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Efforts to modulate the electronic properties of atomically thin crystalline nanoribbons requires precise control over their morphology. Here, we perform atomistic simulations on freestanding graphene nanoribbons (GNRs) to first identify…
The elastic field around a crack opening is known to be described by continuum linearised elasticity in leading order. In this work, we explicitly develop the next term in the atomistic asymptotic expansion in the case of a Mode III crack…
We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous…
We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents. The exact remainder…
We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…
A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal the balance between the contributions from the higher and…
We consider a system of many hard rods moving in one dimension. As it is an integrable system, it possesses an extensive number of conserved quantities and its evolution on macroscopic scale can be described by generalised hydrodynamics.…
The simulation of hypersonic flows is computationally demanding due to large gradients of the flow variables caused by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely…
Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers.…
A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…
A convenient approach to derive simple expressions for properties of Stokes flows with low levels of slip is presented. The method is based on a series expansion of a Stokes-flow solution (one satisfying a Navier slip boundary condition)…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a…
The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…