气体放电系统中多臂螺旋波的数值分析

采用Purwins的三变量模型, 在二维空间对气体放电系统中多臂螺旋波的形成和转化进行了数值研究. 通过分析方程参数对系统空间的影响, 确定了系统获得稳定螺旋波的参数空间; 得到了斑图由简单静态六边形到螺旋波的演化过程, 分析了螺旋波的形成机制和时空特性; 进一步获得六种不同臂数的多臂螺旋波斑图(例如: 双臂、三臂、四臂、五臂、六臂和七臂螺旋波). 结果表明: 螺旋波斑图出现在图灵-霍普夫(Turing-Hopf)空间, 是Turing模和Hopf模相互竞争、相互作用的结果; 不同臂数的螺旋波波头均在持续地旋转运动, 其运动速度随螺旋波臂数的增加而增大; 随着螺旋波臂数的增加, 其波头的运动形式愈加复杂; 由于受微扰及边界条件的影响, 多臂螺旋波可以向臂数少一的螺旋波发生转变, 数值模拟结果与实验结果符合较好. 关键词： 螺旋波 数值模拟 气体放电     

Self-Similar 2d Euler Solutions with Mixed-Sign Vorticity

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The boundaries between regions of positive and negative vorticity form algebraic spirals, similar to the Kaden spiral and as opposed to Prandtl’s logarithmic vortex spirals. Also unlike the Prandtl case, spirals are not initially present.     

Gradient induced spiral drift in heterogeneous excitable media

Nonlinear excitable systems far from equilibrium can exhibit pattern formation such as spirals, target patterns, etc. One such system is the heterogeneous catalytic reaction of CO with oxygen on platinum single crystals. It has been established that the resonant periodic forcing of spirals in such excitable systems can cause a spiral drift. Here, we investigate the effects of a linear thermal gradient on the spiral dynamics during CO oxidation on platinum (110) for the first time, both in simulations and with experiments. Our results suggest that a spatial thermal gradient established across the surface can act as an internal forcing drive and cause the spiral patterns to drift. This drift has components both parallel and perpendicular to the external gradient.     

Multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games

We study the formation of multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games with mobile individuals. We discover a set of seed distributions of species, which is able to produce multi-armed spirals and multi-pairs antispirals with a finite number of arms and pairs based on stochastic processes. The joint spiral waves are also predicted by a theoretical model based on partial differential equations associated with specific initial conditions. The spatial entropy of patterns is introduced to differentiate the multi-armed spirals and multi-pairs antispirals. For the given mobility, the spatial entropy of multi-armed spirals is higher than that of single armed spirals. The stability of the waves is explored with respect to individual mobility. Particularly, we find that both two armed spirals and one pair antispirals transform to the single armed spirals. Furthermore, multi-armed spirals and multi-pairs antispirals are relatively stable for intermediate mobility. The joint spirals with lower numbers of arms and pairs are relatively more stable than those with higher numbers of arms and pairs. In addition, comparing to large amount of previous work, we employ the no flux boundary conditions which enables quantitative studies of pattern formation and stability in the system of stochastic interactions in the absence of excitable media.     

Size transition of spiral waves using the pulse array method

The domain size of spiral waves is an important issue in studies of two-dimensional (2D) spatiotemporal patterns. In this work, we use the 2D complex Ginzburg--Landau equation (CGLE) as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.     

Importance of packing in spiral defect chaos

We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions evolve towards a unique distribution with increasing Rayleigh number that suggests power-law scaling for the dynamics in the limit of infinite system size. The techniques are generally applicable to patterns that are reducible to a binary representation.      

Scroll waves in spherical shell geometries

The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.     

An Efficacious Target-Field Approach to Design Shim Coils for Halbach Magnet of Mobile NMR Sensors

The main magnetic fields of mobile nuclear magnetic resonance (NMR) magnets differ from those of conventional NMR and magnetic resonance imaging (MRI) magnets. In the Halbach magnet, the main field B ₀ is perpendicular to the longitudinal axis, the symmetry of the current distribution with respect to the symmetry of the magnetic field differs from that in conventional target-field applications, and the current distribution on the coil surface cannot be expressed in terms of periodic basis functions. To obtain the winding pattern of the coil, an efficacious target-field approach. The surface of a coil is divided into small discrete elements, where each element is represented by a magnetic dipole. From the stream function of the elements, the resultant magnetic field is calculated. The optimization strategy follows an objective function defined by the power dissipation or efficiency of the coil. This leads to the optimum stream function on the coil surface, whose contour lines define the winding patterns of the coil. This paper shows winding patterns designed of shim coils for Halbach magnet and illustrates the craft of a shim coil using flexible printed circuit board. The performance of the coils is verified by simulating the fields they produce over the sensitive volume.     

