On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions

Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.     

The inertial dynamics of thin film flow of non-Newtonian fluids

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case where the viscosity depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a relatively large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible foundation for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids when the flow is not creeping.     

The incompressible Navier–Stokes equations from black hole membrane dynamics

We consider the dynamics of a d+1 space–time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de Sitter space–time and show that it is described by the d-dimensional incompressible Navier–Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier–Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.     

Wire coating by withdrawal from a bath of fourth order fluid

This Letter looks an analysis for withdrawal of cylinder. The flow depends upon the wire velocity. The fluid considered is a fourth order fluid. The problem is modeled using cylindrical coordinates for velocity and pressure distributions. The solution of the governing equation is obtained using homotopy analysis method (HAM). The variations of the velocity, volume flow rate, radius of coated wire, shear stress and force on the total wire are presented graphically and discussed for emerging non-Newtonian parameter.     

Formation of the preheated zone ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation transition

The Letter presents analytical, numerical and experimental studies of the mechanism underlying the deflagration-to-detonation transition (DDT). Insight into how, when, and where DDT occurs is obtained by analyzing analytically and by means of multidimensional numerical simulations dynamics of a flame accelerating in a tube with no-slip walls. It is shown that the deflagration-to-detonation transition exhibits three separate stages of evolution corroborating majority experimental observations. During the first stage flame accelerates and generates shocks far ahead of the flame front. During the second stage the flame slows down, shocks are formed in the immediate proximity of the flame front and the preheated zone ahead of the flame front is created. The third stage is self-restructuring of the steep temperature profile within the flame, formation of a reactivity gradient and the actual formation of the detonation wave itself. The mechanism for the detonation wave formation, given an appropriate formation of the preheated zone, seems to be universal and involves a reactivity gradient formed from the initially steep flame temperature profile in the presence of the preheated zone. The developed theory and numerical simulations are found to be well consistent with extensive experiments of the DDT in hydrogen-oxygen and ethylene-oxygen mixtures in tubes with smooth and rough walls.     

On isoperimetric surfaces in general relativity,II

We determine the optimal way to enclose volume in a class of domains inside certain Friedmann–Robertson–Walker metrics. The method employed is an adaptation of the Bray–Morgan isoperimetric comparison procedure to the Lorentzian setting. We also make some remarks on isoperimetric comparison in the Riemannian setting, for rotationally-symmetric space-like slices in non-vacuum space-times.     

On one-eighth law in unforced two-dimensional turbulence

We critically revisit the various attempts to prove one-eighth law in two-dimensional (2D) turbulence and reconcile them. Herein, the one-eighth law has been proved for unforced 2D incompressible high Reynolds number turbulence. An exact expression of the time derivative of two-point second order velocity correlation function is also derived for the enstrophy cascade dominated regime.     

Vortex fields and the Lamb-Stokes dissipation relation of fluid dynamics

Energy dissipation in Newtonian fluids containing a unified vortex field is shown to depend on , where η, ? and ζ=u×? are viscosity, vorticity and swirl. This term augments viscous dissipation where stream tube geometry is curved, e.g., in turbulent or helical flows.     

On geometric approach to Lie symmetries of differential-difference equations

Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach.     

Relativistic particles and the geometry of 4-D null curves

We study actions in (d+1)$(d+1)$-dimensions associated with null curves, mainly when d=3$d=3$, whose Lagrangian is a linear function on the curvature of the particle path, showing that null helices are always possible trajectories of the particles. We find Killing vector fields along critical curves of the action which correspond to the linear and the angular momenta of the particle. They provide two constants of the motion which can be interpreted in terms of the mass and the spin of the system. Moreover, we are able to integrate both the Euler–Lagrange equations and the Cartan equations in cylindrical coordinates around a certain plane.     

On the supersymmetric limit of Kerr-NUT-AdS metrics

Generalizing the scaling limit of Martelli and Sparks [D. Martelli, J. Sparks, Phys. Lett. B 621 (2005) 208, hep-th/0505027] into an arbitrary number of spacetime dimensions we re-obtain the (most general explicitly known) Einstein–Sasaki spaces constructed by Chen et al. [W. Chen, H. Lü, C.N. Pope, Class. Quantum Grav. 23 (2006) 5323, hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical meaning which links together the principal conformal Killing–Yano tensor of the original Kerr-NUT-(A)dS spacetime, the Kähler 2-form of the resulting Einstein–Kähler base, and the Sasakian 1-form of the final Einstein–Sasaki space. The obtained Einstein–Sasaki space possesses the tower of Killing–Yano tensors of increasing rank—underlined by the existence of Killing spinors. A similar tower of hidden symmetries is observed in the original (odd-dimensional) Kerr-NUT-(A)dS spacetime. This rises an interesting question whether also these symmetries can be related to the existence of some ‘generalized’ Killing spinor.     

