559 research outputs found
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
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