Orthogonal Gradient Research Articles

Quasi-Minimal Residual Variants of the COCG and COCR Methods for Complex Symmetric Linear Systems in Electromagnetic Simulations

The conjugate orthogonal conjugate gradient (COCG) method has been considered an attractive part of the Lanczos-type Krylov subspace method for solving complex symmetric linear systems. However, it is often faced with apparently irregular convergence behaviors in practical electromagnetic simulations. To avoid such a problem, the symmetric quasi-minimal residual (QMR) method has been developed. On the other hand, the conjugate A-orthogonal conjugate residual (COCR) method, which can be regarded as an extension of the conjugate residual method, also had been established. It shows that the COCR often gives smoother convergence behavior than the COCG method. The purpose of this paper is to apply the QMR approaches to the COCG and COCR to derive two new methods (including their preconditioned versions), and to report the benefits of the modified methods by some practical examples arising in electromagnetic simulations.

Magnetic Particle Imaging Utilizing Orthogonal Gradient Field and Third-Harmonic Signal Detection

We have developed a 2-D magnetic nanoparticle (MNP) imaging system using an orthogonal gradient held and third-harmonic signal detection. An ac excitation held was applied to generate third-harmonic signals from MNP on the basis of their nonlinear magnetization curves, and a dc gradient held was applied perpendicular to the excitation held. The dependence of the third-harmonic signal on the dc held was very different from that in the conventional parallel case. We obtained a contour map of the signal held from the MNP located at z = 35 mm below the pickup coil using an excitation held of 1 mT and gradient held of 0.4 T/m. We could obtain spatial resolution of 10 mm even in this small gradient held. Then, we analyzed the contour map using singular value decomposition (SVD) to improve the spatial resolution of the position estimation of MNP. Using SVD, we converted the held map to the MNP distribution. The spatial resolution was improved from 10 to 6.7 mm. We could clearly distinguish three MNP samples separated with 10 mm spacing located at z = 35 mm.

Imaging with referenceless distortion correction and flexible regions of interest using single-shot biaxial spatiotemporally encoded MRI

Owing to its intrinsic characteristics, spatiotemporally encoded (SPEN) imaging is less sensitive to adverse effects due to field inhomogeneity in comparison with echo planar imaging, a feature highly desired for functional, diffusion, and real-time MRI. However, the quality of images obtained with SPEN MRI is still degraded by geometric distortions when field inhomogeneity exists. In this study, a single-shot biaxial SPEN (bi-SPEN) pulse sequence is implemented, utilizing a 90° and a 180° chirp pulse incorporated with two orthogonal gradients. A referenceless geometric-distortion correction based on the single-shot bi-SPEN sequence is then proposed. The distorted image acquired with the single-shot bi-SPEN sequence is corrected by iterative super-resolved reconstruction involving the field gradients estimated from a field map, which in turn is obtained from its own super-resolved data after a phase-unwrapping procedure without additional scans. In addition, the distortion correction method is applied to improve the quality of the multiple region-of-interest images obtained with single-shot bi-SPEN sequence.

Intravoxel incoherent motion diffusion-weighted imaging in head and neck squamous cell carcinoma: Assessment of perfusion-related parameters compared to dynamic contrast-enhanced MRI

PurposeTo investigate the correlation between perfusion-related parameters obtained with intravoxel incoherent motion (IVIM) and classical perfusion parameters obtained with dynamic contrast-enhanced (DCE) magnetic resonance imaging in patients with head and neck squamous cell carcinoma (HNSCC), and to compare direct and asymptotic fitting, the pixel-by-pixel approach, and a region of interest (ROI)-based approach respectively for IVIM parameter calculation. Materials and methodsSeventeen patients with HNSCC were included in this retrospective study. All magnetic resonance (MR) scanning was performed using a 3T MR unit. Acquisition of IVIM was performed using single-shot spin-echo echo-planar imaging with three orthogonal gradients with 12 b-values (0, 10, 20, 30, 50, 80, 100, 200, 400, 800, 1000, and 2000). Perfusion-related parameters of perfusion fraction ‘f’ and the pseudo-diffusion coefficient ‘D*’ were calculated from IVIM data by using least square fitting with the two fitting methods of direct and asymptotic fitting, respectively. DCE perfusion was performed in a total of 64 dynamic phases with a 3.2-s phase interval. The two-compartment exchange model was used for the quantification of tumor blood volume (TBV) and tumor blood flow (TBF). Each tumor was delineated with a polygonal ROI for the calculation of f, f∙D* performed using both the pixel-by-pixel approach and the ROI-based approach. In the pixel-by-pixel approach, after fitting each pixel to obtain f, f∙D* maps, the mean value in the delineated ROI on these maps was calculated. In the ROI-based approach, the mean value of signal intensity was calculated within the ROI for each b-value in IVIM images, and then fitting was performed using these values. Correlations between f in a total of four combinations (direct or asymptotic fitting and pixel-by-pixel or ROI-based approach) and TBV were respectively analyzed using Pearson's correlation coefficients. Correlations between f∙D* and TBF were also similarly analyzed. ResultsIn all combinations of f and TBV, f∙D* and TBF, there was a significant correlation. In the comparison of f and TBV, a moderate correlation was observed only between f obtained by direct fitting with the pixel-by-pixel approach, whereas a good correlation was observed in the comparisons using the other three combinations. In the comparison of f∙D* and TBF, a good correlation was observed only with f∙D* obtained by asymptotic fitting with the ROI-based approach. In contrast, moderate correlations were observed in the comparisons using the other three combinations. ConclusionIVIM was found to be feasible for the analysis of perfusion-related parameters in patients with HNSCC. Especially, the combination of asymptotic fitting with the ROI-based approach was better correlated with DCE perfusion.

Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons

Efficient excitation of surface plasmon polaritons (SPPs) remains one of the most challenging issues in areas of plasmonics related to information communication technologies. In particular, combining high SPP excitation efficiency and acceptance of any polarization of incident light appeared to be impossible to attain due to the polarized nature of SPPs. Here we demonstrate plasmonic couplers that represent arrays of gap SPP resonators producing upon reflection two orthogonal phase gradients in respective linear polarizations of incident radiation. These couplers are thereby capable of efficiently converting incident radiation with arbitrary polarization into SPPs that propagate in orthogonal directions dictated by the phase gradients. Fabricated couplers operate at telecom wavelengths and feature the coupling efficiency of ∼25% for either of two linear polarizations of incident radiation and directivity of SPP excitation exceeding 100. We further demonstrate that an individual wavelength-sized unit cell, representing a meta-scatterer, can also be used for efficient and polarization sensitive SPP excitation in compact plasmonics circuits. Devices capable of converting light of any polarization into surface plasmon polaritons could aid the development of on-chip optical circuits. Anders Pors and co-workers from the University of Southern Denmark and the University of Burgundy in France have now fabricated such a ‘coupler’ from gradient metasurfaces — arrays of miniature gold patches on a thin dielectric layer covering a metal-coated glass substrate. Their device is compatible with wavelengths of light in the telecommunications window (around 1,500 nm) and does not require a specific polarization in order to excite plasmons. Furthermore, it allows the direction of plasmon propagation to be controlled by changing the polarization of the incident beam. Calculations indicate that the coupling efficiency could be as high as 40%, with a directivity of around 50:1.

The Absorption of Light in Lakes: Negative Impact of Dissolved Organic Carbon on Primary Productivity

Colored dissolved organic matter (CDOM) absorbs a substantial fraction of photosynthetically active radiation (PAR) in boreal lakes. However, few studies have systematically estimated how this light absorption influences pelagic primary productivity. In this study, 75 boreal lakes spanning wide and orthogonal gradients in dissolved organic carbon (DOC) and total phosphorus (TP) were sampled during a synoptic survey. We measured absorption spectra of phytoplankton pigments, CDOM, and non-algal particles to quantify the vertical fate of photons in the PAR region. Area-specific rates of gross primary productivity (PPA) were estimated using a bio-optical approach based on phytoplankton in vivo light absorption and the light-dependent quantum yield of photochemistry in PSII measured by a PAM fluorometer. Subsequently, we calculated the effects of CDOM, DOC, and TP concentration on PPA. CDOM absorbed the largest fraction of PAR in the majority of lakes (mean 56.3%, range 36.9–76.2%), phytoplankton pigments captured a comparatively minor fraction (mean 6.6%, range 2.2–28.2%). PPA estimates spanned from 45 to 993 mg C m−2 day−1 (median 286 mg C m−2 day−1). We found contrasting effects of CDOM (negative) and TP (positive) on PPA. The use of DOC or CDOM as predictors gave very similar results and the negative effect of these variables on PPA can probably be attributed to shading. A future scenario of increased DOC, which is highly correlated with CDOM in these lakes, might impose negative effects on areal primary productivity in boreal lakes.

