Discrete wave mechanics: The hydrogen atom.
Wall, F T
1986-08-01
The quantum mechanical problem of the hydrogen atom is treated by use of a finite difference equation in place of Schrödinger's differential equation. The exact solution leads to a wave vector energy expression that is readily converted to the Bohr-Rydberg formula. (The calculations here reported are limited to spherically symmetric states.) The wave vectors reduce to the familiar solutions of Schrödinger's equation as c --> infinity. The internal consistency and limiting behavior provide support for the view that the equations employed could well constitute an approach to a relativistic formulation of wave mechanics.
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Groupoids, Discrete Mechanics, and Discrete Variation
Institute of Scientific and Technical Information of China (English)
GUO Jia-Feng; JIA Xiao-Yu; WU Ke; ZHAO Wei-Zhong
2008-01-01
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Discrete gravity from statistical mechanics
Romano, Antonio Enea
2011-01-01
We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the quantum wave function of the universe using the sum over the histories approach to quantum gravity. Motivated by this isomorphism we show how the Regge equations, i.e. the discrete equivalent of the vacuum Einstein equations, can be derived using statistical mechanics under the assumption that the energy of a given space time geometry is proportional to the Regge action.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Conservation of wave action under multisymplectic discretizations
Frank, J.E.
2006-01-01
In this paper we discuss the conservation of wave action under numerical discretization by variational and multisymplectic methods. Both the abstract wave action conservation defined with respect to a smooth, periodic, one-parameter ensemble of flow realizations and the specific wave action based on
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Discrete Rogue waves in an array of waveguides
Efe, S
2015-01-01
We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue wave solution of the discrete nonlinear Schrodinger equation.
Discrete control of resonant wave energy devices.
Clément, A H; Babarit, A
2012-01-28
Aiming at amplifying the energy productive motion of wave energy converters (WECs) in response to irregular sea waves, the strategies of discrete control presented here feature some major advantages over continuous control, which is known to require, for optimal operation, a bidirectional power take-off able to re-inject energy into the WEC system during parts of the oscillation cycles. Three different discrete control strategies are described: latching control, declutching control and the combination of both, which we term latched-operating-declutched control. It is shown that any of these methods can be applied with great benefit, not only to mono-resonant WEC oscillators, but also to bi-resonant and multi-resonant systems. For some of these applications, it is shown how these three discrete control strategies can be optimally defined, either by analytical solution for regular waves, or numerically, by applying the optimal command theory in irregular waves. Applied to a model of a seven degree-of-freedom system (the SEAREV WEC) to estimate its annual production on several production sites, the most efficient of these discrete control strategies was shown to double the energy production, regardless of the resource level of the site, which may be considered as a real breakthrough, rather than a marginal improvement.
Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
Institute of Scientific and Technical Information of China (English)
LUO Xu-Dong; GUO Han-Ying; LI Yu-Qi; WU Ke
2004-01-01
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.
Discrete particle modelling of granular roll waves
Tsang, Jonathan; Dalziel, Stuart; Vriend, Nathalie
2016-11-01
A granular current flowing down an inclined chute or plane can undergo an instability that leads to the formation of surface waves, known as roll waves. Examples of roll waves are found in avalanches and debris flows in landslides, and in many industrial processes. Although related to the Kapitza instability of viscous fluid films, granular roll waves are not yet as well understood. Laboratory experiments typically measure the surface height and velocity of a current as functions of position and time, but they do not give insight into the processes below the surface: in particular, the possible formation of a boundary layer at the free surface as well as the base. To overcome this, we are running discrete particle model (DPM) simulations. Simulations are validated against our laboratory experiments, but they also allow us to examine a much larger range of parameters, such as material properties, chute geometry and particle size dispersity, than that which is possible in the lab. We shall present results from simulations in which we vary particle size and dispersity, and examine the implications on roll wave formation and propagation. Future work will include simulations in which the shape of the chute is varied, both cross-sectionally and in the downstream direction. EPSRC studentship (Tsang) and Royal Society Research Fellowship (Vriend).
Wave Mechanics or Wave Statistical Mechanics
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Wave Equations for Discrete Quantum Gravity
Gudder, Stan
2015-01-01
This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a covariant difference operator and this operator acting on a wave function forms the left side of the wave equation. The right side is given by an energy term acting on the wave function. Solutions to the wave equation corresponding to certain pairs of paths in $x$ are added and normalized to form a unique state. The modulus squared of the state gives probabilities that a pair of interacting particles is at various locations given by pairs of vertices in $x$. We illustrate this model for a few of the simplest nontrivial examples of $c$-causets. Three forces are considered, the attractive and repulsive electric forces and the strong nuclear force. Large models get much more complicated and will probably require a computer to analyze.
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
Hooft, Gerard t
2012-01-01
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these t...
Discretizing singular point sources in hyperbolic wave propagation problems
Petersson, N. Anders; O'Reilly, Ossian; Sjögreen, Björn; Bydlon, Samuel
2016-09-01
We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.
Statistical mechanics of a discrete nonlinear system
Rasmussen; Cretegny; Kevrekidis; Gronbech-Jensen
2000-04-24
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
Discrete flavor symmetry and minimal seesaw mechanism
Nam, K H; Siyeon, Kim
2011-01-01
This work proposes a neutrino mass model that is derived using the minimal seesaw mechanism which contains only two right-handed neutrinos, under the non-abelian discrete flavor symmetry $\\mathbb{S}_4\\otimes\\mathbb{Z}_2$. Two standard model doublets, $L_\\mu$ and $L_\\tau$, are assigned simultaneously to a $\\mathbf{2}$ representation of $\\mathbb{S}_4$. When the scalar fields introduced in this model, addition to the Standard Model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tri-bi-maximal neutrino mixing. This study examined the possible deviations from TBM mixing related to the experimental data.
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Mechanics, Waves and Thermodynamics
Ranjan Jain, Sudhir
2016-05-01
Figures; Preface; Acknowledgement; 1. Energy, mass, momentum; 2. Kinematics, Newton's laws of motion; 3. Circular motion; 4. The principle of least action; 5. Work and energy; 6. Mechanics of a system of particles; 7. Friction; 8. Impulse and collisions; 9. Central forces; 10. Dimensional analysis; 11. Oscillations; 12. Waves; 13. Sound of music; 14. Fluid mechanics; 15. Water waves; 16. The kinetic theory of gases; 17. Concepts and laws of thermodynamics; 18. Some applications of thermodynamics; 19. Basic ideas of statistical mechanics; Bibliography; Index.
Increasing the structural variety of discrete nondiffracting wave fields
Energy Technology Data Exchange (ETDEWEB)
Boguslawski, Martin; Rose, Patrick; Denz, Cornelia [Institut fuer Angewandte Physik and Center for Nonlinear Science (CeNoS), Westfaelische Wilhelms-Universitaet Muenster, Corrensstrasse 2/4, D-48149 Muenster (Germany)
2011-07-15
We investigate discrete nondiffracting beams (DNBs) being the foundation of periodic and quasiperiodic intensity distributions. Besides the number of interfering plane waves, the phase relation among these waves is decisive to form a particular intensity lattice. In this manner, we systematize different classes of DNBs and present similarities as well as differences. As one prominent instance, we introduce the class of sixfold nondiffracting beams, offering four entirely different transverse intensity distributions: in detail, the hexagonal, kagome, and honeycomb pattern, as well as a hexagonal vortex beam. We further extend our considerations to quasiperiodic structures and show the changeover to Bessel beams. In addition, we introduce a highly flexible implementation of the experimental analog of DNBs, namely discrete pseudo-nondiffracting beams, and present locally resolved intensity and phase measurements, which underline the nondiffracting character of the generated wave fields.
FPGA Implementations of Bireciprocal Lattice Wave Discrete Wavelet Filter Banks
Directory of Open Access Journals (Sweden)
Jassim M. Abdul-Jabbar
2012-06-01
Full Text Available In this paper, a special type of IIR filter banks; that is the bireciprocal lattice wave digital filter (BLWDF bank, is presented to simulate scaling and wavelet functions of six-level wavelet transform. 1st order all-pass sections are utilized for the realization of such filter banks in wave lattice structures. The resulting structures are a bireciprocal lattice wave discrete wavelet filter banks (BLW-DWFBs. Implementation of these BLW-DWFBs are accomplished on Spartan-3E FPGA kit. Implementation complexity and operating frequency characteristics of such discrete wavelet 5th order filter bank is proved to be comparable to the corresponding characteristics of the lifting scheme implementation of Bio. 5/3 wavelet filter bank. On the other hand, such IIR filter banks possess superior band discriminations and perfect roll-off frequency characteristics when compared to their Bio. 5/3 wavelet FIR counterparts.
Discrete computational mechanics for stiff phenomena
Michels, Dominik L.
2016-11-28
Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.
Optimal Discrete PTO Force Point Absorber Wave Energy Converters in Regular Waves
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.
2013-01-01
the conventional fluid power systems suffer of poor efficiency. Therefore discrete fluid power force systems have been proposed. Limited research has, however, been conducted with focus on choosing the discrete force levels and force profiles for a discrete PTO system for WECs. This paper is to support the design...... of discrete force systems for PTO, by focusing on how to choose the optimal PTO force levels and force profile when seeking to increase energy harvesting. The work concerns point absorber WECs and utilises a simple float model based on linear wave theory. Utilising the principle of superposition...
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure—in doing so we try to bring together various fundamental concepts...
A generation mechanism for discrete very low frequency emissions observed at Varanasi
Indian Academy of Sciences (India)
A K Singh; S B Singh; R P Singh
2005-12-01
A new type of discrete VLF emissions recorded at the low-latitude ground station Varanasi (geomag. lat. 14° 55'$ N, geomag. long. 154°E; = 1.07) during the strong magnetic activity on 29–30 April 1990 have been reported. A generation mechanism for various temporal and spectral features of discrete VLF emissions recorded at Varanasi is presented on the basis of cyclotron resonance interaction between whistler mode wave and energetic electrons ejected by substorm electric fields. An attempt is also made to determine parallel energy and wave growth relevant to the generation process of discrete VLF emissions. Finally, our results are discussed with other published works.
Exterior difference systems and invariance properties of discrete mechanics
Energy Technology Data Exchange (ETDEWEB)
Xie Zheng; Xie Duanqiang; Li Hongbo [Center of Mathematical Sciences, Zhejiang University, Zhejiang 310027 (China); Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080 (China)], E-mail: lenozhengxie@yahoo.com.cn
2008-06-27
Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms.
Effect of spatial discretization of energy on detonation wave propagation
Mi, XiaoCheng; Higgins, Andrew J
2016-01-01
Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are now embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the lab-fixed reference frame. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as grea...
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to p
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, van der A.J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to p
Capillary freak waves in He-II as a manifestation of discrete wave turbulent regime
Kartashova, Elena
2010-05-01
Two fundamental findings of the modern theory of wave turbulence are • existence of Kolmogorov-Zakharov power energy spectra (KZ-spectra) in k-space, [1], and • existence of 'gaps" in KZ-spectra corresponding to the resonance clustering, [2]. Accordingly, three wave turbulent regimes can be singled out: kinetic (described by wave kinetic equations and KZ-spectra, in random phase approximation, [3]); discrete (described by a few dynamical systems, with coherent phases corresponding to resonance conditions, [4]); mesoscopic (where kinetic and discrete evolution of the wave field coexist, [5]). We present an explanation of freak waves appearance in capillary waves in He-II, [6], as a manifestation of discrete wave turbulent regime. Implications of these results for other wave systems are briefly discussed. References [1] V. E. Zakharov and N. N. Filonenko. Weak turbulence of capillary waves. Appl. Mech. Tech. Phys. 4 (1967), 500-15. [2] E. Kartashova. A model of laminated turbulence. JETP Lett., 83 (2006), 341-45. [3] V. E. Zakharov, V. S. L'vov and G. Falkovich. Kolmogorov Spectra of Turbulence (Series in Nonlinear Dynamics, Springer-Verlag, New York, 1992). [4] E. Kartashova. Discrete wave turbulence. EPL 87 (2009), 44001-1-5. [5] V. E. Zakharov, A. O. Korotkevich, A. N. Pushkarev and A. I. Dyachenko. Mesoscopic wave turbulence. JETP Lett. 82 (2005), 487-91. [6] L. V. Abdurakhimov, Y. M. Brazhnikov, G. V. Kolmakov and A. A. Levchenko. Study of high-frequency edge of turbulent cascade on the surface of He-II. J. Phys.: Conf. Ser. 150 (2009) (3): 032001.
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
Institute of Scientific and Technical Information of China (English)
Wu Xiao-Fei; Zhu Jia-Min; Ma Zheng-Yi
2007-01-01
In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus M → 1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.
Discretized energy minimization in a wave guide with point sources
Propst, G.
1994-01-01
An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.
Discrete event simulation of Maglev transport considering traffic waves
Directory of Open Access Journals (Sweden)
Moo Hyun Cha
2014-10-01
Full Text Available A magnetically levitated vehicle (Maglev system is under commercialization as a new transportation system in Korea. The Maglev is operated by an unmanned automatic control system. Therefore, the plan of train operation should be carefully established and validated in advance. In general, when making a train operation plan, statistically predicted traffic data is used. However, a traffic wave often occurs in real train service, and demand-driven simulation technology is required to review a train operation plan and service quality considering traffic waves. We propose a method and model to simulate Maglev operation considering continuous demand changes. For this purpose, we employed a discrete event model that is suitable for modeling the behavior of railway passenger transportation. We modeled the system hierarchically using discrete event system specification (DEVS formalism. In addition, through implementation and an experiment using the DEVSim++ simulation environment, we tested the feasibility of the proposed model. Our experimental results also verified that our demand-driven simulation technology can be used for a priori review of train operation plans and strategies.
Collected papers on wave mechanics
Schrödinger, Erwin
1929-01-01
Quantisation as a problem of proper values ; the continuous transition from micro- to macro-mechanics ; on the relation between the quantum mechanics of Heisenberg, Born, and Jordan, and that of Schrödinger ; the Compton effect ; the energy-momentum theorem for material waves ; the exchange of energy according to wave mechanics
Fluid coupling in a discrete model of cochlear mechanics.
Elliott, Stephen J; Lineton, Ben; Ni, Guangjian
2011-09-01
A discrete model of cochlear mechanics is introduced that includes a full, three-dimensional, description of fluid coupling. This formulation allows the fluid coupling and basilar membrane dynamics to be analyzed separately and then coupled together with a simple piece of linear algebra. The fluid coupling is initially analyzed using a wavenumber formulation and is separated into one component due to one-dimensional fluid coupling and one comprising all the other contributions. Using the theory of acoustic waves in a duct, however, these two components of the pressure can also be associated with a far field, due to the plane wave, and a near field, due to the evanescent, higher order, modes. The near field components are then seen as one of a number of sources of additional longitudinal coupling in the cochlea. The effects of non-uniformity and asymmetry in the fluid chamber areas can also be taken into account, to predict both the pressure difference between the chambers and the mean pressure. This allows the calculation, for example, of the effect of a short cochlear implant on the coupled response of the cochlea.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-01-01
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reprod...
Nambu quantum mechanics on discrete 3-tori
Energy Technology Data Exchange (ETDEWEB)
Axenides, M [National Research Center ' Demokritos' , 15310 Aghia Paraskevi, Athens (Greece); Floratos, E G [Nuclear and Particle Physics Section, University of Athens, 15771 Athens (Greece); Nicolis, S [CNRS-Laboratoire de Mathematiques et Physique Theorique (UMR 6083) Federation Denis Poisson (FR 9164) Universite de Tours ' Francois Rabelais' , Parc Grandmont, 37200 Tours (France)], E-mail: axenides@inp.demokritos.gr, E-mail: mflorato@physics.uoa.gr, E-mail: Stam.Nicolis@lmpt.univ-tours.fr
2009-07-10
We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T{sub N}{sup 3} represented by elements of the group SL(3,Z{sub N}). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of T{sub N}{sup 3}. We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of a element of SL(3,Z{sub N}), which is an SL(2,Z{sub N}) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,Z{sub N}) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.
Discrete-element model for the interaction between ocean waves and sea ice.
Xu, Zhijie; Tartakovsky, Alexandre M; Pan, Wenxiao
2012-01-01
We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds α increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.
Modeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues
Directory of Open Access Journals (Sweden)
Víctor Sánchez-Morcillo
2013-06-01
Full Text Available The dynamics of continuous systems that exhibit circular or spherical symmetry like drops, bubbles or some macromolecules, under the influence of some external excitation, develop surface patters that are hard to predict in most practical situations. In the particular case of acoustically driven microbubbles (ultrasound contrast agent, the study of the behavior of the bubble shell requires complex modeling even for describe the most simple oscillation patterns. Furthermore, due to the smallness of the spatio-temporal scale of the problem, an experimental approach requires expensive hardware setup. Despite the complexity of the particular physical problem, the basic dynamical features of some continuous physical systems can be captured by simple models of coupled oscillators. In this work we consider an analogy between a shelled-gas bubble cavitating under the action of an acoustic field and a discrete mechanical system. Thus, we present a theoretical and experimental study of the spatial instabilities of a circular ring of coupled pendulums parametrically driven by a vertical harmonic force. The system is capable of wave propagation and exhibit nonlinearities and dispersion, so manifest rich dynamics: normal oscillation modes (breathing, dipole, quadrupole... and localized patterns of different types (breathers and kinks witch are predicted by finite-differences numerical solutions and observed experimentally. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.
Discrete wave-packet representation in nuclear matter calculations
Müther, H.; Rubtsova, O. A.; Kukulin, V. I.; Pomerantsev, V. N.
2016-08-01
The Lippmann-Schwinger equation for the nucleon-nucleon t matrix as well as the corresponding Bethe-Goldstone equation to determine the Brueckner reaction matrix in nuclear matter are reformulated in terms of the resolvents for the total two-nucleon Hamiltonians defined in free space and in medium correspondingly. This allows one to find solutions at many energies simultaneously by using the respective Hamiltonian matrix diagonalization in the stationary wave-packet basis. Among other important advantages, this approach simplifies greatly the whole computation procedures both for the coupled-channel t matrix and the Brueckner reaction matrix. Therefore this principally novel scheme is expected to be especially useful for self-consistent nuclear matter calculations because it allows one to accelerate in a high degree single-particle potential iterations. Furthermore the method provides direct access to the properties of possible two-nucleon bound states in the nuclear medium. The comparison between reaction matrices found via the numerical solution of the Bethe-Goldstone integral equation and the straightforward Hamiltonian diagonalization shows a high accuracy of the method suggested. The proposed fully discrete approach opens a new way to an accurate treatment of two- and three-particle correlations in nuclear matter on the basis of the three-particle Bethe-Faddeev equation by an effective Hamiltonian diagonalization procedure.
Discrete mechanics, “time machines” and hybrid systems
Directory of Open Access Journals (Sweden)
Elze Hans-Thomas
2013-09-01
Full Text Available Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of “time machines” which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs. In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.
Foundations of the probabilistic mechanics of discrete media
Axelrad, D R
1984-01-01
This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of s
Asymptotic Speed of Wave Propagation for A Discrete Reaction-Diffusion Equation
Institute of Scientific and Technical Information of China (English)
Xiu-xiang Liu; Pei-xuan Weng
2006-01-01
We deal with asymptotic speed of wave propagation for a discrete reaction-diffusion equation. We find the minimal wave speed c* from the characteristic equation and show that c* is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed.
Distinct timing mechanisms produce discrete and continuous movements.
Directory of Open Access Journals (Sweden)
Raoul Huys
2008-04-01
Full Text Available The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems to accomplish varying behavioral functions such as speed constraints.
Corpuscle-Wave Duality of Discrete Systems at Nano-Scale Level
Directory of Open Access Journals (Sweden)
Kharkhardin Аnatolii Nikolaevich
2016-09-01
Full Text Available In the paper the results of study of wave properties for discrete systems with using of mathematical apparatus of discrete topology and application of its basic regularities for disperse materials, micro- and nanoparticles, topological and phase transportations as well as resulting effects and prognosis.
Control of a 420 KN Discrete Displacement Cylinder Drive for the Wavestar Wave Energy Converter
DEFF Research Database (Denmark)
Hansen, Rico H.; Andersen, Torben Ole; Pedersen, Henrik C.
2014-01-01
To improve the power production of their 1 MW wave energy converter, Wavestar is developing a new transmission based on discrete hydraulics. The discrete hydraulic system allows all cylinders to supply a common accumulator storage while maintaining low-loss individual force control of the 20 abso...
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS - University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-06-15
In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail.
Backward-wave propagation and discrete solitons in a left-handed electrical lattice
Energy Technology Data Exchange (ETDEWEB)
English, L.Q.; Wheeler, S.G. [Department of Physics and Astronomy, Dickinson College, Carlisle, PA 17013 (United States); Shen, Y. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Veldes, G.P. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece); Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G., E-mail: kevrekid@math.umass.ed [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2011-02-28
We study experimentally, analytically and numerically the backward-wave propagation, and formation of discrete bright and dark solitons in a nonlinear electrical lattice. We observe experimentally that a focusing (defocusing) effect occurs above (below) a certain carrier frequency threshold, and backward-propagating bright (dark) discrete solitons are formed. We develop a discrete model emulating the relevant circuit and benchmark its linear properties against the experimental dispersion relation. Using a perturbation method, we derive a nonlinear Schroedinger equation, that predicts accurately the carrier frequency threshold. Finally, we use numerical simulations to corroborate our findings and monitor the space-time evolution of the discrete solitons.
Schmidt, Burkhard; Lorenz, Ulf
2017-04-01
WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. The graphical capabilities allow visualization of quantum dynamics 'on the fly', including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry. The present Part I deals with the description of closed quantum systems in terms of Schrödinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization. The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics. The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
Modification of Crum's Theorem for 'Discrete' Quantum Mechanics
Garcia-Gutierrez, Leonor; Odake, Satoru; Sasaki, Ryu
2010-01-01
Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eigenfunctions. The associated system is iso-spectral to the original one except for the lowest energy state, which is deleted. A modification due to Krein-Adler provides algebraic construction of a new complete Hamiltonian system by deleting a finite number of energy levels. Here we present a discrete version of the m...
Discrete and continuous Hamiltonian systems for wave modelling
Nurijanyan, S.
2013-01-01
The main focus of this thesis is to develop numerical discretisations for both compressible and incompressible inviscid flows that also preserve conservation laws at the discrete level. Two alternative approaches are discussed in detail: a semi-analytical solution; and, a fully numerical
Directory of Open Access Journals (Sweden)
K. R. McCall
1996-01-01
Full Text Available The velocity of sound in rock is a strong function of pressure, indicating that wave propagation in rocks is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory on equal footing. The starting point of the new theory is closer to a microscopic description of a rock than the starting point of the traditional five-constant theory of nonlinear elasticity. However, this starting point (the number density Ï? of generic mechanical elements in an abstract space is deliberately independent of a specific microscopic model. No prejudice is imposed as to the mechanism causing nonlinear response in the microscopic mechanical elements. The new theory (1 relates suitable stress-strain measurements to the number density Ï? and (2 uses the number density Ï? to find the behaviour of nonlinear elastic waves. Thus the new theory provides for the synthesis of the full spectrum of elastic behaviours of a rock. Early development of the new theory is sketched in this contribution.
Impedance Matching for Discrete, Periodic Media and Application to Two-Scale Wave Propagation Models
Thirunavukkarasu, Senganal
This dissertation introduces the idea of an equivalent continuous medium (ECM) that has the same impedance as that of an unbounded discrete periodic medium. Contrary to existing knowledge, we constructively show that it is indeed possible to achieve perfect matching for periodic and discrete media. We present analytical results relating the propagation characteristics of periodic media and the corresponding ECM, leading to the development of numerical methods for wave propagation in these media. In this dissertation, we present the main idea of ECM and apply it, with mixed results, to seemingly different problems requiring effective numerical methods for modeling wave propagation in unbounded media. An immediate application of ECM is in developing absorbing boundary conditions (ABCs) for wave propagation in unbounded discrete media. Using the idea of ECM, and building on class of continuous ABCs called perfectly matched discrete layers (PMDL), we propose a new class of discrete ABCs called discrete PMDL and develop frequency domain formulations that are shown to be superior to continuous ABCs. Another application that is explored in this dissertation is the design of interface conditions for concurrent coupling of two-scale wave propagation models, e.g. Atomistic-to-Continuum (AtC) coupling. We propose a domain-decomposition (DD) approach and develop accurate interface conditions that are critical for the concurrent coupling of the two-scale models. It turns out that time-domain discrete ABCs are key to the the accuracy of these interface conditions. Since discrete PMDL is well-posed and accurate for the model problem, we build on it to propose an efficient and accurate interface condition for two-scale wave propagation models. Although many open problems remain with respect to implementation, we believe that the proposed DD based approach is a good first step towards achieving efficient coupling of two-scale wave propagation models. Time-domain discrete PMDL can
Pilot-Wave Quantum Theory in Discrete Space and Time and the Principle of Least Action
Gluza, Janusz; Kosek, Jerzy
2016-11-01
The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a |Ψ |^2-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.
A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves.
Choi, Sun-Ho; Kim, Yong-Jung
2017-02-01
We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, [Formula: see text] and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant [Formula: see text] with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.
A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
Institute of Scientific and Technical Information of China (English)
Xiu-min Shao; Zhi-ling Lan
2002-01-01
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
Investigation and Optimisation of a Discrete Fluid Power PTO-system for Wave Energy Converters
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard
recently focused research on improving the power take off (PTO) system converting the mechanical motion of the floats into electricity. This has brought attention to discrete fluid power (DFP) technology, especially secondary controlled common pressure rail systems. A novel discrete PTO-system has been...... proposed and found feasible for the Wavestar WEC. However, with a technology shift from a continuous to a discrete fluid power PTO-system, new challenges emerge. The current project investigates and optimises the novel discrete fluid power PTO-system proposed for the Wavestar WEC. Initiating from...... an investigation of energy extraction by WECs utilising a discrete PTO force, an investigation of the system configuration is conducted. Hence, the configuration of the multi-chamber cylinder and the common pressure rails are investigated for the discrete fluid power force system. A method for choosing the system...
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
Discrete-Spectrum Waves in the Vicinity of Cyclotron Resonance in Silver
DEFF Research Database (Denmark)
Henningsen, J. O.
1970-01-01
Cyclotron-resonance studies of silver have revealed two additional series of oscillations, one between the fundamental and the second harmonic, the other above the fundamental resonance. These series are caused by the excitation of weakly damped discrete-spectrum waves propagating perpendicular...
Certain Discrete Element Methods in Problems of Fracture Mechanics
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available In this paper two discrete element methods (DEM are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness, is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.. The problem consists in the fact that the material properties of continuum methods (FEM, BEM are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium, but applies static equilibrium. The second method is called the static particle flow code (SPFC. The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
Discrete Wave-Packet Representation in Nuclear Matter Calculations
Müther, H; Kukulin, V I; Pomerantsev, V N
2016-01-01
The Lippmann-Schwinger equation for the nucleon-nucleon $t$-matrix as well as the corresponding Bethe-Goldstone equation to determine the Brueckner reaction matrix in nuclear matter are reformulated in terms of the resolvents for the total two-nucleon Hamiltonians defined in free space and in medium correspondingly. This allows to find solutions at many energies simultaneously by using the respective Hamiltonian matrix diagonalization in the stationary wave packet basis. Among other important advantages, this approach simplifies greatly the whole computation procedures both for coupled-channel $t$-matrix and the Brueckner reaction matrix. Therefore this principally novel scheme is expected to be especially useful for self-consistent nuclear matter calculations because it allows to accelerate in a high degree single-particle potential iterations. Furthermore the method provides direct access to the properties of possible two-nucleon bound states in the nuclear medium. The comparison between reaction matrices f...
Determining required valve performance for discrete control of PTO cylinders for wave energy
DEFF Research Database (Denmark)
Hansen, Rico Hjerm; Andersen, Torben Ole; Pedersen, Henrik C.
2012-01-01
Within wave energy a large challenge remains in designing a Power Take-Off (PTO) system capable of converting the slow oscillations induced by waves into electricity. Fluid power is an essential part of most PTO-concepts. To implement an efficient control of the load force produced by a cylinder...... on a floating body, throttle-less force control by discrete variation of the effective cylinder area has been investigated and found feasible for the Wavestar wave energy concept. However, the feasibility study assumes adequate valve performance, such that only the compression loss remains. This paper...
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.
2001-12-01
We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.
The canonical Kravchuk basis for discrete quantum mechanics
Hakioglu, Tugrul; Wolf, Kurt Bernardo
2000-04-01
The well known Kravchuk formalism of the harmonic oscillator obtained from the direct discretization method is shown to be a new way of formulating discrete quantum phase space. It is shown that the Kravchuk oscillator Hamiltonian has a well defined unitary canonical partner which we identify with the quantum phase of the Kravchuk oscillator. The generalized discrete Wigner function formalism based on the action and angle variables is applied to the Kravchuk oscillator and its continuous limit is examined.
Design of Bidirectional Check Valve for Discrete Fluid Power Force System for Wave Energy Converters
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.; Andersen, Torben Ole
2014-01-01
Discrete fluid power force systems consisting of a multichamber cylinder, a witching manifold and common pressure lines have been proposed as a technology for increasing the efficiency of the power take off system in ocean wave energy converters. However the force shifting of these discrete systems...... enables passive force switching under minimal pressure difference, hence minimal energy loss. The bidirectional check valve is designed with a rated flow in the range of 1000L/min@5bar. The flow direction of the bidirectional check valve is set by the setting the pilot pressure. This paper presents...... a functionality test of a 125 L/min@5bar bidirectional check, leading to the design and modelling of a bidirectional check valve for ocean wave energy. It shows that a feasible bidirectional check valve may be configured by employing a multi-poppet topology for the main stage and utilising a 3/2 switching valve...
Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses
Salerno; Malomed; Konotop
2000-12-01
Propagation of a shock wave (SW), converting an energy-carrying domain into an empty one, is studied in a discrete version of the normal-dispersion nonlinear Schrodinger equation with viscosity, which may describe, e.g., an array of optical fibers in a weakly lossy medium. It is found that the SW in the discrete model is stable, as well as in its earlier studied continuum counterpart. In a strongly discrete case, the dependence of the SWs velocity upon the amplitude of the energy-carrying background is found to obey a simple linear law, which differs by a value of the proportionality coefficient from a similar law in the continuum model. For the underdamped case, the velocity of the shock wave is found to be vanishing along with the viscosity constant. We argue that the latter feature is universal for long but finite systems, both discrete and continuum. The dependence of the SW's width on the parameters of the system is also discussed.
Discrete Displacement Hydraulic Power Take-Off System for the Wavestar Wave Energy Converter
DEFF Research Database (Denmark)
Hansen, Rico Hjerm; Kramer, Morten; Vidal, Enrique
2013-01-01
The Wavestar Wave Energy Converter (WEC) is a multiple absorber concept, consisting of 20 hemisphere shaped floats attached to a single platform. The heart of the Wavestar WEC is the Power Take-Off (PTO) system, converting the wave induced motion of the floats into a steady power output to the grid....... In the present work, a PTO based on a novel discrete displacement fluid power technology is explored for the Wavestar WEC. Absorption of power from the floats is performed by hydraulic cylinders, supplying power to a common fixed pressure system with accumulators for energy smoothing. The stored pressure energy...
A fault location method using Lamb waves and discrete wavelet transform
Souza, Pablo Rodrigo de; Nobrega, Eurípedes Guilherme de Oliveira
2012-01-01
Non-destructive evaluation methods and signal process techniques are important steps in structural health monitoring systems to assess the structure integrity. This paper presents a method for fault location in aluminum beams based on time of flight of Lamb waves. The dynamic response signal captured from the structure was processed using the discrete wavelet transform. The information accuracy obtained from the processed signal depends on the correct choice of the mother wavelet. The best mo...
Bai, Xiao-Dong; Malomed, Boris A.; Deng, Fu-Guo
2016-09-01
We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.
Applications of the discrete element method in mechanical engineering
Energy Technology Data Exchange (ETDEWEB)
Fleissner, Florian, E-mail: fleissner@itm.uni-stuttgart.de; Gaugele, Timo, E-mail: gaugele@itm.uni-stuttgart.de; Eberhard, Peter [University of Stuttgart, Institute of Engineering and Computational Mechanics (Germany)], E-mail: eberhard@itm.uni-stuttgart.de
2007-08-15
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples.
Directory of Open Access Journals (Sweden)
Adam Martowicz
2015-01-01
Full Text Available The paper addresses the problem of numerical dispersion in simulations of wave propagation in solids. This characteristic of numerical models results from both spatial discretization and temporal discretization applied to carry out transient analyses. A denser mesh of degrees of freedom could be a straightforward solution to mitigate numerical dispersion, since it provides more advantageous relation between the model length scale and considered wavelengths. However, this approach also leads to higher computational effort. An alternative approach is the application of nonlocal discretization schemes, which employ a relatively sparse spatial distribution of nodes. Numerical analysis carried out to study the propagation of elastic waves in isotropic solid materials is demonstrated. Fourier-based nonlocal discretization for continuum mechanics is introduced for a two-dimensional model undergoing out-of-plane wave propagation. The results show gradual increase of the effectiveness of this approach while expanding the region of nonlocal interactions in the numerical model. A challenging case of high ratio between the model length scale and wavelength is investigated to present capability of the proposed approach. The elaborated discretization method also provides the perspective of accurate representation of any arbitrarily shaped dispersion relation based on physical properties of modelled materials.
Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier
Jenkinson, M.; Weinstein, M. I.
2017-04-01
We study a class of discrete focusing nonlinear Schrödinger equations (DNLS) with general nonlocal interactions. We prove the existence of onsite and offsite discrete solitary waves, which bifurcate from the trivial solution at the endpoint frequency of the continuous spectrum of linear dispersive waves. We also prove exponential smallness, in the frequency-distance to the bifurcation point, of the Peierls-Nabarro energy barrier (PNB), as measured by the difference in Hamiltonian or mass functionals evaluated on the onsite and offsite states. These results extend those of the authors for the case of nearest neighbor interactions to a large class of nonlocal short-range and long-range interactions. The appearance of distinct onsite and offsite states is a consequence of the breaking of continuous spatial translation invariance. The PNB plays a role in the dynamics of energy transport in such nonlinear Hamiltonian lattice systems. Our class of nonlocal interactions is defined in terms of coupling coefficients, J m , where {min{Z}} is the lattice site index, with {J_m˜eq m^{-1-2s}, sin[1,∞)} and {J_m˜ e^{-γ|m|}, s=∞, γ > 0,} (Kac-Baker). For {s≥1}, the bifurcation is seeded by solutions of the (effective/homogenized) cubic focusing nonlinear Schrödinger equation (NLS). However, for {1/4 equation, FNLS, with {(-Δ)^s} replacing {-Δ}. The proof is based on a Lyapunov-Schmidt reduction strategy applied to a momentum space formulation. The PN barrier bounds require appropriate uniform decay estimates for the discrete Fourier transform of DNLS discrete solitary waves. A key role is also played by non-degeneracy of the ground state of FNLS, recently proved by Frank, Lenzmann and Silvestrie.
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.
DEFF Research Database (Denmark)
Pu, Minhao; Chen, Yaohui; Hu, Hao
2014-01-01
An on-chip wavelength switch is proposed based on discrete four-wave mixing in a silicon waveguide. Switching operation can be realized by thermal tuning the waveguide dispersion. We also discuss optimal dimension design concerning device performances.......An on-chip wavelength switch is proposed based on discrete four-wave mixing in a silicon waveguide. Switching operation can be realized by thermal tuning the waveguide dispersion. We also discuss optimal dimension design concerning device performances....
Mechanic waves in sand: effect of polydispersity
Luding, S.; Mouraille, O.; Peukert, W.; Schreglmann, C.
2008-01-01
The sound propagation mechanisms inside dense granular matter are challenging the attempts to describe it because of the discrete nature of the material. Phenomena like dissipation, scattering, and dispersion are hard to predict based on the material state and/or properties and vice-versa. We propos
Discrete Element Simulation of Elastoplastic Shock Wave Propagation in Spherical Particles
Directory of Open Access Journals (Sweden)
M. Shoaib
2011-01-01
Full Text Available Elastoplastic shock wave propagation in a one-dimensional assembly of spherical metal particles is presented by extending well-established quasistatic compaction models. The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading, and adhesion at contacts with typical dynamic loading parameters. Of particular interest is to study the development of the elastoplastic shock wave, its propagation, and reflection during entire loading process. Simulation results yield information on contact behavior, velocity, and deformation of particles during dynamic loading. Effects of shock wave propagation on loading parameters are also discussed. The elastoplastic shock propagation in granular material has many practical applications including the high-velocity compaction of particulate material.
Vainchtein, Dmitri; Fridman, Greg; Artemyev, Anton
2017-10-01
The wave-particle resonant interaction plays an important role in the charged particle energization by trapping (capture) into resonance. For the systems with waves propagating through inhomogeneous plasma, the key small parameter is the ratio of the wave wavelength to a characteristic spatial scale of inhomogeneity. When that parameter is very small, the asymptotic methods are applicable for the system description, and the resultant energy distribution of trapped particle ensemble has a typical Gaussian profile around some mean value. However, for moderate values of that parameter, the energy distribution has a fine structure including several maxima, each corresponding to the discrete number of oscillations a particle makes in the trapped state. We explain this novel effect which can play important role for generation of unstable distributions of accelerated particles in many space plasma systems.
Discrete Displacement Hydraulic Power Take-Off System for the Wavestar Wave Energy Converter
Directory of Open Access Journals (Sweden)
Enrique Vidal
2013-08-01
Full Text Available The Wavestar Wave Energy Converter (WEC is a multiple absorber concept, consisting of 20 hemisphere shaped floats attached to a single platform. The heart of the Wavestar WEC is the Power Take-Off (PTO system, converting the wave induced motion of the floats into a steady power output to the grid. In the present work, a PTO based on a novel discrete displacement fluid power technology is explored for the Wavestar WEC. Absorption of power from the floats is performed by hydraulic cylinders, supplying power to a common fixed pressure system with accumulators for energy smoothing. The stored pressure energy is converted into electricity at a steady pace by hydraulic motors and generators. The storage, thereby, decouples the complicated process of wave power absorption from power generation. The core for enabling this PTO technology is implementing a near loss-free force control of the energy absorbing cylinders. This is achieved by using special multi-chambered cylinders, where the different chambers may be connected to the available system pressures using fast on/off valves. Resultantly, a Discrete Displacement Cylinder (DDC is created, allowing near loss free discrete force control. This paper presents a complete PTO system for a 20 float Wavestar based on the DDC. The WEC and PTO is rigorously modeled from incident waves to the electric output to the grid. The resulting model of +600 states is simulated in different irregular seas, showing that power conversion efficiencies above 70% from input power to electrical power is achievable for all relevant sea conditions.
