<i>Classical Dynamics: A Contemporary Approach</i>

José, Jörge V.; Saletan, Eugene J.; Robinett, R. W.

doi:10.1119/1.19450

Cited by 201 publications

(335 citation statements)

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“…The configuration state of a colloidal particle is, however, determined not only by the translational DoF and its linear momentum, = ( ) X r p , i i i , but also by the rotational DoF, e.g. the Eulerian angles a q f c = ( ) , , [7,45,46], which determine the orientation of the principal-axes frame of the particles, B, relative to the space-fixed frame, S. Thus, the dynamics of the colloidal particles will be determined by the evolution of a p W = ( ) , i i i , with p i being the rotational conjugate momenta [8], whose relationship with the angular momenta L i will be specified below. We know that  w = L i i i with w i the angular velocity and  i the inertial tensor.…”

Section: Microscopic Description 21 Hamilton's and Liouville's Equamentioning

confidence: 99%

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General framework for fluctuating dynamic density functional theory

et al. 2017

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We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical densityfunctional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

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Section: Microscopic Description 21 Hamilton's and Liouville's Equamentioning

confidence: 99%

“…where the dot denotes time derivative, F i highlights the fact that w i is the vector accounting for the rate of change of angular displacement over the Cartesian frame B [7,46], and L i can be found elsewhere [11,46]. Accordingly,…”

Section: Microscopic Description 21 Hamilton's and Liouville's Equamentioning

confidence: 99%

General framework for fluctuating dynamic density functional theory

et al. 2017

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“…Now, however, those intervals have greatly increased in number, and the qualitative distinction between the dynamical regimes identified for weak coupling blurs out. In this situation, according to (21), the frequency ν of the oscillations in  W 1 2 grows because, as j becomes larger, the difference between the frequencies Ω a,b increases; cf (13) and (15). At the same time, superimposed fast, small-amplitude oscillations of frequency W = W + W ( ) 2 a b 0 -disregarded in the approximation of (21)become clearly visible.…”

Section: Numerical Resultsmentioning

confidence: 96%

“…This oscillatory behavior is enhanced as the coupling strength between the oscillators grows. In fact, stronger interactions promote the separation between the oscillation frequencies involved in the motion, which in turn controls the oscillations of the power transfer; cf (13), (15), and (21). Numerical results show that, for sufficiently strong coupling, the power transfer is dominated by these oscillations, and the contrast between the two regimes blurs out ( figure 5).…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Namely, 1,2 . It is customary to characterize the resonant response of an oscillating system to harmonic external forcing of frequency Ω by specifying the oscillation amplitudes and phases as functions of Ω [21]. A more comprehensive description -absorbing all the parameters into non-dimensional rescaled quantities-is obtained in the present case in terms of the rescaled detunings…”

Section: Equations Of Motion and Stationary Oscillationsmentioning

confidence: 99%

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Energy exchange between coupled mechanical oscillators: linear regimes

Zanette

2018

J. Phys. Commun.

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Nonlinear mechanisms are frequently invoked to explain unexpected observations during processes of energy exchange in mechanical systems. However, whether the same phenomena could be observed in a purely linear system is seldom considered. In this paper, we revisit the problem of two linearly coupled, damped, harmonic oscillators, with emphasis on the dynamics of their mutual exchange of energy. A novel criterion is established to discern between two well-differentiated regimes of energy exchange under ringdown conditions, when all external excitations are turned off and the oscillatory motion is left to decay by dissipation. The two regimes are induced by different sets of initial conditions, and correspond to extremal values of the total net energy transferred during ringdown. Although the problem is in principle fully solvable, its algebraic involvedness requires in practice to resort to approximated expressions for oscillation frequencies and decay rates. We explicitly provide such approximations in the limit of high quality factors and weak coupling. This limit is relevant to current experiments on micro-and nanomechanical oscillators, whose physical behavior is usually explained by extensive allusion to energy exchange. Our results should help to discern between observations that are genuinely due to nonlinear effects, and those that can be explained in terms of linear mechanisms only.

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Nonlinear subcyclotron resonance as a formationmechanism for gaps in banded chorus

Guo

Dong

et al. 2015

Geophysical Research Letters

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An interesting characteristic of magnetospheric chorus is the presence of a frequency gap at ω≃0.5Ωe, where Ωe is the electron cyclotron angular frequency. Recent chorus observations sometimes show additional gaps near 0.3Ωe and 0.6Ωe. Here we present a novel nonlinear mechanism for the formation of these gaps using Hamiltonian theory and test particle simulations in a homogeneous, magnetized, collisionless plasma. We find that an oblique whistler wave with frequency at a fraction of the electron cyclotron frequency can resonate with electrons, leading to effective energy exchange between the wave and particles.

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Classical Dynamics: A Contemporary Approach

Cited by 201 publications

References 0 publications

General framework for fluctuating dynamic density functional theory

General framework for fluctuating dynamic density functional theory

Energy exchange between coupled mechanical oscillators: linear regimes

Nonlinear subcyclotron resonance as a formationmechanism for gaps in banded chorus

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