Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

Influence of absorbed water on the dielectric properties and glass-transition temperature of silica-filled epoxy nanocomposites

Work on dielectric spectroscopy of epoxy resin filled with nano-SiO2 at different relative humidities and temperatures is reported. Above the glass-transition temperature (Tg), dc-like imperfect charge transport (QDC or LFD) dominates the low frequency dielectric spectrum. Another mid-frequency relaxation process was found in the non-dried composites. Water also induces glass-transition temperature decreases, which can be measured both by dielectric spectroscopy and DSC. Both theory and experiment demonstrated that a higher water content could exist in nanocomposites than unfilled epoxy suggesting a bigger free volume when nanostructured. In our system, the hydrophilic surface of silica is likely to cause water to surround and lead to delamination of the epoxy from SiO2. This is a potential mechanical and dielectric weakness in the nanocomposites, which may lead to an ageing phenomenon. Hydrophobic surface group may reduce the water adsorption in nanocomposites

Hemodynamic evaluation using four-dimensional flow magnetic resonance imaging for a patient with multichanneled aortic dissection

The hemodynamic function of multichanneled aortic dissection (MCAD) requires close monitoring and effective management to avoid potentially catastrophic sequelae. This report describes a 47-year-old man who underwent endovascular repair based on findings from four-dimensional (4D) flow magnetic resonance imaging of an MCAD. The acquired 4D flow data revealed complex, bidirectional flow patterns in the false lumens and accelerated blood flow in the compressed true lumen. The collapsed abdominal true lumen expanded unsatisfactorily after primary tear repair, which required further remodeling with bare stents. This case study demonstrates that hemodynamic analysis using 4D flow magnetic resonance imaging can help understand the complex pathologic changes of MCAD

Integral geometry of complex space forms

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and complex euclidean space. In particular, we compute the family of kinematic formulas for invariant valuations and invariant curvature measures in these spaces. In addition to new and more efficient framings of the tube formulas of Gray and the kinematic formulas of Shifrin, this approach yields a new formula expressing the volumes of the tubes about a totally real submanifold in terms of its intrinsic Riemannian structure. We also show by direct calculation that the Lipschitz-Killing valuations stabilize the subspace of invariant angular curvature measures, suggesting the possibility that a similar phenomenon holds for all Riemannian manifolds. We conclude with a number of open questions and conjectures.Comment: 68 pages; minor change

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry ${{Diff}}(M, {\cal{F}})$ to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet (UV) and infrared (IR), but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.Comment: 19 pages, comments are welcome!!

On the Dichotomy between the Nodal and Antinodal Excitations in High-temperature Superconductors

Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations.Comment: 11 pages, 9 figure

Phenomenological and mechanics aspects of nondestructive evaluation and characterization by sound and ultrasound of material and fracture properties

Developments in fracture mechanics and elastic wave theory enhance the understanding of many physical phenomena in a mathematical context. Available literature in the material, and fracture characterization by NDT, and the related mathematical methods in mechanics that provide fundamental underlying principles for its interpretation and evaluation are reviewed. Information on the energy release mechanism of defects and the interaction of microstructures within the material is basic in the formulation of the mechanics problems that supply guidance for nondestructive evaluation (NDE)

Auto-generation methodology of complex-shaped coarse aggregate set of 3D concrete numerical test specimen

In this paper, a novel numerical method for random generation of aggregates in concrete is presented. Compared with some other models, the aggregates model generated by this method offers a better approximation to the geometric shape of real aggregates and the target gradation. The research incudes that (1) a surface reconstruction method is developed first on the basis of the implicit T-spline surface algorithm through defining a modified knot vector, determining the off-set point locations and their sign distances, which aims at avoiding occurrence of unclosed curved surface or spurious sheets and reconstructing accurately the complex surface according to a set of scattered surface points of a gravel aggregate; (2) a sinusoidal generatrix function, of which the amplitude represents the aggregate size range and the period reflects the aggregate flatness, is proposed to auto-generate a set of scattered points on the surface of a gravel aggregate. Further modifications are made to improve the quality of the scattered points that agree well with the real crushed aggregate surface; (3) An efficient aggregate packing method is proposed by combining and modifying the “occupation and removal method” and the “layering disposition method” to improve the efficiency of aggregate packing; and (4) a MATLAB computing program for auto-generating aggregates in concrete is developed and validated by examples. The simulation results have demonstrated that the method presented in this paper can generate aggregates for any given mix proportions and gradations and the method can serve as an effective tool for numerical evaluation of mechanical properties of concrete materials