Natural operators of smooth mappings of manifoldswith metric fields

In this paper we introduce the concepts of both a natural bundle and a natural operator generalized for the case of the category Mf_m × Mf_m of cartesian products of two manifolds and products of local diffeomorphisms. It is shown that any r-th order natural bundle over M × N has a structure of an associated bundle (P^rM × P^rN)Z G_{m^r × Gm^r}]. We consider prolongations of such associated bundles and their reduction with respect to a chosen subgroup. The existence of a bijective correspondence between natural operators of order k and the equivariant mappings of the corresponding type fibers are proved. A basis of invariants of arbitrary order is constructed for natural operators of smooth mappings of manifolds endowed with metric fields or connections, with values in a natural bundle of order one.     

Dissipative-Hamiltonian decomposition of smooth vector fields based on symmetries

We propose a method to decompose a smooth vector field into conservative and dissipative components. The procedure is based on the identification of the kernel of a linear operator associated with a given Hamiltonian combined with the use of Lie transformations for vector fields. Moreover, under certain conditions the nonconservative part of the splitting can be dropped at a given order of the transformation, obtaining after truncation, a Hamilton vector field. The technique is illustrated through the application to the motion of a particle subject to the potential of a champagne bottle plus a small friction.     

Real-time near-field acoustic holography for continuously visualizing nonstationary acoustic fields

Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.     

Stability of bumps in piecewise smooth neural fields with nonlinear adaptation

We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather.     

Real-time visualisation of deformation fields using speckle interferometry and temporal phase unwrapping

A real-time system for analysing data from speckle interferometers, and speckle shearing interferometers, has been developed. Interferograms are continuously recorded by a digital camera at a rate of 60 frames s⁻¹ with temporal phase shifting carried out at the same rate. The images are analysed using a pipeline image processor. With a standard 4-frame phase-shifting algorithm (phase steps of π/2), wrapped phase maps are calculated and displayed at 15 frames s⁻¹. These are unwrapped using a temporal phase unwrapping algorithm to provide a real-time colour-coded display of the relevant displacement component. Each camera pixel (or cluster of pixels) behaves in effect as an independent displacement sensor. The reference speckle interferogram is updated automatically at regular user-defined intervals, allowing arbitrarily large deformations to be measured and errors due to speckle decorrelation to be minimised. The system has been applied to the problem of detecting sub-surface delamination cracks in carbon fibre composite panels.     

Real-time holograms generated by second-harmonic cross correlation of object and reference optical wave fields

Three-dimensional holographic images of extended diffusing objects are simultaneously recorded and reconstructed by optical cross correlation in a second-order nonlinear crystal. An interaction geometry in which the phase-matched object and reference fields propagate slightly noncollinearly is particularly convenient for producing these second-harmonic-generated holograms.     

Numerical visualization by rapid isosurface extractions using 3D span spaces

In this paper, we focus on visualization of a 3D scalar field composed of volume data by means of semi-transparent multiple isosurface extraction. A new method for displaying semi-transparent multiple isosurfaces will be proposed to fulfill real-time rendering of scalar fields. The proposed method is considered to be an extension of ISSUE, which is a known algorithm to quickly generate isosurfaces. ISSUE uses a 2D span space, where minimum values of computational cells are assigned to the horizontal axis, and maximum values of cells are assigned to the vertical axis. In the proposed algorithm, computational cells are placed onto a 3D span space. The third axis is the distance from the viewpoint. The proposed algorithm can quickly search for the cells intersecting with isosurfaces using the span space in back-to-front order and can realize representation of semi-transparent multiple isosurfaces.     

Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields

The present paper discusses magnetic confinement of the Dirac excitations in graphene in the presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to 1/r is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in the presence of the 1/r (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cutoff Coulomb potential to dictate the excitation spectra of graphene. The spectrum of the graphene excitations in the presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.     

The room acoustic rendering equation

An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.     

A composition-free parallel volume rendering method

Journal of Visualization - In the in situ visualization of large-scale simulation, if using the traditional sort-last parallel rendering method, the performance cannot be fully improved due to the...     

Growing smooth interfaces with inhomogeneous moving external fields: dynamical transitions,devil's staircases,and self-assembled ripples

We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field with a profile designed to stabilize a flat interface and translated with velocity v(e). For small v(e), the interface is stuck to the profile, is macroscopically smooth, and is rippled with a periodicity in general incommensurate with the lattice parameter. For arbitrary orientations of the profile, the local slope of the interface locks in to one of infinitely many rational values (devil's staircase) which most closely approximates the profile. These "lock-in" structures and ripples disappear as v(e) increases. For still larger v(e) the profile detaches from the interface.     

