scholarly journals Phase Diagram and Order Reconstruction Modeling for Nematics in Asymmetric π-Cells

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2156
Author(s):  
Antonino Amoddeo ◽  
Riccardo Barberi
Keyword(s):  
Differential Equation ◽  
Phase Diagram ◽  
Electric Fields ◽  
Numerical Technique ◽  
Moving Mesh ◽  
The Finite Element Method ◽  
Order Tensor ◽  
Fast Switching ◽  
Tensor Theory ◽  
Order Reconstruction

Intense electric fields applied to an asymmetric π-cell containing a nematic liquid crystal subjected to strong mechanical stresses induce distortions that are relaxed through a fast-switching mechanism: the order reconstruction transition. Topologically different nematic textures are connected by such a mechanism that is spatially driven by the intensity of the applied electric fields and by the anchoring angles of the nematic molecules on the confining plates of the cell. Using the finite element method, we implemented the moving mesh partial differential equation numerical technique, and we simulated the nematic evolution inside the cell in the context of the Landau–de Gennes order tensor theory. The order dynamics have been well captured, putting in evidence the possible existence of a metastable biaxial state, and a phase diagram of the nematic texture has been built, therefore confirming the appropriateness of the used technique for the study of this type of problem.

The Effect of Curvature and Torsion on the Temperature Distribution in a Helix

1985 ◽  
Vol 52 (3) ◽  
pp. 529-532 ◽  
Author(s):  
D. D. Sayers ◽  
M. C. Potter
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Temperature Distribution ◽  
Strong Dependence ◽  
Maximum Temperature ◽  
Nonuniform Heating ◽  
The Finite Element Method ◽  
Curvature Parameter ◽  
Curvature And Torsion

Traditional analysis treats the helix as a straight wire with the effects of nonuniform heating, torsion, and large curvature ignored. Using a helical coordinate system the governing partial differential equation including these effects is derived. The equation is then solved numerically using the finite element method. The results indicate a strong dependence of the temperature on the torsion parameter when the curvature parameter is significant. As the curvature parameter increases, the temperature distribution becomes skew-symmetric and the maximum temperature in the helix increases. Nonuniform heating influences the temperature distribution independent of the curvature and torsion.

Drift Instability in Plasmas with Nonuniform Macroscopic Rotation Profiles

1972 ◽  
Vol 50 (16) ◽  
pp. 1795-1799
Author(s):  
M. Caplan ◽  
C. E. Capjack ◽  
C. R. James
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Electric Fields ◽  
Charge Neutrality ◽  
Drift Instability ◽  
Hermite Approximation

The drift instability is examined in a collisionless low β plasma in the presence of nonuniform radial electric fields in the limit where charge neutrality cannot be assumed. A numerical solution and a Weber–Hermite approximation for the resulting differential equation describing the drift instability are presented.

scholarly journals Design of Cable Termination for AC Breakdown Voltage Tests

Energies ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 3075 ◽  
Author(s):  
Arthur F. Andrade ◽  
Edson G. Costa ◽  
Filipe L.M. Andrade ◽  
Clarice S.H. Soares ◽  
George R.S. Lira
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Breakdown Voltage ◽  
Electric Field Distribution ◽  
International Standards ◽  
The Finite Element Method ◽  
Cable Model ◽  
Voltage Measurement ◽  
Insulating Material ◽  
Purpose Computer

International standards prescribe overvoltage tests to evaluate the insulating material performance of high-voltage cables. However, it is difficult to manage the electric fields at the cable ends when laboratory measurements are carried out because surface and external discharges occur at the cable termination. Therefore, this paper presents a procedure for designing cable terminations to reduce the electric field at the cable ends to appropriate levels even in the case of overvoltage tests. For this purpose, computer simulations of electric field distribution using the finite element method (FEM) were performed. A 35 kV cable model was employed as a sample. An voltage with RMS (root mean square) value of 300 kV was used as an overestimate of breakdown voltage for the internal insulating material. The cable termination model obtained through the proposed methodology allows an electric field reduction in air, preventing the occurrence of external discharges, and thus permitting the breakdown voltage measurement of the cable’s inner insulation.

WETTING AND PREWETTING PHENOMENA IN NEMATIC LIQUID CRYSTAL DISK-LIKE DROPLET

2019 ◽  
Vol 26 (04) ◽  
pp. 1850171
Author(s):  
ERFAN KADIVAR ◽  
SHAHRAM AHMADI DARANI
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Phase Diagram ◽  
Free Energy ◽  
Liquid Crystal ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Critical Droplet ◽  
Quadratic Surface ◽  
Maxwell Construction

We present a theoretical investigation of wetting and prewetting phenomena in a nematic-disk like droplet under a concentric anchoring configuration. Our theoretical model is based on Landau–de Gennes free energy together with a quadratic surface energy. By using the Maxwell construction, we numerically solve the Euler–Lagrange differential equation. The occurrence of boundary layer transition is summarized in the phase diagram scanned by temperature and surface potential. We find that prewetting phenomenon disappear below a critical droplet size and critical temperature.

