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Long A, Eloranta J. Density functional theory of superfluid helium at finite temperatures. J Chem Phys 2021; 155:074102. [PMID: 34418920 DOI: 10.1063/5.0060132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A density functional theory-based method is developed to describe the static and dynamic response of superfluid helium at finite temperatures. The model relies on the well-established 0 K Orsay-Trento functional, which has been extensively used to study the response of bulk superfluid helium as well as superfluid helium droplets. By including a phenomenological stochastic term in this model, it is possible to obtain thermodynamic equilibrium corresponding to a given temperature by propagating the system in imaginary time. The temperature dependence of thermodynamic quantities, such as the internal energy and entropy, is computed and is compared well with experimental reference data for the bulk liquid up to about 2 K, but begins to gradually deviate above that temperature. Inspection of pseudovorticity during real-time evolution of the system near 2 K reveals the presence of roton quasiparticles, which are suggested to be precursors for quantized vortex rings (Onsager's ghosts), as well as weaker analogs of extended vortex loops.
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Affiliation(s)
- Austin Long
- Department of Physics and Astronomy, California State University at Northridge, 18111 Nordhoff St., Northridge, California 91330, USA
| | - Jussi Eloranta
- Department of Chemistry and Biochemistry, California State University at Northridge, 18111 Nordhoff St., Northridge, California 91330, USA
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Zhang H, Wang X, Yu HB, Douglas JF. Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:56. [PMID: 33871722 DOI: 10.1140/epje/s10189-021-00060-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 03/21/2021] [Indexed: 06/12/2023]
Abstract
We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology(NIST), Gaithersburg, MD, 20899, USA.
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Forrester A, Williams GA. Vortex-loop calculation of the specific heat of superfluid ^{4}He under pressure. Phys Rev E 2020; 100:060104. [PMID: 31962471 DOI: 10.1103/physreve.100.060104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Indexed: 11/07/2022]
Abstract
Vortex-loop renormalization is used to compute the specific heat of superfluid ^{4}He near the lambda point at various pressures up to 26 bars. The input parameters are the pressure dependence of T_{λ} and the superfluid density, which determine the nonuniversal parameters of the vortex core energy and core size. The results for the specific heat are found to be in good agreement with experimental data, matching the expected universal pressure dependence to within about 5%. The nonuniversal critical amplitude of the specific heat is found to be in reasonable agreement, a factor of four larger than the experiments. We point out problems with recent Gross-Pitaevskii simulations that claimed the vortex-loop percolation temperature did not match the critical temperature of the superfluid phase transition.
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Affiliation(s)
- Andrew Forrester
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - Gary A Williams
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
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4
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Karpov P, Brazovskii S. Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems. Phys Rev E 2019; 99:022114. [PMID: 30934327 DOI: 10.1103/physreve.99.022114] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Indexed: 11/07/2022]
Abstract
Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase θ and the amplitude A sign of the order parameter Aexp(iθ). These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge densities. To understand statistical properties and the phase diagram in the course of cooling under the controlled parameters, we present here an analytical treatment supported by Monte Carlo simulations for a generic coarse-grained two-field model of XY-Ising type. The degeneracies give rise to two coexisting types of topologically nontrivial configurations: phase vortices and amplitude kinks, i.e., the solitons. In two- and three-dimensional states with long-range (or Berezinskii--Kosterlitz--Thouless-type) orders, the topological confinement sets in at a temperature T=T_{1} which binds together the kinks and unusual half-integer vortices. At a lower T=T_{2}, the solitons start to aggregate into walls formed as rods of amplitude kinks which are ultimately terminated by half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. The presented results indicate a possible physical realization of a peculiar system of half-integer vortices with rods of amplitude kinks connecting their cores. Its experimental realization becomes feasible in view of recent successes in real-space observations and even manipulations of domain walls in correlated electronic systems.
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Affiliation(s)
- P Karpov
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.,National University of Science and Technology MISiS, 119991 Moscow, Russia
| | - S Brazovskii
- National University of Science and Technology MISiS, 119991 Moscow, Russia.,LPTMS, CNRS, UMR No. 8626, University of Paris-Sud, University of Paris-Saclay, 91405 Orsay, France.,Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
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5
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Iazzi M, Bassan N, Trombettoni A, Schmidt KE, Fantoni S. Vortex lines distribution in inhomogeneous lattices. Mol Phys 2011. [DOI: 10.1080/00268976.2011.637083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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6
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Barenghi CF, Hänninen R, Tsubota M. Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:046303. [PMID: 17155169 DOI: 10.1103/physreve.74.046303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2006] [Indexed: 05/12/2023]
Abstract
We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave amplitude. In particular, we show that, if the amplitude of the Kelvin waves is sufficiently large, the perturbed vortex ring moves backwards.
