Showing papers on "Equations of motion published in 2006"
TL;DR: In this article, a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure was developed, in which the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach-Koehler formula.
Abstract: We develop a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure. The expressions are self-consistent in that the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach–Koehler formula. The singularity intrinsic to the classical continuum theory is removed here by spreading the Burgers vector isotropically about every point on the dislocation line using a spreading function characterized by a single parameter a, the spreading radius. A particular form of the spreading function chosen here leads to simple analytic formulations for stress produced by straight dislocation segments, segment self and interaction energies, and forces on the segments. For any value a > 0 , the total energy and the stress remain finite everywhere, including on the dislocation lines themselves. Furthermore, the well-known singular expressions are recovered for a = 0 . The value of the spreading radius a can be selected for numerical convenience, to reduce the stiffness of the dislocation equations of motion. Alternatively, a can be chosen to match the atomistic and continuum energies of dislocation configurations.
403 citations
TL;DR: The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the quantum-classical Liouville formalism.
Abstract: Quantum-classical Liouville dynamics can be used to study the properties of open quantum systems that are coupled to bath or environmental degrees of freedom whose dynamics can be approximated by classical equations of motion. In contrast to many open quantum system approaches, quantum-classical dynamics provides a detailed description of the bath molecules. Such a description is especially appropriate for the study of quantum rate processes, such as proton and electron transport, where the detailed dynamics of the bath has a strong influence on the quantum rate. The quantum-classical Liouville equation can also serve as a starting point for the derivation of reduced descriptions where all or some of the bath degrees of freedom are projected out. Quantum-classical Liouville dynamics can be simulated in terms of an ensemble of surface-hopping trajectories whose character differs from that in other surface-hopping schemes. The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the formalism.
277 citations
TL;DR: In this article, the authors present a detailed account of the physics of the relativistic Lorentz model of a charged particle coupled to its own electromagnetic field, which is the basis for our work.
Abstract: The motion of a charged particle interacting with its own electromagnetic field is an area of research that has a long history; this problem has never ceased to fascinate its investigators. On the one hand the theory ought to be straightforward to formulate: one has Maxwell's equations that tell the field how to behave (given the motion of the particle), and one has the Lorentz-force law that tells the particle how to move (given the field). On the other hand the theory is fundamentally ambiguous because of the field singularities that necessarily come with a point particle. While each separate sub-problem can easily be solved, to couple the field to the particle in a self-consistent treatment turns out to be tricky. I believe it is this dilemma (the theory is straightforward but tricky) that has been the main source of the endless fascination. For readers of Classical and Quantum Gravity, the fascination does not end there. For them it is also rooted in the fact that the electromagnetic self-force problem is deeply analogous to the gravitational self-force problem, which is of direct relevance to future gravitational wave observations. The motion of point particles in curved spacetime has been the topic of a recent Topical Review [1], and it was the focus of a recent Special Issue [2]. It is surprising to me that radiation reaction is a subject that continues to be poorly covered in the standard textbooks, including Jackson's bible [3]. Exceptions are Rohrlich's excellent text [4], which makes a very useful introduction to radiation reaction, and the Landau and Lifshitz classic [5], which contains what is probably the most perfect summary of the foundational ideas (presented in characteristic terseness). It is therefore with some trepidation that I received Herbert Spohn's book, which covers both the classical and quantum theories of a charged particle coupled to its own field (the presentation is limited to flat spacetime). Is this the text that graduate students and researchers should turn to in order to get a complete and accessible education in radiation reaction? My answer is that while the book does indeed contain a lot of useful material, it is not a very accessible source of information, and it is certainly not a student-friendly textbook. Instead, the book presents a technical account of the author's personal take on the theory, and represents a culminating summary of the author's research contributions over more than a decade. The book is written in a fairly mathematical style (the author is Professor of Mathematical Physics at the Technische Universitat in Munich), and it very much emphasises mathematical rigour. This makes the book less accessible than I would wish it to be, but this is perhaps