The breakdown of superfluidity in liquid 4 He III. Nucleation of quantized vortex rings

1982 ◽  
Vol 307 (1498) ◽  
pp. 201-260 ◽  
Keyword(s):  
Critical Velocity ◽  
Electric Fields ◽  
Isotopic Ratio ◽  
Negative Ions ◽  
Quantum Transition ◽  
Vortex Rings ◽  
Transition Model ◽  
Spontaneous Nucleation ◽  
The Matrix ◽  
Vortex Nucleation

We have measured the rate v at which negative ions nucleate charged vortex rings in isotopically pure superfluid 4 He for pressures, P , temperatures, T , and electric fields, E , within the ranges: 15 < P <25 bar; 0.3 < T < 0.9 K; 5 x 10 4 < E < 10 6 V m -1 . The measurements were done by a novel electrostatic induction technique specially developed for the purpose, and this is described in some detail. It was found that: at fixed E and P , v increases rapidly with T for T ca. 0.5 K, but approaches a temperature-independent limiting value v s for T < 0.5 K; at fixed P and T , v at first increases rapidly with E but then passes through a maximum at ca. 7 x 10 5 V m -1 and decreases again for larger values of E ;at fixed E and T , v increases rapidly with decreasing P until, below ca. 15 bar, the signal becomes too small to use. In all cases, v was found to be considerably smaller than had been measured for low E by earlier workers using helium of the natural isotopic ratio ( ca. 2 x 10 -7 ). The same signals were also used for measuring ionic drift velocities, v for v < ca . 3 x 1O 4 s -1 . Values of the matrix element for roton pair emission have been deduced from the v ( E ) measurements for several pressures in the range 17 < P < 25 bar. The pressure dependence of the Landau critical velocity was measured and is compared with predictions based on accepted values of the roton parameters. Analysis of the nucleation data showed that, at fixed v and P ,( v — vs ) oc n r ,where n r is the thermal roton density, suggesting that v is the sum of contributions from two independent nucleation mechanisms: a spontaneous mechanism responsible for v s and a roton driven mechanism responsible for the increase in v with T above 0.5 K. The existence of a maximum in v ( E ) appears to be inconsistent with the peeling model of vortex nucleation; but it is entirely to be expected on the basis of the quantum transition model. It is shown that all the nucleation rate measurements reported herein are consistent with the quantum transition model, provided that due account is taken of the possibility that roton absorption may give rise to a critical velocity v r that is smaller than the critical velocity v v characteristic of the spontaneous nucleation mechanism. Values of v v and v r are deduced from the experimental data for several pressures. The fact that exponential decay of the bare ion signal still occurs even when v > v v (or v r ) constitutes the first experimental evidence that the microscopic mechanisms responsible for vortex nucleation are probabilistic in nature.

The breakdown of superfluidity in liquid 4 He V. Measurement of the Landau critical velocity for roton creation

1985 ◽  
Vol 315 (1532) ◽  
pp. 259-300 ◽  
Keyword(s):  
Critical Velocity ◽  
Electric Fields ◽  
High Pressures ◽  
Negative Ions ◽  
Pure Liquid ◽  
Small Deviations ◽  
Theoretical Predictions ◽  
The Matrix ◽  
Excitation Model

We report a precise experimental determination of the Landau critical velocity v L for roton creation in Hen. The technique used was based on measurements of the drift velocity, v , of negative ions through isotopically pure liquid 4 He at ca . 80 m K , under the influence of weak electric fields, E , for pressures, P , within the range 13 < P < 25 bar. It relied on the use of the equation ( v — v L ) oc E 1/3 , which is believed to correspond to the creation of rotons occurring predominantly in pairs and which fitted the experimental data to very high precision for E > 500 V m -1 . At lower values of E , however, small deviations from this equation were observed. These are tentatively attributed, not to the predicted onset of single-roton emission, but to a novel form of ion-vortex scattering. The values of v L ( P ) deduced from the measurements of v ( E ) at various pressures for E > 500 V m -1 agree to within 1.5% with theoretical predictions based on Landau’s excitation model of HeII, incorporating accepted numerical values of the roton parameters. The observed pressure dependence of v L ( P ) is significantly stronger than that predicted ; however, a discrepancy that appears to point towards the decreasing accuracy with which the roton parameters are known at high pressures. The modulus of the matrix element | V k0,k0 | characterizing roton-pair emission has also been deduced and is found to decrease rapidly with falling pressure. A linear extrapolation of the data suggests that | V k0,k0 | falls to zero at P « 3 bar (1 bar = 10 5 Pa).