Analysis of 50Hz Electric Fields Generated by Multi-Circuit Transmission Lines on the Same Tower

2014 ◽  
Vol 700 ◽  
pp. 67-70 ◽  
Author(s):  
Bin Liu ◽  
Tao Wang ◽  
Fei Gu ◽  
Jie Wei ◽  
Hong Wei Cui ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Transmission Lines ◽  
The Finite Element Method ◽  
Protection Measures ◽  
Overhead Transmission Lines ◽  
Domestic Security ◽  
Phase Sequence ◽  
The Cross ◽  
Security Standards

The finite element method has been applied to calculate the 50Hz electric fields nearby the transmission lines. The electric field strengths nearby multi-circuit transmission lines on the same tower under different arrangement of phase sequence, nearby the cross-arm are calculated. According to the foreign and domestic security standards of 50Hz electric field, the impacts of overhead transmission lines on environment are evaluated and the adoptable measures to reduce electric field strength are proposed. Meanwhile the distributing pattern of the electric field nearby the cross-arm is analyzed and proposals for further protection measures during maintenance operation are provided.

A hybrid solver based on the integral equation method and vector finite-element method for 3D controlled-source electromagnetic method modeling

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. E319-E333 ◽  
Author(s):  
Rong Liu ◽  
Rongwen Guo ◽  
Jianxin Liu ◽  
Changying Ma ◽  
Zhenwei Guo
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Integral Equation ◽  
Finite Element ◽  
Differential Equations ◽  
Electric Fields ◽  
Hybrid Method ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Controlled Source

The integral equation method (IEM) and differential equation methods have been widely applied to provide numerical solutions of the electromagnetic (EM) fields caused by inhomogeneity for the controlled-source EM method. IEM has a bounded computational domain and has been well-known for its efficiency, whereas differential equation methods are commonly used for complex geologic models. To use the advantages of the two types of approaches, a hybrid method is developed based on the combination of IEM and the edge-based finite-element method (vector FEM). In the hybrid scheme, Maxwell’s differential equations of the secondary electric fields in the frequency domain are derived for a volume with boundary placed slightly away from the inhomogeneity. The vector FEM is applied to solve Maxwell’s differential equations, and a system of linear equations for the secondary electric fields can be derived by the minimum theorem. The secondary electric fields on the boundary are represented by IEM in terms of the secondary electric fields inside the inhomogeneity. The linear equations from substituting the boundary values into the vector FEM linear equations then can be solved to obtain the secondary electric fields inside the inhomogeneity. The secondary electric fields at receivers are calculated by IEM based on the secondary electric field solutions inside the inhomogeneity. The hybrid algorithm is verified by comparison of simulated results with earlier works on canonical 3D disc models with a high accuracy. Numerical comparisons with two conventional IEMs demonstrate that the hybrid method is more accurate and efficient for high-conductivity contrast media.

Out-of-Plane Stability Analysis for Crane Jib with Single Cable Considering Lateral Flexibility of the Cable Fixed Joint

2014 ◽  
Vol 685 ◽  
pp. 240-244 ◽  
Author(s):  
Peng Lan ◽  
Teng Fei Wang ◽  
Nian Li Lu
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Characteristic Equation ◽  
Lateral Stiffness ◽  
Stiffness Coefficient ◽  
The Finite Element Method ◽  
Lateral Direction ◽  
Out Of Plane ◽  
Lateral Constraint ◽  
The Stability

The out-of-plane stability of crane jib is studied considering the lateral flexibility of the fixed joint. The analytical expression of the out-of-plane buckling characteristic equation for the crane jib with single cable is obtained by establishing the bending deflection differential equation of jib under the instability critical state with the method of differential equation. The equilibrium equation of the fixed point in the lateral direction is introduced to solve the differential equation besides the boundary conditions. The analytical results obtained agree very well with the finite element method (FEM) results. To consider the lateral flexibility of the cable fixed joint, a dimensionless stiffness coefficient measuring the lateral constraint was introduced to derive the out-of-plane buckling characteristic equation. The degeneration forms of the characteristic equation under the limit cases of zero lateral stiffness, infinite lateral stiffness are further discussed. And the influence of the lateral stiffness of fixed joint on the stability of jib is investigated. It is shown that the increase of the lateral stiffness will significantly improve the buckling load of the crane jib especially when the lateral stiffness is very small.

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