scholarly journals Electrostatic Circular Membrane MEMS: An Approach to the Optimal Control

Computation ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 41
Author(s):  
Mario Versaci ◽  
Francesco Carlo Morabito
Keyword(s):  
Optimal Control ◽  
Stable Equilibrium ◽  
Equilibrium Configuration ◽  
Micro Electro Mechanical System ◽  
Circular Membrane ◽  
Differential Model ◽  
Equilibrium Configurations ◽  
Electrostatic Effect ◽  
The Mean ◽  
The Stability

The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) is an important issue, because, when an external electrical voltage is applied, the membrane deforms with the risk of touching the upper plate of the device producing an unwanted electrostatic effect. Therefore, it is important to know whether the movement admits stable equilibrium configurations especially when the membrane is closed to the upper plate. In this framework, this work analyzes the behavior of a two-dimensional (2D) electrostatic circular membrane MEMS device subjected to an external voltage. Specifically, starting from a well-known 2D non-linear second-order differential model in which the electrostatic field in the device is proportional to the mean curvature of the membrane, the stability of the only possible equilibrium configuration is studied. Furthermore, when considering that the membrane is equipped with mechanical inertia and that it must not touch the upper plate of the device, a useful range of possible values has been obtained for the applied voltage. Finally, the paper concludes with some computations regarding the variation of potential energy, identifying some optimal control conditions.

scholarly journals Curvature Dependent Electrostatic Field in the Deformable MEMS Device: Stability and Optimal Control

2020 ◽  
Vol 11 (1) ◽  
pp. 35-54
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Optimal Control ◽  
Electrostatic Field ◽  
Stable Equilibrium ◽  
Micro Electro Mechanical System ◽  
Operating Conditions ◽  
Electric Voltage ◽  
External Voltage ◽  
Device Stability ◽  
Equilibrium Configurations ◽  
Mems Device

AbstractThe recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

scholarly journals Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 487 ◽  
Author(s):  
Mario Versaci ◽  
Giovanni Angiulli ◽  
Alessandra Jannelli
Keyword(s):  
Convergence Analysis ◽  
Electrostatic Field ◽  
Mean Curvature ◽  
Mechanical Systems ◽  
Numerical Approach ◽  
Second Order ◽  
Circular Membrane ◽  
Differential Model ◽  
The Mean

In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.

scholarly journals A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1193 ◽  
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Steady State ◽  
Mean Curvature ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Circular Membrane ◽  
Mems Devices ◽  
Differential Model ◽  
Non Linear ◽  
The Mean ◽  
State Case

In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

scholarly journals A 2D Membrane MEMS Device Model with Fringing Field: Curvature-Dependent Electrostatic Field and Optimal Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 465
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Optimal Control ◽  
Electrostatic Field ◽  
Circular Membrane ◽  
Differential Model ◽  
Field Curvature ◽  
Fringing Field ◽  
Uniqueness Of The Solution ◽  
Stable Equilibrium Position ◽  
The One ◽  
Fringing Field Effect

An important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field E near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is applied. In the framework of a 2D circular membrane MEMS, representing the fringing-field effect depending on |∇u|2 with the u profile of the membrane, and since strong E produces strong deformation of the membrane, we consider |E| proportional to the mean curvature of the membrane, obtaining a new nonlinear second-order differential model without explicit singularities. In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter δ that weighs the terms |∇u|2. However, even if the the study of the model did not ensure the uniqueness of the solution, it made it possible to achieve the goal of finding a stable equilibrium position. Moreover, a range of admissible values of V were obtained in order, on the one hand, to win the mechanical inertia of the membrane and, on the other hand, to ensure that the membrane did not touch the upper disk of the device. Lastly, some optimal control conditions based on the variation of potential energy are presented and discussed.

scholarly journals A Theoretical MHD Model for Extragalactic Jets and its Comparison with the Observations

1990 ◽  
Vol 140 ◽  
pp. 441-442
Author(s):  
P. Pietrini
Keyword(s):  
Stability Analysis ◽  
Equilibrium Model ◽  
Stable Equilibrium ◽  
Point Of View ◽  
Observational Constraints ◽  
Radio Sources ◽  
Equilibrium Configurations ◽  
Extragalactic Jets ◽  
Thermal Confinement ◽  
The Stability

Two aspects of the MHD stationary equilibrium model developed by Chiuderi et al.(1989) to describe extragalactic jets are analyzed and compared with the observational constraints: the global energy flux convected by the cylindrical jet and the ranges of the equilibrium parameters allowed by the stability analysis. In particular, the results obtained from the temporal stability analysis are converted into a spatial point of view. In this context, it is easier to find essentially “stable” equilibrium configurations for shorter jets. In conclusion, the fundamental hypotheses of this model (like thermal confinement and substantial equipartition among the various forms of energy considered) are such that the model turns out to be suitable for the description of class I jets, associated with rather low-power radio sources.

