On Growth and Form

Thompson, D’Arcy Wentworth

doi:10.1017/cbo9781107325852

Cited by 485 publications

(183 citation statements)

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“…In order to get an insight into the evolution of the bubble shape with its growth, one can evaluate allometric changes in its proportion (Thompson, 1992). If the bubble would grow isometrically with respect to its initial shape, its surface area would scale with its linear dimension as S ∼ l 2 , and the volume as V ∼ l 3 .…”

Section: Resultsmentioning

confidence: 99%

Methane bubble growth in fine-grained muddy aquatic sediment: Insight from modeling

Katsman

Ostrovsky

Makovsky

2013

Earth and Planetary Science Letters

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Section: Resultsmentioning

confidence: 99%

Methane bubble growth in fine-grained muddy aquatic sediment: Insight from modeling

Katsman

Ostrovsky

Makovsky

2013

Earth and Planetary Science Letters

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“…Surprisingly, this depiction is close to the picture oen used intuitively for chiral structures, such as gastropods or chiral swirls. [46][47][48] The difference between Fig. 7c and d is that the main axis is of nite length and pitch and radii taper, but they could interconvert, simply by the alignment of domains.…”

Section: -39mentioning

confidence: 97%

The design and investigation of the self-assembly of dimers with two nematic phases

2015

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A series of non-symmetric dimers were synthesised containing either cyanobiphenyl or difluoroterphenyl moieties on one side and a range of long, short, bent, polar or apolar mesogens on the other side of the molecules. The dielectric anisotropy of the mesogens was varied systematically. The systems were characterised by differential scanning calorimetry (DSC), optical polarizing microscopy (OPM) and detailed X-ray diffraction (XRD) studies, both in the nematic and the N x phase. The results are compared and structure-property relationships are discussed. A model for the assembly in the N x phase is developed discussing N tb structures, coaxial helices, swiss roll structures and chiral domain formation.

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“…T he formation of ordered structures by self assembly is interesting both theoretically and practically, with implications for chemistry (1,2), physics (3)(4)(5), materials science (6)(7)(8)(9), and biology (10)(11)(12). Although self assembly and self organization in systems operating at or near thermodynamic equilibrium are relatively well understood, the theoretical description of dynamic self-assembling systems (13,15)-those that operate away from equilibrium and develop order only when dissipating energy-is incomplete.…”

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confidence: 99%

Dynamics of self assembly of magnetized disks rotating at the liquid–air interface

Grzybowski

Stone²,

Whitesides³

2002

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

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This paper is a theoretical study of dynamic self assembly in a system of millimeter-sized magnetized disks floating at a liquid-air interface and spinning under the influence of a rotating magnetic field. Equations of motions are derived that account for the hydrodynamic and magnetic forces acting in the system. Numerical integration of these equations predicts formation of ordered structures of spinning disks; the simulated structures reproduce the patterns observed experimentally.T he formation of ordered structures by self assembly is interesting both theoretically and practically, with implications for chemistry (1, 2), physics (3-5), materials science (6-9), and biology (10-12). Although self assembly and self organization in systems operating at or near thermodynamic equilibrium are relatively well understood, the theoretical description of dynamic self-assembling systems (13, 15)-those that operate away from equilibrium and develop order only when dissipating energy-is incomplete. In the absence of a general analytical description of such systems, numerical analysis is a convenient (and often the only) method for studying their dynamics.In previous work (16, 17), we described a dynamic selfassembling system composed of a limited number (Ͻ40) of millimeter-sized magnetized disks floating on a liquid-air interface and subject to an external magnetic field produced by a rotating permanent magnet with a dipole length much larger (ϳ6 cm) than the radii (ϳ0.5 mm) of the disks. In the presence of the rotating external field, the disks spin around their axes with angular frequency equal to that of the external magnet ( ϳ200-1,200 rpm). All disks are attracted toward the axis of rotation of the magnet and are repelled by one another by hydrodynamic interactions associated with the motion of the fluid surrounding the disks. The interplay between attractive magnetic and repulsive hydrodynamic interactions in this system leads to the formation of macroscopic patterns. We quantified both the hydrodynamic repulsive force between the disks and the central magnetic force acting on all disks. On the basis of the experimental data for the simplest case of two interacting disks, we derived the equations that describe the forces acting in the system (17) and proposed that interactions in aggregates composed of a larger number of disks can be treated pairwise.This work describes the equations of motion of the rotating disks and uses them to model self organization of different numbers of such disks in ordered aggregates. The simulated patterns are in excellent agreement with those observed experimentally. Our model not only correctly predicts the symmetry and dimensions of the aggregates at various rotational speeds but also allows estimation of the frequencies of occurrence of polymorphic patterns (i.e., different patterns that arise in the same system). We identify dimensionless parameters that control the formation of the aggregates and compare and contrast the results of our simulations with those for systems of twodimen...

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On Growth and Form

Cited by 485 publications

References 0 publications

Methane bubble growth in fine-grained muddy aquatic sediment: Insight from modeling

Methane bubble growth in fine-grained muddy aquatic sediment: Insight from modeling

The design and investigation of the self-assembly of dimers with two nematic phases

Dynamics of self assembly of magnetized disks rotating at the liquid–air interface

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