Related papers: Impulse response of a generalized fractional secon…
In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
The hybrid Stimulated Raman Scattering - Two Plasmon Decay instability had shown to play the dominant role for plasma waves excitation and energy absorption at interaction of very intense femtosecond obliquely incident $p$-polarized laser…
We report optical second-harmonic generation (SHG) in reflection from GaSe crystals of 1 to more than 100 layers using a fundamental picosecond pulsed pump at 1.58 eV and a supercontinuum white light pulsed laser with energies ranging from…
Second-order nonlinear optical interactions, including second harmonic generation (SHG) and sum-frequency generation (SFG), can reveal a wealth of information about chemical, electronic, and vibrational dynamics at the nanoscale. Here, we…
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a non-perturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the…
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $\alpha\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing…
We investigate the asymptotic behavior as $\varepsilon \to 0$ of singularly perturbed phase transition models of order $n \geq 2$, given by \begin{align} G_\varepsilon^{\lambda,n}[u] := \int_I \frac 1\varepsilon W(u)…
We simulate and discuss novel spatio-temporal propagation effects that relate specifically to pulsed, phase-mismatched second harmonic generation in a negative index material having finite length. Using a generic Drude model for the…
Gravitational waves from inspiralling binaries are expected to be detected using a data analysis technique known as {\it matched filtering.} This technique is applicable whenever the form of the signal is known accurately. Though we know…
We present models where $\gamma_+$ and $\gamma_-$, the exponents of the susceptibility in the high and low temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete…
We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the…
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…
A novel kind of irreversible phase transitions (IPT's) driven by an oscillatory input parameter is studied by means of computer simulations. Second order IPT's showing scale invariance in relevant dynamic critical properties are found to…
Second harmonic generation is considered in lossy negative-index metamaterials. It is shown that energy transfer from fundamental to harmonic takes place in the entire sample for the range of phase mismatch values. Note that in conventional…