Multi-point distribution of discrete time periodic TASEP

We 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.

An isogeometric mortar method for the coupling of multiple NURBS domains with optimal convergence rates

We investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patches $$\Omega _k$$ Ω k with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces $$X_{h,k}$$ X h , k on each patch $$\Omega _k$$ Ω k as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of Brivadis et al. (Comput Methods Appl Mech Eng 284:292–319, 2015) and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces $$X_{h,k}$$ X h , k which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected.

A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations

We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax–Milgram theorem with the curl-free constraint built into the target (or cost) functional, the discrete spaces require no inf-sup stabilization. We show that standard conforming finite elements can be used yielding a priori and a posteriori convergence results. We illustrate our findings with numerical experiments with uniform or adaptive mesh refinement.

Accurate discretization of poroelasticity without Darcy stability

In this manuscript we focus on the question: what is the correct notion of Stokes–Biot stability? Stokes–Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot’s equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage coefficient and a vanishing hydraulic conductivity. The basic premise of a Stokes–Biot stable discretization is: one part Stokes stability and one part mixed Darcy stability. In this manuscript we remark on the observation that the latter condition can be generalized to a wider class of discrete spaces. In particular: a parameter-uniform inf-sup condition for a mixed Darcy sub-problem is not strictly necessary to retain the practical advantages currently enjoyed by the class of Stokes–Biot stable Euler–Galerkin discretization schemes.

METHODOLOGY OF DISCRETE SPATIAL-PARAMETRIC REAL ESTATE MARKET MODELLING

This paper gives a formalized description of the procedure for constructing widely used discrete spatial-parametric models of the real estate market in terms of set theory – an apparatus specially created for describing discrete spaces. The presentation is carried out in comparison with the approaches and concepts of a related methodology – regression models of mass appraisal of real estate objects. The methodology of discrete spatial-parametric modeling of the real estate market is used for market monitoring, for building dynamic market indices and for mass appraisal of real estate objects. The methodology is based on statistical cluster analysis and also allows for static interpolation spatial-parametric forecasting of the values of market indicators in small clusters with insufficient sample size and in narrow markets with little or no supply. The application of the methodology of discrete spatial-parametric modeling of the real estate market is demonstrated on the example of the residential real estate market in Moscow.

Exact sampling of determinantal point processes without eigendecomposition

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm.