Exact plasma wave solutions for isothermal electron fluid plasma

Quasistationary electron plasma waves of arbitrary amplitude and speed that are exact solutions of the isothermal electron fluid equations are shown to exist.     

Dynamic Studies on Kinetic H2/D2 Quantum Sieving in a Narrow Pore Metal–Organic Framework Grown on a Sensor Chip

The separation of deuterium from hydrogen still remains a challenging and industrially relevant task. Compared to traditional cryogenic methods for separation, based on different boiling points of H₂ and D₂, the use of ultramicroporous materials offers a more efficient alternative method. Due to their rigid structures, permanently high porosity, tunable pore sizes and adjustable internal surface properties, metal–organic frameworks (MOFs), a class of porous materials built through the coordination between organic linkers and metal ions/clusters, are more suitable for this approach than zeolites or carbon-based materials. Herein, dynamic gas flow studies on H₂/D₂ quantum sieving in MFU-4, a metal-organic framework with ultra-narrow pores of 2.5 Å, are presented. A specially designed sensor with a very fast response based on surface acoustic waves is used. On-chip measurements of diffusion rates in the temperature range 27–207 K reveal a quantum sieving effect, with D₂ diffusing faster than H₂ below 64 K and the opposite selectivity above this temperature. The experimental results obtained are confirmed by molecular dynamic simulation regarding quantum sieving of H₂ and D₂ on MOFs for which a flexible framework approach was used for the first time.     

On the linear and nonlinear characteristics of electrostatic solitary waves propagating in magnetized electron-positron-ion plasmas

Both linear and nonlinear propagation of electrostatic solitary waves (ESWs) in magnetized electron-positron-ion (e-p-i) plasmas are analyzed. The electrons and positrons are assumed to be dynamic, whereas positively charged ions are considered stationary. Using the reductive perturbation method, a Zakharov-Kuznetsov (ZK) equation is derived and exact soliton solutions are presented. It is found that both compressive and rarefactive ESWs can propagate. The conditions of transitions from compressive to rarefactive ESWs are specified. The nature of these electrostatic solitary waves structures which depends on the magnetic field, the obliqueness, the ion-to-electron number density ratio, and the positron-to-electron temperature ratio, are discussed.     

On the treatment of transient area variation in 1D discontinuous Galerkin simulations of train‐induced pressure waves in tunnels

To simulate the pressure wave generated by a train travelling through a tunnel, we implement a discontinuous Galerkin (DG) method for the solution of the one‐dimensional equations of variable area flow. This formulation uses a spatial discretisation via Legendre polynomials of arbitrary degree, and the resulting semi‐discrete system is integrated using an explicit Runge–Kutta scheme. A simulation of subsonic steady flow in a nozzle shows that the scheme produces stable solutions, without the need for artificial dissipation, and that its performance is optimal for polynomial degrees between 5 and 7. However, when dealing with an unsteady area, we report the presence of numerical oscillations that are not due to the steep pressure fronts in the flow but rather to the projection of a moving area, with piecewise continuous derivatives onto a fixed grid. We propose a reformulation of the DG method to eliminate these oscillations that, put in simple terms, amount to splitting the integrals where the derivatives of the cross‐sectional area are discontinuous into subintegrals where they are continuous. The resulting method does not exhibit oscillations, and it is applied here to two practical cases involving train‐induced pressure waves in a tunnel. The first application is a validation of the DG method through comparison of its computational results with pressure data measured during transit at the Patchway tunnel near Bristol (UK). The second application is a study of the influence of the nose shape and length on the pressure wave gradients responsible for sonic boom at tunnel exit portals to show that the proposed modification is able to deal with realistic train shapes. Copyright © 2012 John Wiley & Sons, Ltd.     

Angle-dependent spin wave spectra of permalloy ring arrays

We investigated the angle-dependent spin wave spectra of permalloy ring arrays with the fixed outer diameter and various inner diameters by ferromagnetic resonance spectroscopy and micromagnetic simulation. When the field is obliquely applied to the ring, local resonance mode can be observed in different parts of the rings. And the resonance mode will change to perpendicular spin standing waves if the magnetic field is applied along the perpendicular direction. The simulation results demonstrated this evolution and implied more resonance modes that maybe exist. And the mathematical fitting results based on the Kittel equation further proved the existence of local resonance mode.     

Finite volume methods for unidirectional dispersive wave models

We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM‐type equation. Explicit and implicit–explicit Runge–Kutta‐type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions. Copyright © 2012 John Wiley & Sons, Ltd.     

Regularity results and optimal control problems for the perturbation of boussinesq equations of the ocean

We study in this article a method which computes the variability of current, density and pressure in an oceanic domain. The equations are of Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the density. They are linearized around a given mean circulation and modified by the Boussinesq approximation: density variations are neglected except in the terms of gravity acceleration. The existence and uniqueness of a solution are proved for two sets of equations: first the three-dimensional problem and then the two-dimensional cyclic problem derived by assuming a sinusoidal x-dependence for the perturbation of mean flow. The latter corresponds to a modelization of tropical instability waves which are illustrated by the El Nino phenomenon.

The value of the pressure p on the surface of ocean is of great interest for physical interpretation. To define that quantity, it is necessary to have the regularity p ? H ¹. We have proved that the perturbation (u,ρ,p) of mean circulation is such that: u ? L ²(0T,H ²), ρ ? L ²(0,T H ²) and p ? L ² L ²(0,T H ¹), provided the perturbation of the windstress is sufficiently regular and satisfies compatibility relations. It is proved by means of an extension method, with even-odd reflection. We then develop a problem of control. The observation is the Variability of pressure on the surface of ocean. The control is the variability of windstress f, which acts as to forcing of the perturbation. We prove the existence and uniqueness of an optimal control, which is characterized by a set of equations including the direct problem and the adjoint problem. These results are valid for the three-dimensional problem and the two-dimensional cyclic problem.     

A high‐resolution scheme for compressible multicomponent flows with shock waves

A simple methodology for a high‐resolution scheme to be applied to compressible multicomponent flows with shock waves is investigated. The method is intended for use with direct numerical simulation or large eddy simulation of compressible multicomponent flows. The method dynamically adds non‐linear artificial diffusivity locally in space to capture different types of discontinuities such as a shock wave, contact surface or material interface while a high‐order compact differencing scheme resolves a broad range of scales in flows. The method is successfully applied to several one‐dimensional and two‐dimensional compressible multicomponent flow problems with shock waves. The results are in good agreement with experiments and earlier computations qualitatively and quantitatively. The method captures unsteady shock and material discontinuities without significant spurious oscillations if initial start‐up errors are properly avoided. Comparisons between the present numerical scheme and high‐order weighted essentially non‐oscillatory (WENO) schemes illustrate the advantage of the present method for resolving a broad range of scales of turbulence while capturing shock waves and material interfaces. Also the present method is expected to require less computational cost than popular high‐order upwind‐biased schemes such as WENO schemes. The mass conservation for each species is satisfied due to the strong conservation form of governing equations employed in the method. Copyright © 2010 John Wiley & Sons, Ltd.