A compound problem for a degenerate elliptical equation of the first kind

1976 ◽  
Vol 16 (3) ◽  
pp. 377-382
Author(s):  
V. N. Vragov
Keyword(s):  
Elliptical Equation

Shape Memory Alloy As Artificial Muscles for Facial Prosthesis

2017 ◽  
Author(s):  
Paul Mazza ◽  
Moochul Shin ◽  
Anthony Santamaria
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Response Times ◽  
Electrical Current ◽  
Artificial Muscles ◽  
Elliptical Equation ◽  
Facial Motion ◽  
Facial Prosthesis ◽  
Nitinol Wire ◽  
Original Length

Facial paralysis affects hundreds of thousands of people each year; a common result of infection, trauma, stroke, and Bell’s palsy, among others. Achieving facial prosthetics that are lightweight, comfortable, aesthetically pleasing, energy efficient, and that allow human-like facial motion is a challenge. This study focuses on examining the feasibility of the use of a shape memory alloy as a means of low-power artificial muscles. Nitinol is a shape memory alloy (SMA) that can recover up to four percent of its original length when exposed to either a large enough change in temperature which can be controlled via electrical current or a stress. In this work, human eyelid muscles are replicated using Nitinol embedded in silicon. Silicone is used due to its elasticity, texture, flexibility, compatibility and ease of manufacturing. A mold is created based on human facial geometry around the orbital using a 3D printer. Based on average human eyelid dimensions, as well as the contraction properties of the Nitinol wire, an elliptical equation is used determine the length of wire required to completely close the eyelid from an open position. Temperature change of the system is controlled by modulating current through the resistive Nitinol wire. The contraction and expansion times of the eyelids are measured. The circuit is then optimized so that response times mimicked that of the human eyelid. Finally, based on the amount of times the average human blinks, the average daily power consumption is calculated. Future directions including miniaturization of the control system, bonding between SMA wires and silicone, and energy management are discussed.

scholarly journals A prediction model of compressor with variable-geometry diffuser based on elliptic equation and partial least squares

2018 ◽  
Vol 5 (1) ◽  
pp. 171468 ◽  
Author(s):  
Xu Li ◽  
Chuanlei Yang ◽  
Yinyan Wang ◽  
Hechun Wang
Keyword(s):  
Diesel Engine ◽  
Prediction Model ◽  
Least Squares ◽  
Partial Least Squares ◽  
Performance Prediction ◽  
Variable Geometry ◽  
Elliptical Equation ◽  
Look Up Table ◽  
Comparison Results ◽  
The Look

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future.

INFLUENCE OF A VOLUMETRIC CHEMICAL REACTION ON THE CONVECTIVE MASS TRANSFER NEAR A DROP

2013 ◽  
Vol 13 (07) ◽  
pp. 1340002
Author(s):  
RUSTYAM AKHMETOV ◽  
RUSLAN KUTLUEV
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Saddle Point ◽  
Chemical Reaction ◽  
Rate Constant ◽  
Peclet Number ◽  
Convective Mass Transfer ◽  
Elliptical Equation ◽  
Spherical Drop ◽  
Péclet Number

The problem of steady convective mass transfer between a spherical drop and a flow with distributed chemical reaction is considered. It is investigated in case where both Peclet number and the rate constant of the chemical reaction tend to infinity. The quantity of rate constant of the chemical reaction and Peclet number is assumed to have a constant value. It is a boundary value problem for a quasilinear partial elliptical equation with a small parameter multiplying in higher derivatives. In the neighborhood of the saddle point the additional boundary layer arises. The asymptotics of solution is constructed in the neighborhood of the saddle point. The leading term of the asymptotic expansion of solution is constructed in the boundary layer near the rear stagnation point of the drop as the solution for the quasilinear ordinary differential equation.

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