications. The continuum damage model is described and the resulting prediction of size effects are compared against the standard benchmark solutions. The stress analysis for strength prediction of rotary wing aircraft cabin door is carried out. The goal of this study is to extend the proposed continuum damage model such that it can be accurately predict the failure around stress concentration regions. The finite element-based continuum damage mechanics model can be applied to the structures and components of arbitrary configurations where analytical solutions could not be developed.

Geometric continuum regularization of quantum field theory

International Nuclear Information System (INIS)

Halpern, M.B.

1989-01-01

An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

From cells to tissue: A continuum model of epithelial mechanics

Science.gov (United States)

Ishihara, Shuji; Marcq, Philippe; Sugimura, Kaoru

2017-08-01

A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangements, we elucidated dynamical behavior underlying passive relaxation, active contraction-elongation, and tissue shear flow, including a mechanism for contraction-elongation, whereby tissue flows perpendicularly to the axis of cell elongation. This study provides an integrated scheme for the understanding of the orchestration of morphogenetic processes in individual cells to achieve epithelial tissue morphogenesis.

Non-linear finite element analysis in structural mechanics

CERN Document Server

Rust, Wilhelm

2015-01-01

This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash

2012-03-09

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

Effect of continuum damage mechanics on spring back prediction in metal forming processes

International Nuclear Information System (INIS)

Nayebi, Ali; Shahabi, Mehdi

2017-01-01

The influence of considering the variations in material properties was investigated through continuum damage mechanics according to the Lemaitre isotropic unified damage law to predict the bending force and spring back in V-bending sheet metal forming processes, with emphasis on Finite element (FE) simulation considerations. The material constants of the damage model were calibrated through a uniaxial tensile test with an appropriate and convenient repeating strategy. Holloman’s isotropic and Ziegler’s linear kinematic hardening laws were employed to describe the behavior of a hardening material. To specify the ideal FE conditions for simulating spring back, the effect of the various numerical considerations during FE simulation was investigated and compared with the experimental outcome. Results indicate that considering continuum damage mechanics decreased the predicted bending force and improved the accuracy of spring back prediction.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.

Dynamical response of multi-walled carbon nanotube resonators based on continuum mechanics modeling for mass sensing applications

Energy Technology Data Exchange (ETDEWEB)

Choi, Myungseok; Olshevskiy, Alexander; Kim, Chang-Wan [Konkuk University, Seoul (Korea, Republic of); Eom, Kilho [Sungkyunkwan University, Suwon (Korea, Republic of); Gwak, Kwanwoong [Sejong University, Seoul (Korea, Republic of); Dai, Mai Duc [Ho Chi Minh City University of Technology and Education, Ho Chi Minh (Viet Nam)

2017-05-15

Carbon nanotube (CNT) has recently received much attention due to its excellent electromechanical properties, indicating that CNT can be employed for development of Nanoelectromechanical system (NEMS) such as nanomechanical resonators. For effective design of CNT-based resonators, it is required to accurately predict the vibration behavior of CNT resonators as well as their frequency response to mass adsorption. In this work, we have studied the vibrational behavior of Multi-walled CNT (MWCNT) resonators by using a continuum mechanics modeling that was implemented in Finite element method (FEM). In particular, we consider a transversely isotropic hollow cylinder solid model with Finite element (FE) implementation for modeling the vibration behavior of Multi-walled CNT (MWCNT) resonators. It is shown that our continuum mechanics model provides the resonant frequencies of various MWCNTs being comparable to those obtained from experiments. Moreover, we have investigated the frequency response of MWCNT resonators to mass adsorption by using our continuum model with FE implementation. Our study sheds light on our continuum mechanics model that is useful in predicting not only the vibration behavior of MWCNT resonators but also their sensing performance for further effective design of MWCNT- based NEMS devices.

Stabilization of nonlinear excitations by disorder

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

1998-01-01

Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem...... are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce...... a high degree of controllability of the spatial extent of the stable excitations in the continuum system....

Nonlinear Klein-Gordon soliton mechanics

International Nuclear Information System (INIS)

Reinisch, G.

1992-01-01

Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems

Coupling Langevin Dynamics With Continuum Mechanics: Exposing the Role of Sarcomere Stretch Activation Mechanisms to Cardiac Function

Directory of Open Access Journals (Sweden)

Takumi Washio

2018-04-01

Full Text Available High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with overcoming the large spatial (from 1 nm to 10 cm and temporal (from 1 ns to 1 ms gaps between the two scales. In this paper, we propose an efficient parallel scheme to couple a microscopic model using Langevin dynamics for a protein motor with a finite element continuum model of a beating heart. The proposed scheme allows us to use a macroscale time step that is an order of magnitude longer than the microscale time step of the Langevin model, without loss of stability or accuracy. This reduces the overhead required by the imbalanced loads of the microscale computations and the communication required when switching between scales. An example of the Langevin dynamics model that demonstrates the usefulness of the coupling approach is the molecular mechanism of the actomyosin system, in which the stretch-activation phenomenon can be successfully reproduced. This microscopic Langevin model is coupled with a macroscopic finite element ventricle model. In the numerical simulations, the Langevin dynamics model reveals that a single sarcomere can undergo spontaneous oscillation (15 Hz accompanied by quick lengthening due to cooperative movements of the myosin molecules pulling on the common Z-line. Also, the coupled simulations using the ventricle model show that the stretch-activation mechanism contributes to the synchronization of the quick lengthening of the sarcomeres at the end of the systolic phase. By comparing the simulation results given by the molecular model with and without the stretch-activation mechanism, we see that this synchronization contributes to

An industrial educational laboratory at Ducati Foundation: narrative approaches to mechanics based upon continuum physics

Science.gov (United States)

Corni, Federico; Fuchs, Hans U.; Savino, Giovanni

2018-02-01

This is a description of the conceptual foundations used for designing a novel learning environment for mechanics implemented as an Industrial Educational Laboratory - called Fisica in Moto (FiM) - at the Ducati Foundation in Bologna. In this paper, we will describe the motivation for and design of the conceptual approach to mechanics used in the lab - as such, the paper is theoretical in nature. The goal of FiM is to provide an approach to the teaching of mechanics based upon imaginative structures found in continuum physics suitable to engineering and science. We show how continuum physics creates models of mechanical phenomena by using momentum and angular momentum as primitive quantities. We analyse this approach in terms of cognitive linguistic concepts such as conceptual metaphor and narrative framing of macroscopic physical phenomena. The model discussed here has been used in the didactical design of the actual lab and raises questions for an investigation of student learning of mechanics in a narrative setting.

Multiscale synchrony behaviors of paired financial time series by 3D multi-continuum percolation

Science.gov (United States)

Wang, M.; Wang, J.; Wang, B. T.

2018-02-01

Multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated, in an attempt to study the cross correlation relationships between two stock markets. A random stock price model is developed by a new system called three-dimensional (3D) multi-continuum percolation system, which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series. We assume that the price fluctuations are caused by the spread of investment information. The cluster of 3D multi-continuum percolation represents the cluster of investors who share the same investment attitude. In this paper, we focus on the paired return series, the paired volatility series, and the paired intrinsic mode functions which are decomposed by empirical mode decomposition. A new cross recurrence quantification analysis is put forward, combining with multiscale cross-sample entropy, to investigate the multiscale synchrony of these paired series from the proposed model. The corresponding research is also carried out for two China stock markets as comparison.

Nonlinearity induced synchronization enhancement in mechanical oscillators

Science.gov (United States)

Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.

2018-05-08

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

Anisotropic creep damage in the framework of continuum damage mechanics

International Nuclear Information System (INIS)

Caboche, J.L.

1983-01-01

For some years, various works have shown the possibility of applying continuum mechanics to model the evolution of the damage variable, initially introduced by Kachanov. Of interest here are the complex problems posed by the anisotropy which affects both the elastic behaviour and the viscoplastic one, and also the rupture phenomenon. The main concepts of the Continuum Damage Mechanics are briefly reviewed together with some classical ways to introduce anisotropy of damage in the particular case of proportional loadings. Based on previous works, two generalizations are presented and discussed, which use different kinds of tensors to describe the anisotropy of creep damage: - The first one, by Murakami and Ohno introduces a second rank damage tensor and a net stress tensor through a net area definition. The effective stress-strain behaviour is then obtained by a fourth rank tensor. - The second theory, by the author, uses one effective stress tensor only, defined in terms of the macroscopic strain behaviour, through a fourth-order non-symmetrical damage tensor. The two theories are compared at several levels: difference and similarities are pointed out for the damage evolution during tensile creep as well as for anisotropy effects. The possibilities are discussed and compared on the basis of some existing experimental results, which leads to a partial validation of the two approaches. (orig.)

Nonlinear theory of localized standing waves

OpenAIRE

Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul

1992-01-01

An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...

Continuum damage mechanics analysis of crack tip zone

International Nuclear Information System (INIS)

Yinchu, L.; Jianping, Z.

1989-01-01

The crack tip field and its intensity factor play an important role in fracture mechanics. Generally, the damage such as microcracks, microvoids etc. will initiate and grow in materials as the cracked body is subjected to external loadings, especially in the crack tip zone. The damage evolution will load to the crack tip damage field and the change of the stress, strain and displacement fields of cracks tip zone. In this paper, on the basis of continuum damage mechanics, the authors have derived the equations which the crack tip field and its intensity factor must satisfy in a loading process, calculated the angle distribution curves of stress, strain and displacement fields in a crack tip zone and have compared them with the corresponding curves of HRR field and linear elastic field in undamaged materials. The equations of crack tip field intensity factors have been solved and its solutions give the variation of the field intensity factors with the loading parameter

An improved particle population balance equation in the continuum-slip regime

Directory of Open Access Journals (Sweden)

Xie Mingliang

2016-01-01

Full Text Available An improved moment model is proposed to solve the population balance equation for Brownian coagulation in the continuum-slip regime, and it reduces to a known one in open literature when the non-linear terms in the slip correction factor are ignored. The present model shows same asymptotic behavior as that in the continuum regime.

JAC, 2-D Finite Element Method Program for Quasi Static Mechanics Problems by Nonlinear Conjugate Gradient (CG) Method

International Nuclear Information System (INIS)

Biffle, J.H.

1991-01-01

1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory

Methods of stability analysis in nonlinear mechanics

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.

1989-01-01

We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs

Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

Science.gov (United States)

Todo, Y.; Berk, H. L.; Breizman, B. N.

2012-09-01

This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

Nonlinear beam mechanics

NARCIS (Netherlands)

Westra, H.J.R.

2012-01-01

In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.; Scacchi, S.; Zampini, Stefano

2015-01-01

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.

2015-07-18

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

The Human Cochlear Mechanical Nonlinearity Inferred via Psychometric Functions

Directory of Open Access Journals (Sweden)

Nizami Lance

2013-12-01

Extension of the model of Schairer and colleagues results in credible cochlear nonlinearities in man, suggesting that forward-masking provides a non-invasive way to infer the human mechanical cochlear nonlinearity.

Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report

International Nuclear Information System (INIS)

Tataronis, J. A.

2004-01-01

This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory

A method of integration of atomistic simulations and continuum mechanics by collecting of dynamical systems with dimensional reduction

International Nuclear Information System (INIS)

Kaczmarek, J.

2002-01-01

Elementary processes responsible for phenomena in material are frequently related to scale close to atomic one. Therefore atomistic simulations are important for material sciences. On the other hand continuum mechanics is widely applied in mechanics of materials. It seems inevitable that both methods will gradually integrate. A multiscale method of integration of these approaches called collection of dynamical systems with dimensional reduction is introduced in this work. The dimensional reduction procedure realizes transition between various scale models from an elementary dynamical system (EDS) to a reduced dynamical system (RDS). Mappings which transform variables and forces, skeletal dynamical system (SDS) and a set of approximation and identification methods are main components of this procedure. The skeletal dynamical system is a set of dynamical systems parameterized by some constants and has variables related to the dimensionally reduced model. These constants are identified with the aid of solutions of the elementary dynamical system. As a result we obtain a dimensionally reduced dynamical system which describes phenomena in an averaged way in comparison with the EDS. Concept of integration of atomistic simulations with continuum mechanics consists in using a dynamical system describing evolution of atoms as an elementary dynamical system. Then, we introduce a continuum skeletal dynamical system within the dimensional reduction procedure. In order to construct such a system we have to modify a continuum mechanics formulation to some degree. Namely, we formalize scale of averaging for continuum theory and as a result we consider continuum with finite-dimensional fields only. Then, realization of dimensional reduction is possible. A numerical example of realization of the dimensional reduction procedure is shown. We consider a one dimensional chain of atoms interacting by Lennard-Jones potential. Evolution of this system is described by an elementary

Nonlinear and stochastic dynamics of coherent structures

DEFF Research Database (Denmark)

Rasmussen, Kim

1997-01-01

This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-01-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear

Perturbative approach to continuum generation in a fiber Bragg grating.

Science.gov (United States)

Westbrook, P S; Nicholson, J W

2006-08-21

We derive a perturbative solution to the nonlinear Schrödinger equation to include the effect of a fiber Bragg grating whose bandgap is much smaller than the pulse bandwidth. The grating generates a slow dispersive wave which may be computed from an integral over the unperturbed solution if nonlinear interaction between the grating and unperturbed waves is negligible. Our approach allows rapid estimation of large grating continuum enhancement peaks from a single nonlinear simulation of the waveguide without grating. We apply our method to uniform and sampled gratings, finding good agreement with full nonlinear simulations, and qualitatively reproducing experimental results.

On non-linear dynamics of a coupled electro-mechanical system

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2012-01-01

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅱ)-MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

Institute of Scientific and Technical Information of China (English)

戴天民

2003-01-01

The purpose is to reestablish the balance laws of momentum, angular momentumand energy and to derive the corresponding local and nonlocal balance equations formicromorphic continuum mechanics and couple stress theory. The desired results formicromorphic continuum mechanics and couple stress theory are naturally obtained via directtransitions and reductions from the coupled conservation law of energy for micropolarcontinuum theory, respectively. The basic balance laws and equation s for micromorphiccontinuum mechanics and couple stress theory are constituted by combining these resultsderived here and the traditional conservation laws and equations of mass and microinertiaand the entropy inequality. The incomplete degrees of the former related continuum theoriesare clarified. Finally, some special cases are conveniently derived.

Continuum description for jointed media

International Nuclear Information System (INIS)

Thomas, R.K.

1982-04-01

A general three-dimensional continuum description is presented for a material containing regularly spaced and approximately parallel jointing planes within a representative elementary volume. Constitutive relationships are introduced for linear behavior of the base material and nonlinear normal and shear behavior across jointing planes. Furthermore, a fracture permeability tensor is calculated so that deformation induced alterations to the in-situ values can be measured. Examples for several strain-controlled loading paths are presented

Multiscale methods coupling atomistic and continuum mechanics: analysis of a simple case

OpenAIRE

Blanc , Xavier; Le Bris , Claude; Legoll , Frédéric

2007-01-01

International audience; The description and computation of fine scale localized phenomena arising in a material (during nanoindentation, for instance) is a challenging problem that has given birth to many multiscale methods. In this work, we propose an analysis of a simple one-dimensional method that couples two scales, the atomistic one and the continuum mechanics one. The method includes an adaptive criterion in order to split the computational domain into two subdomains, that are described...

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

Santo, Daniele; Lannes, David

2017-01-01

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

On localization in the discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Bang, O.; Juul Rasmussen, J.; Christiansen, P.L.

1993-01-01

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits...

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash; Goriely, Alain

2012-01-01

but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed

Continuum analogues of contragredient Lie algebras

International Nuclear Information System (INIS)

Saveliev, M.V.; Vershik, A.M.

1989-03-01

We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates

Science.gov (United States)

Song, Kyonchan; Li, Yingyong; Rose, Cheryl A.

2011-01-01

The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Linear differential equations to solve nonlinear mechanical problems: A novel approach

OpenAIRE

Nair, C. Radhakrishnan

2004-01-01

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Energy Technology Data Exchange (ETDEWEB)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Peshkov, Ilya, E-mail: peshkov@math.nsc.ru [Open and Experimental Center for Heavy Oil, Université de Pau et des Pays de l' Adour, Avenue de l' Université, 64012 Pau (France); Romenski, Evgeniy, E-mail: evrom@math.nsc.ru [Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk (Russian Federation); Zanotti, Olindo, E-mail: olindo.zanotti@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy)

2016-06-01

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier�

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

International Nuclear Information System (INIS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2016-01-01

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier�

A novel auto-tuning PID control mechanism for nonlinear systems.

Science.gov (United States)

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

International Nuclear Information System (INIS)

Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

1995-01-01

In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

Continuum mechanics through the ages from the renaissance to the twentieth century : from hydraulics to plasticity

CERN Document Server

Maugin, Gérard A

2016-01-01

Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on cont...

Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

Energy Technology Data Exchange (ETDEWEB)

Rafii-Tabar, Hashem, E-mail: rafii-tabar@nano.ipm.ac.ir [Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Shahid Beheshti University of Medical Sciences, Tehran (Iran, Islamic Republic of); Ghavanloo, Esmaeal, E-mail: ghavanloo@shirazu.ac.ir [School of Mechanical Engineering, Shiraz University, Shiraz 71963-16548 (Iran, Islamic Republic of); Fazelzadeh, S. Ahmad [School of Mechanical Engineering, Shiraz University, Shiraz 71963-16548 (Iran, Islamic Republic of)

2016-06-06

Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models

Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

International Nuclear Information System (INIS)

Rafii-Tabar, Hashem; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad

2016-01-01

Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models

Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis

Science.gov (United States)

Giorgio, I.; Rizzi, N. L.; Turco, E.

2017-11-01

A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of the 2D body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions. The expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2D continuum. To account for the modelling abilities of the 2D continuum in the linear range, the eigenmode and eigenfrequencies of a given specimen are determined. The buckling and post-buckling behaviour of the same specimen, subjected to two different loading conditions are analysed as tests in the nonlinear range. The problems have been solved numerically by means of the COMSOL Multiphysics finite element software.

Nonlinear wave mechanics from classical dynamics and scale covariance

International Nuclear Information System (INIS)

Hammad, F.

2007-01-01

Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed

Static third-harmonic lines in widely variable fiber continuum generation

Science.gov (United States)

Tu, Haohua; Zhao, Youbo; Liu, Yuan; Boppart, Stephen A.

2014-01-01

An intriguing phenomenon of third-harmonic generation under fiber continuum generation is the emission of an anharmonic signal. One popular interpretation of this effect has developed into a general theory of fiber third-harmonic generation. Here we produce "static" third-harmonic lines dictated fully by fiber properties independent of pump parameters, in contrast to the signals of all known phase-matched nonlinear optical processes that vary dynamically with these parameters. We argue that the anharmonic signal is an illusion of the continuum generation, that it is in fact harmonic, and that this theory should be reevaluated.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling.

Science.gov (United States)

Wang, Changhao; Ren, Pengyu; Luo, Ray

2017-12-14

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Nonlinear operators and nonlinear transformations studied via the differential form of the completeness relation in quantum mechanics

International Nuclear Information System (INIS)

Fan Hongyi; Yu Shenxi

1994-01-01

We show that the differential form of the fundamental completeness relation in quantum mechanics and the technique of differentiation within an ordered product (DWOP) of operators provide a new approach for calculating normal product expansions of some nonlinear operators and study some nonlinear transformations. Their usefulness in perturbative calculations is pointed out. (orig.)

Performance test of multicomponent quantum mechanical calculation with polarizable continuum model for proton chemical shift.

Science.gov (United States)

Kanematsu, Yusuke; Tachikawa, Masanori

2015-05-21

Multicomponent quantum mechanical (MC_QM) calculations with polarizable continuum model (PCM) have been tested against liquid (1)H NMR chemical shifts for a test set of 80 molecules. Improvement from conventional quantum mechanical calculations was achieved for MC_QM calculations. The advantage of the multicomponent scheme could be attributed to the geometrical change from the equilibrium geometry by the incorporation of the hydrogen nuclear quantum effect, while that of PCM can be attributed to the change of the electronic structure according to the polarization by solvent effects.

Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics

CERN Document Server

Baumann, Gerd

2005-01-01

Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...

N=4 supersymmetric mechanics with nonlinear chiral supermultiplet

International Nuclear Information System (INIS)

Bellucci, S.; Beylin, A.; Krivonos, S.; Nersessian, A.; Orazi, E.

2005-01-01

We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system

Foundations of the non-linear mechanics of continua

CERN Document Server

Sedov, L I

1966-01-01

International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable

Mechanics of inter-modal tunneling in nonlinear waveguides

Science.gov (United States)

Jiao, Weijian; Gonella, Stefano

2018-02-01

In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.

Nonlinear mechanics of non-rigid origami: an efficient computational approach

Science.gov (United States)

Liu, K.; Paulino, G. H.

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Determination of strain concentration by microfluorescent densitometry of X-ray topography: a bridge between microfracture and continuum mechanics

International Nuclear Information System (INIS)

Kalman, Z.H.; Chaudhuri, J.; Weng, G.J.; Weissmann, S.

1980-01-01

The strain distribution in the vicinity of the notches of a double-notched, elastically bent silicon crystal was determined by measuring the diffracted X-ray intensities. The measurements were carried out on traverse-oscillation topographs of a crystal section extending through both notches. Strain distributions were determined by measuring the local densities of silver deposits (measurements of 'opacities') with a scanning electron microscope. It was shown that both the density range and spatial resolution of X-ray densitometry were larger by an order of magnitude than those of optical densitometry. The strain concentration factors associated with the notches were measured experimentally and calculated by continuum mechanics. The results were in satisfactory agreement. Also, the experimentally found rise of strains, to a maximum in the critical area adjacent to the notch root, followed the trend predicted by continuum mechanics. (Auth.)

Studies of nonlinear femtosecond pulse propagation in bulk materials

Science.gov (United States)

Eaton, Hilary Kaye

2000-10-01

Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This

A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale

KAUST Repository

Sendova, T.; Walton, J. R.

2010-01-01

In this paper we focus on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. It is shown that ascribing constant surface tension

Experimental analysis of nonlinear problems in solid mechanics

International Nuclear Information System (INIS)

1982-01-01

The booklet presents abstracts of papers from the Euromech Colloqium No. 152 held from Sept. 20th to 24th, 1982 in Wuppertal, Federal Republic of Germany. All the papers are dealing with Experimental Analysis of Nonlinear Problems in Solid Mechanics. (RW)

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

Burger, Martin; Di Francesco, Marco; Pietschmann, Jan-Frederik; Schlake, Bä rbel

2010-01-01

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double

A bimodal temom model for particle Brownian coagulation in the continuum-slip regime

Directory of Open Access Journals (Sweden)

He Qing

2016-01-01

Full Text Available In this paper, a bimodal Taylor-series expansion moment of method is proposed to deal with Brownian coagulation in the continuum-slip regime, where the non-linear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that both the number concentration and volume fraction decrease with time in the smaller mode due to the intra and inter coagulation, and the asymptotic behavior of the larger mode is as same as that in the continuum regime.

