Low Dimensional Approximations to Ferroelastic Dynamics and Hysteretic Behavior Due to Phase Transformations

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Linxiang X. Wang ◽  
Roderick V. N. Melnik
Keyword(s):  
Phase Transformations ◽  
Landau Theory ◽  
Hysteretic Behavior ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
Thermally Induced ◽  
Different Temperatures ◽  
Martensite Transformations ◽  
Low Dimensional Approximations ◽  
Low Dimensional

In this paper, a low dimensional model is constructed to approximate the nonlinear ferroelastic dynamics involving mechanically and thermally-induced martensite transformations. The dynamics of the first order martensite transformation is first modeled by a set of nonlinear coupled partial differential equations (PDEs), which is obtained by using the modified Ginzburg–Landau theory. The Chebyshev collocation method is employed for the numerical analysis of the PDE model. An extended proper orthogonal decomposition is then carried out to construct a set of empirical orthogonal eigenmodes of the dynamics, with which system characteristics can be optimally approximated (in a specified sense) within a range of different temperatures and under various mechanical and thermal loadings. The performance of the low dimensional model is analyzed numerically. Results on the dynamics involving mechanically and thermally-induced phase transformations and the hysteresis effects induced by such transformations are presented.

scholarly journals Effect of Higher Landau Levels on the Transverse Thermoelectric Conductivity in High-\(T_{c}\) Superconductors

2017 ◽  
Vol 26 (3) ◽  
pp. 279
Author(s):  
Bui Duc Tinh
Keyword(s):  
Gaussian Approximation ◽  
Landau Theory ◽  
Landau Levels ◽  
Time Dependent ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
High Tc ◽  
High Tc Superconductor ◽  
Self Consistent ◽  
Good Agreement

We investigate effect of higher Ladau levels on the transverse thermoelectricconductivity \(\alpha_{xy}\), describing the Nernst effect in high-\(T_c\) superconductors, by using the time-dependent Ginzburg-Landau theory in two dimensional model withthermal noise. The transverse thermoelectric conductivity is calculated inthe self-consistent Gaussian approximation. Our results indicate that thehigher Landau levels are, the less these levels contribute to the transversethermoelectric conductivity. Our results are in good agreement with experimental dataon high-Tc superconductor.

MAGNETIZATION STUDIES OF Rb3C60 IN SUPERCONDUCTING STATE

1993 ◽  
Vol 07 (11) ◽  
pp. 2163-2176 ◽  
Author(s):  
C. POLITIS ◽  
V. BUNTAR ◽  
V.P. SEMINOZHENKO
Keyword(s):  
Magnetic Field ◽  
Temperature Dependence ◽  
Critical Current ◽  
Magnetic Measurements ◽  
Landau Theory ◽  
Critical Magnetic Field ◽  
Zero Temperature ◽  
Ginzburg Landau ◽  
Different Temperatures ◽  
Increasing Temperature

We present the results of magnetic measurements in fields up to 50 kOe for superconducting Rb 3 C 60. The temperature dependence of upper H c 2 critical magnetic field is determined, from which the zero temperature value Hc2(0)=465±50 kOe is evaluated. The magnitudes of penetration depth and coherence length are calculated as ξ(0)=26.7±3 Å; λ L (0)=2150±100 Å at zero temperature. The temperature dependence of ξ(T) and λ L (T) for T≧23 K is in good agreement with the Ginzburg-Landau theory. The critical current densities for different temperatures are calculated, showing a strong decrease of Jc with increasing temperature for T≤7 K . Two regions of fading critical current density on a magnetic field dependence are found.

Characterization of Work per Volume Density of VO2-Based MEMS Actuators

2012 ◽  
Author(s):  
Emmanuelle Merced ◽  
Jun Zhang ◽  
Xiaobo Tan ◽  
Nelson Sepúlveda
Keyword(s):  
Smart Materials ◽  
Figure Of Merit ◽  
Volume Density ◽  
Hysteretic Behavior ◽  
Contact Mode ◽  
Thermally Induced ◽  
Mems Actuators ◽  
Different Temperatures ◽  
Insulator Phase Transition

Vanadium dioxide (VO2)-coated silicon microcantilevers have gained attention due to the large stress produced during VO2’s thermally induced metal-to-insulator phase transition, which produces a curvature change of over ∼2,000 m−1. Work per volume density is an important figure of merit used to compare the performance of smart materials in micro-actuation. In this paper, the work per volume density of five fully actuated VO2-coated microcantilevers was calculated based on experimentally measured force vs. displacement curves obtained from an AFM operated in contact mode. The work per volume density for the five microactuators was found to be similar, which is around ∼1.5×104 J/m3. The work per volume density of a single microactuator was also obtained under different temperatures across the material’s transition, which exhibits the hysteretic behavior during the heating-cooling cycle.

scholarly journals Analysis of the 2D complex Ginzburg-Landau Equation using Singular Value Decomposition

2021 ◽  
Author(s):  
Emily Gottry ◽  
Edwin Ding
Keyword(s):  
Singular Value Decomposition ◽  
Landau Equation ◽  
Singular Value ◽  
Optical Systems ◽  
Qualitative Behavior ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Low Dimensional ◽  
Value Decomposition

The cubic-quintic Ginzburg-Landau equation (CQGLE) governs the dynamics of solitons in lasers and many optical systems. Using data obtained from the simulations of the CQGLE, we performed a singular value decomposition (SVD) to create a low dimensional model that qualitatively predicts the stability of the solitons as a function of the energy gain constant. It was found both in the full simulations and in the low dimensional model that the soliton becomes unstable when the gain exceeds a certain threshold value. Both the low dimensional model and the full simulation demonstrated the same qualitative behavior when the soliton loses stability.

scholarly journals Possible Alterations of Local Gravitational Field Inside a Superconductor

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 193 ◽  
Author(s):  
Giovanni Alberto Ummarino ◽  
Antonio Gallerati
Keyword(s):  
Gravitational Field ◽  
Landau Theory ◽  
Time Dependent ◽  
Qualitative Comparison ◽  
Ginzburg Landau ◽  
High Tc ◽  
Gravitational Fields ◽  
Favorable Conditions

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.

scholarly journals Different length scales for order parameters in two-gap superconductors: Extended Ginzburg-Landau theory

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
L. Komendová ◽  
M. V. Milošević ◽  
A. A. Shanenko ◽  
F. M. Peeters
Keyword(s):  
Landau Theory ◽  
Order Parameters ◽  
Ginzburg Landau ◽  
Length Scales
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