in this work, we dissect the performance of  two modern perdew-burke-ernzerhof (pbe)-based double-hybrid (dh) density functionals to predict the isotropic and anisotropic polarizabilities of water nanoclusters (h2o)n [n = 2-6]. the considered models include the cubic integrand (ci) and quadratic integrand (qi) functions as well as the spin-opposite-scaled (sos) scheme for perturbative correlati...

By using the geometric concept of PDEs with prescribed curvature representation, we prove that the 1+2 dimensional isotropic Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schrödinger-type system. From the nonlinear Schrödinger-type system, we construct blowing up H3(R2)-solutions to the Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.

We face a business need of discovering a pattern in locations of a great number of points in a high-dimensional space. We assume that there should be a certain structure, so that in some locations the points are close while in other locations the points are more dispersed. Our goal is to group the close points together. The process of grouping close objects is known under the name of clustering...

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the c...

The isotropic matroid M [IAS(G)] of a graph G is a binary matroid, which is equivalent to the isotropic system introduced by Bouchet. In this paper we discuss four notions of connectivity related to isotropic matroids and isotropic systems. We show that the isotropic system connectivity defined by Bouchet is equivalent to vertical connectivity of M [IAS(G)], and if G has at least four vertices,...

There is currently growing interest in small magnetic resonant structures. This interest has been spurred by the demonstration that specific subwavelength structures can exhibit effective magnetic permeability which can be tuned to negative values over a finite frequency range, and by the utilization of these structures to produce a left-handed medium ~LHM! in the microwave regime. Thus LHM has...

Theory of drift of spiral waves has been developed for isotropic and anisotropic plane and isotropic sphere. Here, we proceed to parts of the isotropic torus surface with no-flux boundary conditions and show how velocity components and drift coefficients depend on core position, grid size and local surface curvature.

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transiti...