A Fourier transform treatment of the quantum mechanical two-level system in an applied electric field. I. Single field case

1984 ◽  
Vol 62 (8) ◽  
pp. 741-750 ◽  
Author(s):  
J. Grindlay ◽  
J. Mizia
Keyword(s):  
Fourier Transform ◽  
Differential Equations ◽  
Electric Field ◽  
Numerical Integration ◽  
Applied Electric Field ◽  
Approximate Expression ◽  
Quantum Mechanical ◽  
Level System ◽  
Single Field ◽  
Applied Fields

Fourier transform techniques are used to obtain an approximate expression for the response of a quantum mechanical two-level system to a small monochromatic applied electric field. A comparison with the results of a numerical integration of the differential equations shows that the approximation is equally satisfactory close to and far from resonance. The method is easily extended to two or more applied fields.

The quantum-mechanical two-level system with dissipation and feedback: multimode applied electric-field case

1987 ◽  
Vol 65 (4) ◽  
pp. 417-420
Author(s):  
J. Grindlay
Keyword(s):  
Dipole Moment ◽  
Electric Field ◽  
Applied Electric Field ◽  
Quantum Mechanical ◽  
Third Order ◽  
First Order ◽  
Common Value ◽  
Induced Dipole ◽  
Upper Level

A two-level dissipative quantum-mechanical system subjected to a small applied multimode electric field plus a feedback term proportional to the induced dipole moment is discussed. The long-term behaviour of the induced dipole moment and of the upper level occupation probability is represented by a series expansion in terms of the applied electric-field amplitudes. First-order and third-order internal, external, and intrinsic polarizabilites are introduced and calculated for the model. Certain ratios of third-order to first-order polarizabilities are shown to have a common value for the internal, external, and intrinsic cases. Clausius–Mossotti relations for the linear and third-order susceptibilities are derived.

LIQUID CRYSTLASLIGHT SCATTERING BY FLUCTUATIONS INDUCED BY AN APPLIED ELECTRIC FIELD IN A NEMATIC LIQUID CRYSTAL (APAPA)

1972 ◽  
Vol 33 (C1) ◽  
pp. C1-63-C1-67 ◽  
Author(s):  
M. BERTOLOTTI ◽  
B. DAINO ◽  
P. Di PORTO ◽  
F. SCUDIERI ◽  
D. SETTE
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Applied Electric Field

Improved technique for measuring mechanical deformations induced by an applied electric field to an organic insulator

2012 ◽  
Vol 15 (2-3) ◽  
pp. 127-139
Author(s):  
Tung Tran Anh ◽  
Laurent Berquez ◽  
Laurent Boudou ◽  
Juan Martinez-Vega ◽  
Alain Lacarnoy
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Mechanical Deformations ◽  
Improved Technique

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

Synergistic use of electroosmotic flow and magnetic forces for nucleic acid extraction

The Analyst ◽  
2020 ◽  
Vol 145 (6) ◽  
pp. 2412-2419 ◽  
Author(s):  
Rachel N. Deraney ◽  
Lindsay Schneider ◽  
Anubhav Tripathi
Keyword(s):  
Nucleic Acid ◽  
Electric Field ◽  
Microfluidic Chip ◽  
Applied Electric Field ◽  
Electroosmotic Flow ◽  
Acid Extraction ◽  
Nucleic Acid Extraction ◽  
Magnetic Forces ◽  
Extraction And Purification

NA extraction and purification utilitzing a microfluidic chip with applied electric field to induce electroosmotic flow opposite the magnetic NA-bound bead mix.

Investigation on dynamic holographic display in liquid crystal film doped with carbon dots

2020 ◽  
Vol 10 (6) ◽  
pp. 780-787
Author(s):  
Hongyue Gao ◽  
Suna Li ◽  
Jicheng Liu ◽  
Wen Zhou ◽  
Fan Xu ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Real Time ◽  
Diffraction Efficiency ◽  
Carbon Dots ◽  
Applied Electric Field ◽  
Light Polarization ◽  
Forming Process ◽  
Time Dynamic ◽  
Holographic Display

In this paper, we studied the holographic properties of liquid crystal (LC) thin film doped with carbon dots (CDs) which can be used as real-time holographic display screen. The maximum value of diffraction efficiency can reach up to 30% by using a low applied electric field 0.2 V/μm. Holograms in the LC film can be dynamically formed and self-erased. The hologram build-up time and the hologram self-erasure time in the material is fast enough to realize video refresh rate. In addition, the forming process of hologram was studied. The holographic diffraction efficiency was measured depending on the intensity of recording light, applied electric field, the intensity of readout light, and readout light polarization direction. Triple enhancement of the diffraction efficiency value by the modulation of voltage under the condition of low recording energy is presented. Therefore, we develop an easy way to obtain real-time dynamic holographic red, green and blue displays with high diffraction efficiency, which allow the LC film doped with CDs to be used as a holographic 3D display screen.

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