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{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in…
A detailed qualitative analysis and numerical modeling of the evolution of cosmological models based on nonlinear classical and phantom scalar fields with self-action are performed. Complete phase portraits of the corresponding dynamical…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
A magnetometric technique is demonstrated that may be suitable for precision measurements of fields ranging from the sub-microgauss level to above the Earth field. It is based on resonant nonlinear magneto-optical rotation caused by atoms…
Nonlinear optical effects in vacuum have been investigated as a means to verify quantum electrodynamics in a region of low photon energy. By considering nonlinear electromagnetic waves in a three-dimensional cylindrical cavity, we report…
Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
We explore a subtle and fundamental nature of spin-orbit interaction (SOI) in a general paraxial beam-field by mathematically characterizing the orbital angular momentum (OAM) flux densities of the spin-polarized component fields via…
We propose and demonstrate theoretically a method to achieve and design optical nonlinear responses through a light-mediated spatial hybridization of different standard nonlinearities. The mechanism is based on the fact that optical…
A self-consistent semi-analytical theory of beam loading in inhomogeneous accelerating structures based on the generalized theory of coupled modes is proposed. A single-mode approximation was used when the fields are represented as a sum of…
We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the…
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…
The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…
We derive the key expressions to robustly address the eigenfunction expansion-based analysis of electromagnetic (EM) fields produced by current sources within planar non-birefringent anisotropic medium (NBAM) layers. In NBAM, the highly…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
We investigate the dynamics of multi-lump waves in a new version of a generalized spatial-symmetric higher-dimensional nonlinear dispersive water wave model using an analytical approach. This involves the proposition of a new…
We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space.…
The measurement of an electromagnetic radiation field by a linearly accelerated observer is discussed. The nonlocality of this process is emphasized. The nonlocal theory of accelerated observers is briefly described and the consequences of…