Pilot Wave Steerage: A Mechanism and Test
Kracklauer, A. F.
1997-01-01
An intuitive, generic, physical model, or conceptual paradigm for pilot wave steerage of particle beams based on Stochastic Electrodynamics is presented. The utility of this model for understanding the Pauli Exclusion Principle is briefly considered, and a possible experimental verification for the underlying concepts is proposed. \\\\[7mm] Key words: Quantum Mechanics, Pilot Wave, Pauli Exclusion Principle, Stochastic Electrodynamics
A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling
Zeng, Xi-Ping; Tao, Wei-Kuo; Simpson, Joanne
2003-01-01
Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.
Dispersion Analysis of Gravity Waves in Fluid Media Discretized by Energy-Orthogonal Finite Elements
José Brito Castro, Francisco
2014-11-01
This article studies the dispersion of gravity waves in fluid media discretized by the finite element method. The element stiffness matrix is split into basic and higher-order components which are respectively related to the mean and deviatoric components of the gradient of displacement potential. This decomposition is applied to the kinetic energy. The dispersion analysis yields a correlation between the higher-order kinetic energy and the kinetic energy error. The use of this correlation as a reference to apply the higher-order energy as an error indicator for the sloshing modes computed by the finite element method is explored.
Mechanical discrete simulator of the electro-mechanical lift with n:1 roping
Alonso, F. J.; Herrera, I.
2016-05-01
The design process of new products in lift engineering is a difficult task due to, mainly, the complexity and slenderness of the lift system, demanding a predictive tool for the lift mechanics. A mechanical ad-hoc discrete simulator, as an alternative to ‘general purpose’ mechanical simulators is proposed. Firstly, the synthesis and experimentation process that has led to establish a suitable model capable of simulating accurately the response of the electromechanical lift is discussed. Then, the equations of motion are derived. The model comprises a discrete system of 5 vertically displaceable masses (car, counterweight, car frame, passengers/loads and lift drive), an inertial mass of the assembly tension pulley-rotor shaft which can rotate about the machine axis and 6 mechanical connectors with 1:1 suspension layout. The model is extended to any n:1 roping lift by setting 6 equivalent mechanical components (suspension systems for car and counterweight, lift drive silent blocks, tension pulley-lift drive stator and passengers/load equivalent spring-damper) by inductive inference from 1:1 and generalized 2:1 roping system. The application to simulate real elevator systems is proposed by numeric time integration of the governing equations using the Kutta-Meden algorithm and implemented in a computer program for ad-hoc elevator simulation called ElevaCAD.
Wu, Junru; Layman, Christopher; Liu, Jun
2004-02-01
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry
Latini, D.; Riglioni, D.
2016-10-01
The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed.
Ricchiuto, M.; Filippini, A. G.
2014-08-01
In this paper we consider the solution of the enhanced Boussinesq equations of Madsen and Sørensen (1992) [55] by means of residual based discretizations. In particular, we investigate the applicability of upwind and stabilized variants of continuous Galerkin finite element and Residual Distribution schemes for the simulation of wave propagation and transformation over complex bathymetries. These techniques have been successfully applied to the solution of the nonlinear Shallow Water equations (see e.g. Hauke (1998) [39] and Ricchiuto and Bollermann (2009) [61]). In a first step toward the construction of a hybrid model coupling the enhanced Boussinesq equations with the Shallow Water equations in breaking regions, this paper shows that equal order and even low order (second) upwind/stabilized techniques can be used to model non-hydrostatic wave propagation over complex bathymetries. This result is supported by theoretical (truncation and dispersion) error analyses, and by thorough numerical validation.
Optical Synthesis of Terahertz and Millimeter-Wave Frequencies with Discrete Mode Diode Lasers
O'Brien, Stephen; Bitauld, David; Brandonisio, Nicola; Amann, Andreas; Phelan, Richard; Kelly, Brian; O'Gorman, James
2010-01-01
It is shown that optical synthesis of terahertz and millimeter-wave frequencies can be achieved using two-mode and mode-locked discrete mode diode lasers. These edge-emitting devices incorporate a spatially varying refractive index profile which is designed according to the spectral output desired of the laser. We first demonstrate a device which supports two primary modes simultaneously with high spectral purity. In this case sinusoidal modulation of the optical intensity at terahertz frequencies can be obtained. Cross saturation of the material gain in quantum well lasers prevents simultaneous lasing of two modes with spacings in the millimeter-wave region. We show finally that by mode-locking of devices that are designed to support a minimal set of four primary modes, we obtain a sinusoidal modulation of the optical intensity in this frequency region.
Chacko, Nikhil; Liebling, Michael; Blu, Thierry
2013-10-01
Discretization of continuous (analog) convolution operators by direct sampling of the convolution kernel and use of fast Fourier transforms is highly efficient. However, it assumes the input and output signals are band-limited, a condition rarely met in practice, where signals have finite support or abrupt edges and sampling is nonideal. Here, we propose to approximate signals in analog, shift-invariant function spaces, which do not need to be band-limited, resulting in discrete coefficients for which we derive discrete convolution kernels that accurately model the analog convolution operator while taking into account nonideal sampling devices (such as finite fill-factor cameras). This approach retains the efficiency of direct sampling but not its limiting assumption. We propose fast forward and inverse algorithms that handle finite-length, periodic, and mirror-symmetric signals with rational sampling rates. We provide explicit convolution kernels for computing coherent wave propagation in the context of digital holography. When compared to band-limited methods in simulations, our method leads to fewer reconstruction artifacts when signals have sharp edges or when using nonideal sampling devices.
Lamb wave feature extraction using discrete wavelet transformation and Principal Component Analysis
Ghodsi, Mojtaba; Ziaiefar, Hamidreza; Amiryan, Milad; Honarvar, Farhang; Hojjat, Yousef; Mahmoudi, Mehdi; Al-Yahmadi, Amur; Bahadur, Issam
2016-04-01
In this research, a new method is presented for eliciting the proper features for recognizing and classifying the kinds of the defects by guided ultrasonic waves. After applying suitable preprocessing, the suggested method extracts the base frequency band from the received signals by discrete wavelet transform and discrete Fourier transform. This frequency band can be used as a distinctive feature of ultrasonic signals in different defects. Principal Component Analysis with improving this feature and decreasing extra data managed to improve classification. In this study, ultrasonic test with A0 mode lamb wave is used and is appropriated to reduce the difficulties around the problem. The defects under analysis included corrosion, crack and local thickness reduction. The last defect is caused by electro discharge machining (EDM). The results of the classification by optimized Neural Network depicts that the presented method can differentiate different defects with 95% precision and thus, it is a strong and efficient method. Moreover, comparing the elicited features for corrosion and local thickness reduction and also the results of the two's classification clarifies that modeling the corrosion procedure by local thickness reduction which was previously common, is not an appropriate method and the signals received from the two defects are different from each other.
Wave-Particle Duality in Classical Mechanics
Davydov, Alexander Y
2012-01-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after surprising discovery of "walkers" - droplets that bounce on a vertically vibrating bath of the same fluid and can form wave-particle symbiotic structures with the surface waves they generate. Macroscopic walkers were shown experimentally to exhibit particle and wave properties simultaneously. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to walkers, no constant inflow of energy is required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show that such quantum phenomena as p...
Wave forming mechanisms in explosive welding
Carton, E.P.
2004-01-01
Experimental results of wavy metal interfaces obtained by explosive welding are presented and used to determine which wave forming mechanism occurred. It was found that for small collision angles (smaller than about 20°) the Von Karman or jet indentation mechanism occurs, while for large collision
Riccati-coupled similarity shock wave solutions for multispeed discrete Boltzmann models
Energy Technology Data Exchange (ETDEWEB)
Cornille, H. (Service de Physique Theorique, Gif-sur-Yvette (France)); Platkowski, T. (Warsaw Univ. (Poland))
1993-05-01
The authors study nonstandard shock wave similarity solutions for three multispeed discrete boltzmann models: (1) the square 8[upsilon][sub i] model with speeds 1 and [radical]2 with the x axis along one median, (2) the Cabannes cubic 14[upsilon][sub i] model with speeds 1 and [radical]3 and the x axis perpendicular to one face, and (3) another 14[upsilon][sub i] model with speeds 1 and [radical]2. These models have five independent densities and two nonlinear Riccati-coupled equations. The standard similarity shock waves, solutions of scalar Riccati equations, are monotonic and the same behavior holds for the conservative macroscopic quantities. First, the exact similarity shock-wave solutions of coupled Riccati equations are determined and the nonmonotonic behavior for one density and a smaller effect for one conservative macroscopic quantity are observed when a violation of the microreversibility is allowed. Second, new results are obtained on the Whitham weak shock wave propagation. Third, the corresponding dynamical system is numerically solved, with microreversibility satisfied or not, and the analogous nonmonotonic behavior is observed. 9 refs., 2 figs., 1 tab.
Johansson; Aubry
2000-05-01
We investigate the long-time evolution of weakly perturbed single-site breathers (localized stationary states) in the discrete nonlinear Schrodinger equation. The perturbations we consider correspond to time-periodic solutions of the linearized equations around the breather, and can be either (i) spatially localized or (ii) spatially extended. For case (i), which corresponds to the excitation of an internal mode of the breather, we find that the nonlinear interaction between the breather and its internal mode always leads to a slow growth of the breather amplitude and frequency. In case (ii), corresponding to interaction between the breather and a standing-wave phonon, the breather will grow provided that the wave vector of the phonon is such that the generation of radiating higher harmonics at the breather is possible. In other cases, breather decay is observed. This condition yields a limit value for the breather frequency above which no further growth is possible. We also discuss another mechanism for breather growth and destruction which becomes important when the amplitude of the perturbation is non-negligible, and which originates from the oscillatory instabilities of the nonlinear standing-wave phonons.
Power Generation Using Mechanical Wave Energy Converter
Directory of Open Access Journals (Sweden)
Srinivasan Chandrasekaran
2012-03-01
Full Text Available Ocean wave energy plays a significant role in meeting the growing demand of electric power. Economic, environmental, and technical advantages of wave energy set it apart from other renewable energy resources. Present study describes a newly proposed Mechanical Wave Energy Converter (MEWC that is employed to harness heave motion of floating buoy to generate power. Focus is on the conceptual development of the device, illustrating details of component level analysis. Employed methodology has many advantages such as i simple and easy fabrication; ii easy to control the operations during rough weather; and iii low failure rate during normal sea conditions. Experimental investigations carried out on the scaled model of MWEC show better performance and its capability to generate power at higher efficiency in regular wave fields. Design Failure Mode and Effect Analysis (FMEA shows rare failure rates for all components except the floating buoy.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A.
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
Quantum mechanics as electrodynamics of curvilinear waves
2002-01-01
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.
Han, Xuesong
2014-09-01
Machining technology about ceramics has been developed very fast over recent years due to the growing industrial demand of higher machining accuracy and better surface quality of ceramic elements, while the nature of hard and brittle ceramics makes it difficult to acquire damage-free and ultra-smooth surface. Ceramic bulk can be treated as an assemblage of discrete particles bonded together randomly as the micro-structure of ceramics consists of crystal particles and pores, and the inter-granular fracture of the ceramics can be naturally represented by the separation of particles due to breakage of bonds. Discrete element method (DEM) provides a promising approach for constructing an effective model to describe the tool-workpiece interaction and can serve as a predicting simulation tool in analyzing the complicated surface generation mechanism and is employed in this research to simulate the mechanical polishing process of ceramics and surface integrity. In this work, a densely packed particle assembly system of the polycrystalline Si3N4 has been generated using bonded-particle model to represent the ceramic workpiece numerically. The simulation results justify that the common critical depth of cut cannot be used as the effective parameters for evaluating brittle to ductile transformation in ceramic polishing process. Therefore, a generalized criterion of defining the range of ductile regime machining has been developed based on the numerical results. Furthermore, different distribution of pressure chain is observed with different depth of cut which ought to have intense relationship with special structure of ceramics. This study also justified the advantage of DEM model in its capability of revealing the mechanical behaviors of ceramics at micro-scale.
Mechanics of a crushable pebble assembly using discrete element method
Energy Technology Data Exchange (ETDEWEB)
Annabattula, R.K., E-mail: ratna.annabattula@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany); Gan, Y., E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, University of Sydney, 2006 NSW, Sydney (Australia); Zhao, S. [College of Mechanical and Electronics Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018 (China); Kamlah, M., E-mail: marc.kamlah@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany)
2012-11-15
The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression ({epsilon}{sub 33}=1.5%) with periodic boundary conditions. The crushable pebble assembly shows a significant difference in stress-strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour (constant stress with increase in strain) is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor ({eta}) of the assembly.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
Chen, Huaiyu; Liu, Yan; Zhang, Qiang; Shi, Yuhan; Pang, Wei; Li, Yongyao
2016-05-01
We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.
Frank, J.E.
2006-01-01
In this note we show that multisymplectic Runge-Kutta box schemes, of which the Gauss-Legendre methods are the most important, preserve a discrete conservation law of wave action. The result follows by loop integration over an ensemble of flow realizations, and the local energy-momentum conservation
Gui, Y. L.; Zhao, Z. Y.; Zhou, H. Y.; Wu, W.
2016-10-01
In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.
Wave-particle duality in classical mechanics
Davydov, Alexander Y.
2012-05-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in a strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propel via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, an observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level.
Galiana-Merino, J. J.; Rosa-Herranz, J. L.; Rosa-Cintas, S.; Martinez-Espla, J. J.
2013-01-01
A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of multichannel seismic data. The considered time-frequency transforms include the continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform. The developed approaches provide a fast and precise time-frequency examination of the seismograms at different frequency bands. Moreover, filtering methods for noise, transients or even baseline removal, are implemented. The primary motivation is to support seismologists with a user-friendly and fast program for the wavelet analysis, providing practical and understandable results. Program summaryProgram title: SeismicWaveTool Catalogue identifier: AENG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 611072 No. of bytes in distributed program, including test data, etc.: 14688355 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.8.0.347 (R2009a) or higher. Wavelet Toolbox is required. Computer: Developed on a MacBook Pro. Tested on Mac and PC. No computer-specific optimization was performed. Operating system: Any supporting MATLAB (MathWorks Inc.) v7.8.0.347 (R2009a) or higher. Tested on Mac OS X 10.6.8, Windows XP and Vista. Classification: 13. Nature of problem: Numerous research works have developed a great number of free or commercial wavelet based software, which provide specific solutions for the analysis of seismic data. On the other hand, standard toolboxes, packages or libraries, such as the MathWorks' Wavelet Toolbox for MATLAB, offer command line functions and interfaces for the wavelet analysis of one-component signals. Thus, software usually is focused on very specific problems
Why were Matrix Mechanics and Wave Mechanics considered equivalent?
Perovic, Slobodan
A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence ("Schrödinger-equivalence") of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave
Localization and solitary waves in solid mechanics
Champneys, A R; Thompson, J M T
1999-01-01
This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classi
Martinez-Pedrero, Fernando; Tierno, Pietro; Johansen, Tom H; Straube, Arthur V
2016-02-03
The emergence of wave fronts in dissipative driven systems is a fascinating phenomenon which can be found in a broad range of physical and biological disciplines. Here we report the direct experimental observation of discrete fronts propagating along chains of paramagnetic colloidal particles, the latter propelled above a traveling wave potential generated by a structured magnetic substrate. We develop a rigorously reduced theoretical framework and describe the dynamics of the system in terms of a generalized one-dimensional dissipative Frenkel-Kontorova model. The front dynamics is explored in a wide range of field parameters close to and far from depinning, where the discrete and continuum limits apply. We show how symmetry breaking and finite size of chains are used to control the direction of front propagation, a universal feature relevant to different systems and important for real applications.
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2006-01-01
The annihilation-creation operators $a^{(\\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\\pm)}$ are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the `discrete' quantum mechanics.
Symmetry breaking of localized discrete matter waves induced by spin–orbit coupling
Energy Technology Data Exchange (ETDEWEB)
Salerno, M. [Dipartimento di Fisica “E.R. Caianiello”, CNISM and INFN–Gruppo Collegato di Salerno, Universitá di Salerno, Via Giovanni Paolo II, 84084 Fisciano (Italy); Abdullaev, F.Kh., E-mail: fatkhulla@yahoo.com [Department of Physics, Kulliyyah of Science, International Islamic University of Malaysia, 25200 Kuantan, Pahang (Malaysia)
2015-10-02
We study localized nonlinear excitations of a dilute Bose–Einstein condensate (BEC) with spin–orbit coupling in a deep optical lattice (OL). For this we introduce a tight-binding model that includes the spin–orbit coupling (SOC) at the discrete level in the form of a generalized discrete nonlinear Schrödinger equation. Existence and stability of discrete solitons of different symmetry types is demonstrated. Quite interestingly, we find three distinctive regions in which discrete solitons undergo spontaneously symmetry breaking, passing from on-site to inter-site and to asymmetric, simply by varying the interatomic interactions. Existence ranges of discrete solitons with inter-site symmetry depend on SOC and shrink to zero as the SOC parameter is increased. Asymmetric discrete solitons appear as novel excitations specific of the SOC. Possible experimental implementation of these results is briefly discussed.
Kengne, E; Lakhssassi, A
2015-03-01
We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave. With the help of the analytical solutions of the CNLS equation, we investigate analytically the effects of the linear capacitance CS on the dynamics of matter-wave solitons in the network. Our results reveal that the linear parameter CS can be used to manipulate the motion of bright, dark, and kink soliton in the network.
Intercellular Ca2+ Waves: Mechanisms and Function
Sanderson, Michael J.
2012-01-01
Intercellular calcium (Ca2+) waves (ICWs) represent the propagation of increases in intracellular Ca2+ through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca2+ from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs. PMID:22811430
Wave mechanics of the hydrogen atom
Ogilvie, J F
2016-01-01
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the latter solution is reported for the first time. Applications of these solutions include angular momenta, a quantitative calculation of the absorption spectrum and accurate plots of surfaces of amplitude functions. The shape of an amplitude function, and even the quantum numbers in a particular set to specify such an individual function, depend on the coordinates in a particular chosen system, and are therefore artefacts of that particular coordinate representation within wave mechanics. All discussion of atomic or molecular properties based on such shapes or quantum numbers therefore lacks general significance
Directory of Open Access Journals (Sweden)
Xiaolin Huang
2016-12-01
Full Text Available This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM. A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i initial compaction stage; (ii crushing stage; and (iii crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV, of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.
Institute of Scientific and Technical Information of China (English)
Zha Qi-Lao; Sirendaoreji
2006-01-01
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach.This approach can also be applied to other nonlinear differential-difference equations.
Discrete phase space - II: The second quantization of free relativistic wave fields
Das, A
2008-01-01
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defned on the space-time continuum.
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-01-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population. PMID:28195135
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-02-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.
Continuum modeling of the mechanical and thermal behavior of discrete large structures
Nayfeh, A. H.; Hefzy, M. S.
1980-01-01
In the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss-like repetitive structures. Once the actual structure is specified, the construction procedure can be outlined by the following three steps: (a) all sets of parallel members are identified, (b) unidirectional 'effective continuum' properties are derived for each of these sets and (c) orthogonal transformations are finally used to determine the contribution of each set to the 'overall effective continuum' properties of the structure. Here the properties includes mechanical (stiffnesses), thermal (coefficients of thermal expansions) and material densities. Once expanded descriptions of the steps (b) and (c) are done, the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods.
Some thoughts on discrete physics and the reconstruction of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1996-04-01
The authors explore how relativistic quantum mechanics might be reconstructed on a finite and discrete basis, starting from the observation that strong interactions break scale invariance at the pion Compton wavelength and provide an event horizon for space-time description. Regions of this size act coherently, and can only be explored by studying the momentum and quantum number distribution of particles produced in high energy collisions that attempt to probe them. This leads to the concept of measurement accuracy bounded from below, from which they have derived finite and discrete replacements for the Maxwell and Dirac equations. They suggest how the Dirac equation could provide the sources and sinks for the Maxwell equations. A lower bound for mass measurement accuracy is proposed.
Cosmology and the pilot wave interpretation of quantum mechanics
Tipler, Frank J.
1984-07-01
Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.
Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
A Discrete Event Simulator for Extensive Defense Mechanism for Denial of Service Attacks Analysis
Directory of Open Access Journals (Sweden)
Maryam Tanha
2012-01-01
Full Text Available Problem statement: Seeking for defense mechanisms against low rate Denial of Service (DoS attacks as a new generation of DoS attacks has received special attention during recent years. As a decisive factor, evaluating the performance of the offered mitigation techniques based on different metrics for determining the viability and ability of these countermeasures requires more research. Approach: The development of a new generalized discrete event simulator has been deliberated in detail. The research conducted places high emphasis on the benefits of creating a customized discrete event simulator for the analysis of security and in particular the DoS attacks. The simulator possesses a niche in terms of the small scale, low execution time, portability and ease of use. The attributes and mechanism of the developed simulator is complemented with the proposed framework. Results: The simulator has been extensively evaluated and has proven to provide an ideal tool for the analysis and exploration of DoS attacks. In-depth analysis is enabled by this simulator for creating multitudes of defense mechanisms against HTTP low rate DoS attacks. The acquired results from the simulation tool have been compared against a simulator from the same domain. Subsequently, it enables the validation of developed simulator utilizing selected performance metrics including mean in-system time, average delay and average buffer size. Conclusion: The proposed simulator serves as an efficient and scalable performance analysis tool for the analysis of HTTP low rate DoS attack defense mechanism. Future work can encompass the development of discrete event simulators for analysis of other security issues such as Intrusion Detection Systems.
Gürcan, Ö D
2016-01-01
A discretization of the wave-number space of the Navier-Stokes equation, using a logarithmically spaced chain of alternating icosa-dodeca-hedral spheres is proposed. This strange choice allows the possibility of forming triangles using only discretized wave-vectors when the scaling between two consecutive dodecahedra is equal to the golden ratio, and the icosahedron between the two dodecahedra is the dual of the inner dodecahedron. Alternatively, the same discretization can be described as a logarithmically spaced (with a scaling equal to the golden ratio) dodecahedron-icosahedron compounds. A wave-vector which points from the origin to a vertex of such a mesh, can always find two other discretized wave-vectors that are also on the vertices of the mesh (which is not true for an arbitrary mesh). For each vertex (i.e. discretized wave-vector) in this space, there are either 9 or 15 pairs of vertices (i.e. wave-vectors) with which the initial vertex can interact to form a triangle. This allows the reduction of t...
Wave-like variables of a classical particle and their connections to quantum mechanics
Yang, Chen
2017-01-01
In many texts, the transition from classical mechanics to quantum mechanics is achieved by substituting the action for the phase angle. The paper presents a different approach to show some connections between classical and quantum mechanics for a single particle for an audience at graduate and postgraduate levels. Firstly, it is shown that a wave equation of action can be derived under the free particle condition and the Legendre transform. The wave-like solutions of the action, Hamiltonian and momentum of the free particle are presented. Using the discrete approximation, the equation of motion of a single particle, in scalar potential field, is obtained in a similar form to Schrödinger’s equation. The rest of the paper discusses the propagation, superposition of the wave-like dynamic variables and their connections to quantum mechanics. The superposition of the variables of a particle is generally distinct from the superposition of classical waves (e.g. acoustics). The quantum superposition provides a self-consistent interpretation of the wave-like solutions of the variables. Connections between the classical and quantum relations for corresponding variables are observed from the one-to-one comparisons.
Directory of Open Access Journals (Sweden)
Changwei Zhou
2017-02-01
Full Text Available In this article, the analytical homogenization method of periodic discrete media (HPDM and the numerical condensed wave finite element method (CWFEM are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.
LENUS (Irish Health Repository)
Curtis, Andrew R
2009-02-01
To assess the mechanical properties of discrete filler particles representative of several inorganic fillers in modern dental resin-based composites (RBCs) and to assess the validity of a novel micromanipulation technique.
Institute of Scientific and Technical Information of China (English)
Feng Lixin; Jia Niannian
2007-01-01
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.
Ocean wave imaging mechanism by imaging radar
Institute of Scientific and Technical Information of China (English)
何宜军
2000-01-01
Analytical representations of the high frequency spectra of ocean wave and its variation due to the variation of ocean surface current are derived from the wave-number spectrum balance equation. The ocean surface imaging formulation of real aperture radar (RAR) is given using electromagnetic wave backscattering theory of ocean surface and the modulations of ocean surface winds, currents and their variations to RAR are described. A general representation of the phase modulation induced by the ocean surface motion is derived according to standard synthetic aperture radar (SAR) imaging theory. The detectability of ocean current and sea bottom topography by imaging radar is discussed. The results constitute the theoretical basis for detecting ocean wave fields, ocean surface winds, ocean surface current fields, sea bottom topography, internal wave and so on.
Developmental waves in myxobacteria: A distinctive pattern formation mechanism
Igoshin, Oleg A.; Neu, John; Oster, George
2004-10-01
In early stages of their development, starving myxobacteria organize their motion to produce a periodic pattern of traveling cell density waves. These waves arise from coordination of individual cell reversals by contact signaling when they collide. Unlike waves generated by reaction-diffusion instabilities, which annihilate on collision, myxobacteria waves appear to pass through one another unaffected. Here we analyze a mathematical model of these waves developed earlier [Igoshin , Proc. Natl. Acad. Sci. USA 98, 14 913 (2001)]. The mechanisms which generate and maintain the density waves are clearly revealed by tracing the reversal loci of individual cells. An evolution equation of reversal point density is derived in the weak-signaling limit. Linear stability analysis determines parameters favorable for the development of the waves. Numerical solutions demonstrate the stability of the fully developed nonlinear waves.
Industrial Discretization Mechanism and Agglomeration Counter-measures for Industrial Parks
Institute of Scientific and Technical Information of China (English)
Shuangyan; ZHOU
2013-01-01
With rapid development of industrial parks in China,it lacks strict control in planning for establishment and land use of industrial parks.The supply is seriously surplus,and cut-throat competition takes place in investment inviting activities,leading to discretized development of industries in industrial parks.Industrial park and enterprise cluster have a common foundation,namely,geographic concentration of industries.Industrial parks with enterprise cluster development show various advantages,so industrial parks should take industrial cluster development as their ultimate direction.From problems in construction of industrial parks,this paper analyzes mechanism of discretized industrial parks,and accordingly puts forward countermeasures for promoting cluster development:(1)Scientifically distributing administrative power of local government,improving supervision and assessment mechanism,and guaranteeing reasonable supply of industrial parks from system;(2)Introducing market-oriented industrial park construction mechanism,to promote market-oriented supply of industrial parks;(3)Strengthening construction of administrative ethics and abilities of local government,to promote coordinated and healthy development of industrial parks;(4)Forming excellent enterprise cluster development expectation and strengthening cluster-based decisions of enterprises entering industrial parks.
Approximation of mechanical properties of sintered materials with discrete element method
Dosta, Maksym; Besler, Robert; Ziehdorn, Christian; Janßen, Rolf; Heinrich, Stefan
2017-06-01
Sintering process is a key step in ceramic processing, which has strong influence on quality of final product. The final shape, microstructure and mechanical properties, e.g. density, heat conductivity, strength and hardness are depending on the sintering process. In order to characterize mechanical properties of sintered materials, in this contribution we present a microscale modelling approach. This approach consists of three different stages: simulation of the sintering process, transition to final structure and modelling of mechanical behaviour of sintered material with discrete element method (DEM). To validate the proposed simulation approach and to investigate products with varied internal structures alumina powder has been experimentally sintered at different temperatures. The comparison has shown that simulation results are in a very good agreement with experimental data and that the novel strategy can be effectively used for modelling of sintering process.
Discrete Phase Space: Quantum mechanics and non-singular potential functions
Das, Anadijiban
2015-01-01
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\\mathbb{E}_{3}$ where the potential is singular but invariant under the continuous inhomogeneous orthogonal group $\\mathcal{I}O(3)$. The invariance under the translation subgroup is compared to the corresponding unitary transformation in the Schr\\"{o}dinger representation of quantum mechanics. This scenario is well known but serves as a reference point for the other scenarios. (ii) Next, the discrete potential equation as a partial difference equation in a three-dimensional lattice space is studied. In this arena the potential is non-singular but invariance under $\\mathcal{I}O(3)$ is broken. This is the usual picture of lattice theories and numerical approximations. (iii) Next we study the six-dimensional continuous phase space. Here a phase space representation of quantum mechanics is utilized. The resulting potential is singular but posse...
Louis, L.; Henry, P.; Humbert, F.; Knuth, M.; Likos, W.; Scientists, I.
2008-12-01
We present results of electrical conductivity and P-wave velocity measurements in discrete samples processed onboard Chikyu during Nantroseize expeditions 315 and 316 in the Mega Splay fault and Frontal Thrust of the Nankai accretionary prism. Quasi cubes of 20 mm thickness nominally saturated with seawater were measured across the three parallel sets of faces, first for electrical conductivity, then for P-wave velocity. Average properties and their anisotropies appeared to show some sensitivity to both lithological and fault related features. Overall, strong transverse anisotropy due to sedimentary compaction was observed for both properties with minimum electrical conductivity and P-wave velocity along the vertical core axis direction. Within the horizontal plane perpendicular to the core axis, slight anisotropies were also measured, which are likely related to tectonically driven horizontal shortening, affecting noticeably the original compaction fabric. In order to get some structural insight, samples were reoriented in our laboratories using alternative field demagnetization technique and the in-plane (i.e. perpendicular to the core axis) data rotated accordingly. For the P-wave anisotropy, initial cubes were shaped into polyhedrons in order to get even more accurate estimates. These additional measurements allowed for retrieving for each sample the 3 principal values and vectors of the best fitting ellipsoidal function. Resulting stereoplots were then compared with electrical resistivity, magnetic susceptibility (AMS) and structural data.
Numerical simulation and mechanism analysis of freak waves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A numerical wave model based on the modified fourth-order nonlinear Schroe dinger equation (mNLSE) in deep water was developed to simulate the formation of freak waves and a standard split-step, pseudo-spectral method was used to solve the equation. The validation of the model is firstly verified, then the simulation of freak waves was performed by changing sideband conditions, and the variation of wave energy was also analyzed in the evolution. The results indicate that Benjamin-Feir instability (sideband instability) is an important mechanism for freak wave formation.
Discrete fracture modeling of hydro-mechanical damage processes in geological systems
Kim, K.; Rutqvist, J.; Houseworth, J. E.; Birkholzer, J. T.
2014-12-01
This study presents a modeling approach for investigating coupled thermal-hydrological-mechanical (THM) behavior, including fracture development, within geomaterials and structures. In the model, the coupling procedure consists of an effective linkage between two codes: TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach; and an implementation of the rigid-body-spring network (RBSN) method, a discrete (lattice) modeling approach to represent geomechanical behavior. One main advantage of linking these two codes is that they share the same geometrical mesh structure based on the Voronoi discretization, so that a straightforward representation of discrete fracture networks (DFN) is available for fluid flow processes. The capabilities of the TOUGH-RBSN model are demonstrated through simulations of hydraulic fracturing, where fluid pressure-induced fracturing and damage-assisted flow are well represented. The TOUGH-RBSN modeling methodology has been extended to enable treatment of geomaterials exhibiting anisotropic characteristics. In the RBSN approach, elastic spring coefficients and strength parameters are systematically formulated based on the principal bedding direction, which facilitate a straightforward representation of anisotropy. Uniaxial compression tests are simulated for a transversely isotropic material to validate the new modeling scheme. The model is also used to simulate excavation fracture damage for the HG-A microtunnel in the Opalinus Clay rock, located at the Mont Terri underground research laboratory (URL) near Saint-Ursanne, Switzerland. The Opalinus Clay has transversely isotropic material properties caused by natural features such as bedding, foliation, and flow structures. Preferential fracturing and tunnel breakouts were observed following excavation, which are believed to be strongly influenced by the mechanical anisotropy of the rock material. The simulation results are qualitatively
Directory of Open Access Journals (Sweden)
Tatsuya Kai
2013-09-01
Full Text Available This paper addresses a gait generation problem for the compass-type biped robot on periodically unlevel grounds. We first derive the continuous/discrete compass-type biped robots (CCBR/DCBR via continuous/discrete mechanics, respectively. Next, we formulate a optimal gait generation problem on periodically unlevel grounds for the DCBR as a finite dimensional nonlinear optimization problem, and show that a discrete control input can be obtained by solving the optimization problem with the sequential quadratic programming. Then, we develop a transformation method from a discrete control input into a continuous zero-order hold input based on the discrete Lagranged’Alembert principle. Finally, we show numerical simulations, and it turns out that our new method can generate a stable gaits on a periodically unlevel ground for the CCBR.
Complete classification of discrete resonant Rossby/drift wave triads on periodic domains
Bustamante, Miguel D
2013-01-01
We consider the set of Diophantine equations that arise in the context of the barotropic vorticity equation on periodic domains, when nonlinear wave interactions are studied to leading order in the amplitudes. The solutions to this set of Diophantine equations are of interest in atmosphere (Rossby waves) and Tokamak plasmas (drift waves), because they provide the values of the spectral wavevectors that interact resonantly via three-wave interactions. These come in "triads", i.e., groups of three wavevectors. We provide the full solution to the Diophantine equations in the case of infinite Rossby deformation radius. The method is completely new, and relies on mapping the unknown variables to rational points on quadratic forms of "Minkowski" type. Classical methods invented centuries ago by Fermat, Euler, Lagrange and Minkowski, are used to classify all solutions to our original Diophantine equations, thus providing a computational method to generate numerically all the resonant triads in the system. Our method...
Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity.
Samuelsen, Mogens R; Khare, Avinash; Saxena, Avadh; Rasmussen, Kim Ø
2013-04-01
We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is nontrivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS, in fact, becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.
Discretization on the cosmic scale inspired from the Old Quantum Mechanics
Agnese, A G
1998-01-01
The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are used to calculate a few mechanical quantities pertinent to the periodic motions of celestial bodies. Several values have been obtained which result in reasonable agreement with the corresponding experimental data. A gravitational dimensionless structure constant has been determined, using the data relative to the solar sistem, which allows to quantitatively account for phenomena on a much wider scale. In particular, some information is acquired about the recently discovered extrasolar planetary systems and about the general empirical law which connects the spin of a celestial body with the square of its mass.
Photon physics: from wave mechanics to quantum electrodynamics
Keller, Ole
2009-05-01
When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wave-mechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.
Mechanism for Triggered Waves in Atrial Myocytes.
Shiferaw, Yohannes; Aistrup, Gary L; Wasserstrom, J Andrew
2017-08-08
Excitation-contraction coupling in atrial cells is mediated by calcium (Ca) signaling between L-type Ca channels and Ryanodine receptors that occurs mainly at the cell boundary. This unique architecture dictates essential aspects of Ca signaling under both normal and diseased conditions. In this study we apply laser scanning confocal microscopy, along with an experimentally based computational model, to understand the Ca cycling dynamics of an atrial cell subjected to rapid pacing. Our main finding is that when an atrial cell is paced under Ca overload conditions, Ca waves can then nucleate on the cell boundary and propagate to the cell interior. These propagating Ca waves are referred to as "triggered waves" because they are initiated by L-type Ca channel openings during the action potential. These excitations are distinct from spontaneous Ca waves originating from random fluctuations of Ryanodine receptor channels, and which occur after much longer waiting times. Furthermore, we argue that the onset of these triggered waves is a highly nonlinear function of the sarcoplasmic reticulum Ca load. This strong nonlinearity leads to aperiodic response of Ca at rapid pacing rates that is caused by the complex interplay between paced Ca release and triggered waves. We argue further that this feature of atrial cells leads to dynamic instabilities that may underlie atrial arrhythmias. These studies will serve as a starting point to explore the nonlinear dynamics of atrial cells and will yield insights into the trigger and maintenance of atrial fibrillation. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao
2017-09-01
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
Ultrasonic guided wave mechanics for composite material structural health monitoring
Gao, Huidong
The ultrasonic guided wave based method is very promising for structural health monitoring of aging and modern aircraft. An understanding of wave mechanics becomes very critical for exploring the potential of this technology. However, the guided wave mechanics in complex structures, especially composite materials, are very challenging due to the nature of multi-layer, anisotropic, and viscoelastic behavior. The purpose of this thesis is to overcome the challenges and potentially take advantage of the complex wave mechanics for advanced sensor design and signal analysis. Guided wave mechanics is studied in three aspects, namely wave propagation, excitation, and damage sensing. A 16 layer quasi-isotropic composite with a [(0/45/90/-45)s]2 lay up sequence is used in our study. First, a hybrid semi-analytical finite element (SAFE) and global matrix method (GMM) is used to simulate guided wave propagation in composites. Fast and accurate simulation is achieved by using SAFE for dispersion curve generation and GMM for wave structure calculation. Secondly, the normal mode expansion (NME) technique is used for the first time to study the wave excitation characteristics in laminated composites. A clear and simple definition of wave excitability is put forward as a result of NME analysis. Source influence for guided wave excitation is plotted as amplitude on a frequency and phase velocity spectrum. This spectrum also provides a guideline for transducer design in guided wave excitation. The ultrasonic guided wave excitation characteristics in viscoelastic media are also studied for the first time using a modified normal mode expansion technique. Thirdly, a simple physically based feature is developed to estimate the guided wave sensitivity to damage in composites. Finally, a fuzzy logic decision program is developed to perform mode selection through a quantitative evaluation of the wave propagation, excitation and sensitivity features. Numerical simulation algorithms are
Optimisation of Working Areas in Discrete Hydraulic Power Take off-system for Wave Energy Converters
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Hansen, Rico Hjerm; Pedersen, Henrik C.
2012-01-01
Fluid power is the leading technology in Power Take Off(PTO) systems in Wave Energy Converters(WEC’s), due to the capability of generating high force at low velocity. However, as hydraulic force controlling system may suffer from large energy losses the efficiency of the hydraulic PTO systems may...... be a limiting factor for wave energy. Therefore, a secondary controlled force system has been proposed as PTO element for WEC’s. This paper investigates the configuration of a multi-chamber cylinder utilising two common pressure lines. By usage of model based optimisation an optimal number and size of working...
The discrete Lamb problem: Elastic lattice waves in a block medium
Aleksandrova, Nadezhda
2014-01-01
We study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the directions of the axes x, y, and in the diagonal directions. The problem is solved by two methods. Analytically, we obtain asymptotic solutions in the vicinity of the Rayleigh wave at large time intervals. Numerically, we obtain a solution for any finite time interval. We compare these solutions with each other and with the solution to the Lamb problem for an elastic medium.
Sun, Zhuang; Espinoza, D. Nicolas; Balhoff, Matthew T.