Nonlinear Analysis on Cross-Correlation of Financial Time Series by Continuum Percolation System

Science.gov (United States)

Niu, Hongli; Wang, Jun

We establish a financial price process by continuum percolation system, in which we attribute price fluctuations to the investors’ attitudes towards the financial market, and consider the clusters in continuum percolation as the investors share the same investment opinion. We investigate the cross-correlations in two return time series, and analyze the multifractal behaviors in this relationship. Further, we study the corresponding behaviors for the real stock indexes of SSE and HSI as well as the liquid stocks pair of SPD and PAB by comparison. To quantify the multifractality in cross-correlation relationship, we employ multifractal detrended cross-correlation analysis method to perform an empirical research for the simulation data and the real markets data.

Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth

1998-01-01

Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can

A morphing strategy to couple non-local to local continuum mechanics

KAUST Repository

Lubineau, Gilles

2012-06-01

A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

A morphing strategy to couple non-local to local continuum mechanics

KAUST Repository

Lubineau, Gilles; Azdoud, Yan; Han, Fei; Rey, Christian C.; Askari, Abe H.

2012-01-01

A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

Continuum of active nuclei of galaxies

International Nuclear Information System (INIS)

Boisson, C.; Durret, F.

1987-01-01

Most of the luminosity of active galactic nuclei (NAG) is radiated in the form of a continuum extending from radio to X-ray energies. It is important to understand the origin of this continuum in order to explain the relative importance of thermal and non-thermal processes in the different classes of NAG. We present here the observational aspect. A detailed study of the mechanisms will be presented by J.L. Masnou [fr

Crack Propagation Calculations for Optical Fibers under Static Bending and Tensile Loads Using Continuum Damage Mechanics

Science.gov (United States)

Chen, Yunxia; Cui, Yuxuan; Gong, Wenjun

2017-01-01

Static fatigue behavior is the main failure mode of optical fibers applied in sensors. In this paper, a computational framework based on continuum damage mechanics (CDM) is presented to calculate the crack propagation process and failure time of optical fibers subjected to static bending and tensile loads. For this purpose, the static fatigue crack propagation in the glass core of the optical fiber is studied. Combining a finite element method (FEM), we use the continuum damage mechanics for the glass core to calculate the crack propagation path and corresponding failure time. In addition, three factors including bending radius, tensile force and optical fiber diameter are investigated to find their impacts on the crack propagation process and failure time of the optical fiber under concerned situations. Finally, experiments are conducted and the results verify the correctness of the simulation calculation. It is believed that the proposed method could give a straightforward description of the crack propagation path in the inner glass core. Additionally, the predicted crack propagation time of the optical fiber with different factors can provide effective suggestions for improving the long-term usage of optical fibers. PMID:29140284

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

Science.gov (United States)

Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

2018-04-01

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique

Directory of Open Access Journals (Sweden)

Charles M. Reinke

2011-12-01

Full Text Available Recent work has demonstrated that nanostructuring of a semiconductor material to form a phononic crystal (PnC can significantly reduce its thermal conductivity. In this paper, we present a classical method that combines atomic-level information with the application of Bloch theory at the continuum level for the prediction of the thermal conductivity of finite-thickness PnCs with unit cells sized in the micron scale. Lattice dynamics calculations are done at the bulk material level, and the plane-wave expansion method is implemented at the macrosale PnC unit cell level. The combination of the lattice dynamics-based and continuum mechanics-based dispersion information is then used in the Callaway-Holland model to calculate the thermal transport properties of the PnC. We demonstrate that this hybrid approach provides both accurate and efficient predictions of the thermal conductivity.

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

MECHANISM OF OPTICAL NONLINEARITY IN “LYOTROPIC LIQUID CRYSTAL — VIOLOGEN” SYSTEM

Directory of Open Access Journals (Sweden)

Hanna Bordyuh

2014-06-01

Full Text Available In the present work we analyze the characteristics of holographic grating recording and consider a mechanism of optical nonlinearity in the lyotropic liquid crystal (LLC — viologen samples. Taking into account structural and electrooptical properties of the admixture molecules it is possible to suggest that the recording is realized due to the change of polarizability of π-electron system of coloured viologen derivatives under the action of laser radiation. The main nonlinear optical parameters such as nonlinear refraction coefficient n2, cubic nonlinear susceptibility χ(3, and hyperpolarizability γ were calculated.

Technical report on micro-mechanical versus conventional modelling in non-linear fracture mechanics

International Nuclear Information System (INIS)

2001-07-01

While conventional fracture mechanics is capable of predicting crack growth behaviour if sufficient experimental observations are available, micro-mechanical modelling can both increase the accuracy of these predictions and model phenomena that are inaccessible by the conventional theory such as the ductile-cleavage temperature transition. A common argument against micro-mechanical modelling is that it is too complicated for use in routine engineering applications. This is both a computational and an educational problem. That micro-mechanical modelling is unnecessarily complicated is certainly true in many situations. The on-going development of micro-mechanical models, computational algorithms and computer speed will however most probably diminish the computational problem rather rapidly. Compare for instance the rate of development of computational methods for structural analysis. Meanwhile micro-mechanical modelling may serve as a tool by which more simplified engineering methods can be validated. The process of receiving a wide acceptance of the new methods is probably much slower. This involves many steps. First the research community must be in reasonable agreement on the methods and their use. Then the methods have to be implemented into computer software and into code procedures. The development and acceptance of conventional fracture mechanics may serve as an historical example of the time required before a new methodology has received a wide usage. The CSNI Working Group on Integrity and Ageing (IAGE) decided to carry out a report on micro-mechanical modeling to promote this promising and valuable technique. The report presents a comparison with non-linear fracture mechanics and highlights key aspects that could lead to a better knowledge and accurate predictions. Content: - 1. Introduction; - 2. Concepts of non-linear fracture mechanics with point crack tip modelling; - 3. Micro-mechanical models for cleavage fracture; - 4, Micro-mechanical modelling of

Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities

DEFF Research Database (Denmark)

Birkedal, Dan; Vadim, Lyssenko; Hvam, Jørn Märcher

1996-01-01

We present an experimental and theoretical investigation of ultrafast transient four-wave mixing of GaAs/AlxGa1-xAs quantum wells for coherent excitation of exciton and continuum states. The signal appears at the exciton resonance and is shown to consist of two contributions: an intense spectrall...

Optical continuum generation on a silicon chip

Science.gov (United States)

Jalali, Bahram; Boyraz, Ozdal; Koonath, Prakash; Raghunathan, Varun; Indukuri, Tejaswi; Dimitropoulos, Dimitri

2005-08-01

Although the Raman effect is nearly two orders of magnitude stronger than the electronic Kerr nonlinearity in silicon, under pulsed operation regime where the pulse width is shorter than the phonon response time, Raman effect is suppressed and Kerr nonlinearity dominates. Continuum generation, made possible by the non-resonant Kerr nonlinearity, offers a technologically and economically appealing path to WDM communication at the inter-chip or intra-chip levels. We have studied this phenomenon experimentally and theoretically. Experimentally, a 2 fold spectral broadening is obtained by launching ~4ps optical pulses with 2.2GW/cm2 peak power into a conventional silicon waveguide. Theoretical calculations, that include the effect of two-photon-absorption, free carrier absorption and refractive index change indicate that up to >30 times spectral broadening is achievable in an optimized device. The broadening is due to self phase modulation and saturates due to two photon absorption. Additionally, we find that free carrier dynamics also contributes to the spectral broadening and cause the overall spectrum to be asymmetric with respect to the pump wavelength.

Global mass conservation method for dual-continuum gas reservoir simulation

KAUST Repository

Wang, Yi; Sun, Shuyu; Gong, Liang; Yu, Bo

2018-01-01

In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference method. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

Global mass conservation method for dual-continuum gas reservoir simulation

KAUST Repository

Wang, Yi

2018-03-17

In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference method. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Nonlinear Viscoelastic Mechanism for Aftershock Triggering and Decay

Science.gov (United States)

Shcherbakov, R.; Zhang, X.

2016-12-01

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. They also occur in other natural or experimental systems, for example, in solar flares, in fracture experiments on porous materials and acoustic emissions, after stock market crashes, in the volatility of stock prices returns, in internet traffic variability and e-mail spamming, to mention a few. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle control the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and

Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics. M.S. Thesis Final Report

Science.gov (United States)

Coats, Timothy William

1994-01-01

Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.

Integral equation hierarchy for continuum percolation

International Nuclear Information System (INIS)

Given, J.A.

1988-01-01

In this thesis a projection operator technique is presented that yields hierarchies of integral equations satisfied exactly by the n-point connectedness functions in a continuum version of the site-bond percolation problem. The n-point connectedness functions carry the same structural information for a percolation problem as then-point correlation functions do for a thermal problem. This method extends the Potts model mapping of Fortuin and Kastelyn to the continuum by exploiting an s-state generalization of the Widom-Rowlinson model, a continuum model for phase separation. The projection operator technique is used to produce an integral equation hierarchy for percolation similar to the Born-Green heirarchy. The Kirkwood superposition approximation (SA) is extended to percolation in order to close this hierarchy and yield a nonlinear integral equation for the two-point connectedness function. The fact that this function, in the SA, is the analytic continuation to negative density of the two-point correlation function in a corresponding thermal problem is discussed. The BGY equation for percolation is solved numerically, both by an expansion in powers of the density, and by an iterative technique due to Kirkwood. It is argued both analytically and numerically, that the BYG equation for percolation, unlike its thermal counterpart, shows non-classical critical behavior, with η = 1 and γ = 0.05 ± .1. Finally a sequence of refinements to the superposition approximations based in the theory of fluids by Rice and Lekner is discussed

Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics

OpenAIRE

Beretta, Gian Paolo

2006-01-01

We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...

Computational Method for Atomistic-Continuum Homogenization

National Research Council Canada - National Science Library

Chung, Peter

2002-01-01

The homogenization method is used as a framework for developing a multiscale system of equations involving atoms at zero temperature at the small scale and continuum mechanics at the very large scale...

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

Science.gov (United States)

Shang, Xituan; Yen, Michael R T; Gaber, M Waleed

2010-06-01

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.

New numerical methods for quantum field theories on the continuum

Energy Technology Data Exchange (ETDEWEB)

Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C

2000-03-01

The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.

Lectures in nonlinear mechanics and chaos theory

CERN Document Server

Stetz, Albert W

2016-01-01

This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...

4th International Conference on Nonlinear Mechanics

CERN Document Server

Maugin, G

2003-01-01

The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to exte...

IUTAM-Symposium on The Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications

CERN Document Server

1968-01-01

5 The symposium was held in Freudenstadt from 28\\h to 31 \\ ofAugust st nd 1967 and in Stuttgart from 1 to 2 of September 1967. The proposal to hold this symposium originated with the German Society of Applied Mathematics and Mechanics (GAMM) late in 1964 and was examined by a committee of IUTAM especially appointed for this purpose. The basis of this examination was a report in which the present situation in the field and the possible aims of the symposium were surveyed. Briefly, the aims of the symposium were stated to be 1. the unification of the various approaches developed in recent years with the aim of penetrating into the microscopic world of matter by means of continuum theories; 2. the bridging of the gap between microscopic (or atomic) research on mechanics on one hand, and the phenomenological (or continuum mechanical) approach on the other hand; 3. the physical interpretation and the relation to actual material behaviour of the quantities and laws introduced into the new theories, together with ap...

Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage

Science.gov (United States)

Kearns, Sarah; Das, Moumita

2015-03-01

We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

Science.gov (United States)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-12-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear static and dynamic behavior of rectangular microplates under small and large actuating forces. In the first part, we present and compare various approaches to develop reduced order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. In the second part, we present an investigation of the static and dynamic behavior of a fully clamped microplate. We investigate the effect of different non-dimensional design parameters on the static response. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of midplane stretching. However, the behavior switches to softening as the DC load is increased. Next, near-square plates are studied to understand the effect of geometric imperfections of microplates. In the final part of the dissertation, we investigate the mechanical behavior of

GPU-based acceleration of computations in nonlinear finite element deformation analysis.

Science.gov (United States)

Mafi, Ramin; Sirouspour, Shahin

2014-03-01

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.

Modeling of Nonlinear Mechanical Response in CFRP Angle-Ply Laminates

Science.gov (United States)

Ogihara, Shinji

2014-03-01

It is known that the failure process in angle-ply laminate involves matrix cracking and delamination and that they exhibit nonlinear stress-strain relation. There may be a significant effect of the constituent blocked ply thickness on the mechanical behavior of angle-ply laminates. These days, thin prepregs whose thickness is, for example 50 micron, are developed and commercially available. Therefore, we can design wide variety of laminates with various constituent ply thicknesses. In this study, effects of constituent ply thickness on the nonlinear mechanical behavior and the damage behavior of CFRP angle-ply laminates are investigated experimentally. Based on the experimental results, the mechanical response in CFRP angle-ply laminates is modeled by using the finite strain viscoplasticity model. We evaluated the mechanical behavior and damage behavior in CFRP angle-ply laminates with different constituent ply thickness under tensile loading experimentally. It was found that as the constituent ply thickness decreases, the strength and failure strain increases. We also observed difference in damage behavior. The preliminary results of finite strain viscoplasticity model considering the damage effect for laminated composites are shown. A qualitative agreement is obtained.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Science.gov (United States)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Continuum Vlasov Simulation in Four Phase-space Dimensions

Science.gov (United States)

Cohen, B. I.; Banks, J. W.; Berger, R. L.; Hittinger, J. A.; Brunner, S.

2010-11-01

In the VALHALLA project, we are developing scalable algorithms for the continuum solution of the Vlasov-Maxwell equations in two spatial and two velocity dimensions. We use fourth-order temporal and spatial discretizations of the conservative form of the equations and a finite-volume representation to enable adaptive mesh refinement and nonlinear oscillation control [1]. The code has been implemented with and without adaptive mesh refinement, and with electromagnetic and electrostatic field solvers. A goal is to study the efficacy of continuum Vlasov simulations in four phase-space dimensions for laser-plasma interactions. We have verified the code in examples such as the two-stream instability, the weak beam-plasma instability, Landau damping, electron plasma waves with electron trapping and nonlinear frequency shifts [2]^ extended from 1D to 2D propagation, and light wave propagation.^ We will report progress on code development, computational methods, and physics applications. This work was performed under the auspices of the U.S. DOE by LLNL under contract no. DE-AC52-07NA27344. This work was funded by the Lab. Dir. Res. and Dev. Prog. at LLNL under project tracking code 08-ERD-031. [1] J.W. Banks and J.A.F. Hittinger, to appear in IEEE Trans. Plas. Sci. (Sept., 2010). [2] G.J. Morales and T.M. O'Neil, Phys. Rev. Lett. 28,417 (1972); R. L. Dewar, Phys. Fluids 15,712 (1972).

Nonlinear Thermo-mechanical Finite Element Analysis of Polymer Foam Cored Sandwich Structures including Geometrical and Material Nonlinearity

DEFF Research Database (Denmark)

Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi

In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...

A continuum mechanics constitutive framework for transverse isotropic soft tissues

Science.gov (United States)

Garcia-Gonzalez, D.; Jérusalem, A.; Garzon-Hernandez, S.; Zaera, R.; Arias, A.

2018-03-01

In this work, a continuum constitutive framework for the mechanical modelling of soft tissues that incorporates strain rate and temperature dependencies as well as the transverse isotropy arising from fibres embedded into a soft matrix is developed. The constitutive formulation is based on a Helmholtz free energy function decoupled into the contribution of a viscous-hyperelastic matrix and the contribution of fibres introducing dispersion dependent transverse isotropy. The proposed framework considers finite deformation kinematics, is thermodynamically consistent and allows for the particularisation of the energy potentials and flow equations of each constitutive branch. In this regard, the approach developed herein provides the basis on which specific constitutive models can be potentially formulated for a wide variety of soft tissues. To illustrate this versatility, the constitutive framework is particularised here for animal and human white matter and skin, for which constitutive models are provided. In both cases, different energy functions are considered: Neo-Hookean, Gent and Ogden. Finally, the ability of the approach at capturing the experimental behaviour of the two soft tissues is confirmed.

Defining and testing a granular continuum element

Energy Technology Data Exchange (ETDEWEB)

Rycroft, Chris H.; Kamrin, Ken; Bazant, Martin Z.

2007-12-03

Continuum mechanics relies on the fundamental notion of amesoscopic volume "element" in which properties averaged over discreteparticles obey deterministic relationships. Recent work on granularmaterials suggests a continuum law may be inapplicable, revealinginhomogeneities at the particle level, such as force chains and slow cagebreaking. Here, we analyze large-scale Discrete-Element Method (DEM)simulations of different granular flows and show that a "granularelement" can indeed be defined at the scale of dynamical correlations,roughly three to five particle diameters. Its rheology is rather subtle,combining liquid-like dependence on deformation rate and solid-likedependence on strain. Our results confirm some aspects of classicalplasticity theory (e.g., coaxiality of stress and deformation rate),while contradicting others (i.e., incipient yield), and can guide thedevelopment of more realistic continuum models.

Single-nary philosophy for non-linear study of mechanics of materials

International Nuclear Information System (INIS)

Tran, C.

2005-01-01

Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

Computational optogenetics: A novel continuum framework for the photoelectrochemistry of living systems

Science.gov (United States)

Wong, Jonathan; Abilez, Oscar J.; Kuhl, Ellen

2012-06-01

Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second-order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to

The Continuum of Aging and Age-Related Diseases: Common Mechanisms but Different Rates

Directory of Open Access Journals (Sweden)

Claudio Franceschi

2018-03-01

Full Text Available Geroscience, the new interdisciplinary field that aims to understand the relationship between aging and chronic age-related diseases (ARDs and geriatric syndromes (GSs, is based on epidemiological evidence and experimental data that aging is the major risk factor for such pathologies and assumes that aging and ARDs/GSs share a common set of basic biological mechanisms. A consequence is that the primary target of medicine is to combat aging instead of any single ARD/GSs one by one, as favored by the fragmentation into hundreds of specialties and sub-specialties. If the same molecular and cellular mechanisms underpin both aging and ARDs/GSs, a major question emerges: which is the difference, if any, between aging and ARDs/GSs? The hypothesis that ARDs and GSs such as frailty can be conceptualized as accelerated aging will be discussed by analyzing in particular frailty, sarcopenia, chronic obstructive pulmonary disease, cancer, neurodegenerative diseases such as Alzheimer and Parkinson as well as Down syndrome as an example of progeroid syndrome. According to this integrated view, aging and ARDs/GSs become part of a continuum where precise boundaries do not exist and the two extremes are represented by centenarians, who largely avoided or postponed most ARDs/GSs and are characterized by decelerated aging, and patients who suffered one or more severe ARDs in their 60s, 70s, and 80s and show signs of accelerated aging, respectively. In between these two extremes, there is a continuum of intermediate trajectories representing a sort of gray area. Thus, clinically different, classical ARDs/GSs are, indeed, the result of peculiar combinations of alterations regarding the same, limited set of basic mechanisms shared with the aging process. Whether an individual will follow a trajectory of accelerated or decelerated aging will depend on his/her genetic background interacting lifelong with environmental and lifestyle factors. If ARDs and GSs are

Hidden Area and Mechanical Nonlinearities in Freestanding Graphene

Science.gov (United States)

Nicholl, Ryan J. T.; Lavrik, Nickolay V.; Vlassiouk, Ivan; Srijanto, Bernadeta R.; Bolotin, Kirill I.

2017-06-01

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area ˜0 % obeyed linear mechanics with biaxial stiffness 428 ±10 N /m , specimens with hidden area in the range 0.5%-1.0% were found to obey an anomalous nonlinear Hooke's law with an exponent ˜0.1 .

Control mechanisms for a nonlinear model of international relations

Energy Technology Data Exchange (ETDEWEB)

Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.

1997-07-15

Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.

Relating Deformation and Thermodynamics: An Opportunity for Rethinking Basic Concepts of Continuum Mechanics

Directory of Open Access Journals (Sweden)

Giuseppe Guzzetta

2013-06-01

Full Text Available In order to treat deformation as one of the processes taking place in an irreversible thermodynamic transformation, two main conditions must be satisfied: (1 strain and stress should be defined in such a way that the modification of the symmetry of these tensorial quantities reflects that of the structure of the actual material of which the deforming ideal continuum is the counterpart; and (2 the unique decomposition of the above tensors into the algebraic sum of an isotropic and an anisotropic part with different physical meanings should be recognized. The first condition allows the distinction of the energy balance in irrotational and rotational deformations; the second allows the description of a thermodynamic transformation involving deformation as a function of both process quantities, whose values depend on the specific transition, or path, between two equilibrium states, and of state quantities, which describe equilibrium states of a system quantitatively. One of the main conclusions that can be drawn is that, dealing with deformable materials, the quantities that must appear in thermodynamic equations cannot be tensorial quantities, such as the stress tensor and the infinitesimal or finite strain tensor usually considered in continuum mechanics (or, even worse, their components. The appropriate quantities should be invariants involved by the strain and stress tensors here defined. Another important conclusion is that, from a thermodynamic point of view, the consideration of the measurable volume change occurring in an isothermal deformation does not itself give any meaningful information.

Is there a relativistic nonlinear generalization of quantum mechanics?

Energy Technology Data Exchange (ETDEWEB)

Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)

2007-05-15

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

Nonlinear buckling analyses of a small-radius carbon nanotube

International Nuclear Information System (INIS)

Liu, Ning; Li, Min; Jia, Jiao; Wang, Yong-Gang

2014-01-01

Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained

Nonlinear buckling analyses of a small-radius carbon nanotube

Energy Technology Data Exchange (ETDEWEB)

Liu, Ning, E-mail: liuxiao@ase.buaa.edu.cn; Li, Min; Jia, Jiao [School of Aeronautic Science and Engineering, Beihang University, Beijing 100091 (China); Wang, Yong-Gang [Department of Applied Mechanics, China Agricultural University, Beijing 100083 (China)

2014-04-21

Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Hyperbolic conservation laws in continuum physics

CERN Document Server

Dafermos, Constantine M

2016-01-01

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conser...

