Unified approach to crossover phenomena

Gluzman, S.; Yukalov, V. I.

doi:10.1103/physreve.58.4197

Cited by 60 publications

(106 citation statements)

References 83 publications

(180 reference statements)

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“…The maximal percentage errors are between 4 − 12% for E * 1 ; between 2 − 5% for E * 2 ; and of order 1% for E * 3 . In conclusion, by employing the self-similar approximation theory [8][9][10][11][12][13], we have found an approximate solution of the Gross-Pitaevskii equation for a spherical trap. This solution, presented by the self-similar approximant (2), is compared with the optimized Gaussian approximation and Thomas-Fermi approximation.…”

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confidence: 99%

“…All mathematical foundations of the theory and technical prescriptions are expounded in detail in Refs. [8][9][10][11][12][13]. The result of the self-similar interpolation between the asymptotic expressions is the self-similar approximant…”

mentioning

confidence: 99%

“…To find an approximate solution to the problem (1), we shall employ the self-similar approximation theory [8][9][10][11], using the variant [12,13] designed for constructing crossover approximants satisfying the prescribed asymptotic conditions. Thus, we may notice that in the Hamiltonian there are two terms of different physical nature.…”

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confidence: 99%

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Self-similar approximations for a trapped Bose-Einstein condensate

2002

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An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed. 03.75.Fi

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Self-similar approximations for a trapped Bose-Einstein condensate

2002

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“…Using the analytical expression (18) with the values of 7 Li Condensate [18][19] and considering the ground state, with n = m = l = 0, p = l = 1 and I 000 = 0.063494,we can obtain N c in Figure 1.…”

Section: Resultsmentioning

confidence: 99%

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Sousa¹,

Bagnato²,

Silva³

2008

Braz. J. Phys.

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We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

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“…Using a change of variables z ¼ w max 2 w and the simplest root approximant [28], one can easily obtain the simplest expression for the effective critical index from the first-order expansion…”

Section: Transformation Of Independent Variablementioning

confidence: 99%

Effective viscosity of puller-like microswimmers: a renormalization approach

Gluzman

Karpeev

Berlyand

2013

J. R. Soc. Interface.

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Effective viscosity (EV) of suspensions of puller-like microswimmers ( pullers), for example Chlamydamonas algae, is difficult to measure or simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytical determination of the passive EV for all concentrations remains unsatisfactory. At the same time, the EV of bacterial suspensions is closely linked to collective motion in these systems and is biologically significant. We develop an approach for determining analytical EV estimates at all concentrations for suspensions of pullers as well as for passive suspensions. The proposed methods are based on the ideas of renormalization group (RG) theory and construct the EV formula based on the known asymptotics for small concentrations and near the critical point (i.e. approaching dense packing). For passive suspensions, the method is verified by comparison against known theoretical results. We find that the method performs much better than an earlier RG-based technique. For pullers, the validation is done by comparing them to experiments conducted on Chlamydamonas suspensions.

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Unified approach to crossover phenomena

Cited by 60 publications

References 83 publications

Self-similar approximations for a trapped Bose-Einstein condensate

Self-similar approximations for a trapped Bose-Einstein condensate

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Effective viscosity of puller-like microswimmers: a renormalization approach

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