Interactive effects of area and connectivity on the diversity of tachinid parasitoids in highly fragmented landscapes

Although many empirical and theoretical studies have elucidated the effects of habitat fragmentation on the third trophic level, little attention has been paid to the impacts of this driver on more generalist groups of non-hymenopteran parasitoids. Here, we used the highly-diverse group of tachinid flies as an alternative model to test the effects of landscape fragmentation on insect parasitoids. Our aims were: (i) to evaluate the relative importance of habitat area and connectivity losses and their potential interaction on tachinid diversity, (ii) to test whether the effects of habitat fragmentation changes seasonally, and (iii) to further assess the effect of habitat diversity on tachinid diversity and whether different parasitoid-host associations modify the species richness response to fragmentation. In 2012 a pan-trap sampling was conducted in 18 semi-natural grasslands embedded in intensive agricultural landscapes along statistically orthogonal gradients of habitat area, connectivity and habitat diversity. We found an interaction between habitat area and connectivity indicating that tachinid abundance and species richness were more negatively affected by habitat loss in landscapes with low rather than with relatively large habitat connectivity. Although tachinid communities exhibited large within-year species turnover, we found that the effects of landscape fragmentation did not change seasonally. We found that habitat diversity and host association did not affect tachinid species diversity. Our results have important implications for biodiversity conservation as any attempts to mitigate the negative effects of habitat loss need to take the general level of habitat connectivity in the landscape into account.

Performance of Preconditioned Linear Solvers Based on Minimum Residual for Complex Symmetric Linear Systems

Fast computation of linear systems is essential for reducing the elapsed time when using finite element analysis. The incomplete Cholesky conjugate orthogonal conjugate gradient method is widely used as a linear solver for complex symmetric systems derived from the edge-based FEM in the frequency domain. On the other hand, the performance of the preconditioned minimized residual method based on the three-term recurrence (MRTR) formula of the conjugate gradient-type method has been demonstrated on various symmetric sparse linear systems obtained from edge-based FEM formulated in the magnetostatic and time domain. This paper shows for the first time the performance of the preconditioned conjugate orthogonal MRTR method applied to complex symmetric linear systems.

Thin film synthesis and properties of copper nitride, a metastable semiconductor

Copper nitride (Cu3N) thin films were grown by reactive sputtering using a high-throughput combinatorial approach with orthogonal gradients of substrate temperature and target–substrate distance.

Combinatorial sputtering in planetary type systems for alloy libraries with perpendicular gradients of layer thickness and composition realised by a timing approach

We present a combinatorial sputtering technique to fabricate alloy thin films with orthogonal gradients of thickness and stoichiometry in a planetary type sputtering system. Using this approach we prepared a library of planar Nb Josephson junctions with a magnetic compound layer made from Si and Fe on one wafer. The independent investigation of thickness and composition changes of the Fe\(_x\)Si\(_{1-x}\) layer allows the identification of transition regions where the phase difference of the superconducting order parameter across the barrier changes from 0 to \(\pi \). A mapping technique which allows to identify the different coupling regimes depending on material properties might facilitate the fabrication of \(\pi \) junctions with tailored critical current, damping and normal resistance parameters for applications.

An investigation of axial dispersion enhanced by thermosolutal natural convection in a horizontal annular-like enclosure

The objective of the experimental investigation was to quantify the axial dispersion of a dilute secondary gas that was subjected to orthogonal thermal and solutal buoyancy gradients in a horizontal annular-like enclosure. Test results showed that a linear axial concentration profile existed at steady-state for the secondary gas. Unheated tests with only solutal buoyancy gradients resulted in a dispersion multiple, DM, of approximately 8 times molecular diffusion. The combined thermal and solutal buoyancy tests, in which a thermal plume from the simulated heater packages aided in mixing, yielded an axial dispersion multiple coefficient of approximately 23 times molecular diffusion, a 188% increase as compared to solutal buoyancy alone. A correlation describing the experimental data trend for the dispersion multiple as a function of buoyancy ratio, N=RaS/RaT, was computed to be DM=19.2N−0.061, which is valid for for binary mixtures where the solutal and thermal gradients are orthogonal with Pr and Le of order 1, 0<RaT<3.5×106, and 0.1<N<0.6.

