Related papers: Dynamic Spatial Treatment Effect Boundaries: A Con…
I develop a continuous functional framework for spatial treatment effects grounded in Navier-Stokes partial differential equations. Rather than discrete treatment parameters, the framework characterizes treatment intensity as continuous…
This paper develops a unified framework for identifying spatial and temporal boundaries of treatment effects in difference-in-differences designs. Starting from fundamental fluid dynamics equations (Navier-Stokes), we derive conditions…
This paper develops a unified theoretical framework for detecting and estimating boundaries in treatment effects across both spatial and temporal dimensions. We formalize the concept of treatment effect boundaries as structural parameters…
This paper develops a nonparametric framework for identifying and estimating spatial boundaries of treatment effects in settings with geographic spillovers. While atmospheric dispersion theory predicts exponential decay of pollution under…
Emergency medical services (EMS) response times are critical determinants of patient survival, yet existing approaches to spatial coverage analysis rely on discrete distance buffers or ad-hoc geographic information system (GIS) isochrones…
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-similar initial data and are known to be regular outside of a…
This paper develops a continuous functional framework for treatment effects propagating through geographic space and economic networks. We derive a master equation from three independent economic foundations -- heterogeneous agent…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier-Stokes equations for the fluid…
This paper introduces a novel framework for causal inference in spatial economics that explicitly models the stochastic transition from partial to general equilibrium effects. We develop a Denoising Diffusion Probabilistic Model (DDPM)…
This paper is devoted to the numerical study of droplet impact on solid substrates in presence of surfactants. We formulate the problem in an energetically variational framework and introduce an incompressible Cahn-Hilliard-Navier-Stokes…
We provide a mathematical analysis of the `diffusion-free' boundary conditions recently introduced by Lin and Kerswell for the numerical treatment of inertial waves in a fluid contained in a rotating sphere. We consider here the full…
We study the pointwise decay properties of solutions to the incompressible Navier-Stokes equations, both in the space and time variables. It is well known that generic global solutions on $\mathbb{R}^n$ do not decay faster at infinity than…
The transient growth of disturbances made possible by the non-normality of the linearized Navier-Stokes equations plays an important role in bypass transition for many shear flows. Transient growth is typically quantified by the maximum…
This paper presents the first energy-dissipative level-set method for the incompressible Navier-Stokes equations with surface tension. The methodology relies on the recently proposed concept of functional entropy variables. Discretization…
In the hydrodynamic theory, the non-equilibrium dynamics of a many-body system is approximated, at large scales of space and time, by irreversible relaxation to local entropy maximisation. This results in a convective equation corrected by…
This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity…
We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by…
The potential outcomes framework serves as a fundamental tool for quantifying causal effects. The average dose-response function (also called the effect curve), denoted as (\mu(t)), is typically of interest when dealing with a continuous…
We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…