光散射聚集速率测定中T矩阵方法的应用

聚集速率是评估胶体体系特性及稳定性的关键参数, 静态光散射和动态光散射则是测量聚集速率的两个重要方法. 然而, 用静态光散射和动态光散射测量聚集速率时, 需要知道有关单粒子和双粒子聚集体光散射特性的数据. 为此, 通常需要把动、静两种方法结合, 才能消去这个数据. 以前各种近似理论曾用来解决这个问题, 但因粒子尺寸和形状的限制, 结果并不理想. 而T矩阵方法可以不受粒子大小和形状的限制计算其光散射特性. 本工作用T矩阵方法直接计算静态光散射和动态光散射所必须的粒子散射特性, 并将该法得到的聚集速率与动静态光散射结合法得到的聚集速率进行了比较, 两者结果很接近. 本工作为简化静态光散射和动态光散射测量聚集速率, 扩展其应用范围开辟了新途径. 关键词： T矩阵')" href="#">T矩阵 光散射法 聚集速率     

The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size

We develop a modification of the T-matrix method that allows efficient studies of scattering properties of ensembles of independent irregular particles of different size. The advantage of the modification is quick calculations using the so-called shape-matrices (Sh-matrices), which allow more rapid calculations of scattering by particles of different size and can be used for averaging scattering properties over particle size. To illustrate the advantage we calculate the scattering-angle dependence of the intensity and degree of linear polarization of ensembles of cubes and Chebyshev particles of different size using both the new and traditional methods. Our time savings in calculating scattering properties for the particles with the new methodology is approximately a factor of ten when calculating scattering properties of one hundred of the same type of particles with different size parameter. As can be anticipated, increasing the size interval results in a smoothing of the structure of the photometric curves and a decrease in the linear polarization.     

Comprehensive T-matrix reference database: A 2006–07 update

This paper presents an update to the comprehensive database of T-matrix publications authored by us previously and mostly includes the publications that appeared since 2005. It also lists several earlier publications not included in the original database.     

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Spin relaxation is a sensitive probe of molecular structure and dynamics. Correlation of relaxation time constants, such as T₁ and T₂, conceptually similar to the conventional multidimensional spectroscopy, have been difficult to determine primarily due to the absense of an efficient multidimensional Laplace inversion program. We demonstrate the use of a novel computer algorithm for fast two-dimensional inverse Laplace transformation to obtain T₁–T₂ correlation functions. The algorithm efficiently performs a least-squares fit on two-dimensional data with a nonnegativity constraint. We use a regularization method to find a balance between the residual fitting errors and the known noise amplitude, thus producing a result that is found to be stable in the presence of noise. This algorithm can be extended to include functional forms other than exponential kernels. We demonstrate the performance of the algorithm at different signal-to-noise ratios and with different T₁–T₂ spectral characteristics using several brine-saturated rock samples.     

Comprehensive T-matrix reference database: A 2007-2009 update

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.     

电子与钠原子散射的S, T, U参数研究

电子原子散射中的S，T，U参数可用来描述散射前后自旋状态的变化，研究精细结构水平上的散射激发振幅之间的关系，进而揭示电子原子碰撞过程中电子自旋-轨道耦合以及电子-电子交换等自旋相关效应.采用扭曲波玻恩近似计算了钠原子受电子散射S→P跃迁中的S，T，U参数，分析了多种入射能(2.2—60 eV)的电子与钠原子激发S→P跃迁过程的S,T,U参数随散射角的分布，其中对10 eV入射能的S_p参数与已报道实验数据符合一致.结果表明，较低能电子入射下的S,T,U参数随散射角的分布幅度和起伏都比较明显，入射能大于40 eV的电子入射，S,T,U参数的散射角分布变化很小. 关键词： 散射激发 S')" href="#">S T')" href="#">T U参数')" href="#">U参数 散射振幅 自旋相关效应     

A multiple sphere T-matrix Fortran code for use on parallel computer clusters

A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized-approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres. The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.     