less a criticism than a statement about my taste, expectation, and attitude. The presentation of the classical theory begins with a point particle, but Spohn immediately smears the charge distribution to eliminate the vexing singularities of the retarded field. He considers both the nonrelativistic Abraham model (in which the extended particle is spherically symmetric in the laboratory frame) and the relativistic Lorentz model (in which the particle is spherical in its rest frame). In Spohn's work, the smearing of the charge distribution is entirely a mathematical procedure, and I would have wished for a more physical discussion. A physically extended body, held together against electrostatic repulsion by cohesive forces (sometimes called Poincar? stresses) would make a sound starting point for a classical theory of charged particles, and would have nicely (and physically) motivated the smearing operation adopted in the book. Spohn goes on to derive energy?momentum relations for the extended objects, and to obtain their equations of motion. A compelling aspect of his presentation is that he formally introduces the 'adiabatic limit', the idea that the external fields acting on the charged body should have length and time scales that are long compared with the particle's internal scales (respectively the electrostatic classical radius and its associated time scale). As a consequence, the equations of motion do not involve a differentiated acceleration vector (as is the case for the Abraham?Lorentz?Dirac equations) but are proper second-order differential equations for the position vector. In effect, the correct equations of motion are obtained from the Abraham?Lorentz?Dirac equations by a reduction-of-order procedure that was first proposed (as far as I know) by Landau and Lifshitz [5]. In Spohn's work this procedure is not {\it ad hoc}, but a natural consequence of the adiabatic approximation. An aspect of the classical portion of the book that got me particularly excited is Spohn's proposal for an experimental test of the predictions of the Landau?Lifshitz equations. His proposed experiment involves a Penning trap, a device that uses a uniform magnetic field and a quadrupole electric field to trap an electron for very long times. Without radiation reaction, the motion of an electron in the trap is an epicycle that consists of a rapid (and small) cyclotron orbit superposed onto a slow (and large) magnetron orbit. Spohn shows that according to the Landau?Lifshitz equations, the radiation reaction produces a damping of the cyclotron motion. For reasonable laboratory situations this damping occurs over a time scale of the order of 0.1 second. This experiment might well be within technological reach. The presentation of the quantum theory is based on the nonrelativistic Abraham model, which upon quantization leads to the well-known Pauli-Fierz Hamiltonian of nonrelativistic quantum electrodynamics. This theory, an approximation to the fully relativistic version of QED, has a wide domain of validity that includes many aspects of quantum optics and laser-matter interactions. As I am not an expert in this field, my ability to review this portion of Spohn's book is limited, and I will indeed restrict myself to a few remarks. I first admit that I found Spohn's presentation to be tough going. Unlike the pair of delightful books by Cohen-Tannoudji, Dupont-Roc, and Grynberg [6, 7], this is not a gentle introduction to the quantum theory of a charged particle coupled to its own electromagnetic field. Instead, Spohn proceeds rather quickly through the formulation of the theory (defining the Hamiltonian and the Hilbert space) and then presents some applications (for example, he constructs the ground states of the theory, he examines radiation processes, and he explores finite-temperature aspects). There is a lot of material in the eight chapters devoted to the quantum theory, but my insufficient preparation and the advanced nature of Spohn's presentation were significant obstacles; I was not able to draw much appreciation for this material. One of the most useful resources in Spohn's book are the historical notes and literature reviews that are inserted at the end of each chapter. I discovered a wealth of interesting articles by reading these, and I am grateful that the author made the effort to collect this information for the benefit of his readers. References [1] Poisson E 2004 Radiation reaction of point particles in curved spacetime Class. Quantum Grav 21 R153?R232 [2] Lousto C O 2005 Special issue: Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach, Class. Quantum Grav22 S543?S868 [3] Jackson J D 1999 Classical Electrodynamics Third Edition (New York: Wiley) [4] Rohrlich F 1990 Classical Charged Particles (Redwood City, CA: Addison?Wesley) [5] Landau L D and Lifshitz E M 2000 The Classical Theory of Fields Fourth Edition (Oxford: Butterworth?Heinemann) [6] Cohen-Tannoudji C Dupont-Roc J and Grynberg G 1997 Photons and Atoms - Introduction to Quantum Electrodynamics (New York: Wiley-Interscience) [7] Cohen-Tannoudji C, Dupont-Roc J and G Grynberg G 1998 Atom?Photon Interactions: Basic Processes and Applications (New York: Wiley-Interscience)
258 citations
Book•
01 Jan 2006
TL;DR: In this article, the authors present a general solution for transversally isotropic body displacement in Cartesian coordinates and a generalized solution in cylindrical coordinates with axisymmetric problems.