2016-11-01
During CO2 injection into geological formations, petrophysical and geomechanical properties of host formations can be altered due to mineral dissolution and precipitation. Field and laboratory results have shown that sandstone and siltstone can be altered by CO2-water mixtures, but few quantitative studies have been performed to fully investigate underlying mechanisms. Based on the hypothesis that CO2-water mixtures alter the integrity of rock structure by attacking cements rather than grains, we attempt to explain the degradation of cementation due to long-term contact with CO2 and water and mechanisms for changes in rock mechanical properties. Many sandstones, including calcite-cemented quartzitic sandstone, chlorite-cemented quartzitic sandstone, and hematite-cemented quartzitic sandstone, contain interparticle cements that are more readily affected by CO2-water mixtures than grains. A model that couples the discrete element method and the bonded-particle model is used to perform simulations of indentation tests on synthetic rocks with crystal and random packings. The model is verified against the analytical cavity expansion model and validated against laboratory indentation tests on Entrada sandstone with and without CO2 alteration. Sensitivity analysis is performed for cementation microscopic parameters including stiffness, size, axial, and shear strength. The simulation results indicate that the CO2-related degradation of mechanical properties in bleached Entrada sandstone can be attributed to the reduction of cement size rather than cement strength. Our study indicates that it is possible to describe the CO2-related rock alteration through particle-scale mechanisms.
Probing the Core-Collapse Supernova Mechanism with Gravitational Waves
Ott, C D
2009-01-01
The mechanism of core-collapse supernova explosions must draw on the energy provided by gravitational collapse and transfer the necessary fraction to the kinetic and internal energy of the ejecta. Despite many decades of concerted theoretical effort, the detailed mechanism of core-collapse supernova explosions is still unknown, but indications are strong that multi-D processes lie at its heart. This opens up the possibility of probing the supernova mechanism with gravitational waves, carrying direct dynamical information from the supernova engine deep inside a dying massive star. I present a concise overview of the physics and primary multi-D dynamics in neutrino-driven, magnetorotational, and acoustically-driven core-collapse supernova explosion scenarios. Discussing and contrasting estimates for the gravitational-wave emission characteristics of these mechanisms, I argue that their gravitational-wave signatures are clearly distinct and that the observation (or non-observation) of gravitational waves from a ...
Zhu, P. Y.
1991-01-01
The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.
L2 discretization of Sturmian wave functions for Coulomb-like potentials
Frapiccini, A. L.; Gonzalez, V. Y.; Randazzo, J. M.; Colavecchia, F. D.; Gasaneo, G.
In this work we introduce a method to construct Sturmian functions for general interaction potentials in two-body problems. We expand these Sturmians on a finite L2 space, using N Laguerre basis functions to obtain a discrete set of eigenvalues for positive and negative energies. Orthogonality and closure relations are thus rewritten for these expansions; completeness is achieved through increasing the basis size. We apply the method to the Coulomb and Herman and Skillman potential. We study the behavior of the functions obtained and their convergence for an overall range of energies. The Sturmian functions are applied to solve the Schrödinger equation for an active electron in a He-like system.
Institute of Scientific and Technical Information of China (English)
AN Xi-Zhong
2007-01-01
The crystallization, corresponding to the fcc structure (with packing density p ≈ 0.74), of smooth equal hard spheres under batch-wised feeding and three-dimensional interval vibration is numerically obtained by using the discrete element method. The numerical experiment shows that the ordered packing can be realized by proper control of the dynamic parameters such as batch of each feeding § and vibration amplitude A. The radial distribution function and force network are used to characterize the ordered structure. The defect formed during vibrated packing is characterized as well The results in our work fill the gap of getting packing density between random close packing and fcc packing in phase diagram which provides an effective way of theoretically investigating the complex process and mechanism of hard sphere crystallization and its dynamics.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006 and tension development (adjusted Niederer, Hunter, Smith, 2006 model with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material. Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.
Cisneros, G Andrés; Piquemal, Jean-Philip; Darden, Thomas A
2006-07-20
A quantum mechanics/molecular mechanics (QM/MM) implementation that uses the Gaussian electrostatic model (GEM) as the MM force field is presented. GEM relies on the reproduction of electronic density by using auxiliary basis sets to calculate each component of the intermolecular interaction. This hybrid method has been used, along with a conventional QM/MM (point charges) method, to determine the polarization on the QM subsystem by the MM environment in QM/MM calculations on 10 individual H(2)O dimers and a Mg(2+)-H(2)O dimer. We observe that GEM gives the correct polarization response in cases when the MM fragment has a small charge, while the point charges produce significant over-polarization of the QM subsystem and in several cases present an opposite sign for the polarization contribution. In the case when a large charge is located in the MM subsystem, for example, the Mg(2+) ion, the opposite is observed at small distances. However, this is overcome by the use of a damped Hermite charge, which provides the correct polarization response.
Celestial Mechanics, Conformal Structures, and Gravitational Waves
Duval, C; Horvathy, P
1991-01-01
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and L\\'evy-Leblond). At the quantum level, the $N$-body Schr\\"odinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time indep...
Cellular mechanisms underlying spatiotemporal features of cholinergic retinal waves
Ford, Kevin J.; Félix, Aude L.; Feller, Marla B.
2012-01-01
Prior to vision, a transient network of recurrently connected cholinergic interneurons, called starburst amacrine cells (SACs), generates spontaneous retinal waves. Despite an absence of robust inhibition, cholinergic retinal waves initiate infrequently and propagate within finite boundaries. Here we combine a variety of electrophysiological and imaging techniques and computational modeling to elucidate the mechanisms underlying these spatial and temporal properties of waves in developing mouse retina. Waves initiate via rare spontaneous depolarizations of SACs. Waves propagate through recurrent cholinergic connections between SACs and volume release of ACh as demonstrated using paired recordings and a cell-based ACh optical sensor. Perforated patch recordings and two-photon calcium imaging reveal that individual SACs have slow afterhyperpolarizations that induce SACs to have variable depolarizations during sequential waves. Using a computational model in which the properties of SACs are based on these physiological measurements, we reproduce the slow frequency, speed, and finite size of recorded waves. This study represents a detailed description of the circuit that mediates cholinergic retinal waves and indicates that variability of the interneurons that generate this network activity may be critical for the robustness of waves across different species and stages of development. PMID:22262883
Sub-discretized surface model with application to contact mechanics in multi-body simulation
Energy Technology Data Exchange (ETDEWEB)
Johnson, S; Williams, J
2008-02-28
The mechanics of contact between rough and imperfectly spherical adhesive powder grains are often complicated by a variety of factors, including several which vary over sub-grain length scales. These include several traction factors that vary spatially over the surface of the individual grains, including high energy electron and acceptor sites (electrostatic), hydrophobic and hydrophilic sites (electrostatic and capillary), surface energy (general adhesion), geometry (van der Waals and mechanical), and elasto-plastic deformation (mechanical). For mechanical deformation and reaction, coupled motions, such as twisting with bending and sliding, as well as surface roughness add an asymmetry to the contact force which invalidates assumptions for popular models of contact, such as the Hertzian and its derivatives, for the non-adhesive case, and the JKR and DMT models for adhesive contacts. Though several contact laws have been offered to ameliorate these drawbacks, they are often constrained to particular loading paths (most often normal loading) and are relatively complicated for computational implementation. This paper offers a simple and general computational method for augmenting contact law predictions in multi-body simulations through characterization of the contact surfaces using a hierarchically-defined surface sub-discretization. For the case of adhesive contact between powder grains in low stress regimes, this technique can allow a variety of existing contact laws to be resolved across scales, allowing for moments and torques about the contact area as well as normal and tangential tractions to be resolved. This is especially useful for multi-body simulation applications where the modeler desires statistical distributions and calibration for parameters in contact laws commonly used for resolving near-surface contact mechanics. The approach is verified against analytical results for the case of rough, elastic spheres.
Tuning Acoustic Wave Properties by Mechanical Resonators on a Surface
DEFF Research Database (Denmark)
Dühring, Maria Bayard; Laude, Vincent; Khelif, Abdelkrim
Vibrations generated by high aspects ratio electrodes are studied by the finite element method. It is found that the modes are combined of a surface wave and vibration in the electrodes. For increasing aspect ratio most of the mechanical energy is confined to the electrodes which act as mechanical...
Nonlinear wave mechanics from classical dynamics and scale covariance
Energy Technology Data Exchange (ETDEWEB)
Hammad, F. [Departement TC-SETI, Universite A.Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2007-10-29
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.
Radiation losses and dark mode for spin-wave propagation through a discrete magnetic micro-waveguide
Barabanenkov, Yuri; Osokin, Sergey; Kalyabin, Dmitry; Nikitov, Sergey
2016-11-01
This paper presents the quantum mechanical type T -scattering operator approach to studying the forward volume magnetostatic spin-wave multiple scattering by a finite ensemble of cylindrical magnetic inclusions in a ferromagnetic thin film. The approach is applied to the problem of spin-wave excitation transfer along a linear chain of inclusions. The substantial results are deriving the optical theorem for the T -scattering operator and, as a consequence, deriving a formula for collective extinction cross section of inclusion ensemble, where only the first inclusion of the chain is irradiated by an incident narrow spin-wave beam. From this formula it can be shown that only irradiated inclusion makes a direct contribution in the collective extinction cross section of the total number of inclusions. In this case the direct summarized contribution of all the other inclusions from the chain into the spin-wave scattering is invisible; we call such phenomenon the dark mode. Applying a one-multipole and closest neighbor coupling approximation, we reveal a regime of distant resonant transfer for spin-wave excitation along the linear chain of an essentially big but finite number of particles with the dark mode. Because we also found a resonant mechanism of filtering this mode from radiation losses, the revealed regime shows that at resonant conditions the linear chain of magnetic inclusions can play the role of a spin-wave micro-waveguide, which transfers a signal over a big distance in a form of the dark mode, where the controllable level of radiation losses can tend to reach nearly zero values.
Wind-wave amplification mechanisms: possible models for steep wave events in finite depth
Directory of Open Access Journals (Sweden)
P. Montalvo
2013-11-01
Full Text Available We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.
Yamgoué, Serge Bruno; Pelap, François Beceau
2016-05-01
We revisit the derivation of the equation modeling envelope waves in a discrete nonlinear electrical transmission line (NLTL) considered a few years back in Physics Letters A 373 (2009) 3801-3809. Using a combination of rotating wave approximation and the Gardner-Morikawa transformation, we show that the modulated waves are described by a new type of extended nonlinear Schrödinger equation. In addition the expressions of several coefficients of this equation are found to be strongly different from those given earlier. As a consequence, key relationships between these coefficients that sustained the previous analysis are broken.
Calantoni, Joseph; Holland, K Todd; Drake, Thomas G
2004-09-15
Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.
Extensional Elastica in large deformation as $Gamma $ Γ -limit of a discrete 1D mechanical system
Alibert, Jean-Jacques; Della Corte, Alessandro; Giorgio, Ivan; Battista, Antonio
2017-04-01
The present paper deals with the rigorous homogenization of a discrete system consisting of extensible rods linked by rotational springs. Specifically, a Γ -convergence result is proven for a sequence of discrete measure functionals En, describing the energy of the discrete system, toward the continuous energy functional for the extensible Euler beam model ( Elastica) in large deformation regime. A relative compactness result for the sequence En is also proven. Moreover, numerical results are shown on the deformed shape and on the total energy of the system when the number of elements of the discrete system increases. The numerical convergence of the energy to a definite value is shown in two cases. The results provide rigorous justification of a very commonly used algorithm for the discretization of the extensible Euler beam, namely Hencky-type beam model.
Enhancement of sleep slow waves: underlying mechanisms and practical consequences.
Directory of Open Access Journals (Sweden)
Michele eBellesi
2014-10-01
Full Text Available Even modest sleep restriction, especially the loss of sleep slow wave activity, is invariably associated with slower EEG activity during wake, the occurrence of local sleep in an otherwise awake brain, and impaired performance due to cognitive and memory deficits. Recent studies not only confirm the beneficial role of sleep in memory consolidation, but also point to a specific role for sleep slow waves. Thus, the implementation of methods to enhance sleep slow waves without unwanted arousals or lightening of sleep could have significant practical implications. Here we first review the evidence that it is possible to enhance sleep slow waves in humans using transcranial direct-current stimulation and transcranial magnetic stimulation. Since these methods are currently impractical and their safety is questionable, especially for chronic long-term exposure, we then discuss novel data suggesting that it is possible to enhance slow waves using sensory stimuli. We consider the physiology of the K-complex, a peripheral evoked slow wave, and show that, among different sensory modalities, acoustic stimulation is the most effective in increasing the magnitude of slow waves, likely through the activation of non-lemniscal ascending pathways to the thalamo-cortical system. In addition, we discuss how intensity and frequency of the acoustic stimuli, as well as exact timing and pattern of stimulation, affect sleep enhancement. Finally, we discuss automated algorithms that read the EEG and, in real-time, adjust the stimulation parameters in a closed-loop manner to obtain an increase in sleep slow waves and avoid undesirable arousals. In conclusion, while discussing the mechanisms that underlie the generation of sleep slow waves, we review the converging evidence showing that acoustic stimulation is safe and represents an ideal tool for slow wave sleep enhancement.
Enhancement of sleep slow waves: underlying mechanisms and practical consequences.
Bellesi, Michele; Riedner, Brady A; Garcia-Molina, Gary N; Cirelli, Chiara; Tononi, Giulio
2014-01-01
Even modest sleep restriction, especially the loss of sleep slow wave activity (SWA), is invariably associated with slower electroencephalogram (EEG) activity during wake, the occurrence of local sleep in an otherwise awake brain, and impaired performance due to cognitive and memory deficits. Recent studies not only confirm the beneficial role of sleep in memory consolidation, but also point to a specific role for sleep slow waves. Thus, the implementation of methods to enhance sleep slow waves without unwanted arousals or lightening of sleep could have significant practical implications. Here we first review the evidence that it is possible to enhance sleep slow waves in humans using transcranial direct-current stimulation (tDCS) and transcranial magnetic stimulation. Since these methods are currently impractical and their safety is questionable, especially for chronic long-term exposure, we then discuss novel data suggesting that it is possible to enhance slow waves using sensory stimuli. We consider the physiology of the K-complex (KC), a peripheral evoked slow wave, and show that, among different sensory modalities, acoustic stimulation is the most effective in increasing the magnitude of slow waves, likely through the activation of non-lemniscal ascending pathways to the thalamo-cortical system. In addition, we discuss how intensity and frequency of the acoustic stimuli, as well as exact timing and pattern of stimulation, affect sleep enhancement. Finally, we discuss automated algorithms that read the EEG and, in real-time, adjust the stimulation parameters in a closed-loop manner to obtain an increase in sleep slow waves and avoid undesirable arousals. In conclusion, while discussing the mechanisms that underlie the generation of sleep slow waves, we review the converging evidence showing that acoustic stimulation is safe and represents an ideal tool for slow wave sleep (SWS) enhancement.
Waves and Oscillations A Prelude to Quantum Mechanics
Smith, Walter Fox
2010-01-01
Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and oscillations form the foundation for quantum mechanics. Once they have mastered these ideas in a classical context, students will be ready to focus on the challenging concepts of quantum mechanics when they encounter them, rather than struggling with techniques. This lively textbook gives a thorough grounding in complex exponentials and the key aspects of d
Understanding the mechanisms of sickle cell disease by simulations with a discrete particle model
Hui, Katrina; Lin, Guang; Pan, Wenxiao
2013-01-01
Sickle cell disease (SCD) is an inherited blood disorder characterized by rigid, sickle-shaped red blood cells (RBCs). Because of their rigidity and shape, sickle cells can get stuck in smaller blood vessels, causing blockages and depriving oxygen to tissues. This study develops and applies mathematical models to better understand the mechanism of SCD. Two-dimensional models of RBCs and blood vessels have been constructed by representing them as discrete particles interacting with different forces. The nonlinear, elastic property of healthy RBCs could be adequately reproduced using a cosine angle bending force and a worm-like chain spring force. With the ability to deform, RBCs can squeeze through narrow blood vessels. In modeling sickle cells as rigid bodies and applying repelling and friction forces from the blood vessel, this study shows that geometrical factors (dimensions of the sickle cell and blood vessels) as well as rigidity and adhesiveness of the sickle cell all play an important role in determining how, and if, sickle cells become trapped within narrow blood capillaries. With lack of data to validate the model, this study primarily provides a sensitivity analysis of factors influencing sickle cell occlusion and identified critical data to support future modeling.
Payton, John L; Morton, Seth M; Moore, Justin E; Jensen, Lasse
2012-06-07
We have derived and implemented analytical gradients for the discrete interaction model/quantum mechanics (DIM/QM) method. DIM/QM combines an atomistic electrodynamics model with time-dependent density functional theory and thus enables modeling of the optical properties for a molecule while taking into account the local environment of a nanoparticle's surface. The DIM/QM analytical gradients allow for geometry optimizations, vibrational frequencies, and Raman spectra to be simulated for molecules interacting with metal nanoparticles. We have simulated the surface-enhanced Raman scattering (SERS) spectra for pyridine adsorbed on different sites of icosahedral nanoparticles with diameters between 1 and 8 nm. To describe the adsorption of the pyridine molecule onto the metal surface, we have implemented a coordination-dependent force field to differentiate the various local surface environments. We find that the DIM/QM method predicts geometries and frequencies that are in good agreement with full QM simulations and experiments. For the simulated SERS spectra of pyridine, we find a significant dependence on the adsorption site and the size of the metal nanoparticle. This illustrates the importance of accounting for the local environment around the molecule. The Raman enhancement factors are shown to roughly mirror the magnitude of the nanoparticle's local field about the molecule. Because the simulated nanoparticles are small, the plasmon peaks are quite broad which results in weak local electric fields and thus modest Raman enhancement factors.
STATISTICAL MECHANICS IN A DISCRETE SPACE-TIME. THERMODYNAMICS AND TIME-IRREVERSIBILITY
Directory of Open Access Journals (Sweden)
J.P.Badiali
2003-01-01
Full Text Available The introduction of a discrete space-time represents an attempt to describe the physics at the Planck's scale. We show that this concept can be also very useful in describing thermodynamics in a pre-relativistic world. From this concept a new approach of statistical mechanics based on a dynamic viewpoint and an entropy representation is presented. The entropy is connected with the counting of the paths in space-time. It contains a time interval that represents the time that we have to wait in order to relax the quantum fluctuations and to reach the thermal regime. It is shown that this time is β hbar. The mathematical expressions we derive for thermal quantities like the entropy and the free energy are identical to those obtained by the traditional path-integral formalism starting from the canonical form of the thermal density matrix. However, the introduction of a quantized space-time shows that thermodynamics is consistent with an equation of motion that is time-irreversible at a microscopic level. As a consequence, the problem of irreversibility is revisited and the derivation of a H-theorem becomes possible in the future.
Chesnais, Céline; Boutin, Claude; Hans, Stéphane
2012-10-01
This work is devoted to the study of the wave propagation in infinite two-dimensional structures made up of the periodic repetition of frames. Such materials are highly anisotropic and, because of lack of bracing, can present a large contrast between the shear and compression deformabilities. Moreover, when the thickness to length ratio of the frame elements is small, these elements can resonate in bending at low frequencies when compressional waves propagate in the structure. The frame size being small compared to the wavelength of the compressional waves, the homogenization method of periodic discrete media is extended to situations with local resonance, and it is applied to identify the macroscopic behavior at the leading order. In particular, the local resonance in bending leads to an effective mass different from the real mass and to the generalization of the Newtonian mechanics at the macroscopic scale. Consequently, compressional waves become dispersive and frequency bandgaps occur. The physical origin of these phenomena at the microscopic scale is also presented. Finally, a method is proposed for the design of such materials.
On the cascade mechanism of short surface wave modulation
Directory of Open Access Journals (Sweden)
M. Charnotskii
2002-01-01
Full Text Available Modulation of short surface ripples by long surface or internal waves by a cascade mechanism is considered. At the first stage, the orbital velocity of the long wave (LW adiabatically modulates an intermediate length nonlinear gravity wave (GW, which generates a bound (parasitic capillary wave (CW near its crest in a wide spatial frequency band. Due to strong dependence of the CW amplitude on that of the GW, the resulting ripple modulation by LW can be strong. Adiabatic modulation at the first stage is calculated for an arbitrarily strong LW current. The CWs are calculated based on the Lonquet-Higgins theory, in the framework of a steady periodic solution, which proves to be sufficient for the cases considered. Theoretical results are compared with data from laboratory experiments. A discussion of related sea clutter data is given in the conclusion.
"Slowing" Mechanical Waves with a Consumer-Type High-Speed Digital Camera
Ng, Pun-hon; Chan, Kin-lok
2015-01-01
In most secondary physics textbooks, waves are first introduced with examples of mechanical waves because they can be illustrated by drawings and photographs. However, these illustrations are static and cannot reflect the dynamic nature of waves. Although many mechanical waves (e.g. water waves and vibrating strings) can be easily shown using…
"Slowing" Mechanical Waves with a Consumer-Type High-Speed Digital Camera
Ng, Pun-hon; Chan, Kin-lok
2015-01-01
In most secondary physics textbooks, waves are first introduced with examples of mechanical waves because they can be illustrated by drawings and photographs. However, these illustrations are static and cannot reflect the dynamic nature of waves. Although many mechanical waves (e.g. water waves and vibrating strings) can be easily shown using…
A possible mechanism of current in medium under electromagnetic wave
Institute of Scientific and Technical Information of China (English)
Zhang Tao
2006-01-01
In this paper a possible mechanism of current in medium is presented. Comparison between this current and the magnetization current was made. Expression for this current was derived. This work is helpful to understanding the interaction between medium and electromagnetic wave.
Extremely stable piezo mechanisms for the New Gravitational Wave Observatory
Pijnenburg, J.A.C.M.; Rijnveld, N.; Hogenhuis, H.
2012-01-01
Detection and observation of gravitational waves requires extreme stability in the frequency range 3e-5 Hz to 1 Hz. NGO/LISA will attain this by creating a giant interferometer in space, based on free floating proof masses in three spacecrafts. To operate NGO/LISA, the following piezo mechanisms are
Schrödinger and the genesis of wave mechanics
Renn, J.
2013-01-01
In the context of a new analysis of the notebooks of Erwin Schrödinger, the paper deals with the question of the relation between Schrödinger's creation of wave mechanics and the contemporary efforts by Werner Heisenberg and his colleagues to establish a new quantum mechanics. How can one explain, from a broader historical and epistemological perspective, the astonishing simultaneity and complementarity of these discoveries? The paper argues that neither the physical problems with which both ...
Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2016-06-01
Full Text Available An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.
Lecture Notes for the Course in Water Wave Mechanics
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Frigaard, Peter; Burcharth, Hans F.
The present notes are written for the course in water wave mechanics given on the 7th semester of the education in civil engineering at Aalborg University. The prerequisites for the course are the course in fluid dynamics also given on the 7th semester and some basic mathematical and physical...... knowledge. The course is at the same time an introduction to the course in coastal hydraulics on the 8th semester. The notes cover the first four lectures of the course: • Definitions. Governing equations and boundary conditions. • Derivation of velocity potential for linear waves. Dispersion relationship...
Lecture Notes for the Course in Water Wave Mechanics
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Frigaard, Peter
The present notes are written for the course in water wave mechanics given on the 7th semester of the education in civil engineering at Aalborg University. The prerequisites for the course are the course in fluid dynamics also given on the 7th semester and some basic mathematical and physical...... knowledge. The course is at the same time an introduction to the course in coastal hydraulics on the 8th semester. The notes cover the following five lectures: 1. Definitions. Governing equations and boundary conditions. Derivation of velocity potential for linear waves. Dispersion relationship. 2. Particle...
Wave mechanics in quantum phase space: hydrogen atom
Institute of Scientific and Technical Information of China (English)
LU Jun
2007-01-01
The rigorous sohutions of the stationary Schr(o)dinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like"projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.
Mechanism of an acoustic wave impact on steel during solidification
Directory of Open Access Journals (Sweden)
K. Nowacki
2013-04-01
Full Text Available Acoustic steel processing in an ingot mould may be the final stage in the process of quality improvement of a steel ingot. The impact of radiation and cavitation pressure as well as the phenomena related to the acoustic wave being emitted and delivered to liquid steel affect various aspects including the internal structure fragmentation, rigidity or density of steel. The article provides an analysis of the mechanism of impact of physical phenomena caused by an acoustic wave affecting the quality of a steel ingot.
Monteiro, André O.
2013-09-25
The mechanical response to a uniaxial compressive force of a single carbon nanotube (CNT) filled (or partially-filled) with ZnS has been modelled. A semi-empirical approach based on the finite element method was used whereby modelling outcomes were closely matched to experimental observations. This is the first example of the use of the continuum approach to model the mechanical behaviour of discrete filled CNTs. In contrast to more computationally demanding methods such as density functional theory or molecular dynamics, our approach provides a viable and expedite alternative to model the mechanics of filled multi-walled CNTs. © 2013 Springer Science+Business Media New York.
The wave function essays on the metaphysics of quantum mechanics
Albert, David Z
2013-01-01
This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.
Dynamics of mechanical waves in periodic graphene nanoribbon assemblies
Directory of Open Access Journals (Sweden)
Chowdhury Rajib
2011-01-01
Full Text Available Abstract We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs of the type (8,0 and (0,8 using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length. We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures. PACS 62.23.Kn · 62.25.Fg · 62.25.Jk
Spectral Theory for Dissipation Mechanism of Wind Waves
Polnikov, Vladislav G
2010-01-01
A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind waves is provided by the viscosity due to interaction between wave motions and turbulence of the water upper layer. The latter, in turn, is supposed to be induced by the whole aggregate of dissipation processes taking place at the air-sea interface. In the frame of phenomenological constructions of nonlinear closure for Reynolds stresses, it is shown that the dissipation function is generally a power series with respect to wave spectrum, starting from a quadratic term. Attracting previous results of the author, a simplified parameterization of the general theoretical result is done. Physical meaning for parameters of the dissipation function and its compliance with the new experimental facts established in this field for the last 5-10 years is discussed. Summarized theoreti...
Study of the Internal Mechanical response of an asphalt mixture by 3-D Discrete Element Modeling
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Hofko, Bernhard
2015-01-01
In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties for ...
Cosmic Tsunamis in Modified Gravity: Scalar waves disrupting screening mechanisms
Hagala, R; Mota, D F
2016-01-01
Extending General Relativity by adding extra degrees of freedom is a popular approach to explain the accelerated expansion of the universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test General Relativity in a wide range of scales. The viability of a given modified theory of gravity therefore strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of the screening mechanisms, thereby spoiling the viability of modified gravity theories. Specifically, we show that the waves produced can increase the amplitude of the fifth force and the Parametrized Post Newtonian parameters by several orders of magnitude.
Transferring Data from Smartwatch to Smartphone through Mechanical Wave Propagation.
Kim, Seung-Chan; Lim, Soo-Chul
2015-08-28
Inspired by the mechanisms of bone conduction transmission, we present a novel sensor and actuation system that enables a smartwatch to securely communicate with a peripheral touch device, such as a smartphone. Our system regards hand structures as a mechanical waveguide that transmits particular signals through mechanical waves. As a signal, we used high-frequency vibrations (18.0-20.0 kHz) so that users cannot sense the signals either tactually or audibly. To this end, we adopted a commercial surface transducer, which is originally developed as a bone-conduction actuator, for mechanical signal generation. At the receiver side, a piezoelement was adopted for picking up the transferred mechanical signals. Experimental results have shown that the proposed system can successfully transfer data using mechanical waves. We also validate dual-frequency actuations under which high-frequency signals (18.0-20.0 kHz) are generated along with low-frequency (up to 250 Hz) haptic vibrations. The proposed method has advantages in terms of security in that it does not reveal the signals outside the body, meaning that it is not possible for attackers to eavesdrop on the signals. To further illustrate the possible application spaces, we conclude with explorations of the proposed approach.
Transferring Data from Smartwatch to Smartphone through Mechanical Wave Propagation
Directory of Open Access Journals (Sweden)
Seung-Chan Kim
2015-08-01
Full Text Available Inspired by the mechanisms of bone conduction transmission, we present a novel sensor and actuation system that enables a smartwatch to securely communicate with a peripheral touch device, such as a smartphone. Our system regards hand structures as a mechanical waveguide that transmits particular signals through mechanical waves. As a signal, we used high-frequency vibrations (18.0–20.0 kHz so that users cannot sense the signals either tactually or audibly. To this end, we adopted a commercial surface transducer, which is originally developed as a bone-conduction actuator, for mechanical signal generation. At the receiver side, a piezoelement was adopted for picking up the transferred mechanical signals. Experimental results have shown that the proposed system can successfully transfer data using mechanical waves. We also validate dual-frequency actuations under which high-frequency signals (18.0–20.0 kHz are generated along with low-frequency (up to 250 Hz haptic vibrations. The proposed method has advantages in terms of security in that it does not reveal the signals outside the body, meaning that it is not possible for attackers to eavesdrop on the signals. To further illustrate the possible application spaces, we conclude with explorations of the proposed approach.
Surface Catalytic Mechanism in Square-Wave Voltammetry
Mirceski, Valentin; Gulaboski, Rubin
2001-01-01
A pseudo-first-order catalytic mechanism in which both reactant and product of the redox reaction are strongly immobilized on the electrode surface is theoretically analyzed under conditions of square-wave voltammetry (SWV). A mathematical procedure is developed for diffusionless conditions. The relationships between the properties of the voltammetric response and both the kinetic parameters of the redox reaction and the parameters of the excitement signal are studied. The phenomenon...
Wave dynamics and composite mechanics for microstructured materials and metamaterials
2017-01-01
This volume deals with topical problems concerning technology and design in construction of modern metamaterials. The authors construct the models of mechanical, electromechanical and acoustical behavior of the metamaterials, which are founded upon mechanisms existing on micro-level in interaction of elementary structures of the material. The empiric observations on the phenomenological level are used to test the created models. The book provides solutions, based on fundamental methods and models using the theory of wave propagation, nonlinear theories and composite mechanics for media with micro- and nanostructure. They include the models containing arrays of cracks, defects, with presence of micro- and nanosize piezoelectric elements and coupled physical-mechanical fields of different nature. The investigations show that the analytical, numerical and experimental methods permit evaluation of the qualitative and quantitative properties of the materials of this sort, with diagnosis of their effective characte...
DEFF Research Database (Denmark)
Hu, Hao; Peucheret, Christophe; Pu, Minhao;
2012-01-01
We have demonstrated wavelength conversion over 468 nm based on discrete bands phase matching in a silicon nanowire. CW light is converted from 1258 nm to 1726 nm with a CW pump at 1455 nm.......We have demonstrated wavelength conversion over 468 nm based on discrete bands phase matching in a silicon nanowire. CW light is converted from 1258 nm to 1726 nm with a CW pump at 1455 nm....
Mean flow generation mechanism by inertial waves and normal modes
Will, Andreas; Ghasemi, Abouzar
2016-04-01
The mean flow generation mechanism by nonlinearity of the inertial normal modes and inertial wave beams in a rotating annular cavity with longitudinally librating walls in stable regime is discussed. Inertial normal modes (standing waves) are excited when libration frequency matches eigenfrequencies of the system. Inertial wave beams are produced by Ekman pumping and suction in a rotating cylinder and form periodic orbits or periodic ray trajectories at selected frequencies. Inertial wave beams emerge as concentrated shear layers in a librating annular cavity, while normal modes appear as global recirculation cells. Both (inertial wave beam and mode) are helical and thus intrinsically non-linear flow structures. No second mode or wave is necessary for non-linearity. We considered the low order normal modes (1,1), (2,1) and (2,2) which are expected to be excited in the planetary objects and investigate the mean flow generation mechanism using two independent solutions: 1) analytical solution (Borcia 2012) and 2) the wave component of the flow (ω0 component) obtained from the direct numerical simulation (DNS). It is well known that a retrograde bulk mean flow is generated by the Ekman boundary layer and E1/4-Stewartson layer close to the outer cylinder side wall due to libration. At and around the normal mode resonant frequencies we found additionally a prograde azimuthal mean flow (Inertial Normal Mode Mean Flow: INMMF) in the bulk of the fluid. The fluid in the bulk is in geostrophic balance in the absence of the inertial normal modes. However, when INMMF is excited, we found that the geostrophic balance does not hold in the region occupied by INMMF. We hypothesize that INMMF is generated by the nonlinearity of the normal modes or by second order effects. Expanding the velocity {V}(u_r,u_θ,u_z) and pressure (p) in a power series in ɛ (libration amplitude), the Navier-Stokes equations are segregated into the linear and nonlinear parts at orders ɛ1 and ɛ^2
Bayly, Philip V; Wilson, Kate S
2014-10-07
The motion of flagella and cilia arises from the coordinated activity of dynein motor protein molecules arrayed along microtubule doublets that span the length of axoneme (the flagellar cytoskeleton). Dynein activity causes relative sliding between the doublets, which generates propulsive bending of the flagellum. The mechanism of dynein coordination remains incompletely understood, although it has been the focus of many studies, both theoretical and experimental. In one leading hypothesis, known as the geometric clutch (GC) model, local dynein activity is thought to be controlled by interdoublet separation. The GC model has been implemented as a numerical simulation in which the behavior of a discrete set of rigid links in viscous fluid, driven by active elements, was approximated using a simplified time-marching scheme. A continuum mechanical model and associated partial differential equations of the GC model have remained lacking. Such equations would provide insight into the underlying biophysics, enable mathematical analysis of the behavior, and facilitate rigorous comparison to other models. In this article, the equations of motion for the flagellum and its doublets are derived from mechanical equilibrium principles and simple constitutive models. These equations are analyzed to reveal mechanisms of wave propagation and instability in the GC model. With parameter values in the range expected for Chlamydomonas flagella, solutions to the fully nonlinear equations closely resemble observed waveforms. These results support the ability of the GC hypothesis to explain dynein coordination in flagella and provide a mathematical foundation for comparison to other leading models.
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2017-04-01
In this study, a numerical manifold method (NMM) model was developed for fully coupled analysis of hydro-mechanical (HM) processes in porous rock masses with discrete fractures. Using an NMM two-cover-mesh system of mathematical and physical covers, fractures are conveniently discretized by dividing the mathematical cover along fracture traces to physical cover, resulting in a discontinuous model on a non-conforming mesh. In this model, discrete fracture deformation (e.g. open and slip) and fracture fluid flow within a permeable and deformable porous rock matrix are rigorously considered. For porous rock, direct pore-volume coupling was modeled based on an energy-work scheme. For mechanical analysis of fractures, a fracture constitutive model for mechanically open states was introduced. For fluid flow in fractures, both along-fracture and normal-to-fracture fluid flow are modeled without introducing additional degrees of freedom. When the mechanical aperture of a fracture is changing, its hydraulic aperture and hydraulic conductivity is updated. At the same time, under the effect of coupled deformation and fluid flow, the contact state may dynamically change, and the corresponding contact constraint is updated each time step. Therefore, indirect coupling is realized under stringent considerations of coupled HM effects and fracture constitutive behavior transfer dynamically. To verify the new model, examples involving deformable porous media containing a single and two sets of fractures were designed, showing good accuracy. Last, the model was applied to analyze coupled HM behavior of fractured porous rock domains with complex fracture networks under effects of loading and injection.
Mechanically robust microfluidics and bulk wave acoustics to sort microparticles
Dauson, Erin R.; Gregory, Kelvin B.; Greve, David W.; Healy, Gregory P.; Oppenheim, Irving J.
2016-04-01
Sorting microparticles (or cells, or bacteria) is significant for scientific, medical and industrial purposes. Research groups have used lithium niobate SAW devices to produce standing waves, and then to align microparticles at the node lines in polydimethylsiloxane (PDMS, silicone) microfluidic channels. The "tilted angle" (skewed) configuration is a recent breakthrough producing particle trajectories that cross multiple node lines, making it practical to sort particles. However, lithium niobate wafers and PDMS microfluidic channels are not mechanically robust. We demonstrate "tilted angle" microparticle sorting in novel devices that are robust, rapidly prototyped, and manufacturable. We form our microfluidic system in a rigid polymethyl methacrylate (PMMA, acrylic) prism, sandwiched by lead-zirconium-titanate (PZT) wafers, operating in through-thickness mode with inertial backing, that produce standing bulk waves. The overall configuration is compact and mechanically robust, and actuating PZT wafers in through-thickness mode is highly efficient. Moving to this novel configuration introduced new acoustics questions involving internal reflections, but we show experimental images confirming the intended nodal geometry. Microparticles in "tilted angle" devices display undulating trajectories, where deviation from the straight path increases with particle diameter and with excitation voltage to create the mechanism by which particles are sorted. We show a simplified analytical model by which a "phase space" is constructed to characterize effective particle sorting, and we compare our experimental data to the predictions from that simplified model; precise correlation is not expected and is not observed, but the important physical trends from the model are paralleled in the measured particle trajectories.
Draine, B. T.; Goodman, Jeremy
1993-01-01
We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.
Erwin Schrödinger and Quantum Wave Mechanics
Directory of Open Access Journals (Sweden)
John J. O'Connor
2017-08-01
Full Text Available The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world. Quanta 2017; 6: 48–52.
Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals
Chaunsali, Rajesh; Li, Feng; Yang, Jinkyu
2016-08-01
We present an active, purely mechanical stress wave isolator that consists of short cylindrical particles arranged in a helical architecture. This phononic structure allows us to change inter-particle stiffness dynamically by controlling the contact angles of the cylinders. We use torsional travelling waves to control the contact angles, thereby imposing a desired spatio-temporal stiffness variation to the phononic crystal along the longitudinal direction. Such torsional excitation is a form of parametric pumping in the system, which results in the breakage of the time-reversal symmetry. We report that, in quasi-static sense, the system shows topologically non-trivial band-gaps. However, in a dynamic regime where the pumping effect is significant, these band-gaps become asymmetric with respect to the frequency and wavenumber domains in the dispersion relationship. By using numerical simulations, we show that such asymmetry has a direct correspondence to the topological invariant, i.e., Chern number, of the system. We propose that this asymmetry, accompanied by selective inter-band transition, can be utilized for directional isolation of the stress wave propagating along the phononic crystal.
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.
Contribution of ultrasonic traveling wave to chemical-mechanical polishing.