On the geometrical representation of the Jacobian in the path integral reduction problem

By using the formula for the scalar curvature of the manifold with the Kaluza-Klein metric we obtain the geometrical representation of the Jacobian resulted from the path integral reduction problem in Wiener path integrals for a scalar particle on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie group.     

Hydrodynamic screening and axisymmetric turbulence in the transient sedimentation of a dilute suspension at small Reynolds number

A theory of settling of a dilute suspension of identical spherical particles in a viscous incompressible fluid is developed on the basis of the equations of transient Stokesian dynamics. The equations describe hydrodynamic interactions between particles moving under the influence of a constant force, starting to act at a particular instant of time. For a dilute suspension, a monopole approximation can be used. It is argued that the growth of velocity fluctuations is bounded by a combination of two effects, destructive interference of the flow patterns of individual particles, and a rearrangement of particle positions leading to a time-dependent microstructure of the suspension. After a long time, the microstructure tends to a steady state. The corresponding structure factor is described phenomenologically. The corresponding pair correlation function and the velocity correlation functions describing axisymmetric turbulence on the length scale of the mean distance between particles are evaluated.     

Integrable motion of a vortex dipole in an axisymmetric flow

The evolution of a self-propelling vortex dipole, embedded in an external nondivergent flow with constant potential vorticity, is studied in an equivalent-barotropic model commonly used in geophysical, astrophysical and plasma studies. In addition to the conservation of the Hamiltonian for an arbitrary point vortex dipole, it is found that the angular momentum is also conserved when the external flow is axisymmetric. This reduces the original four degrees of freedom to only two, so that the solution is expressed in quadratures. In particular, the scattering of antisymmetric dipoles approaching from the infinity is analyzed in the presence of an axisymmetric oceanic flow typical for the vicinity of isolated seamounts.     

The exact behavior of electromagnetic Faraday rotation in crossing a gravitational sandwich wave in general relativity

We have analyzed the exact behavior of the polarization vector of a linearly polarized electromagnetic shock wave upon crossing a gravitational sandwich wave, by using Einstein's theory of general relativity. The Faraday rotation in the polarization vector of the electromagnetic field is induced in this nonlinear process. We show that the Faraday's angle highly depends on the electromagnetic parameter, gravitational parameter and the width of the gravitational sandwich wave.     

Essence of Inviscid Shear Instability: a Point View of Vortex Dynamics

The essence of shear instability is reviewed both mathematically and physically, which extends the instability theory of a sheet vortex from the viewpoint of vortex dynamics. For this, the Kelvin-Arnol＇d theorem is retrieved in linear context, i.e., the stable flow minimizes the kinetic energy associated with vorticity. Then the mechanism of shear instability is explored by combining the mechanisms of both Kelvin Helmholtz instability （K-H instability） and resonance of waves. The waves, which have the same phase speed with the concentrated vortex, have interactions with the vortex to trigger the instability. The physical explanation of shear instability is also sketched by extending Batchelor＇s theory. These results should lead to a more comprehensive understanding on shear instabilities.     

Fractal Analysis of Surface Roughness of Particles in Porous Media

A fractal dimension for roughness height （RH） is introduced to characterize the degree of roughness or disorder of particle surface characters which significantly influence physical-chimerical processes in porous media. An analytical expression for the fractal dimension of RH on statistically self-similar fractal surfaces is derived and is expressed as a function of roughness parameters. The specific surface area （SSA） of porous materials with spherical particles is also derived, and the proposed fractal model for the SSA of particles with rough surfaces is expressed as a function of fractal dimension for RH and fractal dimension for particle size distribution, relative roughness of particle surface, and ratio of the minimum to the maximum particle diameters of spherical particles.     

Geometric Property of the Faddeev Model

Two functions u and v are used in expressing the solutions of the Faddeev model. The geometric property of the surface S determined by u and v is discussed and the shape of the surface is demonstrated as an example. The Gaussian curvature of the surface S is negative.