Variational data assimilation for two interface problems

“Variational data assimilation (VDA) is a process that uses optimization techniques to determine an initial condition of a dynamical system such that its evolution best fits the observed data. In this dissertation, we develop and analyze the variational data assimilation method with finite element discretization for two interface problems, including the Parabolic Interface equation and the Stokes-Darcy equation with the Beavers-Joseph interface condition. By using Tikhonov regularization and formulating the VDA into an optimization problem, we establish the existence, uniqueness and stability of the optimal solution for each concerned case. Based on weak formulations of the Parabolic Interface equation and Stokes-Darcy equation, the dual method and Lagrange multiplier rule are utilized to derive the first order optimality system (OptS) for both the continuous and discrete VDA problems, where the discrete data assimilations are built on certain finite element discretization in space and the backward Euler scheme in time. By introducing auxiliary equations, rescaling the optimality system, and employing other subtle analysis skills, we present the finite element convergence estimation for each case with special attention paid to recovering the properties missed in between the continuous and discrete OptS. Moreover, to efficiently solve the OptS, we present two classical gradient methods, the steepest descent method and the conjugate gradient method, to reduce the computational cost for well-stabilized and ill-stabilized VDA problems, respectively. Furthermore, we propose the time parallel algorithm and proper orthogonal decomposition method to further optimize the computing efficiency. Finally, numerical results are provided to validate the proposed methods”--Abstract, page iii

Modeling and a Domain Decomposition Method with Finite Element Discretization for Coupled Dual-Porosity Flow and Navier–Stokes Flow

In This Paper, We First Propose and Analyze a Steady State Dual-Porosity-Navier–Stokes Model, Which Describes Both Dual-Porosity Flow and Free Flow (Governed by Navier–Stokes Equation) Coupled through Four Interface Conditions, Including the Beavers–Joseph Interface Condition. Then We Propose a Domain Decomposition Method for Efficiently Solving Such a Large Complex System. Robin Boundary Conditions Are Used to Decouple the Dual-Porosity Equations from the Navier–Stokes Equations in the Coupled System. based on the Two Decoupled Sub-Problems, a Parallel Robin-Robin Domain Decomposition Method is Constructed and Then Discretized by Finite Elements. We Analyze the Convergence of the Domain Decomposition Method with the Finite Element Discretization and Investigate the Effect of Robin Parameters on the Convergence, Which Also Provide Instructions for How to Choose the Robin Parameters in Practice. Three Cases of Robin Parameters Are Studied, Including a Difficult Case Which Was Not Fully Addressed in the Literature, and the Optimal Geometric Convergence Rate is Obtained. Numerical Experiments Are Presented to Verify the Theoretical Conclusions, Illustrate How the Theory Can Provide Instructions on Choosing Robin Parameters, and Show the Features of the Proposed Model and Domain Decomposition Method

Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation

This paper considers improving the Picard and Newton iterative solvers for the Navier-Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilation (CDA) style nudging to incorporate the known solution data into the solvers. For CDA-Picard, we prove the method has an improved convergence rate compared to usual Picard, and the rate improves as more measurement data is incorporated. We also prove that CDA-Picard is contractive for larger Reynolds numbers than usual Picard, and the more measurement data that is incorporated the larger the Reynolds number can be with CDA-Picard still being contractive. For CDA-Newton, we prove that the domain of convergence, with respect to both the initial guess and the Reynolds number, increases as as the amount of measurement data is increased. Additionally, for both methods we show that CDA can be implemented as direct enforcement of measurement data into the solution. Numerical results for common benchmark Navier-Stokes tests illustrate the theory

Evolutionary Stages and Disk Properties of Young Stellar Objects in the Perseus Cloud

We investigated the evolutionary stages and disk properties of 211 Young stellar objects (YSOs) across the Perseus cloud by modeling the broadband optical to mid-infrared (IR) spectral energy distribution (SED). By exploring the relationships among the turnoff wave bands lambda_turnoff (longward of which significant IR excesses above the stellar photosphere are observed), the excess spectral index alpha_excess at lambda <~ 24 microns, and the disk inner radius R_in (from SED modeling) for YSOs of different evolutionary stages, we found that the median and standard deviation of alpha_excess of YSOs with optically thick disks tend to increase with lambda_turnoff, especially at lambda_turnoff >= 5.8 microns, whereas the median fractional dust luminosities L_dust/L_star tend to decrease with lambda_turnoff. This points to an inside-out disk clearing of small dust grains. Moreover, a positive correlation between alpha_excess and R_in was found at alpha_excess > ~0 and R_in > ~10 $\times$ the dust sublimation radius R_sub, irrespective of lambda_turnoff, L_dust/L_star and disk flaring. This suggests that the outer disk flaring either does not evolve synchronously with the inside-out disk clearing or has little influence on alpha_excess shortward of 24 microns. About 23% of our YSO disks are classified as transitional disks, which have lambda_turnoff >= 5.8 microns and L_dust/L_star >10^(-3). The transitional disks and full disks occupy distinctly different regions on the L_dust/L_star vs. alpha_excess diagram. Taking L_dust/L_star as an approximate discriminator of disks with (>0.1) and without (<0.1) considerable accretion activity, we found that 65% and 35% of the transitional disks may be consistent with being dominantly cleared by photoevaporation and dynamical interaction respectively. [abridged]Comment: 31 pages, 13 figures, 2 tables. To appear in a special issue of RAA on LAMOST science