Abstract: Preface Chapter 1 BASIC EQUATIONS OF ANISOTROPIC ELASTICITY: 1.1 Transformation of Strains and Stresses 1.2 Basic Equations 1.2.1 Geometric equations 1.2.2 Equations of motion 1.2.3 Constitutive equations 1.3 Boundary and Initial Conditions 1.3.1 Boundary conditions 1.3.2 Initial conditions 1.4 Thermoelasticity. Chapter 2 GENERAL SOLUTION FOR TRANSVERSELY ISOTROPIC PROBLEMS: 2.1 Governing Equations 2.1.1 Methods of solution 2.1.2 Governing equations for the displacement method 2.1.3 Equations for a mixed method - the state-space method 2.2 Displacement Method 2.2.1 General solution in Cartesian coordinates 2.2.2 General solution in cylindrical coordinates 2.3 Stress Method for Axisymmetric Problems 2.4 Displacement Method for Spherically Isotropic Bodies 2.4.1 General solution 2.4.2 Relationship between transversely isotropic and spherically isotropic solutions. Chapter 3 PROBLEMS FOR INFINITE SOLIDS: 3.1 The Unified Point Force Solution 3.1.1 A point force perpendicular to the isotropic plane 3.1.2 A point force within the isotropic plane 3.2 The Point Force Solution for an Infinite Solid Composed of two Half-Spaces 3.2. 1 A point force perpendicular to the isotropic plane 3.2.2 A point force within the isotropic plane 3.2.3 Some remarks 3.3 An Infinite Transversely Isotropic Space with an Inclusions 3.4 Spherically Isotropic Materials 3.4.1 An infinite space subjected to a point force 3.4.2 Stress concentration in neighbourhood of a spherical cavity. Chapter 4 HALF-SPACE AND LAYERED MEDIA: 4.1 Unified Solution for a Half-Space Subjected to a Surface Point Force 4.1.1 A point force normal to the half-space surface 4.1.2 A point force tangential to the half-space surface 4.2 A Half-Space Subjected to an Interior Point Force 4.2. 1 A point force normal to the half-space surface 4.2.2 A point force tangential to the half-spacesurface 4.3 General Solution by Fourier Transform 4.4 Point Force Solution of an Elastic Layer 4.5 Layered Elastic Media. Chapter 5 EQUILIBRIUM OF BODIES OF REVOLUTION: 5.1 Some Harmonic Functions 5.1.1 Harmonic polynomials 5.1.2 Harmonic functions containing ln(r I ij ) 5.1.3 Harmonic functions containing R 5.2 An Annular (Circular) Plate Subjected to Axial Tension and Radial Compression 5.3 An Annular (Circular) Plate Subjected to Pure Bending 5.4 A Simply-Supported Annular (Circular) Plate Under Uniform Transverse Loading 5.5 A Uniformly Rotating Annular (Circular) Plate 5.6 Transversely Isotropic Cones 5.6.1 Compression of a cone under an axial force 5.6.2 Bending of a cone under a transverse force 5.7 Spherically Isotropic Cones 5.7.1. Equilibrium and boundary conditions 5.7.2. A cone under tip forces 5.7.3. A cone under concentrated moments at its apex 5.7.4. Conical shells. Chapter 6 THERMAL STRESSES: 6.1 Transversely Isotropic Materials 6.2 A Different General Solution for Transversely Isotropic Thermoelasticity 6.2. 1 General solution for dynamic problems 6.2.2 General solution for static problems 6.3 Spherically Isotropic Materials. Chapter 7 FRICTIONAL CONTACT: 7.1 Two Elastic Bodies in Contact 7.1.1 Mathematical description of a contact system 7.1.2 Deformation of transversely isotropic bodies under frictionless contact 7.1.3 A half-space under point forces 7.2 Contact of a Sphere with a Half-Space 7.2.1 Contact with normal loading 7.2.2 Contact with tangential loading 7.3 Contact of a Cylindrical Punch with a Half-Space 7.3.1 Contact with normal loading 7.3.2 Contact with tangential loading 7.4 Indentation by a Cone 7.4.1 Contact with normal loading 7.4.2 Contact with tangential loading 7.5 Inclined Contact of a Cylindrical Punch with a Half-Space 7.5.1 Contact with normal loading 7.5.2 Contact with tangential loading 7.6 Discussions on Solu
236 citations
