arXiv subjects
Publications and source records attributed to Jing Niu.
Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.
The Hubble parameter, $H(z)$, plays a crucial role in understanding the expansion history of the universe and constraining the Hubble constant, $\mathrm{H}_0$. The Cosmic Chronometers (CC) method provides an independent approach to measuring $H(z)$, but existing studies either neglect off-diagonal elements in the covariance matrix or use an incomplete covariance matrix, limiting the accuracy of $\mathrm{H}_0$ constraints. To address this, we use a Positive-Definite Covariance Network (PD-CovNet) to simulate the full $33 \times 33$ covariance matrix based on a previously published $15 \times 15$ covariance matrix. Hyperparameters are chosen via leave-one-z-out validation, and performance is benchmarked against a Gaussian-process (GP) baseline. Under identical five-fold cross-validation over redshift groups, we prove that PD-CovNet is a reliable generator of the full covariance compared to the GP baseline. Using this full PD-CovNet-simulated covariance alongside three comparators with different covariance specifications, we constrain $\mathrm{H}_0$ with two independent methods (EMCEE and GP). Across all covariance specifications and both constraint methods, standardized differences and two-sided p-values show no statistically meaningful shift in the central value of the constrained $\mathrm{H}_0$. However, the precision of the constrained $\mathrm{H}_0$ depends on both covariance and method: EMCEE is uniformly more precise than GP once covariance is modeled; within a fixed method, incorporating more covariance reduces precision; and PD-CovNet hyperparameters have a modest effect on uncertainty. These results indicate the importance of accurate covariance modeling in CC-based $\mathrm{H}_0$ constraints.
The Hubble constant ($H_0$) is essential for understanding the universe's evolution. Different methods, such as Affine Invariant Markov chain Monte Carlo Ensemble sampler (EMCEE), Gaussian Process (GP), and Masked Autoregressive Flow (MAF), are used to constrain $H_0$ using $H(z)$ data. However, these methods produce varying $H_0$ values when applied to the same dataset. To investigate these differences, we compare the methods based on their sensitivity to individual data points and their performance in constraining $H_0$. We apply Monte Carlo delete-$d$ jackknife (MCDJ) to assess their sensitivity to individual data points. Our findings reveal that GP is more sensitive to individual data points than both MAF and EMCEE, with MAF being more sensitive than EMCEE. Sensitivity also depends on redshift: EMCEE and GP are more sensitive to $H(z)$ at higher redshifts, while MAF is more sensitive at lower redshifts. In simulation-based performance tests, we generate an ensemble of mock CC datasets with a fixed input truth $H_{0,\mathrm{true}}$, apply each method to recover $H_0$ posteriors, and summarise performance by comparing the recovered posterior to $H_{0,\mathrm{true}}$: (i) posterior central value accuracy (bias and RMSE), (ii) credible-interval calibration (68\% and 95\% coverage), and (iii) overall posterior quality (log score), under two simulation prescriptions ($\Lambda$CDM-based and GP-based). Overall, EMCEE performs best, GP is intermediate, and MAF performs worst across the performance metrics.
It is well-known that a multilinear system with a nonsingular M-tensor and a positive right-hand side has a unique positive solution. Tensor splitting methods generalizing the classical iterative methods for linear systems have been proposed for finding the unique positive solution. The Alternating Anderson-Richardson (AAR) method is an effective method to accelerate the classical iterative methods. In this study, we apply the idea of AAR for finding the unique positive solution quickly. We first present a tensor Richardson method based on tensor regular splittings, then apply Anderson acceleration to the tensor Richardson method and derive a tensor Anderson-Richardson method, finally, we periodically employ the tensor Anderson-Richardson method within the tensor Richardson method and propose a tensor AAR method. Numerical experiments show that the proposed method is effective in accelerating tensor splitting methods.
Dark energy is believed to be responsible for the acceleration of the universe. In this paper, we reconstruct the dark energy scalar field potential $V(\phi)$ using the Hubble parameter $H(z)$ through Gaussian Process analysis. Our goal is to investigate dark energy using various $H(z)$ datasets and priors. We find that the selection of prior and the $H(z)$ dataset significantly affects the reconstructed $V(\phi)$. And we compare two models, Power Law and Free Field, to the reconstructed $V(\phi)$ by computing the reduced chi-square. The results suggest that the models are generally in agreement with the reconstructed potential within a $3\sigma$ confidence interval, except in the case of Observational $H(z)$ data (OHD) with the Planck 18 (P18) prior. Additionally, we simulate $H(z)$ data to measure the effect of increasing the number of data points on the accuracy of reconstructed $V(\phi)$. We find that doubling the number of $H(z)$ data points can improve the accuracy rate of reconstructed $V(\phi)$ by 5$\%$ to 30$\%$.
The measurements of expansion rate $H(z)$ and the growth rate $f\sigma_8(z)$ describe the evolution of the universe, and both of them can constrain the cosmological models through data analysis. Due to the lack of data points, these datasets are combined by the traditional combined method ($\chi^2$ method) to select a best-fitting cosmological model. In 2017, Linder proposed a joint method, which describes the evolution of the universe through $H(z)-f\sigma_8$ diagram instead of the redshift z. Compared to individual datasets, Linder demonstrated the advantages of the joint method to distinguish cosmologies. In this paper, we compare the significance between the traditional combined method and Linder's joint method by constraining the density parameter $\Omega_M$ using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The result shows that the joint method is more significant than the traditional combined method.
