WIND GENERATED EQUATORIAL GERSTNER-TYPE WAVES
A class of non-stationary surface gravity waves propagating in the
zonal direction in the equatorial region is described in the f -plane approx-
imation. These waves are described by exact solutions of the equations of
hydrodynamics in Lagrangian formulation and are generalizations of Gerstner
waves. The wave shape and non-uniform pressure distribution on a free sur-
face depend on two arbitrary functions. The trajectories of uid particles are
circumferences. The solutions admit a variable meridional current. The dy-
namics of a single breather on the background of a Gerstner wave is studied as
A nonlinear Schrцdinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously
vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function
of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is
shown that the modulational instability criteria for the weakly vortical waves and potential Stokes waves on
deep water coincide. The effect of vorticity manifests itself in a shift of the wavenumber of high-frequency filling.
A special case of Gerstner waves with a zero coefficient at the nonlinear term in the NSE is noted.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
We consider a fractional 0-1 programming problem arising in manufacturing. The problem consists in clustering of machines together with parts processed on these machines into manufacturing cells so that intra-cell processing of parts is maximized and inter-cell movement is minimized. This problem is called Cell Formation Problem (CFP) and it is an NP-hard optimization problem with Boolean variables and constraints and with a fractional objective function. Because of its high computational complexity there are a lot of heuristics developed for it. In this paper we suggest a branch and bound algorithm which provides exact solutions for the CFP with a variable number of cells and grouping efficacy objective function. This algorithm finds optimal solutions for 21 of the 35 popular benchmark instances from literature and for the remaining 14 instances it finds good solutions close to the best known.
Filtration describes a variety of the construction complex problems: strengthening loose soil to create a solid foundation, the movement of groundwater with solid impurities near underground structures, and many others. A model of two-sized deep bed filtration particles moving with different velocities in a porous medium with three-size pores is considered. The competition of pores and various size particles for deposit formation is modeled. Solutions are constructed at the porous medium inlet and on the concentrations front of the fast particles. For constant filtration coefficients, a global exact solution is obtained. Numerical calculation illustrates the evolution of the filtration process.
We present an analytical description of the class of unsteady vortex surface waves generated by non- uniformly distributed, time-harmonic pressure. The fluid motion is described by an exact solution of the equations of hydrodynamics generalizing the Gerstner solution. The trajectories of the fluid particles are circumferences. The particles on a free surface rotate around circumferences of the same radii, with the centers of the circumferences lying on different horizons. A family of waves has been found in which a variable pressure acts on a limited section of the free surface. The law of external pressure distribution includes an arbitrary function. An example of the evolution of a non-uniform wave packet is considered. The wave and pressure profiles, as well as vorticity distribution are studied. It is shown that, in the case of a uniform traveling wave of external pressure, the Gerstner solution is valid but with a different form of the dispersion relation. A possibility of observing the studied waves in laboratory and in the real ocean is discussed.
By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.