TL;DR: The Immirzi parameter is a constant appearing in the general-relativity action used as a starting point for the loop quantization of gravity as mentioned in this paper, and it determines the coupling constant of a four-fermion interaction.
Abstract: The Immirzi parameter is a constant appearing in the general-relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to appear in the equations of motion and not to have any physical effect besides nonperturbatrive quantum gravity. We show that this is not true in general: in the presence of minimally coupled fermions, the parameter appears in the equations of motion: it determines the coupling constant of a four-fermion interaction. Under some general assumptions, there is therefore a relation between the Immirzi parameter and physical effects that are observable in principle, independently from nonperturbative quantum gravity
216 citations
TL;DR: In this paper, the spin-orbit effects up to 2.5PN in the conserved (Noetherian) integrals of motion were derived for black holes maximally spinning and the spin precession equations at 1PN order beyond the leading term.
Abstract: We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely the energy, the total angular momentum, the linear momentum and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA type interferometric detectors.
210 citations
Book•
17 Feb 2006TL;DR: In this article, the potential of nanoscale engineering and the potential for multiple scale modeling was discussed, and an educational approach was proposed for the multiple scale modeling (MSM) approach.
Abstract: Preface 1 Introduction 11 Potential of Nanoscale Engineering 12 Motivation for Multiple Scale Modeling 13 Educational Approach 2 Classical Molecular Dynamics 21 Mechanics of a System of Particles 22 Molecular Forces 23 Molecular Dynamics Applications 3 Lattice Mechanics 31 Elements of Lattice Symmetries 32 Equation of Motion of a Regular Lattice 33 Transforms 34 Standing Waves in Lattices 35 Green's Function Methods 36 Quasistatic Approximation 4 Methods of Thermodynamics and Statistical Mechanics 41 Basic Results of the Thermodynamic Method 42 Statistics of Multiparticle Systems in Thermodynamic Equilibrium 43 Numerical Heat Bath Techniques 5 Introduction to Multiple Scale Modeling 51 MAAD 52 Coarse Grained Molecular Dynamics 53 Quasicontinuum Method 54 CADD 55 Bridging Domain 6 Introduction to Bridging Scale 61 Bridging Scale Fundamentals 62 Removing Fine Scale Degrees of Freedom in Coarse Scale Region 3D Generalization 63 Discussion on the Damping Kernel Technique 64 Cauchy-Born Rule 65 Virtual Atom Cluster Method 66 Staggered Time Integration Algorithm 67 Summary of Bridging Scale Equations 68 Discussion on the Bridging Scale Method 7 Bridging Scale Numerical Examples 71 Comments On Time History Kernel 74 Two-Dimensional Wave Propagation 75 Dynamic Crack Propagation in Two Dimensions 76 Dynamic Crack Propagation in Three Dimensions 77 Virtual Atom Cluster Numerical Examples 8 Non-Nearest Neighbor MD Boundary Condition 81 Introduction 82 Theoretical Formulation in 3D 83 Numerical Examples - 1D Wave Propagation 84 Time History Kernels for FCC Gold 85 Conclusion on the Bridging Scale Method 9 Multiscale Methods for Material Design 91 Multiresolution Continuum Analysis 92 Multiscale Constitutive Modeling of Steels 93 Bio-Inspired Materials 94 Summary and Future Research Directions 10 Bio-Nano Interface 103 Vascular Flow and Blood Rheology 104 Electrohydrodynamic Coupling 105 CNT/DNA Assembly Simulation 106 Cell Migration and Cell-Substrate Adhesion 107 Conclusions Appendix A: Kernel Matrices for EAM Potential Bibliography Index
209 citations
TL;DR: In this paper, the authors examined a general governing equation of motion for a class of electrostatically driven microelectromechanical (MEM) oscillators and used it to provide a complete description of the dynamic response and its dependence on the system parameters.
