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A new scheme that tightly couples kinetic turbulence codes across a spatial interface is introduced. This scheme evolves from considerations of competing strategies and down-selection. It is found that the use of a composite kinetic…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…
All observations of photodegradation and self healing follow the predictions of the correlated chromophore domain model. [Ramini et.al. Polym. Chem., 2013, 4, 4948.] In the present work, we generalize the domain model to describe the…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
Low density plasmas in curved spacetimes, such as those found in accretion flows around black holes, are challenging to model from first principles, owing to the large scale separation between the characteristic scales of the microscopic…
Stationary subdivision schemes have been extensively studied and have numerous applications in CAGD and wavelet analysis. To have high-order smoothness of the scheme, it is usually inevitable to enlarge the support of the mask that is used,…
Traditional general circulation models, or GCMs -- i.e. 3D dynamical models with unresolved terms represented in equations with tunable parameters -- have been a mainstay of climate research for several decades, and some of the pioneering…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
Geographic distribution shift arises when the distribution of locations on Earth in a training dataset is different from what is seen at inference time. Using standard empirical risk minimization (ERM) in this setting can lead to uneven…
We study the cosmological evolution of domain wall networks in two and three spatial dimensions in the radiation and matter eras using a large number of high-resolution field theory simulations with a large dynamical range. We investigate…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
A large number of powerful, high-quality, and open-source simulation packages exist to efficiently perform molecular dynamics simulations, and their prevalence has greatly accelerated discoveries across a wide range of scientific domains.…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…