Li, Liang; He, Qing; Zheng, Mian; Liu, Zheng
2015-02-01
The ultrasonic vibrators are introduced into the chemical-mechanical polishing devices, and in this polishing system, the ultrasonic vibrators generate ultrasonic traveling wave and keep coaxial with the polished silicon wafer rotating at given speed so as to compare the texture of the polished silicon wafers. And the experiments on the chemical-mechanical polishing with assisted ultrasonic vibration are accomplished in order to investigate the effect of the ultrasonic vibration on the chemical-mechanical polishing. Via comparing the roughness average of the two silicon wafers polished with assisted ultrasonic vibration and without assisted vibration, it is found that the morphology of the silicon wafer polished with assisted vibration is superior to that without assisted vibration, that is, this series of experiments indicate that the ultrasonic vibration is beneficial to the chemical-mechanical polishing. Aiming at understanding the contribution of the ultrasonic vibration to chemical-mechanical polishing in detail, the model of the chemical-mechanical polishing with the assisted ultrasonic vibration is built up, which establishes the relationship of the removal rate and the polishing variables such as the rotary speed of silicon wafers, the amplitude and the frequency of vibrators, the particle density of polishing slurry and the characteristics of polishing pad etc. This model not only could be used to explain the experimental results but also to illuminate the roles played by the polishing variables.
Directory of Open Access Journals (Sweden)
Chernchok Soankwan
2011-07-01
Full Text Available We recently developed a multiple-choice conceptual survey in mechanical waves. The development, evaluation, and demonstration of the use of the survey were reported elsewhere [ A. Tongchai et al. Int. J. Sci. Educ. 31 2437 (2009]. We administered the survey to 902 students from seven different groups ranging from high school to second year university. As an outcome of that analysis we were able to identify several conceptual models which the students seemed to be using when answering the questions in the survey. In this paper we attempt to investigate the strength with which the students were committed to these conceptual models, as evidenced by the consistency with which they answered the questions. For this purpose we focus on the patterns of student responses to questions in one particular subtopic, wave propagation. This study has three main purposes: (1 to investigate the consistency of student conceptions, (2 to explore the relative usefulness of different analysis techniques, and (3 to determine what extra information a study of consistency can give about student understanding of basic concepts. We used two techniques: first, categorizing and counting, which is widely used in the science education community, and second, model analysis, recently introduced into physics education research. The manner in which categorizing and counting is used is very diverse while model analysis has been employed only in prescriptive ways. Research studies have reported that students often use their conceptual models inconsistently when solving a series of questions that test the same idea. Our results support their conclusions. Moreover, our findings suggest that students who have had more experiences in physics learning seem to use the scientifically accepted models more consistently. Further, the two analysis techniques have different advantages and disadvantages. Our findings show that model analysis can be used in more diverse ways, provides
Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.
2001-12-01
Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an n-th order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer polynomial transforms.
Institute of Scientific and Technical Information of China (English)
HOU Shuguang; ZHANG Dong; HUANG Xiaoming; ZHAO Yongli
2015-01-01
The micro-mechanical response of asphalt mixtures was studied using the discrete element method. The discrete element sample of stone mastic asphalt was generated first and the vehicle load was applied to the sample. A user-written program was coded with the FISH language in PFC3D to extract the contact forces within the sample and the displacements of the particles. Then, the contact forces within the whole sample, in asphalt mastic, in coarse aggregates and between asphalt mastic and coarse aggregates were investigated. Finally, the movement of the particles in the sample was analyzed. The sample was divided into 15 areas and a figure was drawn to show how the balls move in each area according to the displacements of the balls in each area. The displacements of asphalt mastic balls and coarse aggregates were also analyzed. The experimental results explain how the asphalt mixture bears vehicle load and the potential reasons why the rutting forms from a micro-mechanical view.
Vadyak, J.; Hoffman, J. D.; Bishop, A. R.
1978-01-01
The calculation procedure is based on the method of characteristics for steady three-dimensional flow. The bow shock wave and the internal shock wave system were computed using a discrete shock wave fitting procedure. The general structure of the computer program is discussed, and a brief description of each subroutine is given. All program input parameters are defined, and a brief discussion on interpretation of the output is provided. A number of sample cases, complete with data deck listings, are presented.
Mechanisms of Fluid-Mud Interactions Under Waves
2011-09-30
lutocline that occurred when the lutocline was within a few centimeters of the water surface. This three-wave instability led to generation of subharmonic ... Subharmonic standing waves on the surface of the lutocline, generated by a long surface wave train traveling from left to right in the figure...Superharmonic waves (hard to see) and the turbulent structures (middle left) within the subharmonic waves are also present. Theoretical modeling—We
Coupling Discrete and Continuum Mechanics in Low Concentration, Particle-Laden Flows
Boyle, Paul; Houchens, Brent; Kim, Albert
2008-11-01
The study of particle-laden flow plays a critical role in pressure-driven membrane filtration such as microfiltration (MF), ultrafiltration (UF), nanofiltration (NF), and reverse osmosis (RO). Hydrodynamic and inter-particle interactions, coupled to the ambient crossflow field, are well documented in literature. Transport of particles is originated due to Brownian and shear-induced diffusion, and convection due to the axial crossflow and transverse permeate flow. These effects are modeled using Hydrodynamic Force Bias Monte Carlo (HFBMC) simulations to predict the deposition of the particles on the membrane surface. In addition, the particles in the simulation are also subject to electrostatic double layer repulsion and van der Waals attraction both between particles and between the particles and membrane surfaces. In conjunction with the hydrodynamics, the change in particle potential determines the transition probability that a proposed, random move of a particle will be accepted. In the current study, these discrete particle effects at the microscopic level are coupled to the continuum flow via an apparent local viscosity, yielding a quasi-steady-state velocity profile. This velocity profile is dynamically updated in order to refine the hydrodynamic interactions. The resulting simulation predicts the formation of a cake layer of deposited interacting particles on the membrane surface.
A non-discrete method for computation of residence time in fluid mechanics simulations.
Esmaily-Moghadam, Mahdi; Hsia, Tain-Yen; Marsden, Alison L
2013-11-01
Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.
Elastodynamic metasurface: Depolarization of mechanical waves and time effects
Energy Technology Data Exchange (ETDEWEB)
Boutin, Claude, E-mail: claude.boutin@entpe.fr [Ecole Nationale des Travaux Publics de l' Etat, Université de Lyon, LGCB, UMR CNRS 5513, Vaulx-en-Velin (France); Schwan, Logan [Acoustics Research Center, University of Salford, Newton Building, Salford M5 4WT (United Kingdom); Dietz, Matthew S. [Department of Civil Engineering, University of Bristol, Queen' s Building, Bristol BS8 1TR (United Kingdom)
2015-02-14
We report the concept of microstructured surfaces with inner resonance in the field of elastodynamics, so-called elastodynamic metasurfaces. Such metasurfaces allow for wavefield manipulation of mechanical waves by tuning the boundary conditions at specific frequencies. In particular, they can be used to depolarize elastic waves without introducing heterogeneities in the medium itself; the physical means to do so in homogeneous elastic media used to remain, surprisingly, an open question while depolarization is commonplace in electromagnetism. The principle relies on the anisotropic behaviour of a subwavelength array of resonators: Their subwavelength configuration confines the Bragg interferences scattered by resonators into a boundary layer. The effective behaviour of the resonating array is expressed with homogenization as an unconventional impedance, the frequency-dependence, and anisotropy of which lead to depolarization and time effects. The concept of the elastodynamic metasurface is tested experimentally and results bear testament to its efficacy and robustness. Elastodynamic metasurfaces are easily realized and analytically predictable, opening new possibilities in tomography techniques, ultrasonics, geophysics, vibration control, materials and structure design.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Energy Technology Data Exchange (ETDEWEB)
Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu
2009-05-22
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
Atanackovic, Teodor M; Stankovic, Bogoljub; Zorica, Du?an
2014-01-01
The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillati
CMDS9: Continuum Mechanics and Discrete Systems 9, Istanbul Technical University, Macka. Abstracts.
1998-07-01
CONSTITUTIVE DIFFERENTIAL EQUATIONS IN CONTINUUM MECHANICS E.I. Romensky Sobolev Institute of Mathematics, Novosibirsk, RUSIA Wellposedness of...ROMANOV A.F. Ioffe Physico- Technical Institute Academy of Sciences of Rusia Polytechnicheskaya 26, 194021 St.Petersburg, RUSSIA e-mail: romanov
Fazio, Claudio; Guastella, Ivan; Sperandeo-Mineo, Rosa Maria; Tarantino, Giovanni
2008-01-01
The present paper reports the design process and the experimentation of a teaching-learning sequence about the concept of mechanical wave propagation and the role played by media where waves are propagating. The sequence focuses on the central issue of the relationships between observable phenomena, like macroscopic behaviours of waves, and their…
On the mechanisms of interaction of low-intensity millimeter waves with biological objects
Energy Technology Data Exchange (ETDEWEB)
Betskii, O.V.
1994-07-01
The interaction of low-intensity millimeter-band electromagnetic waves with biological objects is examined. These waves are widely used in medical practice as a means of physiotherapy for the treatment of various human disorders. Principal attention is given to the mechanisms through which millimeter waves act on the human organism.
Morton, Seth Michael; Jensen, Lasse
2010-08-21
A new polarizable quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This method, which we denote the discrete interaction model/quantum mechanics (DIM/QM) method, represents the nanoparticle atomistically which enables the modeling of the influence of the local environment of a nanoparticle surface on the optical properties of a molecule. Using DIM/QM, we investigate the excitation energies of rhodamine-6G (R6G) and crystal violet (CV) adsorbed on silver and gold nanoparticles of different quasispherical shapes and sizes. The metal nanoparticle is characterized by its static total polarizability, a reasonable approximation for frequencies far from the plasmon resonance. We observe that for both R6G and CV, the presence of the nanoparticle shifts the strongest excitation to the red approximately 40 nm and also increases the oscillator strength of that excitation. The shifts in excitation energies due to the nanoparticle surface are found to be comparable to those due to solvation. We find that these shifts decay quickly as the molecule is moved away from the surface. We also find that the wavelength shift is largest when the transition dipole moment is aligned with the edges of the nanoparticle surface where the electric field is expected to be the largest. These results show that the molecular excitations are sensitive to the local environment on the nanoparticle as well as the specific orientation of the molecule relative to the surface.
Two-scale meshes in quasilinear discretized problems of computational mechanics
Jarošová, P.; Vala, J.
2016-06-01
Some problems of continuum mechanics, as the analysis of crack formation in the cohesive zone modelling, require (at least) two-scale numerical approach to finite element (or volume, difference, etc.) computations: i) at the macro-scale for a whole (nearly elastic, partially damaged) body and ii) at the micro-scale near the crack (a new interior surface). The paper presents an always convergent procedure handling overlapping two-scale meshes for such model problems, open to generalizations in many directions.
Characterization of Heat Waves in the Sahel and associated mechanisms
Oueslati, Boutheina; Pohl, Benjamin; Moron, Vincent; Rome, Sandra
2016-04-01
Large efforts are made to investigate the heat waves (HW) in developed countries because of their devastating impacts on society, economy and environment. This interest increased after the intense event over Europe during summer 2003. However, HWs are still understudied over developing countries. This is particularly true in West Africa, and especially in the Sahel, where temperatures recurrently reach critical values, such as during the 2010 HW event. Understanding the Sahelian HWs and associated health risks constitute the main objective of ACASIS, a 4-year project funded by the French Agence Nationale de la Recherche. Our work contributes to this project and aims at characterizing the Sahelian HWs and understanding the mechanisms associated with such extreme events. There is no universal definition of a HW event, since it is highly dependent on the sector (human health, agriculture, transport...) and region of interest. In our case, a HW is defined when the heat index of the day and of the night exceeds the 90th percentile for at least 3 consecutive days (Rome et al. 2016, in preparation). This index combines temperature and relative humidity in order to determine the human-perceived equivalent temperature (definition adapted from Steadman, 1979). Intrinsic properties of Sahelian HW are analyzed from the Global Summary of the Day (GSOD) synoptic observations and ERA-interim reanalyses over 1979-2014 during boreal spring seasons (April-May-June), the warmest period of the year in the Central Sahel. ERA-interim captures well the observed interannual variability and seasonal cycle at the regional scale, as well as the 1979-2014 increasing linear trend of springtime HW occurrences in the Sahel. Reanalyses, however, overestimate the duration, spatial extent of HW, and underestimate their intensity. For both GSOD and ERA-interim, we show that, over the last three decades, Sahelian HWs tend to become more frequent, last longer, cover larger areas and reach higher
A review of nondestructive testing approaches using mechanical and electromagnetic waves
Lau, Denvid; Qiu, Qiwen
2016-04-01
Mechanical and electromagnetic waves are commonly used in nondestructive testing (NDT) techniques for evaluating the materials and structures in civil engineering industry, due to their good examination of defects inside the matter. However, the individual use of mechanical wave or electromagnetic wave in NDT methods sometimes does not fulfill the satisfactory detection in practice because of the operational inconvenience and low sensitivity. It has been demonstrated that the combination of using both types of waves can achieve a better performance for NDT application and would be the future direction for defect detection, as the advantages of each physical wave are picked out whereas the weaknesses are mitigated. This paper discusses the fundamental mechanisms and the current applications of using mechanical and electromagnetic waves for defect detection, with the goal of providing the physical knowledge and the perspectives of developing the NDT applications with these two types of waves. Typical mechanical-wave-based NDT methods such as acoustic emission, ultrasonic technique, and impact-echo method are reviewed. In addition, NDT methods using electromagnetic wave, which include optical fiber sensing technique, laser speckle interferometry and laser reflection technique are discussed. Advantages and disadvantages of these methods are outlined. In particular, we focus on a recent NDT method called acoustic-laser technique, which utilizes both the mechanical and electromagnetic waves. The basic principles and some important experimental data recorded by the acoustic-laser technique are described and its future development in the field of defect detection in civil infrastructure is presented.
Pair density wave superconducting states and statistical mechanics of dimers
Soto Garrido, Rodrigo Andres
The following thesis is divided in two main parts. Chapters 2, 3 and 4 are devoted to the study of the so called pair-density-wave (PDW) superconducting state and some of its connections to electronic liquid crystal (ELC) phases, its topological aspects in a one dimensional model and its appearance in a quasi-one dimensional system. On the other hand, chapter 5 is focused on the investigation of the classical statistical mechanics properties of dimers, in particular, the dimer model on the Aztec diamond graph and its relation with the octahedron equation. In chapter 2 we present a theory of superconducting states where the Cooper pairs have a nonzero center-of-mass momentum, inhomogeneous superconducting states known as a pair-density-waves (PDWs) states. We show that in a system of spin-1/2 fermions in two dimensions in an electronic nematic spin-triplet phase where rotational symmetry is broken in both real and spin space PDW phases arise naturally in a theory that can be analysed using controlled approximations. We show that several superfluid phases that may arise in this phase can be treated within a controlled BCS mean field theory, with the strength of the spin-triplet nematic order parameter playing the role of the small parameter of this theory. We find that in a spin-triplet nematic phase, in addition to a triplet p-wave and spin-singlet d-wave (or s depending on the nematic phase) uniform superconducting states, it is also possible to have a d-wave (or s) PDW superconductor. The PDW phases found here can be either unidirectional, bidirectional, or tridirectional depending on the spin-triplet nematic phase and which superconducting channel is dominant. In addition, a triple-helix state is found in a particular channel. We show that these PDW phases are present in the weak-coupling limit, in contrast to the usual Fulde-Ferrell-Larkin-Ovchinnikov phases, which require strong coupling physics in addition to a large magnetic field (and often both). In chapter
Wave propagation in nanostructures nonlocal continuum mechanics formulations
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...
Comment to the note "Counting of discrete Rossby/drift wave resonant triads", arXiv:1309.0405
Kartashov, A
2013-01-01
The main purpose of this note is clarify the following misunderstanding apparent in the note arXiv:1309.0405 by M. Bustamante, U. Hayat, P. Lynch, B. Quinn; [1]: the authors erroneously assume that in the manuscript arXiv:1307.8272 by A. Kartashov and E. Kartashova, [2], resonant triads with real amplitudes are counted whereas it can be seen explicitly from the form of dynamical system that wave amplitudes are complex.
Enhancement of sleep slow waves: underlying mechanisms and practical consequences.
Michele eBellesi; Brady A Riedner; Garcia-Molina, Gary N.; Chiara eCirelli; Giulio eTononi
2014-01-01
Even modest sleep restriction, especially the loss of sleep slow wave activity, is invariably associated with slower EEG activity during wake, the occurrence of local sleep in an otherwise awake brain, and impaired performance due to cognitive and memory deficits. Recent studies not only confirm the beneficial role of sleep in memory consolidation, but also point to a specific role for sleep slow waves. Thus, the implementation of methods to enhance sleep slow waves without unwanted arousals ...
Quantum Mechanics of Neutrino Oscillations - Hand Waving for Pedestrians
Lipkin, Harry J.
1999-01-01
Why Hand Waving? All calculations in books describe oscillations in time. But real experiments don't measure time. Hand waving is used to convert the results of a "gedanken time experiment" to the result of a real experiment measuring oscillations in space. Right hand waving gives the right answer; wrong hand waving gives the wrong answer. Many papers use wrong handwaving to get wrong answers. This talk explains how to do it right and also answers the following questions: 1. A neutrino which ...
Mechanisms of sharp wave initiation and ripple generation.
Schlingloff, Dániel; Káli, Szabolcs; Freund, Tamás F; Hájos, Norbert; Gulyás, Attila I
2014-08-20
Replay of neuronal activity during hippocampal sharp wave-ripples (SWRs) is essential in memory formation. To understand the mechanisms underlying the initiation of irregularly occurring SWRs and the generation of periodic ripples, we selectively manipulated different components of the CA3 network in mouse hippocampal slices. We recorded EPSCs and IPSCs to examine the buildup of neuronal activity preceding SWRs and analyzed the distribution of time intervals between subsequent SWR events. Our results suggest that SWRs are initiated through a combined refractory and stochastic mechanism. SWRs initiate when firing in a set of spontaneously active pyramidal cells triggers a gradual, exponential buildup of activity in the recurrent CA3 network. We showed that this tonic excitatory envelope drives reciprocally connected parvalbumin-positive basket cells, which start ripple-frequency spiking that is phase-locked through reciprocal inhibition. The synchronized GABA(A) receptor-mediated currents give rise to a major component of the ripple-frequency oscillation in the local field potential and organize the phase-locked spiking of pyramidal cells. Optogenetic stimulation of parvalbumin-positive cells evoked full SWRs and EPSC sequences in pyramidal cells. Even with excitation blocked, tonic driving of parvalbumin-positive cells evoked ripple oscillations. Conversely, optogenetic silencing of parvalbumin-positive cells interrupted the SWRs or inhibited their occurrence. Local drug applications and modeling experiments confirmed that the activity of parvalbumin-positive perisomatic inhibitory neurons is both necessary and sufficient for ripple-frequency current and rhythm generation. These interneurons are thus essential in organizing pyramidal cell activity not only during gamma oscillation, but, in a different configuration, during SWRs.
A discrete twin-boundary approach for simulating the magneto-mechanical response of Ni-Mn-Ga
Faran, Eilon; Shilo, Doron
2016-09-01
The design and optimization of ferromagnetic shape memory alloys (FSMA)-based devices require quantitative understanding of the dynamics of twin boundaries within these materials. Here, we present a discrete twin boundary modeling approach for simulating the behavior of an FSMA Ni-Mn-Ga crystal under combined magneto-mechanical loading conditions. The model is based on experimentally measured kinetic relations that describe the motion of individual twin boundaries over a wide range of velocities. The resulting calculations capture the dynamic response of Ni-Mn-Ga and reveal the relations between fundamental material parameters and actuation performance at different frequencies of the magnetic field. In particular, we show that at high field rates, the magnitude of the lattice barrier that resists twin boundary motion is the important property that determines the level of actuation strain, while the contribution of twinning stress property is minor. Consequently, type II twin boundaries, whose lattice barrier is smaller compared to type I, are expected to show better actuation performance at high rates, irrespective of the differences in the twinning stress property between the two boundary types. In addition, the simulation enables optimization of the actuation strain of a Ni-Mn-Ga crystal by adjusting the magnitude of the bias mechanical stress, thus providing direct guidelines for the design of actuating devices. Finally, we show that the use of a linear kinetic law for simulating the twinning-based response is inadequate and results in incorrect predictions.
Mares, J. O.; Miller, J. K.; Gunduz, I. E.; Rhoads, J. F.; Son, S. F.
2014-11-01
High-frequency mechanical excitation can induce heating within energetic materials and may lead to advances in explosives detection and defeat. In order to examine the nature of this mechanically induced heating, samples of an elastic binder (Sylgard 184) were embedded with inert and energetic particles placed in a fixed spatial pattern and were subsequently excited with an ultrasonic transducer at discrete frequencies from 100 kHz to 20 MHz. The temperature and velocity responses of the sample surfaces suggest that heating due to frictional effects occurred near the particles at excitation frequencies near the transducer resonance of 215 kHz. An analytical solution involving a heat point source was used to estimate heating rates and temperatures at the particle locations in this frequency region. Heating located near the sample surface at frequencies near and above 1 MHz was attributed to viscoelastic effects related to the surface motion of the samples. At elevated excitation parameters near the transducer resonance frequency, embedded particles of ammonium perchlorate and cyclotetramethylene-tetranitramine were driven to chemical decomposition.
Karampinos, Efstratios; Hadjigeorgiou, John; Turcotte, Pascal
2016-12-01
Structurally defined squeezing mechanisms in hard rock mining often result in buckling failures and large deformations. In mining drives, the primary objective is to mitigate and manage, in a cost-effective way, as opposed to arrest the deformation. This paper is a contribution to an improved understanding of the impact of several reinforcement scenarios in structurally controlled deformations in hard rock mines. The influence of reinforcement in the 3D discrete element method is explored, extending previous numerical work that has captured the squeezing buckling mechanism driven by foliation and high stresses in the selected mine site. A comprehensive strategy for explicitly modelling rock reinforcement using the DEM was developed and implemented in a series of 3D numerical models. The models were calibrated based on field testing of reinforcement and observations at the LaRonde Mine. They were used to investigate the influence of different reinforcement strategies at different deformation stages. The numerical results were in agreement with the field observations and demonstrated the practical implications of using yielding reinforcement elements. This was supported by field data where the use of yielding bolts reduced the drift convergence and rehabilitation. The methodology is applicable to other mine sites facing structurally controlled large deformations.
Directory of Open Access Journals (Sweden)
D. A. Eliseev
2015-01-01
Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.
Waldron, Wayne L.; Klein, Larry; Altner, Bruce
1994-01-01
We model the evolution of a density shell propagating through the stellar wind of an early-type star, in order to investigate the effects of such shells on UV P Cygni line profiles. Unlike previous treatments, we solve the mass, momentum, and energy conservation equations, using an explicit time-differencing scheme, and present a parametric study of the density, velocity, and temperature response. Under the assumed conditions, relatively large spatial scale, large-amplitude density shells propagate as stable waves through the supersonic portion of the wind. Their dynamical behavior appears to mimic propagating 'solitary waves,' and they are found to accelerate at the same rate as the underlying steady state stellar wind (i.e., the shell rides the wind). These hydrodynamically stable structures quantitatively reproduce the anomalous 'discrete absorption component' (DAC) behavior observed in the winds of luminous early-type stars, as illustrated by comparisons of model predictions to an extensive International Ultraviolet Explorer (IUE) time series of spectra of zeta Puppis (O4f). From these comparisons, we find no conclusive evidence indicative of DACs accelerating at a significantly slower rate than the underlying stellar wind, contrary to earlier reports. In addition, these density shells are found to be consistent within the constraints set by the IR observations. We conclude that the concept of propagating density shells should be seriously reconsidered as a possible explanation of the DAC phenomenon in early-type stars.
Application of local wave time-frequency method in reciprocating mechanical fault diagnosis
Institute of Scientific and Technical Information of China (English)
Wang Lei; Wang Fengtao; Ma Xiaojiang
2006-01-01
To diagnose the reciprocating mechanical fault. We utilized local wave time-frequency approach. Firstly,we gave the principle. Secondly, the application of local wave time-frequency was given. Finally, we discussed its virtue in reciprocating mechanical fault diagnosis.
Rojas, R.; Robles, P.
2011-01-01
We discuss common features in mechanical, electromagnetic and quantum systems, supporting identical results for the transmission and reflection coefficients of waves arriving perpendicularly at a plane interface. Also, we briefly discuss the origin of special notions such as refractive index in quantum mechanics, massive photons in wave guides and…
Rojas, R.; Robles, P.
2011-01-01
We discuss common features in mechanical, electromagnetic and quantum systems, supporting identical results for the transmission and reflection coefficients of waves arriving perpendicularly at a plane interface. Also, we briefly discuss the origin of special notions such as refractive index in quantum mechanics, massive photons in wave guides and…
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
On the Spectral Problems for the Discrete Boltzmann Models
Institute of Scientific and Technical Information of China (English)
Aq Kwang-Hua Chu; J. FANG Jing
2000-01-01
The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propaogation in monatomic gases which are fundamental in the nonequilibrium tatistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation of sound modes quite well, after comparison with the continuum-mechanical results.
A study of surface acoustic wave devices with discrete Green function%声表面波滤波器的离散Green函数分析法
Institute of Scientific and Technical Information of China (English)
张燕华; 徐方迁
2011-01-01
A Japanese scholar, Hashimoto, proposed using the effective permittivity of grating and the discrete Green function to investigate the properties of surface acoustic wave propagation in periodic metal gratings with the finite element method, and developed a program compiled by Fortran, which has been used to design the surface acoustic wave devices by many international companies. This paper gives the results of Hashimoto program with an example of Rayleigh waves propagation in aluminium grating on 128°YX-LiNbO3 substrate. The frequencies of the upper and lower stopband edges are read out and taken into the expression of the dispersion relation of COM theory. The figure drawn by this expression is the wavenumber dispersion curve to obtain COM parameters.%日本学者Hashimoto提出栅格有效介电常数和离散Green函数,并结合有限元方法分析了短路金属栅阵中声表面波的传输特性.由此开发了相应的Fortran应用程序.国际上许多从事声表面波器件的研发公司都使用该程序设计他们的产品.以Rayleigh波在128°YX-LiNbO3基片、铝金属栅中传播为例,给出根据Hashimoto程序运算的结果,读取禁带下边缘和禁带上边缘所对应的相对频率的数值,代入COM理论色散关系的数学表达式中,该表达式的图形就是由COM理论色散关系而确定的波数色散曲线,以提取耦合模参数.
Lisjak, Andrea; Tatone, Bryan S. A.; Mahabadi, Omid K.; Grasselli, Giovanni; Marschall, Paul; Lanyon, George W.; Vaissière, Rémi de la; Shao, Hua; Leung, Helen; Nussbaum, Christophe
2016-05-01
The analysis and prediction of the rock mass disturbance around underground excavations are critical components of the performance and safety assessment of deep geological repositories for nuclear waste. In the short term, an excavation damaged zone (EDZ) tends to develop due to the redistribution of stresses around the underground openings. The EDZ is associated with an increase in hydraulic conductivity of several orders of magnitude. In argillaceous rocks, sealing mechanisms ultimately lead to a partial reduction in the effective hydraulic conductivity of the EDZ with time. The goal of this study is to strengthen the understanding of the phenomena involved in the EDZ formation and sealing in Opalinus Clay, an indurated claystone currently being assessed as a host rock for a geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are performed. With its explicit consideration of fracturing processes, FDEM modeling is applied to the HG-A experiment, an in situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. A quantitative simulation of the EDZ formation process around the microtunnel is first carried out, and the numerical results are compared with field observations. Then, the re-compression of the EDZ under the effect of a purely mechanical loading, capturing the increase of swelling pressure from the backfill onto the rock, is considered. The simulation results highlight distinctive rock failure kinematics due to the bedded structure of the rock mass. Also, fracture termination is simulated at the intersection with a pre-existing discontinuity, representing a fault plane oblique to the bedding orientation. Simulation of the EDZ re-compression indicates an overall reduction of the total fracture area as a function of the applied pressure, with locations of ineffective sealing associated with self
Morton, Seth Michael; Jensen, Lasse
2011-10-07
A frequency-dependent quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This discrete interaction model/quantum mechanics (DIM/QM) method represents the nanoparticle atomistically, thus accounting for the local environment of the nanoparticle surface on the optical properties of the adsorbed molecule. Using the DIM/QM method, we investigate the coupling between the absorption of a silver nanoparticle and of a substituted naphthoquinone. This system is chosen since it shows strong coupling due to a molecular absorption peak that overlaps with the plasmon excitation in the metal nanoparticle. We show that there is a strong dependence not only on the distance of the molecule from the metal nanoparticle but also on its orientation relative to the nanoparticle. We find that when the transition dipole moment of an excitation is oriented towards the nanoparticle there is a significant increase in the molecular absorption as a result of coupling to the metal nanoparticle. In contrast, we find that the molecular absorption is decreased when the transition dipole moment is oriented parallel to the metal nanoparticle. The coupling between the molecule and the metal nanoparticle is found to be surprisingly long range and important on a length scale comparable to the size of the metal nanoparticle. A simple analytical model that describes the molecule and the metal nanoparticle as two interacting point objects is found to be in excellent agreement with the full DIM/QM calculations over the entire range studied. The results presented here are important for understanding plasmon-exciton hybridization, plasmon enhanced photochemistry, and single-molecule surface-enhanced Raman scattering.
A review of wave mechanics in the pulmonary artery with an emphasis on wave intensity analysis.
Su, J; Hilberg, O; Howard, L; Simonsen, U; Hughes, A D
2016-12-01
Mean pulmonary arterial pressure and pulmonary vascular resistance (PVR) remain the most common haemodynamic measures to evaluate the severity and prognosis of pulmonary hypertension. However, PVR only captures the non-oscillatory component of the right ventricular hydraulic load and neglects the dynamic compliance of the pulmonary arteries and the contribution of wave transmission. Wave intensity analysis offers an alternative way to assess the pulmonary vasculature in health and disease. Wave speed is a measure of arterial stiffness, and the magnitude and timing of wave reflection provide information on the degree of impedance mismatch between the proximal and distal circulation. Studies in the pulmonary artery have demonstrated distinct differences in arterial wave propagation between individuals with and without pulmonary vascular disease. Notably, greater wave speed and greater wave reflection are observed in patients with pulmonary hypertension and in animal models exposed to hypoxia. Studying wave propagation makes a valuable contribution to the assessment of the arterial system in pulmonary hypertension, and here, we briefly review the current state of knowledge of the methods used to evaluate arterial waves in the pulmonary artery.
Discrete breathers in crystals
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
A Thoracic Mechanism of Mild Traumatic Brain Injury Due to Blast Pressure Waves
Courtney, Amy; 10.1016/j.mehy.2008.08.015
2008-01-01
The mechanisms by which blast pressure waves cause mild to moderate traumatic brain injury (mTBI) are an open question. Possibilities include acceleration of the head, direct passage of the blast wave via the cranium, and propagation of the blast wave to the brain via a thoracic mechanism. The hypothesis that the blast pressure wave reaches the brain via a thoracic mechanism is considered in light of ballistic and blast pressure wave research. Ballistic pressure waves, caused by penetrating ballistic projectiles or ballistic impacts to body armor, can only reach the brain via an internal mechanism and have been shown to cause cerebral effects. Similar effects have been documented when a blast pressure wave has been applied to the whole body or focused on the thorax in animal models. While vagotomy reduces apnea and bradycardia due to ballistic or blast pressure waves, it does not eliminate neural damage in the brain, suggesting that the pressure wave directly affects the brain cells via a thoracic mechanism. ...
Investigating EMIC Waves as a Precipitation Mechanism for Relativistic Electrons
Li, Z.; Millan, R. M.; Woodger, L. A.
2012-12-01
Evidence has indicated that EMIC waves may be one of the major causes of relativistic electron precipitation (REP). We solved the pitch-angle diffusion equation for the scattering of relativistic electrons by EMIC waves, and generated flux-energy spectra of the precipitating electrons. After being converted into Bremsstrahlung X-ray counts, these spectra can be directly compared with previous (e.g. MAXIS, MINIS, BARREL test campaigns) and future (e.g. BARREL) balloon spectra measurements to determine if EMIC waves are the causes of the REP events. Parameter studies have also been conducted to investigate the influence of various geomagnetic parameters and environmental conditions on the REP spectra.
Indian Academy of Sciences (India)
S PREMILA DEVI; TEJESHWORI SALAM; R H DUNCAN LYNGDOH
2016-05-01
Alkene aziridination by azides through uncatalyzed thermal gas phase routes has been studiedusing the DFT B3LYP/6-31G(d,p) method, where the possible role of discrete nitrene intermediates is emphasized.The thermal decomposition of azides is studied using the MP2/aug-cc-pVDZ strategy as well. The MP2(but not the B3LYP) results discount the existence of singlet alkylnitrenes where the alkyl group has an α-hydrogen. Addition of the lowest lying singlet and triplet nitrenes R-N (R = H, Me, Ac) to four different alkenesubstrates leading to aziridine formation was studied by the B3LYP method. Singlet nitrenes with alkenes canyield aziridines via a concerted mechanism, where H-N insertion takes place without a barrier, whereas Me-Nshows larger barriers than Ac-N. Methyl substitution in the alkene favors this reaction. Triplet nitrene additionto alkenes is studied as a two-step process, where the initially formed diradical intermediates cyclize to formaziridines by ISC (intersystem crossing) and collapse. Scope for C-C bond rotation in the diradical leads to lossof stereochemical integrity for triplet nitrene addition to cis- and trans-2-butenes. Geometries of the transitionstates in the various reaction steps studied here are described as “early” or “late” in good accordance with theHammond postulate.
Chulhai, Dhabih V; Jensen, Lasse
2015-05-28
Plasmonic circular dichroism (CD) of chiral molecules in the near field of plasmonic nanoparticles (NPs) may be used to enhance molecular CD signatures or to induce a CD signal at the plasmon resonance. A recent few-states theory explored these effects for model systems and showed an orientation dependence of the sign of the induced CD signal for spherical NPs. Here, we use the discrete interaction model/quantum mechanical (DIM/QM) method to simulate the CD and plasmonic CD of the 310- and α-helix conformations of a short alanine peptide. We find that the interactions between the molecule and the plasmon lead to significant changes in the CD spectra. In the plasmon region, we find that the sign of the CD depends strongly on the orientation of the molecule as well as specific interactions with the NP through image dipole effects. A small enhancement of the CD is found in the molecular region of the spectrum, however, the molecular signatures may be significantly altered through interactions with the NP. We also show that the image dipole effect can result in induced plasmonic CD even for achiral molecules. Overall, we find that the specific interactions with the NP can lead to large changes to the CD spectrum that complicates the interpretation of the results.
High order Hamiltonian water wave models with wave-breaking mechanism
Kurnia, R.; Groesen, van E.
2014-01-01
Based on the Hamiltonian formulation of water waves, using Hamiltonian consistent modelling methods, we derive higher order Hamiltonian equations by Taylor expansions of the potential and the vertical velocity around the still water level. The polynomial expansion in wave height is mixed with pseudo
Origin of quantum randomness in the pilot wave quantum mechanics
Shtanov, Yuri
1997-01-01
We account for the origin of the laws of quantum probabilities in the de Broglie-Bohm (pilot wave) formulation of quantum theory by considering the property of ergodicity likely to characterise the dynamics of microscopic quantum systems.
Elastic Wave Propagation Mechanisms in Underwater Acoustic Environments
2015-09-30
excited flexural mode that propagates in the ice layer at certain acoustic frequencies in ice-covered environments.[3] • Previously implemented EPE self...and ks,3, corresponding to the water layer sound speed, bottom compressional and shear wave speed, and ice layer compressional and shear wave speed... excitation of the Scholte interface mode. Dashed curve shows spectra for a source at 1 m depth and receiver at 25 m, showing the excitation of the
The effects of shock wave and quasi-traveling wave in the mechanical impact test
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
It is well-known that the numerical value is always larger than the measured value,amounting to many times,if we calculate the stress of the specimen in the impulse test using the NASTRAN and ANSYS (N-A) software.We believe that the impact induces shock wave or quasi-traveling wave in the specimen,which can qualitatively explain the discrepancy of the two values.In order to verify it,the Lax-Friedrichs (L-F) scheme is taken to simulate the transmission of shock wave and quasi-traveling wave in solid.Numerical results show that the action area of the stress wave is small and the action time is very short,so the resulting stress and actual work are not big.In addition,the distribution of the impact values obtained by the numerical simulation is in accordance with the trend of the measured impact values.
Mechanism of laser-induced plasma shock wave evolution in air
Institute of Scientific and Technical Information of China (English)
Zhao Rui; Liang Zhong-Cheng; Han Bing; Zhang Hong-Chao; Xu Rong-Qing; Lu Jian; Ni Xiao-Wu
2009-01-01
A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.
Lee, Taeyoung; McClamroch, N Harris
2007-01-01
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics. In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability, controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of the corresponding control problems. Despite the critical role of geometry and mechanics in the analysis of nonlinear control systems, non...
Redkov, V M
1998-01-01
Particles of spin 1/2 and 1 in external Abelian monopole field are considered. P-inversion like operators N-s commuting with the respective Hamiltonians are constructed: N(bisp.) is diagonalized onto the relevant wave functions, whereas N(vect.) does not. Such a paradox is rationalized through noting that both these operators are not self-conjugate. It is shown that any N-parity selection rules cannot be produced. Non-Abelian problems for doublets of spin 1/2 and 1 particles are briefly discussed; the statement is given of that corresponding discrete operators are self-conjugate and selection rules are available.
A wave-mechanical model of incoherent neutron scattering II. Role of the momentum transfer
Frauenfelder, Hans; Young, Robert D.; Fenimore, Paul W.
2015-01-01
We recently introduced a wave-mechanical model for quasi-elastic neutron scattering (QENS) in proteins. We call the model ELM for "Energy Landscape Model". We postulate that the spectrum of the scattered neutrons consists of lines of natural width shifted from the center by fluctuations. ELM is based on two facts: Neutrons are wave packets; proteins have low-lying substates that form the free-energy landscape (FEL). Experiments suggest that the wave packets are a few hundred micrometers long....
The realization of the wave function collapse in the linguistic interpretation of quantum mechanics
Ishikawa, Shiro
2015-01-01
Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized in the linguistic interpretation. And furthermore, I propose the justification of the von Neumann-L\\"uders projection postulate. After all, I conclude that the wave function collapse should not be adopted in the Copenhagen interpretation.
Barniol, Pablo; Zavala, Genaro
2017-01-01
The Mechanical Waves Conceptual Survey (MWCS), presented in 2009, is the most important test to date that has been designed to evaluate university students' understanding of four main topics: propagation, superposition, reflection, and standing waves. In a literature review, we detected a significant need for a study that uses this test as an…
Barniol, Pablo; Zavala, Genaro
2017-01-01
The Mechanical Waves Conceptual Survey (MWCS), presented in 2009, is the most important test to date that has been designed to evaluate university students' understanding of four main topics: propagation, superposition, reflection, and standing waves. In a literature review, we detected a significant need for a study that uses this test as an…
Picometer stable scan mechanism for gravitational wave detection in space
Rijnveld, N.; Pijnenburg, J.A.C.M.