Improved reliability of planar power interconnect with ceramic-based structure

This paper proposes an advanced Si3N4 ceramic-based structure with through vias designed and filled with brazing alloy as a reliable interconnect solution in planar power modules. Finite element (FE) modeling and simulation were first used to predict the potential of using the proposed Si3N4 ceramic-based structure to improve the heat dissipation and reliability of planar interconnects. Power cycling tests and non-destructive microstructural characterization were then performed on Si3N4 ceramic-based structures, flexible printed circuit boards (PCB) and conventional Al wire interconnect samples to evaluate the FE predictions. Both the FE simulations and experimental tests were carried out on single Si diode samples where both the ceramic-based structures and flexible PCBs were bonded on the top sides of Si diodes with eutectic Sn-3.5Ag solder joints. The results obtained demonstrate that Si3N4 ceramic-based structures can significantly improve the reliability of planar interconnects. The experimental average lifetimes and FE simulated maximum creep strain accumulations for the ceramic-based structure and flexible PCB interconnect samples can reasonably be fitted to existing lifetime models for Sn-3.5Ag solder joints. Discrepancies between the models and experimental results can be attributed to defects and poor filling of the brazing alloy in the vias through the Si3N4 ceramic

NMA: Neural Multi-slot Auctions with Externalities for Online Advertising

Online advertising driven by auctions brings billions of dollars in revenue for social networking services and e-commerce platforms. GSP auctions, which are simple and easy to understand for advertisers, have almost become the benchmark for ad auction mechanisms in the industry. However, most GSP-based industrial practices assume that the user click only relies on the ad itself, which overlook the effect of external items, referred to as externalities. Recently, DNA has attempted to upgrade GSP with deep neural networks and models local externalities to some extent. However, it only considers set-level contexts from auctions and ignores the order and displayed position of ads, which is still suboptimal. Although VCG-based multi-slot auctions (e.g., VCG, WVCG) make it theoretically possible to model global externalities (e.g., the order and positions of ads and so on), they lack an efficient balance of both revenue and social welfare. In this paper, we propose novel auction mechanisms named Neural Multi-slot Auctions (NMA) to tackle the above-mentioned challenges. Specifically, we model the global externalities effectively with a context-aware list-wise prediction module to achieve better performance. We design a list-wise deep rank module to guarantee incentive compatibility in end-to-end learning. Furthermore, we propose an auxiliary loss for social welfare to effectively reduce the decline of social welfare while maximizing revenue. Experiment results on both offline large-scale datasets and online A/B tests demonstrate that NMA obtains higher revenue with balanced social welfare than other existing auction mechanisms (i.e., GSP, DNA, WVCG) in industrial practice, and we have successfully deployed NMA on Meituan food delivery platform.Comment: 10 pages, 3figure

CO-CHANGES I: IRAM 30m CO Observations of Molecular Gas in the Sombrero Galaxy

Molecular gas plays a critical role in explaining the quiescence of star formation (SF) in massive isolated spiral galaxies, which could be a result of either the low molecular gas content and/or the low SF efficiency. We present IRAM 30m observations of the CO lines in the Sombrero galaxy (NGC~4594), the most massive spiral at $d\lesssim30\rm~Mpc$. We detect at least one of the three CO lines covered by our observations in all 13 observed positions located at the galactic nucleus and along a $\sim25\rm~kpc$-diameter dusty ring. The total extrapolated molecular gas mass of the galaxy is $M_{\rm H_2}\approx4\times10^{8}\rm~M_\odot$. The measured maximum CO gas rotation velocity of $\approx379\rm~km~s^{-1}$ suggests that NGC~4594 locates in a dark matter halo with a mass $M_{\rm200}\gtrsim10^{13}\rm~M_\odot$. Comparing to other galaxy samples, NGC~4594 is extremely gas poor and SF inactive, but the SF efficiency is apparently not inconsistent with that predicted by the Kennicutt-Schmidt law, so there is no evidence of enhanced SF quenching in this extremely massive spiral with a huge bulge. We also calculate the predicted gas supply rate from various sources to replenish the cold gas consumed in SF, and find that the galaxy must experienced a starburst stage at high redshift, then the leftover or recycled gas provides SF fuels to maintain the gradual growth of the galactic disk at a gentle rate.Comment: 21 pages, 13 figures, accepted for publication in MNRA

DNA Polymorphism of Insulin-like Growth Factor-binding Protein-3 Gene and Its Association with Cashmere Traits in Cashmere Goats

Insulin-like growth factor binding protein-3 (IGFBP-3) gene is important for regulation of growth and development in mammals. The present investigation was carried out to study DNA polymorphism by PCR-RFLP of IGFBP-3 gene and its effect on fibre traits of Chinese Inner Mongolian cashmere goats. The fibre traits data investigated were cashmere fibre diameter, combed cashmere weight, cashmere fibre length and guard hair length. Four hundred and forty-four animals were used to detect polymorphisms in the hircine IGFBP-3 gene. A 316-bp fragment of the IGFBP-3 gene in exon 2 was amplified and digested with HaeIII restriction enzyme. Three patterns of restriction fragments were observed in the populations. The frequency of AA, AB and BB genotypes was 0.58, 0.33 and 0.09 respectively. The allelic frequency of the A and B allele was 0.75 and 0.25 respectively. Nucleotide sequencing revealed a C>G transition in the exon 2 region of the IGFBP-3 gene resulting in R158G change which caused the polymorphism. Least squares analysis revealed a significant effect of genotypes on cashmere weight (p0.05). The animals of AB and BB genotypes showed higher cashmere weight, cashmere fibre length and hair length than the animals possessing AA genotype. These results suggested that polymorphisms in the hircine IGFBP-3 gene might be a potential molecular marker for cashmere weight in cashmere goats