On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…     

Charge transport across the metal–polymer film boundary

Thin polyaniline films were fabricated by thermal vacuum evaporation from a Knudsen effusion cell. The conducting properties of films synthesized under different evaporation conditions were studied. The enhancement of the emission capacity of a wolfram tip coated with a polyaniline film of a nanometer thickness was demonstrated experimentally. A model of the discovered effect was proposed. The obtained Fowler–Nordheim current–voltage characteristics were used to estimate the change in the electronic work function occurring when a thin film is deposited on the tip surface. The effective temperature of electrons emitted from the polyaniline film was determined based on the results of analysis of energy distributions, and the specific features of charge transport in the metal–polyaniline–vacuum system were examined. A model of energy bands of the metal–polymer film contact was also constructed.     

Fourier spectral embedded boundary solution of the Poisson’s and Laplace equations with Dirichlet boundary conditions

A Fourier spectral embedded boundary method, for solution of the Poisson’s equation with Dirichlet boundary conditions and arbitrary forcing functions (including zero forcing function), is presented in this paper. This iterative method begins by transformation of the Dirichlet boundary conditions from the physical boundaries to some corresponding regular grid points (which are called the numerical boundaries), using a second order interpolation method. Then the transformed boundary conditions and the forcing function are extended to a square, smoothly and periodically, via multiplying them by some suitable error functions. Instead of direct solution of the resulting extended Poisson’s problem, it is suggested to define and solve an equivalent transient diffusion problem on the regular domain, until achievement of the steady solution (which is considered as the solution of the original problem). Without need of any numerical time integration method, time advancement of the solution is obtained directly, from the exact solution of the transient problem in the Fourier space. Consequently, timestep sizes can be chosen without stability limitations, which it means higher rates of convergence in comparison with the classical relaxation methods. The method is presented in details for one- and two-dimensional problems, and a new emerged phenomenon (which is called the saturation state) is illustrated both in the physical and spectral spaces. The numerical experiments have been performed on the one- and two-dimensional irregular domains to show the accuracy of the method and its superiority (from the rate of convergence viewpoint) to the other classical relaxation methods. Capability of the method, in dealing with complex geometries, and in presence of discontinuity at the boundaries, has been shown via some numerical experiments on a four-leaf shape geometry.     

T-duality simplifies bulk–boundary correspondence: the noncommutative case

We state and prove a general result establishing that T-duality, or the Connes–Thom isomorphism, simplifies the bulk–boundary correspondence, given by a boundary map in K-theory, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to string theory and to the study of the quantum Hall effect and topological insulators with defects in condensed matter physics.     

The dominant deformation mechanism of nanocrystalline materials with the finest grains: grain boundary sliding or grain boundary migration?

We report an efficient room-temperature synthesis of Au nanoparticles (NPs) using carbon dots (C-dots) as mediator in poly(ethylene glycol). The synthesis does not require any irradiation or heating for the reduction of the metal precursor and it yields smaller sized particles of ~15 nm, mostly octahedron in shape. The effect of varying concentrations of the Au precursor and C-dots on the synthesis was studied, which demonstrated the variation in particle size and shape with change in either the precursor or C-dots concentration. Time-resolved absorbance study for the synthesis of Au NPs showed the sigmoidal behavior for the autocatalytic growth having the lagging phase of induction period. The optimum concentration of the precursor and the C-dots were determined for the synthesis of well-dispersed Au NPs. The stability of the prepared Au NPs was also determined, showing that at optimum concentration of the precursor and C-dots, the particles were stable and did not precipitate for several days.     

A novel derivation of the boundary term for the action in Lanczos–Lovelock gravity

We present a novel derivation of the boundary term for the action in Lanczos–Lovelock gravity, starting from the boundary contribution in the variation of the Lanczos–Lovelock action. The derivation presented here is straightforward, i.e., one starts from the Lanczos–Lovelock action principle and the action itself dictates the boundary structure and hence the boundary term one needs to add to the action to make it well-posed. It also gives the full structure of the contribution at the boundary of the complete action, enabling us to read off the degrees of freedom to be fixed at the boundary, their corresponding conjugate momenta and the total derivative contribution on the boundary. We also provide a separate derivation of the Gauss–Bonnet case.     