181 citations
TL;DR: In this paper, the authors considered a one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction and showed how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on α.
Abstract: We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1∕∣n−m∣α+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order α, when 0<α<2. We consider a few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on α. The presence of a fractional derivative also leads to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.
166 citations
TL;DR: In this article, the authors considered a wide class of long-range interactions that give fractional medium equations in the continuous limit and formulated the consistent definition of continuous limit for these systems.
Abstract: Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.
162 citations
Book•
20 Apr 2006
TL;DR: The Rigid Finite Element Method (RFI) as mentioned in this paper is an extension of the rigid finite element method (RFEM) for homogeneous transformations of a cantilever beam.
Abstract: Homogenous Transformations.- The Rigid Finite Element Method.- Modification of the Rigid Finite Element Method.- Calculations for a Cantilever Beam and Methods of Integrating the Equations of Motion.- Verification of the Method.- Applications.
TL;DR: The set of equations is applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity.
Abstract: Vegetation is the most common and most reliable stabilizer of loose soil or sand. This ancient technique is for the first time cast into a set of equations of motion describing the competition between aeolian sand transport and vegetation growth. Our set of equations is then applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity. We find a fixation index theta(c) below which the dunes are stabilized, characterized by scaling laws.
TL;DR: In this article, an analytical analysis of the transport and capture of magnetic micro/nanoparticles in a magnetophoretic micro system that consists of an array of integrated soft-magnetic elements embedded beneath a microfluidic channel is presented.
Abstract: An analytical analysis is presented of the transport and capture of magnetic micro/nanoparticles in a magnetophoretic microsystem that consists of an array of integrated soft-magnetic elements embedded beneath a microfluidic channel. The elements, which are polarized by a bias field, produce a nonuniform field distribution that gives rise to a force on magnetic particles within the microchannel. The equations governing particle motion are derived using analytical expressions for the dominant magnetic and fluidic forces. The magnetic force is obtained using an analytical expression for the field distribution in the microchannel combined with a linear magnetization model for the magnetic response of the particles. The theory takes into account particle size and material properties, the bias field, the dimensions of the microchannel, the fluid properties, and the flow velocity. The equations of motion are solved to study particle transport and capture. The analysis indicates that the particles exhibit an oscillatory motion as they traverse the microsystem, and that a high capture efficiency can be obtained in practice.
TL;DR: In this paper, a special class of Lovelock gravity is considered, which is called pure Lovelocks gravity, where only one Euler density term exists, and some interesting features are found, which are quite different from the corresponding ones in general relativity.
