Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Valosin-containing protein regulates the proteasome-mediated degradation of DNA-PKcs in glioma cells.

DNA-dependent protein kinase (DNA-PK) has an important role in the repair of DNA damage and regulates the radiation sensitivity of glioblastoma cells. The VCP (valosine-containing protein), a chaperone protein that regulates ubiquitin-dependent protein degradation, is phosphorylated by DNA-PK and recruited to DNA double-strand break sites to regulate DNA damage repair. However, it is not clear whether VCP is involved in DNA-PKcs (DNA-PK catalytic subunit) degradation or whether it regulates the radiosensitivity of glioblastoma. Our data demonstrated that DNA-PKcs was ubiquitinated and bound to VCP. VCP knockdown resulted in the accumulation of the DNA-PKcs protein in glioblastoma cells, and the proteasome inhibitor MG132 synergised this increase. As expected, this increase promoted the efficiency of DNA repair in several glioblastoma cell lines; in turn, this enhanced activity decreased the radiation sensitivity and prolonged the survival fraction of glioblastoma cells in vitro. Moreover, the VCP knockdown in glioblastoma cells reduced the survival time of the xenografted mice with radiation treatment relative to the control xenografted glioblastoma mice. In addition, the VCP protein was also downregulated in ~25% of GBM tissues from patients (WHO, grade IV astrocytoma), and the VCP protein level was correlated with patient survival (R(2)=0.5222, P<0.05). These findings demonstrated that VCP regulates DNA-PKcs degradation and increases the sensitivity of GBM cells to radiation

A Particle Element Approach for Modelling the 3D Printing Process of Fibre Reinforced Polymer Composites

This paper presents a new numerical approach for modelling the 3D printing process of fibre reinforced polymer composites by fused deposition modelling (FDM). The approach is based on the coupling between two particle methods, namely smoothed particle hydrodynamics (SPH) and discrete element method (DEM). The coupled SPH-DEM model has distinctive advantages in dealing with the free surface flow, large deformation of fibres, and/or fibre-fibre interaction that are involved in the FDM process. A numerical feasibility study is carried out to demonstrate its capability for both short and continuous fibre reinforced polymer composites, with promising results achieved for the rheological flow and fibre orientation and deformation. View Full-Tex

Quantum Hall Effect on the Hofstadter Butterfly

Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical energies where the states are extended for each of butterfly subbands, and obtain the trajectory as a function of the disorder. Remarkably, we find that when the modulation becomes anisotropic, the critical energy branches accompanying a change of the Hall conductivity.Comment: 4 pages, 6 figure

Piecewise linear transformation in diffusive flux discretization

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along material discontinuities using only cell concentration values. This is often resolved by introducing auxiliary node, edge, or face concentration values that are explicitly interpolated from the surrounding cell concentrations. We propose to discretize the diffusive flux after applying a local piecewise linear coordinate transformation that effectively removes the discontinuities. The resulting scheme does not need any auxiliary concentrations and is therefore remarkably simpler, while being second-order accurate under the assumption that the structure of the domain is locally layered.Comment: 11 pages, 1 figures, preprint submitted to Journal of Computational Physic

Hyperfine interaction and magnetoresistance in organic semiconductors

We explore the possibility that hyperfine interaction causes the recently discovered organic magnetoresistance (OMAR) effect. Our study employs both experiment and theoretical modelling. An excitonic pair mechanism model based on hyperfine interaction, previously suggested by others to explain magnetic field effects in organics, is examined. Whereas this model can explain a few key aspects of the experimental data, we, however, uncover several fundamental contradictions as well. By varying the injection efficiency for minority carriers in the devices, we show experimentally that OMAR is only weakly dependent on the ratio between excitons formed and carriers injected, likely excluding any excitonic effect as the origin of OMAR.Comment: 10 pages, 7 figures, 1 tabl

Optical effects of spin currents in semiconductors

A spin current has novel linear and second-order nonlinear optical effects due to its symmetry properties. With the symmetry analysis and the eight-band microscopic calculation we have systematically investigated the interaction between a spin current and a polarized light beam (or the "photon spin current") in direct-gap semiconductors. This interaction is rooted in the intrinsic spin-orbit coupling in valence bands and does not rely on the Rashba or Dresselhaus effect. The light-spin current interaction results in an optical birefringence effect of the spin current. The symmetry analysis indicates that in a semiconductor with inversion symmetry, the linear birefringence effect vanishes and only the circular birefringence effect exists. The circular birefringence effect is similar to the Faraday rotation in magneto-optics but involves no net magnetization nor breaking the time-reversal symmetry. Moreover, a spin current can induce the second-order nonlinear optical processes due to the inversion-symmetry breaking. These findings form a basis of measuring a pure spin current where and when it flows with the standard optical spectroscopy, which may provide a toolbox to explore a wealth of physics connecting the spintronics and photonics.Comment: 16 pages, 7 fig

Dielectric behaviour of graded spherical cells with an intrinsic dispersion

The dielectric properties of single-shell spherical cells with an intrinsic dielectric dispersion has been investigated. By means of the dielectric dispersion spectral representation (DDSR) for the Clausius-Mossotti (CM) factor, we express the dispersion strengths as well as the characteristic frequencies of the CM factor analytically in terms of the parameters of the cell model. These analytic expressions enable us to assess the influence of various model parameters on the electrokinetics of cells. Various interesting behaviours have been reported. We extend our considerations to a more realistic cell model with a graded core, which can have spatial gradients in the conductivity and/or permittivity. To this end, we address the effects of a graded profile in a small-gradient expansion in the framework of DDSR.Comment: accepted by European Physical Journal

Quasispecies distribution of Eigen model

We study sharp peak landscapes (SPL) of Eigen model from a new perspective about how the quasispecies distribute in the sequence space. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can get a visual and in-depth result about how the sequences distribute. We find that there are several local optima around the center (global optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears as linear behavior near the threshold.Comment: 13 pages, 6 figure