Pathways to state-selective control of vibrational wavepackets in the deuterium molecular ion

The capability of intense ultrashort laser pulses to initiate, control and image vibrational wavepacket dynamics in the deuterium molecular ion has been simulated with a view to inform and direct future femtosecond pump-control-probe experiments. The intense-field coherent control of the vibrational superposition has been studied as a function of pulse intensity and delay time, to provide an indication of key constraints for experimental studies. For selected cases of the control mechanism, probing of the subsequent vibrational wavepacket dynamics has been simulated via the photodissociation (PD) channel. Such PD probing is shown to elucidate the modified wavepacket dynamics where the position of the quantum revival is sensitive to the control process. Through Fourier transform analysis the PD yield is also shown to provide a characterisation of the vibrational distribution. It has been shown that a simple 'critical R cut-off' approximation can be used to reproduce the effect of a probe pulse interaction, providing a convenient and efficient alternative to intensive computer simulations of the PD mechanism in the deuterium molecular ion.

Collective excitations of trapped Bose-Einstein condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-de Gennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, extremely efficient in our implementation with parallel fast Fourier transform methods, and produces highly accurate results. For high dimensionality or low symmetry the time-dependent approach is a more practical computational scheme and produces accurate and reliable data. The method is suitable for general trap geometries, condensate flows and condensates permeated with defects and vortex structures.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Analyzing laser plasma interferograms with a continuous wavelet transform ridge extraction technique: the method

Laser plasma interferograms are currently analyzed by extraction of the phase-shift map with fast Fourier transform (FFT) techniques [Appl. Opt. 18, 3101 (1985)]. This methodology works well when interferograms are only marginally affected by noise and reduction of fringe visibility, but it can fail to produce accurate phase-shift maps when low-quality images are dealt with. We present a novel procedure for a phase-shift map computation that makes extensive use of the ridge extraction in the continuous wavelet transform (CWT) framework. The CWT tool is flexible because of the wide adaptability of the analyzing basis, and it can be accurate because of the intrinsic noise reduction in the ridge extraction. A comparative analysis of the accuracy performances of them new tool and the FFT-based one shows that the CWT-based tool produces phase maps considerably less noisy and that it can better resolve local inhomogeneties. (C) 2001 Optical Society of America.

64-point Fourier transform chip for digital television applications

A 64-point Fourier transform chip is described that performs a forward or inverse, 64-point Fourier transform on complex two's complement data supplied at a rate of 13.5MHz and can operate at clock rates of up to 40MHz, under worst-case conditions. It uses a 0.6µm double-level metal CMOS technology, contains 535k transistors and uses an internal 3.3V power supply. It has an area of 7.8×8mm, dissipates 0.9W, has 48 pins and is housed in a 84 pin PLCC plastic package. The chip is based on a FFT architecture developed from first principles through a detailed investigation of the structure of the relevant DFT matrix and through mapping repetitive blocks within this matrix onto a regular silicon structure.

Bit-level systolic array implementation of the Winograd Fourier transform algorithm

A bit level systolic array system is proposed for the Winograd Fourier transform algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest-neighbor interconnections, regularity and high throughput. The short interconnections in this method contrast favorably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform a short length transform. These components build into longer transforms preserving the regularity and structure of the short length transform design.

A 64-point fourier transform chip for video motion compensation using phase correlation

Details of a new low power fast Fourier transform (FFT) processor for use in digital television applications are presented. This has been fabricated using a 0.6-µm CMOS technology and can perform a 64 point complex forward or inverse FFT on real-time video at up to 18 Megasamples per second. It comprises 0.5 million transistors in a die area of 7.8 × 8 mm and dissipates 1 W. The chip design is based on a novel VLSI architecture which has been derived from a first principles factorization of the discrete Fourier transform (DFT) matrix and tailored to a direct silicon implementation.

SYSTOLIC IMPLEMENTATION OF THE WINOGRAD FOURIER TRANSFORM ALGORITHM.

A bit-level systolic array system is proposed for the Winograd Fourier transform algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest neighbor interconnections, regularity, and high throughput. The short interconnections in this method contrast favorably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform short-length transforms. These components build into longer transforms, preserving the regularity and structure of the short-length transform design.

Identification of a suitable sterilisation method for collagen derived from a marine Demosponge

Collagen is widely used as a biomedical material, and its importance is likely to grow as research and understanding progresses in this field. As a biomedical material, ensuring the sterility of collagen before use as, or incorporation into, a medical device is paramount. However, common sterilisation techniques can induce changes in the physical structure and protein chemistry of collagen, potentially affecting the performance. In this preliminary study, the influence of autoclaving, gamma irradiation and ethylene oxide gas sterilisation on the denaturation temperature and helical content of the collagen was evaluated using differential scanning calorimetry and Fourier transform infrared spectroscopy. Early results indicate that all sterilisation techniques affect collagen properties but suggest that the least damaging of the techniques investigated was y irradiation.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

Performance of Nonlocal Optics When Applied to Plasmonic Nanostructures

Semiclassical nonlocal optics based on the hydrodynamic description of conduction electrons might be an adequate tool to study complex phenomena in the emerging field of nanoplasmonics. With the aim of confirming this idea, we obtain the local and nonlocal optical absorption spectra in a model nanoplasmonic device in which there are spatial gaps between the components at nanometric and subnanometric scales. After a comparison against time-dependent density functional calculations, we conclude that hydrodynamic nonlocal optics provides absorption spectra exhibiting qualitative agreement but not quantitative accuracy. This lack of accuracy, which is manifest even in the limit where induced electric currents are not established between the constituents of the device, is mainly due to the poor description of induced electron densities.

Fourier Transform using a Rotman Lens

In this paper, the design constraints that are required for a Rotman lens to realize discrete Fourier transform (DFT) amplitude and phase functionality are derived. A Fourier Rotman lens has been designed, fabricated and validated. The amplitude and phase response and the array pattern based on the CST™ results are validated with the theoretical DFT results. To the best of the authors' knowledge, this is the first Fourier Rotman lens to be fabricated and validated. The solution provided replaces multilayer Butler matrix solutions with a simple single layer microstrip technology.

Forensic analysis of architectural finishes using fourier transform infrared and raman spectroscopy, part II:White paint

White household paints are commonly encountered as evidence in the forensic laboratory but they often cannot be readily distinguished by color alone so Fourier transform infrared (FT-IR) microscopy is used since it can sometimes discriminate between paints prepared with different organic resins. Here we report the first comparative study of FT-IR and Raman spectroscopy for forensic analysis of white paint. Both techniques allowed the 51 white paint samples in the study to be classified by inspection as either belonging to distinct groups or as unique samples. FT-IR gave five groups and four unique samples; Raman gave seven groups and six unique samples. The basis for this discrimination was the type of resin and/ or inorganic pigments/extenders present. Although this allowed approximately half of the white paints to be distinguished by inspection, the other half were all based on a similar resin and did not contain the distinctive modifiers/pigments and extenders that allowed the other samples to be identified. The experimental uncertainty in the relative band intensities measured using FT-IR was similar to the variation within this large group, so no further discrimination was possible. However, the variation in the Raman spectra was larger than the uncertainty, which allowed the large group to be divided into three subgroups and four distinct spectra, based on relative band intensities. The combination of increased discrimination and higher sample throughput means that the Raman method is superior to FT-IR for samples of this type. © 2005 Society for Applied Spectroscopy.