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1.
In this paper we consider the asymptotic behavior of the Ginzburg–Landau model for superconductivity in three dimensions, in various energy regimes. Through an analysis via Γ-convergence, we rigorously derive a reduced model for the vortex density and deduce a curvature equation for the vortex lines. In the companion paper (Baldo et al. Commun. Math. Phys. 2012, to appear) we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H c1, and the critical angular velocity of rotating Bose–Einstein condensates. 相似文献
2.
Didier Smets Fabrice Bethuel Giandomenico Orlandi 《Archive for Rational Mechanics and Analysis》2007,183(2):315-370
We study the vortex trajectories for the two-dimensional complex parabolic Ginzburg–Landau equation without a well-preparedness
assumption. We prove that the trajectory set is rectifiable, and satisfies a weak motion law. In the case of degree ± 1
vortices, the motion law is satisfied in the classical sense. Moreover, dissipation occurs only at a finite number of times.
Away from these times, possible collisions and splittings of vortices are constrained by algebraic equations involving their
topological degrees.
Quantization properties of the energy and potential densities play a central role in the proofs. 相似文献
3.
P. G. Siddheshwar R. K. Vanishree Anthony Christy Melson 《Transport in Porous Media》2012,92(2):277-288
The effects of temperature-dependent viscosity, gravity modulation and thermo-mechanical anisotropies on heat transport in
a low-porosity medium are studied using the Ginzburg–Landau model. The effect of gravity modulation is to decrease the Nusselt
number, Nu and variable viscosity leads to increase in Nu. The thermo-mechanical anisotropies have opposite effect on Nu with thermal anisotropy decreasing the heat transport. 相似文献
4.
We prove the asymptotic stability of kink for the nonlinear relativistic wave equations of the Ginzburg–Landau type in one
space dimension: for any odd initial condition in a small neighborhood of the kink, the solution, asymptotically in time,
is the sum of the kink and dispersive part described by the free Klein–Gordon equation. The remainder converges to zero in
a global norm. 相似文献
5.
The injection of a liquid jet into a crossing Mach 6 air flow is investigated. Experiments were conducted on a sharp leading
edge flat plate with flush mounted injectors. Water jets were introduced through different nozzle shapes at relevant jet-to-air
momentum–flux ratios. Sufficient temporal resolution to capture small scale effects was obtained by high-speed recording,
while directional illumination allowed variation in field of view. Shock pattern and flow topology were visualized by Schlieren-technique.
Correlations are proposed on relating water jet penetration height and lateral extension with the injection ratio and orifice
diameter for circular injector jets. Penetration height and lateral extension are compared for different injector shapes at
relevant jet-to-air momentum–flux ratios showing that penetration height and lateral extension decrease and increase, respectively,
with injector’s aspect ratio. Probability density function analysis has shown that the mixing of the jet with the crossflow
is completed at a distance of x/d
j
~ 40, independent of the momentum–flux ratio. Mean velocity profiles related with the liquid jet have been extracted by means
of an ensemble correlation PIV algorithm. Finally, frequency analyses of the jet breakup and fluctuating shock pattern are
performed using a Fast Fourier algorithm and characteristic Strouhal numbers of St = 0.18 for the liquid jet breakup and of St = 0.011 for the separation shock fluctuation are obtained. 相似文献
6.
In the present study laminar transition to oscillatory convection of fluids having different Prandtl numbers in a laterally
heated vertical cylindrical enclosure for different aspect ratios (melt height to crucible radius) of 2–4 is investigated
numerically for 0.01 ≤ Pr ≤ 10. Numerical solution to two-dimensional axisymmetric transient Navier Stokes equations and energy equation were solved
by finite volume method using SIMPLE algorithm. Numerical results illustrate that there exists a critical Rayleigh number
for each Prandtl number beyond which sustained laminar oscillatory flow sets in. The oscillatory regime was characterised
by the oscillation of the average kinetic energy and average thermal energy of the melt. For a given aspect ratio, critical
Rayleigh number increases with Pr upto 1 and then flattens. It was observed that for low Prandtl number fluids, Pr < 1.0, critical Rayleigh number is found to increase with increase in aspect ratio while for high Prandtl number fluids,
Pr ≥ 1.0, it is found to decrease with increase in aspect ratio. The influence of aspect ratio on the transient behaviour of
the melt volume below and above the critical Rayleigh number was studied. 相似文献
7.
