Extended Time-Dependent Ginzburg–Landau Theory

We formulate the gauge invariant Lorentz covariant Ginzburg–Landau theory which describes nonstationary regimes: relaxation of a superconducting system accompanied by eigen oscillations of internal degrees of freedom (Higgs mode and Goldstone mode) and also forced oscillations under the action of an external gauge field. The theory describes Lorentz covariant electrodynamics of superconductors where Anderson–Higgs mechanism occurs, at the same time the dynamics of conduction electrons remains non-relativistic. It is demonstrated that Goldstone oscillations cannot be accompanied by oscillations of charge density and they generate the transverse field only. In addition, we consider Goldstone modes and features of Anderson–Higgs mechanism in two-band superconductors. We study dissipative processes, which are caused by movement of the normal component of electron liquid and violate the Lorentz covariance, on the examples of the damped oscillations of the order parameter and the skin-effect for electromagnetic waves. An experimental consequence of the extended time-dependent Ginzburg–Landau theory regarding the penetration of the electromagnetic field into a superconductor is proposed.

     

Solution of the Landau–Ginzburg Equations Using Lattice–Boltzmann

In this paper, we solve the time dependent Ginzburg–Landau (TDGL) equations in two dimensions, using Lattice–Boltzmann (LB) technique and the velocity discretization scheme D2Q9, for a square region with periodic boundary conditions. In order to obtain the solution, we use three distribution functions, each of them obeying the LB equation, and making a proper redefinition of the tensor Π ⁰, we find the (TDGL) equations. Further, we obtain the equilibrium distribution functions for the three LB equations, and then the solution for the components of the magnetic potential vector and the order parameter.     

Anisotropy Parameters of Critical Fields in LiFeAs Using Two-Band Ginzburg–Landau Theory

Analytical calculations of anisotropy parameter of upper and lower critical fields were conducted using two-band Ginzburg–Landau equations for layered systems. With the results applied to LiFeAs, comparisons with available experimental data and theoretical calculations are conducted and agreement is achieved.     

Ginzburg–Landau Study of Superconductor with Regular Pinning Array

The vortex distributions and dynamics in superconductors with triangular and honeycomb pinning arrays are investigated by numerical simulation of the two- dimensional (2-D) time-dependent Ginzburg–Landau equations. Periodic boundary conditions are implemented through specific gauge transformations under lattice translations. We model the pinning sites as holes. The simulation results at different magnetic fields are presented. For film with regular triangular pinning array, the vortices are all captured within the holes for a wide range of magnetic fields. For film with regular honeycomb pinning array, the interstitial vortices appear at relatively low magnetic fields. With an increase of magnetic field, the new vortices may enter the holes again and keep the number of vortices at the interstitial positions unchanged. These results confirm our explanations of the experimental results we obtained earlier.     

Stable spatiotemporal dissipative soliton clusters in the complex Ginzburg–Landau equation

Stable spatiotemporal soliton clusters in the cubic–quintic complex Ginzburg–Landau equation are investigated theoretically. It is revealed that spatiotemporal soliton clusters carrying zero and nonzero topological charges can stably propagate and the clusters don't substantially rotate despite the value of topological charges due to the effect of friction force in such a model. It is found that if the separation of solitons is larger than a critical value, the cluster is maintained, otherwise solitons exhibit too strong an attraction for each other due to being in-phase, which leads to their instability. Prediction of the minimum separation of solitons for bound clusters is demonstrated by use of energy and momentum balance methods.     

Onset of Superconductivity and Hysteresis in Magnetic Field for a Long Cylinder as Obtained from a Self-Consistent Solution of the Ginzburg–Landau Equations

Based on the self-consistent solution of a nonlinear system of one-dimensional GL-equations, the onset and destruction of superconductivity, the phase transitions and hysteresis phenomena are discussed for a cylinder (radius R) in the axial magnetic field (H) for arbitrary R, , H, m ( is the GL-parameter, m is the total vorticity of the system). The edge-suppressed solutions (which correspond to the jumps of the magnetization in the states with fixed vorticity m), the depressed solutions (which are responsible for the hysteresis in type-II superconductors), and the precursor solutions (which describe the onset of superconductivity in type-I superconductors) are also studied. The limits of applicability of the linear equation approximation are discussed.     

