Related papers: Nonlinear response theory for Markov processes II:…
Hopping parameter expansions are convergent power series. Under general conditions they allow for the quantitative investigation of phase transition and critical behaviour. The critical information is encoded in the high order coefficients.…
We study the third-order nonlinear optical susceptibility $\chi^{(3)}$ and photoexcited states of two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the…
The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtained numerically. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary…
We study in this paper the problem of adaptive trajectory tracking control for a class of nonlinear systems with parametric uncertainties. We propose to use a modular approach, where we first design a robust nonlinear state feedback which…
We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…
Nonresonant Hopf-Hopf singularity in neutral functional differential equation (NFDE) is considered. An algorithm for calculating the third-order normal form is established by using the formal adjoint theory, center manifold theorem and the…
We investigate the process of the second harmonic generation by plasmonic nano-antennas that exhibit Fano-like resonances. A rigorous fully vectorial Maxwell-hydrodynamics approach is employed to directly calculate the second order…
We study the nonequilibrium dynamics of an ultracold, non-degenerate dipolar gas of $^{164}$Dy atoms in a cylindrically symmetric harmonic trap. To do so, we investigate the normal modes and linear response of the gas when driven by means…
Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…
For the hopping dynamics in a one-dimensional model, containing energy and barrier disorder, we determine the linear and nonlinear response to an external field for arbitrary external frequencies. The calculation is performed in analytical…
This work presents an illustrative application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci (2015) to a paradigm nonlinear heat conduction benchmark, which models a conceptual experimental test…
In this paper, a concurrent learning based adaptive observer is developed for a class of second-order nonlinear time-invariant systems with uncertain dynamics. The developed technique results in simultaneous online state and parameter…
We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection…
This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a…
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…
The second order optical response of centrosymmetric materials manifests itself mostly at their surface, being strongly suppressed in their bulk. However, the overall surface response is also suppressed in nanoparticles with a…
Following our earlier work we argue in detail for the equivalence of the nonlinear $\sigma$ model with Hopf term at~$\theta=\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\sigma$ model and show the…
Multiparameter quantum estimation becomes challenging when the parameters are incompatible, i.e., when their respective symmetric logarithmic derivatives do not commute, or when the model is sloppy, meaning that the quantum probe depends…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…