Injuries to the Coronoid Process of the Ulna with Involvement of the Lesser Sigmoid Notch

2020 ◽  
Author(s):  
Valentin Rausch ◽  
Sina Neugebauer ◽  
Tim Leschinger ◽  
Lars Müller ◽  
Kilian Wegmann ◽  
...  
Keyword(s):  
Fragment Size ◽  
Coronoid Process ◽  
Annular Ligament ◽  
Concomitant Injuries ◽  
Proximal Ulna ◽  
Sigmoid Notch ◽  
Coronoid Fractures ◽  
The Mean ◽  
The Stability ◽  
Arthritic Changes

Abstract Introduction This study aimed to describe the involvement of the lesser sigmoid notch in fractures to the coronoid process. We hypothesized that injuries to the lateral aspect of the coronoid process regularly involve the annular ligament insertion at the anterior lesser sigmoid notch. Material and Methods Patients treated for a coronoid process fracture at our institution between 06/2011 and 07/2018 were included. We excluded patients < 18 years, patients with arthritic changes or previous operative treatment to the elbow, and patients with concomitant injuries to the proximal ulna. In patients with involvement of the lesser sigmoid notch, the coronoid height and fragment size (anteroposterior, mediolateral, and craniocaudal) were measured. Results Seventy-two patients (mean age: 47 years ± 17.6) could be included in the study. Twenty-one patients (29.2%) had a fracture involving the lateral sigmoid notch. The mean anteroposterior fragment length was 7 ± 1.6 mm. The fragment affected a mean of 43 ± 10.8% of the coronoid height. The mean mediolateral size of the fragment was 10 ± 5.0 mm, and the mean cranio-caudal size was 7 ± 2.7 mm. Conclusion Coronoid fractures regularly include the lesser sigmoid notch. These injuries possibly affect the anterior annular ligament insertion which is important for the stability of the proximal radioulnar joint and varus stability of the elbow.

Instant 99mTc-Labelled Glucoheptonate Kit for Kidney Imaging

1983 ◽  
Vol 22 (05) ◽  
pp. 246-250 ◽  
Author(s):  
M. Al-Hilli ◽  
H. M. A. Karim ◽  
M. H. S. Al-Hissoni ◽  
M. N. Jassim ◽  
N. H. Agha
Keyword(s):  
Sodium Hydroxide Solution ◽  
Normal Subjects ◽  
Organ Distribution ◽  
Stable Complex ◽  
Scintillation Camera ◽  
Ph Adjustment ◽  
The Mean ◽  
The Stability ◽  
Kidney Imaging ◽  
Mean Concentration

Gelchromatography column scanning has been used to study the fractions of reduced hydrolyzed 99mTc, 99mTc-pertechnetate and 99mTc-chelate in a 99mTc-glucoheptonate (GH) preparation. A stable high labelling yield of 99mTc-GH complex in the radiopharmaceutical has been obtained with a concentration of 40-50 mg of glucoheptonic acid-calcium salt and not less than 0.45 mg of SnCl2 2 H2O at an optimal pH between 6.5 and 7.0. The stability of the complex has been found significantly affected when sodium hydroxide solution was used for the pH adjustment. However, an alternative procedure for final pH adjustment of the preparation has been investigated providing a stable complex for the usual period of time prior to the injection. The organ distribution and the blood clearance data of 99mTc-GH in rabbits were relatively similar to those reported earlier. The mean concentration of the radiopharmaceutical in both kidneys has been studied in normal subjects for one hour with a scintillation camera and the results were satisfactory.

scholarly journals The force effects of two types of polyethylene terephthalate glyc-olmodified clear aligners immersed in artificial saliva

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Biao Xiang ◽  
Xingxing Wang ◽  
Gang Wu ◽  
Yichen Xu ◽  
Menghan Wang ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Polyethylene Terephthalate ◽  
Artificial Saliva ◽  
Orthodontic Force ◽  
The Mean ◽  
The Stability ◽  
Scanning Electron

AbstractNumerous factors can influence the force exerted by clear aligners on teeth. This study aimed to investigate the stability of the force delivered by two different material appliances. 90 clear aligners with 2 materials and three different activations were designed and fabricated. Then, a device was employed to measure the force generated by the two types of PET-G material appliances immersed in artificial saliva for 0, 3, 7, 10, 14 days. Scanning electron microscopy was applied to observe the morphologic alterations on the aligner surfaces, respectively. The forces generated by different activation appliance exhibited differently, 0.0 mm < 0.1 mm < 0.2 mm. In addition, increasing the immersion times and the orthodontic force also decreased, but the forces decreased differently. Compared with the forces of conventional PETG appliances with 0.20 mm activation, the modified PETG appliances with the same activation exhibited significantly higher mean force. When comparing the mean force for modified PETG appliances after 10 and 14 days with conventional PETG appliances, the delivery forces exhibited significant differences (P < 0.05). The force delivered by both materials decreased obviously following artificial saliva immersion, and the force generated by modified aligners exhibited better stability than conventional aligners.

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