相关论文: Hierarchical cascade model leading to 7-th order i…
The hydrodynamic equation derived by N-particle statistical mechanics is investigated. This is an attempt to provide additional information concerning the closure problem of turbulence theory. The equation is interpreted as mean velocity…
A universal particle velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
The variances of the fluid-particle acceleration and of the pressure-gradient and viscous force are given. The scaling parameters for these variances are velocity statistics measureable with a single-wire anemometer. For both high and low…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
Nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions. Using a discrete set of values for the solution, we derive a hierarchy of equations in…
The Hierarchical Clustering (HC) problem consists of building a hierarchy of clusters to represent a given dataset. Motivated by the modern large-scale applications, we study the problem in the \streaming model, in which the memory is…
In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic…
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…
Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how…
This article is concerned with the reconstruction of obstacle $\O$ immersed in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make…