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Affiliation(s)
- C F Barenghi
- School of Mathematics, University of Newcastle, Newcastle NE1 7RU, United Kingdom
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7
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Moriconi L, Nobre FAS. Stochastic perturbations in vortex-tube dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056309. [PMID: 15600755 DOI: 10.1103/physreve.70.056309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2004] [Indexed: 05/24/2023]
Abstract
A dual lattice vortex formulation of homogeneous turbulence is developed, within the Martin-Siggia-Rose field theoretical approach. It consists of a generalization of the usual dipole version of the Navier-Stokes equations, known to hold in the limit of vanishing external forcing. We investigate, as a straightforward application of our formalism, the dynamics of closed vortex tubes, randomly stirred at large length scales by Gaussian stochastic forces. We find that besides the usual self-induced propagation, the vortex tube evolution may be effectively modeled through the introduction of an additional white-noise correlated velocity field background. The resulting phenomenological picture is closely related to observations previously reported from a wavelet decomposition analysis of turbulent flow configurations.
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Affiliation(s)
- L Moriconi
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970, Rio de Janeiro, RJ, Brazil
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8
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Pfeiffer FO, Rieger H. Critical properties of loop percolation models with optimization constraints. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056113. [PMID: 12786226 DOI: 10.1103/physreve.67.056113] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2002] [Indexed: 05/24/2023]
Abstract
We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form a closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional percolation. In contrast to this, an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a universality class for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.
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Affiliation(s)
- Frank O Pfeiffer
- Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
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Minnhagen P, Kim BJ, Weber H. Evidence of two distinct dynamic critical exponents in connection with vortex physics. PHYSICAL REVIEW LETTERS 2001; 87:037002. [PMID: 11461582 DOI: 10.1103/physrevlett.87.037002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2001] [Indexed: 05/23/2023]
Abstract
The dynamic critical exponent z is determined from numerical simulations for the three-dimensional (3D) lattice Coulomb gas (LCG) and the 3D XY models with relaxational dynamics. It is suggested that the dynamics is characterized by two distinct dynamic critical indices z0 and z related to the divergence of the relaxation time tau by tau proportional to xi(z0) and tau proportional to k(-z), where xi is the correlation length and k the wave vector. The values determined are z0 approximately 1.5 and z approximately 1 for the 3D LCG and z0 approximately 1.5 and z approximately 2 for the 3D XY model. Comparisons with other results are discussed.
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Affiliation(s)
- P Minnhagen
- Department of Theoretical Physics, Umeå University, 901 87 Umeå, Sweden
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Schakel AM. Percolation, Bose-Einstein condensation, and string proliferation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026115. [PMID: 11308550 DOI: 10.1103/physreve.63.026115] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2000] [Indexed: 05/23/2023]
Abstract
The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological line defects, are described by a distribution parametrized by only two exponents. On approaching the critical point, the string tension vanishes and the loops proliferate, thereby signalling the onset of Bose-Einstein condensation (in the case of worldlines) or the disordering of the ordered state (in the case of vortices). The ideal Bose gas with modified energy spectrum is used as a stepping stone to derive general expressions for the critical exponents in terms of the two exponents parametrizing the loop distribution near criticality.
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Affiliation(s)
- A M Schakel
- Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland
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11
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Sobnack MB, Kusmartsev FV. Suppression of superconductivity in mesoscopic superconductors. PHYSICAL REVIEW LETTERS 2001; 86:716-719. [PMID: 11177920 DOI: 10.1103/physrevlett.86.716] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2000] [Indexed: 05/23/2023]
Abstract
We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lower the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinskĭ-Kosterlitz-Thouless temperature.
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Affiliation(s)
- M B Sobnack
- Department of Physics, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
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12
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Dudowicz J, Freed KF, Douglas JF. Lattice model of living polymerization. I. Basic thermodynamic properties. J Chem Phys 1999. [DOI: 10.1063/1.480004] [Citation(s) in RCA: 104] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Nguyen AK, Sudbo A, Hetzel RE. Vortex-Loop Unbinding and Flux-Line Lattice Melting in Superconductors. PHYSICAL REVIEW LETTERS 1996; 77:1592-1595. [PMID: 10063117 DOI: 10.1103/physrevlett.77.1592] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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14
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Kusmartsev FV. Fluctuative mechanism of vortex nucleation in the flow of 4He. PHYSICAL REVIEW LETTERS 1996; 76:1880-1883. [PMID: 10060544 DOI: 10.1103/physrevlett.76.1880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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15
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Schultka N, Manousakis E. Specific heat of superfluids near the transition temperature. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7528-7536. [PMID: 9979699 DOI: 10.1103/physrevb.52.7528] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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16
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Domínguez D, Gronbech-Jensen N, Bishop AR, Shenoy SR. Transformer configuration in three dimensional Josephson lattices at zero magnetic field. PHYSICAL REVIEW LETTERS 1995; 75:717-720. [PMID: 10060096 DOI: 10.1103/physrevlett.75.717] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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18
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Chorin AJ, Hald OH. Vortex renormalization in three space dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:11969-11972. [PMID: 9977946 DOI: 10.1103/physrevb.51.11969] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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19