Abstract: Lovelock gravity is a fascinating extension of general relativity, whose action consists of dimensionally extended Euler densities Compared to other higher order derivative gravity theories, Lovelock gravity is attractive since it has a lot of remarkable features such as the fact that there are no more than second order derivatives with respect to the metric in its equations of motion, and that the theory is free of ghosts Recently, in the study of black strings and black branes in Lovelock gravity, a special class of Lovelock gravity is considered, which is named pure Lovelock gravity, where only one Euler density term exists In this paper we study black hole solutions in the special class of Lovelock gravity and associated thermodynamic properties Some interesting features are found, which are quite different from the corresponding ones in general relativity
TL;DR: In this article, the time-dependent configuration interaction singles (TDCIS) method is reformulated in terms of an effective one-electron theory with coupled channels, and a simplified version of this theory, referred to as the determinantal single-active electron (d-SAE) method, is derived.
Abstract: The time-dependent configuration interaction singles (TDCIS) method---an ab initio electronic-structure technique with predictive character---is reformulated in terms of an effective one-electron theory with coupled channels. In this form, the TDCIS equations of motion may be evaluated using standard wave-packet propagation techniques in real space. The time-dependent orbital formulation of TDCIS has computational and conceptual advantages for studying strong-field phenomena in many-electron systems. A simplified version of this theory, referred to as the determinantal single-active-electron (d-SAE) method, is derived. TDCIS and d-SAE are tested by their application to a one-dimensional two-electron model in a strong laser field. The numerically exact time-dependent dipole moment of the interacting system is found to be very well reproduced with TDCIS. The d-SAE method is less accurate, but still provides superior performance in comparison to the standard single-active-electron approach.
01 Jan 2006
TL;DR: In this paper, the authors present a generalization of the coupling equations for non-linear and non-dissipative acoustics, including sound radiation and transparency of walls.
Abstract: Preface. Chapter 1. Equations of Motion in Non-dissipative Fluid. Chapter 2. Equations of Motion in Dissipative Fluid. Chapter 3. Problems of Acoustics in Dissipative Fluids. Chapter 4. Basic Solutions to the Equations of Linear Propagation in Cartesian Coordinates. Chapter 5. Basic Solutions to the Equations of Linear Propagation in Cylindrical and Spherical Coordinates. Chapter 6. Integral Formalism in Linear Acoustics. Chapter 7. Diffusion, Diffraction and Geometrical Approximation. Chapter 8. Introduction to Sound Radiation and Transparency of Walls. Chapter 9. Acoustics in Closed Spaces. Chapter 10. Introduction to Non-linear Acoustics, Acoustics in Uniform Flow and Aero-acoustics. Chapter 11. Methods in Electro-acoustics. Appendix A.1 Reminder about linear electrical circuits with localized constants. Appendix A.2 Generalization of the coupling equations. Bibliography. Index.
TL;DR: In this paper, a third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics, and a derivative model is employed to describe the coupled restoring actions up to third order.
TL;DR: In this paper, a gauge-invariant and sigma-model-covariant approach to the dynamics of 5-dimensional bulk fluctuations was developed for confining gauge theories, where the system under scrutiny is a 5D consistent truncation of type IIB supergravity obtained using the Papadopoulos Tseytlin ansatz with boundary momentum added.
TL;DR: In this paper, the authors present a general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices, which may have holonomic and non-holonomic constraints.
Abstract: We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.
TL;DR: A variable time lag between e-e collision and double ionization is reported, and it is found that the time lag plays a key role in the emergence directions of the electrons.
Abstract: Ensembles of 400 000 two-electron trajectories in three space dimensions are used with Newtonian equations of motion to track atomic double ionization under very strong laser fields. We report a variable time lag between $e\mathrm{\text{\ensuremath{-}}}e$ collision and double ionization, and find that the time lag plays a key role in the emergence directions of the electrons. These are precursors to production of electron momentum distributions showing substantial new agreement with experimental data.
TL;DR: In this paper, a general relativistic force-free (GRFFE) formulation was proposed to directly evolve the GRFFE equations of motion, which can be incorporated into an existing GRMHD code (HARM) for Minkowski and black hole space-times.
