In this paper we present, in a framework of 1D-membrane Micro-Electro-MechanicalSystems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steadystate case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychonoff's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.

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.Mathematics 2019, 7, 1193 2 of 18 the design, realization, and distribution of the MEMS devices used in the various applications [17]. Biomedical diagnostics increasingly require efficient, low-cost, and reliable micro-components, which can be of help to health-care personnel both in on-line and off-line modes [18,19]. Many mathematical models have been theoretically conceived of in special functional spaces, in order to provide the conditions of the existence and uniqueness of the solutions, which are otherwise difficult to detect [20,21]. Cassani et al. [22] built a sophisticated mathematical model of a MEMS device constituted of two metallic plates (one fixed and one deformable), which was clumped at the edges and subjected to a drop voltage, which deformed the deformable plate towards the other one. Obviously, determining a solution for this model is very difficult, and some simplifications were necessarily required. In particular, neglecting the inertial and non-local effects, Cassani et al. obtained a simplified model in [23], which was studied using Steklov boundary conditions to achieve Dirichlet and Navier boundary conditions. Starting from this simplified model, the authors studied a new elliptical semi-linear dimensionless model for a 1D membrane MEMS, based on the proportionality between the electric field magnitude |E| and the curvature of the membrane, achieving results of the existence and uniqueness for the solution. In particular, in [7], the algebraic condition ensuring the uniqueness of the solution did not depend on the electro-mechanical properties of the material constituting the membrane. Consequently, in [10], the authors achieved a new algebraic condition depending on these properties, ensuring the uniqueness of the solution.In this work, for applicative reasons, the authors focus their attention on a 2D circular membrane MEMS device, which is useful in several industrial and/or biomedical applications [1,19]. In addition, the authors consider |E| to be proportional to the mean curvature of the membrane of the device, in order to achieve a non-linear second-order differential model with singularity in the steady-state case. Finally, an algebraic condition, depending on both the mechanical and electrical properties of the membrane, guarantees the existence of at least one solution to the proposed model. However, the uniqueness of the solution is not ensured.The paper is structured as follows. After presenting how the proposed model was achieved in ...

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In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller–Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.

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A novel technique of quantitative EEG for differentiating patients with early-stage Creutzfeldt-Jakob disease (CJD) from other forms of rapidly progressive dementia (RPD) is proposed. The discrimination is based on the extraction of suitable features from the time-frequency representation of the EEG signals through continuous wavelet transform (CWT). An average measure of complexity of the EEG signal obtained by permutation entropy (PE) is also included. The dimensionality of the feature space is reduced through a multilayer processing system based on the recently emerged deep learning (DL) concept. The DL processor includes a stacked auto-encoder, trained by unsupervised learning techniques, and a classifier whose parameters are determined in a supervised way by associating the known category labels to the reduced vector of high-level features generated by the previous processing blocks. The supervised learning step is carried out by using either support vector machines (SVM) or multilayer neural networks (MLP-NN). A subset of EEG from patients suffering from Alzheimer's Disease (AD) and healthy controls (HC) is considered for differentiating CJD patients. When fine-tuning the parameters of the global processing system by a supervised learning procedure, the proposed system is able to achieve an average accuracy of 89%, an average sensitivity of 92%, and an average specificity of 89% in differentiating CJD from RPD. Similar results are obtained for CJD versus AD and CJD versus HC.