2010-01-01
Detection and observation of gravitational waves requires extremely accurate displacement measurement in the frequency range 0.03 mHz to 1 Hz. The Laser Interferometer Space Antenna (LISA) mission will attain this by creating a giant interferometer in space, based on free floating proof masses in th
Picometer stable scan mechanism for gravitational wave detection in space
Rijnveld, N.; Pijnenburg, J.A.C.M.
2010-01-01
Detection and observation of gravitational waves requires extremely accurate displacement measurement in the frequency range 0.03 mHz to 1 Hz. The Laser Interferometer Space Antenna (LISA) mission will attain this by creating a giant interferometer in space, based on free floating proof masses in
A mechanism study of sound wave-trapping barriers.
Yang, Cheng; Pan, Jie; Cheng, Li
2013-09-01
The performance of a sound barrier is usually degraded if a large reflecting surface is placed on the source side. A wave-trapping barrier (WTB), with its inner surface covered by wedge-shaped structures, has been proposed to confine waves within the area between the barrier and the reflecting surface, and thus improve the performance. In this paper, the deterioration in performance of a conventional sound barrier due to the reflecting surface is first explained in terms of the resonance effect of the trapped modes. At each resonance frequency, a strong and mode-controlled sound field is generated by the noise source both within and in the vicinity outside the region bounded by the sound barrier and the reflecting surface. It is found that the peak sound pressures in the barrier's shadow zone, which correspond to the minimum values in the barrier's insertion loss, are largely determined by the resonance frequencies and by the shapes and losses of the trapped modes. These peak pressures usually result in high sound intensity component impinging normal to the barrier surface near the top. The WTB can alter the sound wave diffraction at the top of the barrier if the wavelengths of the sound wave are comparable or smaller than the dimensions of the wedge. In this case, the modified barrier profile is capable of re-organizing the pressure distribution within the bounded domain and altering the acoustic properties near the top of the sound barrier.
The meaning of the wave function in search of the ontology of quantum mechanics
Gao, Shan
2017-01-01
At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...
On the classical limit of Bohmian mechanics for Hagedorn wave packets
Dürr, Detlef
2010-01-01
We consider the classical limit of quantum mechanics in terms of Bohmian trajectories. For wave packets as defined by Hagedorn we show that the Bohmian trajectories converge to Newtonian trajectories in probability.
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
Characterization of Wave Dispersion in Viscoelastic Cellular Assemblies by Doublet Mechanics
Institute of Scientific and Technical Information of China (English)
JIN Yan-Fang; XIONG Chun-Yang; FANG Jing; FERRARI Mauro
2009-01-01
Using the Voigt model, we analyze wave propagation in viscoelastic granular media with a monatomic lattice, planar simple cubic package and cubical-tetrahedral assembly within the context of doublet mechanics. Microstrains of elongation between the doublet particles are considered in the models. Wave dispersive relations are derived from dynamic equations of the particles involved in the media, and phase velocities and attenuations of the dispersive waves are obtained for the different assemblies. Variations in these dispersion characteristics are analyzed with the changes of cell interval, modulus, and wave frequency. The relations between micro-constants and macro-parameters are presented under the condition of non-scale continuity of the media.
Study on the formation mechanism of shock wave in process of coal and gas outburst
Institute of Scientific and Technical Information of China (English)
SUN Dong-ling; MIAO Fa-tian; LIANG Yun-pei
2009-01-01
According to the research results of motion parameters of coal-gas flow, ana-lyzed the formation mechanism of shock waves at different states of coal-gas flow in the process of coal and gas outburst, and briefly described the two possible cases of outburst shock wave formation and their formation conditions in the process of coal and gas out-burst, and then pointed out that a high degree of under-expanded coal-gas flow was the main reason for the formation of a highly destructive shock wave. The research results improved the shock wave theory in coal and gas outburst.
Efficiency of a gyroscopic device for conversion of mechanical wave energy to electrical energy
DEFF Research Database (Denmark)
Carlsen, Martin; Darula, Radoslav; Gravesen, Jens;
2011-01-01
We consider a recently proposed gyroscopic device for conversion of mechanical ocean wave energy to electrical energy. Two models of the device derived from standard engineering mechanics from the literature are analysed, and a model is derived from analytical mechanics considerations. From...
Energy Technology Data Exchange (ETDEWEB)
Muller, J. [IRSID, Institut de Recherches Siderurgie, 57 - Maizieres-les-Metz (France)
1996-12-31
Radiant heat transfer is the main solution retained in many iron and steel metallurgy installations (re-heating and annealing furnaces etc..). Today, it has become important to dispose of performing radiant heat transfer models in heat transfer and fluid mechanics simulation softwares, and well adapted to multidimensional industrial problems. This work presents the discrete ordinate radiant heat transfer model developed at the IRSID (the French institute of research in iron and steel metallurgy) and coupled with the PHOENICS heat transfer-fluid mechanics software. Three modeling approaches are presented concerning the radiative properties of gases (H{sub 2}O-CO{sub 2}). A ``weighted grey gases sum`` model gives satisfactory results for several 1-D validation cases. (J.S.) 20 refs.
New aspects of the electrochemical-catalytic (EC’) mechanism in square-wave voltammetry
Gulaboski, Rubin; Mirceski, Valentin
2015-01-01
Several new theoretical aspects of the electrocatalytic (regenerative) EC’ mechanism under conditions of square-wave (SWV) and staircase cyclic voltammetry (SCV) are presented. Elaborating the effect of the rate of the catalytic reaction in the diffusion-controlled catalytic mechanism (diffusional EC’ mechanism) and surface catalytic mechanism (surface EC’ mechanism), we refer to several phenomena related to the shift of the position and the half-peak width of the net peak in ...
Mechanical Limits to Size in Wave-Swept Organisms.
1983-11-10
sponges produce taller colonies in deeper water where wave action is attenuated (Reidl 1971). Simi’ar trends in maximum body size have been noted in...grows taller . While for • .similar free-stream velocities turbulent boundary layers are thicker than -- laminar ones, they have, in general, blunter...coral reefs: rigid, brittle organisms such as stony coras suffered more breakage than did flexible, deformable organisms like gorgonians (Woodley et a_
Mechanisms of Fluid-Mud Interactions Under Waves
2011-01-01
surface a corrugated appearance (Figure 12). Through careful analysis of these tests, it has been concluded that the waves are the result of a resonant...square meter per month. Analysis of X-radiographs from this field program has contributed to development of new theory relating hydrodynamics of...Shear near the base of the mobile fluid mud layer mixes coarser underlying rippled sediment with overlying finer sediment, producing laminations
Imaging mechanical shear waves induced by piezoelectric ceramics in magnetic resonance elastography
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Magnetic Resonance Elastography (MRE) is a noninvasive technique to measure elasticity of tissues in vivo. In this paper, a mechanical shear wave MR imaging system experiment is set for MRE. A novel actuator is proposed to generate mechanical shear waves propagating inside a gel phantom. The actuator is made of piezoelectric ceramics, and fixed on a plexiglass bracket. Both of the gel phantom and the actuator are put into a head coil inside the MR scanner's bore. The actuator works synchronously with an MR imaging sequence running on the MR scanner. The sequence is modified from a FLASH sequence into a motion-sensitizing phase- contrast sequence for shear wave MR imaging. Shear wave images are presented, and these effects on the shear wave MR imaging system, including the stiffness of phantoms, the frequency of the actuator, the parameters of the motion-sensitizing gradient, and the oscillation of the patient bed, are discussed.
Comparison of Damping Mechanisms for Transverse Waves in Solar Coronal Loops
Montes-Solís, María; Arregui, Iñigo
2017-09-01
We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink waves in the Alfvén continuum, phase mixing of Alfvén waves, and wave leakage. Our methods make use of Bayesian inference and model comparison techniques. We first infer the values for the physical parameters that control the wave damping, under the assumption of a particular mechanism, for typically observed damping timescales. Then, the computation of marginal likelihoods and Bayes factors enable us to quantify the relative plausibility between the alternative mechanisms. We find that, in general, the evidence is not large enough to support a single particular damping mechanism as the most plausible one. Resonant absorption and wave leakage offer the most probable explanations in strong damping regimes, while phase mixing is the best candidate for weak/moderate damping. When applied to a selection of 89 observed transverse loop oscillations, with their corresponding measurements of damping timescales and taking into account data uncertainties, we find that positive evidence for a given damping mechanism is only available in a few cases.
DEFF Research Database (Denmark)
Dühring, Maria Bayard; Laude, Vincent; Khelif, Abdelkrim
2009-01-01
It has been shown previously that surface acoustic waves can be efficiently trapped and slowed by steep ridges on a piezoelectric substrate, giving rise to two families of shear-horizontal and vertically polarized surface waves. The mechanisms of energy storage and dispersion are explored by using...... as resonators storing mechanical energy. These resonators are evanescently coupled by the surface. The dispersion diagram is presented and shows very low group velocities as the wave vector approaches the limit of the first Brillouin zone. ©2009 American Institute of Physics...
Generation mechanism of whistler waves produced by electron beam injection in space
Pritchett, P. L.; Karimabadi, H.; Omidi, N.
1989-01-01
Electromagnetic particle simulations are used to determine the generation mechanism of the whistler waves observed in connection with the artificial injection of electron beams in the ionosphere. The production of the waves is shown to be closely connected with the beam-plasma interaction, which leads to the formation of a current structure which acts like an antenna and emits the whistler waves in a coherent manner. This process, in contrast to a mechanism involving amplification of radiation by a whistler mode plasma instability within the beam, allows the whistlers to be generated even though the beam width is less than one wavelength.
Using high speed smartphone cameras and video analysis techniques to teach mechanical wave physics
Bonato, Jacopo; Gratton, Luigi M.; Onorato, Pasquale; Oss, Stefano
2017-07-01
We propose the use of smartphone-based slow-motion video analysis techniques as a valuable tool for investigating physics concepts ruling mechanical wave propagation. The simple experimental activities presented here, suitable for both high school and undergraduate students, allows one to measure, in a simple yet rigorous way, the speed of pulses along a spring and the period of transverse standing waves generated in the same spring. These experiments can be helpful in addressing several relevant concepts about the physics of mechanical waves and in overcoming some of the typical student misconceptions in this same field.
da Silva, Jose C. B.; Magalhaes, J. M.; Buijsman, M. C.; Garcia, C. A. E.
2016-08-01
Mode-2 internal waves are usually not as energetic as larger mode-1 Internal Solitary Waves (ISWs), but they have attracted a great deal of attention in recent years because they have been identified as playing a significant role in mixing shelf waters [1]. This mixing is particularly effective for mode-2 ISWs because the location of these waves in the middle of the pycnocline plays an important role in eroding the barrier between the base of the surface mixed layer and the stratified deep layer below. An urgent problem in physical oceanography is therefore to account for the magnitude and distribution of ISW-driven mixing, including mode-2 ISWs. Several generation mechanisms of mode-2 ISWs have been identified. These include: (1) mode-1 ISWs propagating onshore (shoaling) and entering the breaking instability stage, or propagating over a steep sill; (2) a mode-1 ISW propagating offshore (antishoaling) over steep slopes of the shelf break, and undergoing modal transformation; (3) intrusion of the whole head of a gravity current into a three-layer fluid; (4) impingement of an internal tidal beam on the pycnocline, itself emanating from critical bathymetry; (5) nonlinear disintegration of internal tide modes; (6) lee wave mechanism. In this paper we provide methods to identify internal wave features denominated "Wave Tails" in SAR images of the ocean surface, which are many times associated with second mode internal waves. The SAR case studies that are presented portray evidence of the aforementioned generation mechanisms, and we further discuss possible methods to discriminate between the various types of mode-2 ISWs in SAR images, that emerge from these physical mechanisms. Some of the SAR images correspond to numerical simulations with the MITgcm in fully nonlinear and nonhydrostatic mode and in a 2D configuration with realistic stratification, bathymetry and other environmental conditions.Results of a global survey with some of these observations are presented
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
Whistler wave-induced ionospheric plasma turbulence: Source mechanisms and remote sensing
Pradipta, R.; Rooker, L. A.; Whitehurst, L. N.; Lee, M. C.; Ross, L. M.; Sulzer, M. P.; Gonzalez, S.; Tepley, C.; Aponte, N.; See, B. Z.; Hu, K. P.
2013-10-01
We report a series of experiments conducted at Arecibo Observatory in the past, aimed at the investigation of 40.75 kHz whistler wave interactions with ionospheric plasmas and the inner radiation belts at L=1.35. The whistler waves are launched from a Naval transmitter (code-named NAU) operating in Aguadilla, Puerto Rico at the frequency and power of 40.75 kHz and 100 kW, respectively. Arecibo radar, CADI, and optical instruments were used to monitor the background ionospheric conditions and detect the induced ionospheric plasma effects. Four-wave interaction processes produced by whistler waves in the ionosphere can excite lower hybrid waves, which can accelerate ionospheric electrons. Furthermore, whistler waves propagating into the magnetosphere can trigger precipitation of energetic electrons from the radiation belts. Radar and optical measurements can distinguish wave-wave and wave-particle interaction processes occurring at different altitudes. Electron acceleration by different mechanisms can be verified from the radar measurements of plasma lines. To facilitate the coupling of NAU-launched 40.75 kHz whistler waves into the ionosphere, we can rely on naturally occurring spread F irregularities to serve as ionospheric ducts. We can also use HF wave-created ducts/artificial waveguides, as demonstrated in our earlier Arecibo experiments and recent Gakona experiments at HAARP. The newly constructed Arecibo HF heater will be employed in our future experiments, which can extend the study of whistler wave interactions with the ionosphere and the magnetosphere/radiation belts as well as the whistler wave conjugate propagation between Arecibo and Puerto Madryn, Argentina.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Mechanical Properties of Laminate Materials: From Surface Waves to Bloch Oscillations
DEFF Research Database (Denmark)
Liang, Z.; Willatzen, Morten; Christensen, Johan
2015-01-01
for designing Bloch oscillations in classical plate structures and show how mechanical Bloch oscillations can be generated in arrays of solid plates when the modal wavelength is gradually reduced. The design recipe describes how Bloch oscillations in classical structures of arbitrary dimensions can be generated......We propose hitherto unexplored and fully analytical insights into laminate elastic materials in a true condensed-matter-physics spirit. Pure mechanical surface waves that decay as evanescent waves from the interface are discussed, and we demonstrate how these designer Scholte waves are controlled......, and we demonstrate this numerically for structures with millimeter and centimeter dimensions in the kilohertz to megahertz range. Analytical predictions agree entirely with full wave simulations showing how elastodynamics can mimic quantum-mechanical condensed-matter phenomena....
Yoon, Jeoung Seok; Zang, Arno; Zimmermann, Günter; Stephansson, Ove
2016-04-01
Operation of fluid injection into and withdrawal from the subsurface for various purposes has been known to induce earthquakes. Such operations include hydraulic fracturing for shale gas extraction, hydraulic stimulation for Enhanced Geothermal System development and waste water disposal. Among these, several damaging earthquakes have been reported in the USA in particular in the areas of high-rate massive amount of wastewater injection [1] mostly with natural fault systems. Oil and gas production have been known to induce earthquake where pore fluid pressure decreases in some cases by several tens of Mega Pascal. One recent seismic event occurred in November 2013 near Azle, Texas where a series of earthquakes began along a mapped ancient fault system [2]. It was studied that a combination of brine production and waste water injection near the fault generated subsurface pressures sufficient to induced earthquakes on near-critically stressed faults. This numerical study aims at investigating the occurrence mechanisms of such earthquakes induced by fluid injection [3] and withdrawal by using hydro-geomechanical coupled dynamic simulator (Itasca's Particle Flow Code 2D). Generic models are setup to investigate the sensitivity of several parameters which include fault orientation, frictional properties, distance from the injection well to the fault, amount of fluid withdrawal around the injection well, to the response of the fault systems and the activation magnitude. Fault slip movement over time in relation to the diffusion of pore pressure is analyzed in detail. Moreover, correlations between the spatial distribution of pore pressure change and the locations of induced seismic events and fault slip rate are investigated. References [1] Keranen KM, Weingarten M, Albers GA, Bekins BA, Ge S, 2014. Sharp increase in central Oklahoma seismicity since 2008 induced by massive wastewater injection, Science 345, 448, DOI: 10.1126/science.1255802. [2] Hornbach MJ, DeShon HR
Heege, J.H. ter; Orlic, B.; Hoedeman, G.C.
2015-01-01
Wellbore zonal isolation is particularly important for subsurface storage of CO2, where well integrity must be ensured for very long time spans. In this study, three dimensional discrete element models of wellbore systems have been used to simulate failure and damage of wellbore cement and surroundi
Drift and breakup of spiral waves in reaction-diffusion-mechanics systems.
Panfilov, A V; Keldermann, R H; Nash, M P
2007-05-08
Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences.
Linearity stabilizes discrete breathers
Indian Academy of Sciences (India)
T R Krishna Mohan; Surajit Sen
2011-11-01
The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi–Pasta–Ulam (FPU) and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced by the harmonic term stabilize the discrete breather by suppressing the breather’s tendency to delocalize and disperse. We conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these systems.
The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics
Gao, Shan
2016-01-01
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by derivin...
Discrete Multiscale Analysis: A Biatomic Lattice System
Contra, G A Cassatella; 10.1142/S1402925110000957
2010-01-01
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\\"odinger differential equation.
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Advances in one-dimensional wave mechanics. Towards a unified classical view
Energy Technology Data Exchange (ETDEWEB)
Cao, Zhuangqi [Shanghai Jiao Tong Univ., (China). Dept. of Physics and Astronomy; Yin, Cheng [Hohai Univ., Changzhou, Jiangsu (China). College of IoT Engineering
2014-06-01
Introduces a completely new concept of the scattered sub-waves via the Analytical Transfer Matrix (ATM) method. Develops a relatively simple method to accurately solve one-dimensional problems in quantum mechanics. Based on the analogy between the Quantum Mechanics and Electromagnetism, several interesting issues in quantum mechanics, such as tunneling, quantum reflection and scattering time are restudied. Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics.
An analysis of interfacial waves and air ingestion mechanisms
Galimov, Azat
This research was focused on developing analytical methods with which to derive the functional forms of the various interfacial forces in two-fluid models [Galimov et al., 2004], and on the Direct Numerical Simulations (DNS) of traveling breaking waves and plunging liquid jets. Analytical results are presented for a stable stratified wavy two-phase flow and the associated interfacial force densities of a two-fluid model. In particular, the non-drag interfacial force density [Drew & Passman, 1998], the Reynolds stress tensor, and the term ( p˜cli -pcl)∇alphacl, which drives surface waves, were derived, where p˜cli is interfacial average pressure, pcl is the average pressure, and alphacl is the volume fraction of the continuous liquid phase. These functional forms are potentially useful for developing two-fluid model closure relations for computational multiphase fluid dynamics (CMFD) numerical solvers. Moreover, it appears that this approach can be generalized to other flow regimes (e.g., annular flows). A comparison of the analytical and ensemble-averaged DNS results show good agreement, and it appears that this approach can be used to develop phenomenological flow-regime-specific closure laws for two-fluid models [Lahey & Drew, 2004], [Lahey, 2005]. A successful 2-D DNS of breaking traveling waves was performed. These calculations had periodic boundary conditions and the physical parameters for air/water flow at atmospheric pressure, including a liquid/gas density ratio of 1,000 and representative surface tension and viscosities. Detailed 3-D DNS was also made for a plunging liquid jet. The processes of forming the liquid jet, the associated air cavity, capturing an initial large donut-shaped air bubble, and developing and breaking-up this bubble into smaller bubbles due to liquid shear, were shown. These simulations showed that the inertia of the liquid jet initially depressed the pool's surface and the toroidal liquid eddy formed subsequently resulted in air
Mechanical Values Transformer on the Surface Acoustic Waves
Directory of Open Access Journals (Sweden)
V. O. Piddubnyi
2008-05-01
Full Text Available Calculation of parameters of the membrane type mechanical values transformer into the frequency electric signal is rewired. The article deals with the issues of deformational and heat sensitivity. Results of research are shown.
A review of wave mechanics in the pulmonary artery with an emphasis on wave intensity analysis
DEFF Research Database (Denmark)
Su, Junjing; Hilberg, Ole; Howard, Luke
2016-01-01
Mean pulmonary arterial pressure and pulmonary vascular resistance (PVR) remain the most common haemodynamic measures to evaluate the severity and prognosis of pulmonary hypertension. However, PVR only captures the non-oscillatory component of the right ventricular hydraulic load and neglects...... reflection are observed in patients with pulmonary hypertension and in animal models exposed to hypoxia. Studying wave propagation makes a valuable contribution to the assessment of the arterial system in pulmonary hypertension, and here, we briefly review the current state of knowledge of the methods used...
Wave-optics description of self-healing mechanism in Bessel beams.
Aiello, Andrea; Agarwal, Girish S
2014-12-15
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.
Mechanical constraint converts planar waves into helices on tunicate and sea urchin sperm flagella.
Ishijima, Sumio
2012-01-01
The change in the flagellar waves of spermatozoa from a tunicate and sea urchins was examined using high-speed video microscopy to clarify the regulation of localized sliding between doublet microtubules in the axoneme. When the tunicate Ciona spermatozoa attached to a coverslip surface by their heads in seawater or they moved in seawater with increased viscosity, the planar waves of the sperm flagella were converted into left-handed helical waves. On the other hand, conversion of the planar waves into helical waves in the sea urchin Hemicentrotus spermatozoa was not seen in seawater with an increased viscosity as well as in ordinary seawater. However, the sea urchin Clypeaster spermatozoa showed the conversion, albeit infrequently, when they thrust their heads into seawater with an increased viscosity. The chirality of the helical waves of the Clypeaster spermatozoa was right-handed. When Ciona spermatozoa swam freely near a glass surface, they moved in relatively large circular paths (yawing motion). There was no difference in the proportion of spermatozoa yawing in either a clockwise or counterclockwise direction when viewed from above, which was also different from that of the sea urchin spermatozoa. These observations suggest that the planar waves generally observed on the sperm flagella are mechanically regulated, although their stability must depend on the Ca(2+) concentration in the cell. Furthermore, the chirality of the helical waves may be determined by the intracellular Ca(2+) concentration and changed by transmitting the localized active sliding between the doublet microtubules around the axoneme in an alternative direction.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Directory of Open Access Journals (Sweden)
Augusto Hernández Vidal
2011-12-01
Full Text Available In order to strengthen the concept of municipal autonomy, this essay proposes an extensive interpretation of administrative discretion. Discretion is the exercise of free judgment given by law to authorities for performing official acts. This legislative technique seems to be suitable whenever the legislative is intended to legislate over the essential core of municipal autonomy. This way, an eventual abuse of that autonomy could be avoided, for the disproportional restriction of the local faculty to oversee the local issues. This alternative is presented as a tool to provide with dynamism the performing of administrative activities as well, aiming to assimilate public administration new practices.
Low Model Analysis and Synchronous Simulation of the Wave Mechanics
Directory of Open Access Journals (Sweden)
Wenyuan Duan
2016-01-01
Full Text Available The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.
Nonlinear mechanisms for drift wave saturation and induced particle transport
Energy Technology Data Exchange (ETDEWEB)
Dimits, A.M. (Maryland Univ., College Park, MD (USA). Lab. for Plasma Research); Lee, W.W. (Princeton Univ., NJ (USA). Plasma Physics Lab.)
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E {times} B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional ( pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs.
Directory of Open Access Journals (Sweden)
S. I. Sherman
2015-09-01
Full Text Available Deformation waves as a trigger mechanism of seismic activity and migration of earthquake foci have been under discussion by researchers in seismology and geodynamics for over 50 years. Four sections of this article present available principal data on impacts of wave processes on seismicity and new data. The first section reviews analytical and experimental studies aimed at identification of relationships between wave processes in the lithosphere and seismic activity manifested as space-and-time migration of individual earthquake foci or clusters of earthquakes. It is concluded that with a systematic approach, instead of using a variety of terms to denote waves that trigger seismic process in the lithosphere, it is reasonable to apply the concise definition of ‘deformation waves’, which is most often used in fact.The second section contains a description of deformation waves considered as the trigger mechanism of seismic activity. It is concluded that a variety of methods are applied to identify deformation waves, and such methods are based on various research methods and concepts that naturally differ in sensitivity concerning detection of waves and/or impact of the waves on seismic process. Epicenters of strong earthquakes are grouped into specific linear or arc-shaped systems, which common criterion is the same time interval of the occurrence of events under analysis. On site the systems compose zones with similar time sequences, which correspond to the physical notion of moving waves (Fig. 9. Periods of manifestation of such waves are estimated as millions of years, and a direct consideration of the presence of waves and wave parameters is highly challenging. In the current state-of-the-art, geodynamics and seismology cannot provide any other solution yet.The third section presents a solution considering record of deformation waves in the lithosphere. With account of the fact that all the earthquakes with М≥3.0 are associated with
Mechanisms of realization of THz-waves of nitrogen oxide occurrence physiological effects
Directory of Open Access Journals (Sweden)
Vyacheslav F. Kirichuk
2013-11-01
Full Text Available In this review, there is generalized material of many experimental researches in interaction of THz-waves molecular emission and absorption spectrum (MEAS of nitrogen oxide occurrence with bioobjects. Thrombocytes and experimental animals were used as bioobjects. The experiments let indicate changes caused by THz-waves: at the cellular, tissular, system, organismic levels. There are all data of changes in physiological mechanisms of reglations at all levels: autocrine, paracrine, endocrine and nervous. There is a complex overview of experimental material firstly performed in the article. There had been shown that the effect of THz-waves of the given occurrence is realized by the changed activity of nitroxidergic system. It had been proved that THz-waves of nitrogen oxide occurrence can stimulate nitrogen oxide producing in organs and tissues in condition of its low concentration. Possible mechanisms of antiaggregative effect of the given waves had been described. There had been shown the possibility of regulating of vascular tone and system hemodynamics with the help of the studying these frequencies. The represented data of lipid peroxidation and enzymatic and nonenzymatic components of organism system under the influence of THz-waves of nitrogen oxide occurrence in stress conditions. Besides, there were shown changes of stress-regulating system activity and in concentration of important mediators - catecholamines and glucocorticosteroids. These data let characterize mechanism of realization of THz-waves basic effects. The research had shown the possibility of THz-waves of nitrogen oxide occurrence usage as a method of natural physiological noninvasive regulation of significant organism functions.
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.; Andersen, Torben Ole
2014-01-01
Fluid power systems are the leading technology for power take off systems in ocean wave energy converters. However, fluid power systems often suffer from poor efficiency, especially in part loads. This degrades the PTO system efficiency and therefore lowers the energy production. To overcome...... less than 10 ms. The pilot stage is directly actuated and utilises internal valve pressure as supply and an external tank connection as drain. The current paper presents the multi-disciplinary design process leading to the final valve design. This includes the geometric design of the main stage......, the choice of pilot valve, structural mechanical issues and modelling and simulation of various valve configurations. Hence, a mechatronic design process is utilised to choose the best valve configuration....
Electro-thermo-mechanical model for bulk acoustic wave resonators.
Rocas, Eduard; Collado, Carlos; Mateu, Jordi; Orloff, Nathan D; Aigner, Robert; Booth, James C
2013-11-01
We present the electro-thermo-mechanical constitutive relations, expanded up to the third order, for a BAW resonator. The relations obtained are implemented into a circuit model, which is validated with extensive linear and nonlinear measurements. The mathematical analysis, along with the modeling, allows us to identify the dominant terms, which are the material temperature derivatives and two intrinsic nonlinear terms, and explain, for the first time, all observable effects in a BAW resonator by use of a unified physical description. Moreover, the terms that are responsible for the second-harmonic generation and the frequency shift with dc voltage are shown to be the same.
An Alternative to Wave Mechanics on Curved Spaces
Tomaschitz, R
1992-01-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, non-semiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set L(G) of the Kleinian group G of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(L)/G, C(L) being the hyperbolic convex hull of L(G). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products I x S, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimen...
An alternative to wave mechanics on curved spaces
Tomaschitz, Roman
1992-02-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, nonsemiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H 3 in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set λ(γ) of the Kleinian group γ of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(λ)γ, C(λ) being the hyperbolic convex hull of λ(γ). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products I× S, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimension δ of λ, and give various examples for the calculation of δ from the tessellations of the boundary of H 3, induced by the universal coverings of the manifolds.
Simoes, Fernando; Pfaff, Robert; Berthelier, Jean-Jacques; Klenzing, Jeffrey
2012-01-01
Investigation of coupling mechanisms between the troposphere and the ionosphere requires a multidisciplinary approach involving several branches of atmospheric sciences, from meteorology, atmospheric chemistry, and fulminology to aeronomy, plasma physics, and space weather. In this work, we review low frequency electromagnetic wave propagation in the Earth-ionosphere cavity from a troposphere-ionosphere coupling perspective. We discuss electromagnetic wave generation, propagation, and resonance phenomena, considering atmospheric, ionospheric and magnetospheric sources, from lightning and transient luminous events at low altitude to Alfven waves and particle precipitation related to solar and magnetospheric processes. We review in situ ionospheric processes as well as surface and space weather phenomena that drive troposphere-ionosphere dynamics. Effects of aerosols, water vapor distribution, thermodynamic parameters, and cloud charge separation and electrification processes on atmospheric electricity and electromagnetic waves are reviewed. We also briefly revisit ionospheric irregularities such as spread-F and explosive spread-F, sporadic-E, traveling ionospheric disturbances, Trimpi effect, and hiss and plasma turbulence. Regarding the role of the lower boundary of the cavity, we review transient surface phenomena, including seismic activity, earthquakes, volcanic processes and dust electrification. The role of surface and atmospheric gravity waves in ionospheric dynamics is also briefly addressed. We summarize analytical and numerical tools and techniques to model low frequency electromagnetic wave propagation and solving inverse problems and summarize in a final section a few challenging subjects that are important for a better understanding of tropospheric-ionospheric coupling mechanisms.
Evaluation of major heat waves' mechanisms in EURO-CORDEX RCMs over Central Europe
Lhotka, Ondřej; Kyselý, Jan; Plavcová, Eva
2017-09-01
The main aim of the study is to evaluate the capability of EURO-CORDEX regional climate models (RCMs) to simulate major heat waves in Central Europe and their associated meteorological factors. Three reference major heat waves (1994, 2006, and 2015) were identified in the E-OBS gridded data set, based on their temperature characteristics, length and spatial extent. Atmospheric circulation, precipitation, net shortwave radiation, and evaporative fraction anomalies during these events were assessed using the ERA-Interim reanalysis. The analogous major heat waves and their links to the aforementioned factors were analysed in an ensemble of EURO-CORDEX RCMs driven by various global climate models in the 1970-2016 period. All three reference major heat waves were associated with favourable circulation conditions, precipitation deficit, reduced evaporative fraction and increased net shortwave radiation. This joint contribution of large-scale circulation and land-atmosphere interactions is simulated with difficulties in majority of the RCMs, which affects the magnitude of modelled major heat waves. In some cases, the seemingly good reproduction of major heat waves' magnitude is erroneously achieved through extremely favourable circulation conditions compensated by a substantial surplus of soil moisture or vice versa. These findings point to different driving mechanisms of major heat waves in some RCMs compared to observations, which should be taken into account when analysing and interpreting future projections of these events.
Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning
2017-08-01
Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.
Mechanism of destruction of transport barriers in geophysical jets with Rossby waves
Uleysky, M Yu; Prants, S V; 10.1103/PhysRevE.81.017202
2012-01-01
The mechanism of destruction of a central transport barrier in a dynamical model of a geophysical zonal jet current in the ocean or the atmosphere with two propagating Rossby waves is studied. We develop a method for computing a central invariant curve which is an indicator of existence of the barrier. Breakdown of this curve under a variation of the Rossby wave amplitudes and onset of chaotic cross-jet transport happen due to specific resonances producing stochastic layers in the central jet. The main result is that there are resonances breaking the transport barrier at unexpectedly small values of the amplitudes that may have serious impact on mixing and transport in the ocean and the atmosphere. The effect can be found in laboratory experiments with azimuthal jets and Rossby waves in rotating tanks under specific values of the wave numbers that are predicted in the theory.
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
A dendritic mechanism for decoding traveling waves: principles and applications to motor cortex.
Directory of Open Access Journals (Sweden)
Stewart Heitmann
2013-10-01
Full Text Available Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons - the principle outputs of the motor cortex - decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.
Laboratory investigation on mechanisms of stress wave propagations in porous media
Institute of Scientific and Technical Information of China (English)
JU Yang; YANG YongMing; MAO YanZhe; LIU HongBin; WANG HuiJie
2009-01-01
A number of porous models having the similar statistical characteristics of pores and physical properties with natural sandstones have been produced using reactive powder concrete (RPC) and polystyrene. Spit-Hopkinson-Pressure -Bar tests and CT scans have been carried out on the models with the various porosities to probe the performance of wave propagations and the responses of pores and the matrix during wave propagations. It is shown that porosities significantly influence wave propagations. For an identical impact strain rate, the greater the porosity is, the larger the amplitude of the reflected wave appears, the more the peak in the reflected wave presents, and the smaller the amplitude of the trans-mitted wave turns out. A single peak emerges in the reflected wave when the porosity falls down to 5%.The larger the impact strain rate, the much remarkable the phenomena. The energy-dissipated ratio of porous models, i.e., WJ/Wb linearly increases with the increment of porosities. The ratio is sensitive to the impact strain rate. Differences in the performance of wave propagations and energy dissipation result from the varied mechanisms that pores response to impacts. For the porosity less than 10%, the mechanism appears to be a process fracturing the matrix to generate new surfaces or pores. Energy has primarily been dissipated in creating new surfaces or pores. No apparent pore deformation takes place. The impact strain rate takes little effect on pore geometry. For the porosity of 15% or more, the mechanism works depending on the impact strain rate. When a low impact strain rate applies, the mechanism still appears to crack the matrix to generate surfaces or pores, but the amount is lower as compared to the case with a low porosity. If a large impact stain rate applies, the mechanism combines both fracturing the matrix and deforming the pores, with the deforming pores predominating. The vast majority of energy has been dissipated to deform pores. Only high
Laboratory investigation on mechanisms of stress wave propagations in porous media
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A number of porous models having the similar statistical characteristics of pores and physical properties with natural sandstones have been produced using reactive powder concrete(RPC) and polystyrenes.Spit-Hopkinson-Pressure-Bar tests and CT scans have been carried out on the models with the various porosities to probe the performance of wave propagations and the responses of pores and the matrix during wave propagations.It is shown that porosities significantly influence wave propagations.For an identical impact strain rate,the greater the porosity is,the larger the amplitude of the reflected wave appears,the more the peak in the reflected wave presents,and the smaller the amplitude of the trans-mitted wave turns out.A single peak emerges in the reflected wave when the porosity falls down to 5%.The larger the impact strain rate,the much remarkable the phenomena.The energy-dissipated ratio of porous models,i.e.,WJ /WI,linearly increases with the increment of porosities.The ratio is sensitive to the impact strain rate.Differences in the performance of wave propagations and energy dissipation result from the varied mechanisms that pores response to impacts.For the porosity less than 10%,the mechanism appears to be a process fracturing the matrix to generate new surfaces or pores.Energy has primarily been dissipated in creating new surfaces or pores.No apparent pore deformation takes place.The impact strain rate takes little effect on pore geometry.For the porosity of 15% or more,the mechanism works depending on the impact strain rate.When a low impact strain rate applies,the mechanism still appears to crack the matrix to generate surfaces or pores,but the amount is lower as compared to the case with a low porosity.If a large impact stain rate applies,the mechanism combines both fracturing the matrix and deforming the pores,with the deforming pores predominating.The vast majority of energy has been dissipated to deform pores.Only high porosity and impact strain rate
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios
2016-10-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
A Mechanism of the Effect of Non-uniform Current on the Spectrum of Short Wind Waves
Institute of Scientific and Technical Information of China (English)
ZHENG Guizhen; SHENG Lifang; CONG Peixiu
2004-01-01
A mechanism is suggested in this paper concerning the effect of non-uniform current on the spectrum of short wind waves. According to this mechanism, a non-uniform current brings changes to the breaking criteria of short wind waves through modulating the surface drift, and hence enhances or weakens wave breaking. Some modification is proposed to the source term, which represents the spectral rate of wave energy dissipation due to wave breaking so that the source term can incorporate this mechanism. In order to illustrate whether this mechanism is significant, a real case is studied, in which the wind waves propagate on a tidal current flowing over the sea bottom covered with sand waves. Finally, the effect of the new mechanism on the equilibrium spectrum of small scale gravity waves is discussed. Numerical estimates suggest that, for water depths less than 50 m and wavelengths less than 1 m, this current field may result in distinct spatial variations of the wave breaking criteria, the spectral rate of wave energy dissipation and the equilibrium spectrum of short gravity waves.
On coherent-state representations of quantum mechanics: Wave mechanics in phase space
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Torres-Vega, Gabino
1997-01-01
one wants to solve the stationary Schrodinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented...
Tunneling time distribution by means of Nelson’s quantum mechanics and wave-particle duality
Indian Academy of Sciences (India)
Koh'Ichiro Hara; Ichiro Ohba
2002-08-01
We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we ﬁnd that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.
Directory of Open Access Journals (Sweden)
V. V. Piddubnyi
2010-01-01
Full Text Available Normal 0 false false false RU X-NONE X-NONE MicrosoftInternetExplorer4 Examined the problems usage differential amplifier as an active part of the secondary transformer mechanical values in the electrical signal to the surface acoustic wave. Description and results of his researches is resulted.
The blowup mechanism for 3-D quasilinear wave equations with small data
Institute of Scientific and Technical Information of China (English)
尹会成
2000-01-01
For a class of special three-dimensional quasilinear wave equations, we study the blowup mechanism of classical solutions. More precisely, under the nondegenerate conditions, any radially symmetric solution with small initial data is shown to develop singularities in the second order derivatives while the first order derivatives and itself remain continuous, moreover the blowup of solution is of "cusp type".
Using High Speed Smartphone Cameras and Video Analysis Techniques to Teach Mechanical Wave Physics
Bonato, Jacopo; Gratton, Luigi M.; Onorato, Pasquale; Oss, Stefano
2017-01-01
We propose the use of smartphone-based slow-motion video analysis techniques as a valuable tool for investigating physics concepts ruling mechanical wave propagation. The simple experimental activities presented here, suitable for both high school and undergraduate students, allows one to measure, in a simple yet rigorous way, the speed of pulses…
Reducing pressure oscillations in discrete fluid power systems
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik Clemmensen
2016-01-01
Discrete fluid power systems featuring transmission lines inherently include pressure oscillations. Experimental verification of a discrete fluid power power take off system for wave energy converters has shown the cylinder pressure to oscillate as force shifts are performed. This article...
