A Spatial Structural Derivative Model for Ultraslow Diffusion

This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function exp(x)is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function exp(x)in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.Comment: 13 pages, 3 figure

Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion (FBM) with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time". We derive the statistical properties of this process such as non-Gaussianity and non-ergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean squared displacements. We pay specific emphasis on the comparisons between the cases with and without drift

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.Comment: 10 pages, 11 figures, and 3 table

Evidence of the off-shell Higgs and Higgs decay width constraints at ATLAS

This paper reports a search for off-shell Higgs boson production and the measurement of the Higgs decay width using the full Run-2 pp collision dataset, corresponding to an integrated luminosity of 139 fb−1, collected by the ATLAS detector at the Large Hadron Collider. In this analysis, the Higgs boson production modes include gluon-gluon fusion, vector-boson fusion, and VH, while the Higgs boson decay channels ZZ → 4l and Z'Z → 22ν (l = e or μ) are considered. The background-only hypothesis is rejected at the confidence level of 3.3 σ (2.2 σ) for the observed (expected) result, providing evidence of the off-shell Higgs boson. The combination of the off-shell and on-shell Higgs boson measurements can constrain the Higgs decay width to be 4.5+3.3−2.5 MeV, with an upper limit of 10.5 MeV at the 95% confidence level

Flow Structures of Gaseous Jet Injected into Liquid for Underwater Propulsion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83627/1/AIAA-2010-6911-166.pd

A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold

Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in Euclidean space cannot fully exploit the geometric structure of the solution space. As a promising alternative solution, Riemannian-based DL uses geometric optimization to update parameters on Riemannian manifolds and can leverage the underlying geometric information. Accordingly, this article presents a comprehensive survey of applying geometric optimization in DL. At first, this article introduces the basic procedure of the geometric optimization, including various geometric optimizers and some concepts of Riemannian manifold. Subsequently, this article investigates the application of geometric optimization in different DL networks in various AI tasks, e.g., convolution neural network, recurrent neural network, transfer learning, and optimal transport. Additionally, typical public toolboxes that implement optimization on manifold are also discussed. Finally, this article makes a performance comparison between different deep geometric optimization methods under image recognition scenarios.Comment: 41 page