Orthogonalizing crusher and diffusion‐encoding gradients to suppress undesired echo pathways in the twice‐refocused spin echo diffusion sequence

The twice-refocused spin echo sequence is widely used in diffusion imaging due to its excellent performance in reducing eddy currents. The three radio frequency pulses give rise to eight separate signal pathways. Because there is no general solution for the size and arrangement for crusher gradients, with constant size and orientation, that is effective for all arbitrary diffusion-sensitizing b-values and directions, this article introduces and validates a solution whereby the crusher and diffusion-encoding gradients are always kept orthogonal, thus ensuring their independence. The cancellation of the crusher and diffusion gradients was demonstrated. Subsequently, crusher gradients were implemented in such a way that they were always orthogonal to the diffusion gradient. Phantom and in-vivo experiments were performed to ascertain that orthogonally implemented crusher gradients alleviate the problem without lowering image quality. In all experiments, when the crusher gradients' action was cancelled by the diffusion-encoding gradients artifactual signal modulation was observed. When orthogonal gradients were implemented the artifacts were eliminated without detrimental effects on image quality. Orthogonal crushers are easy to implement and can be used for any variant of diffusion imaging sequences (e.g., diffusion tensor imaging, fiber diameter mapping) where the twice-refocused scheme is used.

Facile fabrication of "dual click" one- and two-dimensional orthogonal peptide concentration gradients.

Peptides, proteins, and extracellular matrix act synergistically to influence cellular function at the biotic-synthetic interface. However, identifying the individual and cooperative contributions of the various combinations and concentration regimes is extremely difficult. The confined channel deposition method we describe affords highly tunable orthogonal reactive concentration gradients that greatly expand the dynamic range, spatial control, and chemical versatility of the reactive silanes that can be controllably deposited. Using metal-free "dual click" immobilization chemistries, multiple peptides with a variety of functionality can be immobilized efficiently and reproducibly enabling optimal concentration profiling and the assessment of synergistic interactions.

The magnet system for rapid scan electron paramagnetic resonance imaging and spectroscopy

The magnet and gradient systems suitable for electron paramagnetic res- onance imaging experiments at RF range are presented. The air-core magnet based on the Helmholtz design in the article has a unique conical shape. A comprehensive study regarding the coils adjustment providing for the maximum field homogeneity is given. The z gradient is a four-coil system (seventh order), the transverse gradients are Golay coils (fifth order), and the scan system is the Helmholtz coil (fourth order). The magnet generates continuously a field of 37 mT (370 G), and the orthogonal gradient coils are designed to yield 100 mT/m (10 G/cm). The experimental tests have shown that the field generated is homogeneous to 610 ppm in the 6 3 6 3 3c m 3 region (x/y/z), which is our field of interest, and to 650 ppm in the 8 3 8 3 4c m 3 region (x/y/z). The system has the potential to monitor temporal changes of oxygen concentration in biological samples. 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 43B: 22-31, 2013

Single‐trait functional indices outperform multi‐trait indices in linking environmental gradients and ecosystem services in a complex landscape

Summary Functional traits can be used to describe the composition of communities through indices that seek to explain the factors that drive community assembly, biotic effects on ecosystem processes or both. Appropriately representing functional composition is therefore essential for predicting the consequences of environmental context and management actions for the provisioning of multiple ecosystem services (ESs) in heterogeneous landscapes. Functional indices can be constructed from single or multiple traits; however, it is not clear how they differ in information content or ability to predict biodiversity – ecosystem function relationships in complex landscapes. Here, we compare the utility of analogous single‐ and multi‐trait indices in linking environmental variation and functional composition to ESs in a heterogeneous landscape, relating functional indices based on three plant traits [height, relative growth rate and root density (RD)] to variation in the physical environment and to two ESs (forage production and soil carbon) and their net ES level. Two orthogonal gradients, elevation and soil bulk density (BD), explained significant variation in several dimensions of functional composition comprised of single traits. These traits in turn significantly predicted variation in ESs and their net values. Only one index measured with multiple traits (functional richness) varied with the physical environment, while none predicted variation in ES or net ES levels. One ES, soil carbon, increased with the community‐average value of RD, while the other, forage production, was related to the range and community‐average value of height. In turn, average RD increased with soil BD while the average and range of height declined with elevation. Due to these environmental patterns, soil carbon and forage production did not covary strongly, leading to moderate net ES levels across the landscape. Synthesis: Single‐trait indices of functional composition best linked variation in environmental gradients with productivity and soil carbon. Because the environment–trait functioning relationships were independent of one another, the ESs were independently distributed across the landscape, providing little evidence of synergies or trade‐offs. Single‐ and multi‐trait indices contained unique information about functional composition of these communities, and both are likely to have a place in predicting variation in ESs under different scenarios.