Improvement of color rendering index of BGYR laser illuminants

Optical Review - Laser-driven phosphor conversion (PC)-type white light sources are receiving a great deal of attention in next-generation high-intensity lighting and display technologies. Laser...     

工业CT切片序列任意方向剖面的绘制方法

为获得工业CT切片序列在三维空间任意方向的剖面,提出了一种基于三维纹理映射技术的任意剖面绘制方法。该方法首先把工业CT图片序列存储为体数据,然后使用传递函数对体数据进行分类,并将分类处理后的体数据定义为三维纹理,结合人机交互给出的平面参数计算出剖切多边形各顶点及其对应的纹理坐标,最后进行纹理映射得到剖面图像。该方法的特点是利用图形处理器支持的纹理映射功能完成剖面像素的采样和插值。实验结果表明,该方法成像质量较高,显示速度较快,能够满足人机交互实际应用需要。     

Adaptive model simplification in real-time rendering for visualization

In this paper, we propose four different geometric measures to identify appropriate triangles to be simplified in 3D complex model. Each measure yields different weight on the same surface and produces a unique simplified model that worth to be analyzed. The proposed measures involve consideration on the resulting of the surfaces collapse, the high peak and low peak of the triangles mesh, the irregular triangle shape, the capacity and boundary view on the triangles mesh. The chosen triangle is to be collapsed based criterion on Half-edge Collapse Transformation method. From the empirical results, one of the proposed measures presents almost excellence in all the criteria mentioned above. The empirical results include the quality of the surface models (visualization purpose), the efficiency of the measures and the overall appearance preservation of the simplified models. The proposed measures are then to be compared to three existing measures. From the analyzed results, we combine the measures to adapt to the user’s response for generating the user-desired simplified models.     

高显色指数白光LED光源的研究

根据光源混合原理和模拟黑体轨迹的Chebyshev法,推导了三通道脉冲宽度调制(PWM)占空比与色坐标、光通量、相对色温之间的关系式,同时确定调光约束条件。在上述推导公式基础上,设计出一种智能调光控制系统,该系统通过手机客户端分别控制暖白/绿/蓝3种LED光源模组,实现高显色指数R_a下混合白光的调光调色。实验结果表明:设置光源色温为3 600 K时,光通量在600 lm之内,设定值与测试值最大误差为0.74%;当光源光通量设定为300 lm时,色温在[3 200, 7 600]之间连续可调,其最大误差为1.82%,且光通量波动小于4%;混合光源具有较高的显色指数,在调光范围内,一般Ra在90以上,最大可达95.3。     

Cache-aware volume rendering methods with dynamic data reorganization

Journal of Visualization -  We present two cache-aware methods for accelerating volume rendering on graphics processing units (GPUs). The proposed methods extend a previous method such...     

Space-time fields and exchange fields

We derive discrete symmetries of braid group statistics related to charge conjugation and outer automorphisms of the local algebra. The structure of the latter (which are abelian superselection charges) is analyzed in some detail. We use the results to study in great generality a phenomenon recently observed in conformal quantum field theories: the existence of two-dimensional space-time fields with conventional (local, fermionic, dual) commutation relations, expressible as bilinear sums over light-cone fields with exchange algebra commutation relations.     

Real-time cosmology

In recent years, improved astrometric and spectroscopic techniques have opened the possibility of measuring the temporal change of radial and transverse position of sources in the sky over relatively short time intervals. This has made at least conceivable to establish a novel research domain, which we dub “real-time cosmology”. We review for the first time most of the work already done in this field, analysing the theoretical framework as well as some foreseeable observational strategies and their capability to constrain models. We first focus on real-time measurements of the overall redshift drift and angular separation shift in distant sources, which allows the observer to trace the background cosmic expansion and large scale anisotropy, respectively. We then examine the possibility of employing the same kind of observations to probe peculiar and proper accelerations in clustered systems, and therefore their gravitational potential. The last two sections are devoted to the future change of the cosmic microwave background on “short” time scales, as well as to the temporal shift of the temperature anisotropy power spectrum and maps. We conclude revisiting in this context the usefulness of upcoming experiments (like CODEX and Gaia) for real-time observations.