A Class of First Order Non-Linear Odes

2021 ◽  
pp. 130-175
Author(s):  
Anindya Dey
Keyword(s):  
Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 1968 ◽  
Author(s):  
Sylvie Bilent ◽  
Thi Hong Nhung Dinh ◽  
Emile Martincic ◽  
Pierre-Yves Joubert

This paper reports on the study of microporous polydimethylsiloxane (PDMS) foams as a highly deformable dielectric material used in the composition of flexible capacitive pressure sensors dedicated to wearable use. A fabrication process allowing the porosity of the foams to be adjusted was proposed and the fabricated foams were characterized. Then, elementary capacitive pressure sensors (15 × 15 mm2 square shaped electrodes) were elaborated with fabricated foams (5 mm or 10 mm thick) and were electromechanically characterized. Since the sensor responses under load are strongly non-linear, a behavioral non-linear model (first order exponential) was proposed, adjusted to the experimental data, and used to objectively estimate the sensor performances in terms of sensitivity and measurement range. The main conclusions of this study are that the porosity of the PDMS foams can be adjusted through the sugar:PDMS volume ratio and the size of sugar crystals used to fabricate the foams. Additionally, the porosity of the foams significantly modified the sensor performances. Indeed, compared to bulk PDMS sensors of the same size, the sensitivity of porous PDMS sensors could be multiplied by a factor up to 100 (the sensitivity is 0.14 %.kPa−1 for a bulk PDMS sensor and up to 13.7 %.kPa−1 for a porous PDMS sensor of the same dimensions), while the measurement range was reduced from a factor of 2 to 3 (from 594 kPa for a bulk PDMS sensor down to between 255 and 177 kPa for a PDMS foam sensor of the same dimensions, according to the porosity). This study opens the way to the design and fabrication of wearable flexible pressure sensors with adjustable performances through the control of the porosity of the fabricated PDMS foams.


Cybersecurity ◽  
2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jingdian Ming ◽  
Yongbin Zhou ◽  
Huizhong Li ◽  
Qian Zhang

AbstractDue to its provable security and remarkable device-independence, masking has been widely accepted as a noteworthy algorithmic-level countermeasure against side-channel attacks. However, relatively high cost of masking severely limits its applicability. Considering the high tackling complexity of non-linear operations, most masked AES implementations focus on the security and cost reduction of masked S-boxes. In this paper, we focus on linear operations, which seems to be underestimated, on the contrary. Specifically, we discover some security flaws and redundant processes in popular first-order masked AES linear operations, and pinpoint the underlying root causes. Then we propose a provably secure and highly efficient masking scheme for AES linear operations. In order to show its practical implications, we replace the linear operations of state-of-the-art first-order AES masking schemes with our proposal, while keeping their original non-linear operations unchanged. We implement four newly combined masking schemes on an Intel Core i7-4790 CPU, and the results show they are roughly 20% faster than those original ones. Then we select one masked implementation named RSMv2 due to its popularity, and investigate its security and efficiency on an AVR ATMega163 processor and four different FPGA devices. The results show that no exploitable first-order side-channel leakages are detected. Moreover, compared with original masked AES implementations, our combined approach is nearly 25% faster on the AVR processor, and at least 70% more efficient on four FPGA devices.


Author(s):  
Hemavathy P.R. ◽  
Mohamed Shuaib Y ◽  
S.K. Lakshmanaprabu

In this paper, an Internal model Controller (IMC) based PID with fractional filter for a first order plus time delay process is proposed. The structure of the controller has two parts, one is integer PID controller part cascaded with fractional filter. The proposed controller has two tuning factors λ, filter time constant and a, fractional order of the filter. In this work, the two factors are decided in order to obtain low Integral Time Absolute Error (ITAE). The effectiveness of the proposed controller is studied by considering a non linear (hopper tank) process. The experimental set up is fabricated in the laboratory and then data driven model is developed from the experimental data. The non linear process model is linearised using piecewise linearization and two linear regions are obtained. At each operating point, linear first order plus dead time model is obtained and the controller is designed for the same. To show the practical applicability, the proposed controller is implemented for the proposed experimental laboratory prototype.


Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.


Author(s):  
Houssem Maghrebi ◽  
Claude Carlet ◽  
Sylvain Guilley ◽  
Jean-Luc Danger
Keyword(s):  

2021 ◽  
Vol 18 (2) ◽  
pp. 226-242
Author(s):  
Valerii Samoilenko ◽  
Yuliia Samoilenko

The paper deals with constructing an asymptotic one-phase soliton-like solution to the Benjamin--Bona--Mahony equation with variable coefficients and a strong singularity making use of the non-linear WKB technique. The influence of the small-parameter value on the structure and the qualitative properties of the asymptotic solution, as well as the accuracy with which the solution satisfies the considerable equation, have been analyzed. It was demonstrated that due to the strong singularity, it is possible to write explicitly not only the main term of the asymptotics but at least its first-order term.


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