Reflective mode of deformed-helix ferroelectric liquid crystal cells for sensing applications

We present a detailed theoretical and experimental study of the reflectance response of a deformed-helix ferroelectric (DHF) liquid crystal (LC) cell to an applied voltage under cross-polarisers. Using a model based on the effective dielectric tensor approximation, we derive simple analytical formulas to design a LC cell with maximum modulation depth and optimal linearity of the electro-optical response intensity versus the electric field. Our experimental results show that the cell works at frequencies up to 10 kHz and exhibits excellent linearity, with a total harmonic distortion as low as ?70 dB. These findings suggest that DHF-LCs can be exploited to develop simple and accurate optical sensors.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.     

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given.     

Quantitative assessment of motion correction for high angular resolution diffusion imaging

Several methods have been proposed for motion correction of high angular resolution diffusion imaging (HARDI) data. There have been few comparisons of these methods, partly due to a lack of quantitative metrics of performance. We compare two motion correction strategies using two figures of merit: displacement introduced by the motion correction and the 95% confidence interval of the cone of uncertainty of voxels with prolate tensors. What follows is a general approach for assessing motion correction of HARDI data that may have broad application for quality assurance and optimization of postprocessing protocols. Our analysis demonstrates two important issues related to motion correction of HARDI data: (1) although neither method we tested was dramatically superior in performance, both were dramatically better than performing no motion correction, and (2) iteration of motion correction can improve the final results. Based on the results demonstrated here, iterative motion correction is strongly recommended for HARDI acquisitions.     

Combined prostate diffusion tensor imaging and dynamic contrast enhanced MRI at 3T — quantitative correlation with biopsy

The purpose of this work was to compare diagnostic accuracy of Diffusion Tensor Imaging (DTI), dynamic contrast-enhanced magnetic resonance imaging (DCE MRI) and their combination in diagnosing prostate cancer. Twenty-five patients with clinical suspicion of prostate cancer underwent MRI, prior to transrectal ultrasound-guided biopsies. MRI data were correlated to biopsy results. Logistic regression models were constructed for the DTI parameters, DCE MRI parameters, and their combination. The areas under the receiver operator characteristic curves (AUC) were compared between the models. The nonparametric Wilcoxon signed rank test was used for statistical analysis. The sensitivity and specificity values were respectively 81% (74–87%) and 85% (79–90%) for DTI and 63% (55–70%) and 90% (85–94%) for DCE. The combination “DTI or DCE MRI” had 100% (97–100%) sensitivity and 77% (69–83%) specificity, while “DTI and DCE MRI” had 44% (37–52%) sensitivity and 98% (94–100%) specificity. The AUC for DTI+DCE parameters was significantly higher than that for either DTI (0.96 vs. 0.92, P=.0143) or DCE MRI parameters (0.96 vs. 0.87, P=.00187) alone. In conclusion, the combination of DTI and DCE MRI has significantly better accuracy in prostate cancer diagnosis than either technique alone.     

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs

This paper addresses the solution of parabolic evolution equations simultaneously in space and time as may be of interest in, for example, optimal control problems constrained by such equations. As a model problem, we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual Petrov–Galerkin variational formulation of the heat equation in space–time results in a generalized least squares problem. This formulation admits a unique, quasi‐optimal solution in the natural space–time Hilbert space and serves as a basis for the development of space–time compressive solution algorithms. The solution of the heat equation is obtained by applying the conjugate gradient method to the normal equations of the generalized least squares problem. Starting from stable subspace splittings in space and in time, multilevel space–time preconditioners for the normal equations are derived. In order to reduce the complexity of the full space–time problem, all computations are performed in a compressed or sparse format called the hierarchical Tucker format, supposing that the input data are available in this format. In order to maintain sparsity, compression of the iterates within the hierarchical Tucker format is performed in each conjugate gradient iteration. Its application to vectors in the hierarchical Tucker format is detailed. Finally, numerical results in up to five spatial dimensions based on the recently developed htucker toolbox for MATLAB are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.