Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

Tripleclouds: an efficient method for representing horizontal cloud inhomogeneity in 1D radiation schemes by using three regions at each height

Radiation schemes in general circulation models currently make a number of simplifications when accounting for clouds, one of the most important being the removal of horizontal inhomogeneity. A new scheme is presented that attempts to account for the neglected inhomogeneity by using two regions of cloud in each vertical level of the model as opposed to one. One of these regions is used to represent the optically thinner cloud in the level, and the other represents the optically thicker cloud. So, along with the clear-sky region, the scheme has three regions in each model level and is referred to as “Tripleclouds.” In addition, the scheme has the capability to represent arbitrary vertical overlap between the three regions in pairs of adjacent levels. This scheme is implemented in the Edwards–Slingo radiation code and tested on 250 h of data from 12 different days. The data are derived from cloud retrievals using radar, lidar, and a microwave radiometer at Chilbolton, southern United Kingdom. When the data are grouped into periods equivalent in size to general circulation model grid boxes, the shortwave plane-parallel albedo bias is found to be 8%, while the corresponding bias is found to be less than 1% using Tripleclouds. Similar results are found for the longwave biases. Tripleclouds is then compared to a more conventional method of accounting for inhomogeneity that multiplies optical depths by a constant scaling factor, and Tripleclouds is seen to improve on this method both in terms of top-of-atmosphere radiative flux biases and internal heating rates.

A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models

The acceptance of broadband ultrasound attenuation for the assessment of osteoporosis suffers from a limited understanding of ultrasound wave propagation through cancellous bone. It has recently been proposed that the ultrasound wave propagation can be described by a concept of parallel sonic rays. This concept approximates the detected transmission signal to be the superposition of all sonic rays that travel directly from transmitting to receiving transducer. The transit time of each ray is defined by the proportion of bone and marrow propagated. An ultrasound transit time spectrum describes the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit times over the surface of the receiving ultrasound transducer. The aim of this study was to provide a proof of concept that a transit time spectrum may be derived from digital deconvolution of input and output ultrasound signals. We have applied the active-set method deconvolution algorithm to determine the ultrasound transit time spectra in the three orthogonal directions of four cancellous bone replica samples and have compared experimental data with the prediction from the computer simulation. The agreement between experimental and predicted ultrasound transit time spectrum analyses derived from Bland–Altman analysis ranged from 92% to 99%, thereby supporting the concept of parallel sonic rays for ultrasound propagation in cancellous bone. In addition to further validation of the parallel sonic ray concept, this technique offers the opportunity to consider quantitative characterisation of the material and structural properties of cancellous bone, not previously available utilising ultrasound.

Inhomogeneity of asteroid 2008 TC3 (Almahata Sitta meteorites) revealed through magnetic susceptibility measurements

Magnetic susceptibility measurements were performed on freshly fallen Almahata Sitta meteorites. Most recovered samples are polymict ureilites. Those found in the first four months since impact, before the meteorites were exposed to rain, have a magnetic susceptibility in the narrow range of 4.92 ± 0.08 log 10-9 Am2/kg close to the range of other ureilite falls 4.95 ± 0.14 log 10-9 Am2/kg reported by Rochette et al. (2009). The Almahata Sitta samples collected one year after the fall have similar values (4.90 ± 0.06 log 10-9 Am2/kg), revealing that the effect of one-year of terrestrial weathering was not severe yet. However, our reported values are higher than derived from polymict (brecciated) ureilites 4.38 ± 0.47 log 10-9 Am2/kg (Rochette et al. 2009) containing both falls and finds confirming that these are significantly weathered. Additionally other fresh-looking meteorites of non-ureilitic compositions were collected in the Almahata Sitta strewn field. Magnetic susceptibility measurements proved to be a convenient non-destructive method for identifying non-ureilitic meteorites among those collected in the Almahata Sitta strewn field, even among fully crusted. Three such meteorites, no. 16, 25, and 41, were analyzed and their composition determined as EH6, H5 and EL6 respectively (Zolensky et al., 2010). A high scatter of magnetic susceptibility values among small (< 5 g) samples revealed high inhomogeneity within the 2008 TC3 material at scales below 1-2 cm.