Numerical study of the stability of solutions for the half-space Ginzburg–Landau model

Based on a shooting alternative that allows one to numerically solve the one-dimensional system of Ginzburg–Landau in an unbounded domain, a numerical study of the stability of solutions of this system is performed here. This stability notion, from a physical point of view, means that each solution of the system is identified as stable when it minimizes the corresponding Ginzburg–Landau functional. As opposed to a previous paper, the present one is concerned with a more general study since the weak and large regimes of the Ginzburg–Landau parameter are considered and the initial data are no longer subject to the de Gennes condition. Certain conjectures regarding the superheating field are also investigated numerically.     

Simulation of the initial polarization curves and hysteresis loops for ferroelectric films by an extensive time-dependent Ginzburg–Landau model

The polarization hysteresis loops as well as the initial curves of ferroelectric films with 180° domain boundaries perpendicular to the film surface are simulated based on an extensive time-dependent Ginzburg–Landau model. The result shows that the curve and loop strongly depend on the frequency ω of the applied electric field, the effective mass density ρ, and the viscosity coefficient K of the material, however, the constant ωK/ρ can induce the same curve and loop. The hysteresis area of the saturated loop is increased with field amplitude, which is consistent with the previous experimental observation. In addition, it is found that the latent domains in the film can result in a remarkable decrease in the remanent polarization and coercive field.     

Simulation of Gas Motion in a Reservoir–Pipeline System

Journal of Engineering Physics and Thermophysics - A model has been constructed for the process of unsteady-state gas motion in a reservoir–pipeline system. A boundary-problem of...     

Effective Surface Impedance of a High-Temperature Superconducting Film in Semiconductor Plasma Substrate at Mid-infrared Frequency

The effective surface impedance of a high-temperature superconducting thin film on a semiconductor plasma substrate is calculated. Two possible configurations are considered. The first one is a superconducting film deposited on a semi-infinite semiconductor substrate. It is seen that there exists a critical film thickness for the superconductor such that a minimum effective surface resistance is attained. The effective surface resistance is strongly dependent on the high-frequency permittivity of semiconductor plasma. The second will be limited to the more practical case, that is, the semiconductor substrate is of finite thickness. The investigation of substrate resonance in the effective surface resistance shows some fundamental distinctions when a semiconductor plasma substrate is introduced.     

Vortex Dynamics in a Superconducting Film with a Kagome and?a?Honeycomb Pinning Landscape

The vortex dynamics in a superconducting thin Al film with a periodic Honeycomb or Kagome array of antidots has been investigated by electrical transport measurements. The large values of the superconducting coherence length and penetration depth of the Al films guarantee a maximum of one flux quantum trapped per pinning site. This allows us to directly compare the experimental results with previous theoretical investigations based on molecular dynamics simulations. For the Kagome lattice, two submatching features not anticipated theoretically at H/H ₁=1/3 and 2/3, where H ₁ is the field at which the number of vortices coincides with the number of pinning sites, are observed. Possible corresponding stable vortex patterns are suggested. For the Honeycomb pinning landscape, the commensurability effects are in agreement with the theoretical expectations. A preliminary analysis of the vortex mobility in this lattice shows the presence of a weak vortex guidance.     

