To construct generalized Lorenz systems, higher-order modes in doubled Fourier expansions of a stream function and temperature variations must be considered. Selection of these modes is guided by the requirements that they conserve energy in the dissipationless limit and lead to systems that have bounded solutions. The previous study showed how to select the modes by using either vertical or ho...

We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity ν 1 in an infinite channel. Taylor observed in the 1950’s that, in such a setting, the tracer diffuses at a rate proportional to 1/ν, rather than the expected rate proportional to ν. We provide a mathematical explanation for this enhanced diffusion using a c...

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of...

The Fourier transform infrared (FTIR) and FT-Raman spectra of 4-methyl-1,3-dioxolan-2-one and 4,5-dichloro-1,3-dioxolan-2-one have been recorded in the range 3700-400 and 3700-100 cm(-1), respectively. The complete vibrational assignment and analysis of the fundamental modes of the compounds were carried out using the observed FTIR and FT-Raman data. The vibrational frequencies determined exper...

The transition from localized to delocalized plasmons (i.e. the transition from a situation where the decay length of a travelling surface plasma wave is greater than its propagation distance to a situation where it is smaller) and hence the onset of plasmon delocalization is studied in a single 2D silver nanoparticle of increasing length. A fourier analysis in the near-field of the nanoparticl...

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the ...

In addition to their inestimable importance in mathematics and its applications, Fourier series also serve as the entry point into the wonderful world of Fourier analysis and its wide-ranging extensions and generalizations. An entire industry is devoted to further developing the theory and enlarging the scope of applications of Fourier–inspired methods. New directions in Fourier analysis contin...

A variety of stationary and wave patterns that show a complicated spatial structure but are ordered in the Fourier space can be constructed by considering interaction of noncollinear modes near a symmetry breaking bifurcation point. The planform selection is particularly rich in the presence of resonant (phase-dependent) interactions among degenerate modes. We consider the problem of pattern se...

Static flux-closure structures in three-dimensional 3D mesoscopic ferromagnets are known to differ quite significantly from their 2D counterparts. How these differences reflect in the dynamic properties of the magnetization is, to date, an open question. Micromagnetic simulations are employed to study the normal modes of magnetic oscillations in thick 60–80 nm rectangular Permalloy prisms with ...

We present a general, rigorous, modal formalism for modeling light propagation and light emission in three-dimensional (3D) periodic waveguides and in aggregates of them. In essence, the formalism is a generalization of well-known modal concepts for translation-invariant waveguides to situations involving stacks of periodic waveguides. By surrounding the actual stack by perfectly-matched layers...