An Exact Solution of the Reaction-Diffusion Equation for the Speed of the Interface Propagation in Superconductors

The speed of interface propagation in superconductors for the scalar reaction-diffusion equation ut = ∇2u+ F(u) is studied in detail. Here the non linear reaction term F (u) is the time-dependent Ginzburg-Landau or TDGL equation F(u)=u-u3 which describes the dynamics of the order-disorder transition. In contrast to what has been done in previous work [1] here an improved exact solution has derived by using TDGL equation to determine the speed of the front propagation. The analytical treatment of this study has been found in good agreement with the numerical simulation of V. Mendez et al. [2] and Di Bartolo and Dorsey [3]. The Chittagong Univ. J. Sci. 40(1) : 85-95, 2019

Pengaruh Variasi Dimensi Superkonduktor Berbentuk Persegi Panjang Terhadap Medan Kritis Pada Pada κ = 1,5

<p class="AbstractEnglish"><strong>Abstract:</strong> The Time Dependent Ginzburg-Landau (TDGL) equation can be used to study the characteristics of a superconductor in the evolution of time until it reaches an equilibrium state. This study uses the ѰU method to calculate the critical field value numerically which has been tested stable and consistent. Previous research has been carried out regarding the critical field ratio of rectangular and rectangular superconductors with the same area at κ = 1.5. This research examines the variation of the dimensions of the type II superconductor with a rectangular shape, then it is found that the critical field of the Hc₃ surface forms a pattern that can be used to study the characteristics of the type II superconductor.</p><p class="AbstrakIndonesia"><strong>Abstrak: </strong>Persamaan Ginzburg-Landau Gayut Waktu (Time Dependent Ginzburg-Landau/TDGL) dapat digunakan untuk mempelajari karakteristik superkonduktor dalam evolusi waktu sampai mencapai keadaan setimbang. Penelitian ini menggunakan metode ѰU untuk menghitung nilai medan kritis secara numerik yang telah teruji stabil dan konsisten. Telah dilakukan penelitian sebelumnya mengenai perbandingan medan kritis superkonduktor berbentuk persegi dan persegi panjang dengan luas sama pada κ = 1,5. Dalam penelitian ini dikaji variasi dimensi superkonduktor tipe II dengan bentuk persegi panjang, kemudian didapatkan bahwa medan kritis permukaan Hc₃ membentuk pola yang dapat digunakan untuk mempelajari karakteristik superkonduktor tipe II.</p>

Comparison of the superconducting rectangular critical fields with the same area at κ = 1.5

<span>The Time Dependent Ginzburg-Landau (TDGL) equation can be used to study the characteristics of superconductors in the evolution of time to reach equilibrium. This study uses the <em>ѰU</em> method to numerically calculate critical field values more easily. Previous research has been carried out on size variations, kappa variations, proximity effects and so on. In this study, a comparison between squares and rectangles with the same size of area for type II superconductor , then it is found that the critical field Hc₃ is the same value for each of the same area.</span>

Numerical investigation of the growth kinetics for macromolecular microsphere composite hydrogel based on the TDGL equation

We present results of a detailed numerical investigation of the phase separation kinetic process of the macromolecular microsphere composite (MMC) hydrogel. Based on the Flory-Huggins-de Gennes-like reticular free energy, we use the time-dependent Ginzburg–Landau (TDGL) mesoscopic model (called MMC-TDGL model) to simulate the phase separation process. Domain growth is investigated through the pair correlation function. Then we obtain the time-dependent characteristic domain size, which reflects the growth kinetics of the MMC hydrogel. The results indicate that the growth law based on the MMC-TDGL equation is consistent with the modified Lifshitz–Slyozov theory.

The Nernst effect in layered superconductors under a magnetic field

We calculated the Nernst signal [Formula: see text], describing the Nernst effect in type-II superconductor in the vortex–liquid regime, by using the time-dependent Ginzburg–Landau (TDGL) equation with thermal noise. The nonlinear interaction term in the TDGL equation is treated within self-consistent Gaussian approximation. The expression of the Nernst signal [Formula: see text] including all the Landau levels is presented in explicit form which is applicable essentially to the whole phase. Our results are compared with the recent experimental data on high-[Formula: see text] superconductor.