Related papers: A Fitting Formula for the Non-Linear Evolution of …
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are…
Following an elegant approach that merge the effects of the stringy spacetime uncertainty relation into primordial perturbations suggested by Brandenberger and Ho, we show the mode equation up to the first order of non-commutative…
We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…
Multiscale modelling methodologies build macroscale models of materials with complicated fine microscale structure. We propose a methodology to derive boundary conditions for the macroscale model of a prototypical non-linear heat exchanger.…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
I present a specific worked example of evolution through inflation to the initial conditions for an isocurvature CDM model for structure formation. The model invokes three scalar fields, one that drives power law inflation, one that…
We present nonlinear (NL) and higher twist (HT) corrections to the color dipole model (CDM) bounds at low values of $x$ and $Q^{2}$ using the parameterization method. Consistency between the bounds at this region describe that a transition…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…
In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear…
This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
A systematic study of the nonlinear response of Silicon Photomultipliers (SiPMs) has been conducted through Monte Carlo simulations. SiPMs have been proven to show a universal nonlinear response when it is expressed in terms of relative…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
We introduce an emulator approach to predict the non-linear matter power spectrum for broad classes of beyond-$\Lambda$CDM cosmologies, using only a suite of $\Lambda$CDM $N$-body simulations. By including a range of suitably modified…
We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another…