Recovery of multiple parameters in subdiffusion from one lateral boundary measurement

This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary measurement corresponding to a fairly general boundary excitation uniquely determines the order of the fractional derivative and the polygonal support of the diffusion coefficient, without knowing either the initial condition or the source. The uniqueness analysis further inspires the development of a robust numerical algorithm for recovering the fractional order and diffusion coefficient. The proposed algorithm combines small-time asymptotic expansion, analytic continuation of the solution and the level set method. We present extensive numerical experiments to illustrate the feasibility of the simultaneous recovery. In addition, we discuss the uniqueness of recovering general diffusion and potential coefficients from one single partial boundary measurement, when the boundary excitation is more specialized

A new topological aspect of the arbitrary dimensional topological defects

We present a new generalized topological current in terms of the order parameter field $\vec \phi$ to describe the arbitrary dimensional topological defects. By virtue of the $$-mapping method, we show that the topological defects are generated from the zero points of the order parameter field $\vec \phi$, and the topological charges of these topological defects are topological quantized in terms of the Hopf indices and Brouwer degrees of $\phi$-mapping under the condition that the Jacobian $$. When $J(\frac \phi v)=0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function $\vec \phi$ but the total charge of the topological defects is still unchanged.Comment: 24 pages, 10 figures, Revte

Tailoring a two-dimensional electron gas at the LaAlO3/SrTiO3 (001) interface by epitaxial strain

Recently a metallic state was discovered at the interface between insulating oxides, most notably LaAlO3 and SrTiO3. Properties of this two-dimensional electron gas (2DEG) have attracted significant interest due to its potential applications in nanoelectronics. Control over this carrier density and mobility of the 2DEG is essential for applications of these novel systems, and may be achieved by epitaxial strain. However, despite the rich nature of strain effects on oxide materials properties, such as ferroelectricity, magnetism, and superconductivity, the relationship between the strain and electrical properties of the 2DEG at the LaAlO3/SrTiO3 heterointerface remains largely unexplored. Here, we use different lattice constant single crystal substrates to produce LaAlO3/SrTiO3 interfaces with controlled levels of biaxial epitaxial strain. We have found that tensile strained SrTiO3 destroys the conducting 2DEG, while compressively strained SrTiO3 retains the 2DEG, but with a carrier concentration reduced in comparison to the unstrained LaAlO3/SrTiO3 interface. We have also found that the critical LaAlO3 overlayer thickness for 2DEG formation increases with SrTiO3 compressive strain. Our first-principles calculations suggest that a strain-induced electric polarization in the SrTiO3 layer is responsible for this behavior. It is directed away from the interface and hence creates a negative polarization charge opposing that of the polar LaAlO3 layer. This both increases the critical thickness of the LaAlO3 layer, and reduces carrier concentration above the critical thickness, in agreement with our experimental results. Our findings suggest that epitaxial strain can be used to tailor 2DEGs properties of the LaAlO3/SrTiO3 heterointerface

A Numerical Method Based On Element Free Galerkin Method For Lower Bound Limit Analysis

Summary A solution procedure for lower bound limit analysis is presented making use of the element free Galerkin (EFG) method rather than of the traditional numerical methods such as finite element method and boundary element method. A reduced basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. Numerical example in this paper shows that it is feasible and efficient to solve the problems of limit analysis by using the EFG method

In situ construction of heterostructured bimetallic sulfide/phosphide with rich interfaces for high-performance aqueous Zn-ion batteries

It is still challenging to develop suitable cathode structures for high-rate and stable aqueous Zn-ion batteries. Herein, a phosphating-assisted interfacial engineering strategy is designed for the controllable conversion of NiCo_{2}S_{4} nanosheets into heterostructured NiCoP/NiCo_{2}S_{4} as the cathodes in aqueous Zn-ion batteries. The multicomponent heterostructures with rich interfaces can not only improve the electrical conductivity but also enhance the diffusion pathways for Zn-ion storage. As expected, the NiCoP/NiCo_{2}S_{4} electrode has high performance with a large specific capacity of 251.1 mA h g^{−1} at a high current density of 10 A g^{−1} and excellent rate capability (retaining about 76% even at 50 A g^{−1}). Accordingly, the Zn-ion battery using NiCoP/NiCo_{2}S_{4} as the cathode delivers a high specific capacity (265.1 mA h g^{−1} at 5A g^{−1}), a long-term cycling stability (96.9% retention after 5000 cycles), and a competitive energy density (444.7 W h kg^{−1} at the power density of 8.4 kW kg^{−1}). This work therefore provides a simple phosphating-assisted interfacial engineering strategy to construct heterostructured electrode materials with rich interfaces for the development of high-performance energy storage devices in the future

Rewritable nanoscale oxide photodetector

Nanophotonic devices seek to generate, guide, and/or detect light using structures whose nanoscale dimensions are closely tied to their functionality. Semiconducting nanowires, grown with tailored optoelectronic properties, have been successfully placed into devices for a variety of applications. However, the integration of photonic nanostructures with electronic circuitry has always been one of the most challenging aspects of device development. Here we report the development of rewritable nanoscale photodetectors created at the interface between LaAlO3 and SrTiO3. Nanowire junctions with characteristic dimensions 2-3 nm are created using a reversible AFM writing technique. These nanoscale devices exhibit a remarkably high gain for their size, in part because of the large electric fields produced in the gap region. The photoconductive response is gate-tunable and spans the visible-to-near-infrared regime. The ability to integrate rewritable nanoscale photodetectors with nanowires and transistors in a single materials platform foreshadows new families of integrated optoelectronic devices and applications.Comment: 5 pages, 5 figures. Supplementary Information 7 pages, 9 figure