The breakdown of superfluidity in liquid 4 He. IV. Influence of 3 He isotopic impurities on the nucleation of quantized vortex rings

1985 ◽  
Vol 313 (1527) ◽  
pp. 537-606 ◽  
Keyword(s):  
Electric Fields ◽  
Nucleation Rate ◽  
Negative Ions ◽  
Vortex Rings ◽  
Isotopic Ratios ◽  
A Value ◽  
Upward Curvature ◽  
Few Data ◽  
He Atom ◽  
Average Occupancy

We have investigated the rate v at which negative ions nucleate charged vortex rings in a series of extremely dilute superfluid 3 He/ 4 He solutions. Measurements of v were made at a pressure P = 23 bar (23 x 105 Pa) for temperatures, T , electric fields, E , and 3 He/ 4 He isotopic ratios, x 3 , within the ranges: 0.33 < T <0.61 K, 1.0 x 10 4 < E < 1.5 x 10 6 V m -1 , 2.1 x 10 -8 < x 3 < 1.7 x 10 -7 . A few data were also recorded at other pressures within the range 19 < P < 25 bar. For each concentration, and also for nominally pure 4 He ( x 3 = 1.9 x 10 -10 ), v was measured for the same set of E and T . For all the chosen values of x 3 and P , the form of v ( E, T ) was qualitatively much the same, and considerably more complicated than for pure 4 He. It was found that v became equal to the nucleation rate in pure 4 He for large , but that for smaller values of E at low T . The 3 He-influenced contribution to the overall nucleation rate, A v = v — v 0 , passed through a pronounced maximum at a value of E that increased with increasing T ; but the magnitude of A v itself decreased rapidly with increasing T . Plots of v against x 3 for fixed P, E and T show a marked upward curvature for the lower values of E and T , but become linear within experimental error above ca . 0.5 K. A model is proposed (in two variants) in which the complicated behaviour of v ( E, T ) is accounted for in terms of changes in the average occupancy by 3 He atoms of trapping states on the surface of the ion, it being proposed that the nucleation rate v 1 , due to ions each having one trapped 3 He atom, is very much greater than v 0 for bare ions. The nonlinearities in v ( x 3 ) are interpreted in terms of the simultaneous trapping of two (or more) 3 He atoms on a significant fraction of the ions. It is shown that the model can be fitted closely to the experimental data, thereby yielding numerical values of v 1 )of the 3 He binding energy on the ion, and of a number of other relevant quantities. From the form of v 1 ( E ), it is deduced that the addition of a 3 He atom to a bare ion affects its propensity to create vortex rings in two ways: the critical velocity for the process is reduced by ca . 4 m s -1 , and the rate constant is increased by a factor of ca . 10 3 . The implications of these results for microscopic theories of the vortex nucleation mechanism are discussed.

Critical-velocity effects in vibrating superleaks: Vortex nucleation processes

1986 ◽  
Vol 34 (7) ◽  
pp. 4634-4644
Author(s):  
Paul Muzikar ◽  
N. Giordano
Keyword(s):  
Critical Velocity ◽  
Vortex Nucleation

Electroelastic Response of Isotropic Dielectric Elastomer Composites with Deformation-Dependent Apparent-Permittivity Matrix

2020 ◽  
Vol 87 (9) ◽  
Author(s):  
Victor Lefèvre
Keyword(s):  
Free Energy ◽  
Electric Fields ◽  
Dielectric Response ◽  
Dielectric Elastomer ◽  
Spherical Particles ◽  
Full Field ◽  
The Matrix ◽  
Elastomer Composites ◽  
Non Gaussian ◽  
Elastic Dielectric

Abstract This paper puts forth an approximate yet accurate free energy for the elastic dielectric response—under finite deformations and finite electric fields—of non-percolative dielectric elastomer composites made out of a non-Gaussian dielectric elastomer matrix with deformation-dependent apparent permittivity isotropically filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. While the proposed free energy applies in its most general form to arbitrary isotropic non-percolative microstructures, closed-form specializations are recorded for the practically relevant cases of rigid or liquid-like spherical particles. The proposed free energy is exact by construction in the asymptotic context of small deformations and moderate electric fields and is shown to remain accurate for arbitrary large deformations and electric fields via comparisons with full-field finite-element simulations. The proposed constitutive model is deployed to probe the electrostriction response of these dielectric elastomer composites and corresponding results reveal that their elastic dielectric response strongly depends on the deformation-dependent apparent permittivity of the matrix they comprise.

A Tomographic Segmented Gamma Scanner for the Measurement of Decommissioning Wastes

2003 ◽  
Author(s):  
J. A. Mason ◽  
A. C. Tolchard ◽  
A. C. N. Towner ◽  
K. Burke ◽  
R. A. Price ◽  
...  
Keyword(s):  
Gamma Ray ◽  
Isotopic Ratio ◽  
Source Distribution ◽  
Geometric Transformation ◽  
Measurement Technology ◽  
Emission Data ◽  
Attenuation Coefficients ◽  
Distribution Maps ◽  
Transmission Scan ◽  
The Matrix

