Strong convergence for the modified Mann's iteration of λ\lambda-strict pseudocontraction

In this paper, for an $\lambda$-strict pseudocontraction $T$, we prove strong convergence of the modified Mann's iteration defined by $$x_{n+1}=\beta_{n}u+\gamma_nx_n+(1-\beta_{n}-\gamma_n)[\alpha_{n}Tx_n+(1-\alpha_{n})x_n],$$ where $\{\alpha_{n}\}$, $\{\beta_{n}\}$ and $\{\gamma_n\}$ in $(0,1)$ satisfy: (i) $0 \leq \alpha_{n}\leq \frac{\lambda}{K^2}$ with $\liminf\limits_{n\to\infty}\alpha_n(\lambda-K^2\alpha_n)> 0$; (ii) $\lim\limits_{n\to\infty}\beta_n= 0$ and $\sum\limits_{n=1}^\infty\beta_n=\infty$; (iii) $\limsup\limits_{n\to\infty}\gamma_n<1$.Our results unify and improve some existing results.Comment: 8 pages, 201

Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design

Observation of spin-orbit magnetoresistance in metallic thin films on magnetic insulators

A magnetoresistance effect induced by the Rashba spin-orbit interaction was predicted, but not yet observed, in bilayers consisting of normal metal and ferromagnetic insulator. Here, we present an experimental observation of this new type of spin-orbit magnetoresistance (SOMR) effect in a bilayer structure Cu[Pt]/Y3Fe5O12 (YIG), where the Cu/YIG interface is decorated with nanosize Pt islands. This new MR is apparently not caused by the bulk spin-orbit interaction because of the negligible spin-orbit interaction in Cu and the discontinuity of the Pt islands. This SOMR disappears when the Pt islands are absent or located away from the Cu/YIG interface, therefore we can unambiguously ascribe it to the Rashba spin-orbit interaction at the interface enhanced by the Pt decoration. The numerical Boltzmann simulations are consistent with the experimental SOMR results in the angular dependence of magnetic field and the Cu thickness dependence. Our finding demonstrates the realization of the spin manipulation by interface engineering.Comment: 12 pages, 4 figures, 14 pages in supplementary. To appear on Science Advance

Tet3 regulates synaptic transmission and homeostatic plasticity via DNA oxidation and repair.

Contrary to the long-held belief that DNA methylation of terminally differentiated cells is permanent and essentially immutable, post-mitotic neurons exhibit extensive DNA demethylation. The cellular function of active DNA demethylation in neurons, however, remains largely unknown. Tet family proteins oxidize 5-methylcytosine to initiate active DNA demethylation through the base-excision repair (BER) pathway. We found that synaptic activity bi-directionally regulates neuronal Tet3 expression. Functionally, knockdown of Tet or inhibition of BER in hippocampal neurons elevated excitatory glutamatergic synaptic transmission, whereas overexpressing Tet3 or Tet1 catalytic domain decreased it. Furthermore, dysregulation of Tet3 signaling prevented homeostatic synaptic plasticity. Mechanistically, Tet3 dictated neuronal surface GluR1 levels. RNA-seq analyses further revealed a pivotal role of Tet3 in regulating gene expression in response to global synaptic activity changes. Thus, Tet3 serves as a synaptic activity sensor to epigenetically regulate fundamental properties and meta-plasticity of neurons via active DNA demethylation

Projection-Based Reduced Order Modeling for Spacecraft Thermal Analysis

This paper presents a mathematically rigorous, subspace projection-based reduced order modeling (ROM) methodology and an integrated framework to automatically generate reduced order models for spacecraft thermal analysis. Two key steps in the reduced order modeling procedure are described: (1) the acquisition of a full-scale spacecraft model in the ordinary differential equation (ODE) and differential algebraic equation (DAE) form to resolve its dynamic thermal behavior; and (2) the ROM to markedly reduce the dimension of the full-scale model. Specifically, proper orthogonal decomposition (POD) in conjunction with discrete empirical interpolation method (DEIM) and trajectory piece-wise linear (TPWL) methods are developed to address the strong nonlinear thermal effects due to coupled conductive and radiative heat transfer in the spacecraft environment. Case studies using NASA-relevant satellite models are undertaken to verify the capability and to assess the computational performance of the ROM technique in terms of speed-up and error relative to the full-scale model. ROM exhibits excellent agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with salient computational acceleration (up to two orders of magnitude speed-up) over the full-scale analysis. These findings establish the feasibility of ROM to perform rational and computationally affordable thermal analysis, develop reliable thermal control strategies for spacecraft, and greatly reduce the development cycle times and costs

