Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases,the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Intrinsic anisotropy of the effective acoustic properties in metafluids made of two-dimensional cylinder arrays

Within a unified theoretical framework, we extract the omnidirectional effective acoustic parameters for the metafluid consisting of isotropic fluid cylinders embedded in an isotropic fluid background. Besides the analytical formulas for the effective parameters reported previously, i.e., the bulk modulus and the mass density perpendicular to the cylinders, we also derive a simple expression for the effective mass density parallel to the cylinders. As expected, these two effective mass densities are not identical and constitute an anisotropic density tensor. Such intrinsic anisotropy can be engineered much stronger than the pure in-plane anisotropy induced by either anisotropic lattices or anisotropic scatterers.     

Diffusion properties of cortical and pericortical tissue: regional variations, reliability and methodological issues

Characterizing the diffusion properties of cortical tissue is complicated by intersubject variability in the relative locations of gyri and sulci. Here we extend methods of measuring the average diffusion properties of gyral and sulcal structures after they have been aligned to a common template of cortical surface anatomy. Diffusion tensor image (DTI) data were gathered from 82 young subjects and co-registered with high-resolution T1 images that had been inflated and co-registered to a hemispherically unified spherical coordinate system based on FreeSurfer. We analyzed fractional anisotropy (FA), mean diffusivity (MD) and the novel quantity of cortical primary diffusion direction (cPDD) at five surfaces parallel to the white/gray junction, spanning approximately 5 mm from the pial surface into white matter. FA increased with increasing depth, whereas MD and cPDD were reduced. There were highly significant and reliable regional differences in FA, MD and cPDD as well as systematic differences between cortical lobes and between the two hemispheres. The influence of nearby cortical spinal fluid (CSF), local cortical curvature and thickness, and sulcal depth was also investigated. We found that FA correlated significantly with cortical curvature and sulcal depth, while MD was strongly influenced by nearby CSF. The measurement of FA, MD and cPDD near the cortical surface clarifies the organization of fiber projections to and from the cortex.     

A quantum dissipative system in an anisotropic non-linear absorbing environment

A canonical quantization scheme is represented for a quantum system interacting with a non-linear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The non-linear response equation of the environment against the motion of the main system is obtained. The non-linear Langevin-Schrödinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of non-linearity of the environment is investigated on the spontaneous emission of an initially excited two-level atom imbedded in such an environment.     

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.     

On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

The nonsymmetric pressure tensor in polyatomic fluids

Nonequilibrium molecular dynamics calculations are used to show that polyatomic fluids can support antisymmetric stress. In a homogeneous system where the time dependence of vorticity is a step function, it is shown that the rate at which intrinsic angular velocity approaches its steady-state value ( = 1/2 × u) is determined by the magnitude of the antisymmetric part of the pressure tensor.     

Mappings of Domains in Rn and Their Metric Tensors

We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)     

Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.