Thaker, A. A.; Chelliah, H. K.
1997-12-01
Modelling of the structure and the limiting flow turning angles of an oblique detonation wave, established by a two-dimensional wedge, requires the implementation of detailed chemical kinetic models involving a large number of chemical species. In this paper, a method of reducing the computational effort involved in simulating such high-speed reacting flows by implementing a systematically reduced reaction mechanism is presented. For a hydrogen - air mixture, starting with an elementary mechanism having eight species in 12 reactions, three alternate four-step reduced reaction mechanisms are developed by introducing the steady-state approximation for the reaction intermediates HO2, O and OH, respectively. Additional reduction of the computational effort is achieved by introducing simplifications to the thermochemical data evaluations. The influence of the numerical grid used in predicting the induction process behind the shock is also investigated. Comparisons of the induction zone predicted by two-dimensional oblique detonation wave calculations with that of a static reactor model (with initial conditions of the gas mixture specified by those behind the nonreactive oblique shock wave) are also presented. The reasonably good agreement between the three four-step reduced mechanism predictions and the starting mechanism predictions indicates that further reduction to a two-step mechanism is feasible for the physical flow time scales (corresponding to inflow Mach numbers of 8 - 10) considered here, and needs to be pursued in the future.
The Role of Waves in the Explosion Mechanism of Core-Collapse Supernovae
Gossan, Sarah; Fuller, Jim; Roberts, Luke
2017-01-01
The core-collapse supernova (CCSN) explosion mechanism is not well understood. For garden variety CCSNe, the favored explosion scenario is delayed revival of the stalled shock powered by neutrino-driven convection. Despite huge computational advances, many simulations must use parameterized `light-bulb' models for neutrino heating or mask out inner regions of the proto-neutron star (PNS) for computational efficiency. These approximations can fail to capture hydrodynamical processes in the PNS core where nearly all the binding energy resides, and from which much of the explosion energy may originate. We show that gravity waves excited by core PNS convection may represent a significant heating source for the post-shock region. Using 1D simulations, we calculate the wave heating rate in the post-shock region out to one second after core bounce, showing that wave heating rates in excess of 1051 erg/s may persist for several hundreds of milliseconds, even after neutrino heating rates have decreased. Waves excited by PNS convection may therefore significantly contribute to shock revival and, subsequently, a successful and energetic explosion. We discuss how simulations can miss the effect of waves, and how future simulations can more accurately quantify wave heating rates.
Mittermayr, Rainer; Antonic, Vlado; Hartinger, Joachim; Kaufmann, Hanna; Redl, Heinz; Téot, Luc; Stojadinovic, Alexander; Schaden, Wolfgang
2012-01-01
For almost 30 years, extracorporeal shock wave therapy has been clinically implemented as an effective treatment to disintegrate urinary stones. This technology has also emerged as an effective noninvasive treatment modality for several orthopedic and traumatic indications including problematic soft tissue wounds. Delayed/nonhealing or chronic wounds constitute a burden for each patient affected, significantly impairing quality of life. Intensive wound care is required, and this places an enormous burden on society in terms of lost productivity and healthcare costs. Therefore, cost-effective, noninvasive, and efficacious treatments are imperative to achieve both (accelerated and complete) healing of problematic wounds and reduce treatment-related costs. Several experimental and clinical studies show efficacy for extracorporeal shock wave therapy as means to accelerate tissue repair and regeneration in various wounds. However, the biomolecular mechanism by which this treatment modality exerts its therapeutic effects remains unclear. Potential mechanisms, which are discussed herein, include initial neovascularization with ensuing durable and functional angiogenesis. Furthermore, recruitment of mesenchymal stem cells, stimulated cell proliferation and differentiation, and anti-inflammatory and antimicrobial effects as well as suppression of nociception are considered important facets of the biological responses to therapeutic shock waves. This review aims to provide an overview of shock wave therapy, its history and development as well as its current place in clinical practice. Recent research advances are discussed emphasizing the role of extracorporeal shock wave therapy in soft tissue wound healing.
On the mechanism of self gravitating Rossby interfacial waves in proto-stellar accretion discs
Yellin-Bergovoy, Ron; Heifetz, Eyal; Umurhan, Orkan M.
2016-05-01
The dynamical response of edge waves under the influence of self-gravity is examined in an idealized two-dimensional model of a proto-stellar disc, characterized in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius r0. The fluid in basic state is prescribed to rotate with a Keplerian profile $\\Omega_k(r)\\sim r^{-3/2}$ modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabilizer irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of vorticity edge waves. The roles of both Boussinesq and non-Boussinesq effects upon the stability and propagation of these waves with and without the inclusion of self-gravity are then quantified. The dynamics involved with self-gravity non- Boussinesq effect is shown to be a source of vorticity production where there is a jump in the basic state density, in addition, self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect . Further applications of these mechanical insights are presented in the conclusion including the ways in which multiple density jumps or gaps may or may not be stable.
The Role of Waves in the Explosion Mechanism of Core-Collapse Supernovae
Gossan, Sarah; Fuller, Jim; Roberts, Luke
2017-01-01
The core-collapse supernova (CCSN) explosion mechanism is not well understood. For garden variety CCSNe, the favored scenario for explosion is delayed revival of the stalled shock powered by neutrino-driven convection. Despite tremendous computational advances, many simulations must use parameterized ‘light-bulb’ models for neutrino heating or mask out inner regions of the proto-neutron star (PNS) for computational efficiency. These approximations can fail to capture hydrodynamical processes in the core of the PNS where nearly all the binding energy resides, and from which much of the explosion energy may originate. We show that gravity (buoyancy) waves excited by core PNS convection (within the central 20 km of the PNS) may represent a significant heating source for the post-shock region. The gravity waves propagate out of the PNS and transform into acoustic waves before depositing their energy at the shock, converting a small fraction of the PNS binding energy into explosion energy. Using 1D simulations, we calculate the wave heating rate in the post-shock region out to one second after core bounce, showing that wave heating rates in excess of 1051 erg/s may persist for several hundreds of milliseconds, even after neutrino heating rates have declined to smaller values. Waves excited by PNS convection may therefore significantly contribute to shock revival and, subsequently, a successful and energetic explosion. We discuss how simulations can miss the effect of waves (or have not recognized them), and how future simulations can more accurately quantify wave heating rates.
Manipulating the Magnetization of a Nanomagnet with Surface Acoustic Waves: Spin-Rotation Mechanism
Chudnovsky, Eugene M.; Jaafar, Reem
2016-03-01
We show that the magnetic moment of a nanoparticle embedded in the surface of a solid can be switched by surface acoustic waves in the GHz frequency range via a universal mechanism that does not depend on the structure of the particle and the structure of the substrate. It is based upon the generation of the effective ac magnetic field in the coordinate frame of the nanoparticle by the shear deformation of the surface due to surface acoustic waves. The magnetization reversal occurs via a consecutive absorption of surface phonons of the controlled variable frequency. We derive analytical equations governing this process and solve them numerically for the practical range of parameters.
Numerical modeling and analysis of the mechanism of a novel shock wave regulator for impact test
Institute of Scientific and Technical Information of China (English)
Wang Gongxian; Zhang Zhiyi; Wang Yu
2008-01-01
Based on the concept of hydraulic dissipation of kinetic energy, a novel shock wave regulator, which is composed of a damper and an externally triggered valve, is presented with thorough analyses on its working mechanism. By establishing motion equations of each component of the regulator and simulating the dynamic behavior of the whole system, the shock wave regulator is demonstrated numerically to be able to change the width and amplitude of shock pulses. Prompt and easy adjustment can be achieved by changing the equivalent flow area of damping orifices and consequently the closing velocity of the flow area of a valve, which makes it applicable to different impact testing.
Barniol, Pablo; Zavala, Genaro
2016-06-01
In this article we present several modifications of the mechanical waves conceptual survey, the most important test to date that has been designed to evaluate university students' understanding of four main topics in mechanical waves: propagation, superposition, reflection, and standing waves. The most significant changes are (i) modification of several test questions that had some problems in their original design, (ii) standardization of the number of options for each question to five, (iii) conversion of the two-tier questions to multiple-choice questions, and (iv) modification of some questions to make them independent of others. To obtain a final version of the test, we administered both the original and modified versions several times to students at a large private university in Mexico. These students were completing a course that covers the topics tested by the survey. The final modified version of the test was administered to 234 students. In this study we present the modifications for each question, and discuss the reasons behind them. We also analyze the results obtained by the final modified version and offer a comparison between the original and modified versions. In the Supplemental Material we present the final modified version of the test. It can be used by teachers and researchers to assess students' understanding of, and learning about, mechanical waves.
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
2017-01-01
We report a computational fluid dynamics–discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas–solid contact efficiencies. Cluster gas–solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors. PMID:28553011
Double-slit experiment with single wave-driven particles and its relation to quantum mechanics.
Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T; Bohr, Tomas
2015-07-01
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.
Surface acoustic wave opto-mechanical oscillator and frequency comb generator.
Savchenkov, A A; Matsko, A B; Ilchenko, V S; Seidel, D; Maleki, L
2011-09-01
We report on realization of an efficient triply resonant coupling between two long lived optical modes and a high frequency surface acoustic wave (SAW) mode of the same monolithic crystalline whispering gallery mode resonator. The coupling results in an opto-mechanical oscillation and generation of a monochromatic SAW. A strong nonlinear interaction of this mechanical mode with other equidistant SAW modes leads to mechanical hyperparametric oscillation and generation of a SAW pulse train and associated frequency comb in the resonator. We visualized the comb by observing the modulation of the light escaping the resonator.
A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment
Goodman, Roy H.; Rahman, Aminur; Bellanich, Michael J.; Morrison, Catherine N.
2015-04-01
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to exhibit the two-bounce resonance.
Schaeffer, Marshall; Ruzzene, Massimo
2016-01-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behavior, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centering image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subsequent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing ...
Institute of Scientific and Technical Information of China (English)
JingLiu; XingguoSun; 等
1996-01-01
To make it possible for the thermal wave theory on temperature oscillation (TO)effects in living tissues to be founded on the substantial experimental basis,a series of typical decisive experiments in vivo as well as in artificially simulating costructions were carred out.COnclusions obtained including some other scholars animal experimental results all greatly support the thermal wave viewpoint qualitatively,A few experimental facts used not to be easily understood from the classical viewpoint are also well reinterpreted.The revealing on the thermal wave mechanisms of TO in living tissues is a brand new discovery and deep insight into this important thermophysiological phenomenon,It may possibly promote new investigations on the corresponding topics in the field of bioheat transfer science.
Photonic Rutherford Scattering: A Classical and Quantum Mechanical Analogy in Ray- and Wave-Optics
Selmke, Markus
2012-01-01
Using Fermat's least optical path principle the family of ray-trajectories through a special but common type of a gradient refractive index lens, n(r)=n_0+\\Delta n R/r, is solved analytically. The solution, i.e. the ray-equation r(phi), is shown to be closely related to the famous Rutherford scattering and therefore termed photonic Rutherford scattering. It is shown that not only do these classical limits correspond, but also the wave-mechanical pictures coincide: The time-independent Schr\\"odingier equation and the inhomogeneous Helmholz equation permit the same mapping between massive particle scattering and diffracted optical scalar waves. Scattering of narrow wave-packets finally recovers the classical trajectories. The analysis suggests that photothermal single particle microscopy infact measures photonic Rutherford scattering in specific limits.
The operation of stochastic heating mechanisms in an electromagnetic standing wave configuration
Energy Technology Data Exchange (ETDEWEB)
Gell, Y.; Nakach, R.
1991-10-01
The possibility of the operation of stochastic heating mechanisms of charged particles in a configuration consisting of a left-handed circularly polarized standing electromagnetic wave and a uniform magnetic field, has been studied numerically and theoretically. It is found that such a configuration induces stochasticity, the threshold of which is dependent on two independent parameters, determined by the frequency and the amplitude of the wave and the strength of the magnetic field. From the theoretical analysis, it emerges that the origin of onset of large scale stochasticity is the destabilization of fixed points associated with an equation describing the motion of the particles in an electrostatic-type potential having standing wave characteristics. The comparison of the theoretical predictions with the numerical results is found to be quite satisfactory. Possible applications to realistic plasmas have been discussed.
Profit, Matthew; Dutko, Martin; Yu, Jianguo; Cole, Sarah; Angus, Doug; Baird, Alan
2016-04-01
This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretisation. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings, a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretisation. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice, the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microseismic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology.
Institute of Scientific and Technical Information of China (English)
Wen－QingLu
1993-01-01
A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity and temperature gradients are dliminated.and the complete formulation is written in terms of velocity and temperature,This provides considerable reduction is storage and computational requirements while improving accuracy.The non-linear equation systems of boundary element discretization are solved by the quasi-Nweton iterative scheme with Broyden's update.The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained,and the variations of Nusselt numbers along the wall-liquid interface are also given.There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave.This special flow and thermal process can be a mechanism to enhance heat transport.
Wang, Shang; Lopez, Andrew L.; Morikawa, Yuka; Tao, Ge; Li, Jiasong; Larina, Irina V.; Martin, James F.; Larin, Kirill V.
2015-03-01
Optical coherence elastography (OCE) is an emerging low-coherence imaging technique that provides noninvasive assessment of tissue biomechanics with high spatial resolution. Among various OCE methods, the capability of quantitative measurement of tissue elasticity is of great importance for tissue characterization and pathology detection across different samples. Here we report a quantitative OCE technique, termed quantitative shear wave imaging optical coherence tomography (Q-SWI-OCT), which enables noncontact measurement of tissue Young's modulus based on the ultra-fast imaging of the shear wave propagation inside the sample. A focused air-puff device is used to interrogate the tissue with a low-pressure short-duration air stream that stimulates a localized displacement with the scale at micron level. The propagation of this tissue deformation in the form of shear wave is captured by a phase-sensitive OCT system running with the scan of the M-mode imaging over the path of the wave propagation. The temporal characteristics of the shear wave is quantified based on the cross-correlation of the tissue deformation profiles at all the measurement locations, and linear regression is utilized to fit the data plotted in the domain of time delay versus wave propagation distance. The wave group velocity is thus calculated, which results in the quantitative measurement of the Young's modulus. As the feasibility demonstration, experiments are performed on tissuemimicking phantoms with different agar concentrations and the quantified elasticity values with Q-SWI-OCT agree well with the uniaxial compression tests. For functional characterization of myocardium with this OCE technique, we perform our pilot experiments on ex vivo mouse cardiac muscle tissues with two studies, including 1) elasticity difference of cardiac muscle under relaxation and contract conditions and 2) mechanical heterogeneity of the heart introduced by the muscle fiber orientation. Our results suggest the
Educing the emission mechanism of internal gravity waves in the differentially heat rotating annulus
Rolland, Joran; Hien, Steffen; Achatz, Ulrich; Borchert, Sebastian; Fruman, Mark
2016-04-01
Understanding the lifecycle of gravity waves is fundamental to a good comprehension of the dynamics of the atmosphere. In this lifecycle, the emission mechanisms may be the most elusive. Indeed, while the emission of gravity waves by orography or convection is well understood, the so-called spontaneous emission is still a quite open topic of investigation [1]. This type of emission usually occur very near jet-front systems in the troposphere. In this abstract, we announce our numerical study of the question. Model systems of the atmosphere which can be easily simulated or built in a laboratory have always been an important part of the study of atmospheric dynamics, alongside global simulations, in situ measurements and theory. In the case of the study of the spontaneous emission of gravity waves near jet-front systems, the differentially heated rotating annulus set up has been proposed and extensively used. It comprises of an annular tank containing water: the inner cylinder is kept at a cold temperature while the outer cylinder is kept at a warm temperature. The whole system is rotating. Provided the values of the control parameters (temperature, rotation rate, gap between the cylinders, height of water) are well chosen, the resulting flow mimics the troposphere at midlatitudes: it has a jet stream, and a baroclinic lifecycle develops on top of it. A very reasonable ratio of Brunt-Väisälä frequency over rotation rate of the system can be obtained, so as to be as close to the atmosphere as possible. Recent experiments as well as earlier numerical simulations in our research group have shown that gravity waves are indeed emitted in this set up, in particular near the jet front system of the baroclinic wave [2]. After a first experimental stage of characterising the emitted wavepacket, we focused our work on testing hypotheses on the gravity wave emission mechanism: we have tested and validated the hypothesis of spontaneous imbalance generated by the flow in
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Institute of Scientific and Technical Information of China (English)
高伟; 耿建华
2013-01-01
介绍一种基于离散粒子理论地震波传播数值模拟的网格剖分计算方法.根据离散粒子理论,将研究区域划分为由一系列相互作用的粒子组成的正六边形网格,这些粒子在它们的接触点处发生相互作用,并用Hooke定律和Newton定律描述.为解决六边形网格带来的网格交错而难以计算以及波场输出问题,将横向网格进行加密,加密处赋予假想的粒子,输出波场时选取偶数行偶数列点或奇数行奇数列点的波场值.均匀介质和层状介质模型的数值模拟结果表明,该网格剖分计算方法能够将离散粒子理论用于模拟弹性波在非均匀各向同性介质中地震波的传播.%A mesh generation calculation method based on discrete particle scheme for numerical modeling seismic waves is presented.According to the discrete particle theory,the study area can be divided into regular hexagon grid composed of a series of interacting particles.These particles interact at their contact points and the motion of particles in space is described by Hook's Law and Newton's Law.To solve the problem of the grid crisscross brought by hexagon grids which may lead to difficulty in calculation and output wave field's value,we encrypt the imaginary particles at the horizontal grids and output the wave field value of the even lines＇ points in the even column or odd lines＇ points in odd column.The numerical simulation results of homogeneous model and layer model proved that this mesh generation calculation method based on discrete particle theory is capable of modeling the propagation of elastic waves through heterogeneous isotropic media.
Invariants of Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Discrete Variational Optimal Control
Jimenez, Fernando; de Diego, David Martin
2012-01-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.
Discrete Variational Optimal Control
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Abdoulaye Hama, Nadjibou; Ouahbi, Tariq; Taibi, Said; Souli, Hanène; Fleureau, Jean-Marie; Pantet, Anne
2017-06-01
Non-cohesive soils subjected to a flow may have a behavior in which fine particles migrate through the interstices of the solid skeleton formed by the large particles. This phenomenon is termed internal instability, internal erosion or suffusion, and can occur both in natural soil deposits and also in geotechnical structures such as dams, dikes or barrages. Internal instability of a granular material is its inability to prevent the loss of its fine particles under flow effect. It is geometrically possible if the fine particles can migrate through the pores of the coarse soil matrix and results in a change in its mechanical properties. In this work, we uses the three-dimensional Particle Flow Code (PFC3D/DEM) to study the stability/instability of granular materials and their mechanical behavior. Kenney and Lau criterion sets a safe boundary for engineering design. However, it tends to identify stable soils as unstable ones. The effects of instability and erosion, simulated by clipping fine particles from the grading distribution, on the mechanical behaviour of glass ball samples were analysed. The mechanical properties of eroded samples, in which erosion is simulated and gives a new approach for internal stability. A proposal for a new internal stability criterion is established, it is deduced from the analysis of relations between the mechanical behaviour and internal stability, including material contractance.
Cosmic Tsunamis in Modified Gravity: Disruption of Screening Mechanisms from Scalar Waves.
Hagala, R; Llinares, C; Mota, D F
2017-03-10
Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of some screening mechanisms, thereby threatening the viability of these modified gravity theories. Specifically, we show that the waves produced in the symmetron model can increase the amplitude of the fifth force and the parametrized post Newtonian parameters by several orders of magnitude.
Influence of air pressure on mechanical effect of laser plasma shock wave
Institute of Scientific and Technical Information of China (English)
Zhang Yu-Zhu; Wang Guang-An; Zhu Jin-Rong; Shen Zhong-Hua; Ni Xiao-Wu; Lu Jian
2007-01-01
The influence of air pressure on mechanical effect of laser plasma shock wave in a vacuum chamber produced by a Nd:YAG laser has been studied. The laser pulses with pulse width of 10ns and pulse energy of about 320mJ at 1.06μm wavelength is focused on the aluminium target mounted on a ballistic pendulum, and the air pressure in the chamber changes from 2.8 × 103 to 1.01×105pa. The experimental results show that the impulse coupling coefficient changes as the air pressure and the distance of the target from focus change. The mechanical effects of the plasma shock wave on the target are analysed at different distances from focus and the air pressure.
Influence of air pressure on mechanical effect of laser plasma shock wave
Zhang, Yu-Zhu; Wang, Guang-An; Zhu, Jin-Rong; Shen, Zhong-Hua; Ni, Xiao-Wu; Lu, Jian
2007-09-01
The influence of air pressure on mechanical effect of laser plasma shock wave in a vacuum chamber produced by a Nd:YAG laser has been studied. The laser pulses with pulse width of 10ns and pulse energy of about 320mJ at 1.06μm wavelength is focused on the aluminium target mounted on a ballistic pendulum, and the air pressure in the chamber changes from 2.8 × 103 to 1.01 × 105Pa. The experimental results show that the impulse coupling coefficient changes as the air pressure and the distance of the target from focus change. The mechanical effects of the plasma shock wave on the target are analysed at different distances from focus and the air pressure.
Cosmic Tsunamis in Modified Gravity: Disruption of Screening Mechanisms from Scalar Waves
Hagala, R.; Llinares, C.; Mota, D. F.
2017-03-01
Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of some screening mechanisms, thereby threatening the viability of these modified gravity theories. Specifically, we show that the waves produced in the symmetron model can increase the amplitude of the fifth force and the parametrized post Newtonian parameters by several orders of magnitude.
Yingxiang Liu; Weishan Chen; Junkao Liu; Shengjun Shi
2010-01-01
BACKGROUND: Ultrasonic motors (USM) are based on the concept of driving the rotor by a mechanical vibration excited on the stator via piezoelectric effect. USM exhibit merits such as simple structure, quick response, quiet operation, self-locking when power off, nonelectromagnetic radiation and higher position accuracy. PRINCIPAL FINDINGS: A cylindrical type traveling wave ultrasonic motor using cantilever type composite transducer was proposed in this paper. There are two cantilevers on the ...
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
Institute of Scientific and Technical Information of China (English)
Deng Qilin; Zhang Lei; Zhou Jinjin
2004-01-01
Filth adhering to metal pipes can be cleaned by shock wave generated by electrical discharge under water. The mechanism of shock wave effect of electrical discharge under water on filth cleaning is analyzed by building a mechanical model. A metal pipe coated with cement to simulate real filth is cleaned by using electrical discharge under water. The experimental results confirm the mechanical analysis and also show the technology of electrical discharge under water is an very effective method for filth cleaning.
Energy Technology Data Exchange (ETDEWEB)
Nenadic, Ivan Z; Urban, Matthew W; Mitchell, Scott A; Greenleaf, James F [Basic Ultrasound Research Laboratory, Department of Physiology and Biophysics, Mayo Clinic, Rochester, MN 55905 (United States)
2011-04-07
Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of shear wave dispersion ultrasound vibrometry (SDUV), a noninvasive ultrasound-based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave dispersion ultrasound vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify the mechanical properties of soft tissues with a plate-like geometry.
Nenadic, Ivan Z; Urban, Matthew W; Mitchell, Scott A; Greenleaf, James F
2011-04-07
Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of shear wave dispersion ultrasound vibrometry (SDUV), a noninvasive ultrasound-based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave dispersion ultrasound vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify the mechanical properties of soft tissues with a plate-like geometry.
Directory of Open Access Journals (Sweden)
Yingxiang Liu
Full Text Available BACKGROUND: Ultrasonic motors (USM are based on the concept of driving the rotor by a mechanical vibration excited on the stator via piezoelectric effect. USM exhibit merits such as simple structure, quick response, quiet operation, self-locking when power off, nonelectromagnetic radiation and higher position accuracy. PRINCIPAL FINDINGS: A cylindrical type traveling wave ultrasonic motor using cantilever type composite transducer was proposed in this paper. There are two cantilevers on the outside surface of cylinder, four longitudinal PZT ceramics are set between the cantilevers, and four bending PZT ceramics are set on each outside surface of cantilevers. Two degenerate flexural vibration modes spatially and temporally orthogonal to each other in the cylinder are excited by the composite transducer. In this new design, a single transducer can excite a flexural traveling wave in the cylinder. Thus, elliptical motions are achieved on the teeth. The actuating mechanism of proposed motor was analyzed. The stator was designed with FEM. The two vibration modes of stator were degenerated. Transient analysis was developed to gain the vibration characteristic of stator, and results indicate the motion trajectories of nodes on the teeth are nearly ellipses. CONCLUSIONS: The study results verify the feasibility of the proposed design. The wave excited in the cylinder isn't an ideal traveling wave, and the vibration amplitudes are inconsistent. The distortion of traveling wave is generated by the deformation of bending vibration mode of cylinder, which is caused by the coupling effect between the cylinder and transducer. Analysis results also prove that the objective motions of nodes on the teeth are three-dimensional vibrations. But, the vibration in axial direction is minute compared with the vibrations in circumferential and radial direction. The results of this paper can guide the development of this new type of motor.
Energy Technology Data Exchange (ETDEWEB)
Cho, H.; Takemoto, M. [Aoyama Gakuin University, Tokyo (Japan). College of Science and Engineering
1994-07-20
A bulk wave is generated when a pulse laser is irradiated to the material, and the characteristics of a Young`s modulus and Poisson`s ratio can be nondestructively estimated from the bulk wave. The generation mechanism of laser ultrasonic waves must be first clarified for such application. In this paper, fundamental research was conducted to study the generation mechanism of the elastic waves excited by a Q-switched Nd-YAG laser, and the generation method and characteristics of Rayleigh waves. The following result was obtained. A bulk wave is generated by the disk-like adiabatic expansion near the surface if the laser power is small when a spot-shape pulse laser was irradiated. A bulk wave is generated by the thin disk-like adiabatic expansion beneath the surface due to the thermal diffusion in the depth direction of a base material when the laser power becomes large. Moreover, a bulk wave is generated by the impact force due to abrasion and plasma when the power becomes still larger. The information on the bulk wave characteristics and Rayleigh wave was also obtained. 25 refs., 15 figs., 1 tab.
On the nature of the change in the wave function in a measurement in quantum mechanics
Snyder, D M
1996-01-01
Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), ift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696).
DEFF Research Database (Denmark)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many t...
Formation and mechanics of granular waves in gravity and shallow overland flow
Römkens, Mathias J. M.; Suryadevara, Madhu R.; Prasad, Shyam N.
2010-05-01
Sediment transport in overland flow is a highly complex process involving many properties relative to the flow regime characteristics, soil surface conditions, and type of sediment. From a practical standpoint, most sediment transport studies are concerned with developing relationships of rates of sediment movement under different hydraulic regimes in channel flow for use in soil erosion and sediment transport prediction models. Relatively few studies have focused on the more basic aspects of sediment movement in which particle-to-particle, particle-to-boundary, and particle-to-fluid interactions determine in an important way the nature of the movement. Our experimental work under highly controlled experimental conditions with both gravity flow of granular material (glass beads) in air and sediment transport (sand particles and glass beads) in shallow overland flow have shown that sediment movement is not a simple phenomenon solely determined by flow rates on a proportional basis, but that it is represented by a highly structured and organized regime determined by sedimentary fluid mechanical principles which yield very characteristic waves during transport. In the gravity flow case involving granular chute flow, two-dimensional grain waves developed into the rolling and saltating moving grain mass at certain grain concentrations. This phenomenon appeared to be related to an energy exchange process as a result of collisions between moving grain particles that led to reduced kinetic velocities. As a result, particle concentration differences in the direction of flow developed that were noted as denser zones. In these zones, particles dropped out at the upstream part of these denser zones to resume their accelerating motion once they reached the downstream part of the zone until, during the next collision event, the process is repeated. Thus a periodic granular wave structure evolved. Depending on the addition rate, the granular flow regime may be a fluidized
Energy cascade in internal wave attractors
Brouzet, Christophe; Joubaud, Sylvain; Sibgatullin, Ilias; Dauxois, Thierry
2016-01-01
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction.
A Mechanism for Land-Atmosphere Feedback Involving Planetary Wave Structures
Koster, Randal D.; Chang, Yehui; Schubert, Siegfried D.
2014-01-01
While the ability of land surface conditions to influence the atmosphere has been demonstrated in various modeling and observational studies, the precise mechanisms by which land-atmosphere feedback occurs are still largely unknown particularly the mechanisms that allow land moisture state in one region to affect atmospheric conditions in another. Such remote impacts are examined here in the context of atmospheric general circulation model (AGCM) simulations, leading to the identification of one potential mechanism: the phase-locking and amplification of a planetary wave through the imposition of a spatial pattern of soil moisture at the land surface. This mechanism, shown here to be relevant in the AGCM, apparently also operates in nature, as suggested by supporting evidence found in reanalysis data.
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-02-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-01-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields. PMID:28205589
Snyder, D
2002-01-01
A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists' consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen's theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level.
Schutzenhofer, L. A.; Jones, J. H.; Jewell, R. E.; Ryan, R. S.
1980-01-01
Anomalous high frequency pressure fluctuations in the Space Shuttle main engine have been experienced during hot firings. Through diagnostic analysis of hot firing engine data, it was determined that this excitation originated at the main oxidizer valve. The intensity of these fluctuations was such that the main oxidizer valve was partially consumed in fire, experienced fretting, and had seal damage. Delineated in this paper are the associated dynamical phenomena and the methodologies leading toward understanding the excitation mechanism. The results presented demonstrate that the source of the anomalous frequencies was suppressed by a simple fix and all main oxidizer valve damage was terminated.
Ruiz, Siul; Capelli, Achille; van Herwijnen, Alec; Schneebeli, Martin; Or, Dani
2017-08-01
Digital cone penetration measurements can be used to infer snow mechanical properties, for instance, to study snow avalanche formation. The standard interpretation of these measurements is based on statistically inferred micromechanical interactions between snow microstructural elements and a well-calibrated penetrating cone. We propose an alternative continuum model to derive the modulus of elasticity and yield strength of snow based on the widely used cavity expansion model in soils. We compare results from these approaches based on laboratory cone penetration measurements in snow samples of different densities and structural sizes. Results suggest that the micromechanical model underestimates the snow elastic modulus for dense samples by 2 orders of magnitude. By comparison with the cavity expansion-based model, some of the discrepancy is attributed to low sensitivity of the micromechanical model to the snow elastic modulus. Reasons and implications of this discrepancy are discussed, and possibilities to enhance both methodologies are proposed.
Lamb Wave Stiffness Characterization of Composites Undergoing Thermal-Mechanical Aging
Seale, Michael D.; Madaras, Eric I.
2004-01-01
The introduction of new, advanced composite materials into aviation systems requires a thorough understanding of the long term effects of combined thermal and mechanical loading upon those materials. Analytical methods investigating the effects of intense thermal heating combined with mechanical loading have been investigated. The damage mechanisms and fatigue lives were dependent on test parameters as well as stress levels. Castelli, et al. identified matrix dominated failure modes for out-of-phase cycling and fiber dominated damage modes for in-phase cycling. In recent years, ultrasonic methods have been developed that can measure the mechanical stiffness of composites. To help evaluate the effect of aging, a suitably designed Lamb wave measurement system is being used to obtain bending and out-of-plane stiffness coefficients of composite laminates undergoing thermal-mechanical loading. The system works by exciting an antisymmetric Lamb wave and calculating the velocity at each frequency from the known transducer separation and the measured time-of-flight. The same peak in the waveforms received at various distances is used to measure the time difference between the signals. The velocity measurements are accurate and repeatable to within 1% resulting in reconstructed stiffness values repeatable to within 4%. Given the material density and plate thickness, the bending and out-of-plane shear stiffnesses are calculated from a reconstruction of the dispersion curve. A mechanical scanner is used to move the sensors over the surface to map the time-of-flight, velocity, or stiffnesses of the entire specimen. Access to only one side of the material is required and no immersion or couplants are required because the sensors are dry coupled to the surface of the plate. In this study, the elastic stiffnesses D(sub 11), D(sub 22), A(sub 44), and A(sub 55) as well as time-of-flight measurements for composite samples that have undergone combined thermal and mechanical aging for
Nenadic, Ivan Z.; Urban, Matthew W.; Mitchell, Scott A.; Greenleaf, James F.
2011-01-01
Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of Shearwave Dispersion Ultrasound Vibrometry (SDUV), a noninvasive ultrasound based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave Dispersion Ultrasound Vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify mechanical properties of soft tissues with a plate-like geometry. PMID:21403186
On the propagation mechanism of a detonation wave in a round tube with orifice plates
Ciccarelli, G.; Cross, M.
2016-09-01
This study deals with the investigation of the detonation propagation mechanism in a circular tube with orifice plates. Experiments were performed with hydrogen air in a 10-cm-inner-diameter tube with the second half of the tube filled with equally spaced orifice plates. A self-sustained Chapman-Jouguet (CJ) detonation wave was initiated in the smooth first half of the tube and transmitted into the orifice-plate-laden second half of the tube. The details of the propagation were obtained using the soot-foil technique. Two types of foils were used between obstacles, a wall-foil placed on the tube wall, and a flat-foil (sooted on both sides) placed horizontally across the diameter of the tube. When placed after the first orifice plate, the flat foil shows symmetric detonation wave diffraction and failure, while the wall foil shows re-initiation via multiple local hot spots created when the decoupled shock wave interacts with the tube wall. At the end of the tube, where the detonation propagated at an average velocity much lower than the theoretical CJ value, the detonation propagation is much more asymmetric with only a few hot spots on the tube wall leading to local detonation initiation. Consecutive foils also show that the detonation structure changes after each obstacle interaction. For a mixture near the detonation propagation limit, detonation re-initiation occurs at a single wall hot spot producing a patch of small detonation cells. The local overdriven detonation wave is short lived, but is sufficient to keep the global explosion front propagating. Results associated with the effect of orifice plate blockage and spacing on the detonation propagation mechanism are also presented.
Chen, Jun; Friesen, W. Otto; Iwasaki, Tetsuya
2012-01-01
SUMMARY Undulatory animal locomotion arises from three closely related propagating waves that sweep rostrocaudally along the body: activation of segmental muscles by motoneurons (MNs), strain of the body wall, and muscle tension induced by activation and strain. Neuromechanical models that predict the relative propagation speeds of neural/muscle activation, muscle tension and body curvature can reveal crucial underlying control features of the central nervous system and the power-generating mechanisms of the muscle. We provide an analytical explanation of the relative speeds of these three waves based on a model of neuromuscular activation and a model of the body–fluid interactions for leech anguilliform-like swimming. First, we deduced the motoneuron spike frequencies that activate the muscle and the resulting muscle tension during swimming in intact leeches from muscle bending moments. Muscle bending moments were derived from our video-recorded kinematic motion data by our body–fluid interaction model. The phase relationships of neural activation and muscle tension in the strain cycle were then calculated. Our study predicts that the MN activation and body curvature waves have roughly the same speed (the ratio of curvature to MN activation speed ≈0.84), whereas the tension wave travels about twice as fast. The high speed of the tension wave resulting from slow MN activation is explained by the multiplicative effects of MN activation and muscle strain on tension development. That is, the product of two slower waves (activation and strain) with appropriate amplitude, bias and phase can generate a tension wave with twice the propagation speed of the factors. Our study predicts that (1) the bending moment required for swimming is achieved by minimal MN spike frequency, rather than by minimal muscle tension; (2) MN activity is greater in the mid-body than in the head and tail regions; (3) inhibitory MNs not only accelerate the muscle relaxation but also reduce
Rauch, Helmut
2015-01-01
The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivation...
Double-slit experiment with single wave-driven particles and its relation to quantum mechanics
DEFF Research Database (Denmark)
Andersen, Anders Peter; Madsen, Jacob; Reichelt, Christian Günther
2015-01-01
even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes...... place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our...... results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schro...
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
Directory of Open Access Journals (Sweden)
Rintaro Hojo, MD
2015-02-01
Full Text Available A 74-year-old woman with takotsubo cardiomyopathy developed polymorphic ventricular tachycardia during the acute phase. She exhibited prominent J-wave and T-wave alternans preceding ventricular tachycardia. These abnormalities disappeared after recovery from myocardial stunning.
Mechanical design and analysis for a low beta squeezed half-wave resonator
He, Shoubo; Zhang, Shenghu; Yue, Weiming; Zhang, Cong; Wang, Zhijun; Wang, Ruoxu; Xu, Mengxin; Huang, Shichun; Huang, Yulu; Jiang, Tiancai; Wang, Fengfeng; Zhang, Shengxue; Zhao, Hongwei
2013-01-01
A superconducting half-wave resonator (HWR) of frequency=162.5 MHz and {\\beta}=0.09 has been developed at Institute of Modern Physics. Mechanical stability of the low beta HWR cavity is a big challenge in cavity design and optimization. The mechanical deformations of a radio frequency superconducting cavity could be a source of instability, both in continues wave(CW) operation or in pulsed mode. Generally, the lower beta cavities have stronger Lorentz force detuning than that of the higher beta cavities. In this paper, a basic design consideration in the stiffening structure for the detuning effect caused by helium pressure and Lorentz force has been presented. The mechanical modal analysis has been investigated with finite element method(FEM). Based on these considerations, a new stiffening structure has been promoted for the HWR cavity. The computation results concerning the frequency shift show that the low beta HWR cavity with new stiffening structure has low frequency sensitivity coefficient, Lorentz for...
McKenzie, Alan
2016-01-01
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic to the group of block universes containing all of the outcomes of all of the events, and so, in that sense, the group of block universes is a more fundamental representation. Different branches of the MWI tree, representing different universes in MWI, ultimately share the same quantum state in a common ancestor branch. This branching topology is incompatible with that of the Minkowski block universe; the resolution is to replace the branches with discrete, parallel block universes, each of which extends from the trunk to the outermost twigs. The number of universes in a branch is proportional to its thickness which, in turn, depends upon the absolute square of the probability amplitude for the state in that branch. Every quantum event may be represented by a kernel of unive...
Critical Assessment of Wave-Particle Complementarity via Derivation from Quantum Mechanics
Herbut, Fedor
2009-01-01
After introducing sketchily Bohr's wave-particle complementarity principle in his own words, a derivation of an extended form of the principle from standard quantum mechanics is performed. Reality-evaluation of each step is given. The derived theory is applied to simple examples and the extended entities are illustrated in a thought experiment. Assessment of the approach of Bohr and of this article is taken up again with a rather negative conclusion as far as reflecting reality is concerned. The paper ends with selected incisive opinions on Bohr's dogmatic attitude and with some comments by the present author.