Influence of the glass-to-plasma boundary layers in a T-tube on the Hβ line profile

We have used a simple glass-to-plasma boundary layer (bl) model to evaluate the influence of bls on measured H_β line profiles emitted from a T-tube hydrogen plasma. Calculations were performed for a wide range of electron densities and temperatures. The results show that the calculated line profiles for temperatures of 3 × 10⁴ K and higher are significantly wider than they would be if the bls were absent. At the most frequently encountered temperatures of the T-tube plasmas (∽2 × 10⁴ K), the calculated profiles influenced by bls resemble theoretical profiles. No significant influence of the bls on the H_β central part was found, except when the optical thickness of the whole plasma becomes significant.     

Wada boundary bifurcations induced by boundary saddle–saddle collision

In this letter, a Wada boundary bifurcation (WBB) induced by a boundary saddle touching another boundary saddle is first found through the study of a forced damped pendulum. The WBB can be quantitatively described by the change both in the number of basins involved and in the geometrical size of the boundary. We perceive the manifold structures of the two saddles, that is, a pre-existence of heteroclinic crossing and the other nearly forming heteroclinic tangency exist before the WBB. So we schematically construct the equivalent topological structure of the manifolds of arbitrary two saddles, and rigorously prove two theorems that indicate the existence of the heteroclinic tangency and thus generically confirm the mechanism of such WBB.     

Stable Robin solid wall boundary conditions for the Navier–Stokes equations

In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.     

Absorbing boundary conditions for the Euler and Navier–Stokes equations with the spectral difference method

Two absorbing boundary conditions, the absorbing sponge zone and the perfectly matched layer, are developed and implemented for the spectral difference method discretizing the Euler and Navier–Stokes equations on unstructured grids. The performance of both boundary conditions is evaluated and compared with the characteristic boundary condition for a variety of benchmark problems including vortex and acoustic wave propagations. The applications of the perfectly matched layer technique in the numerical simulations of unsteady problems with complex geometries are also presented to demonstrate its capability.     

Spectrally-accurate algorithm for moving boundary problems for the Navier–Stokes equations

A spectral algorithm based on the immersed boundary conditions (IBC) concept is developed for simulations of viscous flows with moving boundaries. The algorithm uses a fixed computational domain with flow domain immersed inside the computational domain. Boundary conditions along the edges of the time-dependent flow domain enter the algorithm in the form of internal constraints. Spectral spatial discretization uses Fourier expansions in the stream-wise direction and Chebyshev expansions in the normal-to-the-wall direction. Up to fourth-order implicit temporal discretization methods have been implemented. It has been demonstrated that the algorithm delivers the theoretically predicted accuracy in both time and space. Performances of various linear solvers employed in the solution process have been evaluated and a new class of solver that takes advantage of the structure of the coefficient matrix has been proposed. The new solver results in a significant acceleration of computations as well as in a substantial reduction in memory requirements.     

Effect of element Re on the grain boundary cohesion of α-Fe

The effect of Re segregation on the α-Fe ∑5 [001] （010） grain boundary （GB） is investigated by using a software called DMol and discrete variational method （DVM）. Based on the Rice Wang model, the calculated segregation energy and defect formation energy show that Re is a strong cohesive enhancer. We also calculated the interatomic energy （IE） and bond order （BO） of several atomic pairs to investigate the mechanism of the cohesive effect of Re microscopically and locally. The results show that IEs of atomic pairs formed by those atoms which cross the plane of GB are strengthened due to the segregation of Re, while the BOs of the corresponding pairs are slightly decreased. This discrepancy demonstrates that IE which contains the Hamiltoniaa of interaction between atoms is a good quantity to describe the bonding strength. The analysis suggests that the electronic effect between atomic pair which comes directly from Hamiltonian is the key factor, The charge density is also presented, and the result indicates that the bonding strength between the Fe atoms on the GB is enhanced due to the segregation of Re, which is consistent with the analysis of IE.     

