Conservative arbitrary order finite difference schemes for shallow-water flows

AbstractThe classical nonlinear shallow-water model (SWM) of an ideal fluid is considered. For the model, a new method for the construction of mass and total energy conserving finite difference schemes is suggested. In fact, it produces an infinite family of finite difference schemes, which are either linear or nonlinear depending on the choice of certain parameters. The developed schemes can be applied in a variety of domains on the plane and on the sphere. The method essentially involves splitting of the model operator by geometric coordinates and by physical processes, which provides substantial benefits in the computational cost of solution. Besides, in case of the whole sphere it allows applying the same algorithms as in a doubly periodic domain on the plane and constructing finite difference schemes of arbitrary approximation order in space. Results of numerical experiments illustrate the skillfulness of the schemes in describing the shallow-water dynamics

Hexa-μ-chlorido-hexa­chlorido(η6-hexa­methyl­benzene)trialuminium(III)lanthanum(III) benzene solvate

In the title compound, [Al3LaCl12(C12H18)]·C6H6, all mol­ecules are located on a mirror plane. Three chloridoaluminate groups and a hexa­methyl­benzene mol­ecule are bound to the central lanthanum(III) ion, forming a distorted penta­gonal bipyramid with the η6-coordinated arene located at the apical position. The hexa­methyl­benzene ligand disordered between two orientations in a 1:1 ratio is also involved in parallel-slipped π–π stacking inter­molecular inter­actions with a benzene solvent mol­ecule [centroid–centroid distance 3.612 (4) Å]

Spatial asymmetry of optically excited spin waves in anisotropic ferromagnetic film

We analytically discuss and micromagnetically prove the ways to tune the spatial asymmetry of the initial phase, amplitude, and wavevectors of magnetostatic waves driven by ultrafast laser excitation. We consider that the optical pulse heats a thin ferromagnetic metallic film and abruptly decreases the saturation magnetization and the parameter of uniaxial anisotropy. The two corresponding terms of laser-induced torque have different azimuthal symmetries, with the 4-fold symmetry of the demagnetization-related term, and the isotropic distribution of the anisotropy-related term. As a result, the initial phase and amplitude of excited magnetostatic waves have a non-trivial azimuthal distribution tunable with the angle between the external magnetic field and anisotropy axis, and the laser spot diameter. Moreover, the variation of these parameters tunes the distribution of wavevectors, resulting in additional asymmetry between the spectral components of the waves propagating in different directions.Comment: 8 pages, 5 figure

Resting Potential–dependent Regulation of the Voltage Sensitivity of Sodium Channel Gating in Rat Skeletal Muscle In Vivo

Normal muscle has a resting potential of −85 mV, but in a number of situations there is depolarization of the resting potential that alters excitability. To better understand the effect of resting potential on muscle excitability we attempted to accurately simulate excitability at both normal and depolarized resting potentials. To accurately simulate excitability we found that it was necessary to include a resting potential–dependent shift in the voltage dependence of sodium channel activation and fast inactivation. We recorded sodium currents from muscle fibers in vivo and found that prolonged changes in holding potential cause shifts in the voltage dependence of both activation and fast inactivation of sodium currents. We also found that altering the amplitude of the prepulse or test pulse produced differences in the voltage dependence of activation and inactivation respectively. Since only the Nav1.4 sodium channel isoform is present in significant quantity in adult skeletal muscle, this suggests that either there are multiple states of Nav1.4 that differ in their voltage dependence of gating or there is a distribution in the voltage dependence of gating of Nav1.4. Taken together, our data suggest that changes in resting potential toward more positive potentials favor states of Nav1.4 with depolarized voltage dependence of gating and thus shift voltage dependence of the sodium current. We propose that resting potential–induced shifts in the voltage dependence of sodium channel gating are essential to properly regulate muscle excitability in vivo

Prevention of ecological safety by waste neutralization

Проанализирована ситуация, сложившаяся в мире вследствие активного действия вируса H5N1. Определен дополнительный источник заражения птичьим гриппом – технологические отстойники птицефабрик. Даны технические и технологические предложения по переработке материала отстойников, позволяющие снизить риск возникновения эпидемии и получить биотопливо.Проаналізована ситуація, що склалася у світі в наслідок активної дії вірусу H5N1. Визначено додаткове джерело зараження пташиним грипом – технологічні відстійники птахофабрик. Надані технічні та технологічні пропозиції переробки матеріалу відстійників, що дозволяють знищити різні появи епідемії та отримати біопаливо