Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Enhanced Metastatic Potential in a 3D Tissue Scaffold toward a Comprehensive in Vitro Model for Breast Cancer Metastasis

Metastasis is clinically the most challenging and lethal aspect of breast cancer. While animal-based xenograft models are expensive and time-consuming, conventional two-dimensional (2D) cell culture systems fail to mimic in vivo signaling. In this study we have developed a three-dimensional (3D) scaffold system that better mimics the topography and mechanical properties of the breast tumor, thus recreating the tumor microenvironment in vitro to study breast cancer metastasis. Porous poly(e-caprolactone) (PCL) scaffolds of modulus 7.0 +/- 0.5 kPa, comparable to that of breast tumor tissue were fabricated, on which MDA-MB-231 cells proliferated forming tumoroids. A comparative gene expression analysis revealed that cells growing in the scaffolds expressed increased levels of genes implicated in the three major events of metastasis, viz., initiation, progression, and the site-specific colonization compared to cells grown in conventional 2D tissue culture polystyrene (TCPS) dishes. The cells cultured in scaffolds showed increased invasiveness and sphere efficiency in vitro and increased lung metastasis in vivo. A global gene expression analysis revealed a significant increase in the expression of genes involved in cell cell and cell matrix interactions and tissue remodeling, cancer inflammation, and the PI3K/Akt, Wnt, NF-kappaB, and HIFI signaling pathways all of which are implicated in metastasis. Thus, culturing breast cancer cells in 3D scaffolds that mimic the in vivo tumor-like microenvironment enhances their metastatic potential. This system could serve as a comprehensive in vitro model to investigate the manifold mechanisms of breast cancer metastasis.

Temperature-Dependent Photoluminescence of g-C3N4: Implication for Temperature Sensing

We report the temperature-dependent photoluminescence (PL) properties of polymeric graphite-like carbon nitride (g-C3N4) and a methodology for the determination of quantum efficiency along with the activation energy. The PL is shown to originate from three different pathways of transitions: sigma*-LP, pi*-LP, and pi*-pi, respectively. The overall activation energy is found to be similar to 73.58 meV which is much lower than the exciton binding energy reported theoretically but ideal for highly sensitive wide-range temperature sensing. The quantum yield derived from the PL data is 23.3%, whereas the absolute quantum yield is 5.3%. We propose that the temperature-dependent PL can be exploited for the evaluation of the temperature dependency of quantum yield as well as for temperature sensing. Our analysis further indicates that g-C3N4 is well-suited for wide-range temperature sensing.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

A hybrid finite element formulation for flexible multibody dynamics

This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.

Green Nanosilver as Reinforcing Eco-Friendly Additive to Epoxy Coating for Augmented Anticorrosive and Antimicrobial Behavior

Epoxy resin GY250 representing diglycidyl ethers of bisphenol-A (DGEBA) was reinforced with 1, 3 and 5 wt % of surface functionalized silver nanoparticles (F-AgNPs) which were synthesized using Couroupita guianensis leaves extract with a view of augmenting the corrosion control property of the epoxy resin and also imparting antimicrobial activity to epoxy coatings on mild steel. Corrosion resistance of the coatings was evaluated by EIS, potentiodynamic polarization studies and cross scratch tests. AFM, SEM, HRTEM and EDX were utilized to investigate the surface topography, morphology and elemental composition of the coatings on MS specimens. Results showed that the corrosion resistance, hardness and T-g of the DGEBA/F-AgNPs coatings increased at 1 wt % of F-AgNPs. The DGEBA/F-AgNPs coatings also offered manifold antimicrobial protection to the MS surfaces by inhibiting the growth of biofilm forming bacteria like P. aeruginosa, B. subtilis, the most common human pathogen E. coli and the most virulent human pathogenic yeast C. albicans.