In this article, we investigate the response of a thin superconducting shell to an arbitrary external magnetic field. We identify
the intensity of the applied field that forces the emergence of vortices in minimizers, the so-called first critical field
H
c1 in Ginzburg–Landau theory, for closed simply connected manifolds and arbitrary fields. In the case of a simply connected
surface of revolution and vertical and constant field, we further determine the exact number of vortices in the sample as
the intensity of the applied field is raised just above H
c1. Finally, we derive via Γ-convergence similar statements for three-dimensional domains of small thickness, where in this setting point vortices are
replaced by vortex lines. 相似文献
8.
The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular
porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and
the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left
wall are adiabatic. The vorticity–stream function formulation of the governing equations is numerically solved using an implicit
finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the
flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified
Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate
is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum
temperature decreases with the modified Rayleigh number and increases with the aspect ratio. 相似文献
9.
Javad Rostami 《Heat and Mass Transfer》2008,44(9):1079-1087
In this paper, unsteady heat transfer and fluid flow characteristics in an enclosure are investigated. The enclosure consists
of two vertical wavy and two horizontal straight walls. The top and the bottom walls are considered adiabatic. Two wavy walls
are kept isothermal and their boundaries are approximated by a cosine function. Governing equations including continuity,
momentum and energy were discretized using the finite-volume method and solved by SIMPLE method in curvilinear coordinate.
Simulation was carried out for a range of Grashof number Gr = 103–106, Prandtl number Pr = 0.5–4.0, wave ratio A (defined by amplitude/wavelength) 0.0–0.35 and aspect ratio W (defined by average width/wavelength) 0.5–1.0. Streamlines and isothermal lines are presented to corresponding flow and thermal
fields. Local and average Nusselt number distributions are presented. The obtained results are in good agreement with available
numerical and experimental data. 相似文献
10.
The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified
numerically. The parameters considered were: the Rayleigh number 109–1012, the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total
heat transfer has a maximum value of 15.19% (Ra = 109, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 1012, A = 80) with ε* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed
Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation
does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity
were observed. Two different temperature patterns were observed a conductive regime Ra = 109 and a boundary layer regime Ra = 1012. 相似文献
11.
The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures
could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θv = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry.
Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled
vortex at the lowest swirl ratio (S = 0.03, θv = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θv = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important
and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component,
has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity
variance is about twice at the high swirl ratio (θv = 45°) that at the low swirl ratio (θv = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not
only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The
intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause
dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex
structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in
improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately
leading to better predictions of tornado-induced wind loads on civil structures. 相似文献
12.
In this paper, we establish analyticity of the Navier–Stokes equations with small data in critical Besov spaces . The main method is Gevrey estimates, the choice of which is motivated by the work of Foias and Temam (Contemp Math 208:151–180, 1997). We show that mild solutions are Gevrey regular, that is, the energy bound holds in , globally in time for p < ∞. We extend these results for the intricate limiting case p = ∞ in a suitably designed E ∞ space. As a consequence of analyticity, we obtain decay estimates of weak solutions in Besov spaces. Finally, we provide a regularity criterion in Besov spaces. 相似文献
13.
Sébastien Barré Christophe Bogey Christophe Bailly 《Theoretical and Computational Fluid Dynamics》2008,22(1):65-82
The aerodynamic evolution and the acoustic radiation of elliptic vortices with various aspect ratios and moderate Mach numbers
are investigated by solving numerically the full compressible Navier–Stokes equations. Three behaviours are observed according
to the aspect ratio σ = a/b where a and b are the major and minor semi-axes of the vortices. At the small aspect ratio σ = 1.2, the vortex rotates at a constant angular velocity and radiates like a rotating quadrupole. At the moderate aspect
ratio σ = 5, the vortex is initially unstable. However the growth of instability waves is inhibited by the return to axisymmetry
which decreases its aspect ratio. The noise level becomes lower with time and the radiation frequency increases. For vortices
with larger aspect ratios σ ≥ 6, the return to axisymmetry does not occur quickly enough to stop the growth of instabilities, which splits the vortices.
Various mergers are then found to occur. For instance in the case σ = 6, several successive switches between an elliptic state and a configuration of two co-rotating vortices are observed.
