A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Interleaved winding and suppression of natural frequencies

Ideally, it is desirable to design and manufacture a transformer winding that can render all its internal resonances non-excitable. This study examines the effectiveness of an interleaved winding in achieving this goal. While investigating its effectiveness, it led to the establishment of a much desired theoretical basis that reinforces the reasons put forward in the literature to explain internal insulation failures observed in interleaved windings used in extra high voltage (EHV) transformers. Numerical calculations along with experimental verification on actual transformer windings are presented. This study reveals that most of the natural frequencies that are normally non-excitable in the line and neutral current responses of an interleaved winding have been rendered excitable in the disk-to-disk voltages, thus, providing favourable conditions for insulation overstress because of resonant overvoltages. Prevalence of such a condition is an inherent characteristic of interleaved windings.

Observation of Enhanced Diffusivity in Magnetically Powered Reciprocal Swimmers

We report on the development of a system of micron-sized reciprocal swimmers that can be powered with small homogeneous magnetic fields, and whose motion resembles that of a helical flagellum moving back and forth. We have measured the diffusivities of the swimmers to be higher compared to nonactuated objects of identical dimensions at long time scales, in accordance with the theoretical predictions made by Lauga Phys. Rev. Lett. 106, 178101 (2011)]. Randomness in the reciprocity of the actuation strokes was found to have a strong influence on the enhancement of the diffusivity, which has been investigated with numerical calculations.

Adiabatic Eigenfunction Based Approach to Coherent Transfer: Application to the Fenna-Matthews-Olson (FMO) Complex and the Role of Correlations in the Efficiency of Energy Transfer

We have recently suggested a method (Pallavi Bhattacharyya and K. L. Sebastian, Physical Review E 2013, 87, 062712) for the analysis of coherence in finite-level systems that are coupled to the surroundings and used it to study the process of energy transfer in the Fenna-Matthews-Olson (FMO) complex. The method makes use of adiabatic eigenstates of the Hamiltonian, with a subsequent transformation of the Hamiltonian into a form where the terms responsible for decoherence and population relaxation could be separated out at the lowest order. Thus one can account for decoherence nonperturbatively, and a Markovian type of master equation could be used for evaluating the population relaxation. In this paper, we apply this method to a two-level system as well as to a seven-level system. Comparisons with exact numerical results show that the method works quite well and is in good agreement with numerical calculations. The technique can be applied with ease to systems with larger numbers of levels as well. We also investigate how the presence of correlations among the bath degrees of freedom of the different bacteriochlorophyll a molecules of the FMO Complex affect the rate of energy transfer. Surprisingly, in the cases that we studied, our calculations suggest that the presence of anticorrelations, in contrast to correlations, make the excitation transfer more facile.

Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density rho, viscosity eta, relaxation time lambda, and retardation time beta lambda flowing past a linear elastic solid medium of thickness HR, density rho, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re c which scales as Sigma(3/4), where Reynolds number Re = rho VR/eta, V is the top-plate velocity, and dimensionless parameter Sigma = rho GR(2)/eta(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re-c similar to Sigma(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in beta-H parametric space, corresponding to very dilute polymer solution (0.9 less than or similar to beta < 1) and thin solids (H less than or similar to 1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

A new model for the energy release rate of fibre/matrix interfacial fracture

On the basis of the well-known shear-lag analysis of fibre/matrix interface stresses and the assumption of identical axial strains in the fibre and matrix, a new model for predicting the energy release rate of interfacial fracture of the fibre pull-out test model is attempted. The expressions for stresses in the fibre, matrix and interface are derived. The formula for interfacial debonding energy release rate is given. Numerical calculations are conducted and the results obtained are compared with those of the existing models.

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

A finite element method for cracked components of structures

In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.

Cross-relaxation dynamics on anomalous saturation processes in low pressure supersonic cw HF chemical laser amplifier

It is assumed that both translational and rotational nonequilibrium cross-relaxations play a role simultaneoulsy in low pressure supersonic cw HF chemical laser amplifier. For two-type models of gas flow medium with laminar and turbulent flow diffusion mixing, the expressions of saturated gain spectrum are derived respectively, and the numerical calculations are performed as well. The numerical results show that turbulent flow diffusion mixing model is in the best agreement with the experimental result.