Microwave Resonant Transmission in a Superconducting Fabry–Perot Bilayer

Microwave resonant transmission properties in a superconducting Fabry–Perot bilayer made of a high-temperature superconductor (YBa₂Cu₃O_7−x ) and a nearly ferroelectric superconductor (n-SrTiO₃) are theoretically investigated. The effect of high-temperature superconducting layer on the unusual resonant transmittance existing in a nearly ferroelectric superconductor is investigated. It is shown that a frequency-agile two-layer coating can be obtained with the addition of the high-temperature superconducting coating. Resonant frequencies can be shifted by varying the thickness of this coating. In addition, the ultra-narrow filtering feature makes such a bilayer resonator useful in the superconducting microwave electronics, such as a frequency sampler or spectrum analyzer in the signal processing.     

Self-Consistent Theory of Transport in Quasi–One-Dimensional Superconducting Wires

We study superconducting transport in quasi–one-dimensional homogeneous wires in the cases of both equilibrium and nonequilibrium quasiparticle populations, using the quasiclassical Green's function technique. We consider superconductors with arbitrary current densities and impurity concentrations ranging from the clean to the dirty limit. Local current conservation is guaranteed by ensuring that the order parameter satisfies the self-consistency equation at each point. For equilibrium transport, we compute the current, the order parameter amplitude, and the quasiparticle density of states as a function of the superfluid velocity, temperature, and disorder strength. Nonequilibrium is characterized by incoming quasiparticles with different chemical potentials at each -end of the superconductor. We calculate the profiles of the electrostratic potential, order parameter, and effective quasiparticle gap. We find that a transport regime of current-induced gapless superconductivity can be achieved in clean superconductors, the stability of this state being enhanced by nonequilibrium.     

Temperature and Current Dependent Matching Fields in?Superconducting NbN Film

Patterned superconducting thin films having a periodic array of submicrometric pinning centers have been of great interest due to their excellence for the studies of the vortex pinning mechanisms in the type-II superconductors. Square hole array has been fabricated over a micro-bridge 60 mm??60 mm of NbN thin film by electron beam lithography. Previous works have been carried out in Nb, Pb and Al thin films where the vortex pinning effect is assumed to be small. In this work, we study the matching pinning effect by the artificial hole array in superconducting NbN thin films. We observed the interplay between the vortex quantization and the artificial hole array. Magneto-resistance minima at integer matching fields up to five times of H ₁ (the first matching field corresponding to one vortex inside each hole) and fractional matching fields at 1/2H ₁, 3/2H ₁ and 5/2H ₁ have been observed.     

Simulation of delamination–migration and core crushing in a CFRP sandwich structure

Following the onset of damage caused by an impact load on a composite laminate structure, delaminations often form propagating outwards from the point of impact and in some cases can migrate via matrix cracks between plies as they grow. The goal of the present study is to develop an accurate finite element modeling technique for simulation of the delamination–migration phenomena in laminate impact damage processes. An experiment was devised where, under a quasi-static indentation load, an embedded delamination in the facesheet of a laminate sandwich specimen migrates via a transverse matrix crack and then continues to grow on a new ply interface. Using data from this test for validation purposes, several finite element damage simulation methods were investigated. Comparing the experimental results with those of the different models reveals certain modeling features that are important to include in a numerical simulation of delamination–migration and some that may be neglected.     

Simulation of material flow in friction stir processing of a cast Al–Si alloy

The objective of the current paper is using DEFORM-3D software to develop a 3-D Lagrangian incremental finite element method (FEM) simulation of friction stir processing (FSP). The developed simulation allows prediction of the defect types, temperature distribution, effective plastic strain, and especially material flow in the weld zone. Three-dimensional results of the material flow patterns in the center, advancing and retreating sides were extracted using the point tracking. The results reveal that the main part of the material flow occurs near the top surface and at the advancing side (AS). Material near the top surface was stretched to the advancing side resulting in a non-symmetrical shape of the stir zone (SZ). Furthermore, macrostructure and temperature rise were experimentally acquired to evaluate the accuracy of the developed simulation. The comparison shows that the stir zone shape, defect types, powder agglomeration, and temperature rise, which were predicted by simulation, are in good agreement with the corresponding experimental results.