scholarly journals Nonlinear effects in memristors with mobile vacancies

2021 ◽  
Vol 8 (10) ◽  
Author(s):  
I. V. Boylo ◽  
K. L. Metlov
Keyword(s):  
Relaxation Time ◽  
Simple Model ◽  
Electric Field ◽  
Nonlinear Boundary ◽  
Burgers Equation ◽  
Switching Time ◽  
Nonlinear Effects ◽  
Nonlinear Boundary Conditions ◽  
Local Concentration ◽  
Applied Current

Because local concentration of vacancies in any material is bounded, their motion must be accompanied by nonlinear effects. Here, we look for such effects in a simple model for electric field-driven vacancy motion in a memristor, solving the corresponding nonlinear Burgers’ equation with impermeable nonlinear boundary conditions exactly. We find non-monotonous relaxation of the resistance while switching between the stable (‘on’ and ‘off’) states, and qualitatively different dependencies of switching time (under applied current) and relaxation time (under no current) on the memristor length. Our solution can serve as a useful benchmark for simulations of more complex memristor models.

scholarly journals Burgers' equation with nonlinear boundary feedback:H1stability, well-posedness and simulation

2000 ◽  
Vol 6 (2-3) ◽  
pp. 189-200 ◽  
Author(s):  
Andras Balogh ◽  
Miroslav Krstić
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Boundary ◽  
Burgers Equation ◽  
Nonlinear Boundary Conditions ◽  
Classical Solutions ◽  
Well Posedness ◽  
Global Asymptotic Stabilization ◽  
Numerical Result ◽  
Linear Parabolic Equations ◽  
Global Existence And Uniqueness

We consider the viscous Burgers' equation under recently proposed nonlinear boundary conditions and show that it guarantees global asymptotic stabilization and semiglobal exponential stabilization inH1sense. Our result is global in time and allows arbitrary size of initial data. It strengthens recent results by Byrnes, Gilliam, and Shubov, Ly, Mease, and Titi, and Ito and Yan. The global existence and uniqueness of classical solutions follows from the general theory of quasi-linear parabolic equations. We include a numerical result which illustrates the performance of the boundary controller.

scholarly journals Sensing Electrochemical Signals Using a Nitrogen-Vacancy Center in Diamond

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 358
Author(s):  
Hossein T. Dinani ◽  
Enrique Muñoz ◽  
Jeronimo R. Maze
Keyword(s):  
Electric Field ◽  
Electron Spin ◽  
Electrolyte Solution ◽  
High Sensitivity ◽  
Theoretical Work ◽  
Coherence Time ◽  
Nitrogen Vacancy ◽  
Local Concentration ◽  
Concentration Of Ions ◽  
Nv Center

Chemical sensors with high sensitivity that can be used under extreme conditions and can be miniaturized are of high interest in science and industry. The nitrogen-vacancy (NV) center in diamond is an ideal candidate as a nanosensor due to the long coherence time of its electron spin and its optical accessibility. In this theoretical work, we propose the use of an NV center to detect electrochemical signals emerging from an electrolyte solution, thus obtaining a concentration sensor. For this purpose, we propose the use of the inhomogeneous dephasing rate of the electron spin of the NV center (1/T2★) as a signal. We show that for a range of mean ionic concentrations in the bulk of the electrolyte solution, the electric field fluctuations produced by the diffusional fluctuations in the local concentration of ions result in dephasing rates that can be inferred from free induction decay measurements. Moreover, we show that for a range of concentrations, the electric field generated at the position of the NV center can be used to estimate the concentration of ions.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

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