MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies

An Orbifold Relative Index Theorem

In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.Comment: Accepted for publication by the Journal of geometry and Physic

Extremal metrics for spectral functions of Dirac operators in even and odd dimensions

Let (M^n, g) be a closed smooth Riemannian spin manifold and denote by D its Atiyah-Singer-Dirac operator. We study the variation of Riemannian metrics for the zeta function and functional determinant of D^2, and prove finiteness of the Morse index at stationary metrics, and local extremality at such metrics under general, i.e. not only conformal, change of metrics. In even dimensions, which is also a new case for the conformal Laplacian, the relevant stability operator is of log-polyhomogeneous pseudodifferential type, and we prove new results of independent interest, on the spectrum for such operators. We use this to prove local extremality under variation of the Riemannian metric, which in the important example when (M^n, g) is the round n-sphere, gives a partial verification of Branson's conjecture on the pattern of extremals. Thus det(D^2) has a local (max, max, min, min) when the dimension is (4k, 4k + 1, 4k + 2, 4k + 3), respectively.Comment: 45 pages; title and content edited to reflect subsequent related wor

Uncertainty Quantification of Nonlinear Lagrangian Data Assimilation Using Linear Stochastic Forecast Models

Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact Bayesian formulae for the state estimation of high-dimensional systems. In this paper, an analytically tractable mathematical framework for continuous-in-time Lagrangian data assimilation is developed. It preserves the nonlinearity in the observational processes while approximating the forecast model of the underlying flow field using linear stochastic models (LSMs). A critical feature of the framework is that closed analytic formulae are available for solving the posterior distribution, which facilitates mathematical analysis and numerical simulations. First, an efficient iterative algorithm is developed in light of the analytically tractable statistics. It accurately estimates the parameters in the LSMs using only a small number of the observed tracer trajectories. Next, the framework facilitates the development of several computationally efficient approximate filters and the quantification of the associated uncertainties. A cheap approximate filter with a diagonal posterior covariance derived from the asymptotic analysis of the posterior estimate is shown to be skillful in recovering incompressible flows. It is also demonstrated that randomly selecting a small number of tracers at each time step as observations can reduce the computational cost while retaining the data assimilation accuracy. Finally, based on a prototype model in geophysics, the framework with LSMs is shown to be skillful in filtering nonlinear turbulent flow fields with strong non-Gaussian features

Development of COTS ADC SEE Test System for the ATLAS LAr Calorimeter Upgrade

Radiation-tolerant, high speed, high density and low power commercial off-the-shelf (COTS) analog-to-digital converters (ADCs) are planned to be used in the upgrade to the Liquid Argon (LAr) calorimeter front end (FE) trigger readout electronics. Total ionization dose (TID) and single event effect (SEE) are two important radiation effects which need to be characterized on COTS ADCs. In our initial TID test, Texas Instruments (TI) ADS5272 was identified to be the top performer after screening a total 17 COTS ADCs from different manufacturers with dynamic range and sampling rate meeting the requirements of the FE electronics. Another interesting feature of ADS5272 is its 6.5 clock cycles latency, which is the shortest among the 17 candidates. Based on the TID performance, we have designed a SEE evaluation system for ADS5272, which allows us to further assess its radiation tolerance. In this paper, we present a detailed design of ADS5272 SEE evaluation system and show the effectiveness of this system while evaluating ADS5272 SEE characteristics in multiple irradiation tests. According to TID and SEE test results, ADS5272 was chosen to be implemented in the full-size LAr Trigger Digitizer Board (LTDB) demonstrator, which will be installed on ATLAS calorimeter during the 2014 Long Shutdown 1 (LS1).Comment: 8 pages, 14 figure

MVOC: a training-free multiple video object composition method with diffusion models

Video composition is the core task of video editing. Although image composition based on diffusion models has been highly successful, it is not straightforward to extend the achievement to video object composition tasks, which not only exhibit corresponding interaction effects but also ensure that the objects in the composited video maintain motion and identity consistency, which is necessary to composite a physical harmony video. To address this challenge, we propose a Multiple Video Object Composition (MVOC) method based on diffusion models. Specifically, we first perform DDIM inversion on each video object to obtain the corresponding noise features. Secondly, we combine and edit each object by image editing methods to obtain the first frame of the composited video. Finally, we use the image-to-video generation model to composite the video with feature and attention injections in the Video Object Dependence Module, which is a training-free conditional guidance operation for video generation, and enables the coordination of features and attention maps between various objects that can be non-independent in the composited video. The final generative model not only constrains the objects in the generated video to be consistent with the original object motion and identity, but also introduces interaction effects between objects. Extensive experiments have demonstrated that the proposed method outperforms existing state-of-the-art approaches. Project page: https://sobeymil.github.io/mvoc.com