One Dimensional
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2022 ◽  
Vol 169 ◽  
pp. 108774
Haiyan Fan ◽  
He Gao ◽  
Shuowei An ◽  
Zhongming Gu ◽  
Shanjun Liang ◽  

2022 ◽  
Vol 45 (2) ◽  
pp. 20210199
Shunhua Zhou ◽  
Haibo Jiang ◽  
Longlong Fu ◽  
Yao Shan ◽  
Peijun Guo

Yuchen Liao

AbstractWe study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint distribution, under the relaxation time scale $$t=O(L^{3/2})$$ t = O ( L 3 / 2 ) when the height fluctuations are critically affected by the finite geometry. The assumptions are verified for the step and flat initial conditions. As a corollary we obtain the multi-point distribution of discrete time TASEP on the whole integer lattice $${\mathbb {Z}}$$ Z by taking the period L large enough so that the finite-time distribution is not affected by the boundary. The large time limit for the multi-time distribution of discrete time TASEP on $${\mathbb {Z}}$$ Z is then obtained for the step initial condition.

Manuel Friedrich ◽  
Lennart Machill

AbstractWe consider a two-dimensional model of viscoelastic von Kármán plates in the Kelvin’s-Voigt’s rheology derived from a three-dimensional model at a finite-strain setting in Friedrich and Kružík (Arch Ration Mech Anal 238: 489–540, 2020). As the width of the plate goes to zero, we perform a dimension-reduction from 2D to 1D and identify an effective one-dimensional model for a viscoelastic ribbon comprising stretching, bending, and twisting both in the elastic and the viscous stress. Our arguments rely on the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004) and complement the $$\Gamma $$ Γ -convergence analysis of elastic von Kármán ribbons in Freddi et al. (Meccanica 53:659–670, 2018). Besides convergence of the gradient flows, we also show convergence of associated time-discrete approximations, and we provide a corresponding commutativity result.

2022 ◽  
pp. 875529302110608
Chuanbin Zhu ◽  
Fabrice Cotton ◽  
Hiroshi Kawase ◽  
Annabel Haendel ◽  
Marco Pilz ◽  

Earthquake site responses or site effects are the modifications of surface geology to seismic waves. How well can we predict the site effects (average over many earthquakes) at individual sites so far? To address this question, we tested and compared the effectiveness of different estimation techniques in predicting the outcrop Fourier site responses separated using the general inversion technique (GIT) from recordings. Techniques being evaluated are (a) the empirical correction to the horizontal-to-vertical spectral ratio of earthquakes (c-HVSR), (b) one-dimensional ground response analysis (GRA), and (c) the square-root-impedance (SRI) method (also called the quarter-wavelength approach). Our results show that c-HVSR can capture significantly more site-specific features in site responses than both GRA and SRI in the aggregate, especially at relatively high frequencies. c-HVSR achieves a “good match” in spectral shape at ∼80%–90% of 145 testing sites, whereas GRA and SRI fail at most sites. GRA and SRI results have a high level of parametric and/or modeling errors which can be constrained, to some extent, by collecting on-site recordings.

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