In the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model, the energy conditions provides model-independent bounds on the behavior of the distance modulus. However, this method can not provide us the detailed information about the violation between the energy conditions and the observation. In this paper, we present an extended analysis of the energy conditions based upon the entropy density of the universe. On the one hand, we find that these conditions imply that entropy density s depends on Hubble parameter H(z). On the other hand, we compare the theoretical entropy density from the conservation law of energy-momentum tensor with that from the energy conditions using the observational Hubble parameter. When we consider a FLRW universe, according to the theoretical prediction, OHD, thermodynamics and several independent cosmological probes, show that the dominant energy condition is fitter than other energy conditions.
A hybrid structure of a graphene nanomesh with the gold nanodisks is studied to enhance the light absorption by localized surface plasmon resonance. From the reflection spectra of the visible range for graphene nanomesh samples without and with nanodisks, it is found that the absorption of graphene nanomesh structures is greatly enhanced in the presence of gold nanodisks around the resonance wavelength. Simulation results based on the finite-difference time-domain method support the experimental observations. This study demonstrates the potential of constructing graphene based photodetectors with a high light absorption efficiency and wavelength selectivity.
A clear gate voltage tunable weak antilocalization and a giant magnetoresistance of 400 percent are observed at 1.9 K in single layer graphene with an out-of-plane field. A large magnetoresistance value of 275 percent is obtained even at room temperature implying potential applications of graphene in magnetic sensors. Both the weak antilocalization and giant magnetoresistance persists far away from the charge neutrality point in contrast to previous reports, and both effects are originated from charged impurities. Interestingly, the signatures of Shubnikov-de Haas oscillations and the quantum Hall effect are also observed for the same sample.
Due to its high electrical conductivity and excellent transmittance at terahertz frequencies, graphene is a promising candidate as transparent electrodes for terahertz devices. We demonstrate a liquid crystal based terahertz phase shifter with the graphene films as transparent electrodes. The maximum phase shift is 10.8 degree and the saturation voltage is 5 V with a 50 um liquid crystal cell. The transmittance at terahertz frequencies and electrical conductivity depending on the number of graphene layer are also investigated. The proposed phase shifter provides a continuous tunability, fully electrical controllability, and low DC voltage operation.
Shifting of the surface plasmon resonance wavelength induced by the variation of the thickness of insulating spacer between single layer graphene and Au nanoparticles is studied. The system demonstrates a blue shift of 29 nm as the thickness of the spacer layer increases from 0 to 15 nm. This is due to the electromagnetic coupling between the localized surface plasmons excited in the nanoparticles and the graphene film. The strength of the coupling decays exponentially with a decay length of d/R=0.36, where d is the spacer layer thickness and R is the diameter of the Au nanoparticles. The result agrees qualitatively well with the plasmon ruler equation. Interestingly, a further increment of the spacer layer thickness induces a red shift of 17 nm in the resonance wavelength and the shift saturates when the thickness of the spacer layer increases above 20 nm.
Deposition of various materials onto graphene without causing any disorder is highly desirable for graphene applications. Especially, sputtering is a versatile technique to deposit various metals and insulators for spintronics, and indium tin oxide to make transparent devices. However, the sputtering process causes damage to graphene because of high energy sputtered atoms. By flipping the substrate and using a high Ar pressure, we demonstrate that the level of damage to graphene can be reduced or eliminated in dc, rf, and reactive sputtering processes.
Tunability of the surface plasmon resonance wavelength is demonstrated by varying the thickness of Al2O3 spacer layer inserted between the graphene and nanoparticles. By varying the spacer layer thickness from 0.3 to 1.8 nm, the resonance wavelength is shifted from 583 to 566 nm. The shift is due to a change in the electromagnetic field coupling strength between the localized surface plasmons excited in the gold nanoparticles and a single layer graphene film. In contrast, when the graphene film is absent from the system, no noticeable shift in the resonance wavelength is observed upon varying the spacer thickness.
The electromagnetic enhancement for surface enhanced Raman spectroscopy (SERS) of graphene is studied by inserting a layer of Al2O3 between epitaxial graphene and Au nanoparticles. Different excitation lasers are utilized to study the relationship between laser wavelength and SERS. The theoretical calculation shows that the extinction spectrum of Au nanoparticles is modulated by the presence of graphene. The experimental results of the relationship between the excitation laser wavelength and the enhancement factor fit well with the calculated results. An exponential relationship is observed between the enhancement factor and the thickness of the spacer layer.
Negative differential conductance and tunneling characteristics of two-terminal graphene devices are observed before and after electric breakdown, respectively. The former is caused by the strong scattering under a high E-field, and the latter is due to the appearance of a tunneling barrier in graphene channel induced by a structural transformation from crystalline graphene to disordered graphene because of the breakdown. Using Raman spectroscopy and imaging, the presence of non-uniform disordered graphene is confirmed. A memory switching effect of 100000% ON/OFF ratio is demonstrated in the tunneling regime which can be employed in various applications.