Emergence and transitions of dynamic patterns of thickness oscillation of the plasmodium of the true slime mold Physarum polycephalum

The emergence and transitions of various spatiotemporal patterns of thickness oscillation were studied in the freshly isolated protoplasm of the Physarum plasmodium. New patterns, such as standing waves, and chaotic and rotating spirals, developed successively before the well-documented synchronous pattern appeared. There was also a spontaneous opposite transition from synchrony to chaotic and rotating spirals. Rotating spiral waves were observed in the large migrating plasmodium, where the vein structures were being destroyed. Thus, the Physarum plasmodium exhibits versatile patterns, which are generally expected in coupled oscillator systems. This paper discusses the physiological roles of spatiotemporal patterns, comparing them with other biological systems.     

Darwin curves and galaxy arms

In the natural world, there exists one kind of structure which is beyond the scope of human laboratorial experiment. It is the structure of galaxies which is usually composed of billions of stars. Spiral galaxies are flat disk-shaped. There are two types of spiral galaxies. The spiral galaxies with some bar-shaped pattern are called barred spirals, and the ones without the pattern are called ordinary spirals. Longer-wavelength galaxy images (infrared, for example) show that ordinary spiral galaxies are basically an axi-symmetric disk that is called exponential disk. For a planar distribution of matter, Jin He defined Darwin curves in the plane as such that the ratio of the matter densities at both sides of the curve is constant along the curve. Therefore, the arms of ordinary spiral galaxies are Darwin curves. Now an important question is that: Are the arms of barred spiral galaxies the Darwin curves too? Fortunately, Jin He designed a piece of Galaxy Anatomy graphic software. With the software, not only can people simulate the stellar density distribution of barred spiral galaxies but also can draw the Darwin curves of the simulated galaxy structure. This paper shows partial evidence that the arms of galaxy NGC 3275, 4548 and 5921 follow Darwin curves.     

Pattern formation on anisotropic and heterogeneous catalytic surfaces

We review experimental and theoretical work addressing pattern formation on anisotropic and heterogeneous catalytic surfaces. These systems are typically modeled by reaction-diffusion equations reflecting the kinetics and transport of the involved chemical species. Here, we demonstrate the influence of anisotropy and heterogeneity in a simplified model, the FitzHugh-Nagumo equations. Anisotropy causes stratification of labyrinthine patterns and spiral defect chaos in bistable media. For heterogeneous media, we study the situation where the heterogeneity appears on a length scale shorter than the typical pattern length scale. Homogenization, i.e., computation of effective medium properties, is applied to an example and illustrated with simulations in one (fronts) and two dimensions (spirals). We conclude with a discussion of open questions and promising directions that comprise the coupling of the microscopic structure of the surface to the macroscopic concentration patterns and the fabrication of nanostructures with heterogeneous surfaces as templates. (c) 2002 American Institute of Physics.     

Prandtl-number dependence of heat transport in turbulent Rayleigh-Bénard convection

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma by only about 2%. This result disagrees with the extrapolation of the Grossmann and Lohse theory beyond its range of validity, which implies a decrease by 20% over our sigma range, but agrees with their recent extension of the theory to small Reynolds numbers.     

Instabilities in buoyant flows under localized heating

We study, from the numerical point of view, instabilities developed in a fluid layer with a free surface in a cylindrical container which is nonhomogeneously heated from below. In particular, we consider the case in which the applied heat is localized around the origin. An axisymmetric basic state appears as soon as a nonzero horizontal temperature gradient is imposed. The basic state may bifurcate to different solutions depending on vertical and lateral temperature gradients and on the shape of the heating function. We find different kinds of instabilities: extended patterns growing on the whole domain, which include those known as targets, and spiral waves. Spirals are present even for infinite Prandtl number. Localized structures both at the origin and at the outer part of the cylinder may appear either as Hopf or stationary bifurcations. An overview of the developed instabilities as functions of the dimensionless parameters is presented in this article.     

