Critical behavior of sandpile vortices under variable charge

In the following, we consider a sandpile cellular automaton model (height version), which also takes account of lattice cyclicity for variable charge of grains projected upon the board. The size of the charge or additional grains of sand used to upset the equilibrium and to induce an avalanche is found to affect the distributional forms and in particular the convergence of the estimate for the dynamic exponent. Exponent estimates show slow variation with lattice dimensionL and some evidence of evolution with charge. The scaling region is limited in all cases with noisy decay at all levels of charge. Results presented extend the work of Duarte and Goncalves (1990) on the triangular lattice.     

A note on vortex solutions of Landau–Lifshitz equation

In this short note, by using the ideas of shooting method, we show that there exists no finite energy vortex solution to the Landau–Lifshitz equation without anisotropy for prescribed boundary values. Based on comparisons between the present result and the previous ones, we see that the isotropic terms play an important role in Landau–Lifshitz equation. Copyright © 2009 John Wiley & Sons, Ltd.     

Laser-induced forward-transfer with light possessing orbital angular momentum

Helical light fields may carry both orbital angular and spin angular momentum which is respectively associated with their helical wavefronts (optical vortices) and rotating transverse electric fields. Interestingly, these helical light fields interact with materials and the orbital angular momentum of these fields can physically twist a range of materials, including metals, semiconductors, polymers, and liquids. With the aid of spin angular momentum, these fields can also form a range of helical structures. This light-matter interaction based on transfer of angular momentum has the potential to revolutionize industrial processes and enable technologies, such as advanced non-contact and nozzle-free printing. In this review paper, we focus on this printing technique, a process which we herein refer to as optical vortex laser induced forward transfer, and we show how it can be used for the production of next generation printed photonics/electronics/spintronics devices. Herein we review the interactions between the angular momentum of light and materials, and we discuss the ways in which optical vortices can be used to produce a variety of exotic structures. We also discuss the current state-of-the art of laser-induced forward-transfer technologies and detail some of the most novel devices, which have been fabricated using this optical vortex laser induced forward transfer, including hexagonal close-packed photonic-rings and plasmonic nanocores.     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

Interaction between longitudinal vortices and flat plate boundary layer

The interaction between longitudinal vortices and flat plate boundary layer has been studied numerically for both laminar and turbulent flow situations. The vortices are assumed to be placed in an otherwise two-dimensional boundary layer flow. The flow is assumed to be incompressible and steady. Considering the fact that the velocity, vorticity and temperature gradients in the transverse directions are much larger than the longitudinal (streamwise) gradients for these flows, the original Navier Stokes equations are parabolized in the streamwise direction. A simple model, based on Boussinesq hypothesis, is used for turbulent flow. The discretized equations are then solved step by step in the streamwise direction, using an iterative procedure at each station. Numerical solutions have been obtained for different parameters, such as the Reynolds number, the circulation and the initial position of the vortices. The computed flow patterns and the skin friction coefficient and Stanton number are found to be qualitatively consistent with available experimental results. It is shown that the interaction between the vortices and the boundary layer may severely disturb the boundary layer flow field and thus considerably increase the local skin friction and heat transfer rate on surface of an aircraft.     

Blow-up analysis for an elliptic equation describing stationary vortex flows with variable intensities in 2D-turbulence

We consider the mean field equation arising in the high-energy scaling limit of point vortices with a general circulation constraint, when the circulation number density is subject to a probability measure. Mathematically, such an equation is a non-local elliptic equation containing an exponential nonlinearity which depends on this probability measure. We analyze the behavior of blow-up sequences of solutions in relation to the circulation numbers. As an application of our analysis we derive an improved Trudinger-Moser inequality for the associated variational functional.     

Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations

This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier-Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic-parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference splitting, and the viscous terms are approximated with a fourth-order central compact scheme. Dual-time stepping is implemented for time-accurate calculation in conjunction with Beam-Warming approximate factorization scheme. The present compact scheme is compared with an established non-compact scheme via analysis in a model equation and numerical tests in four benchmark flow problems. Comparisons demonstrate that the present third-order upwind compact scheme is more accurate than the non-compact scheme while having the same computational cost as the latter.     

Electrically charged solitons in gauge field theory

Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.     

Regularization of planar vortices for the incompressible flow

In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {-?u = λ∑kj=1 B_(δ(x_0,j))(u-κ_j)p+, in ?,u = 0, on ??,where 0 p 1, ? R~2 is a bounded simply-connected smooth domain, κi(i = 1, …, k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x0 =(x0,1, …, x0,k) of the Kirchhoff-Routh function defined on ?kcorresponding to(κ1, …, κk), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→ +∞, the vorticity setcal vorticity strength near each x0,j appr y : uλ κjoaches κj, j = ∩ Bδ(x0,j) shrinks to{x0,j}, and the lo 1, …, k. This result makes the study of the above problem with p ≥ 0 complete since the cases p 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.     

纵向涡强度衰减及其干涉的数值分析

本文以空气为介质,在Re=600-2100的范围内对布置有三角翅片的平行通道内的初始段层流状态下涡干涉的流动及换热进行了数值模拟。展示了旋向相反的涡在流道中的产生及发展情况,说明了涡产生器在横向位置变化时对横截面上平均Nu数和涡旋强度(?)的影响,并对单个涡产生器的有效换热区域长度进行了探讨。