A narrow QRS tachycardia and cannon A waves: What is the mechanism?
Ali, Hussam; Epicoco, Gianluca; De Ambroggi, Guido; Lupo, Pierpaolo; Foresti, Sara; Cappato, Riccardo
2016-12-23
Regular narrow QRS tachycardia, particularly if well-tolerated, is usually considered a "benign" arrhythmia of a supraventricular origin. This case concerns an 82-year-old male with ischemic heart disease who presented with recurrent episodes of a narrow QRS tachycardia that was initially diagnosed and treated as atrial tachyarrhythmia. However, careful physical examination and ECG analysis established the correct diagnosis, and the patient was managed appropriately. Remarkably, the observation of irregular cannon A waves, and Lewis lead recording, confirmed atrioventricular dissociation during tachycardia and indicated its underlying mechanism.
Mechanical state assessment using lamb wave technique in static tensile tests
Burkov, M. V.; Shah, R. T.; Eremin, A. V.; Byakov, A. V.; Panin, S. V.
2016-11-01
The paper deals with the investigation of Lamb wave ultrasonic technique for damage (or mechanical state) evaluation of AA7068T3 specimens in the course of tensile testing. Two piezoelectric transducers (PZT), one of which is used as an actuator and the other as sensor, were adhesively bonded on the specimen surface using epoxy. Two frequencies of testing signals (60 kHz and 350 kHz) were used. The set of static tensile tests were performed. The recorded signals were processed to calculate the informative parameters in order to evaluate the changes in stress-strain state of the specimens and their microstructure.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
Energy Technology Data Exchange (ETDEWEB)
Olsson, R. H., III
2012-03-01
The goal of this project was to develop high frequency quality factor (fQ) product acoustic resonators matched to a standard RF impedance of 50 {Omega} using overmoded bulk acoustic wave (BAW) resonators. These resonators are intended to serve as filters in a chip scale mechanical RF spectrum analyzer. Under this program different BAW resonator designs and materials were studied theoretically and experimentally. The effort resulted in a 3 GHz, 50 {Omega}, sapphire overmoded BAW with a fQ product of 8 x 10{sup 13}, among the highest values ever reported for an acoustic resonator.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Energy Technology Data Exchange (ETDEWEB)
Wei, Hong-Xing [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China); Li, Yong-Dong, E-mail: LYDbeijing@163.com [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China); Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing 100072 (China); Xiong, Tao [Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing 100072 (China); Guan, Yong [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China)
2016-09-07
The problem of dispersive SH wave in a piezoelectric/piezomagnetic plate that contains an imperfect interface is considered in the present work. An imperfection coupling model is adopted to describe the magnetic, electric and mechanical imperfections on the interface. A transcendental dispersion equation is derived and numerically solved to get the phase velocity. The validity of the numerical procedure is verified in a degenerated case. The effects of the coupled interfacial imperfections on the dispersion behavior of SH waves are discussed in detail and the related underlying physical mechanisms are explained. - Highlights: • SH-wave is investigated in a multiferroic plate with coupled interfacial imperfections. • SH-wave is affected by both interfacial imperfections and their inter-couplings. • Physical mechanisms of the effects are explained via energy transformations.
Ambroziński, Łukasz; Pelivanov, Ivan; Song, Shaozhen; Yoon, Soon Joon; Li, David; Gao, Liang; Shen, Tueng T.; Wang, Ruikang K.; O'Donnell, Matthew
2016-07-01
A non-contact method for efficient, non-invasive excitation of mechanical waves in soft media is proposed, in which we focus an ultrasound (US) signal through air onto the surface of a medium under study. The US wave reflected from the air/medium interface provides radiation force to the medium surface that launches a transient mechanical wave in the transverse (lateral) direction. The type of mechanical wave is determined by boundary conditions. To prove this concept, a home-made 1 MHz piezo-ceramic transducer with a matching layer to air sends a chirped US signal centered at 1 MHz to a 1.6 mm thick gelatin phantom mimicking soft biological tissue. A phase-sensitive (PhS)-optical coherence tomography system is used to track/image the mechanical wave. The reconstructed transient displacement of the mechanical wave in space and time demonstrates highly efficient generation, thus offering great promise for non-contact, non-invasive characterization of soft media, in general, and for elasticity measurements in delicate soft tissues and organs in bio-medicine, in particular.
Energy Technology Data Exchange (ETDEWEB)
Ambroziński, Łukasz [Department of Bioengineering, University of Washington, Seattle, Washington 98195 (United States); AGH University of Science and Technology, Krakow 30059 (Poland); Pelivanov, Ivan, E-mail: ivanp3@uw.edu [Department of Bioengineering, University of Washington, Seattle, Washington 98195 (United States); Faculty of Physics, Moscow State University, Moscow 119991 (Russian Federation); Song, Shaozhen; Yoon, Soon Joon; Gao, Liang; O' Donnell, Matthew [Department of Bioengineering, University of Washington, Seattle, Washington 98195 (United States); Li, David [Department of Bioengineering, University of Washington, Seattle, Washington 98195 (United States); Department of Chemical Engineering, University of Washington Seattle, Washington 98195 (United States); Shen, Tueng T.; Wang, Ruikang K. [Department of Bioengineering, University of Washington, Seattle, Washington 98195 (United States); Department of Ophthalmology, University of Washington, Seattle, Washington 98104 (United States)
2016-07-25
A non-contact method for efficient, non-invasive excitation of mechanical waves in soft media is proposed, in which we focus an ultrasound (US) signal through air onto the surface of a medium under study. The US wave reflected from the air/medium interface provides radiation force to the medium surface that launches a transient mechanical wave in the transverse (lateral) direction. The type of mechanical wave is determined by boundary conditions. To prove this concept, a home-made 1 MHz piezo-ceramic transducer with a matching layer to air sends a chirped US signal centered at 1 MHz to a 1.6 mm thick gelatin phantom mimicking soft biological tissue. A phase-sensitive (PhS)-optical coherence tomography system is used to track/image the mechanical wave. The reconstructed transient displacement of the mechanical wave in space and time demonstrates highly efficient generation, thus offering great promise for non-contact, non-invasive characterization of soft media, in general, and for elasticity measurements in delicate soft tissues and organs in bio-medicine, in particular.
Pandey, Vikash; Holm, Sverre
2016-12-01
The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation, respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of GS.
Response Mechanism for Surface Acoustic Wave Gas Sensors Based on Surface-Adsorption
Directory of Open Access Journals (Sweden)
Jiansheng Liu
2014-04-01
Full Text Available A theoretical model is established to describe the response mechanism of surface acoustic wave (SAW gas sensors based on physical adsorption on the detector surface. Wohljent’s method is utilized to describe the relationship of sensor output (frequency shift of SAW oscillator and the mass loaded on the detector surface. The Brunauer-Emmett-Teller (BET formula and its improved form are introduced to depict the adsorption behavior of gas on the detector surface. By combining the two methods, we obtain a theoretical model for the response mechanism of SAW gas sensors. By using a commercial SAW gas chromatography (GC analyzer, an experiment is performed to measure the frequency shifts caused by different concentration of dimethyl methylphosphonate (DMMP. The parameters in the model are given by fitting the experimental results and the theoretical curve agrees well with the experimental data.
The acoustical Klein-Gordon equation: the wave-mechanical step and barrier potential functions.
Forbes, Barbara J; Pike, E Roy; Sharp, David B
2003-09-01
The transformed form of the Webster equation is investigated. Usually described as analogous to the Schrödinger equation of quantum mechanics, it is noted that the second-order time dependency defines a Klein-Gordon problem. This "acoustical Klein-Gordon equation" is analyzed with particular reference to the acoustical properties of wave-mechanical potential functions, U(x), that give rise to geometry-dependent dispersions at rapid variations in tract cross section. Such dispersions are not elucidated by other one-dimensional--cylindrical or conical--duct models. Since Sturm-Liouville analysis is not appropriate for inhomogeneous boundary conditions, the exact solution of the Klein-Gordon equation is achieved through a Green's-function methodology referring to the transfer matrix of an arbitrary string of square potential functions, including a square barrier equivalent to a radiation impedance. The general conclusion of the paper is that, in the absence of precise knowledge of initial conditions on the area function, any given potential function will map to a multiplicity of area functions of identical relative resonance characteristics. Since the potential function maps uniquely to the acoustical output, it is suggested that the one-dimensional wave physics is both most accurately and most compactly described within the Klein-Gordon framework.
Microstructure and Mechanical Properties After Shock Wave Loading of Cast CrMnNi TRIP Steel
Eckner, Ralf; Krüger, L.; Ullrich, C.; Rafaja, D.; Schlothauer, T.; Heide, G.
2016-10-01
The mechanical response of shock wave-prestrained high-alloy Cr16-Mn7-Ni6 TRIP steel was investigated under compressive and tensile loading at room temperature. Previous shock wave loading was carried out using a flyer-plate assembly with different amounts of explosives in order to achieve shock pressures of 0.3, 0.6, 0.9, and 1.2 Mbar. A significant increase in hardness and strength was observed as compared with the initial as-cast condition. In contrast, a slight decrease in strain hardening rates was measured together with a decrease in fracture elongation in the tensile test. Microstructural analyses of the shock-loaded samples were performed by light optical and scanning electron microscopy. The microstructure revealed a high density of deformation bands consisting of separated stacking faults, ɛ-martensite, or twins. Significant amounts of deformation-induced α'-martensite were only present at the highest shock pressure of 1.2 Mbar. The thickness of the deformation bands and the number of martensite nuclei at their intersections increased with increasing shock pressure. In all shock-loaded specimens, pronounced phase transformation occurred during subsequent mechanical testing. Consequently, the amount of the deformation-induced α'-martensite in the shock-loaded specimens was higher than in the unshocked as-cast samples.
Kryjevskaia, Lioudmila N.
This dissertation reports on an in-depth investigation of student understanding of wave phenomena at a boundary. The research and curriculum development were conducted in the contexts of the introductory calculus-based physics course and special courses for preservice and inservice teachers. Research methods included pretests, post-tests, and informal observations and discussions with students. Several student difficulties with wave behavior at a boundary and the cause and effect relationship between wavelength, frequency, and propagation speed were identified. The results from this investigation have guided the development of two sets of instructional materials designed to address the conceptual and reasoning difficulties that were identified. The first is a sequence of tutorials intended to supplement standard lecture and laboratory instruction on mechanical waves in a traditional introductory course. The second consists of a module on mechanical waves designed for use in inquiry-oriented courses for preservice and inservice teachers. Ongoing assessment of both sets of materials indicates that they are effective in addressing many of the student difficulties that were found to be persistent. Such difficulties, when not addressed, may hinder student understanding of more advanced topics such as interference and diffraction of waves.
Yuce, C
2015-01-01
We predict the existence of linear discrete rogue waves. We discuss that Josephson effect is the underlying reason for the formation of such waves. We study linear rogue waves in continuous system and present an exact analytical rogue wave solution of the Schrodinger-like equation.
Charles, Alexandre; Ballard, Patrick
2016-08-01
The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this
Xu, Jian-Jun
1989-01-01
The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.
Inferring the core-collapse supernova explosion mechanism with gravitational waves
Powell, Jade; Gossan, Sarah E.; Logue, Joshua; Heng, Ik Siong
2016-12-01
A detection of a core-collapse supernova (CCSN) gravitational-wave (GW) signal with an Advanced LIGO and Virgo detector network may allow us to measure astrophysical parameters of the dying massive star. GWs are emitted from deep inside the core, and, as such, they are direct probes of the CCSN explosion mechanism. In this study, we show how we can determine the CCSN explosion mechanism from a GW supernova detection using a combination of principal component analysis and Bayesian model selection. We use simulations of GW signals from CCSN exploding via neutrino-driven convection and rapidly rotating core collapse. Previous studies have shown that the explosion mechanism can be determined using one LIGO detector and simulated Gaussian noise. As real GW detector noise is both nonstationary and non-Gaussian, we use real detector noise from a network of detectors with a sensitivity altered to match the advanced detectors design sensitivity. For the first time, we carry out a careful selection of the number of principal components to enhance our model selection capabilities. We show that with an advanced detector network we can determine if the CCSN explosion mechanism is driven by neutrino convection for sources in our Galaxy and rapidly-rotating core collapse for sources out to the Large Magellanic Cloud.
Ingber, Lester; Nunez, Paul L
2011-02-01
The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model.
Leclerc, Arnaud
2015-01-01
A global solution of the Schr\\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is proposed in which, however, numerous integrals over time have to be evaluated. This internal work is done using a numerical integrator based on Fast Fourier Transforms (FFT). The case of a transition between two potential wells of a model molecule driven by intense laser pulses is used as an illustrative example. This application reveals some interesting features of the integration technique. Each iteration provides a global approximate solution on grid points regularly distributed over the full time propagation interval. Inside the convergence radius, the complete integration is competitive with standard algorithms, especially when high accuracy is required.
Institute of Scientific and Technical Information of China (English)
赵艳敏; 石东洋
2011-01-01
The infinite dimensional Hamiltonian system of three-dimensional vector wave equation is given and a new numerical approximate scheme is proposed in this paper. Based on the Gauss-Lobatto-Legendre polynomial, the spatial discretization scheme for the proposed infinite dimensional system is established by virtue of the vector spectral element method, and then a finite dimensional Hamiltonian system is attained. Moreover, in order to preserve the structure and energy of the system, the full discretization scheme of the finite dimensional system is derived by utilizing the symplectic difference method. Finally, the stiff matrix and mass matrix are disposed by the diagonal techniques. High accuracy approximation scheme is thus obtained, and simultaneously the computing cost and storage capacity are reduced significantly.%本文给出了三维矢量波动方程的无穷维Hamilton系统形式并提出了一个新的数值逼近格式.基于Gauss-Lobatto-Legendre多项式,建立了该无穷维系统的矢量谱元方法空间离散格式,并得到一个有限维Hamilton系统.进而,利用辛差分方法对该有限维系统进行全离散,以期保持系统的结构和能量.最后,借助于对角化技巧处理刚度矩阵和质量矩阵,在得到高精度逼近格式的同时,大幅降低了计算量和存储量.
Tsukamoto, Akira; Hayashida, Yasunori; Furukawa, Katsuko S; Ushida, Takashi
2010-03-01
Intracellular Ca2+ transients are evoked either by the opening of Ca2+ channels on the plasma membrane or by phospholipase C (PLC) activation resulting in IP3 production. Ca2+ wave propagation is known to occur in mechanically stimulated cells; however, it remains uncertain whether and how PLC activation is involved in intracellular Ca2+ wave propagation in mechanically stimulated cells. To answer these questions, it is indispensable to clarify the spatio-temporal relations between intracellular Ca2+ wave propagation and PLC activation. Thus, we visualized both cytosolic Ca2+ and PLC activation using a real-time dual-imaging system in individual Mardin-Darby Canine Kidney (MDCK) cells. This system allowed us to simultaneously observe intracellular Ca2+ wave propagation and PLC activation in a spatio-temporal manner in a single mechanically stimulated MDCK cell. The results showed that PLC was activated not only in the mechanically stimulated region but also in other subcellular regions in parallel with intracellular Ca2+ wave propagation. These results support a model in which PLC is involved in Ca2+ signaling amplification in mechanically stimulated cells.
Abdel-Gawad, H. I.; Tantawy, M.; Abo Elkhair, R. E.
2016-07-01
Rogue waves are more precisely defined as waves whose height is more than twice the significant wave height. This remarkable height was measured (by Draupner in 1995). Thus, the need for constructing a mechanism for the rogue waves is of great utility. This motivated us to suggest a mechanism, in this work, that rogue waves may be constructed via nonlinear interactions of solitons and periodic waves. This suggestion is consolidated here, in an example, by studying the behavior of solutions of the complex (KdV). This is done here by the extending the solutions of its real version.
Bohmian mechanics in the exact factorization of electron-nuclear wave functions
Suzuki, Yasumitsu; Watanabe, Kazuyuki
2016-09-01
The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010), 10.1103/PhysRevLett.105.123002] allows us to define the rigorous nuclear time-dependent Schrödinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H2 + molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.
Design of acoustic wave biochemical sensors using micro-electro-mechanical systems
Valentine, Jane E.; Przybycien, Todd M.; Hauan, Steinar
2007-03-01
Acoustic wave biochemical sensors work by detecting the frequency shifts resulting from the binding of target molecules to a functionalized resonator. Resonator types currently in use or under development include macroscopic quartz crystal microbalances (QCMs) as well as a number of different integrated Micro-electro-mechanical Systems (MEMS) structures. Due to an increased resonator surface area to mass ratio, we believe that membrane-based MEMS systems are particularly promising with regard to sensitivity. Prototypes have been developed [S. Hauan et al., U.S. Patent Application (filed 6 Nov. 2003)] and preliminary calculations [M. J. Bartkovsky et al., paper 385e presented at the AIChE Annual Meeting, Nov. 2003; J. E. Valentine et al., paper 197h presented at the AICHE Annual Meeting, Nov. 2003] indicate significant improvements over other methods, both macroscopic and MEMS based. In this article we describe our work on a MEMS-based acoustic wave biochemical sensor using a membrane resonator. We demonstrate the effects of spatial distributions of mass on the membrane on sensitivity and show how to use this spatial sensitivity to detect multiple targets simultaneously. To do so we derive a function approximating the membrane response surface to spatial mass loadings under the applicable range of conditions. We verify the agreement using finite element methods, and present our initial sensitivity calculations demonstrating the advantages of variable mass loadings.
Gowtham, P. G.; Labanowski, D.; Salahuddin, S.
2016-07-01
Surface acoustic waves (SAWs) traveling on the surface of a piezoelectric crystal can, through the magnetoelastic interaction, excite traveling spin-wave resonance in a magnetic film deposited on the substrate. This spin-wave resonance in the magnetic film creates a time-ynamic surface stress of magnetoelastic origin that acts back on the surface of the piezoelectric and modifies the SAW propagation. Unlike previous analyses that treat the excitation as a magnon-phonon polariton, here the magnetoelastic film is treated as a perturbation modifying boundary conditions on the SAW. We use acoustical perturbation theory to find closed-form expressions for the back-action surface stress and strain fields and the resultant SAW velocity shifts and attenuation. We demonstrate that the shear stres fields associated with this spin-wave back-action also generate effective surface currents on the piezoelectric both in phase and out of phase with the driving SAW potential. Characterization of these surface currents and their applications in determination of the magnetoelastic coupling are discussed. The perturbative calculation is carried out explicitly to first order (a regime corresponding to many experimental situations of current interest) and we provide a sketch of the implications of the theory at higher order.
Discrete continuous-phase superresolving filters.
Zhou, Sumei; Zhou, Changhe
2004-12-01
A new type of phase-only superresolving pupil filter with a discrete continuous-phase profile is presented that is a combination of discrete multilevel-phase modulation and continuous-phase modulation. This type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003). Therefore, with regard to the superresolution effect, this type of filter deserves study for practical applications. More importantly, the diffraction performance of this type of filter can explain the effect of a discrete-phase filter illuminated with a continuous wave front, whose superresolving performance cannot be analyzed with previous superresolution methods.
Surfing on Protein Waves: Proteophoresis as a Mechanism for Bacterial Genome Partitioning
Walter, J.-C.; Dorignac, J.; Lorman, V.; Rech, J.; Bouet, J.-Y.; Nollmann, M.; Palmeri, J.; Parmeggiani, A.; Geniet, F.
2017-07-01
Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component machinery, fueled by adenosine triphosphate, called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or "volumetric" chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation, and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a nonlinear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and traveling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.
ANALYSIS AND SIMULATION ON THE MECHANISM OF A NOVEL DUAL-WAVE SHOCK TEST MACHINE
Institute of Scientific and Technical Information of China (English)
WANG Gongxian; ZHANG Zhiyi; CHU Deying; SHEN Rongying
2008-01-01
For qualifying the anti-shock performance of shipboard equipments and simulating actual underwater explosion environments, a novel dual-wave shock test machine is proposed to increase testing capability of shock test machines as well as to meet certain shock testing specification. The machine can generate a double-pulse acceleration shock for test articles according to specification defined in BV043/85. On the basis of the impact theory, a nonlinear dynamic model of the hydraulically-actuated test machine is established with thorough analysis on its mechanism which involves conversion of gas potential energy and dissipation of kinetic energy. Simulation results have demonstrated that the machine can produce a double-pulse acceleration shock in the time domain or a desired shock response spectrum in the frequency domain, which sets a theoretical base for the construction of the proposed machine.
First law of compact binary mechanics with gravitational-wave tails
Blanchet, Luc; Le Tiec, Alexandre
2017-08-01
We derive the first law of binary point-particle mechanics for generic bound (i.e. eccentric) orbits at the fourth post-Newtonian (4PN) order, accounting for the non-locality in time of the dynamics due to the occurence of a gravitational-wave tail effect at that order. Using this first law, we show how the periastron advance of the binary system can be related to the averaged redshift of one of the two bodies for a slightly non-circular orbit, in the limit where the eccentricity vanishes. Combining this expression with existing analytical self-force results for the averaged redshift, we recover the known 4PN expression for the circular-orbit periastron advance, to linear order in the mass ratio.
Highly eccentric Kozai mechanism and gravitational-wave observation for neutron-star binaries.
Seto, Naoki
2013-08-09
The Kozai mechanism for a hierarchical triple system could reduce the merger time of inner eccentric binary emitting gravitational waves (GWs) and has been qualitatively explained with the secular theory that is derived by averaging short-term orbital revolutions. However, with the secular theory, the minimum value of the inner pericenter distance could be excessively limited by the averaging operation. Compared with traditional predictions, the actual evolution of an eccentric inner binary could be accompanied by (i) a higher characteristic frequency of the pulselike GWs around its pericenter passages and (ii) a larger residual eccentricity at its final inspiral phase. These findings would be important for GW astronomy with the forthcoming advanced detectors.
Zhou, Jianqin
2011-01-01
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Inferring the core-collapse supernova explosion mechanism with gravitational waves
Powell, Jade; Logue, Joshua; Heng, Ik Siong
2016-01-01
A detection of a core-collapse supernova (CCSN) gravitational-wave (GW) signal with an Advanced LIGO and Virgo detector network may allow us to measure astrophysical parameters of the dying massive star. GWs are emitted from deep inside the core and, as such, they are direct probes of the CCSN explosion mechanism. In this study we show how we can determine the CCSN explosion mechanism from a GW supernova detection using a combination of principal component analysis and Bayesian model selection. We use simulations of GW signals from CCSN exploding via neutrino-driven convection and rapidly-rotating core collapse. Previous studies have shown that the explosion mechanism can be determined using one LIGO detector and simulated Gaussian noise. As real GW detector noise is both non-stationary and non-Gaussian we use real detector noise from a network of detectors with a sensitivity altered to match the advanced detectors design sensitivity. For the first time we carry out a careful selection of the number of princi...
Phase synchronization in the cochlea at transition from mechanical waves to electrical spikes
Bader, Rolf
2015-10-01
Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Cariani, Neural Plast. 6(4), 142-172 (1999) and Kumaresana et al., J. Acoust. Soc. Am. 133(6), 4290-4310 (2013). Physiologically synchronization is found in the anteroventral cochlear nucleus (Joris et al., J. Neurophysiol. 71(3), 1022-1036 (1994)) or in the trapezoid body also between critical bandwidths (Louage et al., Auditory Signal Processing: Physiology, Psychoacoustics, and Models (Springer, New York, 2004), pp. 100-106). The effect is an enhancement of pitch detection, spatial localization, or speech intelligibility. To investigate the presence of synchronization already in the cochlea, in the present paper, a finite-difference time-domain model of the cochlea is implemented with conditions for spike excitation caused by mechanical basilar membrane displacement. This model shows synchronization already in the cochlea at the transition from mechanical waves to nerve spike excitation. Using a sound as model input consisting of ten harmonic overtones with random phase relations, the output spikes are strongly phase aligned after this transition. When using a two-sinusoidal complex as input, and altering the phase relations between the two sinusoidals, the output spikes show the higher sinusoidal shifting the phase of the lower one in its direction in a systematic way. Therefore, already during the transition from mechanical to electrical excitation within the cochlea, synchronization appears to be improving perception of pitch, speech, or localization.
Harvesting broadband kinetic impact energy from mechanical triggering/vibration and water waves.
Wen, Xiaonan; Yang, Weiqing; Jing, Qingshen; Wang, Zhong Lin
2014-07-22
We invented a triboelectric nanogenerator (TENG) that is based on a wavy-structured Cu-Kapton-Cu film sandwiched between two flat nanostructured PTFE films for harvesting energy due to mechanical vibration/impacting/compressing using the triboelectrification effect. This structure design allows the TENG to be self-restorable after impact without the use of extra springs and converts direct impact into lateral sliding, which is proved to be a much more efficient friction mode for energy harvesting. The working mechanism has been elaborated using the capacitor model and finite-element simulation. Vibrational energy from 5 to 500 Hz has been harvested, and the generator's resonance frequency was determined to be ∼100 Hz at a broad full width at half-maximum of over 100 Hz, producing an open-circuit voltage of up to 72 V, a short-circuit current of up to 32 μA, and a peak power density of 0.4 W/m(2). Most importantly, the wavy structure of the TENG can be easily packaged for harvesting the impact energy from water waves, clearly establishing the principle for ocean wave energy harvesting. Considering the advantages of TENGs, such as cost-effectiveness, light weight, and easy scalability, this approach might open the possibility for obtaining green and sustainable energy from the ocean using nanostructured materials. Lastly, different ways of agitating water were studied to trigger the packaged TENG. By analyzing the output signals and their corresponding fast Fourier transform spectra, three ways of agitation were evidently distinguished from each other, demonstrating the potential of the TENG for hydrological analysis.
The Effect of Ultrasonic Waves on Sugar Extraction and Mechanical Properties of Sugar Beet
Directory of Open Access Journals (Sweden)
K Hedayati
2013-09-01
Full Text Available Sugar, which can be extracted from sugar cane and sugar beet, is one of the most important ingredients of food. Conducting more research to increase the extraction efficiency of sugar is necessary due to high production of sugar beet and its numerous processing units in northern Khorasan province. In this research, the effect of temperature, time and the frequency of ultrasonic waves on mechanical properties of sugar beet and its extraction rate of sugar in moisture content of 75% were studied. In this regard, an ultrasonic bath in laboratory scale was used. The studied parameters and their levels were frequency in three levels (zero, 25 and 45 KHz, temperature in three levels (25, 50 and 70 ° C and the imposed time of ultrasonic waves in three levels (10, 20 and 30 min. Samples were prepared using planned experiments and the results were compared with control sugar beet samples. A Saccharimeter was used to measure the concenteration of sugar in samples. Two different types of probe including semi-spherical end and the other one with sharpened edges were used to measure mechanical properties. The studied parameters of frequency, temperature and time showed significant effect on sugar extraction and their resulted effect in optimized levels revealed up to 56% increase in sugar extraction compared with control samples. The obtained values of elastic modulus and shear modulus showed a decreasing trend. The obtained values of total energy of rupture, the total energy of shear, the maximum force of rupture, and the yield point of rupture showed an increasing trend. The frequency had no significant effect on the yield point of rupture and shear force.
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
Investigation on property and mechanism of redox wave of methylhesperidine at Hg electrode
Institute of Scientific and Technical Information of China (English)
ZHENG Jianbin; MENG Zuchao; ZHANG Hongfang
2005-01-01
The voltammetric behaviors of methylhesperidine (MH) were studied by means of linear sweep voltammetry, cyclic voltammetry and normal pulse voltammetry. In the Brit ton-Robinson buffer solutions with pH values from 2.05 to 6.37, MH could yield three reduction waves PC1, PC2 and PC3. PC1 wave is an adsorptive pre-wave. PC2 wave is an irreversible reduc tion of pre-protonated MH involving one electron and one proton. PC3 wave is an irreversible wave of reduction species radical of MH involving one electron.
Yeh, Cheng-Hung; Yang, Che-Hua
2011-05-01
Guided waves propagating in cylindrical tubes are frequently applied for the characterization of material or geometrical properties of tubes. In a tube, guided waves can propagate in the axial direction and called axial guided waves, or in the circumferential direction called circumferential guided waves. Dispersion spectra for the axial and circumferential guided waves share some common behaviors and however exhibit some particular behaviors of their own. This study provides an investigation with theoretical modeling, experimental measurements, and a simplex-based inversion procedure to explore the similarity and difference between the axial guided waves and circumferential guided waves, aiming at providing useful information while axial and circumferential guided waves are applied in the area of material characterization. The sensitivity to the radius curvature for the circumferential guided waves dispersion spectra is a major point that makes circumferential guided waves different from axial guided waves. For the purpose of material characterization, both axial and circumferential guided waves are able to extract an elastic moduli and wall-thickness information from the dispersion spectra, however, radius information can only be extracted from the circumferential guided waves spectra. Copyright © 2010 Elsevier B.V. All rights reserved.
Variational principle and dynamical equations of discrete nonconservative holonomic systems
Institute of Scientific and Technical Information of China (English)
Liu Rong-Wan; Zhang Hong-Bin; Chen Li-Qun
2006-01-01
By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler-Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.
Kirilyuk, A P
1995-01-01
The concept of the fundamental dynamic uncertainty (or the fundamental multivaluedness of dynamical functions) developed in parts I-III of this work and used to re-establish the correspondence principle for chaotic Hamiltonian systems provides also a causal description of the basic properties of quantum measurement, - quantum indeterminacy and wave reduction. The modified Schrödinger formalism involving multivalued effective dynamical functions reveals the dynamical origin of quantum indeterminacy as the intrinsic nonlinear instability in the combined quantum system of the measured object interacting with the instrument. As a result of this instability, the originally wide measured wave dynamically "shrinks" around a random accessible point of the combined configurational space loosing its coherence with respect to other possibilities. We do not use any assumptions on particular "classical", "macroscopic", "stochastic", etc. nature of the instrument or environment: full quantum indeterminacy dynamically appe...
Letters on wave mechanics correspondence with H. A. Lorentz, Max Planck, and Erwin Schrödinger
Einstein, Albert
2011-01-01
A lively collection of Einstein's groundbreaking scientific correspondence on modern physics with Schrödinger, Planck, and LorentzImagine getting four of the greatest minds of modern physics in a room together to explain and debate the theories and innovations of their day. This is the fascinating experience of reading Letters on Wave Mechanics, the correspondence between Erwin Schrödinger and Max Planck, H.A. Lorentz, and Albert Einstein. These remarkable letters illuminate not only the basis of Schrödinger's work in wave mechanics, but also how great scientific minds debated and challenged
Discrete Wigner function dynamics
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B; Munoz, C [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jalisco (Mexico)
2005-12-01
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
Institute of Scientific and Technical Information of China (English)
YANG Ruowen; TAO Yun; CAO Jie
2010-01-01
Based on the 500-hPa geopotential height, surface air temperature, and China summer rain-belt type data from 1978 to 2002, the spatial spectrum function sets which well represent the variation of large scale atmospheric circulations were obtained using the least square method. A mechanism for the interannual variation of the East Asia-Pacific teleconnection (EAP) wave train in early summer was identified with the low-order spectral method and the hypothesis-test method. The results indicate that, when nonlinear wave-wave and wave-flow interactions on large scale are stronger in the inner dynamic process of the atmosphere, there are obvious nonlinear features in the evolution of the atmospheric circulation, and the EAP exhibits a negative-positive-negative ("- +-") spatial distribution in low to high latitudes in early summer. The corresponding EAP index is positive, which leads to a northward shift of the western Pacific subtropical high (WPSH) and the China rain-belt is located in the Huaihe River valley and its north in summer. On the contrary, when nonlinear wave-wave and wave-flow interactions on large scale are weaker, there appears a linear feature in the evolution of the atmospheric circulation, and the EAP shows a positive-negative-positive ("+-+") spatial distribution in low to high latitudes. The corresponding EAP index is negative, which inhibits the WPSH against moving northward, and the China rain-belt is located in the Huaihe and Yangtze River valleys and their south.
Study on the Tidal Wave System and Formation Mechanism of M2 Tide in the Taiwan Strait
Institute of Scientific and Technical Information of China (English)
ZHANG Wei-sheng; SONG Zhi-yao; ZHANG Jin-shan; ZHANG Hong-gui; KONG Jun; WANG Yan-hong
2008-01-01
To study the Taiwan Strait (TS), an unusual sea area, the numerical model in marginal seas of China is used to simulate and analyze the tidal wave motion in the strait. The numerical modeling experiments reproduce the amphidromic system of the M2 tide in the south end of the Taiwan strait, and consequently confirm the existence of the degenerate amphidromic system. On this basis, further discussion is conducted on the M2 system and its formation mechanism. It can be concluded that the tidal waves of the TS is consisted of the progressing wave from the north entrance and the degenerate amphidromic system from the south entrance, in which the progressing wave from the north entrance dominates the tidal wave motion in the strait. Except for the convergent effect caused by the landform and boundary, the degenerate amphidromic system produced in the south of the strait is another important factor for the following phenomena: the large tidal range in the middle of the strait, the concentrative zone of co-amplitude and co-phase line in the south of the strait. The degenerate amphidromic system is mainly produced by the incident Pacific Ocean tidal wave from the Luzon strait and the action by the shoreline and landform. The position of the amphidromic point is compelled to move toward southwest until degenerating by the powerful progressing wave from the north entrance.
Quantum Measurement, Complexity and Discrete Physics
Leckey, Martin
2003-01-01
This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of the theory for a realist view of the quantum realm.
Directory of Open Access Journals (Sweden)
Paul C. Rivera
2006-01-01
Full Text Available A common approach in modeling the generation and propagation of tsunami is based on the assumption of a kinematic vertical displacement of ocean water that is analogous to the ocean bottom displacement during a submarine earthquake and the use of a non-dispersive long-wave model to simulate its physical transformation as it radiates outward from the source region. In this study, a new generation mechanism and the use of a highly-dispersive wave model to simulate tsunami inception, propagation and transformation are proposed. The new generation model assumes that transient ground motion during the earthquake can accelerate horizontal currents with opposing directions near the fault line whose successive convergence and divergence generate a series of potentially destructive oceanic waves. The new dynamic model incorporates the effects of earthquake moment magnitude, ocean compressibility through the buoyancy frequency, the effects of focal and water depths, and the orientation of ruptured fault line in the tsunami magnitude and directivity.For tsunami wave simulation, the nonlinear momentum-based wave model includes important wave propagation and transformation mechanisms such as refraction, diffraction, shoaling, partial reflection and transmission, back-scattering, frequency dispersion, and resonant wave-wave interaction. Using this model and a coarse-resolution bathymetry, the new mechanism is tested for the Indian Ocean tsunami of December 26, 2004. A new flooding and drying algorithm that consider waves coming from every direction is also proposed for simulation of inundation of low-lying coastal regions.It is shown in the present study that with the proposed generation model, the observed features of the Asian tsunami such as the initial drying of areas east of the source region and the initial flooding of western coasts are correctly simulated. The formation of a series of tsunami waves with periods and lengths comparable to observations
Seale, M. D.; Madaras, E. I.
1999-01-01
Lamb waves offer a promising method of evaluating damage in composite materials. The Lamb wave velocity is directly related to the material parameters, so an effective tool exists to monitor damage in composites by measuring the velocity of these waves. The Lamb Wave Imager (LWI) uses a pulse/receive technique that excites an antisymmetric Lamb mode and measures the time-of-flight over a wide frequency range. Given the material density and plate thickness, the bending and out-of-plane shear stiffnesses are calculated from a reconstruction of the dispersion curve. In this study, the time-of-flight as well as the elastic stiffnesses D11, D22, A44, and A55 for composite samples which have undergone combined thermal and mechanical aging are obtained. The samples examined include a baseline specimen with 0 cycles, specimens which have been aged 2350 and 3530 cycles at high strain levels, and one specimen aged 3530 cycles at low strain levels.
Gusakov, E Z
2016-01-01
Novel mechanism leading to excitation of absolute two plasmon parametric decay instability (TPDI) of a pump extraordinary (X) wave is discussed. It is shown that the upper hybrid (UH) plasmon can be 3D trapped in the presence of both a nonmonotonous density profile and a finite-size pump beam in a plane perpendicular to the plasma inhomogeneity direction. This leads to excitation of the absolute TPDI of the pump X wave, which manifests itself in temporal exponential growth of the trapped daughter UH wave amplitude and is perhaps the most dangerous instability for mm-waves, widely utilized nowadays in tokamak and stellarators for local plasma heating and current drive and being considered for application in ITER.
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
Urpin, Vadim
2016-01-01
We consider diffusion caused by a combined influence of the Hall effect and electric currents, and argue that such diffusion forms chemical inhomogeneities in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory and astrophysical plasmas. Such current-driven diffusion can be accompanied by the propagation of a particular type of waves which have not been considered earlier. In these waves, the impurity number density oscillare alone and their frequency is determined by the electric currents and sort of impurity ions. These compositional waves exist if the magnetic pressure in plasma is much greater than the gas pressure. Such waves lead to local variations of chemical composition and, hence, can manifest themselves by variations of the emission in spectral lines.
Continuum limit of discrete Sommerfeld problems on square lattice
Indian Academy of Sciences (India)
BASANT LAL SHARMA
2017-05-01
A low-frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It is established that the exact solution of the discrete model converges to the solution of the continuum model, i.e., the continuous Sommerfeld problem, in the discrete Sobolev space defined by Hackbusch. A proof of convergence has been provided for both types of boundary conditions when the imaginary part of incident wavenumber is positive.