Effects of phase inhomogeneity and boundary conditions on the dynamic response of SMA wire actuators

This paper reports the simulation results from the dynamic analysis of a Shape Memory Alloy (SMA) actuator. The emphasis is on understanding the dynamic behavior under various loading rates and boundary conditions, resulting in complex scenarios such as thermal and stress gradients. Also, due to the polycrystalline nature of SMA wires, presence of microstructural inhomogeneity is inevitable. Probing the effect of inhomogeneity on the dynamic behavior can facilitate the prediction of life and characteristics of SMA wire actuator under varieties of boundary and loading conditions. To study the effect of these factors, an initial boundary value problem of SMA wire is formulated. This is subsequently solved using finite element method. The dynamic response of the SMA wire actuator is analyzed under mechanical loading and results are reported. Effect of loading rate, micro-structural inhomogeneity and thermal boundary conditions on the dynamic response of SMA wire actuator is investigated and the simulation results are reported.

Common Ground Method of Current Injection in Electrical Impedance Tomography

Surface electrodes are essentially required to be switched for boundary data collection in electrical impedance tomography (Ell). Parallel digital data bits are required to operate the multiplexers used, generally, for electrode switching in ELT. More the electrodes in an EIT system more the digital data bits are needed. For a sixteen electrode system. 16 parallel digital data bits are required to operate the multiplexers in opposite or neighbouring current injection method. In this paper a common ground current injection is proposed for EIT and the resistivity imaging is studied. Common ground method needs only two analog multiplexers each of which need only 4 digital data bits and hence only 8 digital bits are required to switch the 16 surface electrodes. Results show that the USB based data acquisition system sequentially generate digital data required for multiplexers operating in common ground current injection method. The profile of the boundary data collected from practical phantom show that the multiplexers are operating in the required sequence in common ground current injection protocol. The voltage peaks obtained for all the inhomogeneity configurations are found at the accurate positions in the boundary data matrix which proved the sequential operation of multiplexers. Resistivity images reconstructed from the boundary data collected from the practical phantom with different configurations also show that the entire digital data generation module is functioning properly. Reconstructed images and their image parameters proved that the boundary data are successfully acquired by the DAQ system which in turn indicates a sequential and proper operation of multiplexers.

A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr-Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. © 2013 Elsevier Ltd.

Performance inhomogeneity of gelatin during gelation process

The structural and performance inhomogeneities of gelatin gel can directly affect its application as a kind of functional material. The structural inhomogeneity of gelatin caused by the uneven and unstable temperature field has been analyzed by the finite element method in our previous work. Further in this paper, the performance inhomogeneity of gelatin which is closely connected with the actual application is numerically analyzed during the gelation process, which includes the inhomogeneities of the optical and mechanical properties of gelatin gels. The time required for reaching the gel point at different spatial grids is exhibited and discussed. The calculated results also show that the equilibrium shear modulus of gelatin is dependent on the thermal history.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.

Magnetic resonance imaging based determination of body compartments with the versatile, interactive sparse sampling (VISS) method

To investigate the inhomogeneity of radiofrequency fields at higher field strengths that can interfere with established volumetric methods, in particular for the determination of visceral (VAT) and subcutaneous adipose tissue (SCAT). A versatile, interactive sparse sampling (VISS) method is proposed to determine VAT, SCAT, and also total body volume (TBV).

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings. especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging. (C) 2004 Elsevier Inc. All rights reserved.

Method for a detailed measurement of image intensity nonuniformity in magnetic resonance imaging

In magnetic resonance imaging (MRI), the MR signal intensity can vary spatially and this spatial variation is usually referred to as MR intensity nonuniformity. Although the main source of intensity nonuniformity arises from B, inhomogeneity of the coil acting as a receiver and/or transmitter, geometric distortion also alters the MR signal intensity. It is useful on some occasions to have these two different sources be separately measured and analyzed. In this paper, we present a practical method for a detailed measurement of the MR intensity nonuniformity. This method is based on the same three-dimensional geometric phantom that was recently developed for a complete measurement of the geometric distortion in MR systems. In this paper, the contribution to the intensity nonuniformity from the geometric distortion can be estimated and thus, it provides a mechanism for estimation of the intensity nonuniformity that reflects solely the spatial characteristics arising from B-1. Additionally, a comprehensive scheme for characterization of the intensity nonuniformity based on the new measurement method is proposed. To demonstrate the method, the intensity nonuniformity in a 1.5 T Sonata MR system was measured and is used to illustrate the main features of the method. (c) 2005 American Association of Physicists in Medicine.