Search results for " Nonlinear"
showing 10 items of 1224 documents
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
Fokker Planck equation solved in terms of complex fractional moments
2014
Abstract In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones, the solution of the FPK equation in terms of a finite number of complex moments may be easily found. It is shown that the probability density function (PDF) solution of the FPK equation is restored in the whole domain, including the trend at infinity with the exception of the value of the PDF in zero.
Poisson white noise parametric input and response by using complex fractional moments
2014
Abstract In this paper the solution of the generalization of the Kolmogorov–Feller equation to the case of parametric input is treated. The solution is obtained by using complex Mellin transform and complex fractional moments. Applying an invertible nonlinear transformation, it is possible to convert the original system into an artificial one driven by an external Poisson white noise process. Then, the problem of finding the evolution of the probability density function (PDF) for nonlinear systems driven by parametric non-normal white noise process may be addressed in determining the PDF evolution of a corresponding artificial system with external type of loading.
Nonlinear conductance and heterogeneity of voltage-gated ion channels allow defining electrical surface domains in cell membranes
2015
Abstract The membrane potential of a cell measured by typical electrophysiological methods is only an average magnitude and experimental techniques allowing a more detailed mapping of the cell surface have shown the existence of spatial domains with locally different electric potentials and currents. Electrical potentials in non-neural cells are regulated by the nonlinear conductance of membrane ion channels. Voltage-gated potassium channels participate in cell hyperpolarization/depolarization processes and control the electrical signals over the cell surface, constituting good candidates to study basic biological questions on a more simplified scale than the complex cell membrane. These ch…
Extending Quantum Links: Modules for Fiber‐ and Memory‐Based Quantum Repeaters
2020
We analyze elementary building blocks for quantum repeaters based on fiber channels and memory stations. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. We evaluate and compare the performances of basic quantum repeater links for these platforms both for present-day, state-of-the-art experimental parameters as well as for parameters that could in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances, up to a few 100 km, in which the repeater-assisted secret key transmission rates exceed the maxi…
Resistive state relaxation time in ZrO2(Y)-based memristive devices under the influence of external noise
2022
The effects of external digitally synthesized Gaussian noise on the resistive state relaxation time of a ZrO2(Y)-based memristive device when switching from a low resistance state to a high resistance state have been experimentally investigated. A nonmonotonic dependence of the resistive state relaxation time on the external noise intensity is found. This behavior is interpreted as a manifestation of the noise-enhanced stability effect previously observed in various complex systems with metastable states. It is shown that the experimental results agree satisfactorily with the theoretical ones. The presented results indicate the constructive role of external noise and its possible use as a m…
The bistable system: an archetypal model for complex systems
2011
Bistable systems often play the role of archetypal models to understand the dynamical behavior of complex systems. Examples range from microphysics to macrophysics, bìology, chemistry and also econophysics. Moreover the statistical mechanics is essential to study the physical properties of complex systems and to investigate stochastic systems in which the microscopic degrees of freedom behave collectively over large scales. We investigate the nonlinear relaxation in a bistable system in classical and quantum systems. (i) As a first classical system, the role of the multiplicative and additive noise in the mean life time of the metastable state of an asymmetric bistable system is investigate…
Nonlinear contractions involving simulation functions in a metric space with a partial order
2015
Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a …
Polarization Modulation Instability in All-Normal Dispersion Microstructured Optical Fibers With Quasi-Continuous Pump
2019
We report the experimental observation of the polarization modulation instability (PMI) effect in all-normal dispersion (ANDi) microstructured optical fibers (MOFs) with quasi-continuous pumping. The small unintentional birefringence (~10-5), that any realistic non-polarization maintaining MOF exhibits, contributes to this nonlinear effect. PMI can produce two sidebands whose polarization state is orthogonal to the polarization of the pump. In this work, only one type of PMI process is observed, i.e., when the pump is polarized along the slow axis of the fiber and sidebands are generated in the fast axis mode. This PMI process was studied experimentally in two ANDi fibers with different dis…
On global solutions of the Maxwell-Dirac equations
1987
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.