T1ρ-weighted MRI using a surface coil to transmit spin-lock pulses

T1rho-weighted MRI is a novel basis for generating tissue contrast. However, it suffers from sensitivity to B1 inhomogeneity. First, excitation with a spatially varying B1 causes flip-angle artifacts and second, spin locking with an inhomogeneous B1 results in non-uniform T1rho contrast. In this study, we overcome the former complication with a specially designed spin-locking pulse sequence and we successfully obtain T1rho-weighted images with a surface coil. In this pulse sequence, the spin-lock pulse was divided into segments of equal duration and alternating phase. This "self-compensating" T1rho-preparatory pulse sequence was analyzed and the effect of an inhomogeneous B1 field was simulated using the Bloch equations. T1rho-weighted MR images of a phantom and a human knee joint in vivo were obtained on a clinical scanner with a surface coil to demonstrate the utility of the pulse sequence. The self-compensating T1rho-prepared pulses sequence resulted in substantially reduced image artifacts compared to the conventional, single-phase spin-lock pulse.     

Near-field computation using the null-field method

In this paper we analyze three methods for computing the total field in the near-zone region. These methods use the expansion of the scattered field outside the minimum circumscribing sphere, an integral representation of the scattered field and a vector spherical wave expansion of the near-zone field. Calculations of the total field within the circumscribing sphere are presented for dielectric prolate spheroids to compare the different methods.     

Giant Nernst effect in the pseudogap phase of high Tc superconductors

We have investigated theoretically the Nernst effect in unconventional (d-wave) charge and spin density waves (UDW). In the presence of magnetic field, Landau levels are formed, and the gapless behaviour of the low energy excitations change into gapped behaviour. When additional electric field is applied, the quasiparticles drift with a velocity of E × B/B², and carry entropy. From this, the Nernst coefficient can be calculated using the Kelvin relation. The present results account very nicely for the measured Nernst signal in the pseudogap phase of high T_c superconductor La_2−xSr_xCuO₄ and Bi₂Sr_2−yLa_yCuO₆. This indicates that the large Nernst effect is a clear signiture of UDW.     

Cluster calculations of the hyperfine properties of copper compounds

Spin-polarized ab-initio cluster procedures are used to investigate the electronic structure of CuO₂-planes in the La₂CuO₄ and YBa₂Cu₃O₇ compounds. In particular, electric field gradients (EFGs) and magnetic hyperfine interaction parameters for the Cu sites were calculated with various theoretical methods. Calculations with density functional theory reproduce the experimentally determined EFGs fairly well while those at the Hartree-Fock level generally yield values which are too large by about 40%. The anisotropic magnetic hyperfine coupling can also be calculated with reasonable accuracy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Decompositioning method to compute scattering by complex shaped particles using a multiple scattering T-matrix approach

In a recent paper we proposed a decompositioning method to compute scattering by aggregated cylindrical fibres using a multiple scattering T-matrix approach. In this paper we extend this approach to scatterers lacking rotational symmetry. To investigate the capability of this method a square prism and a cube are decomposed into a number of subscatterers and scattering of the original particle shape is computed using multiple scattering. The results are validated using discrete dipole approximation (DDA).     

Application of low field NMR T2 measurements to clathrate hydrates

Low field (2 MHz) Nuclear Magnetic Resonance (NMR) proton spin–spin relaxation time (T₂) distribution measurements were employed to investigate tetrahydrofuran (THF)—deuterium oxide (D₂O) clathrate hydrate formation and dissociation processes. In particular, T₂ distributions were obtained at the point of hydrate phase transition as a function of the co-existing solid/liquid ratios. Because T₂ of the target molecules reflect the structural arrangements of the molecules surrounding them, T₂ changes of THF in D₂O during hydrate formation and dissociation should yield insights into the hydrate mechanisms on a molecular level. This work demonstrated that such T₂ measurements could easily distinguish THF in the solid hydrate phase from THF in the coexisting liquid phase. To our knowledge, this is the first time that T₂ of guest molecules in hydrate cages has been measured using this low frequency NMR T₂ distribution technique. At this low frequency, results also proved that the technique can accurately capture the percentages of THF molecules residing in the solid and liquid phases and quantify the hydrate conversion progress. Therefore, an extension of this technique can be applied to measure hydrate kinetics. It was found that T₂ of THF in the liquid phase changed as hydrate formation/dissociation progressed, implying that the presence of solid hydrate influenced the coexisting fluid structure. The rotational activation measured from the proton response of THF in the hydrate phase was 31 KJ/mole, which agreed with values reported in the literature.     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.     

Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids

The use of simplified particle shapes for modeling scattering by irregularly shaped mineral-dust particles is studied using polyhedral prisms and spheroids as model particles. Simulated phase matrices averaged over shape and size distributions at wavelength 633 nm are compared with a laboratory-measured phase matrix of feldspar particles with known size distribution with effective radius of . When an equi-probable shape distribution is assumed, prisms and oblate spheroids agree with measurements to a similar degree, whereas prolate spheroids perform markedly better. Both spheroids and prisms perform much better than spheres. When an automatic fitting method is applied for finding optimal shape distributions, it is found that the most elongated spheroids are most important for good fits, whereas nearly-spherical spheroids are generally of very little importance. The phase matrices for the different polyhedral prisms, on the other hand, are found to be similar, thus their shape-averaged phase matrices are insensitive to the shape distribution assumed. For spheroids, a simple parameterization for the shape distribution, where weights increase with increasing departure from spherical shape, is proposed and tested. This parameterization improves the fit of most phase matrix elements attained with an equi-probable shape distribution, and it performs particularly well for reproducing the measured phase function.     

Feasibility of similarity coefficient map in improving morphological evaluation of T2* weighted MRI for renal cancer

The purpose of this paper is to investigate the feasibility of similarity coefficient map (SCM) in improving morphological evaluation of T₂^* weighted (T₂^*W) magnatic resonance imaging (MRI) for renal cancer. Simulation studies and in vivo 12-echo T₂^*W experiments for renal cancers were performed for this purpose. The results of the first simulation study suggest that SCM can reveal small structures which are hard to be distinguished from the background tissue in T₂^*W images and the corresponding T₂^* map. The capability of improving morphological evaluation is likely due to the improvement in signal to noise ratio (SNR) and carrier to noise ratio (CNR) by SCM technique. Compared with T₂^*W images, SCM can improve SNR by a factor ranging from 1.87 to 2.47. Compared with T₂^* maps, SCM can improve SNR by a factor ranging from 3.85 to 33.31. Compared with T₂^*W images, SCM can improve CNR by a factor raging from 2.09 to 2.43. Compared with T₂^* maps SCM can improve CNR by a factor raging from 1.94 to 8.14. For a given noise level, the improvements of SNR and CNR depend mainly on the original SNRs and CNRs in T₂^*W images, respectively. In vivo experiments confirmed the results of the first simulation study. The results of the second simulation study suggest that more echoes are used to generate SCM, and higher SNR and CNR can be achieved in SCM. In conclusion, SCM can provide improved morphological evaluation of T₂^*W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T₂^*W MR images and T₂^* maps. What is more, in practical application, for a fixed total sampling time, one should increase the number of echoes as much as possible to achieve SCMs with better SNR and CNR.     

Multi-components of T2 relaxation in ex vivo cartilage and tendon

The multi-components of T₂ relaxation in cartilage and tendon were investigated by microscopic MRI (μMRI) at 13 and 26 μm transverse resolutions. Two imaging protocols were used to quantify T₂ relaxation in the specimens, a 5-point sampling and a 60-point sampling. Both multi-exponential and non-negative-least-square (NNLS) fitting methods were used to analyze the μMRI signal. When the imaging voxel size was 6.76 × 10⁻⁴ mm³ and within the limit of practical signal-to-noise ratio (SNR) in microscopic imaging experiments, we found that (1) canine tendon has multiple T₂ components; (2) bovine nasal cartilage has a single T₂ component; and (3) canine articular cartilage has a single T₂ component. The T₂ profiles from both 5-point and 60-point methods were found to be consistent in articular cartilage. In addition, the depletion of the glycosaminoglycan component in cartilage by the trypsin digestion method was found to result in a 9.81–20.52% increase in T₂ relaxation in articular cartilage, depending upon the angle at which the tissue specimen was oriented in the magnetic field.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Facile synthesis and photocatalytic activity of hierarchical WO3 core–shell microspheres

In this work, we present a facile template-free precipitation method for the large-scale preparation of hierarchical WO₃ core–shell microspheres in which the core was composed of aggregated nanoparticles encapsulated by a hierarchical shell layer self-assembled by ultrafine nanoplates with a thickness of about 15 nm. The products are characterized by X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDS), differential scanning calorimetry and thermogravimetry (TG/DSC). The experimental parameters affecting the morphology were discussed in detail. We found that the concentration of citric acid and pH value of the reaction solution had profound effects on the morphology of the products. In addition, a formation mechanism was proposed for producing hierarchical WO₃ core–shell microspheres. Furthermore, the obtained hierarchical WO₃ core–shell microspheres showed superior photocatalytic activities for the degradation of rhodamine B (RhB) under visible light irradiation.     

In vivo NMR T2 relaxation of experimental brain tumors in the cat: A multiparameter tissue characterization

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time t = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.