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The pore characteristics,mineral compositions,physical and mechanical properties of the subarkose sandstones were acquired by means of CT scan,X-ray diffraction and physical tests.A few physical models possessing the same pore characteristics and matrix properties but different porosities compared to the natural sandstones were developed.The 3D finite element models of the rock media with varied porosities were established based on the CT image processing of the physical models and the MIMICS software platform.The failure processes of the porous rock media loaded by the split Hopkinson pressure bar(SHPB) were simulated by satisfying the elastic wave propagation theory.The dynamic responses,stress transition,deformation and failure mechanisms of the porous rock media subjected to the wave stresses were analyzed.It is shown that an explicit and quantitative analysis of the stress,strain and deformation and failure mechanisms of porous rocks under the wave stresses can be achieved by using the developed 3D finite element models.With applied wave stresses of certain amplitude and velocity,no evident pore deformation was observed for the rock media with a porosity less than 15%.The deformation is dominantly the combination of microplasticity(shear strain),cracking(tensile strain) of matrix and coalescence of the cracked regions around pores.Shear stresses lead to microplasticity,while tensile stresses result in cracking of the matrix.Cracking and coalescence of the matrix elements in the neighborhood of pores resulted from the high transverse tensile stress or tensile strain which exceeded the threshold values.The simulation results of stress wave propagation,deformation and failure mechanisms and energy dissipation in porous rock media were in good agreement with the physical tests.The present study provides a reference for analyzing the intrinsic mechanisms of the complex dynamic response,stress transit mode,deformation and failure mechanisms and the disaster
Ternifi, R; Gennisson, J-L; Tanter, M; Beillas, P
2013-12-01
The objective of this study was to evaluate the effects of different conservation techniques on the mechanical properties of the ex vivo porcine kidney in order to select an appropriate conservation protocol to use prior to mechanical testing. Five groups of eight kidneys each were subjected to different methods of conservation: storage at 4°C, -18°C, -34°C and -71°C, for 7 days, or storage at 20°C for 2 days only (as the tissues degraded quickly). Their shear modulus as a function of depth in the organ was evaluated before (fresh) and after conservation using shear wave elastography. Results obtained on fresh kidneys were collected within 6h of death. Freezing lead to a significant decrease (p0.05) in the properties of the renal cortex when stored at 4°C or 20°C. The average moduli in the central region of the kidney (medulla) were much higher than in the cortex and exhibited also exhibited larger specimen to specimen variations. The effects of the conservation method on the central region were not significant. Overall, the results suggest that kidney tissues should not be frozen prior to biomechanical characterization and that inhomogeneity may be important to consider for in biomechanical models.
Supercritical super-Brownian motion with a general branching mechanism and travelling waves
Kyprianou, A E; Murillo-Salas, A; Ren, Y -X
2010-01-01
We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the probabilistic reasoning of Kyprianou (2004) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role of Seneta-Heyde norming which, in the current setting, draws on classical work of Grey (1974). We give a pathwise explanation of Evans' immortal particle picture (the spine decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient. Moreover, in the spirit of Neveu's stopping lines we make repeated use of Dynkin's exit measures. Additional complications arise from the general nature of the branching mechanism. As a consequence of the analysis we also offer an exact X(log X)^2 moment dichotomy for the almost sure convergence of the so-called derivative martingale...
Arif, S.; Armbruster, O.; Kautek, W.
2013-05-01
The mechanisms of graphite particle and polystyrene-co-divinyl benzene microsphere removal from flat polycarbonate substrates by nanosecond pulse laser interaction at 532 nm were studied both experimentally and theoretically. These model contaminants exhibited an extremely contrasting behavior in respect to phase separation and collateral damage to the polycarbonate substrate. Opaque graphite particles within the irradiated spot area either desorbed due to their thermal expansion or undertook vaporization/ablation. The transparent polystyrene microspheres caused local ablation of the substrate in their optical near-field. This process led to the removal of the particles, but eradicated the available cleaning fluence window. The opaque graphite particles, on the other hand, showed efficient clearance, particularly in a practicable cleaning window above 0.5~J/cm2 and low pulse numbers of about two. Besides the mechanisms occurring within the irradiated spot, a separation process in the proximity beyond the laser spot (more than double the Gaussian radius) could be related to the action of high-amplitude surface acoustic waves (SAW). A minimum surface acceleration of 109~cm/s2 was calculated to be sufficient to overcome the adhesion forces in this particle separation model.
Zhang, Xiaoliang; Hu, Ming; Poulikakos, Dimos
2012-07-11
The great majority of investigations of thermal transport in carbon nanotubes (CNTs) in the open literature focus on low heat fluxes, that is, in the regime of validity of the Fourier heat conduction law. In this paper, by performing nonequilibrium molecular dynamics simulations we investigated thermal transport in a single-walled CNT bridging two Si slabs under constant high heat flux. An anomalous wave-like kinetic energy profile was observed, and a previously unexplored, wave-dominated energy transport mechanism is identified for high heat fluxes in CNTs, originated from excited low frequency transverse acoustic waves. The transported energy, in terms of a one-dimensional low frequency mechanical wave, is quantified as a function of the total heat flux applied and is compared to the energy transported by traditional Fourier heat conduction. The results show that the low frequency wave actually overtakes traditional Fourier heat conduction and efficiently transports the energy at high heat flux. Our findings reveal an important new mechanism for high heat flux energy transport in low-dimensional nanostructures, such as one-dimensional (1-D) nanotubes and nanowires, which could be very relevant to high heat flux dissipation such as in micro/nanoelectronics applications.
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ......, Slepian models, Stochastic finite elements.......The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation...
Haney, Sean
The ocean mixed layer serves as buffer through which the deep ocean and atmosphere communicate. Fluxes of heat, momentum, fresh water, and gases must pass through the mixed layer, and phytoplankton flourish most in the mixed layer where light is abundant. The dynamics of the mixed layer influence these fluxes and productivity of phytoplankton by altering the stratification and mean flow. Restratifying hurricane wakes provide a unique setting in which a dramatically perturbed mixed layer is observable from satellite sea surface temperature. Strong horizontal temperature fronts which border these wakes suggest that two and three dimensional, adiabatic processes play a role. These observations provide the necessary parameters to estimate wake restratification timescales by surface heat fluxes (SF), Ekman buoyancy fluxes (EBF), and mixed layer eddies (MLEs). In the four wakes observed, the timescales for SF and EBF were comparable, while MLEs were much slower. The restratification time for MLEs is reduced for deeper and narrower wakes compared with other mechanisms. Therefore, stronger mixed layer fronts make MLEs competitive with surface heat and wind forcing. Fronts are influenced by winds, waves (Langmuir circulations; LC), MLEs, and symmetric instabilities (SI). The wave averaged (Stokes drift) effects on MLEs are subtle, with aligned (anti-aligned) Stokes and geostrophic flows yielding a slight increase (decrease) in wavenumber and growth rate. Frontal effects on LC are very weak, with the primary result confirming that increased vertical stratification suppresses LC. The effect of Stokes drift on SI is profound. It changes the background flow necessary for SI, and it alters the structure of the SI themselves. Analytic stability criteria show that iii SI exist when the Ertel potential vorticity (PV) is negative. When the Stokes drift is aligned (anti-aligned) with the geostrophic shear, the PV is increased (reduced). This PV criterion is confirmed in more
Cherkas, S L
2014-01-01
The asymptotic of the solution of the discrete Wheeler-DeWitt equation is found in the vicinity of small scale factors. It is shown that this problem is equivalent to the solution of the stationary Schr\\"{o}dinger equation in the (super) space of negative constant curvature. The minimum positive eigenvalue is found from which a continuous spectrum begins.
An alternative view on the role of the β-effect in the Rossby wave propagation mechanism
Directory of Open Access Journals (Sweden)
Eyal Heifetz
2014-11-01
Full Text Available The role of the β-effect in the Rossby wave propagation mechanism is examined in the linearised shallow water equations directly in momentum–height variables, without recourse to potential vorticity (PV. Rigorous asymptotic expansion of the equations, with respect to the small non-dimensionalised β parameter, reveals in detail how the Coriolis force acting on the small ageostrophic terms translates the geostrophic leading-order solution to propagate westward in concert. This information cannot be obtained directly from the conventional PV perspective on the propagation mechanism. Furthermore, a comparison between the β-effect in planetary Rossby waves and the sloping-bottom effect in promoting topographic Rossby waves shows that the ageostrophic terms play different roles in the two cases. This is despite the fact that from the PV viewpoint whether the advection of mean PV gradient is set up by changes in planetary vorticity or by mean depth is inconsequential.
Dynamic analysis of propulsion mechanism directly driven by wave energy for marine mobile buoy
Yu, Zhenjiang; Zheng, Zhongqiang; Yang, Xiaoguang; Chang, Zongyu
2016-07-01
Marine mobile buoy(MMB) have many potential applications in the maritime industry and ocean science. Great progress has been made, however the technology in this area is far from maturity in theory and faced with many difficulties in application. A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB, especially with consideration of hydrodynamic force. The principle of wave-driven propulsion mechanism is briefly introduced. To set a theory foundation for study on the MMB, a dynamic model of the propulsion mechanism of the MMB is obtained. The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations. A simplified form of the motion equations is reached by omitting terms with high order small values. The relationship among the heave motion of the buoy, stiffness of the elastic components, and the forward speed can be obtained by using these simplified equations. The dynamic analysis show the following: The angle of displacement of foil is fairly small with the biggest value around 0.3 rad; The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy; The relationship among heaven motion, stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle, therefore, the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant. The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.
Montagnon, Emmanuel; Hadj-Henni, Anis; Schmitt, Cédric; Cloutier, Guy
2013-04-07
This paper presents a semi-analytical model of shear wave scattering by a viscoelastic elliptical structure embedded in a viscoelastic medium, and its application in the context of dynamic elastography imaging. The commonly used assumption of mechanical homogeneity in the inversion process is removed introducing a priori geometrical information to model physical interactions of plane shear waves with the confined mechanical heterogeneity. Theoretical results are first validated using the finite element method for various mechanical configurations and incidence angles. Secondly, an inverse problem is formulated to assess viscoelastic parameters of both the elliptic inclusion and its surrounding medium, and applied in vitro to characterize mechanical properties of agar-gelatin phantoms. The robustness of the proposed inversion method is then assessed under various noise conditions, biased geometrical parameters and compared to direct inversion, phase gradient and time-of-flight methods. The proposed elastometry method appears reliable in the context of estimating confined lesion viscoelastic parameters.
Constructing exact solutions to discrete systems with the trial function method
Institute of Scientific and Technical Information of China (English)
Taogetusang Sirendaoerji
2008-01-01
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear (2+1) dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.
Pandey, Vikash
2015-01-01
An analogy is drawn between the diffusion-wave equations derived from the fractional Kelvin-Voigt model and those obtained from Buckingham's grain-shearing (GS) model [J. Acoust. Soc. Am. 108, 2796-2815 (2000)] of wave propagation in saturated, unconsolidated granular materials. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and shear wave equation derived from the GS model turn out to be the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Also, a physical interpretation of the characteristic fractional-order present in the Kelvin-Voigt fractional derivative wave equation and time-fractional diffusion-wave equation is inferred from the GS model. The shear wave equation from the GS model predicts both diffusion and wave propagation in the fractional framework. The overall goal is intended to show that...
Mechanism of Pendulum-type wave phenomenon in deep block rock mass
Institute of Scientific and Technical Information of China (English)
WU Hao; FANG Qin; ZHANG Ya-dong; LIU Jin-chun; GONG Zi-ming
2009-01-01
Pendulum-type (μ wave) wave is a new type of elastic wave propagated with low frequency and low velocity in deep block rock masses. The μ wave is sharply different from the traditional longitudinal and transverse waves propagated in continuum media and is also a phenomenon of the sign-variable reaction of deep block rock masses to dynamic actions, besides the Anomalous Low Friction (ALF) phenomenon. In order to confirm the existence of the μ wave and study the rule of variation of this μ wave experimentally and theoretically, we first carried out one-dimensional low-speed impact experiments on granite and cement mortar blocks and continuum block models with different characteristic dimensions, based on the multipurpose testing system developed by us independently, The effects of model material and dimensions of models on the propagation properties of 1D stress wave in blocks medium are discussed. Based on a comparison and analysis of the propagation properties (acceleration amplitudes and Fou-rier spectra) of stress wave in these models, we conclude that the fractures in rock mass have considerable effect on the attenuation of the stress wave and retardarce of high frequency waves. We compared our model test data with the data of in-situ measurements from deep mines in Russia and their conclusions. The low-frequency waves occurring in blocks models were validated as Pendu-lum-type wave. The frequencies corresponding to local maxima of spectral density curves of three-directional acceleration satisfied several canonical sequences with the multiple of (√2),most of those frequencies satisfied the quantitative expression(√2)iVP/2△.
The formation mechanism of defects, spiral wave in the network of neurons.
Wu, Xinyi; Ma, Jun
2013-01-01
A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as 'defects' on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.
The formation mechanism of defects, spiral wave in the network of neurons.
Directory of Open Access Journals (Sweden)
Xinyi Wu
Full Text Available A regular network of neurons is constructed by using the Morris-Lecar (ML neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1 The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2 Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area, and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3 Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as 'defects' on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.
Transparent lattices and their solitary waves.
Sadurní, E
2014-09-01
We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.
Energy Technology Data Exchange (ETDEWEB)
Sim, Kyuho; Park, Jisu [Seoul National University, Seoul (Korea, Republic of); Jang, Seon-Jun [Innovation KR, Seoul (Korea, Republic of)
2015-01-15
This paper proposes a floating-type wave energy conversion system that consists of a mechanical part (yo-yo vibrating system, motion rectifying system, and power transmission system) and electrical part (power generation system). The yo-yo vibrating system, which converts translational input to rotational motion, is modeled as a single degree-of-freedom system. It can amplify the wave input via the resonance phenomenon and enhance the energy conversion efficiency. The electromechanical model is established from impedance matching of the mechanical part to the electrical system. The performance was analyzed at various wave frequencies and damping ratios for a wave input acceleration of 0.14 g. The maximum output occurred at the resonance frequency and optimal load resistance, where the power conversion efficiency and electrical output power reached 48% and 290 W, respectively. Utilizing the resonance phenomenon was found to greatly enhance the performance of the wave energy converter, and there exists a maximum power point at the optimum load resistance.
Characteristics and mechanisms of strain waves generated in rock by cylindrical explosive charges
Institute of Scientific and Technical Information of China (English)
刘科伟; 李萧翰; 李夕兵; 姚志华; 舒宗宪; 袁明华
2016-01-01
A superposing principle, by suitably adding the strain waves from a number of concentrated explosive charges to approximate the waves generated by a cylindrical charge based on the strain wave of a point or small spherical explosive charge generated in rock, is used to further study the triggering time of strain gauges installed in radial direction at same distances but different positions surrounding a cylindrical explosive charge in rock. The duration of the first compression phase and peak value of strain wave, and furthermore, their differences are analyzed and some explanations are given. Besides that, the gauge orientation in which the maximum peak value occurs is also discussed. At last, the effect of velocity of detonation (V.O.D.) of a cylindrical explosive charge on the strain waves generated in the surrounding rock is taken as key research and the pattern of peak amplitude of a strain wave varies with the V.O.D. is likely to have been found.
Natural discretization in noncommutative field theory
Energy Technology Data Exchange (ETDEWEB)
Acatrinei, Ciprian Sorin, E-mail: acatrine@theory.nipne.ro [Department of Theoretical Physics, Horia Hulubei National Institute for Nuclear Physics, Bucharest (Romania)
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Institute of Scientific and Technical Information of China (English)
XIE Zhi-nan; LIAO Zhen-peng
2008-01-01
In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional dis- crete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.
A discrete anisotropic model for Scheibe aggregates
Directory of Open Access Journals (Sweden)
O. Bang
1991-05-01
Full Text Available A discrete anisotropic nonlinear model for the dynamics of Scheibe aggregates is investigated. The collapse of the collective excitations found by Möbius and Kuhn is described as a shrinking ring wave, which is eventually absorbed by an acceptor molecule. An optimal acceptor loss is found.
ABOUT THE WAVE MECHANISM OF ACTIVATION OF FAULTS IN SEISMIC ZONES OF THE LITHOSPHERE IN MONGOLIA
Directory of Open Access Journals (Sweden)
M. G. Mel’nikov
2015-09-01
Full Text Available The study is focused on earthquake migrations along active faults in seismic zones of Mongolia. The earthquake migrations are interpreted as a result of the influence of deformational waves. Vector velocities and other parameters of the deformational waves are studied. Based on data from largescale maps, local faults are compared, and differences and similarities of parameters of waves related to faults of different ranks are described.
Drift and breakup of spiral waves in reaction–diffusion–mechanics systems
Panfilov, A. V.; Keldermann, R.H.; Nash, M. P.
2007-01-01
Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction–diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by...
Onorato, M; Osborne, A R; Serio, M
2006-01-13
Here we consider a simple weakly nonlinear model that describes the interaction of two-wave systems in deep water with two different directions of propagation. Under the hypothesis that both sea systems are narrow banded, we derive from the Zakharov equation two coupled nonlinear Schrödinger equations. Given a single unstable plane wave, here we show that the introduction of a second plane wave, propagating in a different direction, can result in an increase of the instability growth rates and enlargement of the instability region. We discuss these results in the context of the formation of rogue waves.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
DEFF Research Database (Denmark)
Song, Sungyoung; Munk-Nielsen, Stig; Uhrenfeldt, Christian
2017-01-01
A commercial discrete enhancement mode gallium nitride power component employing advanced package technology without conventional bond wire possesses the ability for bidirectional conduction. The gallium nitride power components can provide not only higher forward conductivity but also superior r...... of cycles to failure. In physical failure analysis, delamination of a solder joint between a chip and a copper layer of an aluminum print circuit board is observed with a scanning acoustic microscope....
2014-09-15
Lattice Boltzmann Method (LBM) has become increasingly popular as an alternative approach to traditional NS-based techniques for modeling various...CAVS: Center for Advanced Vehicular Systems • CFD : computational fluid dynamics • DEM: discrete element method • FDM: finite difference method...Mach number • MRT: multiple relaxation time • NS: Navier-Stokes method • PISO: pressure implicit with splitting operator • Re: Reynolds number
Memory in an Excitable Medium: A Mechanism for Spiral Wave Breakup in the Low-excitability Limit
Fenton, Flavio H.; Evans, Steven J.; Hastings, Harold M.
2000-03-01
The electrophysiology of cardiac tissue is altered during acute myocardial ischemia, making the tissue less excitable but nonetheless more susceptible to tachyarrythmias which frequently degenerate to fibrillation within several seconds. The transition from tachycardia to fibrillation is associated with the breakup of spiral waves into multiple offspring and has been linked to steep restitution (slope > 1) of action potential duration (APD). However restitution curves become so flat during ischemia that this mechanism does not apply. We found that when the response of APD to the history of recent activations is included in a model of excitable media, spiral wave breakup can occur in ischemia even when the slope in APD restitutions is < 1.
Angraini, Lily Maysari; Suparmi, Variani, Viska Inda
2010-12-01
SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.
Energy Technology Data Exchange (ETDEWEB)
Spielbauer, T.M.; Aidum, C.K. (Institute of Paper Science and Technology, Atlanta, GA (United States))
1992-03-01
This paper reports that both a wave mechanism and a perforation mechanism have been proposed as the first step in the breakup of fluid sheets. For black liquor sprays, the dominant mechanism is the formation and growth of perforations according to either mechanism, cylindrical strands develop and subsequently break up to form drops. By combining the results of analyzing the breakup of both the sheet and strands, only a discrete number of drop sizes can be predicted from the wave mechanism.
Donne, S. E.; Bean, C. J.; Lokmer, I.; Nicolau, M.; O'Neill, M.
2014-12-01
Ocean waves, driven by atmospheric processes, generate faint continuous Earth vibrations known as microseisms (Bromirski, 1999). Under certain conditions, ocean waves travelling in opposite directions may interact with one another producing a partial or full standing wave. This wave-wave interaction produces a pressure profile, unattenuated with depth, which exerts a pressure change at the seafloor, resulting in secondary microseisms in the 0.1-0.33 Hz band. There are clear correlations between microseism amplitude and storm and ocean wave intensity. We aim to determine ocean wave heights in the Northeast Atlantic offshore Ireland at individual buoy locations, using terrestrially recorded microseism signals. Two evolutionary approaches are used: Artificial Neural Networks (ANN) and Grammatical Evolution (GE). These systems learn to interpret particular input patterns and corresponding outputs and expose the often complex underlying relationship between them. They learn by example and are therefore entirely data driven so data selection is extremely important for the success of the methods. An analysis and comparison of the performance of these methods for a five month period in 2013 will be presented showing that ocean wave characteristics may be reconstructed using microseism amplitudes, adopting a purely data driven approach. There are periods during the year when the estimations made from both the GE and ANN are delayed in time by 10 to 20 hours when compared to the target buoy measurements. These delays hold important information about the totality of the conditions needed for microseism generation, an analysis of which will be presented.
Teaching about Mechanical Waves and Sound with a Tuning Fork and the Sun
Leccia, Silvio; Colantonio, Arturo; Puddu, Emanuella; Galano, Silvia; Testa, Italo
2015-01-01
Literature in "Physics Education" has shown that students encounter many difficulties in understanding wave propagation. Such difficulties lead to misconceptions also in understanding sound, often used as context to teach wave propagation. To address these issues, we present in this paper a module in which the students are engaged in…
Teaching about Mechanical Waves and Sound with a Tuning Fork and the Sun
Leccia, Silvio; Colantonio, Arturo; Puddu, Emanuella; Galano, Silvia; Testa, Italo
2015-01-01
Literature in "Physics Education" has shown that students encounter many difficulties in understanding wave propagation. Such difficulties lead to misconceptions also in understanding sound, often used as context to teach wave propagation. To address these issues, we present in this paper a module in which the students are engaged in…
Analysis of Wave Propagation in Mechanical Continua Using a New Variational Approach
Chakraborty, Goutam
2016-06-01
In this paper a new variational principle is presented for studying various wave propagation phenomena without explicitly deriving the equations of motion. The method looks for steady state solutions of linear or non-linear partial differential equations that admit wave-like solutions. Dispersion relations of plane waves propagating in unbounded continuous media, transmission and reflection coefficients of wave incident on the boundary of two semi-infinite media and wave impedance and mobility in an excited medium are studied with the help of the same principle. Numerous examples are given to clarify the method adopted showing distinct advantages over the traditional methods. The scientific insights that this principle provides are also highlighted.
Non-autonomous discrete Boussinesq equation: Solutions and consistency
Nong, Li-Juan; Zhang, Da-Juan
2014-07-01
A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.
First integrals of the discrete nonconservative and nonholonomic systems
Institute of Scientific and Technical Information of China (English)
Zhang Hong-Bin; Chen Li-Qun; Liu Rong-Wan
2005-01-01
In this paper we show that the first integrals of the discrete equation of motion for nonconservative and non holonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations.
Energy Technology Data Exchange (ETDEWEB)
Ricoeur, A.
2000-07-01
The subject under consideration is the development and propagation of sound in two-phase flows. The investigations are focused on fluids, which are composed of liquid and gas. The gaseous phase may consist of both noncondensable gas and of vapour, originating from phase transitions of the liquid. Fields of application are, among others, flow noise, sonochemistry, the acoustical surveillance of industrial flow processes or ocean acoustics. A stochastic model, which describes spectral properties of noise sources, conditioned by imploding vapour bubbles, is connected to transfer functions. The latter are based on constitutive equations, accounting for the wave mechanics of the two-phase fluids. In combination with a numerical algorithm they permit for the calculation of noise spectra at any distance from the noise sources. The field problem is solved by implementing the constitutive equations into a hybrid boundary element method, which combines low discretization effort with fast evaluation of domain variables. The constitutive equations are based on models for the dynamics of gas- and vapour bubbles. Therefore, the nonlinear and linear bubble dynamics are extensively investigated. Furthermore, fundamental knowledge concerning wave dispersion in two-phase fluids is presented. The constitutive equation for pseudocavitation is experimentally verified by means of an acoustical wave guide. Additionally the experimental set-up serves for investigating fluid-structure-interaction. (orig.) [German] Die Arbeit befasst sich mit der Entstehung und Ausbreitung von Schall in Zweiphasenstroemungen. Betrachtet werden Fluide aus Fluessigkeit und Gas, deren Gasphase sowohl als nichtkondensierendes Gas, als auch in Gestalt des Dampfes der Fluessigkeit vorliegt. Anwendungen liegen beispielsweise in der Stroemungsakustik, der Sonochemie, der akustischen Ueberwachung verfahrenstechnischer Prozesse oder der Meeresakustik. Ein stochastisches Modell zur spektralen Beschreibung von
Directory of Open Access Journals (Sweden)
M.L.B. Simas
2005-03-01
Full Text Available An assumption commonly made in the study of visual perception is that the lower the contrast threshold for a given stimulus, the more sensitive and selective will be the mechanism that processes it. On the basis of this consideration, we investigated contrast thresholds for two classes of stimuli: sine-wave gratings and radial frequency stimuli (i.e., j0 targets or stimuli modulated by spherical Bessel functions. Employing a suprathreshold summation method, we measured the selectivity of spatial and radial frequency filters using either sine-wave gratings or j0 target contrast profiles at either 1 or 4 cycles per degree of visual angle (cpd, as the test frequencies. Thus, in a forced-choice trial, observers chose between a background spatial (or radial frequency alone and the given background stimulus plus the test frequency (1 or 4 cpd sine-wave grating or radial frequency. Contrary to our expectations, the results showed elevated thresholds (i.e., inhibition for sine-wave gratings and decreased thresholds (i.e., summation for radial frequencies when background and test frequencies were identical. This was true for both 1- and 4-cpd test frequencies. This finding suggests that sine-wave gratings and radial frequency stimuli are processed by different quasi-linear systems, one working at low luminance and contrast level (sine-wave gratings and the other at high luminance and contrast levels (radial frequency stimuli. We think that this interpretation is consistent with distinct foveal only and foveal-parafoveal mechanisms involving striate and/or other higher visual areas (i.e., V2 and V4.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Institute of Scientific and Technical Information of China (English)
王斌
2014-01-01
运用知识存量理论、知识网络理论的分析方法，提出知识网络中知识存量离散性问题。通过模型假设和案例分析，构建知识存量离散性演化机理模型。认为在知识聚集度、知识转移速度和知识共振度的影响作用下，知识存量离散性经历四个阶段，沿着非线性S型路径演化。%Analyzing from the theories of knowledge stock and knowledge network, the article proposes the issue of knowl-edge discreteness in knowledge network. By model hypothesis and case study, the evolutional mechanism of discreteness of knowledge stock is build up. It thinks that the discreteness of knowledge stock is experienced four stages along with nonlin-ear S type path, which is influenced by knowledge aggregation, knowledge transfer speed and knowledge resonance.
Cassani, W E R
2001-01-01
As a substitute for the current hypothesis of space-time continuity, we show the nature and the characteristics of a Schild's discrete space-time. With the wave perturbations of its metrical structure we formulate the working hypothesis that all subatomic particles are elementary sources of spherical waves constituting on the whole the mass fields, the electromagnetic and the nuclear field we attribute to the particles. The explicative effectiveness of the new wave unification between quantum mechanics and general relativity is shown by a wave interpretation of three experimental phenomena that lie different physics: astrophysics, optics and quantum physics. A further use of wave Compton effect leads us to discover a mechanism of wave resonance which is able to verify the possible existence of a source of elementary waves that shows a wave model of electron and all the particles. The wave nature of masses and the generalized effect of a Relative Symmetry Principle leads us to consider the inertia as a local c...
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We used 71670 P-wave arrival times from 3594 earthquakes recorded by the Sichuan and Yunnan seismic networks to determine the three-dimensional P-wave velocity structure in the crust and uppermost mantle beneath the southeastern Tibetan Plateau. Our results show that prominent low P-wave velocity (low-Vp) anomalies exist in the midto lower crust of the Song- pan-Ganze and Sichuan-Yunnan blocks. In contrast, a high P-wave velocity (high-Vp) anomaly is resolved in the middle and lower crust beneath the Sichuan Basin. Our tomographic results provide seismic evidence for a dynamic model of lower crustal flow. Ongoing lower crustal flow beneath the central and eastern Tibetan Plateau abuts against the mechanically strong Si- chuan Basin resulting in accumulated strain in the Longmen Shan region. When a critical accumulation of strain energy was reached, its sudden release led to the occurrence of 2008 Wenchuan earthquake. Pronounced low-Vp anomalies are observed in the uppermost mantle in the region south of ~26°N. Combining these results with shear-wave splitting investigations, we suggest that the flow of asthenospheric material has impacted the velocity structure of the uppermost mantle and caused the thinning of the southwestern Yangtze Craton.
Kandaurov, Alexander; Troitskaya, Yuliya; Sergeev, Daniil; Ermakova, Olga; Kazakov, Vassily
2015-04-01
The sea spray is considered as a possible mechanism of the reduction of sea surface aerodynamic drag coefficient at hurricane conditions [1]. In this paper the mechanism of generation of spray in the near-surface layer of the atmosphere in a strong wind through the mechanism of «bag-breakup instability» was investigated in laboratory conditions with the help of high-speed video shooting. The laboratory experiments were performed on the Thermostratified Wind-Wave Channel of the IAP RAS (length 10 m, cross section of air channel 0.4 x 0.4 m, wind velocity up to 24 m/s) [2]. Experiments were carried out for the wind speeds from 14 to 22 m/s. In this range spray generation characteristics change dramatically from almost no spray generation to so called catastrophic regime with multiple cascade breakups on each crest. Shooting was performed with High-speed digital camera NAC Memrecam HX-3 in two different setups to obtain both statistical data and detailed spray generation mechanism overview. In first setup bright LED spotlight with mate screen the side of a channel was used for horizontal shadow-method shooting. Camera was placed in semi-submerged box on the opposite side of the channel. Shooting was performed at the distance of 7.5 m from the beginning of the working section. Series of short records of the surface evolution were made at 10 000 fps with 55 to 119 µm/px scale revealed the dominant mechanism of spray generation - bag-breakup instability. Sequences of high resolution images allowed investigating the details of this "bags" evolution. Shadow method provided better image quality for such conditions than side illumination and fluorescence methods. To obtain statistical data on "bags" sizes and densities vertical shadow method was used. Submerged light box was created with two 300 W underwater lamps and mate screen places at the fetch of 6.5 m. Long records (up to 8 seconds) were made with 4500 fps at 124-256 µm/px scales. Specially developed software
Hatanaka, Kazuaki; Ito, Kenta; Shindo, Tomohiko; Kagaya, Yuta; Ogata, Tsuyoshi; Eguchi, Kumiko; Kurosawa, Ryo; Shimokawa, Hiroaki
2016-09-01
We have previously demonstrated that low-energy extracorporeal cardiac shock wave (SW) therapy improves myocardial ischemia through enhanced myocardial angiogenesis in a porcine model of chronic myocardial ischemia and in patients with refractory angina pectoris. However, the detailed molecular mechanisms for the SW-induced angiogenesis remain unclear. In this study, we thus examined the effects of SW irradiation on intracellular signaling pathways in vitro. Cultured human umbilical vein endothelial cells (HUVECs) were treated with 800 shots of low-energy SW (1 Hz at an energy level of 0.03 mJ/mm(2)). The SW therapy significantly upregulated mRNA expression and protein levels of vascular endothelial growth factor (VEGF) and endothelial nitric oxide synthase (eNOS). The SW therapy also enhanced phosphorylation of extracellular signal-regulated kinase 1/2 (Erk1/2) and Akt. Furthermore, the SW therapy enhanced phosphorylation of caveolin-1 and the expression of HUTS-4 that represents β1-integrin activity. These results suggest that caveolin-1 and β1-integrin are involved in the SW-induced activation of angiogenic signaling pathways. To further examine the signaling pathways involved in the SW-induced angiogenesis, HUVECs were transfected with siRNA of either β1-integrin or caveolin-1. Knockdown of either caveolin-1 or β1-integrin suppressed the SW-induced phosphorylation of Erk1/2 and Akt and upregulation of VEGF and eNOS. Knockdown of either caveolin-1 or β1-integrin also suppressed SW-induced enhancement of HUVEC migration in scratch assay. These results suggest that activation of mechanosensors on cell membranes, such as caveolin-1 and β1-integrin, and subsequent phosphorylation of Erk and Akt may play pivotal roles in the SW-induced angiogenesis.
Generation of ROS mediated by mechanical waves (ultrasound) and its possible applications.
Duco, Walter; Grosso, Viviana; Zaccari, Daniel; Soltermann, Arnaldo T
2016-10-15
The thermal decomposition of 9,10 diphenylanthracene peroxide (DPAO2) generates DPA and a mix of triplet and singlet molecular oxygen. For DPAO2 the efficiency to produce singlet molecular oxygen is 0.35. On the other hand, it has shown that many thermal reactions can be carried out through the interaction of molecules with ultrasound. Ultrasound irradiation can create hydrodynamic stress (sonomechanical process), inertial cavitation (pyrolitic process) and long range effects mediated by radicals or ROS. Sonochemical reactions can be originated by pyrolytic like process, shock mechanical waves, thermal reactions and radical and ROS mediated reactions. Sonolysis of pure water can yield hydrogen or hydroxyl radicals and hydrogen peroxide (ROS). When DPAO2 in 1,4 dioxane solution is treated with 20 or 24kHz and different power intensity the production of molecular singlet oxygen is observed. Specific scavengers like tetracyclone (TC) are used to demonstrate it. The efficiency now is 0.85 showing that the sonochemical process is much more efficient that the thermal one. Another endoperoxide, artemisinin was also studied. Unlike the concept of photosensitizer of photodynamic therapy, in spite of large amount of reported results in literature, the term sonosensitizer and the sonosensitization process are not well defined. We define sonosensitized reaction as one in which a chemical species decompose as consequence of cavitation phenomena producing ROS or other radicals and some other target species does undergo a chemical reaction. The concept could be reach rapidly other peroxides which are now under experimental studies. For artemisinin, an important antimalarian and anticancer drug, was established that ultrasound irradiation increases the effectiveness of the treatment but without any explanation. We show that artemisinin is an endoperoxide and behaves as a sonosensitizer in the sense of our definition.
Weak Equivalence Principle and Propagation of the Wave Function in Quantum Mechanics
de Matos, Clovis Jacinto
2010-01-01
The propagation of the wave function of a particle is characterised by a group and a phase velocity. The group velocity is associated with the particle's classical velocity, which is always smaller than the speed of light, and the phase velocity is associated with the propagation speed of the wave function phase and is treated as being unphysical, since its value is always greater than the speed of light. Here we show, using Sciama's Machian formulation of rest mass energy, that this physical interpretation, for the group and the phase velocity of the wave function, is only valid if the weak equivalence principle strictly holds for the propagating particle, except for the photon. In case this constraint is released the phase velocity of the wave function could acquire a physical meaning in quantum condensates.
Revival of the Phase-Amplitude Description of a Quantum-Mechanical Wave Function
Rawitscher, George
2017-01-01
The phase-amplitude description of a wave function is formulated by means of a new linear differential-integral equation, which is valid in the region of turning points. A numerical example for a Coulomb potential is presented.
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Restrepo, Simon; Basler, Konrad
2016-08-01
Calcium signalling is a highly versatile cellular communication system that modulates basic functions such as cell contractility, essential steps of animal development such as fertilization and higher-order processes such as memory. We probed the function of calcium signalling in Drosophila wing imaginal discs through a combination of ex vivo and in vivo imaging and genetic analysis. Here we discover that wing discs display slow, long-range intercellular calcium waves (ICWs) when mechanically stressed in vivo or cultured ex vivo. These slow imaginal disc intercellular calcium waves (SIDICs) are mediated by the inositol-3-phosphate receptor, the endoplasmic reticulum (ER) calcium pump SERCA and the key gap junction component Inx2. The knockdown of genes required for SIDIC formation and propagation negatively affects wing disc recovery after mechanical injury. Our results reveal a role for ICWs in wing disc homoeostasis and highlight the utility of the wing disc as a model for calcium signalling studies.
Restrepo, Simon; Basler, Konrad
2016-08-09
Calcium signalling is a highly versatile cellular communication system that modulates basic functions such as cell contractility, essential steps of animal development such as fertilization and higher-order processes such as memory. We probed the function of calcium signalling in Drosophila wing imaginal discs through a combination of ex vivo and in vivo imaging and genetic analysis. Here we discover that wing discs display slow, long-range intercellular calcium waves (ICWs) when mechanically stressed in vivo or cultured ex vivo. These slow imaginal disc intercellular calcium waves (SIDICs) are mediated by the inositol-3-phosphate receptor, the endoplasmic reticulum (ER) calcium pump SERCA and the key gap junction component Inx2. The knockdown of genes required for SIDIC formation and propagation negatively affects wing disc recovery after mechanical injury. Our results reveal a role for ICWs in wing disc homoeostasis and highlight the utility of the wing disc as a model for calcium signalling studies.
Experimental study of mechanical properties of liquids under shock wave loading
Bannikova, I. A.; Uvarov, S. V.; Zubareva, A. N.; Utkin, A. V.; Naimark, O. B.
2016-11-01
Glycerol and silicone oil were studied experimentally under shock-wave loading conditions at different temperatures and strain rates. It was found that the temperature has a significant influence on the spall strength of glycerol near the point of phase transition and weak influence on the spall strength of silicone oil. The spall strength of the silicone oil does not depend on the strain rate also. Dynamic viscosity of glycerol measured at the wave front found to be strain rate sensitive.
Nanotube Tunneling as a Consequence of Probable Discrete Trajectories
Robinson, Daryl C.
2001-01-01
It has been recently reported that the electrical charge in a semiconductive carbon nanotube is not evenly distributed, but is divided into charge "islands." A clear understanding of tunneling phenomena can be useful to elucidate the mechanism for electrical conduction in nanotubes. This paper represents the first attempt to shed light on the aforementioned phenomenon through viewing tunneling as a natural consequence of "discrete trajectories." The relevance of this analysis is that it may provide further insight into the higher rate of tunneling processes, which makes tunneling devices attractive. In a situation involving particles impinging on a classically impenetrable barrier, the result of quantum mechanics that the probability of detecting transmitted particles falls off exponentially is derived without wave theory. This paper should provide a basis for calculating the charge profile over the length of the tube so that nanoscale devices' conductive properties may be fully exploited.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method.
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca(2+) concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.
Shock Mechanism Analysis and Simulation of High-Power Hydraulic Shock Wave Simulator
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Xiaoqiu Xu
2017-01-01
Full Text Available The simulation of regular shock wave (e.g., half-sine can be achieved by the traditional rubber shock simulator, but the practical high-power shock wave characterized by steep prepeak and gentle postpeak is hard to be realized by the same. To tackle this disadvantage, a novel high-power hydraulic shock wave simulator based on the live firing muzzle shock principle was proposed in the current work. The influence of the typical shock characteristic parameters on the shock force wave was investigated via both theoretical deduction and software simulation. According to the obtained data compared with the results, in fact, it can be concluded that the developed hydraulic shock wave simulator can be applied to simulate the real condition of the shocking system. Further, the similarity evaluation of shock wave simulation was achieved based on the curvature distance, and the results stated that the simulation method was reasonable and the structural optimization based on software simulation is also beneficial to the increase of efficiency. Finally, the combination of theoretical analysis and simulation for the development of artillery recoil tester is a comprehensive approach in the design and structure optimization of the recoil system.
On the mechanism of self gravitating Rossby interfacial waves in proto-stellar accretion discs
Yellin-Bergovoy, Ron; Umurhan, Orkan M
2015-01-01
The dynamical response of edge waves under the influence of self-gravity is examined in an idealized two-dimensional model of a proto-stellar disc, characterized in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius r0. The fluid in basic state is prescribed to rotate with a Keplerian profile $\\Omega_k(r)\\sim r^{-3/2}$ modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabilizer irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of...
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Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...