XMM-{\em Newton} and FUSE Tentative Evidence for a WHIM filament along the Line of Sight to PKS~0558-504

We present a possible OVIII X-ray absorption line at $z=0.117 \pm 0.001$ which, if confirmed, will be the first one associated with a broad HI Ly$\beta$ (BLB: FWHM=$160^{+50}_{-30}$ km s$^{-1}$) absorber. The absorber lies along the line of sight to the nearby ($z=0.1372$) Seyfert 1 galaxy PKS~0558-504, consistent with being a WHIM filament. The X-ray absorber is marginally detected in two independent XMM-Newton spectra of PKS~0558-504, a long $\sim 600$ ks Guest-Observer observation and a shorter, $\sim 300$ ks total, calibration observation, with a combined single line statistical significance of 2.8$\sigma$ (2.7$\sigma$ and 1.2$\sigma$ in the two spectra, respectively). When fitted with our self-consistent hybrid-photoionization WHIM models, the combined XMM-{\em Newton} spectrum is consistent with the presence of OVIII K$\alpha$ at $z=(0.117 \pm 0.001)$. This model gives best fitting temperature and equivalent H column density of the absorber of log$T=6.56_{-0.17}^{+0.19}$ K, and logN$_H=(21.5 \pm 0.3) (Z/Z_{0.01\odot})^{-1}$ cm$^{-2}$. The statistical sigificance of this single X-ray detection is increased by the detection of broad and complex HI Ly$\beta$ absorption in archival FUSE spectra of PKS~0558-504, at redshifts $z=0.1183 \pm 0.0001$ consistent with the best-fitting redshift of the X-ray absorber. The single line statistical significance of this line is 4.1$\sigma$ (3.7$\sigma$ if systematics are considered), and thus the combined (HI+OVIII) statistical significance of the detection is of 5.0$\sigma$. The detection of both metal and H lines at a consistent redshift, in this hot absorbing system, allows us to speculate on its metallicity. By associating the bulk of the X-ray absorber with the BLB line detected in the FUSE spectrum at $z_{BLB}=0.1183 \pm 0.0001$, we obtain a metallicity of 1-4\% Solar.Comment: 37 pages, 12 figures, 3 Tables. Accepted for publication by the ApJ

Time Evolution of Galaxy Formation and Bias in Cosmological Simulations

The clustering of galaxies relative to the mass distribution declines with time because: first, nonlinear peaks become less rare events; second, the densest regions stop forming new galaxies because gas there becomes too hot to cool and collapse; third, after galaxies form, they are gravitationally ``debiased'' because their velocity field is the same as the dark matter. To show these effects, we perform a hydrodynamic cosmological simulation and examine the density field of recently formed galaxies as a function of redshift. We find the bias b_* of recently formed galaxies (the ratio of the rms fluctuations of these galaxies and mass), evolves from 4.5 at z=3 to around 1 at z=0, on 8 h^{-1} Mpc comoving scales. The correlation coefficient r_* between recently formed galaxies and mass evolves from 0.9 at z=3 to 0.25 at z=0. As gas in the universe heats up and prevents star formation, star-forming galaxies become poorer tracers of the mass density field. After galaxies form, the linear continuity equation is a good approximation to the gravitational debiasing, even on nonlinear scales. The most interesting observational consequence of the simulations is that the linear regression of the star-formation density field on the galaxy density field evolves from about 0.9 at z=1 to 0.35 at z=0. These effects also provide a possible explanation for the Butcher-Oemler effect, the excess of blue galaxies in clusters at redshift z ~ 0.5. Finally, we examine cluster mass-to-light ratio estimates of Omega, finding that while Omega(z) increases with z, one's estimate Omega_est(z) decreases. (Abridged)Comment: 31 pages of text and figures; submitted to Ap

Where Are the Baryons? III: Non-Equilibrium Effects and Observables

Numerical simulations of the intergalactic medium have shown that at the present epoch a significant fraction (40-50%) of the baryonic component should be found in the (T~10^6K) Warm-Hot Intergalactic Medium (WHIM) - with several recent observational lines of evidence indicating the validity of the prediction. We here recompute the evolution of the WHIM with the following major improvements: (1) galactic superwind feedback processes from galaxy/star formation are explicitly included; (2) major metal species (O V to O IX) are computed explicitly in a non-equilibrium way; (3) mass and spatial dynamic ranges are larger by a factor of 8 and 2, respectively, than in our previous simulations. We find: (1) non-equilibrium calculations produce significantly different results from ionization equilibrium calculations. (2) The abundance of O VI absorption lines based on non-equilibrium simulations with galactic superwinds is in remarkably good agreement with latest observations, implying the validity of our model, while the predicted abundances for O VII and O VIII absorption lines appear to be lower than observed but the observational errorbars are currently very large. The expected abundances for O VI (as well as Lyman alpha), O VII and O VIII absorption systems are in the range 50-100 per unit redshift at EW=1km/s decreasing to 10-20 per unit redshift at EW=10km/s. The number of O VI absorption lines with EW>100km/s is very small, while there are about 1-3 lines per unit redshift for O VII and O VIII absorption lines at EW=100km/s. (3) Emission lines, primarily O VI and \lya in the UV and O VII and O VIII in the soft X-rays are potentially observable by future missions. The number of emission lines per unit redshift that may be detectable by planned UV and soft X-ray missions are in the order of 0.1-1.Comment: submitted to ApJ, 52 pages, 27 figures, high res version at http://www.astro.princeton.edu/~cen/baryonIII.ps.g