Discrete Element Simulation of Bending Deformation of Geogrid-Reinforced Macadam Base

The pavement bending deformation resistance of the existing macadam base structure is poor. The geogrid-reinforced macadam base can effectively strengthen the bending resistance of the pavement, but no international consensus has been reached at present over bending failure laws of reinforced macadam base structure. Discrete element models of semi-rigid base pavement structure, macadam base pavement structure, and geogrid-reinforced macadam base pavement structure were built based on MATDEM discrete element simulation program; loading calculation of the three models was conducted by taking their centers as loading positions; and model displacement nephogram, strain nephogram, and effects of different spans on their bending deformation were analyzed to reveal bending failure laws of reinforced macadam base and improvement effect of the geogrid on the anti-bending performance of the macadam structural layer. Finally, bending deformation laws of the three pavement structures and improvement effect of geogrid reinforcement on bending properties of the macadam base structure were established. The results show that under bending deformation of semi-rigid base, the vertical strain at the contract surface between the baseplate and soil base and horizontal strain at midspan position reach the maximum, which can easily lead to fracture and shear failure, and the macadam base layer can effectively isolate the tensile strain transmitted from bottom up. Through their own deformation, grids can transform surface pressure load into frictional resistance at the geogrid/soil interface and partial kinetic energy in the system into their own elastic potential energy to reduce the kinetic energy at the subbase layer. Geogrid reinforcement can improve the nonlinearity of macadam materials, reduce the fluctuation amplitude of the strain curve and displacement curve, lengthen the service life of the macadam base pavement structure, and improve its structural soundness under bending deformation. This study can provide a theoretical reference for numerical simulation of bending failure of geogrid-reinforced macadam base

Research on Bending Fatigue Properties of Reinforced Macadam Foundation

Existing macadam base structures have poor resistance to bending deformation of pavement. The structural layer is challenged with serious cracking due to the long-term dynamic loads. Despite these issues, however, studies on reinforcement techniques for macadam base structure have been scarce. No reasonable and feasible method on how to improve the bending resistance of flexible base structures (e.g. macadam base structure) and prolong their bending fatigue life has yet been reported. Thus, this study proposed a method for reinforcing macadam base structures with geogrids to strengthen bending performance, anti-fatigue performance and dynamic stability of flexible base structures under different loading levels. The reinforced macadam base structure was investigated through a laboratory test of flexural-tensile strength and a three-point fatigue bending test. A cyclic loading test of reinforced and non-reinforced girder specimens was carried out under five stress levels. The effect of such a new reinforcement method in improving the bending fatigue properties of macadam base structures was analyzed by comparing the yield curves and fatigue lives of reinforced and non-reinforced specimens under different loading levels. Results demonstrate that the non-reinforced macadam base has poor bending resistance. The yield curve and fatigue life of non-reinforced specimens attenuated quickly as it approached the ultimate loading level. Non-reinforced specimens have low-cycle fatigue failures when the loads reach the 0.8 stress level and the ultimate displacement at failure is relatively small, accompanied by obvious failure surface. After geogrids are added, the fatigue life of specimens improved significantly. The yield curve shows no significant attenuation at a high loading level. The reinforced specimens can still maintain high-cycle fatigue failure under the 0.8 stress level and avoid the occurrence of low-cycle fatigue failures. Moreover, reinforced specimens can inhibit transmission of reflection cracks at midspan of cement-stabilized macadam base, delay the propagation of oblique shearing fractures close to the support, and strengthen the dynamic stability and durability of pavement structure with a macadam base. The conclusions of this study provide theoretical references to practical engineering applications of such new reinforcement technology for macadam bases