Fast inactivation in Shaker K+ channels. Properties of ionic and gating currents.

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as "charge immobilization" (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567-590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at -90 mV return potential changed from a single fast component to at least two components, the slower requiring approximately 200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at -120 and -90 mV. In contrast, at higher potentials (-70 and -50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of "parallel" inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH2-terminus region

Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects

A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required, but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids (i.e. water, air, gas etc.) in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to construct a flux difference splitting scheme in the dual time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling

Consideration of the Mechanisms for Tidal Bore Formation in an Idealized Planform Geometry

A tidal bore is a positive wave traveling upstream along the estuary of a river, generated by a relatively rapid rise of the tide, often enhanced by the funneling shape of the estuary. The swell produced by the tide grows and its front steepens as the flooding tide advances inland, promoting the formation of a sharp front wave, i.e., the tidal bore. Because of the many mechanisms and conditions involved in the process, it is difficult to formulate an effective criterion to predict the bore formation. In this preliminary analysis, aimed at bringing out the main processes and parameters that control tidal bore formation, the degrees of freedom of the problem are largely reduced by considering a rectangular channel of constant width with uniform flow, forced downstream by rising the water level at a constant rate. The framework used in this study is extremely simple, yet the problem is still complex and the solution is far from being trivial. From the results of numerical simulations, three distinctive behaviors emerged related to conditions in which a tidal bore forms, a tidal bore does not form, and a weak bore forms; the latter has a weakly steep front and after the bore formed it rapidly vanishes. Based on these behaviors, some criteria to predict the bore formation are proposed and discussed. The more effective criterion, suitably rearranged, is checked against data from real estuaries and the predictions are found to compare favorably with the available data

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

Three-dimensional Simulations of Accretion to Stars with Complex Magnetic Fields

Disk accretion to rotating stars with complex magnetic fields is investigated using full three-dimensional magnetohydrodynamic (MHD) simulations. The studied magnetic configurations include superpositions of misaligned dipole and quadrupole fields and off-centre dipoles. The simulations show that when the quadrupole component is comparable to the dipole component, the magnetic field has a complex structure with three major magnetic poles on the surface of the star and three sets of loops of field lines connecting them. A significant amount of matter flows to the quadrupole "belt", forming a ring-like hot spot on the star. If the maximum strength of the magnetic field on the star is fixed, then we observe that the mass accretion rate, the torque on the star, and the area covered by hot spots are several times smaller in the quadrupole-dominant cases than in the pure dipole cases. The influence of the quadrupole component on the shape of the hot spots becomes noticeable when the ratio of the quadrupole and dipole field strengths $B_q/B_d\gtrsim0.5$, and becomes dominant when $B_q/B_d\gtrsim1$. In the case of an off-centre dipole field, most of the matter flows through a one-armed accretion stream, forming a large hot spot on the surface, with a second much smaller secondary spot. The light curves may have simple, sinusoidal shapes, thus mimicking stars with pure dipole fields. Or, they may be complex and unusual. In some cases the light curves may be indicators of a complex field, in particular if the inclination angle is known independently. We also note that in the case of complex fields, magnetospheric gaps are often not empty, and this may be important for the survival of close-in exosolar planets.Comment: 13 pages, 21 figures, accepted for publication in MNRA

Quasinormal ringing of acoustic black holes in Laval nozzles: Numerical simulations

Quasinormal ringing of acoustic black holes in Laval nozzles is discussed. The equation for sounds in a transonic flow is written into a Schr\"{o}dinger-type equation with a potential barrier, and the quasinormal frequencies are calculated semianalytically. From the results of numerical simulations, it is shown that the quasinormal modes are actually excited when the transonic flow is formed or slightly perturbed, as well as in the real black hole case. In an actual experiment, however, the purely-outgoing boundary condition will not be satisfied at late times due to the wave reflection at the end of the apparatus, and a late-time ringing will be expressed as a superposition of "boxed" quasinormal modes. It is shown that the late-time ringing damps more slowly than the ordinary quasinormal ringing, while its central frequency is not greatly different from that of the ordinary one. Using this fact, an efficient way for experimentally detecting the quasinormal ringing of an acoustic black hole is discussed.Comment: 9 pages, 8 figures, accepted for publication in Physical Review

Multiscale lattice Boltzmann approach to modeling gas flows

For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost

Helicopter tail rotor thrust and main rotor wake coupling in crosswind flight

The tail rotor of a helicopter with a single main rotor configuration can experience a significant reduction in thrust when the aircraft operates in crosswind flight. Brown’s vorticity transport model has been used to simulate a main rotor and tail rotor system translating at a sideslip angle that causes the tail rotor to interact with the main rotor tip vortices as they propagate downstream at the lateral extremities of the wake. The tail rotor is shown to exhibit a distinct directionally dependent mode during which tail rotors that are configured so that the blades travel forward at the top of the disk develop less thrust than tail rotors with the reverse sense of rotation. The range of flight speeds over which this mode exists is shown to vary considerably with the vertical location of the tail rotor. At low flight speeds, the directionally dependent mode occurs because the tail rotor is immersed within not only the downwash from the main rotor but also the rotational flow associated with clusters of largely disorganized vorticity within the main rotor wake. At higher flight speeds, however, the tail rotor is immersed within a coherent supervortex that strongly influences the velocity field surrounding the tail rotor

Numerical and analytical study of an atherosclerosis inflammatory disease model

We study a reaction–diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction–diffusion system and lead to the complete characterisation of the ωω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical stud