Micro-macro-discrepancies in nonlinear microrheology: I. Quantifying mechanisms in a suspension of Brownian ellipsoids

International Nuclear Information System (INIS)

DePuit, Ryan J; Squires, Todd M

2012-01-01

Active and nonlinear microrheology experiments involve a colloidal probe that is forced to move within a material, with the goal of recovering the nonlinear rheological response properties of the material. Various mechanisms cause discrepancies between the nonlinear rheology measured microrheologically and macroscopically, including direct probe-bath collisions, the Lagrangian unsteadiness experienced by the material elements, and the spatially inhomogeneous and rheologically mixed strain field set up around the probe. Here, we perform computational nonlinear microrheology experiments, in which a colloidal probe translates through a dilute suspension of Brownian ellipsoids, whose results we compare against analogous computational experiments on the macroscopic shear rheology of the same model material. The quantitative impact of each of the mechanisms for micro-macro-discrepancy can thus be computed directly, with additional computational experiments performed where the processes in question are ‘turned off’. We show that all three discrepancy mechanisms impact the microrheological measurement quantitatively, and that none can be neglected. This motivates a search for microrheological probes whose geometry or forcing is optimized to minimize these impacts, which we present in a companion article.

Flare continuum

International Nuclear Information System (INIS)

Robinson, R.D.

1985-01-01

This paper reviews the metre-wave continuum radiation which is related to similar solar emissions observed in the decimetre and centimetre spectral regions. This type of emission, known as Flare Contiuum, is related to the radio bursts of types II and IV. After summarising the history of the phenomenon and reviewing the observational work, the author discusses the various possible radiation mechanisms and their relation to the solar corona, the interplanetary medium and related regions. The theoretical topics covered include the role of high-energy particles, the trapping of such particles, gyro-synchrotron radiation, polarization and plasma interactions. (U.K.)

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Science.gov (United States)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Examination of the use of continuum versus discontinuum models for design and performance assessment for the Yucca Mountain site

International Nuclear Information System (INIS)

Board, M.

1989-08-01

This report examines the use of continuum and discontinuum numerical methods for analysis of the thermomechanical response of the rock mass at Yucca Mountain. Continuum numerical methods consider the rock to be a solid, unfractured body, whereas the discontinuum method is formulated specifically to account for the effects of discrete fractures. The fractures within the rock introduce overall non-linear material response due to slip and separation of rock blocks. Continuum models attempt to simulate this response through the use of non-linear constitutive laws. Discontinuum methods attempt to simulate the true response of the rock mass by correctly modeling the behavior of the joints as well as the deformability of the intact rock blocks. It is shown that, as the joint spacing, s, becomes small with respect to the size of the excavations, the behavior of the jointed rock approaches that of a solid with a form of elasto-plastic constitutive behavior. It is concluded that a continuum model with a form of ''ubiquitous'' or ''compliant joint'' plasticity law is probably sufficient for analysis of the thermomechanical response of excavations in welded tuff. However, one of the questions concerning Yucca Mountain which remains is the effect of fault structures on the stability performance of the repository, particularly under thermal and dynamic loads. Here, a true discontinuum approach seems necessary. 45 refs., 42 figs., 4 tabs

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Supersymmetric quantum mechanics approach to a nonlinear lattice

International Nuclear Information System (INIS)

Ricotta, Regina Maria; Drigo Filho, Elso

2011-01-01

Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)

Continuum modeling of twinning, amorphization, and fracture: theory and numerical simulations

Science.gov (United States)

Clayton, J. D.; Knap, J.

2018-03-01

A continuum mechanical theory is used to model physical mechanisms of twinning, solid-solid phase transformations, and failure by cavitation and shear fracture. Such a sequence of mechanisms has been observed in atomic simulations and/or experiments on the ceramic boron carbide. In the present modeling approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. After development of the general nonlinear theory, a first problem class considers simple shear deformation of a single crystal of this material. For homogeneous fields or stress-free states, algebraic systems or ordinary differential equations are obtained that can be solved by numerical iteration. Results are in general agreement with atomic simulation, without introduction of fitted parameters. The second class of problems addresses the more complex mechanics of heterogeneous deformation and stress states involved in deformation and failure of polycrystals. Finite element calculations, in which individual grains in a three-dimensional polycrystal are fully resolved, invoke a partially linearized version of the theory. Results provide new insight into effects of crystal morphology, activity or inactivity of different inelasticity mechanisms, and imposed deformation histories on strength and failure of the aggregate under compression and shear. The importance of incorporation of inelastic shear deformation in realistic models of amorphization of boron carbide is noted, as is a greater reduction in overall strength of polycrystals containing one or a few dominant flaws rather than many diffusely distributed microcracks.

The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

Directory of Open Access Journals (Sweden)

Baizhou Li

2014-01-01

Full Text Available With the increasing requirement of quiet electrical machines in the civil and defense industry, it is very significant and necessary to predict the vibration and noise characteristics of stator and rotor in the early conceptual phase. Therefore, the combined internal and principal parametric resonances of a stator system excited by radial electromagnetic force are presented in this paper. The stator structure is modeled as a continuum double-shell system which is loaded by a varying distributed electromagnetic load. The nonlinear dynamic equations are derived and solved by the method of multiple scales. The influences of mechanical and electromagnetic parameters on resonance characteristics are illustrated by the frequency-response curves. Furthermore, the Runge-Kutta method is adopted to numerically analyze steady-state response for the further understanding of the resonance characteristics with different parameters.

Nonlinearity Mechanism and Correction of Sapphire Fiber Temperature Sensor on Blackbody Cavity

Directory of Open Access Journals (Sweden)

Tiejun Cao

2014-06-01

Full Text Available Based on the principle of blackbody radiation, sapphire optic fiber temperature sensor has been more widely used in recent years, and its temperature range is between 800 ~ 2000 oC, and the response time is in 10-2 magnitude, and transient temperature measurement can be high precision in harsh environments. Nonlinear constraints on sapphire fiber temperature sensor affect the accuracy and stability of the sensor. In order to solve the nonlinear problems which exist in the measurement, at first, the sapphire fiber optic temperature sensor temperature measurement principle and nonlinear generation mechanism are studied; secondly piecewise linear interpolation and spline interpolation linearization algorithm is designed with combining the nonlinear characteristics of sapphire optical fiber temperature sensor, and the program is designed on its linear and associated signal processing. Experimental results show that a good linearization of sapphire fiber optic temperature sensor can been achieved in this method.

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

Numerical methods for solving the governing equations for a seriated continuum

International Nuclear Information System (INIS)

Narum, R.E.; Noble, C.; Mortensen, G.A.; McFadden, J.H.

1976-09-01

A desire to more accurately predict the behavior of transient two-phase flows has resulted in an investigation of the feasibility of computing unequal phase velocities and unequal phase temperatures. The finite difference forms of a set of equations governing a seriated continuum are presented along with two methods developed for solving the resulting systems of simultaneous nonlinear equations. Results from a one-dimensional computer code are presented to illustrate the capabilities of one of the solution methods

Pore-scale and Continuum Simulations of Solute Transport Micromodel Benchmark Experiments

Energy Technology Data Exchange (ETDEWEB)

Oostrom, Martinus; Mehmani, Yashar; Romero Gomez, Pedro DJ; Tang, Y.; Liu, H.; Yoon, Hongkyu; Kang, Qinjun; Joekar Niasar, Vahid; Balhoff, Matthew; Dewers, T.; Tartakovsky, Guzel D.; Leist, Emily AE; Hess, Nancy J.; Perkins, William A.; Rakowski, Cynthia L.; Richmond, Marshall C.; Serkowski, John A.; Werth, Charles J.; Valocchi, Albert J.; Wietsma, Thomas W.; Zhang, Changyong

2016-08-01

Four sets of micromodel nonreactive solute transport experiments were conducted with flow velocity, grain diameter, pore-aspect ratio, and flow focusing heterogeneity as the variables. The data sets were offered to pore-scale modeling groups to test their simulators. Each set consisted of two learning experiments, for which all results was made available, and a challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice-Boltzmann (LB) approach, and one employed a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used these experiments to appropriately discretize the grid representations. The continuum model use published non-linear relations between transverse dispersion coefficients and Peclet numbers to compute the required dispersivity input values. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values and, resulting in less dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models needed up to several days on supercomputers to resolve the more complex problems.

On the asymptotic stability of nonlinear mechanical switched systems

Science.gov (United States)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

Reconstructing a nonlinear dynamical framework for testing quantum mechanics

International Nuclear Information System (INIS)

Jordan, T.F.

1993-01-01

The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs

On the Nature of Off-limb Flare Continuum Sources Detected by SDO /HMI

Energy Technology Data Exchange (ETDEWEB)

Heinzel, P.; Kašparová, J. [Astronomical Institute, Czech Academy of Sciences, 25165 Ondřejov (Czech Republic); Kleint, L.; Krucker, S., E-mail: pheinzel@asu.cas.cz [University of Applied Sciences and Arts Northwestern Switzerland, Bahnhofstrasse 6, 5210 Windisch (Switzerland)

2017-09-20

The Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory has provided unique observations of off-limb flare emission. White-light continuum enhancements were detected in the “continuum” channel of the Fe 6173 Å line during the impulsive phase of the observed flares. In this paper we aim to determine which radiation mechanism is responsible for such enhancement being seen above the limb, at chromospheric heights around or below 1000 km. Using a simple analytical approach, we compare two candidate mechanisms, the hydrogen recombination continuum (Paschen) and the Thomson continuum due to scattering of disk radiation on flare electrons. Both mechanisms depend on the electron density, which is typically enhanced during the impulsive phase of a flare as the result of collisional ionization (both thermal and also non-thermal due to electron beams). We conclude that for electron densities higher than 10{sup 12} cm{sup −3}, the Paschen recombination continuum significantly dominates the Thomson scattering continuum and there is some contribution from the hydrogen free–free emission. This is further supported by detailed radiation-hydrodynamical (RHD) simulations of the flare chromosphere heated by the electron beams. We use the RHD code FLARIX to compute the temporal evolution of the flare-heating in a semi-circular loop. The synthesized continuum structure above the limb resembles the off-limb flare structures detected by HMI, namely their height above the limb, as well as the radiation intensity. These results are consistent with recent findings related to hydrogen Balmer continuum enhancements, which were clearly detected in disk flares by the IRIS near-ultraviolet spectrometer.

Electrospun microcrimped fibers with nonlinear mechanical properties enhance ligament fibroblast phenotype

International Nuclear Information System (INIS)

Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun

2014-01-01

Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress–strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress–strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure–function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies. (papers)

Electrospun microcrimped fibers with nonlinear mechanical properties enhance ligament fibroblast phenotype.

Science.gov (United States)

Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun

2014-09-01

Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress-strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress-strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure-function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies.

The quantum and the continuum : Einstein's dichotomous legacies

International Nuclear Information System (INIS)

Majumdar, Parthasarathi

2015-01-01

This talk begins with a summary of some of Einstein's seminal contributions in the quantum domain, like Brownian motion and the Light Quantum Hypothesis, as well as on the spacetime continuum enshrined in the theories of special and general relativity. Following up on Einstein's rationale for postulating the Light Quantum Hypothesis, we attempt to point to a possible dichotomy in his thinking about these two legacies of his, which may have been noticed by him, but was not much discussed by him in the public domain. One may speculate that this may have had something to do with his well-known distaste for the probability interpretation of quantum mechanics as a fundamental interpretation. We argue that Einstein's general relativity theory itself contains the seeds of a dramatic modification of our ideas of the Einsteinian spacetime continuum, thus underlining the dichotomy even more strongly. We then survey one modern attempt to resolve the dichotomy, at least partly, by bringing into the spacetime continuum, aspects of quantum mechanics with its underlying statistical interpretation, an approach which Einstein may not have whole-heartedly endorsed, but which seems to work so far, with good prospects for the future. (author)

Fluid mechanics and heat transfer advances in nonlinear dynamics modeling

CERN Document Server

Asli, Kaveh Hariri

2015-01-01

This valuable new book focuses on new methods and techniques in fluid mechanics and heat transfer in mechanical engineering. The book includes the research of the authors on the development of optimal mathematical models and also uses modern computer technology and mathematical methods for the analysis of nonlinear dynamic processes. It covers technologies applicable to both fluid mechanics and heat transfer problems, which include a combination of physical, mechanical, and thermal techniques. The authors develop a new method for the calculation of mathematical models by computer technology, using parametric modeling techniques and multiple analyses for mechanical system. The information in this book is intended to help reduce the risk of system damage or failure. Included are sidebar discussions, which contain information and facts about each subject area that help to emphasize important points to remember.

Assessing continuum postulates in simulations of granular flow

Energy Technology Data Exchange (ETDEWEB)

Rycroft, Chris; Kamrin, Ken; Bazant, Martin

2008-08-26

Continuum mechanics relies on the fundamental notion of a mesoscopic volume"element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale three-dimensional Discrete-Element Method (DEM) simulations of different granular flows and show that an approximate"granular element" defined at the scale of observed dynamical correlations (roughly three to five particle diameters) has a reasonable continuum interpretation. By viewing all the simulations as an ensemble of granular elements which deform and move with the flow, we can track material evolution at a local level. Our results confirm some of the hypotheses of classical plasticity theory while contradicting others and suggest a subtle physical picture of granular failure, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our computational methods and results can be used to guide the development of more realistic continuum models, based on observed local relationships betweenaverage variables.

Application of Galerkin meshfree methods to nonlinear thermo-mechanical simulation of solids under extremely high pulsed loading

International Nuclear Information System (INIS)

Ibáñez, Daniel Iglesias; García Orden, Juan C.; Brañas, B.; Carmona, J.M.; Molla, J.

2013-01-01

Highlights: • The paper presents a novel application of meshfree methods, valid for its implementation on a multibody framework. • Coupled nonlinear thermo-mechanical formulation is detailed and described in the reference configuration, as this allows to compute the shape functions only once. • We show the conditions in which future information induces inefficiency. • Beam parameters are the only information needed to apply the thermal load. • The solution procedure takes charge of updating the volumetric heat rate as the body moves and deforms. -- Abstract: Beam facing elements of the International Fusion Materials Irradiation Facility (IFMIF) Linear Particle Accelerator prototype (LIPAc) must stop 5–40 MeV D + ions with a peak current of 125 mA. The duty cycle of the beam loading varies from 0.1% to 100% (CW), depending on the device, with the ions being stopped in the first hundreds microns of the beam facing material. For intermediate duty cycles up to CW, the thermal load can be considered a heat flux load on the boundary, but this approximation gets too conservative as the duty cycle is reduced because the thermal diffusion becomes more important. Instant heat flux produced by the beam can reach up to 3 GW/m 2 in elements such as the beam dump and slits during short times of hundredths of microseconds. In these cases, the accuracy of the volumetric heat generation is critical for obtaining realistic results. Meshfree Galerkin methods discretize a continuum using scattered nodes. As opposed to FEM, no predefined connectivity is needed between the nodes, so C ∞ (infinitely differentiable) locally supported shape functions can be used to approximate both the trial and the test functions. This feature makes these type of methods well suited for those problems where the domain experiences very large deformations or has high gradients of the state variables. Radial basis (RBF) and moving least squares (MLS) functions have been applied to the

An extended continuum model accounting for the driver's timid and aggressive attributions

Energy Technology Data Exchange (ETDEWEB)

Cheng, Rongjun; Ge, Hongxia [Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211 (China); Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing 210096 (China); National Traffic Management Engineering and Technology Research Centre Ningbo University Sub-centre, Ningbo 315211 (China); Wang, Jufeng, E-mail: wjf@nit.zju.edu.cn [Ningbo Institute of Technology, Zhejiang University, Ningbo 315100 (China)

2017-04-18

Considering the driver's timid and aggressive behaviors simultaneously, a new continuum model is put forwarded in this paper. By applying the linear stability theory, we presented the analysis of new model's linear stability. Through nonlinear analysis, the KdV–Burgers equation is derived to describe density wave near the neutral stability line. Numerical results verify that aggressive driving is better than timid act because the aggressive driver will adjust his speed timely according to the leading car's speed. The key improvement of this new model is that the timid driving deteriorates traffic stability while the aggressive driving will enhance traffic stability. The relationship of energy consumption between the aggressive and timid driving is also studied. Numerical results show that aggressive driver behavior can not only suppress the traffic congestion but also reduce the energy consumption. - Highlights: • A new continuum model is developed with the consideration of the driver's timid and aggressive behaviors simultaneously. • Applying the linear stability theory, the new model's linear stability is obtained. • Through nonlinear analysis, the KdV–Burgers equation is derived. • The energy consumption for this model is studied.

An extended continuum model accounting for the driver's timid and aggressive attributions

International Nuclear Information System (INIS)

Cheng, Rongjun; Ge, Hongxia; Wang, Jufeng

2017-01-01

Considering the driver's timid and aggressive behaviors simultaneously, a new continuum model is put forwarded in this paper. By applying the linear stability theory, we presented the analysis of new model's linear stability. Through nonlinear analysis, the KdV–Burgers equation is derived to describe density wave near the neutral stability line. Numerical results verify that aggressive driving is better than timid act because the aggressive driver will adjust his speed timely according to the leading car's speed. The key improvement of this new model is that the timid driving deteriorates traffic stability while the aggressive driving will enhance traffic stability. The relationship of energy consumption between the aggressive and timid driving is also studied. Numerical results show that aggressive driver behavior can not only suppress the traffic congestion but also reduce the energy consumption. - Highlights: • A new continuum model is developed with the consideration of the driver's timid and aggressive behaviors simultaneously. • Applying the linear stability theory, the new model's linear stability is obtained. • Through nonlinear analysis, the KdV–Burgers equation is derived. • The energy consumption for this model is studied.

Piecewise nonlinear dynamic characteristics study of the control rod drive mechanism

International Nuclear Information System (INIS)

Shen Xiaoyao; Wang Feng

2011-01-01

Piecewise nonlinear dynamics of the control rod mechanism (CRDM), one of the critical components in PWR nuclear power plants, are studied for its lifting process in this paper. Firstly, equations of the electric circuit and the magnetic circuit are set up. Then based on the dynamic lifting process analysis of CRDM, its motion procedure is divided into three stages, and the coupled magnetic-electric-mechanical equation for each stage is derived. By combining the analytical solution method and the numerical simulation method, the piecewise nonlinear governing equations are solved. Finally, parameters which can illustrate the dynamic characteristics of CRDM, such as the magnetic force, the coil current, the armature displacement, the armature velocity and the acceleration are obtained and corresponding curves with the time are drawn and analyzed. The analysis results are confirmed by the test which proves the validity of our method. Work in this paper can be used for design and analysis as well as the site fault diagnosis of CRDM. (author)

Quantum-mechanical Green's functions and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P. de T.S.

1986-01-01

The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt

Quantum-mechanical Green's function and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P.T.S.

1986-01-01

It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field

Nonlinear analysis of flexible plates lying on elastic foundation

Directory of Open Access Journals (Sweden)

Trushin Sergey

2017-01-01

Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.

Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics

International Nuclear Information System (INIS)

Kraczek, B.; Miller, S.T.; Haber, R.B.; Johnson, D.D.

2010-01-01

We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in

Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids : Symposia

CERN Document Server

Sedov, L

1968-01-01

At its meeting on April 23, 1965 in Paris the Bureau of IUTAM decided to have a Symposium on the Irreversible Aspects of Continaum Mechanics held in June 1966 in Vienna. In addition, a Symposium on the Transfer of Physical Characteristics in Moving Fluids which, orig­ inally, had been scheduled to take place in Stockholm was rescheduled to be held in Vienna immediately following the Symposium on the Irre­ versible Aspects of Continuum Mechanics. It was felt that the subjects of the two symposia were so closely related that participants should be given an opportunity to attend both. Both decisions were unanimously approved by the members of the General Assembly of IUTAM. Prof. H. PARKUS, Vienna, was appointed Chairman of the Symposium on the Irreversible Aspects, and Prof. L. I. SEDOV, Moscow, was appointed Chairman of the Symposium on the Transfer of Physical Characteristics, with Prof. P ARKUS being re­ sponsible for the local organization of both symposia. In accordance with the policy set forth by IUTAM...

Tailoring nonlinearity and dispersion of photonic crystal fibers using hybrid cladding

International Nuclear Information System (INIS)

Zhao-lun, Liu; Lan-tian, Hou; Wei, Wang

2009-01-01

We present a hybrid cladding photonic crystal fiber for shaping high nonlinear and flattened dispersion in a wide range of wavelengths. The new structure adopts hybrid cladding with different pitches, air-holes diameters and air-holes arrayed fashions. The full-vector finite element method with perfectly matched layer is used to investigate the characteristics of the hybrid cladding photonic crystal fiber such as nonlinearity and dispersion properties. The influence of the cladding structure parameters on the nonlinear coefficient and geometric dispersion is analyzed. High nonlinear coefficient and the dispersion properties of fibers are tailored by adjusting the cladding structure parameters. A novel hybrid cladding photonic crystal fiber with high nonlinear coefficient and dispersion flattened which is suited for super continuum generation is designed. (author)

Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox

Science.gov (United States)

Polchinski, Joseph

1991-01-01

The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.

Development of Advanced Continuum Models that Incorporate Nanomechanical Deformation into Engineering Analysis.

Energy Technology Data Exchange (ETDEWEB)

Zimmerman, Jonathan A.; Jones, Reese E.; Templeton, Jeremy Alan; McDowell, David L.; Mayeur, Jason R.; Tucker, Garritt J.; Bammann, Douglas J.; Gao, Huajian

2008-09-01

Materials with characteristic structures at nanoscale sizes exhibit significantly different mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscale materials phenomena and macroscale behavior, has eluded the research community.The goal of our project was to develop a consistent theory to model both the evolution ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

Directory of Open Access Journals (Sweden)

Giorgio Kaniadakis

2018-06-01

Full Text Available Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker–Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker–Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker–Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker–Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker–Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP that governs the particle kinetics of many body systems, introduced in G. Kaniadakis, Physica A 296, 405 (2001, univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker–Planck equation in its most general form.

