Related papers: Amplitude response and square wave describing func…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a…
Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function, identifying the respective most linear region of operation with a fixed width. This…
Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…
This paper proposes a frequency-wise approach for stability analysis of multi-input, multi-output (MIMO) Linear Time-Invariant (LTI) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized…
We consider the problem of the nonlinear response of a Rayleigh beam to the passage of a train of forces moving with stochastic velocity. The Fourier transform and the theory of residues is used to estimate the mean-square amplitude of the…
Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
Linear response theory describes quantum measurement with an arbitrary detector weakly coupled to a measured system. This description produces generic quantitative relation characterizing the detector that is analogous to the…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…
A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by It\^o stochastic differential equations. The stochastic differential equations derived for the…
A cylindrical pipe with closed ends and with a partition in-between exhibits acoustic modes in the two, thus formed, one-dimensional cavities at certain frequencies. A partial transmission through the partition leads to interaction between…
In this work, we extend selected configuration interaction (SCI) methods beyond energies and expectation values by introducing a linear response (LR) framework for molecular response properties. Existing SCI approaches are capable of…
A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…