Influence of Blurred Ways on Pattern Recognition of a Scale-Free Hopfield Neural Network

We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of information processing in brain. Due to heterogeneous degree of scale-free network, different blurred ways have different influences on pattern recognition with same errors. Simulation shows that among partial recognition, the larger loading ratio （the number of patterns to average degree P/ （k） ） is, the smaller the overlap of SFHN is. The influence of directed （large） way is largest and the directed （small） way is smallest while random way is intermediate between them. Under the ratio of the numbers of stored patterns to the size of the network PIN is less than O. 1 conditions, there are three families curves of the overlap corresponding to directed （small）, random and directed （large） blurred ways of patterns and these curves are not associated with the size of network and the number of patterns. This phenomenon only occurs in the SFHN. These conclusions are benefit for understanding the relation between neural network structure and brain function.     

Magnetic-field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.     

Spiral cracks in drying precipitates

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces but from a propagating stress front induced by the foldup of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks. Fittings of experimental and simulation data show that the spirals are logarithmic. Theoretical aspects of the logarithmic spirals are discussed. In particular we show that this occurs generally when the crack speed is proportional to the propagating speed of stress front.     

Heat transfer and pressure drop in a spiral square channel

Heat transfer and pressure drop in a spiral square channel is examined experimentally and analytically. The spiral channel was fabricated on a copper plate. The cross-section of the channel is square with 1-mm sides. A copper cap plate was bolted tight to seal the channel. Water and four silicone oils (0.65, 1, 3, and 10 cSt) were used as the working fluid; thus, Prandtl numbers from 5 to 110 were examined. The experiments were done once with the fluids entering from the side of the spiral channel and exiting from the middle of the spiral channel, and once with the fluids entering from the middle and exiting from the side. Heat transfer behavior over a wide range of flow rates from laminar to turbulent has been examined. Heat transfer enhancement due to the spiral geometry was observed, and a slight difference was reported between the side and middle inlet condition. The dimensionless mean wall flux and the dimensionless thermal flow length were used to analyze the experimental data instead of Nusselt and Reynolds numbers. The spiral channel has been discretized so that a single Dean number can be assumed in each cell, and an existing correlation was applied to calculate the average Nusselt number. The model prediction is compared with the experimental points. Pressure drop tests have only been conducted with water as the working fluid.     

Reducing SAR in parallel excitation using variable-density spirals: a simulation-based study

Parallel excitation using multiple transmit channels has emerged as an effective method to shorten multidimensional spatially selective radiofrequency (RF) pulses, which have a number of important applications, including B1 field inhomogeneity correction in high-field MRI. The specific absorption rate (SAR) is a primary concern in high-field MRI, where wavelength effects can lead to local peaks in SAR. In parallel excitation, the subjects are exposed to RF pulses from multiple coils, which makes the SAR problem more complex to analyze, yet potentially enables greater freedom in designing RF pulses with lower SAR. Parallel-excitation techniques typically employ either Cartesian or constant-density (CD) spiral trajectories. In this article, variable-density (VD) spiral trajectories are explored as a means for SAR reduction in parallel-excitation pulse design. Numerical simulations were conducted to study the effects of CD and VD spirals on parallel excitation. Specifically, the electromagnetic fields of a four-channel transmit head coil with a three-dimensional head model at 4.7 T were simulated using a finite-difference time domain method. The parallel RF pulses were designed and the resulting excitation patterns were generated using a Bloch simulator. The SAR distributions due to CD and VD spirals were evaluated quantitatively. The simulation results show that, for the same pulse duration, parallel excitation with VD spirals can achieve a lower SAR compared to CD spirals for parallel excitation. VD spirals also resulted in reduced artifact power in the excitation patterns. This gain came with slight, but noticeable, degrading of the spatial resolution of the resulting excitation patterns.     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Model flames in the Boussinesq limit: Rising bubbles

Using the Boussinesq buoyancy approximation, we study a bubble of reaction products rising in the reactant fluid under the influence of gravity. Reaction on the surface of the bubble (the flame) results in an increase of the volume of the bubble. We consider fluids with low Prandtl and high Froude numbers (heat diffusion dominates over viscous dissipation, and burning dominates over gravitational effects). We show that, under these conditions, all initially small bubbles follow the same growth pattern, regardless of the flame speed, the reaction type, the gravity, the viscosity, the initial size, and, to some extent, the initial shape of the bubble. In the initial stage of this similarity solution a bubble grows radially in an essentially motionless fluid until it reaches some critical size, which is determined by the laminar flame speed, the gravitational acceleration, and the Atwood number. Once the bubble reaches the critical size, convection becomes significant and the bubble evolves into a more complicated, mushroom-like shape. The similarity solution is expressed using the critical bubble size for the unit length and the critical size divided by the laminar flame speed as the unit time.