The ANTECH Tomographic Segmented Gamma Scanner (TSGS) combines: a) Conventional Segmented Gamma Scanner (SGS) analysis (compliant to ASTM C1133-96), b) Tomographic Gamma Scanner (TGS) analysis providing both attenuation and source distribution maps (effectively 3D images) of the interior of drums, and c) Isotopic ratio analysis for uranium and transuranic elements using PC-FRAM. In SGS mode the drum is rotated and scanned segment by segment along its height. A two-pass measurement, one for transmission and one for emission, results in two spectra for each segment. An assay is made by measuring the intensity of a characteristic gamma ray from each nuclide. Corrections are made for count rate-related losses and attenuation by the item (using a transmission source). Calibration standards are used to provide the relationship between observed gamma-ray intensity and nuclide content. On completion, count rates are summed, and mass values for the nuclides of interest in the entire drum are calculated based on comparisons to appropriate calibration materials. In the case of SGS, the matrix is assumed to be homogeneous on a segment by segment basis. TGS involves measuring drums in segments as for SGS. However, in the case of TGS, while the drum is rotated, it is also moved in the horizontal direction (translated). Also, instead of taking a single large spectrum for each segment, 150 separate spectra are taken as the drum rotates and is translated. These 150 spectra are obtained both for transmission and for emission measurements. The 150 spectra taken for transmission constitute a set of data that can be solved to yield the distribution, or map of attenuation coefficients throughout the segment of the sample or drum. The measurement equations are over specified and the solution uses a maximum likelihood analysis. This results in the determination of a map (after a geometric transformation) of attenuation coefficients in a rectangular grid suitably superimposed on each segment. The attenuation map enables the operator to ‘visulise’ the variation of the density (governed by the collimator size and voxe resolution) in regions of the drum. This serves a non-destructive examination function similar to ‘real time radiography’ but with lower resolution. For the analysis of the emission data, the additional information obtained from the transmission data allows the emission data to be corrected for attenuation. This attenuation correction is the essential and important characteristic of TGS measurements not present in other gamma-ray measurement systems. For the first time in the case of the TGS, the map of attenuation is used to correct the measured source distribution in the matrix (segment by segment). The TSGS extends the range of gamma-ray measurement technology, as it is able to correctly determine the attenuation corrected radionuclide inventory in heterogeneous matrices where previous techniques such as the SGS are only applicable to homogeneous matrices. In the case of TGS a single calibration based on a non-interfering or empty matrix is made and then corrections relating back to this non-interfering matrix are made using the attenuation information determined from the transmission scan.

A Model for Ligament Fibroblast Migration Into Provisional Matrix

2011 ◽  
Author(s):  
Yu-Chen Cheng ◽  
Pen-Hsiu Grace Chao
Keyword(s):  
Electric Fields ◽  
Primary Repair ◽  
Cruciate Ligament ◽  
Matrix Material ◽  
Collagen Matrix ◽  
Cell Infiltration ◽  
Gene Expressions ◽  
Knee Ligament ◽  
Fibroblast Migration ◽  
The Matrix

Many strategies have been proposed to enhance the healing capability of the anterior cruciate ligament (ACL). A novel treatment option, called enhanced primary repair, places a provisional matrix at the tear site to promote cell infiltration of the wound and aims to reestablish the structure-function relationship of the ACL [1]. This approach of guided tissue regeneration offers great potential benefits of retaining the complex native tissue matrix structure, innervation, and vascularization as compared with grafts. A major aspect of this procedure is enhancing ligament fibroblast infiltration into the matrix material and promoting matrix synthesis. We have previously demonstrated that applied electric fields (EFs) enhance knee ligament fibroblast migration, alignment, and collagen gene expressions on planar substrates [2]. In the current study, we developed a new system to simulate cell infiltration from the tissue to a provisional collagen matrix. An EF was applied across the construct to investigate its effects of on ACL fibroblast migration into the provisional matrix.

Continuum Modeling of Charged Particle Transport: RF Breakdown and Discharges of SF6

1986 ◽  
Vol 68 ◽  
Author(s):  
Brian E. Thompson ◽  
Herbert H. Sawun ◽  
Aaron Owens
Keyword(s):  
Electric Fields ◽  
Electron Attachment ◽  
Negative Ions ◽  
Rate Coefficients ◽  
Rf Discharge ◽  
Continuity Equations ◽  
Positive Ions ◽  
Discharge Model ◽  
Rf Breakdown ◽  
Charged Particle Transport

AbstractContinuity equations for the concentration of electrons, positive ions, and negative ions were constructed and solved to predict rf breakdown voltages and the electrical properties of SF, discharges.These balances for the three types of charged species include terms for convection (electric field-driven fluxes), diffusion, and reactions (ionization, electron attachment, and negative-positive ion recombination).The mobilities, diffusivities, and reaction rate coefficients necessary for the rf discharge model are based on reported measurements and calculations of these parameters in dc electric fields.The electric fields developed in the rf discharge are calculated from Poisson's equation and applied voltage conditions.Predictions based on this model are compared with measured rf breakdown characteristics of SF6.

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