Simplified expressions of the T-matrix integrals for electromagnetic scattering

The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.     

A longitudinal study of MR diffusion changes in normal appearing white matter of patients with early multiple sclerosis

BACKGROUND AND PURPOSE: The stage at which normal appearing white matter (NAWM) abnormalities first appear in multiple sclerosis (MS) is not clear. The aim of our study was to monitor water diffusion changes over time in NAWM of patients with early MS.METHODS: Out of a consecutive series of patients enrolled in a MR study on clinically isolated syndrome (CIS), we selected 19 subjects who had completed a one year follow-up. The MR scans obtained at baseline and at 12 months were reviewed according to the new criteria on the diagnosis of MS. Lesion load on T2 and T1 weighted images and the trace of the apparent diffusion coefficient in NAWM were measured both at baseline and at 12 months in patients and in 12 healthy controls.RESULTS: In three patients the diagnosis of MS was done at baseline based on MR. Thirteen patients developed MS during the study and in three patients the diagnosis remained "possible MS." TADC in NAWM in patients was significantly higher than in controls at the 12 months' follow-up but not at baseline (controls mean tADC +/- sd = 0.745 +/- 0.02 mm(2)/sec x 10(-3); patients mean tADC(12) +/- sd = 0.767 +/- 0.02 mm(2)/sec x 10(-3); p < 0.02). TADC and T2 lesion load at 12 months were significantly correlated (p < 0.01). Patients exhibiting tADC(12) above a confidence interval had a significantly greater EDSS score at the same time period (EDSS(12) +/- sd = 1.9 +/- 0.5 and = 1.1 +/- 0.4 respectively; p < 0.01).CONCLUSIONS: This study suggests that diffusion MR cannot detect alterations in NAWM of patients with a CIS suggestive of MS. After one year, when most patients develop MS, diffusion MR abnormalities in NAWM become apparent. These abnormalities are correlated with T2 lesion load and may contribute to neurological impairment.     

Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules

We present a new computational method with associated computer program TROVE (Theoretical ROVibrational Energies) to perform variational calculations of rovibrational energies for general polyatomic molecules of arbitrary structure in isolated electronic states. The (approximate) nuclear kinetic energy operator is represented as an expansion in terms of internal coordinates. The main feature of the computational scheme is a numerical construction of the kinetic energy operator, which is an integral part of the computation process. Thus the scheme is self-contained, i.e., it requires no analytical pre-derivation of the kinetic energy operator. It is also general, since it can be used in connection with any internal coordinates. The method represents an extension of our model for pyramidal XY₃ molecules reported previously [S.N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J.J. Zheng, W. Thiel, Mol. Phys. 103 (2005) 359]. Non-rigid molecules are treated in the Hougen-Bunker-Johns approach [J.T. Hougen, P.R. Bunker, J.W.C. Johns, J. Mol. Spectrosc. 34 (1970) 136]. In this case, the variational calculations employ a numerical finite basis representation for the large-amplitude motion using basis functions that are generated by Numerov-Cooley integration of the appropriate one-dimensional Schrödinger equation.     

The topology of interbank payment flows

We explore the network topology of the interbank payments transferred between commercial banks over the Fedwire^®${}^{\circledR }$ Funds Service. We find that the network has both a low average path length and low connectivity. The network includes a tightly connected core of banks to which most other banks connect. The degree distribution is scale free over a substantial range. We find that the properties of the network changed considerably in the immediate aftermath of the events of September 11, 2001.     

Sensitivity ofn-p scattering observables to charge-independence breaking of the3 P N-N phase shifts

The sensitivity of neutron-proton scattering observables to the recently reported charge-independence breaking of the isospinT=1³ P nucleon-nucleon interaction has been calculated. It is shown that only the analyzing powerA _y () at extreme forward angles and at =90° c.m. and the spin-correlation coefficientA _zx () at 90° c.m. exhibit a measurable sensitivity. It is concluded that the determination ofA _y at 90° c.m. is currently the most accurate approach to verify independently charge-independence breaking in the³ P nucleon-nucleon phase shifts, considering the status of present experimental techniques.     

Diffractive multi-beam surface micro-processing using 10 ps laser pulses

A high repetition rate picosecond laser system is combined with a spatial light modulator (SLM) for diffractive multiple beam processing. The effect of the zero order beam is eliminated by adding a Fresnel zone lens (FZL) to defocus the un-diffracted beam at the processing plane. Chromatic dispersion, which is evident with a large bandwidth femtosecond pulses leading to the problem of distorted hole shape is eliminated due to the much narrower spectral bandwidth, 0.1 nm at 10 ps pulselength, resulting in highly uniform intensity spots, independent of diffraction angle. In addition, high-throughput processing is demonstrated by combining the high power laser output, 2.5 W at λ ≈ 1064 nm and fast repetition rate, f ≈ 20 kHz with P > 1.2 W diffracted into 25 parallel beams. This has the effect of creating an “effective” repetition rate of 500 kHz without restrictive scan speeds.     

Time evolution of a fractal distribution: Particle concentrations in free-surface turbulence

Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating particles coagulate and form a fractal structure, a rare manifestation of a strange attractor observable in real space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions D_q(t) (q=1 to 6) of the floating particles starting with the uniform distribution D_q(0)=2 for Taylor Microscale Reynolds number Re_λ?160. Focus is on the time evolution of the correlation dimension D₂(t) as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.     

Universal nature of particle displacements close to glass and jamming transitions

We examine the structure of the distribution of single particle displacements (van Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical model that describes quantitatively numerical and experimental data in supercooled liquids, colloidal hard spheres, and granular materials. The tails of the distributions directly explain the decoupling between translational diffusion and structural relaxation observed in glassy materials.