Foundations of mechanics

International Nuclear Information System (INIS)

Zorski, Henryk; Bazanski, Stanislaw; Gutowski, Roman; Slawianowski, Jan; Wilmanski, Krysztof; Wozniak, Czeslaw

1992-01-01

In the last 3 decades the field of mechanics has seen spectacular progress due to the demand for applications in problems of cosmology, thermonuclear fusion, metallurgy, etc. This book provides a broad and thorough overview on the foundations of mechanics. It discusses theoretical mechanics and continuum mechanics, as well as phenomenological thermodynamics, quantum mechanics and relativistic mechanics. Each chapter presents the basic physical facts of interest without going into details and derivations and without using advanced mathematical formalism. The first part constitutes a classical exposition of Lagrange's and Hamiltonian's analytical mechanics on which most of the continuum theory is based. The section on continuum mechanics focuses mainly on the axiomatic foundations, with many pointers for further research in this area. Special attention is given to modern continuum thermodynamics, both for the foundations and applications. A section on quantum mechanics is also included, since the phenomenological description of various quantum phenomena is becoming of increasing importance. refs.; figs.; tabs

Mechanics from Newton's laws to deterministic chaos

CERN Document Server

Scheck, Florian

2018-01-01

This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science.   Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics.   The book contains more than 150 problems ...

General relativistic continuum mechanics and the post-Newtonian equations of motion

International Nuclear Information System (INIS)

Morrill, T.H.

1991-01-01

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.

Science.gov (United States)

Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen

2008-08-01

Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.

Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.

Science.gov (United States)

Sahin, Buyukdagli; Ralf, Blossey

2014-07-16

We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

Shape Modeling of a Concentric-tube Continuum Robot

DEFF Research Database (Denmark)

Bai, Shaoping; Xing, Charles Chuhao

2012-01-01

Concentric-tube continuum robots feature with simple and compact structures and have a great potential in medical applications. The paper is concerned with the shape modeling of a type of concentric-tube continuum robot built with a collection of super-elastic NiTiNol tubes. The mechanics...... is modeled on the basis of energy approach for both the in-plane and out-plane cases. The torsional influences on the shape of the concentric-tube robots are considered. An experimental device was build for the model validation. The results of simulation and experiments are included and analyzed....

Do reflex seizures and spontaneous seizures form a continuum? - triggering factors and possible common mechanisms.

Science.gov (United States)

Irmen, Friederike; Wehner, Tim; Lemieux, Louis

2015-02-01

Recent changes in the understanding and classification of reflex seizures have fuelled a debate on triggering mechanisms of seizures and their conceptual organization. Previous studies and patient reports have listed extrinsic and intrinsic triggers, albeit their multifactorial and dynamic nature is poorly understood. This paper aims to review literature on extrinsic and intrinsic seizure triggers and to discuss common mechanisms among them. Among self-reported seizure triggers, emotional stress is most frequently named. Reflex seizures are typically associated with extrinsic sensory triggers; however, intrinsic cognitive or proprioceptive triggers have also been assessed. The identification of a trigger underlying a seizure may be more difficult if it is intrinsic and complex, and if triggering mechanisms are multifactorial. Therefore, since observability of triggers varies and triggers are also found in non-reflex seizures, the present concept of reflex seizures may be questioned. We suggest the possibility of a conceptual continuum between reflex and spontaneous seizures rather than a dichotomy and discuss evidence to the notion that to some extent most seizures might be triggered. Copyright © 2014 British Epilepsy Association. Published by Elsevier Ltd. All rights reserved.

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

Experimental investigations of nonlinearities and destruction mechanisms of an experimental phospholipid-based ultrasound contrast agent.

Science.gov (United States)

Casciaro, Sergio; Palmizio Errico, Rosa; Errico, Rosa Palmizio; Conversano, Francesco; Demitri, Christian; Distante, Alessandro

2007-02-01

We sought to characterize the acoustical behavior of the experimental ultrasound contrast agent BR14 by determining the acoustic pressure threshold above which nonlinear oscillation becomes significant and investigating microbubble destruction mechanisms. We used a custom-designed in vitro setup to conduct broadband attenuation measurements at 3.5 MHz varying acoustic pressure (range, 50-190 kPa). We also performed granulometric analyses on contrast agent solutions to accurately measure microbubble size distribution and to evaluate insonification effects. Attenuation did not depend on acoustic pressure less than 100 kPa, indicating this pressure as the threshold for the appearance of microbubble nonlinear behavior. At the lowest excitation amplitude, attenuation increased during insonification, while, at higher excitation levels, the attenuation decreased over time, indicating microbubble destruction. The destruction rate changed with pressure amplitude suggesting different destruction mechanisms, as it was confirmed by granulometric analysis. Microbubbles showed a linear behavior until 100 kPa, whereas beyond this value significant nonlinearities occurred. Observed destruction phenomena seem to be mainly due to gas diffusion and bubble fragmentation mechanisms.

Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities: A numerical study

DEFF Research Database (Denmark)

Sayed, Karim El; Birkedal, Dan; Vadim, Lyssenko

1997-01-01

We present a theoretical investigation of ultrafast transient four-wave mixing (FWM) of GaAs quantum wells for coherent excitation of excitons and a large number of continuum states. It is shown that in this case the line shape of the FWM signal is drastically altered due to an interaction-induce...

A constitutive model of soft tissue: From nanoscale collagen to tissue continuum

KAUST Repository

Tang, Huang

2009-04-08

Soft collagenous tissue features many hierarchies of structure, starting from tropocollagen molecules that form fibrils, and proceeding to a bundle of fibrils that form fibers. Here we report the development of an atomistically informed continuum model of collagenous tissue. Results from full atomistic and molecular modeling are linked with a continuum theory of a fiber-reinforced composite, handshaking the fibril scale to the fiber and continuum scale in a hierarchical multi-scale simulation approach. Our model enables us to study the continuum-level response of the tissue as a function of cross-link density, making a link between nanoscale collagen features and material properties at larger tissue scales. The results illustrate a strong dependence of the continuum response as a function of nanoscopic structural features, providing evidence for the notion that the molecular basis for protein materials is important in defining their larger-scale mechanical properties. © 2009 Biomedical Engineering Society.

Description of an open quantum mechanical system

International Nuclear Information System (INIS)

Rotter, I.; Forschungszentrum Rossendorf e.V.

1994-05-01

A model for the description of an open quantum mechanical many-particle system is formulated. It starts from the shell model and treats the continuous states by a coupled channels method. The mixing of the discrete shell model states via the continuum of decay channels results in the genuine decaying states of the system. These states are eigenstates of a non-Hermitean Hamilton operator the eigenvalues of which give both the energies and the widths of the states. All correlations between two particles which are caused by the two-particle residual interaction, are taken into account including those via the continuum. In the formalism describing the open quantum mechanical system, the coupling between the system and its environment appears nonlinearly. If the resonance states start to overlap, a redistribution of the spectroscopic values ('trapping effect') takes place. As a result, the complexity of the system is reduced at high level density, structures in space and time are formed. This redistribution describes, on the one hand, the transition from the well-known nuclear properties at low level density to those at high level density and fits, on the other hand, into the concept of selforganization. (orig.)

Relativistic viscoelastic fluid mechanics

International Nuclear Information System (INIS)

Fukuma, Masafumi; Sakatani, Yuho

2011-01-01

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

Relativistic viscoelastic fluid mechanics.

Science.gov (United States)

Fukuma, Masafumi; Sakatani, Yuho

2011-08-01

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

Science.gov (United States)

Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

2017-12-27

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

Science.gov (United States)

Koh, Heeyuen; Cannon, James; Chiashi, Shohei; Shiomi, Junichiro; Maruyama, Shigeo

2013-03-01

Based on the finding that the lowest frequency mode of cantilevered SWNT is described by the continuum beam theory in frequency domain, we considered its effect of the symmetric structure for the coupling of orthogonal transverse modes to explain the nonlinear motion of free thermal vibration. This nonlinear motion calculated by our molecular dynamics simulation, once regarded as noise, is observed to have the periodic order with duffing and beating, which is dependent on aspect ratio and temperature. It could be dictated by the governing equation from the Green Lagrangian strain tensor. The nonlinear beam equation from strain tensor described the motion well for various models which has different aspect ratio in molecular dynamics simulation. Since this motion is nothing but the interaction between 2nd mode of radial, tangential mode and 1st longitudinal mode, it was found that Green Lagrangian strain tensor is capable to deal such coupling. The free thermal motion of suspended SWNT is also considered without temperature gradient. The Q factor measured by this theoretical analysis will be discussed. Part of this work was financially supported by Grant-in-Aid for Scientific Research (19054003 and 22226006), and Global COE Program 'Global Center for Excellence for Mechanical Systems Innovation'

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Super continuum generation at 800 nm in highly nonlinear photonic crystal fibers with normal dispersion

DEFF Research Database (Denmark)

Hansen, Kim Per; Larsen, Jacob Juul; Jensen, Jacob Riis

2001-01-01

More than 90 nm broad self-phase modulation (SPM) induced pulses have been created from both 25 and 50 fs pulses in just 12.5 cm of fiber. The broadening is more than 2.5 times that observed in standard SMF. SPM broadening in PCFs has several advantages over more complex super continuum generatio...

Cross-validation of theoretically quantified fiber continuum generation and absolute pulse measurement by MIIPS for a broadband coherently controlled optical source

DEFF Research Database (Denmark)

Tu, H.; Liu, Y.; Lægsgaard, Jesper

2012-01-01

source with the MIIPS-integrated pulse shaper produces compressed transform-limited 9.6 fs (FWHM) pulses or arbitrarily shaped pulses at a central wavelength of 1020 nm, an average power over 100 mW, and a repetition rate of 76 MHz. In comparison to the 229-fs pump laser pulses that generate the fiber......The predicted spectral phase of a fiber continuum pulsed source rigorously quantified by the scalar generalized nonlinear Schrödinger equation is found to be in excellent agreement with that measured by multiphoton intrapulse interference phase scan (MIIPS) with background subtraction. This cross......-validation confirms the absolute pulse measurement by MIIPS and the transform-limited compression of the fiber continuum pulses by the pulse shaper performing the MIIPS measurement, and permits the subsequent coherent control on the fiber continuum pulses by this pulse shaper. The combination of the fiber continuum...

Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets

Science.gov (United States)

Chen, Shu-Peng; He, Ling-Yun

2010-04-01

Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

Creep Tests and Modeling Based on Continuum Damage Mechanics for T91 and T92 Steels

Science.gov (United States)

Pan, J. P.; Tu, S. H.; Zhu, X. W.; Tan, L. J.; Hu, B.; Wang, Q.

2017-12-01

9-11%Cr ferritic steels play an important role in high-temperature and high-pressure boilers of advanced power plants. In this paper, a continuum damage mechanics (CDM)-based creep model was proposed to study the creep behavior of T91 and T92 steels at high temperatures. Long-time creep tests were performed for both steels under different conditions. The creep rupture data and creep curves obtained from creep tests were captured well by theoretical calculation based on the CDM model over a long creep time. It is shown that the developed model is able to predict creep data for the two ferritic steels accurately up to tens of thousands of hours.

Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?

KAUST Repository

Gadelha, H.

2010-05-12

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.

Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1992-12-01

Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

Passing waves from atomistic to continuum

Science.gov (United States)

Chen, Xiang; Diaz, Adrian; Xiong, Liming; McDowell, David L.; Chen, Youping

2018-02-01

Progress in the development of coupled atomistic-continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic-continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic-continuum method to enable a full phonon representation in the continuum description. This permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic-continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic-continuum interfaces. This work is the first step towards developing a concurrent atomistic-continuum simulation tool for non-equilibrium phonon-mediated thermal transport in materials with microstructural complexity.

Accidental bound states in the continuum in an open Sinai billiard

Energy Technology Data Exchange (ETDEWEB)

Pilipchuk, A.S. [Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk (Russian Federation); Siberian Federal University, 660080 Krasnoyarsk (Russian Federation); Sadreev, A.F., E-mail: almas@tnp.krasn.ru [Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk (Russian Federation)

2017-02-19

The fundamental mechanism of the bound states in the continuum is the full destructive interference of two resonances when two eigenlevels of the closed system are crossing. There is, however, a wide class of quantum chaotic systems which display only avoided crossings of eigenlevels. As an example of such a system we consider the Sinai billiard coupled with two semi-infinite waveguides. We show that notwithstanding the absence of degeneracy bound states in the continuum occur due to accidental decoupling of the eigenstates of the billiard from the waveguides. - Highlights: • Bound states in the continuum in open chaotic billiards occur to accidental vanishing of coupling of eigenstate of billiard with waveguides.

Effects of non-linearity of material properties on the coupled mechanical-hydraulic-thermal behavior in rock mass

International Nuclear Information System (INIS)

Kobayashi, Akira; Ohnishi, Yuzo

1986-01-01

The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)

Why ductile fracture mechanics

International Nuclear Information System (INIS)

Ritchie, R.O.

1983-01-01

Until recently, the engineering application of fracture mechanics has been specific to a description of macroscopic fracture behavior in components and structural parts which remain nominally elastic under loading. While this approach, termed linear elastic fracture mechanics, has been found to be invaluable for the continuum analysis of crack growth in brittle and high strength materials, it is clearly inappropriate for characterizing failure in lower strength ductile alloys where extensive inelastic deformation precedes and accompanies crack initiation and subsequent propagation. Accordingly, much effort has been devoted in recent years toward the development of nonlinear or ductile fracture mechanics methodology to characterize fracture behavior under elastic/plastic conditions; an effort which has been principally motivated by problems in nuclear industry. In this paper, the concepts of ductile (elastic/plastic) fracture mechanics are introduced and applied to the problem of both stationary and nonstationary cracks. Specifically, the limitations inherent in this approach are defined, together with a description of the microstructural considerations and applications relevant to the failure of ductile materials by fracture, fatigue, and creep

Mechanical nonlinearity elimination with a micromechanical clamped-free semicircular beams resonator

Science.gov (United States)

Chen, Dongyang; Chen, Xuying; Wang, Yong; Liu, Xinxin; Guan, Yangyang; Xie, Jin

2018-04-01

This paper reports a micro-machined clamped-free semicircular beam resonator aiming to eliminate the nonlinearity that widely exists in traditional mechanical resonators. Cubic coefficients over vibration displacement due to axial extension of the beams are analyzed through theoretical modelling, and the corresponding frequency effect is demonstrated. With the device working in the elastic vibration mode, the cubic coefficients are eliminated by using a free end to release the nonlinear extension of beams and thus the inside axial stress. The amplitude-frequency (A-f) effect is overcome in a large region of source power, and the coefficient of frequency softening is linearized in a large region of polarization voltage. As a result, the resonator can be driven at larger vibration amplitude to achieve a high signal to noise ratio and power handling performance.

Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms

Energy Technology Data Exchange (ETDEWEB)

Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)

2014-11-03

We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.

Nonlinear time reversal signal processing techniques applied to acousto-mechanical imaging of complex materials

Czech Academy of Sciences Publication Activity Database

Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk

2015-01-01

Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics

Characterization of site-specific biomechanical properties of human meniscus-Importance of collagen and fluid on mechanical nonlinearities.

Science.gov (United States)

Danso, E K; Mäkelä, J T A; Tanska, P; Mononen, M E; Honkanen, J T J; Jurvelin, J S; Töyräs, J; Julkunen, P; Korhonen, R K

2015-06-01

Meniscus adapts to joint loads by depth- and site-specific variations in its composition and structure. However, site-specific mechanical characteristics of intact meniscus under compression are poorly known. In particular, mechanical nonlinearities caused by different meniscal constituents (collagen and fluid) are not known. In the current study, in situ indentation testing was conducted to determine site-specific elastic, viscoelastic and poroelastic properties of intact human menisci. Lateral and medial menisci (n=26) were harvested from the left knee joint of 13 human cadavers. Indentation tests, using stress-relaxation and dynamic (sinusoidal) loading protocols, were conducted for menisci at different sites (anterior, middle, posterior, n=78). Sample- and site-specific axisymmetric finite element models with fibril-reinforced poroelastic properties were fitted to the corresponding stress-relaxation curves to determine the mechanical parameters. Elastic moduli, especially the instantaneous and dynamic moduli, showed site-specific variation only in the medial meniscus (pmeniscus. The phase angle showed no statistically significant variation between the sites (p>0.05). The values for the strain-dependent fibril network modulus (nonlinear behaviour of collagen) were significantly different (pmeniscus only between the middle and posterior sites. For the strain-dependent permeability coefficient, only anterior and middle sites showed a significant difference (pmeniscus. This parameter demonstrated a significant difference (pmeniscus shows more site-dependent variation in the mechanical properties as compared to lateral meniscus. In particular, anterior horn of medial meniscus was the stiffest and showed the most nonlinear mechanical behaviour. The nonlinearity was related to both collagen fibrils and fluid. Copyright © 2015 Elsevier Ltd. All rights reserved.

Continuum robots and underactuated grasping

Directory of Open Access Journals (Sweden)

N. Giri

2011-02-01

Full Text Available We discuss the capabilities of continuum (continuous backbone robot structures in the performance of under-actuated grasping. Continuum robots offer the potential of robust grasps over a wide variety of object classes, due to their ability to adapt their shape to interact with the environment via non-local continuum contact conditions. Furthermore, this capability can be achieved with simple, low degree of freedom hardware. However, there are practical issues which currently limit the application of continuum robots to grasping. We discuss these issues and illustrate via an experimental continuum grasping case study.

This paper was presented at the IFToMM/ASME International Workshop on Underactuated Grasping (UG2010, 19 August 2010, Montréal, Canada.

A continuum model for pressure-flow relationship in human pulmonary circulation.

Science.gov (United States)

Huang, Wei; Zhou, Qinlian; Gao, Jian; Yen, R T

2011-06-01

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.

A continuum-based structural modeling approach for cellulose nanocrystals (CNCs)

Science.gov (United States)

Mehdi Shishehbor; Fernando L. Dri; Robert J. Moon; Pablo D. Zavattieri

2018-01-01

We present a continuum-based structural model to study the mechanical behavior of cel- lulose nanocrystals (CNCs), and analyze the effect of bonded and non-bonded interactions on the mechanical properties under various loading conditions. In particular, this model assumes the uncoupling between the bonded and non-bonded interactions and their be- havior is obtained...

Studies of the underlying mechanisms for optical nonlinearities of blue phase liquid crystals (Presentation Recording)

Science.gov (United States)

Chen, Chun-Wei; Khoo, Iam Choon; Zhao, Shuo; Lin, Tsung-Hsien; Ho, Tsung-Jui

2015-10-01

We have investigated the mechanisms responsible for nonlinear optical processes occurring in azobenzene-doped blue phase liquid crystals (BPLC), which exhibit two thermodynamically stable BPs: BPI and BPII. In coherent two wave-mixing experiments, a slow (minutes) and a fast (few milliseconds) side diffractions are observed. The underlying mechanisms were disclosed by monitoring the dynamics of grating formation and relaxation as well as by some supplementary experiments. We found the photothermal indexing and dye/LC intermolecular torque leading to lattice distortion to be the dominant mechanisms for the observed nonlinear response in BPLC. Moreover, the response time of the nonlinear optical process varied with operating phase. The rise time of the thermal indexing process was in good agreement with our findings on the temperature dependence of BP refractive index: τ(ISO) > τ(BPI) > τ(BPII). The relaxation time of the torque-induced lattice distortion was analogue to its electrostriction counterpart: τ'(BPI) > τ'(BPII). In a separate experiment, lattice swelling with selective reflection of direction changed from green to red was also observed. This was attributable to the isomerization-induced change in cholesteric pitch, which directly affects the lattice spacing. The phenomenon was confirmed by measuring the optical rotatory power of the BPLC.

Coupling of nonlocal and local continuum models by the Arlequinapproach

KAUST Repository

Han, Fei

2011-08-09

The objective of this work is to develop and apply the Arlequin framework to couple nonlocal and local continuum mechanical models. A mechanically-based model of nonlocal elasticity, which involves both contact and long-range forces, is used for the \\'fine scale\\' description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can be neglected. Both models overlap in a coupling subdomain called the \\'gluing area\\' in which the total energy is separated into nonlocal and local contributions by complementary weight functions. A weak compatibility is ensured between kinematics of both models using Lagrange multipliers over the gluing area. The discrete formulation of this specific Arlequin coupling framework is derived and fully described. The validity and limits of the technique are demonstrated through two-dimensional numerical applications and results are compared against those of the fully nonlocal elasticity method. © 2011 John Wiley & Sons, Ltd.

Kinetic Monte Carlo simulations compared with continuum models and experimental properties of pattern formation during ion beam sputtering

International Nuclear Information System (INIS)

Chason, E; Chan, W L

2009-01-01

Kinetic Monte Carlo simulations model the evolution of surfaces during low energy ion bombardment using atomic level mechanisms of defect formation, recombination and surface diffusion. Because the individual kinetic processes are completely determined, the resulting morphological evolution can be directly compared with continuum models based on the same mechanisms. We present results of simulations based on a curvature-dependent sputtering mechanism and diffusion of mobile surface defects. The results are compared with a continuum linear instability model based on the same physical processes. The model predictions are found to be in good agreement with the simulations for predicting the early-stage morphological evolution and the dependence on processing parameters such as the flux and temperature. This confirms that the continuum model provides a reasonable approximation of the surface evolution from multiple interacting surface defects using this model of sputtering. However, comparison with experiments indicates that there are many features of the surface evolution that do not agree with the continuum model or simulations, suggesting that additional mechanisms are required to explain the observed behavior.

Wave propagation in nanostructures nonlocal continuum mechanics formulations

CERN Document Server

Gopalakrishnan, Srinivasan

2013-01-01

Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures. The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behav...

Nano-Continuum Modeling of a Nuclear Glass Specimen Altered for 25 Years

Energy Technology Data Exchange (ETDEWEB)

Steefel, Carl

2014-01-06

The purpose of this contribution is to report on preliminary nano-continuum scale modeling of nuclear waste glass corrosion. The focus of the modeling is an experiment involving a French glass SON68 specimen leached for 25 years in a granitic environment. In this report, we focus on capturing the nano-scale concentration profiles. We use a high resolution continuum model with a constant grid spacing of 1 nanometer to investigate the glass corrosion mechanisms.