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Schultka N, Manousakis E. Crossover from two- to three-dimensional behavior in superfluids. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:11712-11720. [PMID: 9977909 DOI: 10.1103/physrevb.51.11712] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Shenoy SR, Chattopadhyay B. Anisotropic three-dimensional XY model and vortex-loop scaling. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:9129-9147. [PMID: 9977555 DOI: 10.1103/physrevb.51.9129] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Sujani S, Chattopadhyay B, Shenoy SR. Kosterlitz-Thouless vortex-scaling equations with nonzero current drives. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:16668-16678. [PMID: 9976055 DOI: 10.1103/physrevb.50.16668] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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22
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Khantha M, Pope D, Vitek V. The brittle-to-ductile transition - I: A cooperative dislocation generation instability. ACTA ACUST UNITED AC 1994. [DOI: 10.1016/0956-716x(94)90116-3] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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23
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Pettersen MS, Balibar S, Maris HJ. Experimental investigation of cavitation in superfluid 4He. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:12062-12070. [PMID: 10010080 DOI: 10.1103/physrevb.49.12062] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chattopadhyay B, Shenoy SR. Kosterlitz-Thouless signatures from 3D vortex loops in layered superconductors. PHYSICAL REVIEW LETTERS 1994; 72:400-403. [PMID: 10056421 DOI: 10.1103/physrevlett.72.400] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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25
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Williams GA. Vortex dynamics and superfluid relaxation near the 4He lambda transition. PHYSICAL REVIEW LETTERS 1993; 71:392-395. [PMID: 10055259 DOI: 10.1103/physrevlett.71.392] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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26
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Chattopadhyay B, Mahato MC, Shenoy SR. Vortex-loop crinkling in the three-dimensional XY model: Numerical evidence in support of an ansatz. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:15159-15169. [PMID: 10005889 DOI: 10.1103/physrevb.47.15159] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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27
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Ramírez AF, Lund F, Hernández R. Effect of vortex bending in the phase transition mediated by vortex rings in three dimensions and its relation to the lambda transition in liquid helium. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:5465-5468. [PMID: 10006721 DOI: 10.1103/physrevb.47.5465] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Kawamura H, Kikuchi M. Free-vortex formation and topological phase transitions of two-dimensional spin systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:1134-1137. [PMID: 10005604 DOI: 10.1103/physrevb.47.1134] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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29
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Lund F. Instability driven by dislocation loops in bulk elastic solids: Melting and superheating. PHYSICAL REVIEW LETTERS 1992; 69:3084-3087. [PMID: 10046721 DOI: 10.1103/physrevlett.69.3084] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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30
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Williams GA. Vortex rings and finite-wave-number superfluidity near the 4He lambda transition. PHYSICAL REVIEW LETTERS 1992; 68:2054-2057. [PMID: 10045292 DOI: 10.1103/physrevlett.68.2054] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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31
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Thoma S, Frey E, Schwabl F. Critical dynamics of planar ferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:5831-5845. [PMID: 9997985 DOI: 10.1103/physrevb.43.5831] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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32
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Vortices and the Superfluid 4He Phase Transition in Two and Three Dimensions. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/978-1-4684-5937-1_30] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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33
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Raman Scattering from Superfluid Helium. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/978-1-4684-5937-1_6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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34
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Shenoy SR. Enhancement and suppression of the transition temperature of a three-dimensional XY ferromagnet by control of vortex-loop fugacity. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:8595-8600. [PMID: 9995036 DOI: 10.1103/physrevb.42.8595] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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35
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Lund F, Reisenegger A, Utreras C. Critical properties of a dilute gas of vortex rings in three dimensions and the lambda transition in liquid helium. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:155-161. [PMID: 9992750 DOI: 10.1103/physrevb.41.155] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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36
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Shenoy SR. Vortex-loop scaling in the three-dimensional XY ferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:5056-5068. [PMID: 9992506 DOI: 10.1103/physrevb.40.5056] [Citation(s) in RCA: 58] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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Rhee I, Gasparini FM, Bishop DJ. Finite-size scaling of the superfluid density of 4He confined between silicon wafers. PHYSICAL REVIEW LETTERS 1989; 63:410-413. [PMID: 10041066 DOI: 10.1103/physrevlett.63.410] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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38
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Gallet F, Williams GA. Superfluid transition of 4He films adsorbed on multiply connected surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:4673-4676. [PMID: 9948823 DOI: 10.1103/physrevb.39.4673] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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39
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Ikeda R. Dislocation-loop theory of the smectic-C-nematic phase transition. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:312-319. [PMID: 9901015 DOI: 10.1103/physreva.39.312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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40
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Kohring GA, Shrock RE, Wills P. Kohring, Shrock, and Wills reply. PHYSICAL REVIEW LETTERS 1988; 61:2970. [PMID: 10039278 DOI: 10.1103/physrevlett.61.2970] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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