Abstract: The force-free limit of magnetohydrodynamics (MHD) is often a reasonable approximation to model black hole and neutron star magnetospheres. We describe a general relativistic force-free (GRFFE) formulation that allows general relativistic magnetohydrodynamic (GRMHD) codes to directly evolve the GRFFE equations of motion. Established, accurate and well-tested conservative GRMHD codes can simply add a new inversion piece of code to their existing code, while continuing to use all the already-developed facilities present in their GRMHD code. We show how to enforce the E · B = 0 constraint and energy conservation, and we introduce a simplified general model of the dissipation of the electric field to enforce the B 2 - E 2 > 0 constraint. We also introduce a simplified yet general method to resolve current sheets, without much reconnection, over many dynamical times. This formulation is incorporated into an existing GRMHD code (HARM), which is demonstrated to give accurate and robust GRFFE results for Minkowski and black hole space-times.
TL;DR: In this article, the authors introduce an original theoretical approach to the modelling of pinion-gear excitations valid for three-dimensional models of single-stage geared transmissions, starting from the instantaneous contact conditions between the teeth, the equations of motion are re-formulated in terms of quasi-static transmission errors under load and no-load transmission errors.
TL;DR: In this article, the von Karman nonlinear strain-displacement relationship is used to describe the geometric nonlinearity of rectangular plates subjected to harmonic excitation, and a specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, is introduced as a consequence that it is very close to the experimental boundary condition.
TL;DR: In this article, a free vibration analysis of laminated composite beams is carried out using two higher order displacement-based shear deformation theories and finite elements based on the theories.
TL;DR: In this article, the out-of-plane free vibration analysis of a double tapered Euler-Bernoulli beam, mounted on the periphery of a rotating rigid hub is performed.
Abstract: In this study, the out-of-plane free vibration analysis of a double tapered Euler–Bernoulli beam, mounted on the periphery of a rotating rigid hub is performed. An efficient and easy mathematical technique called the Differential Transform Method (DTM) is used to solve the governing differential equation of motion. Parameters for the hub radius, rotational speed and taper ratios are incorporated into the equation of motion in order to investigate their effects on the natural frequencies. Calculated results are tabulated in several tables and figures and are compared with the results of the studies in open literature where a very good agreement is observed.
TL;DR: In this paper, energy balance equations are established for the Newmark time integration algorithm, and for the derived algorithms with algorithmic damping introduced via averaging, the so-called α -methods.
TL;DR: In this article, the threshold current of domain wall motion under spin-polarized electric current in ferromagnets is theoretically studied based on the equation of motion of a wall in terms of collective coordinates.
Abstract: Threshold current of domain wall motion under spin-polarized electric current in ferromagnets is theoretically studied based on the equation of motion of a wall in terms of collective coordinates. Effects of non-adiabaticity and a so-called $\beta$-term in Landau-Lifshitz equation, which are described by the same term in the equation of motion of a wall, are taken into account as well as extrinsic pinning. It is demonstrated that there are four different regimes characterized by different dependence of threshold on extrinsic pinning, hard-axis magnetic anisotropy, non-adiabaticity and $\beta$.
Book•
16 Jun 2006
TL;DR: In this article, the authors present a review of mathematical tools for the analysis of fluid dynamics, including vector calculus, physics, and physics of cyclone dynamics, as well as a discussion of the application of these tools in the field of physics.