Geometrical nonlinear free vibration of multi-layered graphene sheets

International Nuclear Information System (INIS)

Wang Jinbao; He Xiaoqiao; Kitipornchai, S; Zhang Hongwu

2011-01-01

A nonlinear continuum model is developed for the nonlinear vibration analysis of multi-layered graphene sheets (MLGSs), in which the nonlinear van der Waals (vdW) interaction between any two layers is formulated explicitly. The nonlinear equations of motion are studied by the harmonic-balance methods. Based on the present model, the nonlinear stiffened amplitude-frequency relations of double-layered graphene sheets (DLGSs) are investigated in the spectral neighbourhood of lower frequencies. The influence of the vdW interaction on the vibration properties of DLGSs is well illustrated by plotting the resulting modes' shapes, in which in-phase and anti-phase vibrations of DLGSs are studied. In particular, the large-amplitude vibration which associates with the anti-phase resonant frequencies, separating DLGS into single-layered GSs, is a promising application that needs to be explored further. In contrast, the vibration modes that are associated with the resonant frequencies are nonidentical and give various vibration patterns, which indicates that MLGSs are highly suited to being used as high-frequency resonators.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

Nonlinear force propagation, anisotropic stiffening and non-affine relaxation in a model cytoskeleton

Science.gov (United States)

Mizuno, Daisuke; Head, David; Ikebe, Emi; Nakamasu, Akiko; Kinoshita, Suguru; Peijuan, Zhang; Ando, Shoji

2013-03-01

Forces are generated heterogeneously in living cells and transmitted through cytoskeletal networks that respond highly non-linearly. Here, we carry out high-bandwidth passive microrheology on vimentin networks reconstituted in vitro, and observe the nonlinear mechanical response due to forces propagating from a local source applied by an optical tweezer. Since the applied force is constant, the gel becomes equilibrated and the fluctuation-dissipation theorem can be employed to deduce the viscoelasticity of the local environment from the thermal fluctuations of colloidal probes. Our experiments unequivocally demonstrate the anisotropic stiffening of the cytoskeletal network behind the applied force, with greater stiffening in the parallel direction. Quantitative agreement with an affine continuum model is obtained, but only for the response at certain frequency ~ 10-1000 Hz which separates the high-frequency power law and low-frequency elastic behavior of the network. We argue that the failure of the model at lower frequencies is due to the presence of non-affinity, and observe that zero-frequency changes in particle separation can be fitted when an independently-measured, empirical nonaffinity factor is applied.

Discrete mechanics

International Nuclear Information System (INIS)

Lee, T.D.

1985-01-01

This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

Science.gov (United States)

Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith

2017-05-01

In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

An extended continuum model considering optimal velocity change with memory and numerical tests

Science.gov (United States)

Qingtao, Zhai; Hongxia, Ge; Rongjun, Cheng

2018-01-01

In this paper, an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory. The new model's stability condition and KdV-Burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis, respectively. Numerical simulation is carried out to study the extended continuum model, which explores how optimal velocity changes with memory affected velocity, density and energy consumption. Numerical results show that when considering the effects of optimal velocity changes with memory, the traffic jams can be suppressed efficiently. Both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently. Furthermore, numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information, which increases the stability of traffic flow on road, and so it improve the traffic flow stability and minimize cars' energy consumptions.

Continuum limbed robots for locomotion

Science.gov (United States)

Mutlu, Alper

This thesis focuses on continuum robots based on pneumatic muscle technology. We introduce a novel approach to use these muscles as limbs of lightweight legged robots. The flexibility of the continuum legs of these robots offers the potential to perform some duties that are not possible with classical rigid-link robots. Potential applications are as space robots in low gravity, and as cave explorer robots. The thesis covers the fabrication process of continuum pneumatic muscles and limbs. It also provides some new experimental data on this technology. Afterwards, the designs of two different novel continuum robots - one tripod, one quadruped - are introduced. Experimental data from tests using the robots is provided. The experimental results are the first published example of locomotion with tripod and quadruped continuum legged robots. Finally, discussion of the results and how far this technology can go forward is presented.

Coupling of nonlocal and local continuum models by the Arlequinapproach

KAUST Repository

Han, Fei; Lubineau, Gilles

2011-01-01

for the 'fine scale' description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can

An introduction to the mechanics of fluids

CERN Document Server

Truesdell, C

2000-01-01

The authors have backgrounds which are ideally suited for writing this book. The late C. Truesdell is well known for his monumental treatises on continuum thermomechanics. K.R. Rajagopal has made many important contributions to the mechanics of continua in general, and to nonlinear fluids in particular. They have produced a compact, moderately general book which encompasses many fluid models of current interest…The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments. This is an excellent book which is highly recommended to students and researchers in fluid mechanics. —Mathematical Reviews The writing style is quintessential Truesdellania: purely mathematical, breathtaking, irrepressible, irreverent, uncompromising, taking no prisoners...The book is filled with historical nuggets…Its pure, exact mathematics will baptize, enlighten and exhilarate. —Applied Mechanics Review...

Continuum deformation of multi-agent systems

CERN Document Server

Rastgoftar, Hossein

2016-01-01

This monograph presents new algorithms for formation control of multi-agent systems (MAS) based on principles of continuum mechanics. Beginning with an overview of traditional methods, the author then introduces an innovative new approach whereby agents of an MAS are considered as particles in a continuum evolving in ℝn whose desired configuration is required to satisfy an admissible deformation function. The necessary theory and its validation on a mobile-agent-based swarm test bed are considered for two primary tasks: homogeneous transformation of the MAS and deployment of a random distribution of agents on a desired configuration. The framework for this model is based on homogeneous transformations for the evolution of an MAS under no inter-agent communication, local inter-agent communication, and intelligent perception by agents. Different communication protocols for MAS evolution, the robustness of tracking of a desired motion by an MAS evolving in ℝn, and the effect of communication delays in an MAS...

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

Directory of Open Access Journals (Sweden)

Walter H. Aschbacher

2009-01-01

Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

Nonlinear analysis of collapse mechanism in superstructure vehicle

Science.gov (United States)

Nor, M. K. Mohd; Ho, C. S.; Ma'at, N.

2017-04-01

The EU directive 2001/85/EC is an official European text which describes the specifications for "single deck class II and III vehicles" required to be approved by the regulation UN/ECE no.66 (R66). To prevent the catastrophic consequences by occupant during an accident, the Malaysian government has reinforced the same regulation upon superstructure construction. This paper discusses collapse mechanism analysis of a superstructure vehicle using a Crash D nonlinear analysis computer program based on this regulation. The analysis starts by hand calculation to define the required energy absorption by the chosen structure. Simple calculations were then performed to define the weakest collapse mechanism after undesirable collapse modes are eliminated. There are few factors highlighted in this work to pass the regulation. Using the selected cross section, Crash D simulation showed a good result. Generally, the deformation is linearly correlates to the energy absorption for the structure with low stiffness. Failure of critical members such as vertical lower side wall must be avoided to sustain safety of the passenger compartment and prevent from severe and fatal injuries to the trapped occupant.

Influences of the Control on the Nonlinear Vibrations of a Variable Compression Ratio Mechanism

Directory of Open Access Journals (Sweden)

Mănescu Bogdan

2018-01-01

Full Text Available For the mechanism described in references the study of the nonlinear vibrations is performed considering a multibody approach for the elements of the mechanism and different laws of motion for the control element. A great attention is paid to the equilibrium of the motion. The influence of different parameters of control is highlighted in the paper. The results are numerically validated.

Bright breathers in nonlinear left-handed metamaterial lattices

Science.gov (United States)

Koukouloyannis, V.; Kevrekidis, P. G.; Veldes, G. P.; Frantzeskakis, D. J.; DiMarzio, D.; Lan, X.; Radisic, V.

2018-02-01

In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber k=π . Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

International Nuclear Information System (INIS)

Xu, X Q

2007-01-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. With our 4D (ψ, θ, ε, μ) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices

Gradient-based optimization in nonlinear structural dynamics

DEFF Research Database (Denmark)

Dou, Suguang

The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

Dissipation consistent fabric tensor definition from DEM to continuum for granular media

Science.gov (United States)

Li, X. S.; Dafalias, Y. F.

2015-05-01

In elastoplastic soil models aimed at capturing the impact of fabric anisotropy, a necessary ingredient is a measure of anisotropic fabric in the form of an evolving tensor. While it is possible to formulate such a fabric tensor based on indirect phenomenological observations at the continuum level, it is more effective and insightful to have the tensor defined first based on direct particle level microstructural observations and subsequently deduce a corresponding continuum definition. A practical means able to provide such observations, at least in the context of fabric evolution mechanisms, is the discrete element method (DEM). Some DEM defined fabric tensors such as the one based on the statistics of interparticle contact normals have already gained widespread acceptance as a quantitative measure of fabric anisotropy among researchers of granular material behavior. On the other hand, a fabric tensor in continuum elastoplastic modeling has been treated as a tensor-valued internal variable whose evolution must be properly linked to physical dissipation. Accordingly, the adaptation of a DEM fabric tensor definition to a continuum constitutive modeling theory must be thermodynamically consistent in regards to dissipation mechanisms. The present paper addresses this issue in detail, brings up possible pitfalls if such consistency is violated and proposes remedies and guidelines for such adaptation within a recently developed Anisotropic Critical State Theory (ACST) for granular materials.

Fault Diagnosis for Nonlinear Hydraulic-Mechanical Drilling Pipe Handling System

DEFF Research Database (Denmark)

Choux, Martin; Blanke, Mogens

2011-01-01

Leakage and increased friction are common faults in hydraulic cylinders that can have serious consequences if they are not detected at early stage. In this paper, the design of a fault detector for a nonlinear hydraulic mechanical system is presented. By considering the system in steady state, two...... residual signals are generated and analysed with a composite hypothesis test which accommodates for unknown parameters. The resulting detector is able to detect abrupt changes in leakage or friction given the noisy pressure and position measurements. Test rig measurements validate the properties...

Nonlinearity from quantum mechanics: Dynamically unstable Bose-Einstein condensate in a double-well trap

International Nuclear Information System (INIS)

Javanainen, Juha

2010-01-01

We study theoretically an atomic Bose-Einstein condensate in a double-well trap, both quantum-mechanically and classically, under conditions such that in the classical model an unstable equilibrium dissolves into large-scale oscillations of the atoms between the potential wells. Quantum mechanics alone does not exhibit such nonlinear dynamics, but measurements of the atom numbers in the potential wells may nevertheless cause the condensate to behave essentially classically.

The Virtuality Continuum Revisited

NARCIS (Netherlands)

Nijholt, Antinus; Traum, D.; Zhai, Sh.; Kellogg, W.

2005-01-01

We survey the themes and the aims of a workshop devoted to the state-of-the-art virtuality continuum. In this continuum, ranging from fully virtual to real physical environments, allowing for mixed, augmented and desktop virtual reality, several perspectives can be taken. Originally, the emphasis

Structural, Linear, and Nonlinear Optical and Mechanical Properties of New Organic L-Serine Crystal

Directory of Open Access Journals (Sweden)

K. Rajesh

2014-01-01

Full Text Available Nonlinear optical single crystal of organic amino acid L-Serine (LS was grown by slow evaporation technique. Solubility study of the compound was measured and metastable zone width was found. Single crystal X-ray diffraction study was carried out for the grown crystal. The linear and nonlinear optical properties of the crystal were confirmed by UV-Vis analysis and powder SHG tester. FT-IR spectrum was recorded and functional groups were analyzed. Vickers’ microhardness studies showed the mechanical strength of the grown crystal. Laser damage threshold value of the crystal was calculated. Photoconductivity studies reveal the conductivity of the crystal.

Nonlinear oscillations

CERN Document Server

Nayfeh, Ali Hasan

1995-01-01

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

Bound states in the continuum generated by supersymmetric quantum mechanics and phase rigidity of the corresponding wavefunctions

International Nuclear Information System (INIS)

Demić, Aleksandar; Milanović, Vitomir; Radovanović, Jelena

2015-01-01

Supersymmetric quantum mechanics (SUSYQM) is a method that can be used for generating complex potentials with entirely real spectrum with bound states in the continuum (BIC). These complex potentials are isospectral with the initial one, but SUSYQM method adds discrete BIC's at selected energies. Corresponding wavefunctions created by SUSYQM are biorthogonal and complex, hence we can discuss their phase rigidity and illustrate the application of SUSYQM on the examples of three specific potential profiles (free electron, negative Dirac potential and quantum well with infinite walls). - Highlights: • We present SUSYQM method for generating complex potentials with entirely real spectrum. • Phase rigidity and normalizability of wavefunctions in complex potential is discussed. • Numerical application is performed on three specific potential profiles.

Continuum Physics

CERN Document Server

Hertel, Peter

2012-01-01

This small book on the properties of continuously distributed matter covers a huge field. It sets out the governing principles of continuum physics and illustrates them by carefully chosen examples. These examples comprise structural mechanics and elasticity, fluid media, electricity and optics, thermoelectricity, fluctuation phenomena and more, from Archimedes' principle via Brownian motion to white dwarfs. Metamaterials, pattern formation by reaction-diffusion and surface plasmon polaritons are dealt with as well as classical topics such as Stokes' formula, beam bending and buckling, crystal optics and electro- and magnetooptic effects, dielectric waveguides, Ohm's law, surface acoustic waves, to mention just some.   The set of balance equations for content, flow and production of particles, mass, charge, momentum, energy and entropy is augmented by material, or constitutive equations. They describe entire classes of materials, such as viscid fluids and gases, elastic media, dielectrics or electrical con...

Application of an enriched FEM technique in thermo-mechanical contact problems

Science.gov (United States)

Khoei, A. R.; Bahmani, B.

2018-02-01

In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton-Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature.

Nonlinear electroelasticity: material properties, continuum theory and applications.

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W

2017-08-01

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

Nonlinear electroelasticity: material properties, continuum theory and applications

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W.

2017-08-01

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

Estimating intratidal nonlinearity of respiratory system mechanics: a model study using the enhanced gliding-SLICE method

International Nuclear Information System (INIS)

Schumann, Stefan; Burcza, Boris; Guttmann, Josef; Haberthür, Christoph; Lichtwarck-Aschoff, Michael

2009-01-01

In the clinical situation and in most research work, the analysis of respiratory system mechanics is limited to the estimation of single-value compliances during static or quasi-static conditions. In contrast, our SLICE method analyses intratidal nonlinearity under the dynamic conditions of mechanical ventilation by calculating compliance and resistance for six conjoined volume portions (slices) of the pressure–volume loop by multiple linear regression analysis. With the gliding-SLICE method we present a new approach to determine continuous intratidal nonlinear compliance. The performance of the gliding-SLICE method was tested both in computer simulations and in a physical model of the lung, both simulating different intratidal compliance profiles. Compared to the original SLICE method, the gliding-SLICE method resulted in smaller errors when calculating the compliance or pressure course (all p 2 O s L −1 to 0.8 ± 0.3 cmH 2 O s L −1 (mathematical model) and from 7.2 ± 3.9 cmH 2 O s L −1 to 0.4 ± 0.2 cmH 2 O s L −1 (physical model) (all p < 0.001). We conclude that the new gliding-SLICE method allows detailed assessment of intratidal nonlinear respiratory system mechanics without discontinuity error

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

Burger, Martin

2010-01-01

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.

FE Analysis of Rock with Hydraulic-Mechanical Coupling Based on Continuum Damage Evolution

Directory of Open Access Journals (Sweden)

Yongliang Wang

2016-01-01

Full Text Available A numerical finite element (FE analysis technology is presented for efficient and reliable solutions of rock with hydraulic-mechanical (HM coupling, researching the seepage characteristics and simulating the damage evolution of rock. To be in accord with the actual situation, the rock is naturally viewed as heterogeneous material, in which Young’s modulus, permeability, and strength property obey the typical Weibull distribution function. The classic Biot constitutive relation for rock as porous medium is introduced to establish a set of equations coupling with elastic solid deformation and seepage flow. The rock is subsequently developed into a novel conceptual and practical model considering the damage evolution of Young’s modulus and permeability, in which comprehensive utilization of several other auxiliary technologies, for example, the Drucker-Prager strength criterion, the statistical strength theory, and the continuum damage evolution, yields the damage variable calculating technology. To this end, an effective and reliable numerical FE analysis strategy is established. Numerical examples are given to show that the proposed method can establish heterogeneous rock model and be suitable for different load conditions and furthermore to demonstrate the effectiveness and reliability in the seepage and damage characteristics analysis for rock.

Computing with networks of nonlinear mechanical oscillators.

Directory of Open Access Journals (Sweden)

Jean C Coulombe

Full Text Available As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to maximize the benefits of distributed sensors, micro-robots or smart materials. Biologically-inspired devices, such as artificial neural networks, can process information with a high level of parallelism to efficiently solve difficult problems, even when implemented using conventional microelectronic technologies. We describe a mechanical device, which operates in a manner similar to artificial neural networks, to solve efficiently two difficult benchmark problems (computing the parity of a bit stream, and classifying spoken words. The device consists in a network of masses coupled by linear springs and attached to a substrate by non-linear springs, thus forming a network of anharmonic oscillators. As the masses can directly couple to forces applied on the device, this approach combines sensing and computing functions in a single power-efficient device with compact dimensions.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

A Concentric Tube Continuum Robot with Piezoelectric Actuation for MRI-Guided Closed-Loop Targeting

OpenAIRE

Su, Hao; Li, Gang; Rucker, D. Caleb; Webster, Robert J.; Fischer, Gregory S.

2016-01-01

This paper presents the design, modeling and experimental evaluation of a magnetic resonance imaging (MRI)-compatible concentric tube continuum robotic system. This system enables MRI-guided deployment of a precurved and steerable concentric tube continuum mechanism, and is suitable for clinical applications where a curved trajectory is needed. This compact 6 degree-of-freedom (DOF) robotic system is piezoelectrically-actuated, and allows simultaneous robot motion and imaging with no visually...

Development of Nonlinear Flight Mechanical Model of High Aspect Ratio Light Utility Aircraft

Science.gov (United States)

Bahri, S.; Sasongko, R. A.

2018-04-01

The implementation of Flight Control Law (FCL) for Aircraft Electronic Flight Control System (EFCS) aims to reduce pilot workload, while can also enhance the control performance during missions that require long endurance flight and high accuracy maneuver. In the development of FCL, a quantitative representation of the aircraft dynamics is needed for describing the aircraft dynamics characteristic and for becoming the basis of the FCL design. Hence, a 6 Degree of Freedom nonlinear model of a light utility aircraft dynamics, also called the nonlinear Flight Mechanical Model (FMM), is constructed. This paper shows the construction of FMM from mathematical formulation, the architecture design of FMM, the trimming process and simulations. The verification of FMM is done by analysis of aircraft behaviour in selected trimmed conditions.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

Science.gov (United States)

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

Science.gov (United States)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the

Analytical Solutions to Non-linear Mechanical Oscillation Problems

DEFF Research Database (Denmark)

Kaliji, H. D.; Ghadimi, M.; Barari, Amin

2011-01-01

In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

Changing public stigma with continuum beliefs.

Science.gov (United States)

Corrigan, Patrick W; Schmidt, Annie; Bink, Andrea B; Nieweglowski, Katherine; Al-Khouja, Maya A; Qin, Sang; Discont, Steve

2017-10-01

Given the egregious effect of public stigma on the lives of people with mental illness, researchers have sought to unpack and identify effective components of anti-stigma programs. We expect to show that continuum messages have more positive effect on stigma and affirming attitudes (beliefs that people with mental illness recover and should be personally empowered) than categorical perspectives. The effect of continuum beliefs will interact with contact strategies. A total of 598 research participants were randomly assigned to online presentations representing one of the six conditions: three messages (continuum, categorical, or neutral control) by two processes (education or contact). Participants completed measures of continuum beliefs (as a manipulation check), stigma and affirming attitudes after viewing the condition. Continuum messages had significantly better effect on views that people with mental illness are "different," a finding that interacted with contact. Continuum messages also had better effects on recovery beliefs, once again an effect that interacted significantly with contact. Implications of these findings for improving anti-stigma programs are discussed.

Theoretical Calculation and Validation of the Water Vapor Continuum Absorption

Science.gov (United States)

Ma, Qiancheng; Tipping, Richard H.

1998-01-01

The primary objective of this investigation is the development of an improved parameterization of the water vapor continuum absorption through the refinement and validation of our existing theoretical formalism. The chief advantage of our approach is the self-consistent, first principles, basis of the formalism which allows us to predict the frequency, temperature and pressure dependence of the continuum absorption as well as provide insights into the physical mechanisms responsible for the continuum absorption. Moreover, our approach is such that the calculated continuum absorption can be easily incorporated into satellite retrieval algorithms and climate models. Accurate determination of the water vapor continuum is essential for the next generation of retrieval algorithms which propose to use the combined constraints of multi-spectral measurements such as those under development for EOS data analysis (e.g., retrieval algorithms based on MODIS and AIRS measurements); current Pathfinder activities which seek to use the combined constraints of infrared and microwave (e.g., HIRS and MSU) measurements to improve temperature and water profile retrievals, and field campaigns which seek to reconcile spectrally-resolved and broad-band measurements such as those obtained as part of FIRE. Current widely used continuum treatments have been shown to produce spectrally dependent errors, with the magnitude of the error dependent on temperature and abundance which produces errors with a seasonal and latitude dependence. Translated into flux, current water vapor continuum parameterizations produce flux errors of order 10 W/ml, which compared to the 4 W/m' magnitude of the greenhouse gas forcing and the 1-2 W/m' estimated aerosol forcing is certainly climatologically significant and unacceptably large. While it is possible to tune the empirical formalisms, the paucity of laboratory measurements, especially at temperatures of interest for atmospheric applications, preclude tuning

A survey of infrared continuum versus line radiation from metal halide lamps

International Nuclear Information System (INIS)

Kato, M; Herd, M T; Lawler, J E

2008-01-01

Near-infrared radiation (near-IR) losses from the arcs of six commercial metal halide high intensity discharge (MH-HID) lamps with various power levels and with both Na/Sc and rare earth doses were surveyed in this paper. A radiometrically calibrated Fourier transform infrared spectrometer was used. Lamps with rare earth doses have appreciably better color rendering indices (CRIs) than lamps with Na/Sc doses. The ratios of near-IR continuum emission over near-IR line emission from these six lamps were compared. The near-IR continuum dominates near-IR losses from lamps with rare earth doses and the continuum is significant, but not dominant, from lamps with Na/Sc doses. There was no strong dependence of this ratio on input power or color temperature (T c ). Total near-IR losses were estimated using absolutely calibrated, horizontal irradiance measurements. Estimated total near-IR losses were correlated with CRI. The lamps with rare earth doses yield the best CRIs, but have appreciably higher near-IR losses due primarily to continuum processes. One of these rare earth MH-HID lamps was used in a more detailed study of the microscopic physics of the continuum mechanism (Herd M T and Lawler E 2007 J. Phys. D: Appl. Phys. 40 3386)

Extension versus Bending for Continuum Robots

Directory of Open Access Journals (Sweden)

George Grimes

2008-11-01

Full Text Available In this paper, we analyze the capabilities of a novel class of continuous-backbone ("continuum" robots. These robots are inspired by biological "trunks, and tentacles". However, the capabilities of established continuum robot designs, which feature controlled bending but not extension, fall short of those of their biological counterparts. In this paper, we argue that the addition of controlled extension provides dual and complementary functionality, and correspondingly enhanced performance, in continuum robots. We present an interval-based analysis to show how the inclusion of controllable extension significantly enhances the workspace and capabilities of continuum robots.

