Shape of a Cracking Whip

Goriely, Alain; McMillen, Tyler

doi:10.1103/physrevlett.88.244301

Cited by 50 publications

(50 citation statements)

References 16 publications

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“…The present work should encourage further theoretical studies in other regions of well deformed nuclei. It is worth noting here that QRPA calculations have been successfully applied to describe other properties in nuclei with open shells where the nucleon pairing correlations are important such as B(E2) values [23] or giant resonances [24].…”

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confidence: 99%

Deformation of theN=ZNucleusSr76usingβ-Decay Studies

et al. 2004

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A novel method of deducing the deformation of the N=Z nucleus 76 Sr is presented. It is based on the comparison of the experimental Gamow-Teller strength distribution B(GT) from its β-decay with the results of QRPA calculations. This method confirms previous indications of the strong prolate deformation of this nucleus in a totally independent way. The measurement has been carried out with a large Total Absorption gamma Spectrometer, "Lucrecia", newly installed at CERN-ISOLDE.PACS numbers: 21.10. Pc, 23.40.Hc, 27.50.+e, 29.30.Kv, 29.40.Mc The shape of the atomic nucleus is conceptually one of the simplest of its macroscopic properties to visualise. However, it turns out to be one of the more difficult properties to measure. In general terms we now have a picture of how the nuclear shape varies across the Segrè Chart. Nuclei near to the closed shells are spherical. In contrast nuclei with the valence nucleons in between two shells have deformed shapes with axial symmetry and the extent of the quadrupole deformation is quite well described as being proportional to the product N p N n of the numbers of pairs of valence protons (N p ) and neutrons (N n ) [1]. This picture is underpinned by both the Shell and Mean Field models of nuclear structure. Experiment and theory concur that, as the N p N n parameterisation would suggest, nuclei rapidly deform as we add only a small number of valence nucleons to the magic numbers. Thus nuclei in the middle of the f 7/2 shell turn out to be deformed even although the numbers of valence nucleons are relatively small.Experimentally this picture is supported by a mass of independent observations: the strongly enhanced quadrupole transition rates between low-lying states, the strongly developed rotational bands built on low-lying states, and measurements of ground state quadrupole moments. Where we have evidence of the shapes of ground and excited states in the same nucleus they are, in general but not always, the same. It turns out that in some cases nuclear states with different shapes co-exist in the same nucleus [2].The nuclei with N≈Z and A≈70-80 are of particular interest in this context. Such nuclei enjoy a particular symmetry since the neutrons and protons are filling the same orbits. This, and the low single-particle level density, lead to rapid changes in deformation with the addition or subtraction of only a few nucleons. In terms of Mean Field models these rapid changes arise because of the proximity in energy of large energy gaps for protons and neutrons at Z,N=34 and 36 on the oblate and Z,N=38 on the prolate side of the Nilsson diagram. As a result Mean Field calculations predict the existence of several energy minima with quite different shapes in some of these nuclei [3,4]. Evidence of this co-existence has been found for instance in Se and Kr nuclei [5,6], and it is also predicted for the lightest Sr isotopes [7]. Thus it is of considerable interest to map out the deformation of the ground and excited states of nuclei in this region. This is easier said than do...

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confidence: 99%

Deformation of theN=ZNucleusSr76usingβ-Decay Studies

et al. 2004

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“…Examples are the study of coiling and loop formation of sub-oceanic cables [1,2,3,4], filamentary structures of biomolecules [5,6,7,8,9] and bacterial fibers [10,11], the phenomenon of helix hand reversal in climbing plants [12] and the shape and dynamics of cracking whips [13].…”

Section: Introductionmentioning

confidence: 99%

Solving the boundary value problem for finite Kirchhoff rods

Fonseca¹,

Aguiar²

2003

Physica D: Nonlinear Phenomena

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The Kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory. In this paper we develop a method, based on a shooting technique, to find equilibrium configurations of finite rods subjected to boundary conditions and given load parameters. The method consists in making a series of small changes on a trial solution satisfying the Kirchhoff equations but not necessarily the boundary conditions. By linearizing the differential equations around the trial solution we are able to push its end point to the desired position, step by step. The method is also useful to obtain configurations of rods with fixed end points but different mechanical parameters, such as tension, components of the moment or inhomogeneities.

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“…A common example is the cracking of a bullwhip [20] that indicates that the speed of the tip of the whip has exceeded that of sound. This letter focuses on the classical and quantum dynamics of freely hanging and supported tapered strings (the bullwhip is a particular case).…”

Section: Prospectsmentioning

confidence: 99%

See a black hole on a shoestring

Heyl

2006

Phys. Rev. D

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The modes of vibration of hanging and partially supported strings provide useful analogies to scalar fields travelling through spacetimes that admit conformally flat spatial sections. This wide class of spacetimes includes static, spherically symmetric spacetimes. The modes of a spacetime where the scale factor depends as a power-law on one of the coordinates provide a useful starting point and yield a new classification of these spacetimes on the basis of the shape of the string analogue. The family of corresponding strings follow a family of curves related to the cycloid, denoted here as hypercycloids (for reasons that will become apparent). Like the spacetimes that they emulate these strings exhibit horizons, typically at their bottommost points where the string tension vanishes; therefore, hanging strings may provide a new avenue for the exploration of the quantum mechanics of horizons.

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Shape of a Cracking Whip

Cited by 50 publications

References 16 publications

Deformation of theN=ZNucleusSr76usingβ-Decay Studies

Deformation of theN=ZNucleusSr76usingβ-Decay Studies

Solving the boundary value problem for finite Kirchhoff rods

See a black hole on a shoestring

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