The mechanism of energy storage by shearing the solar magnetic field

In this paper, a complete set of MHD equations have been solved by numerical calculations in an attempt to study the dynamical evolutionary processes of the initial equilibrium configuration and to discuss the energy storage mechanism of the solar atmosphere by shearing the magnetic field. The initial equilibrium configuration with an arch bipolar potential field obtained from the numerical solution is similar to the configuration in the vicinity of typical solar flare before its eruption. From the magnetic induction equation in the set of MHD equations and dealing with the non-linear coupling effects between the flow field and magnetic field, the quantitative relationship has been derived for their dynamical evolution. Results show that plasma shear motion at the bottom of the solar atmosphere causes the magnetic field to shear; meanwhile the magnetic field energy is stored in local regions. With the increase of time the local magnetic energy increases and it may reach an order of 4×10^25 J during a day. Thus the local storage of magnetic energy is large enough to trigger a big solar flare and can be considered as the energy source of solar flares. The energy storage mechanism by shearing the magnetic field can well explain the slow changes in solar active regions.

Steady axi-symmetrical thermocapillary motion of a short melting column

This paper deals with the steady axi-symmetric thermo-capillary motion in a short meltingcolumn.with the assumptions that the Marangoni number M<<1, the Reynolds number Re<<1 andthe capillary number C<<1, at the leading order, the solutions of the problem are obtained inthe form of series. For two kinds of typical cases, symmetric and anti-symmetric distributionof air temperature, the numerical calculations are made. The results describe the effect ofendwalls on thermo-capillary flow.

Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet

In this paper, the role of vertical component of Surface tension of a droplet on the elastic deformation of a finite-thickness flexible membrane was theoretically analyzed using Hankel transformation. The vertical displacement at the Surface was derived and can be reduced to Lester's or Rusanov's solutions when the thickness is infinite. Moreover, some Simulations of the effect of a liquid droplet on a membrane with a finite thickness were made. The numerical results showed that there exists a saturated membrane thickness of the order of millimeter, when the thickness of a membrane is larger than such a value, the membrane can be regarded as a half-infinite body. Further numerical calculations for soft membrane whose thickness is far below the saturated thickness were made. By comparison between the maximum vertical displacement of an ultrathin soft membrane and a half-infinite body, we found that Lester's or Rusanov's solutions for a half-infinite body cannot correctly describe Such cases. In other words, the thickness of a soft membrane has great effect on the surface deformation of the ultrathin membrane induced by a liquid droplet. (C) 2009 Elsevier Inc. All rights reserved.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

Observational and theoretical advances in cosmological foreground emission

Observational and theoretical work towards the separation of foreground emission from the cosmic microwave background is described. The bulk of this work is in the design, construction, and commissioning of the C-Band All-Sky Survey (C-BASS), an experiment to produce a template of the Milky Way Galaxy's polarized synchrotron emission. Theoretical work is the derivation of an analytical approximation to the emission spectrum of spinning dust grains.

The performance of the C-BASS experiment is demonstrated through a preliminary, deep survey of the North Celestial Pole region. A comparison to multiwavelength data is performed, and the thermal and systematic noise properties of the experiment are explored. The systematic noise has been minimized through careful data processing algorithms, implemented both in the experiment's Field Programmable Gate Array (FPGA) based digital backend and in the data analysis pipeline. Detailed descriptions of these algorithms are presented.

The analytical function of spinning dust emission is derived through the application of careful approximations, with each step tested against numerical calculations. This work is intended for use in the parameterized separation of cosmological foreground components and as a framework for interpreting and comparing the variety of anomalous microwave emission observations.

正弦变化的振幅型光瞳滤波器

光瞳滤波器作为实现超分辨的基本元件之一，它的设计以及制作都非常重要。设计了一种正弦变化的振幅型光瞳滤波器，可以通过调节少量的参量实现各种不同的超分辨模式。选择正弦函数的周期以及光瞳中心点透过率变化两个参量来实现对最终超分辨效果的调节。数值计算结果表明：在整个人射光瞳上的透过率瞳函数分布具有0．5～2个正弦振幅周期时，较为合适。小于0．5个周期将不会有任何超分辨效果，大于2个周期超分辨效果反而变差。数值计算中还注意到，当周期数为整数时，斯特雷尔比将保持0．25不变。对正弦变化振幅型光瞳滤波器的计算结果，显示