The use of the J* integral for non-linear fracture mechanics

International Nuclear Information System (INIS)

Hellen, T.K.

1976-09-01

The Griffith energy balance criterion, first postulated over 50 years ago, is still the basis of linear elastic fracture mechanics. From this, accurate numerical methods for establishing stress intensity factors and energy release rates have been developed. One such method involves path independent contour integrals about the crack tip. An improved contour integral, designated J* is discussed, and shown to have distinct advantages over others in non-linear strain situations. A number of examples are shown including fractures in thermo-plastic and creep situations. (author)

Atom-to-continuum methods for gaining a fundamental understanding of fracture.

Energy Technology Data Exchange (ETDEWEB)

McDowell, David Lynn (Georgia Institute of Technology, Atlanta, GA); Reedy, Earl David, Jr.; Templeton, Jeremy Alan; Jones, Reese E.; Moody, Neville Reid; Zimmerman, Jonathan A.; Belytschko, Ted. (Northwestern University, Evanston, IL); Zhou, Xiao Wang; Lloyd, Jeffrey T. (Georgia Institute of Technology, Atlanta, GA); Oswald, Jay (Northwestern University, Evanston, IL); Delph, Terry J. (Lehigh University, Bethlehem, PA); Kimmer, Christopher J. (Indiana University Southeast, New Albany, IN)

2011-08-01

This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate

Comet Halley: An optical continuum study

International Nuclear Information System (INIS)

Hoban, S.M.

1989-01-01

From an analysis of narrowband CCD images of Comet Halley from 1986 January, March, and April, certain dust structures which are redder than the remainder of the dust coma have become apparent. Mie calculations suggest that this reddening is due to an enhancement of particles with sizes comparable to the observing wavelengths. Although the mass range derived from the calculations presented here is somewhat uncertain as a result of the limitations of Mie theory, these values are in the expected range derived from the calculations presented here is somewhat uncertain as a result of particle sizes which would be both sensitive to radiation pressure and significantly reddened with respect to the solar spectrum at the observing wavelengths. Thus, the red envelopes are plausibly the result of size sorting by solar radiation pressure. The red jets observed on 1986 January 10, March 1 and March 9 can then be explained by the enhanced dust flux at the jet sources, and the subsequent trapping of a relative excess of intermediate mass (i.e. red) particles into the jets which are visible in the continuum images. Analysis of narrowband photometry of the optical continuum of Comet Halley reveals no correlation between the color of the dust and heliocentric distance, phase angle, strength of the continuum or gas-to-dust ratio. The photometric data are thus consistent with a post-ejection sorting mechanism. Chemical inhomogeneities of the nucleus are therefore not necessary to explain the observed structure in the color of the dust in Comet Halley

Topological mechanics: from metamaterials to active matter

Science.gov (United States)

Vitelli, Vincenzo

2015-03-01

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable acoustic response, which originate in the geometry of their unit cell. At the heart of such unusual behavior is often a mechanism: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, these soft motions become the building blocks of robots and smart materials. In this talk, we discuss topological mechanisms that possess two key properties: (i) their existence cannot be traced to a local imbalance between degrees of freedom and constraints (ii) they are robust against a wide range of structural deformations or changes in material parameters. The continuum elasticity of these mechanical structures is captured by non-linear field theories with a topological boundary term similar to topological insulators and quantum Hall systems. We present several applications of these concepts to the design and experimental realization of 2D and 3D topological structures based on linkages, origami, buckling meta-materials and lastly active media that break time-reversal symmetry.

Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene

Science.gov (United States)

Sfyris, D.; Sfyris, G. I.; Bustamante, R.

2016-04-01

Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.

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

Science.gov (United States)

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.

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.

Directory of Open Access Journals (Sweden)

Olga Kononova

2016-01-01

Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

Fully coupled thermal-mechanical-fluid flow model for nonliner geologic systems

International Nuclear Information System (INIS)

Hart, R.D.

1981-01-01

A single model is presented which describes fully coupled thermal-mechanical-fluid flow behavior of highly nonlinear, dynamic or quasistatic, porous geologic systems. The mathematical formulation for the model utilizes the continuum theory of mixtures to describe the multiphase nature of the system, and incremental linear constitutive theory to describe the path dependency of nonlinear material behavior. The model, incorporated in an explicit finite difference numerical procedure, was implemented in two different computer codes. A special-purpose one-dimensional code, SNEAKY, was written for initial validation of the coupling mechanisms and testing of the coupled model logic. A general purpose commercially available code, STEALTH, developed for modeling dynamic nonlinear thermomechanical processes, was modified to include fluid flow behavior and the coupling constitutive model. The fully explicit approach in the coupled calculation facilitated the inclusion of the coupling mechanisms and complex constitutive behavior. Analytical solutions pertaining to consolidation theory for soils, thermoelasticity for solids, and hydrothermal convection theory provided verification of stress and fluid flow, stress and conductive heat transfer, and heat transfer and fluid flow couplings, respectively, in the coupled model. A limited validation of the adequacy of the coupling constitutive assumptions was also performed by comparison with the physical response from two laboratory tests. Finally, the full potential of the coupled model is illustrated for geotechnical applications in energy-resource related areas. Examples in the areas of nuclear waste isolation and cut-and-fill mining are cited

A constitutive model of soft tissue: From nanoscale collagen to tissue continuum

KAUST Repository

Tang, Huang; Buehler, Markus J.; Moran, Brian

2009-01-01

dependence of the continuum response as a function of nanoscopic structural features, providing evidence for the notion that the molecular basis for protein materials is important in defining their larger-scale mechanical properties. © 2009 Biomedical

On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2014-01-01

The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...... or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered......). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications...

Haro 11: Where is the Lyman Continuum Source?

Energy Technology Data Exchange (ETDEWEB)

Keenan, Ryan P.; Oey, M. S. [Department of Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109 (United States); Jaskot, Anne E. [Department of Astronomy, Smith College, Northampton, MA 01063 (United States); James, Bethan L. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)

2017-10-10

Identifying the mechanism by which high-energy Lyman continuum (LyC) photons escaped from early galaxies is one of the most pressing questions in cosmic evolution. Haro 11 is the best known local LyC-leaking galaxy, providing an important opportunity to test our understanding of LyC escape. The observed LyC emission in this galaxy presumably originates from one of the three bright, photoionizing knots known as A, B, and C. It is known that Knot C has strong Ly α emission, and Knot B hosts an unusually bright ultraluminous X-ray source, which may be a low-luminosity active galactic nucleus. To clarify the LyC source, we carry out ionization-parameter mapping (IPM) by obtaining narrow-band imaging from the Hubble Space Telescope WFC3 and ACS cameras to construct spatially resolved ratio maps of [O iii]/[O ii] emission from the galaxy. IPM traces the ionization structure of the interstellar medium and allows us to identify optically thin regions. To optimize the continuum subtraction, we introduce a new method for determining the best continuum scale factor derived from the mode of the continuum-subtracted, image flux distribution. We find no conclusive evidence of LyC escape from Knots B or C, but instead we identify a high-ionization region extending over at least 1 kpc from Knot A. This knot shows evidence of an extremely young age (≲1 Myr), perhaps containing very massive stars (>100 M {sub ⊙}). It is weak in Ly α , so if it is confirmed as the LyC source, our results imply that LyC emission may be independent of Ly α emission.

On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere

Directory of Open Access Journals (Sweden)

I. P. Chunchuzov

2009-11-01

Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.

Sierra/Solid Mechanics 4.48 User's Guide.

Energy Technology Data Exchange (ETDEWEB)

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose; Le, San; Littlewood, David John; Mosby, Matthew David; Pierson, Kendall H.; Porter, Vicki L.; Shelton, Timothy; Thomas, Jesse David; Tupek, Michael R.; Veilleux, Michael; Gampert, Scott; Xavier, Patrick G.; Plews, Julia A.

2018-03-01

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

The KdV—Burgers equation in a modified speed gradient continuum model

International Nuclear Information System (INIS)

Lai Ling-Ling; Ge Hong-Xia; Cheng Rong-Jun; Li Zhi-Peng

2013-01-01

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micro-macro linkage (Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull. 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405). In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries—Burgers (KdV—Burgers) equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis

On Finsler Geometry and Applications in Mechanics: Review and New Perspectives

Directory of Open Access Journals (Sweden)

J. D. Clayton

2015-01-01

direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.

Continuum emission in the 1980 July 1 solar flare

International Nuclear Information System (INIS)

Zirin, H.; Neidig, D.F.

1981-01-01

Comparison of continuum measurements of the 1980 July 1 flare at Big Bear Solar Observatory and Sacramento Peak Observatory show strong blue emission kernels with the ratio of Balmer continuum (Bac):lambda3862 continuum:continuum above 4275 A to be about 10:5:1. The blue continuum at 3862 A is too strong to be explained by unresolved lines. The Bac intensity was 2.5 times the photosphere and the strongest lambda3862 continuum was 2 times the photosphere. The brightest continuum kernel occurred late in the flare, after the hard X-ray peak and related in time to an isolated peak in the 2.2 MeV line, suggesting that the continuum was excited by protons above 20 MeV

Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

Science.gov (United States)

Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

2018-01-01

We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

Computational aspects of nonlinear fracture mechanics

International Nuclear Information System (INIS)

Brocks, W.; Cornec, A.; Scheider, I.

2003-01-01

The following contribution will essentially restrict to the application of the von Mises theory of incremental plasticity to cracked specimens and components. In particular, the classical parameters of EPFM, J and CTOD, as well as subsequently proposed parameters such as energy dissipation rate and crack-tip opening angle (CTOA) and the related computational aspects will be discussed. Some remarks follow on the 'local approach to fracture' which is based on continuum field quantities, namely stresses and strains, and the damage models of Gurson (1977) and Rousselier (1987), which have now found increasing application, will be briefly addressed in Section 3.03.4. The numerical modeling of decohesion and separation phenomena by 'cohesive elements' will be presented in Section 3.03.5. (orig.)

Integrability and soliton in a classical one dimensional site dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

International Nuclear Information System (INIS)

Kavitha, L.; Daniel, M.

2002-07-01

The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)

The continuum of behavior guidance.

Science.gov (United States)

Nelson, Travis

2013-01-01

Behavior guidance is a continuum of techniques, basic and advanced, fundamental to the provision of quality dental care for pediatric patients. This practice must be individualized, pairing the correct method of behavior guidance with each child. To select the appropriate technique, the clinician must have a thorough understanding of each aspect of the continuum and anticipate parental expectations, child temperament, and the technical procedures necessary to complete care. By effectively using techniques within the continuum of behavior guidance, a healing relationship with the family is maintained while addressing dental disease and empowering the child to receive dental treatment throughout their lifetime. Copyright © 2013 Elsevier Inc. All rights reserved.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2015-07-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.

Performance-based shape optimization of continuum structures

International Nuclear Information System (INIS)

Liang Qingquan

2010-01-01

This paper presents a performance-based optimization (PBO) method for optimal shape design of continuum structures with stiffness constraints. Performance-based design concepts are incorporated in the shape optimization theory to achieve optimal designs. In the PBO method, the traditional shape optimization problem of minimizing the weight of a continuum structure with displacement or mean compliance constraints is transformed to the problem of maximizing the performance of the structure. The optimal shape of a continuum structure is obtained by gradually eliminating inefficient finite elements from the structure until its performance is maximized. Performance indices are employed to monitor the performance of optimized shapes in an optimization process. Performance-based optimality criteria are incorporated in the PBO method to identify the optimum from the optimization process. The PBO method is used to produce optimal shapes of plane stress continuum structures and plates in bending. Benchmark numerical results are provided to demonstrate the effectiveness of the PBO method for generating the maximum stiffness shape design of continuum structures. It is shown that the PBO method developed overcomes the limitations of traditional shape optimization methods in optimal design of continuum structures. Performance-based optimality criteria presented can be incorporated in any shape and topology optimization methods to obtain optimal designs of continuum structures.

Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

Science.gov (United States)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.

Chemo-mechanical coupling behaviour of leached concrete

International Nuclear Information System (INIS)

Nguyen, V.H.; Nedjar, B.; Torrenti, J.M.

2007-01-01

The paper is concerned with a coupled chemo-mechanical model describing the interaction between the calcium leaching and the mechanical damage in concrete materials. On the one hand, the phenomenological chemistry is described by the nowadays well-known simplified calcium leaching approach. It is based on the dissolution-diffusion process together with the chemical equilibrium relating the calcium concentration of the solid's skeleton and the calcium in the pore solution. For concrete, a homogenization approach using asymptotic expansions is used to take into account the influence of the presence of the aggregates leading to an equivalent homogeneous medium. On the other hand, the continuum damage mechanics is used to describe the mechanical degradation of concrete. The modelling accounts for the fact that concrete becomes more and more ductile as the leaching process grows. The model also predicts the inelastic irreversible deformation as damage evolves. The growth of inelastic strains observed during the mechanical tests is described by means of an elastoplastic-like model. The coupled nonlinear problem at hand is addressed within the context of the finite element method. And finally, numerical simulations are compared with the experimental results of first part of this work

Nonlinear magnetoacoustic wave propagation with chemical reactions

Science.gov (United States)

Margulies, Timothy Scott

2002-11-01

The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.

Properties of warm nuclei in the quasi-continuum

Directory of Open Access Journals (Sweden)

Voinov A.

2010-03-01

Full Text Available Nuclear thermodynamic quantities are extracted from nuclear level densities measured with the CACTUS detector array at the Oslo Cyclotron Laboratory. The experiments are performed with light-particle inelastic or transfer reactions. A simple combinatorial model is used to describe the underlying mechanisms responsible for the exponential increasing level density as function of excitation energy. The calculated number of broken Cooper pairs and the parity distribution in continuum are discussed.

Area Regge calculus and continuum limit

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2002-01-01

Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area variables or, as we suggest, with area tensor-connection variables. Just for the latter, in particular, we prove that in analogy with corresponding statement in ordinary Regge calculus (by Feinberg, Friedberg, Lee and Ren), passing to the (appropriately defined) continuum limit yields the generalised continuum area tensor-connection general relativity

Nonlinearity and nonclassicality in a nanomechanical resonator

Energy Technology Data Exchange (ETDEWEB)

Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)

2015-12-15

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)

LDRD report nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Segalman, D.; Heinstein, M.

1997-09-01

The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

On nonlinear equations associated with Lie algebras of diffeomorphism groups of two-dimensional manifolds

International Nuclear Information System (INIS)

Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.

1990-01-01

Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs

Some aspects of continuum physics used in fuel pin modeling

International Nuclear Information System (INIS)

Bard, F.E.

1975-06-01

The mathematical formulation used in fuel pin modeling is described. Fuel pin modeling is not a simple extension of the experimental and interpretative methods used in classical mechanics. New concepts are needed to describe materials in a reactor environment. Some aspects of continuum physics used to develop these new constitutive equations for fuel pins are presented. (U.S.)

Block backstepping design of nonlinear state feedback control law for underactuated mechanical systems

CERN Document Server

Rudra, Shubhobrata; Maitra, Madhubanti

2017-01-01

This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...

Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

International Nuclear Information System (INIS)

Czachor, M.

1996-01-01

Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models.

Science.gov (United States)

Valentin, J; Sprenger, M; Pflüger, D; Röhrle, O

2018-05-01

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles. Copyright © 2018 John Wiley & Sons, Ltd.

Continuum of eLearning: 2012 Project Summary Report

Science.gov (United States)

2012-10-01

multimedia, and Continuum of eLearning | Purpose and Vision 19 << UNCLASSIFIED>> (limited) situated learning. Future versions of the CoL self-paced...Continuum of eLearning : 2012 Project Summary Report Continuum of eLearning The Next Evolution of Joint Training on JKO October 2012 Joint...Technical Report November 2011 – August 2012 Continuum of eLearning : 2012 Project Summary Report N00140-06-D-0060 David T. Fautua, Sae Schatz, Andrea

Continuum spectra in light-ion reactions

Energy Technology Data Exchange (ETDEWEB)

Tamura, T.; Udagawa, T. [Texas Univ., Austin (USA). Dept. of Physics; Ikegami, H.; Muraoka, M [eds.

1980-01-01

Recent developments in the use of multi-step direct reaction method, to fit continuum cross sections of light-ion reactions, are reviewed. There has been a long-standing difficulty in reproducing sufficiently large (p, p') continuum cross section, but it has now been all but removed. It will be discussed in some detail, how this was achieved. Analyses of very recent data on analyzing powers in the continuum of (p, p') and (p, ..cap alpha..) reactions will also be discussed. Finally, analysis of the breakup of h into d and p will be presented.

Dispersion of the resonant second order nonlinearity in 2D semiconductors probed by femtosecond continuum pulses

Directory of Open Access Journals (Sweden)

Mohammad Mokim

2017-10-01

Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

2015-01-01

by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

Giant resonances in the deformed continuum

International Nuclear Information System (INIS)

Nakatsukasa, T.; Yabana, K.

2004-01-01

Giant resonances in the continuum for deformed nuclei are studied with the time-dependent Hartree-Fock (TDHF) theory in real time and real space. The continuum effect is effectively taken into account by introducing a complex Absorbing Boundary Condition (ABC). (orig.)

Advances in classical and analytical mechanics: A reviews of author’s results

Directory of Open Access Journals (Sweden)

Hedrih-Stevanović Katica R.

2013-01-01

Full Text Available A review, in subjective choice, of author’s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author’s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelić and Rašković, as well as author’s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author’s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates. [Projekat Ministarstva nauke Republike Srbije, br. ON174001: Dynamics of hybrid systems with complex structures

The shadow continuum : testing the records continuum model through the Djogdja Documenten and the migrated archives

NARCIS (Netherlands)

Karabinos, Michael Joseph

2015-01-01

This dissertation tests the universal suitability of the records continuum model by using two cases from the decolonization of Southeast Asia. The continuum model is a new model of records visualization invented in the 1990s that sees records as free to move throughout four ‘dimensions’ rather than

Sierra/solid mechanics 4.22 user's guide.

Energy Technology Data Exchange (ETDEWEB)

Thomas, Jesse David

2011-10-01

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for the analysis of solids and structures. It provides capabilities for explicit dynamic and implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and an extensive library of material models. The code is written for parallel computing environments, and it allows for scalable solutions of very large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which allows for coupling with other SIERRA mechanics codes. This document describes the functionality and input structure for Sierra/SM.

Forced vibration of nonlinear system with symmetrical piecewise-linear characteristics

International Nuclear Information System (INIS)

Watanabe, Takeshi

1983-01-01

It is fairly difficult to treat exactly the analysis of a vibrating system including some play because it is accompanied by a strong nonlinear phenomenon of collision. The author attempted the theoretical analysis by the exact solution using series solution and the approximate solution, treating the forced vibration of a system having some play as the forced vibration of a continuous system with nonlinear boundary condition or the colliding vibration of a continuum. In this report, the problem of such system with play is treated as a nonlinear system having the symmetrical, piecewise linear characteristics of one degree of freedom. That is, it is considered that at the time of collision due to play, the collided body causes the deformation accompanied by triangular hystersis elastically and plastically, and the spring characteristics of restitution force change piecewise by the collision. The exact solution using series solution and the approximate solution are performed, and the effectiveness of these theoretical solutions is confirmed by comparing with the solution using an analog computer. The relation between the accuracy of two analysis methods and nonlinear parameters is shown by the examples of numerical calculation. (Kako, I.)

A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale

KAUST Repository

Sendova, T.

2010-02-15

In this paper we focus on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. It is shown that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition given by the jump momentum balance leads to a sharp crack opening profile at the crack tip but predicts logarithmically singular crack tip stress. However, a modified model, where the surface excess property is responsive to the curvature of the fracture surfaces, yields bounded stresses and a cusp-like opening profile at the crack tip. Further, two possible fracture criteria in the context of the new theory are discussed. The first is an energy-based crack growth condition, while the second employs the finite crack tip stress the model predicts. The classical notion of energy release rate is based upon the singular solution, whereas for the modeling approach adopted here, a notion analogous to the energy release rate arises through a different mechanism associated with the rate of working of the surface excess properties at the crack tip. © The Author(s), 2010.

Continuum capture in the three-body problem

International Nuclear Information System (INIS)

Sellin, I.A.

1980-01-01

The three-body problem, especially the problem of electron capture to the continuum in heavy particle collisions is reviewed. Major topics covered include: second born-induced asymmetry in electron capture to the continuum; historical context, links to other tests of atomic scattering theory; experiments characterizing the velocity distribution of ECC electrons; other atomic physics tests of high velocity Born expansions; atom capture; capture by positrons; and pion capture to the continuum

Nonlinear Dynamic Analysis of Telescopic Mechanism for Truss Structure Bridge Inspection Vehicle Under Pedestrian Excitation

Directory of Open Access Journals (Sweden)

Wenwen Sui

Full Text Available Abstract Nonlinear dynamic analysis of an axially moving telescopic mechanism for truss structure bridge inspection vehicle under pedestrian excitation is carried out. A biomechanically inspired inverted-pendulum model is utilized to simplify the pedestrian. The nonlinear equations of motion for the beam-pedestrian system are derived using the Hamilton's principle. The equations are transformed into two ordinary differential equations by applying the Galerkin's method at the first two orders. The solutions to the equations are acquired by using the Newmark-β method associated with the Newton-Raphson method. The time-dependent feature of the eigenfunctions for the two beams are taken into consideration in the solutions. Accordingly, the equations of motion for a simplified system, in which the pedestrian is regarded as moving cart, are given. In the numerical examples, dynamic responses of the telescopic mechanism in eight conditions of different beam-telescoping and pedestrian-moving directions are simulated. Comparisons between the vibrations of the beams under pedestrian excitation and corresponding moving cart are carried out to investigate the influence of the pedestrian excitation on the telescopic mechanism. The results show that the displacement of the telescopic mechanism under pedestrian excitation is smaller than that under moving cart especially when the pedestrian approaches the beams end. Additionally, compared with moving cart, the pedestrian excitation can effectively strengthen the vibration when the beam extension is small or when the pedestrian is close to the beams end.

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Science.gov (United States)

Sozio, Fabio; Yavari, Arash

2017-01-01

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

Benchmarking Continuum Solvent Models for Keto-Enol Tautomerizations.

