New soliton equation for dipole chains

Zorski, Henryk; Infeld, E.

doi:10.1103/physrevlett.68.1180

Cited by 29 publications

(10 citation statements)

References 10 publications

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“…Analyses (23)(24)(25) of a one-dimensional string of rotors interacting by electrostatic forces suggest that solitary waves may be possible. Such analyses benefit from a phenomenological characterization of the rotor, e.g., by its friction constant.…”

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confidence: 99%

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Vacek

Michl

2001

Proc. Natl. Acad. Sci. U.S.A.

104

103

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Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E() at T Ӎ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh 2 4؉ in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1͞e) at E() ‫؍‬ ͦE()ͦ > Ec() [Ec() is the critical field strength], (ii) asynchronous (1͞e < a < 1) at Ec() > E() > Ebo() > kT͞, [Ebo() is the break-off field strength], (iii) random driven (a Ӎ 1) at E bo() > E() > kT͞, and (iv) random thermal (a Ӎ 1) at kT͞ > E(). A fifth regime, (v) strongly hindered, W > kT, E, (W is the rotational barrier), has not been examined. We find E bo()͞kVcm ؊1 Ӎ (kT͞)͞kVcm ؊1 ؉ 0.13(͞GHz) 1.9 and E c()͞kVcm ؊1 Ӎ (2.3kT͞)͞kVcm ؊1 ؉ 0.87(͞GHz) 1.6 . For > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, ͞eVps Ӎ 1.14 ͞THz, and for < 20 GHz, it exhibits a uniquely molecular behavior.M olecular construction kits promise access to giant molecules shaped like regular grids and scaffolds carrying active and͞or mobile groups (1-4). A sturdy artificial square grid polymer, albeit irregular and only ϳ150 nm across, has been reported (5, 6), and time appears right to use computer simulation of these ''designer solids'' to analyze the role of thermal motion in molecular machinery and to identify the best synthetic targets.One of the active elements proposed (4, 7) for incorporation in these molecular scaffolds is a dipolar rotor, capable of rotational motion in response to an outside driving force. Molecular rotors driven unidirectionally by light (8), or bidirectionally by heat (9-12) or chemically (13, 14) have been synthesized. Alternating electric field has been used to affect intramolecular motion (15), and intense laser field of rapidly rotating linear polarization has been used to drive the rotation of a chlorine molecule (16). Free hydroxyl groups on oxide surfaces behave as two-dimensional arrays of interacting rotors, as do phospholipids in certain membranes and dipolar molecules adsorbed on flat surfaces or intercalated in layered solids (17). Biological motors (18) are under study. The velocity at which a dissolved chiral molecule is propelled through a solution by circularly polarized microwaves has been theoretically estimated (19)(20)(21).Previously (22), we examined computationally the unidirectional motion of a grid-mounted propeller-shaped rotor driven by a stream of gas. This windmill rotor acted as a microphone, transducing linear motion of gas molecules into rotational motion of electric charges. A propeller-shaped rotor driven by a rotating electric field in the presence of a gas might produce a pressure differential, acting as a loudspeaker or a gas pump.The dielectric response of a dipolar rotor is intrinsically nonlinear and ther...

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confidence: 99%

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Vacek

Michl

2001

Proc. Natl. Acad. Sci. U.S.A.

104

103

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“…What makes it more interesting is that equation (3.1) arises in a number of various physical contexts. For example, it describes, to the first order, the motion of long waves on a dipole chain in the continuum limit, see Zorski and Infeld [40], Grundland and Infeld [16], or Glassey, Hunter, and Zheng [14]. For another example, it is the simplest representative of a large class of variational wave equations in the classical field theories and general relativity, see Glassey, Hunter, and Zheng [14].…”

Section: Weak Solutions To a Nonlinear Variational Wave Equationmentioning

confidence: 99%

Weak solutions to a nonlinear variational wave equation and some related problems

Zhang

2006

Appl Math

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“…Such arrays, assembled in a controlled fashion, would be quite interesting. They could be ferroelectric (hexagonal or trigonal grids) or antiferroelectric (square grids) (33), could support slowly propagating waves of rotational excitation (34)(35)(36), and might exhibit other interesting dielectric and optical properties.…”

Section: Objectivementioning

confidence: 99%