Measurement of crack-tip and punch-tip transient deformations and stress intensity factors using Digital Gradient Sensing technique

The optical method of Digital Gradient Sensing (DGS) is extended to the study of fracture mechanics and impact mechanics problems. DGS is based on the elasto-optic effect exhibited by transparent materials subjected to non-uniform state of stress causing the angular deflection of light rays propagating through the material. Under plane stress conditions, the deflections of light rays can be related to two orthogonal in-plane stress gradients. In this paper, the principle of the method is presented first, followed by crack and punch experiments on PMMA plates for quantifying stress gradients near stress risers. The crack-tip stress intensity factors under both quasi-static and dynamic loading conditions are extracted from DGS measurements and are in good agreement with analytical and finite element results. The problem of a square-punch impacting the edge of a PMMA sheet is also studied using the new method by exploiting punch-tip–crack-tip analogy. The dynamic punch-tip stress intensity factors are extracted from the optical measurements and are again in good agreement with the ones from a complementary finite element analysis of the problem.

Patterning metallic electrodeposits with magnet arrays

The influence of a pattern of a magnetic field on the structure of metal deposits at the cathode of a small electrochemical cell is investigated for cobalt, nickel, copper, and zinc. The different magnetic properties of the ions in their oxidized and reduced states, together with the influence on the patterned electrodeposits of variables, including the structure of the array of small magnets used to generate the field pattern, applied magnetic field, ion concentration, cell orientation, and deposition time lead to an understanding of the physical processes involved. The results for direct deposits from paramagnetic cations such as Cu${}^{2+}$ when convection is minimized are largely explained in terms of magnetic pressure, which modifies the thickness of the diffusion layer that governs mass transport. Patterning is governed by the susceptibility of the electroactive species relative to the nonelectroactive background. No patterning is observed until the diffusion layer begins to form, as it requires orthogonal concentration and magnetic field gradients. An inverse effect, whereby deposits are structured in complementary patterns, such as antidot arrays, is observed when a strongly paramagnetic but nonelectroactive cation such as Dy${}^{3+}$ is present in the electrolyte, together with an electroactive cation such as Cu${}^{2+}$or Zn${}^{2}$. Inverse patterning is related to magnetically induced convection produced by the inhomogeneous magnetic field. Blocking of sites in the double layer by the rare-earth ions may also be involved. The inverse deposits are concentrated in regions where the magnitude of the field is lowest; they can also be produced directly by superposing a uniform magnetic field on that of the magnet array.

A Dual Gradient Assay for the Parametric Analysis of Cell–Surface Interactions

Cellular response to microgrooves is addressed using a new assay format, comprising orthogonal gradients of continuously varied groove pitch and depth. Dual layer etch masks are created using a combination of micropatterning and plasma polymer deposition. A silicon substrate with a constant groove width of 8 μm and with ridge width increasing from 8 μm in 0.5 μm steps across 10 mm is fabricated by photolithography. A plasma-polymerized hexane film which is 120 nm thick at one end of these grooves, and 10 nm at the other, is deposited under a diffusion mask. Reactive etching of the patterned sample transfers a gradient of groove pitch and groove depth into the silicon substrate. A silicon master with a gradient of groove depth spanning more than two orders of magnitude (less than 10 nm to over 1000 nm) is used to create an injection molding inlay for mass replication of the screening topography. Polycarbonate replicas are molded for use in cell culture studies, and the functionality of the topography as a high-throughput screening platform is investigated. The response of MDCK, h-TERT fibroblasts, and LE2 endothelial cells is examined, in terms of attachment and morphological response to the variation in topographical cues, with the aim of pinpointing the optimal combination of groove pitch and depth to elicit a tailored response from each cell type. When the range of topographical features screened on a single substrate is considered, this new assay represents a significant step forward in the parametric design and analysis of topographical cues at the biomaterial interface.

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time.

Reflection characteristics of a composite planar AMC surface

This study investigates the reflection characteristics of a composite Artificial Magnetic Conductor (AMC) surface consisting of multiple orthogonal gradient AMC surfaces arranged in a two-dimensional periodic pattern. The gradient AMC surface in this study consists of square metal patches of variable size printed on a grounded dielectric substrate. Due to the orthogonal placement of the gradient AMC surface, the incident energy of a plane wave normally incident on the composite AMC surface will be reflected into four major lobes away from the impinging direction. To achieve a systematical design, a simple formula based on array antenna theory was developed to determine the reflection pattern of the gradient AMC surface illuminated by a normal incident plane wave. A time-domain full-wave simulation was also carried out to calculate the electromagnetic fields in the structure and the far-field patterns. The scattering patterns of the structure were measured in an electromagnetic anechoic chamber. Results confirm the design principle and procedures in this research. Since such a composite AMC surface can be easily fabricated using the standard printed circuit board technique without via-hole process, it may have potential applications in beam-steering and radar cross section reduction.