Science.gov (United States)

McCann, Billy W; McFarland, Stuart; Acevedo, Orlando

2015-08-13

Experimental free energies of tautomerization, ΔGT, were used to benchmark the gas-phase predictions of 17 different quantum mechanical methods and eight basis sets for seven keto-enol tautomer pairs dominated by their enolic form. The G4 method and M06/6-31+G(d,p) yielded the most accurate results, with mean absolute errors (MAE's) of 0.95 and 0.71 kcal/mol, respectively. Using these two theory levels, the solution-phase ΔGT values for 23 unique tautomer pairs composed of aliphatic ketones, β-dicarbonyls, and heterocycles were computed in multiple protic and aprotic solvents. The continuum solvation models, namely, polarizable continuum model (PCM), polarizable conductor calculation model (CPCM), and universal solvation model (SMD), gave relatively similar MAE's of ∼1.6-1.7 kcal/mol for G4 and ∼1.9-2.0 kcal/mol with M06/6-31+G(d,p). Partitioning the tautomer pairs into their respective molecular types, that is, aliphatic ketones, β-dicarbonyls, and heterocycles, and separating out the aqueous versus nonaqueous results finds G4/PCM utilizing the UA0 cavity to be the overall most accurate combination. Free energies of activation, ΔG(‡), for the base-catalyzed keto-enol interconversion of 2-nitrocyclohexanone were also computed using six bases and five solvents. The M06/6-31+G(d,p) reproduced the ΔG(‡) with MAE's of 1.5 and 1.8 kcal/mol using CPCM and SMD, respectively, for all combinations of base and solvent. That specific enolization was previously proposed to proceed via a concerted mechanism in less polar solvents but shift to a stepwise mechanism in more polar solvents. However, the current calculations suggest that the stepwise mechanism operates in all solvents.

Contributions of non-intrusive coupling in nonlinear structural mechanics

International Nuclear Information System (INIS)

Duval, Mickael

2016-01-01

This PhD thesis, part of the ANR ICARE project, aims at developing methods for complex analysis of large scale structures. The scientific challenge is to investigate very localised areas, but potentially critical as of mechanical systems resilience. Classically, representation models, discretizations, mechanical behaviour models and numerical tools are used at both global and local scales for simulation needs of graduated complexity. Global problem is handled by a generic code with topology (plate formulation, geometric approximation...) and behaviour (homogenization) simplifications while local analysis needs implementation of specialized tools (routines, dedicated codes) for an accurate representation of the geometry and behaviour. The main goal of this thesis is to develop an efficient non-intrusive coupling tool for multi-scale and multi-model structural analysis. Constraints of non-intrusiveness result in the non-modification of the stiffness operator, connectivity and the global model solver, allowing to work in a closed source software environment. First, we provide a detailed study of global/local non-intrusive coupling algorithm. Making use of several relevant examples (cracking, elastic-plastic behaviour, contact...), we show the efficiency and the flexibility of such coupling method. A comparative analysis of several optimisation tools is also carried on, and the interacting multiple patches situation is handled. Then, non-intrusive coupling is extended to globally non-linear cases, and a domain decomposition method with non-linear re-localization is proposed. Such methods allowed us to run a parallel computation using only sequential software, on a high performance computing cluster. Finally, we apply the coupling algorithm to mesh refinement with patches of finite elements. We develop an explicit residual based error estimator suitable for multi-scale solutions arising from the non-intrusive coupling, and apply it inside an error driven local mesh

Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure

Science.gov (United States)

Vorotnikov, K.; Starosvetsky, Y.

2018-01-01

The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

Science.gov (United States)

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Points-Based Safe Path Planning of Continuum Robots

Directory of Open Access Journals (Sweden)

Khuram Shahzad

2015-07-01

Full Text Available Continuum robots exhibit great potential in a number of challenging applications where traditional rigid link robots pose certain limitations, e.g., working in unstructured environments. In order to enable the usage of continuum robots in safety-critical applications, such as surgery and nuclear decontamination, it is extremely important to ensure a safe path for the robot's movement. Existing algorithms for continuum robot path planning have certain limitations that need to be addressed. These include the fact that none of the algorithms provide safety assurance parameters and control for path planning. They are computationally expensive, applicable to a specific type of continuum robots, and mostly they do not incorporate design and kinematics constraints. In this paper, we propose a points-based path planning (PoPP algorithm for continuum robots that computes the path by imposing safety constraints and improves upon the limitations of existing approaches. In the algorithm, we exploit the constant curvature-bending property of continuum robots in their path planning process. The algorithm is computationally efficient and provides a good tradeoff between accuracy and efficiency that can be implemented to enable the safety-critical application of continuum robots. This algorithm also provides information regarding path volume and flexibility in movement. Simulation results confirm that the algorithm possesses promising potential for all types of continuum robots (following the constant curvature-bending property. We believe that this effectively balances the desired safety and efficiency requirements.

Fluctuating nonlinear hydrodynamics of flocking

Science.gov (United States)

Yadav, Sunil Kumar; Das, Shankar P.

2018-03-01

Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.

A 3D steady-state model of a tendon-driven continuum soft manipulator inspired by the octopus arm

International Nuclear Information System (INIS)

Renda, F; Cianchetti, M; Giorelli, M; Arienti, A; Laschi, C

2012-01-01

Control and modelling of continuum robots are challenging tasks for robotic researchers. Most works on modelling are limited to piecewise constant curvature. In many cases they neglect to model the actuators or avoid a continuum approach. In particular, in the latter case this leads to a complex model hardly implemented. In this work, a geometrically exact steady-state model of a tendon-driven manipulator inspired by the octopus arm is presented. It takes a continuum approach, fast enough to be implemented in the control law, and includes a model of the actuation system. The model was experimentally validated and the results are reported. In conclusion, the model presented can be used as a tool for mechanical design of continuum tendon-driven manipulators, for planning control strategies or as internal model in an embedded system. (paper)

Beyond the continuum: how molecular solvent structure affects electrostatics and hydrodynamics at solid-electrolyte interfaces.

Science.gov (United States)

Bonthuis, Douwe Jan; Netz, Roland R

2013-10-03

Standard continuum theory fails to predict several key experimental results of electrostatic and electrokinetic measurements at aqueous electrolyte interfaces. In order to extend the continuum theory to include the effects of molecular solvent structure, we generalize the equations for electrokinetic transport to incorporate a space dependent dielectric profile, viscosity profile, and non-electrostatic interaction potential. All necessary profiles are extracted from atomistic molecular dynamics (MD) simulations. We show that the MD results for the ion-specific distribution of counterions at charged hydrophilic and hydrophobic interfaces are accurately reproduced using the dielectric profile of pure water and a non-electrostatic repulsion in an extended Poisson-Boltzmann equation. The distributions of Na(+) at both surface types and Cl(-) at hydrophilic surfaces can be modeled using linear dielectric response theory, whereas for Cl(-) at hydrophobic surfaces it is necessary to apply nonlinear response theory. The extended Poisson-Boltzmann equation reproduces the experimental values of the double-layer capacitance for many different carbon-based surfaces. In conjunction with a generalized hydrodynamic theory that accounts for a space dependent viscosity, the model captures the experimentally observed saturation of the electrokinetic mobility as a function of the bare surface charge density and the so-called anomalous double-layer conductivity. The two-scale approach employed here-MD simulations and continuum theory-constitutes a successful modeling scheme, providing basic insight into the molecular origins of the static and kinetic properties of charged surfaces, and allowing quantitative modeling at low computational cost.

Analysis of Blood Flow Through a Viscoelastic Artery using the Cosserat Continuum with the Large-Amplitude Oscillatory Shear Deformation Model

DEFF Research Database (Denmark)

Sedaghatizadeh, N.; Atefi, G.; Fardad, A. A.

2011-01-01

In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite differenc...... method was used to solve the governing equations, and the particle swarm optimization algorithm was utilized to identify the non-Newtonian coefficients (kυ and γυ). The numerical results agreed well with previous experimental results....

Fluctuating Finite Element Analysis (FFEA: A continuum mechanics software tool for mesoscale simulation of biomolecules.

Directory of Open Access Journals (Sweden)

Albert Solernou

2018-03-01

Full Text Available Fluctuating Finite Element Analysis (FFEA is a software package designed to perform continuum mechanics simulations of proteins and other globular macromolecules. It combines conventional finite element methods with stochastic thermal noise, and is appropriate for simulations of large proteins and protein complexes at the mesoscale (length-scales in the range of 5 nm to 1 μm, where there is currently a paucity of modelling tools. It requires 3D volumetric information as input, which can be low resolution structural information such as cryo-electron tomography (cryo-ET maps or much higher resolution atomistic co-ordinates from which volumetric information can be extracted. In this article we introduce our open source software package for performing FFEA simulations which we have released under a GPLv3 license. The software package includes a C ++ implementation of FFEA, together with tools to assist the user to set up the system from Electron Microscopy Data Bank (EMDB or Protein Data Bank (PDB data files. We also provide a PyMOL plugin to perform basic visualisation and additional Python tools for the analysis of FFEA simulation trajectories. This manuscript provides a basic background to the FFEA method, describing the implementation of the core mechanical model and how intermolecular interactions and the solvent environment are included within this framework. We provide prospective FFEA users with a practical overview of how to set up an FFEA simulation with reference to our publicly available online tutorials and manuals that accompany this first release of the package.

Fluctuating Finite Element Analysis (FFEA): A continuum mechanics software tool for mesoscale simulation of biomolecules.

Science.gov (United States)

Solernou, Albert; Hanson, Benjamin S; Richardson, Robin A; Welch, Robert; Read, Daniel J; Harlen, Oliver G; Harris, Sarah A

2018-03-01

Fluctuating Finite Element Analysis (FFEA) is a software package designed to perform continuum mechanics simulations of proteins and other globular macromolecules. It combines conventional finite element methods with stochastic thermal noise, and is appropriate for simulations of large proteins and protein complexes at the mesoscale (length-scales in the range of 5 nm to 1 μm), where there is currently a paucity of modelling tools. It requires 3D volumetric information as input, which can be low resolution structural information such as cryo-electron tomography (cryo-ET) maps or much higher resolution atomistic co-ordinates from which volumetric information can be extracted. In this article we introduce our open source software package for performing FFEA simulations which we have released under a GPLv3 license. The software package includes a C ++ implementation of FFEA, together with tools to assist the user to set up the system from Electron Microscopy Data Bank (EMDB) or Protein Data Bank (PDB) data files. We also provide a PyMOL plugin to perform basic visualisation and additional Python tools for the analysis of FFEA simulation trajectories. This manuscript provides a basic background to the FFEA method, describing the implementation of the core mechanical model and how intermolecular interactions and the solvent environment are included within this framework. We provide prospective FFEA users with a practical overview of how to set up an FFEA simulation with reference to our publicly available online tutorials and manuals that accompany this first release of the package.

Continuum-Kinetic Models and Numerical Methods for Multiphase Applications

Science.gov (United States)

Nault, Isaac Michael

This thesis presents a continuum-kinetic approach for modeling general problems in multiphase solid mechanics. In this context, a continuum model refers to any model, typically on the macro-scale, in which continuous state variables are used to capture the most important physics: conservation of mass, momentum, and energy. A kinetic model refers to any model, typically on the meso-scale, which captures the statistical motion and evolution of microscopic entitites. Multiphase phenomena usually involve non-negligible micro or meso-scopic effects at the interfaces between phases. The approach developed in the thesis attempts to combine the computational performance benefits of a continuum model with the physical accuracy of a kinetic model when applied to a multiphase problem. The approach is applied to modeling a single particle impact in Cold Spray, an engineering process that intimately involves the interaction of crystal grains with high-magnitude elastic waves. Such a situation could be classified a multiphase application due to the discrete nature of grains on the spatial scale of the problem. For this application, a hyper elasto-plastic model is solved by a finite volume method with approximate Riemann solver. The results of this model are compared for two types of plastic closure: a phenomenological macro-scale constitutive law, and a physics-based meso-scale Crystal Plasticity model.

Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

CERN Document Server

Gurbatov, S N; Saichev, A I

2012-01-01

"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

Atomistic simulation and continuum modeling of graphene nanoribbons under uniaxial tension

International Nuclear Information System (INIS)

Lu, Qiang; Gao, Wei; Huang, Rui

2011-01-01

Atomistic simulations are performed to study the nonlinear mechanical behavior of graphene nanoribbons under quasistatic uniaxial tension, emphasizing the effects of edge structures (armchair and zigzag, without and with hydrogen passivation) on elastic modulus and fracture strength. The numerical results are analyzed within a theoretical model of thermodynamics, which enables determination of the bulk strain energy density, the edge energy density and the hydrogen adsorption energy density as nonlinear functions of the applied strain based on static molecular mechanics simulations. These functions can be used to describe mechanical behavior of graphene nanoribbons from the initial linear elasticity to fracture. It is found that the initial Young's modulus of a graphene nanoribbon depends on the ribbon width and the edge chirality. Furthermore, it is found that the nominal strain to fracture is considerably lower for graphene nanoribbons with armchair edges than for ribbons with zigzag edges. Molecular dynamics simulations reveal two distinct fracture nucleation mechanisms: homogeneous nucleation for the zigzag-edged graphene nanoribbons and edge-controlled heterogeneous nucleation for the armchair-edged ribbons. The modeling and simulations in this study highlight the atomistic mechanisms for the nonlinear mechanical behavior of graphene nanoribbons with the edge effects, which is potentially important for developing integrated graphene-based devices

Nonlinear-optical generation of short-wavelength radiation controlled by laser-induced interference structures

International Nuclear Information System (INIS)

Popov, A K; Kimberg, V V

1998-01-01

A study is reported of the combined influence of laser-induced resonances in the energy continuum, of splitting of discrete resonances in the field of several strong radiations, and of absorption of the initial and generated radiations on totally resonant parametric conversion to the short-wavelength range. It is shown that the radiation power can be increased considerably by interference processes involving quantum transitions. (nonlinear optical phenomena and devices)

Non-linear calculation of PCRV using dynamic relaxation

International Nuclear Information System (INIS)

Schnellenbach, G.

1979-01-01

A brief review is presented of a numerical method called the dynamic relaxation method for stress analysis of the concrete in prestressed concrete pressure vessels. By this method the three-dimensional elliptic differential equations of the continuum are changed into the four-dimensional hyperbolic differential equations known as wave equations. The boundary value problem of the static system is changed into an initial and boundary value problem for which a solution exists if the physical system is defined at time t=0. The effect of non-linear stress-strain behaviour of the material as well as creep and cracking are considered

Nonlinear Hamiltonian mechanics applied to molecular dynamics theory and computational methods for understanding molecular spectroscopy and chemical reactions

CERN Document Server

Farantos, Stavros C

2014-01-01

This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.

Nonlinear Distortion Mechanisms and Efficiency of Balanced-Armature Loudspeakers

DEFF Research Database (Denmark)

Jensen, Joe

are inherently nonlinear devices, since any displacement of the loudspeaker diaphragm in- evitably changes the magnetic and electrical characteristics of the loudspeaker. Additionally, for the balanced-armature loudspeaker the signal has to be transmitted through the magnetic domain (as a magnetic B -field...... and to validate simpler equivalent circuit models. A large scale model of a balanced-armature loudspeaker has been developed and its inherent nonlinear parameters have been measured and compared to the theoretically predicted values. A measurement setup for determining the magnetic properties of soft magnetic...... materials has also been developed, since it is of great importance to understand what kind of linear and nonlinear transformations the magnetic materials impose on the signal. In hearing aid applications the power efficiency of the loudspeaker is important because every reduction in power consumption...

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining

Modeling nonlinear problems in the mechanics of strings and rods the role of the balance laws

CERN Document Server

O'Reilly, Oliver M

2017-01-01

This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant ...

Field guide to nonlinear optics

CERN Document Server

Powers, Peter E

2013-01-01

Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics

Stability of orbits in nonlinear mechanics for finite but very long times

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.

1990-07-01

In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab

Stability of orbits in nonlinear mechanics for finite but very long times

Energy Technology Data Exchange (ETDEWEB)

Warnock, R.L.; Ruth, R.D.

1990-07-01

In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.

Patients' experiences with continuum of care across hospitals. A multilevel analysis of Consumer Quality Index Continuum of Care

NARCIS (Netherlands)

Kollen, Boudewijn J.; Groenier, Klaas H.; Berendsen, Annette J.

Objective: Communication between professionals is essential because it contributes to an optimal continuum of care. Whether patients experience adequate continuum of care is uncertain. To address this, a questionnaire was developed to elucidate this care process from a patients' perspective. In this

Nonlinearity management in higher dimensions

International Nuclear Information System (INIS)

Kevrekidis, P G; Pelinovsky, D E; Stefanov, A

2006-01-01

In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management

Nonlinear elastic waves in materials

CERN Document Server

Rushchitsky, Jeremiah J

2014-01-01

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

Alfven continuum with toroidicity

International Nuclear Information System (INIS)

Riyopoulos, S.; Mahajan, S.M.

1985-06-01

The symmetry property of the MHD wave propagation operator is utilized to express the toroidal eigenmodes as a superposition of the mutually orthogonal cylindrical modes. Because of the degeneracy among cylindrical modes with the same frequency but resonant surfaces of different helicity the toroidal perturbation produces a zeroth order mixing of the above modes. The toroidal eigenmodes of frequency ω 0 2 have multiple resonant surfaces, with each surface shifted relative to its cylindrical position and carrying a multispectral content. Thus a single helicity toroidal antenna of frequency ω 0 couples strongly to all different helicity resonant surfaces with matching local Alfven frequency. Zeroth order coupling between modes in the continuum and global Alfven modes also results from toroidicity and degeneracy. Our perturbation technique is the MHD counterpart of the quantum mechanical methods and is applicable through the entire range of the MHD spectrum

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Nonlinear drift tearing mode

International Nuclear Information System (INIS)

Zelenyj, L.M.; Kuznetsova, M.M.

1989-01-01

Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

Science.gov (United States)

Momeni, F.; Naderi, M. H.

2018-05-01

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

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...

Continuum mechanics through the eighteenth and nineteenth centuries historical perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)

CERN Document Server

Maugin, Gérard A

2014-01-01

Conceived as a series of more or less autonomous essays, the present book critically exposes the initial developments of continuum thermo-mechanics in a post Newtonian period extending from the creative works of the Bernoullis to the First World war, i.e., roughly during first the “Age of reason” and next the “Birth of the modern world”. The emphasis is rightly placed on the original contributions from the “Continental” scientists (the Bernoulli family, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in competition with their British peers (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the main breakthroughs as well as the secondary ones. It highlights the role of scientists who left essential prints in this history of scientific ideas. The book shows how the formidable developments that blossomed in the twentieth century (and perused in a previous book of the author in...

Lattice gravity near the continuum limit

International Nuclear Information System (INIS)

Feinberg, G.; Friedberg, R.; Lee, T.D.; Ren, H.C.

1984-01-01

We prove that the lattice gravity always approaches the usual continuum limit when the link length l -> 0, provided that certain general boundary conditions are satisfied. This result holds for any lattice, regular or irregular. Furthermore, for a given lattice, the deviation from its continuum limit can be expressed as a power series in l 2 . General formulas for such a perturbative calculation are given, together with a number of illustrative examples, including the graviton propagator. The lattice gravity satisfies all the invariance properties of Einstein's theory of general relativity. In addition, it is symmetric under a new class of transformations that are absent in the usual continuum theory. The possibility that the lattice theory (with a nonzero l) may be more fundamental is discussed. (orig.)

An analytical study of non-linear behaviour of coupled 2+2x0.5 DOF electro-magneto-mechanical system by a method of multiple scales

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2013-01-01

An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force...

Continuum Level Density in Complex Scaling Method

International Nuclear Information System (INIS)

Suzuki, R.; Myo, T.; Kato, K.

2005-01-01

A new calculational method of continuum level density (CLD) at unbound energies is studied in the complex scaling method (CSM). It is shown that the CLD can be calculated by employing the discretization of continuum states in the CSM without any smoothing technique

Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids

Directory of Open Access Journals (Sweden)

Mustapha Lahmar

2015-04-01

Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.

Nonlinear approaches in engineering applications applied mechanics, vibration control, and numerical analysis

CERN Document Server

Jazar, Reza

2015-01-01

This book focuses on the latest applications of nonlinear approaches in different disciplines of engineering. For each selected topic, detailed concept development, derivations, and relevant knowledge are provided for the convenience of the readers. The topics range from dynamic systems and control to optimal approaches in nonlinear dynamics. The volume includes invited chapters from world class experts in the field. The selected topics are of great interest in the fields of engineering and physics and this book is ideal for engineers and researchers working in a broad range of practical topics and approaches. This book also: ·         Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity ·         Enlightens readers to the conceptual significance of nonlinear approaches with examples of applications in scientific and engineering problems from v...

Memory binding in clinical and non-clinical psychotic experiences: how does the continuum model fare?

Science.gov (United States)

Chhabra, S; Badcock, J C; Maybery, M T

2013-07-01

Both clinical and non-clinical auditory hallucinations (AH) have been associated with source memory deficits, supporting a continuum of underlying cognitive mechanisms, though few studies have employed the same task in patient and nonpatient samples. Recent commentators have called for more debate on the continuum model of psychosis. Consequently, the current study investigated the continuity model of AH with reference to memory binding. We used an identical voice and word recognition memory task to assess binding in two separate studies of: (1) healthy hallucination-prone individuals and controls (30 high and 30 low scorers on the Launay-Slade Hallucination Scale-Revised) and (2) schizophrenia patient samples (32 with AH, 32 without AH) and 32 healthy controls. There was no evidence of impaired binding in high hallucination-prone, compared to low hallucination-prone individuals. In contrast, individuals with schizophrenia (both with and without AH) had difficulties binding (remembering "who said what"), alongside difficulties remembering individual words and voices. Binding ability and memory for voices were also negatively linked to the loudness of hallucinated voices reported by patients with AH. These findings suggest that different mechanisms may exist in clinical and non-clinical hallucinators, adding to the growing debate on the continuum model of psychotic symptoms.

Physics of the continuum of borromean nuclei

Energy Technology Data Exchange (ETDEWEB)

Vaagen, J S; Rogde, T [Dept. of Physics, Univ. of Bergen (Norway); Danilin, B V [RRC The Kurchatov Inst., Kurchatov, Moscow (Russian Federation); Ershov, S N [JINR, Dubna, Moscow (Russian Federation); Thompson, I J [Dept. of Physics, Univ. of Surrey, Guildford (United Kingdom); Zhukov, M V [Chalmers Univ. of Technology and Goeteborg Univ., Goeteborg (Sweden); RNBT Collaboration

1998-06-01

The continuum states of two-neutron halo nuclei are calculated in the method of hyperspherical harmonics. Using DWIA theory appropriate for dilute halo matter we have probed the structure of the low-lying {sup 6}He continuum via calculations of charge-exchange and inelastic scattering. (orig.)