Generation of acoustic waves in the hypersonic boundary layer over a wavy wall

The effects of a wavy wall on a hypersonic boundary layer of a flared cone are investigated using experimental measurements and direct numerical simulations(DNSs). Non-contact optical measurements using a focused laser differential interferometer(FLDI) show that a wavy wall can significantly suppress the second mode, and multiple perturbations of new frequencies are generated over the wavy surface, which agrees well with numerical results. Using Lagrangian tracking of marked particles, it is demonstrated that the wavy wall geometry can induce mean flow oscillations while exciting acoustic waves. The frequencies of the excited disturbances over a wavy wall agree with the classical Rossiter model. The superposition of a disturbance propagating downstream and an acoustic wave propagating upstream at the same frequency but with different amplitudes and propagation velocities results in a spatial distribution with a streamwise-oscillatory pattern over the wavy surface. A simple two-wave superposition model that takes into account the phase velocities and wavenumbers of the convective disturbance and acoustic wave can well describe the modal behavior of excited disturbances over a wavy wall.     

Tight-binding calculations of the {211} Σ=3 boundary in diamond

The atomic and electronic structure of the {211} =3 boundary in diamond has been calculated by using the transferable tight-binding method. Several atomic models with symmetry consistent with the electron microscopy observation have been dealt with. The four-fold coordinated model is the most stable, although its interfacial energy is fairly high as compared with four-fold coordinated configurations in Si and other boundaries in diamond. Thus the models with three-fold coordinated sites may exist partially as defects. The electron energy-loss spectra of this boundary have been calculated by the tight-binding method for the first time. The K-edge spectra of the models with three-fold coordinated sites have small peaks below the bulk conduction-band peak caused by unoccupied gap states. These can explain the increases at the position of the * peak below the * peak in the observed spectra of this boundary.     

Influence of uniform momentum zones on frictional drag within the turbulent boundary layer

Based on a set of experimental databases of turbulent boundary layers obtained from particle image velocimetry in the streamwise-wall-normal plane at friction-velocity-based Reynolds number Reτ=612,the influence of uniform momentum zones(UMZs)on the skin-friction drag is investigated.The skin-friction drag is measured by the single-pixel ensemble correlation method.The results show that the velocity fields with the number of UMZs larger than the mean value have a relatively low skin-friction drag,while the velocity fields with the number of UMZs less than the mean value have a relatively high skin-friction drag.By analyzing the statistical characteristics of UMZs,the dynamic correlation between the UMZs and skin-friction drag is explored.The velocity fields with a low number of UMZs present a sweep event.These sweep motions intensify the small-scale Reynolds shear stress in the near-wall region by modulation effects.The enhancement of small-scale Reynolds shear stress is the direct reason for the high skin-friction drag.Increasing the proportion of velocity fields with high UMZs amount may be a direction to reduce the skin-friction drag within the TBL.     

Fermi surface changes across the Néel phase boundary of NdB6

We report de Haas-van Alphen measurements in both the antiferromagetic and paramagnetic regimes of NdB6, which are shown to be separated by a second order upper critical field for antiferromagnetic ordering of H_{c} approximately 30 T when the magnetic field is parallel to [001]. The Fermi surface changes across the transition provide an ideal example of a system in which the effect of a one-dimensional magnetic periodic potential on doubling the unit cell (as originally predicted by Slater [Phys. Rev. 82, 538 (1951)]) can be tuned by varying only the magnetic field. The Fermi surface within the paramagnetic phase resembles that observed in other hexaborides such as LaB6 but with additional exchange splitting effects and weak correlations.