Related papers: Pump and Probe nonlinear processes: new modified s…
The reliability of the approximations commonly adopted in the calculation of static optical (hyper)polarizabilities is tested against exact results obtained for an interesting toy-model. The model accounts for the principal features of…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…
Model-free adaptive optimization methods are capable of optimizing unknown, time-varying processes even when other optimization methods are not. However, their practical application is often limited by perturbations that are used to gather…
The scaling of the fundamental limits of the second hyperpolarizability is used to define the intrinsic second hyperpolarizability, which aids in identifying material classes with ultralarge nonlinear-optical response per unit of molecular…
A theoretical model is developed by exploiting the variational technique to investigate the evolution of an optical beam inside an optically pumped graded-index fiber amplifier. The variational analysis is a semi-analytical method that…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem…
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular…
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…
Advances in high-precision dielectric spectroscopy has enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest…
The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and…
The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between…
Modern hydraulic shock absorbers display a wealth of nonlinear effects such as hysteresis and instabilities at high flow rates. Despite their wide application in practically all vehicles, both on- and off-road, a universal analytical model…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
A theory of pump-probe spectroscopy is developed in which optical fields drive two-quantum, Raman-like transitions between ground state sublevels. Three fields are incident on an ensemble of atoms. Two of the fields act as the pump field…
We analyze the dynamics of a passive colloidal probe immersed in an active bath using an optical trap to study three physical processes: (1) the non-equilibrium fluctuations transferred to the probe by the active bath, (2) the friction…