Search results for " Nonlinear"

Asymptotic mean value formulas for parabolic nonlinear equations

2021

In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games. peerReviewed

Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities

2022

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schr\"{o}dinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearit…

Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations

2022

Abstract We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.

FORMAZIONE DI PATTERN PER IL PROCESSO DELL'ELETTRODEPOSIZIONE IN MODELLI DI TIPO REAZIONE-DIFFUSIONE

2014

PROPAGATING INTERFACES IN A TWO-LAYER BISTABLE NEURAL NETWORK

2006

The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure a…

Pinning of a kink in a nonlinear diffusive medium with a geometrical bifurcation: Theory and experiments

2004

International audience; We study the dynamics of a kink propagating in a Nagumo chain presenting a geometrical bifurcation. In the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink at the bifurcation site. Moreover, real experiments using a nonlinear electrical lattice confirm the theoretical and numerical predictions.

Some nonlinear aspects of a pulsar magnetosphere

2006

Novel qutrit circuit design for multiplexer, De-multiplexer, and decoder

2022

AbstractDesigning conventional circuits present many challenges, including minimizing internal power dissipation. An approach to overcoming this problem is utilizing quantum technology, which has attracted significant attention as an alternative to Nanoscale CMOS technology. The reduction of energy dissipation makes quantum circuits an up-and-coming emerging technology. Ternary logic can potentially diminish the quantum circuit width, which is currently a limitation in quantum technologies. Using qutrit instead of qubit could play an essential role in the future of quantum computing. First, we propose two approaches for quantum ternary decoder circuit in this context. Then, we propose a qua…

Nonlinear Absorption and Refraction of Picosecond and Femtosecond Pulses in HgTe Quantum Dot Films

2021

We report measurements of the saturated intensities, saturable absorption, and nonlinear refraction in 70-nm thick films containing 4 nm HgTe quantum dots. We demonstrate strong nonlinear refraction and saturable absorption in the thin films using tunable picosecond and femtosecond pulses. Studies were carried out using tunable laser pulses in the range of 400–1100 nm. A significant variation of the nonlinear refraction along this spectral range was demonstrated. The maximal values of the nonlinear absorption coefficients and nonlinear refractive indices determined within the studied wavelength range were −2.4 × 10−5 cm2 W−1 (in the case of 28 ps, 700 nm probe pulses) and −3 × 10−9 cm2 W−1 …

Computationally Efficient Innovative Techniques for the Design-Oriented Simulation of Free-Running and Driven Microwave Oscillators

2014

Analysis techniques for injection-locked oscillators/amplifiers (ILO) can be broadly divided into two classes. To the first class belong methods with a strong and rigorous theoretical basis, that can be applied to rather general circuits/systems but which are very cumbersome and/or time-consuming to apply. To the second class belong methods which are very simple and fast to apply, but either lack of validity/accuracy or are applicable only to very simple or particular cases. In this thesis, a novel method is proposed which aims at combining the rigorousness and broad applicability characterizing the first class of analysis techniques above cited with the simplicity and computational efficie…