The present results show that the initial value of the aspect ratio yields the relative weight between the return to axisymmetry
which stabilizes the vortex and the growth of instabilities which tends to split it. Moreover the noise generated by the vortices
is also calculated using the analytical solution derived by Howe (J. Fluid Mech. 71:625–673, 1975) and is compared with the
reference solution provided by the direct computation. This solution is found to be valid for σ = 1.2. An extended solution is proposed for higher aspect ratios. Finally, the pressure field appears weakly affected by
the switches between the two unstable configurations in the case σ = 6, which underlines the difficulty to detect the split or the merger of vortices from the radiated pressure. This study
also shows that elliptic vortices can be used as a basic configuration of aerodynamic noise generation.
相似文献
14.
Sylvia Serfaty 《Archive for Rational Mechanics and Analysis》1999,149(4):329-365
. We find new stable solutions of the Ginzburg‐Landau equation for high κ superconductors with exterior magnetic field h
ex. First, we prove the uniqueness of the Meissner‐type solution. Then, we prove, in the case of a disc domain, the coexistence
of branches of solutions with n vortices of degree one, for any n not too high and for a certain range of h
ex; and describe these branches. Finally, we give an estimate on the nucleation energy barrier, to pass continuously from a
vortexless configuration to a configuration with a centered vortex.
(Accepted October 29, 1998) 相似文献
15.
Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers 总被引:1,自引:1,他引:0
Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8
(cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which
provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re
θ varied from 4.8 × 105 to 1.1 × 106. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable
Re
θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency
spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad
in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral
levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent
with flat plate cases. The convection velocities also display features similar to flat plate cases. 相似文献
16.
We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The
material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic
elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement,
particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained
for surge pressure p(t) = p
0 = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences
the course of material parameters in space and time. All parameters intensively decrease in space together with an increase
of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course
of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about
0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when
ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static
values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration
amplitude and decrease of vibration “damping”.
相似文献
17.
We consider the existence of multi-vortex solutions to the Ginzburg–Landau equations with external potential on
\mathbbR2{\mathbb{R}^2} . These equations model equilibrium states of superconductors and stationary states of the U(1) Higgs model of particle physics. In the former case, the external potential models impurities and defects. We show that
if the external potential is small enough and the magnetic vortices are widely spaced, then one can pin one or an arbitrary
number of vortices in the vicinity of a critical point of the potential. In addition, one can pin an arbitrary number of vortices
near infinity if the potential is radially symmetric and of an algebraic order near infinity. 相似文献
18.
Results of experimental study on DDT in a smooth tube filled with sensitive mixtures having detonation cell size from 1 to
3 orders of magnitude smaller than the tube diameter are presented. Stoichiometric hydrogen–oxygen mixtures were used in the
tests with initial pressure ranging from 0.2 to 8 bar. A dependence of the run-up distance to DDT on the initial pressure
is studied. This dependence is found to be close to the inverse proportionality. It is suggested that the flow ahead of the
flame results in formation of the turbulent boundary layer. This boundary layer controls the scale of turbulent motions in
the flow. A simple model to estimate the maximum scale of the turbulent pulsations (boundary layer thickness) at flame positions
along the tube is presented. The largest scale of the turbulent motions at the location of the onset of detonation is shown
to be 1 order of magnitude greater than the detonation cell widths, λ, in all the tests. It is suggested that the onset of
detonation is triggered during flame acceleration as soon as the maximum scale of the turbulent pulsations increases up to
about 10 λ. The model to estimate the maximum size of turbulent motions, δ, and the correlation δ≈ 10λ, give a basis for estimations
of the run-up distances to DDT in tubes with internal diameter D > 20λ.
PACS 47.40.-x; 47.27.Nz
This paper was based on work that was presented at the 19th Inter-national Colloquium on the Dynamics of Explosions and Reactive
Systems, Hakone, Japan, July 27 - August 1, 2003 相似文献
19.
We study a class of systems of reaction–diffusion equations in infinite cylinders which arise within the context of Ginzburg–Landau
theories and describe the kinetics of phase transformation in second-order or weakly first-order phase transitions with non-conserved
order parameters. We use a variational characterization to study the existence of a special class of traveling wave solutions
which are characterized by a fast exponential decay in the direction of propagation. Our main result is a simple verifiable
criterion for existence of these traveling waves under the very general assumptions of non-linearities. We also prove boundedness,
regularity, and some other properties of the obtained solutions, as well as several sufficient conditions for existence or
non-existence of such traveling waves, and give rigorous upper and lower bounds for their speed. In addition, we prove that
the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are
initially sufficiently localized. We give a sample application of our results using a computer-assisted approach. 相似文献
20.
In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of
the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered
are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the
Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local
heat flux, average Nusselt number and average heat transfer have been presented and discussed. 相似文献