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We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
We propose simple analytic, non-orthogonal but selectively orthogonalizable, generalized Laguerre type atomic orbitals, providing clear physical interpretation and near equivalent accuracy with numerical multi-configuration self-consistent…
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
We investigate the orbital structure of a model triaxial star cluster, centered around a supermassive black hole (BH), appropriate to galactic nuclei. Sridhar and Touma (1999) proved that the presence of the BH enforces some regularity in…
Recent years have seen the discovery of many tidal streams through the Galaxy. Relatively straightforward observations of a stream allow one to deduce three phase-space coordinates of an orbit. An algorithm is presented that reconstructs…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
There are investigated the Lie algebraic structure and integrability properties of a very interesting class of nonlinear dynamical systems called the heavenly equations, which were initiated by Pleba\'nski and later analyzed in a series of…
We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical…
We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction…
Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals…
We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating…
We investigate the phase-space structure of the quintom paradigm in the framework of a spatially flat, open, or closed isotropic and homogeneous universe. We examine the dynamical evolution under the assumption of late-time dark energy…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
We derive some local properties of abstract crystals with logarithmic poles over a smooth base in positive characteristic and obtain the existence of the canonical coordinates of certain ordinary crystals. We then apply the results to…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
An analytical expression of a Floquet operator, which describes the evolution of a wave packet in combined atomic and an intense laser field,is obtained approximately in the stabilization regime. Both the classical and quantum versions of…