Nonlinear sigma models with compact hyperbolic target spaces

Energy Technology Data Exchange (ETDEWEB)

Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)

2016-06-23

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

Nonlinear sigma models with compact hyperbolic target spaces

International Nuclear Information System (INIS)

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James

2016-01-01

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

Morphing continuum theory for turbulence: Theory, computation, and visualization

Science.gov (United States)

Chen, James

2017-10-01

A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

Gamma-ray continuum spectra from heavy ion reactions

International Nuclear Information System (INIS)

Beene, J.R.; Halbert, M.L.; Hensley, D.C.; Sarantites, D.G.; Westerberg, L.W.; Geoffroy, K.; Woodward, R.

1979-01-01

A detailed quantitative analysis of the yrast continuum was attempted by subtracting the underlying statistical continnuum in a way that makes allowance for ignorance of its detailed shape. This procedure makes it possible to obtain the moment of inertia as a function of spin over a wide range of spins. The results of this continuum spectra shape analysis can be used to calculate the first and second moments of the continuum multiplicity distribution. Continuum spectra were taken during the bombardment of 150 Nd by 115- and 130-MeV beams of 20 Ne, also the first and second moments of the γ-ray multiplicity distribution as a function of the gamma energy. The moment of inertia versus spin and the deduced Yrast continuua are shown. 10 references

Schizophrenia and the neurodevelopmental continuum:evidence from genomics.

Science.gov (United States)

Owen, Michael J; O'Donovan, Michael C

2017-10-01

The idea that disturbances occurring early in brain development contribute to the pathogenesis of schizophrenia, often referred to as the neurodevelopmental hypothesis, has become widely accepted. Despite this, the disorder is viewed as being distinct nosologically, and by implication pathophysiologically and clinically, from syndromes such as autism spectrum disorders, attention-deficit/hyperactivity disorder (ADHD) and intellectual disability, which typically present in childhood and are grouped together as "neurodevelopmental disorders". An alternative view is that neurodevelopmental disorders, including schizophrenia, rather than being etiologically discrete entities, are better conceptualized as lying on an etiological and neurodevelopmental continuum, with the major clinical syndromes reflecting the severity, timing and predominant pattern of abnormal brain development and resulting functional abnormalities. It has also been suggested that, within the neurodevelopmental continuum, severe mental illnesses occupy a gradient of decreasing neurodevelopmental impairment as follows: intellectual disability, autism spectrum disorders, ADHD, schizophrenia and bipolar disorder. Recent genomic studies have identified large numbers of specific risk DNA changes and offer a direct and robust test of the predictions of the neurodevelopmental continuum model and gradient hypothesis. These findings are reviewed in detail. They not only support the view that schizophrenia is a disorder whose origins lie in disturbances of brain development, but also that it shares genetic risk and pathogenic mechanisms with the early onset neurodevelopmental disorders (intellectual disability, autism spectrum disorders and ADHD). They also support the idea that these disorders lie on a gradient of severity, implying that they differ to some extent quantitatively as well as qualitatively. These findings have important implications for nosology, clinical practice and research. © 2017 World

Transient behavior of interface state continuum at InP insulator-semiconductor interface

International Nuclear Information System (INIS)

Hasegawa, H.; Masuda, H.; He, L.; Luo, J.K.; Sawada, T.; Ohno, H.

1987-01-01

To clarify the drain current drift mechanism in InP MISFETs, an isothermal capacitance transient spectroscopy (ICTS) study of the interface state continuum is made on the anodic Al 2 O 3 /native oxide/ InP MIS system. Capture behavior is temperature-independent, non-exponential and extremely slow, whereas emission behavior is temperature- and bias- dependent, and is much faster. The observed behavior is explained quantitatively by the disorder induced gap state (DIGS) model, where states are distributed both in energy and in space. By comparing the transient behavior of interface states with the observed drift behavior of MISFETs, it is concluded that the electron capture by the DIGS continuum is responsible for the drain current drift of MISFETs. This led to a complete computer simulation of the observed current drift behavior

Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response

DEFF Research Database (Denmark)

Denisov, S.; Flach, S.; Ovchinnikov, A. A.

2002-01-01

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is em...... is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.......We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response...

On phase, action and canonical conservation laws in kinematic-wave theory

International Nuclear Information System (INIS)

Maugin, G.A.

2008-01-01

Canonical equations of energy and momentum are constructed in the kinematic-wave theory of waves in a continuum. This is done in analogy with what is achieved in nonlinear continuum mechanics. The starting point is a generalized balance of wave action. The standard formulas are recovered when the system follows from the averaged-Lagrangian variational formulation of Whitham

Loop quantization as a continuum limit

International Nuclear Information System (INIS)

Manrique, Elisa; Oeckl, Robert; Weber, Axel; Zapata, Jose A

2006-01-01

We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop-quantized theories is constructed as a continuum limit of the dynamics of effective theories. After presenting the general formalism we show as a first explicit example the 2D Ising field theory, an interacting relativistic quantum field theory with local degrees of freedom quantized by loop quantization techniques

Continuum emission from classical nova winds

International Nuclear Information System (INIS)

Harkness, R.P.

1983-01-01

The emergent continuum of a slow classical nova during outburst is considered in the quasi-steady optically thick, transonic wind model. Models are presented for various steady mass loss rates and are related to the evolution of slow novae during decline and early post-maximum. The continuum emission is found to depart radically from a blackbody spectrum and to exhibit features common to highly extended stellar atmospheres. (author)

Continuum solutions of the Klein-Gordon equation

International Nuclear Information System (INIS)

Jansen, G.; Pusch, M.; Soff, G.

1987-10-01

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interaction we depict solutions for the Coulomb potential of a point-like nucleus as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify pecularities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field. (orig.)

Nonlinear optical spectra having characteristics of Fano interferences in coherently coupled lowest exciton biexciton states in semiconductor quantum dots

Directory of Open Access Journals (Sweden)

Hideki Gotoh

2014-10-01

Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

Continuum robot arms inspired by cephalopods

Science.gov (United States)

Walker, Ian D.; Dawson, Darren M.; Flash, Tamar; Grasso, Frank W.; Hanlon, Roger T.; Hochner, Binyamin; Kier, William M.; Pagano, Christopher C.; Rahn, Christopher D.; Zhang, Qiming M.

2005-05-01

In this paper, we describe our recent results in the development of a new class of soft, continuous backbone ("continuum") robot manipulators. Our work is strongly motivated by the dexterous appendages found in cephalopods, particularly the arms and suckers of octopus, and the arms and tentacles of squid. Our ongoing investigation of these animals reveals interesting and unexpected functional aspects of their structure and behavior. The arrangement and dynamic operation of muscles and connective tissue observed in the arms of a variety of octopus species motivate the underlying design approach for our soft manipulators. These artificial manipulators feature biomimetic actuators, including artificial muscles based on both electro-active polymers (EAP) and pneumatic (McKibben) muscles. They feature a "clean" continuous backbone design, redundant degrees of freedom, and exhibit significant compliance that provides novel operational capacities during environmental interaction and object manipulation. The unusual compliance and redundant degrees of freedom provide strong potential for application to delicate tasks in cluttered and/or unstructured environments. Our aim is to endow these compliant robotic mechanisms with the diverse and dexterous grasping behavior observed in octopuses. To this end, we are conducting fundamental research into the manipulation tactics, sensory biology, and neural control of octopuses. This work in turn leads to novel approaches to motion planning and operator interfaces for the robots. The paper describes the above efforts, along with the results of our development of a series of continuum tentacle-like robots, demonstrating the unique abilities of biologically-inspired design.

Solvent effects on the excited-state double proton transfer mechanism in the 7-azaindole dimer: a TDDFT study with the polarizable continuum model.

Science.gov (United States)

Yu, Xue-Fang; Yamazaki, Shohei; Taketsugu, Tetsuya

2017-08-30

Solvent effects on the excited-state double proton transfer (ESDPT) mechanism in the 7-azaindole (7AI) dimer were investigated using the time-dependent density functional theory (TDDFT) method. Excited-state potential energy profiles along the reaction paths in a locally excited (LE) state and a charge transfer (CT) state were calculated using the polarizable continuum model (PCM) to include the solvent effect. A series of non-polar and polar solvents with different dielectric constants were used to examine the polarity effect on the ESDPT mechanism. The present results suggest that in a non-polar solvent and a polar solvent with a small dielectric constant, ESDPT follows a concerted mechanism, similar to the case in the gas phase. In a polar solvent with a relatively large dielectric constant, however, ESDPT is likely to follow a stepwise mechanism via a stable zwitterionic intermediate in the LE state on the adiabatic potential energy surface, although inclusion of zero-point vibrational energy (ZPE) corrections again suggests the concerted mechanism. In the meantime, the stepwise reaction path involving the CT state with neutral intermediates is also examined, and is found to be less competitive than the concerted or stepwise path in the LE state in both non-polar and polar solvents. The present study provides a new insight into the experimental controversy of the ESDPT mechanism of the 7AI dimer in a solution.

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

Science.gov (United States)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Acoustic-gravity nonlinear structures

Directory of Open Access Journals (Sweden)

D. Jovanović

2002-01-01

Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.

Considering "Nonlinearity" Across the Continuum in Medical Education Assessment: Supporting Theory, Practice, and Future Research Directions.

Science.gov (United States)

Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric

2015-01-01

The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity. © 2015 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.

A model for predicting pellet-cladding interaction induced fuel rod failure, based on nonlinear fracture mechanics

International Nuclear Information System (INIS)

Jernkvist, L.O.

1993-01-01

A model for predicting pellet-cladding mechanical interaction induced fuel rod failure, suitable for implementation in finite element fuel-performance codes, is presented. Cladding failure is predicted by explicitly modelling the propagation of radial cracks under varying load conditions. Propagation is assumed to be due to either iodine induced stress corrosion cracking or ductile fracture. Nonlinear fracture mechanics concepts are utilized in modelling these two mechanisms of crack growth. The novelty of this approach is that the development of cracks, which may ultimately lead to fuel rod failure, can be treated as a dynamic and time-dependent process. The influence of cyclic loading, ramp rates and material creep on the failure mechanism can thereby be investigated. Results of numerical calculations, in which the failure model has been used to study the dependence of cladding creep rate on crack propagation velocity, are presented. (author)

Continuum simulations of water flow past fullerene molecules

DEFF Research Database (Denmark)

Popadic, A.; Praprotnik, M.; Koumoutsakos, P.

2015-01-01

We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently by continuum flow...

Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2016-09-19

This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

Science.gov (United States)

Asadi, Reza; Ouyang, Zhengbiao

2018-03-01

A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

Nonlinearly stacked low noise turbofan stator

Science.gov (United States)

Schuster, William B. (Inventor); Nolcheff, Nick A. (Inventor); Gunaraj, John A. (Inventor); Kontos, Karen B. (Inventor); Weir, Donald S. (Inventor)

2009-01-01

A nonlinearly stacked low noise turbofan stator vane having a characteristic curve that is characterized by a nonlinear sweep and a nonlinear lean is provided. The stator is in an axial fan or compressor turbomachinery stage that is comprised of a collection of vanes whose highly three-dimensional shape is selected to reduce rotor-stator and rotor-strut interaction noise while maintaining the aerodynamic and mechanical performance of the vane. The nonlinearly stacked low noise turbofan stator vane reduces noise associated with the fan stage of turbomachinery to improve environmental compatibility.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

Effect of fiber distribution and realignment on the nonlinear and inhomogeneous mechanical properties of human supraspinatus tendon under longitudinal tensile loading.

Science.gov (United States)

Lake, Spencer P; Miller, Kristin S; Elliott, Dawn M; Soslowsky, Louis J

2009-12-01

Tendon exhibits nonlinear stress-strain behavior that may be partly due to movement of collagen fibers through the extracellular matrix. While a few techniques have been developed to evaluate the fiber architecture of other soft tissues, the organizational behavior of tendon under load has not been determined. The supraspinatus tendon (SST) of the rotator cuff is of particular interest for investigation due to its complex mechanical environment and corresponding inhomogeneity. In addition, SST injury occurs frequently with limited success in treatment strategies, illustrating the need for a better understanding of SST properties. Therefore, the objective of this study was to quantitatively evaluate the inhomogeneous tensile mechanical properties, fiber organization, and fiber realignment under load of human SST utilizing a novel polarized light technique. Fiber distributions were found to become more aligned under load, particularly during the low stiffness toe-region, suggesting that fiber realignment may be partly responsible for observed nonlinear behavior. Fiber alignment was found to correlate significantly with mechanical parameters, providing evidence for strong structure-function relationships in tendon. Human SST exhibits complex, inhomogeneous mechanical properties and fiber distributions, perhaps due to its complex loading environment. Surprisingly, histological grade of degeneration did not correlate with mechanical properties.

Continuum Thermodynamics - Part II: Applications and Examples

Science.gov (United States)

Albers, Bettina; Wilmanski, Krzysztof

The intention by writing Part II of the book on continuum thermodynamics was the deepening of some issues covered in Part I as well as a development of certain skills in dealing with practical problems of oscopic processes. However, the main motivation for this part is the presentation of main facets of thermodynamics which appear when interdisciplinary problems are considered. There are many monographs on the subjects of solid mechanics and thermomechanics, on fluid mechanics and on coupled fields but most of them cover only special problems in great details which are characteristic for the chosen field. It is rather seldom that relations between these fields are discussed. This concerns, for instance, large deformations of the skeleton of porous materials with diffusion (e.g. lungs), couplings of deformable particles with the fluid motion in suspensions, couplings of adsorption processes and chemical reactions in immiscible mixtures with diffusion, various multi-component aspects of the motion, e.g. of avalanches, such as segregation processes, etc...

Map of fluid flow in fractal porous medium into fractal continuum flow.

Science.gov (United States)

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2012-05-01

This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea.

Science.gov (United States)

Meaud, Julien; Grosh, Karl

2012-03-21

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Directory of Open Access Journals (Sweden)

S. L. Han

2012-01-01

Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

Influence of gyroradius and dissipation on the Alfven-wave continuum

International Nuclear Information System (INIS)

Connor, J.W.; Tang, W.M.; Taylor, J.B.

1982-01-01

It is well known that in ideal magnetohydrodynamics there is a continuous spectrum of real frequencies associated with a singularity of the shear Alfven waves on the surface k/sub parallel to/v/sub A/ = omega. It is also known that the introduction of first-order gyroradius effects eliminates the continuum. In the present work we examine the influence of the full gyroradius response and of dissipation on the continuum. In the absence of dissipation we first confirm that if only first-order gyroradius effects are incorporated, the continuum disappears. However, when the full gyroradius response is included, this discrete spectrum vanishes, and a new continuum (associated with singularities at k/sub parallel to/v/sub A/ = 0) appears. The introduction of collisional dissipation removes the original MHD continuum leaving discrete modes whose frequency tends to zero with the collision rate as ν/sup 1/3/. collisions also remove the new continuum of the full gyroradius model leaving discrete modes whose frequency tends to zero as (log ν) -1 . Collisionless Landau damping has a similar effect

Three-space from quantum mechanics

International Nuclear Information System (INIS)

Chew, G.F.; Stapp, H.P.

1988-01-01

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically

A Behavioral Continuum: A Look at Personality Disorders.

Science.gov (United States)

Harris, George; Kirk, Nancy A.

1985-01-01

Suggests that narcissistic, borderline, and antisocial personality disorders are not discrete diagnostic categories, but that they lie along a continuum and have in common the dimensions of degree of self-centeredness and degree of differentiation. Presents evidence supporting existence of continuum of behavior rather than discrete diagnostic…

Hybrid plasmonic nanodevices: Switching mechanism for the nonlinear emission

Energy Technology Data Exchange (ETDEWEB)

Bragas, Andrea V. [Departamento de Física, FCEyN, Universidad de Buenos Aires, IFIBA CONICET, 1428 Buenos Aires (Argentina); Singh, Mahi R. [Department of Physics and Astronomy, Western University, London (Canada)

2014-03-31

Control of the light emission at the nanoscale is of central interest in nanophotonics due to the many applications in very different fields, ranging from quantum information to biophysics. Resonant excitation of surface plasmon polaritons in metal nanoparticles create nanostructured and enhanced light fields around those structures, which produce their strong interaction in a hybrid nanodevice with other plasmonic or non-plasmonic objects. This interaction may in turn also modulate the far field with important consequences in the applications. We show in this paper that the nonlinear emission from semiconductor quantum dots is strongly affected by the close presence of metal nanoparticles, which are resonantly excited. Using a pulsed laser, optical second harmonic is generated in the quantum dot, and it is highly enhanced when the laser is tuned around the nanoparticle plasmon resonance. Even more interesting is the demonstration of a switching mechanism, controlled by an external continuous-wave field, which can enhance or extinguish the SH signal, even when the pulsed laser is always on. Experimental observations are in excellent agreement with the theoretical calculations, based on the dipole-dipole near-field coupling of the objects forming the hybrid system.

Modeling nonlinearities in MEMS oscillators.

Science.gov (United States)

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Coupled nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Chandra, J; Scott, A C

1983-01-01

Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.

Mechanics of couple-stress fluid coatings

Science.gov (United States)

Waxman, A. M.

1982-01-01

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

Extended quantum mechanics

International Nuclear Information System (INIS)

Pavel Bona

2000-01-01

The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics which is related here to some other (more general, but also to more special and 'approximative') theories. Quantum mechanics is here primarily reformulated in an equivalent form of a Poisson system on the phase space consisting of density matrices, where the 'observables', as well as 'symmetry generators' are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfjoint operators. It is shown in this paper that inclusion of additional ('nonlinear') symmetry generators (i. e. 'Hamiltonians') into this reformulation of (linear) quantum mechanics leads to a considerable extension of the theory: two kinds of quantum 'mixed states' should be distinguished, and operator - valued functions of density matrices should be used in the role of 'nonlinear observables'. A general framework for physical theories is obtained in this way: By different choices of the sets of 'nonlinear observables' we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) quantum mechanics, or nonlinear extensions of quantum mechanics; also various 'quasiclassical approximations' to quantum mechanics are all sub theories of the presented extension of quantum mechanics - a version of the extended quantum mechanics. A general interpretation scheme of extended quantum mechanics extending the usual statistical interpretation of quantum mechanics is also proposed. Eventually, extended quantum mechanics is shown to be (included into) a C * -algebraic (hence linear) quantum theory. Mathematical formulation of these theories is presented. The presentation includes an analysis of problems connected with differentiation on infinite-dimensional manifolds, as well as a solution of some problems connected with the work with only densely defined unbounded

Direct detection of male quality can facilitate the evolution of female choosiness and indicators of good genes: Evolution across a continuum of indicator mechanisms.

Science.gov (United States)

Dhole, Sumit; Stern, Caitlin A; Servedio, Maria R

2018-04-01

The evolution of mating displays as indicators of male quality has been the subject of extensive theoretical and empirical research for over four decades. Research has also addressed the evolution of female mate choice favoring such indicators. Yet, much debate still exists about whether displays can evolve through the indirect benefits of female mate choice. Here, we use a population genetic model to investigate how the extent to which females can directly detect male quality influences the evolution of female choosiness and male displays. We use a continuum framework that incorporates indicator mechanisms that are traditionally modeled separately. Counter to intuition, we find that intermediate levels of direct detection of male quality can facilitate, rather than impede, the evolution of female choosiness and male displays in broad regions of this continuum. We examine how this evolution is driven by selective forces on genetic quality and on the display, and find that direct detection of male quality results in stronger indirect selection favoring female choosiness. Our results imply that displays maybe more likely to evolve when female choosiness has already evolved to discriminate perceptible forms of male quality. They also highlight the importance of considering general female choosiness, as well as preference, in studies of "good genes." © 2018 The Author(s). Evolution © 2018 The Society for the Study of Evolution.

The 2017 Nonlinear Mechanics and Dynamics Research Institute.

Energy Technology Data Exchange (ETDEWEB)

Kuether, Robert J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Allensworth, Brooke Marie [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Peebles, Diane E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-02-01

The 2017 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 19 to July 28, 2017. NOMAD seeks to bring together participants with diverse tec hnical backgrounds to work in small teams to utilize an interactive approach to cultivate new ideas and approaches in engineering . NOMAD provides an opportunity for researchers - especially early career researchers - to develop lasting collaborations that go beyond what can be established from the limited interactions at their institutions or at annual conferences. A total of 17 students from around the world came to Albuquerque, New Mexico to participate in the six - week long program held at the University of New Mexico campus. The students collaborated on one of six research projects that were developed by various mentors from Sandia National Laboratories, academia, and other government laboratories. In addition to the research activities, the students atte nded weekly technical seminars, toured the National Museum of Nuclear Science & History, and socialized at various off - hour events including an Albuquerque Isotopes baseball game. At the end of the summer, the students gave a final technical presentation o n their research findings that was broadcast via Skype. Many of the research discoveries made at NOMAD are published as proceedings at t echnical conference s and have direct alignment with the critical mission work performed at Sandia.

Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?

KAUST Repository

Gadelha, H.; Gaffney, E. A.; Smith, D. J.; Kirkman-Brown, J. C.

2010-01-01

. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective

The comparison of two continuum damage mechanics-based material models for formability prediction of AA6082 under hot stamping conditions

Science.gov (United States)

Shao, Z.; Li, N.; Lin, J.

2017-09-01

The hot stamping and cold die quenching process has experienced tremendous development in order to obtain shapes of structural components with great complexity in automotive applications. Prediction of the formability of a metal sheet is significant for practical applications of forming components in the automotive industry. Since microstructural evolution in an alloy at elevated temperature has a large effect on formability, continuum damage mechanics (CDM)-based material models can be used to characterise the behaviour of metals when a forming process is conducted at elevated temperatures. In this paper, two sets of unified multi-axial constitutive equations based on material’s stress states and strain states, respectively, were calibrated and used to effectively predict the thermo-mechanical response and forming limits of alloys under complex hot stamping conditions. In order to determine and calibrate the two material models, formability tests of AA6082 using a developed novel biaxial testing system were conducted at various temperatures and strain rates under hot stamping conditions. The determined unified constitutive equations from experimental data are presented in this paper. It is found that both of the stress-state based and strain-state based material models can predict the formability of AA6082 under hot stamping conditions.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Science.gov (United States)

Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

2018-03-01

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Identification of stochastic interactions in nonlinear models of structural mechanics

Science.gov (United States)

Kala, Zdeněk

2017-07-01

In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.

Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams

Directory of Open Access Journals (Sweden)

A. Carpinteri

Full Text Available In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.

Polarization dynamics in nonlinear anisotropic fibers

International Nuclear Information System (INIS)

Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois

2010-01-01

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.