Abstract: Preface. Acknowledgments. 1. Introduction and Review of Mathematical Tools. Objectives. 1.1 Fluids and the nature of fluid dynamics. 1.2 Review of useful mathematical tools. 1.2.1 Elements of vector calculus. 1.2.2 The Taylor series expansion. 1.2.3 Centred difference approximations to derivatives. 1.2.4 Temporal changes of a continuous variable. 1.3 Estimating with scale analysis. 1.4 Basic kinematics of fluids. 1.4.1 Pure vorticity. 1.4.2 Pure divergence. 1.4.3 Pure stretching deformation. 1.4.4 Pure shearing deformation. 1.5 Mensuration. Selected references. Problems. Solutions. 2. Fundamental and Apparent Forces. Objectives. 2.1 The fundamental forces. 2.1.1 The pressure gradient force. 2.1.2 The gravitational force. 2.1.3 The frictional force. 2.2 Apparent forces. 2.2.1 The centrifugal force. 2.2.2 The Coriolis force. Selected references. Problems. Solutions. 3. Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World. Objectives. 3.1 Mass in the Atmosphere. 3.1.1 The hypsometric equation. 3.2 Conservation of momentum: The equations of motion. 3.2.1 The equations of motion in spherical coordinates. 3.2.2 Conservation of mass. 3.3 Conservation of energy: The energy equation. Selected references. Problems. Solutions. 4. Applications of the Equations of Motion. Objectives. 4.1 Pressure as a vertical coordinate. 4.2 Potential temperature as a vertical coordinate. 4.3 The thermal wind balance. 4.4 Natural coordinates and balanced flows. 4.4.1 Geostrophic flow. 4.4.2 Inertial flow. 4.4.3 Cyclostrophic flow. 4.4.4 Gradient flow. 4.5 The relationship between trajectories and streamlines. Selected references. Problems. Solutions. 5. Circulation, Vorticity, and Divergence. Objectives. 5.1 The Circulation theorem and its physical interpretation. 5.2 Vorticity and potential vorticity. 5.3 The relationship between vorticity and divergence. 5.4 The quasi-geostrophic system of equations. Selected references. Problems. Solutions. 6. The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions. Objectives. 6.1 The nature of the ageostrophic wind: Isolating the acceleration vector. 6.1.1 Sutcliffe's expression for net ageostrophic divergence in a column. 6.1.2 Another perspective on the ageostrophic wind. 6.2 The Sutcliffe development theorem. 6.3 The quasi-geostrophic omega equation. 6.4 The Q--vector. 6.4.1 The geostrophic pradox and its resolution. 6.4.2 A natural coordinate version of the -Q-vector. 6.4.3 The along- and across-isentrope components of -Q. Selected references. Problems. Solutions. 7. The Vertical Circulation at Fronts. Objectives. 7.1 The structural and dynamical characteristics of mid-latitude fronts. 7.2 Frontogenesis and vertical motions. 7.3 The semi-geostrophic equations. 7.4 Upper-level frontogenesis. 7.5 Precipitation processes at fronts. Selected references. Problems. Solutions. 8. Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone. Objectives. 8.1 Introduction: The polar front theory of cyclones. 8.2 Basic structural and energetic characteristics of the cyclone. 8.3 The cyclogenesis stage: The QG tendency equation perspective. 8.4 The cyclogenesis stage: The QG omega equation perspective. 8.5 The cyclogenetic influence of diabatic processes: Explosive cyclogenesis. 8.6 The post-mature stage: Characteristic thermal structure. 8.7 The post-mature stage: The QG dynamics of the occluded quadrant. 8.8 The Decay Stage. Selected references. Problems. Solutions. 9. Potential Vorticity and Applications to Mid-Latitude Weather Systems. Objectives. 9.1 Potential vorticity and isentropic divergence. 9.2 Characteristics of a positive PV anomaly. 9.3 Cyclogenesis from the PV perspective. 9.4 The influence of diabatic heating on PV. 9.5 Additional applications of the PV perspective. 9.5.1 Piecewise PV inversion and some applications. 9.5.2 A PV perspective on occlusion. 9.5.3 A PV perspective on leeside cyclogenesis. 9.5.4 The effects of PV superposition and attenuation. Selected references. Problems. Solutions. Appendix A: Virtual Temperature. Bibliography. Index.
TL;DR: A Hamiltonian is derived from which the SLLOD equations of motion can be obtained in the special case of a symmetric velocity gradient tensor and it is shown that it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.
Abstract: We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.
TL;DR: In this paper, the dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally, focusing on behavior in bending near the critical speeds of rotation.
Abstract: The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.