Related papers: Higher order non-linear parameters with PLANCK
We calculate higher-order quantum contributions in different Lorentz-violating parameters to the gauge sector of the extended QED. As a result of this one-loop calculation, some terms which do not produce first-order corrections, contribute…
Higher-order tree-level processes in strong laser fields, i.e. cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e. nonlinear Compton…
In the well known logistic map, the parameter of interest is weighted by a coefficient that decreases linearly when this parameter increases. Since such a linear decrease forms a specific case, we consider the more general case where this…
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group…
We analyze the structure of higher-order radiative corrections for processes with unstable particles. By subsequently integrating out the various scales that are induced by the presence of unstable particles we obtain a hierarchy of…
Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…
The non-equilibrium two loop self-energy is reexamined in the framework of a scalar quark and gluon model, with specific attention to terms which do not give rise to the standard two -> two particle collisional terms in the semi-classical…
We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often…
This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional…
Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…
The complexity of modern control systems necessitates architectures that achieve high performance while ensuring robust stability, particularly for nonlinear systems. In this work, we tackle the challenge of designing output-feedback…
The effects of small relativistic corrections to the off-resonant polarizability, hyperpolarizability, and second hyperpolarizability are investigated. Corrections to linear and nonlinear optical coefficients are demonstrated in the…
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
We show that the higher moments of the evolution obtained from the Modified Leading Logarithm Approximation may be regarded as spurious higher order terms in perturbation theory, and that neglecting them leads to a good description of the…
In nonlinear systems analysis, minor fractions of higher-order dynamics are often neglected for simplicity. Here, we show that machine epsilon levels of parasitic higher-order dynamics due to computer roundoff alone can cause divergence of…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are…
This paper addresses nonlinearity in reset elements and their effects. Reset elements are known for having less phase lag compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This…