Research
Research
Research
Research
4,220+ open-access research outputs.
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wis…
The gas-kinetic scheme (GKS) provides high computational efficiency and accuracy for continuum flow simulations but is unable to reliably capture rarefaction effects. In contrast, although the discret…
Current robots are capable of computing plans to accomplish complex tasks. However, real-world environments are inherently open and dynamic, and unforeseen situations frequently arise during plan exec…
The decade-long debate over the existence of apsidal clustering in the outer solar system is poised for reignition given the plethora of distant trans-Neptunian object (TNO) discoveries expected from …
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable…
Non-Maxwellian distributions and their origins in space plasma have attracted significant attention due to their prevalence and impact on various astrophysical and space-related phenomena. This paper …
In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These paramete…
Kinetic models based on the Bhatnagar-Gross-Krook (BGK) framework provide an efficient alternative to the Boltzmann equation for rarefied gas flows; however, existing formulations for gas mixtures rem…
We present a survey on multiplicity results for the Allen--Cahn equation and systems in the singular perturbation regime, emphasizing their geometric interpretation through $\Gamma$-convergence and is…
Khintchine's theorem on the measure dichotomy for the set of $\psi$-approximable numbers has been generalized to inhomogeneous and higher-dimensional settings. Allen and Ram\'irez conjectured that the…
There are 7,407 languages in the world. But, what about the languages that are not there in the world? Are humans so narrow minded that we don't care about the languages aliens communicate in? Aliens …
Solar panels are increasingly deployed in cities on rooftops, walls, and urban infrastructure. Although the panel costs have fallen in recent years, the soft costs of installing them have not. These s…
Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dyn…
This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The system comprises the …
As LLMs are increasingly integrated into agentic systems, they must adhere to dynamically defined, machine-interpretable interfaces. We evaluate LLMs as in-context interpreters: given a novel context-…
We propose Annealed Langevin Monte Carlo for Flow ODE Sampling (ALMC-ODE), a method for generating samples from unnormalized target distributions, with a particular emphasis on multimodal densities th…
We study the resurgence structure of the topological string partition function, with an emphasis on the Borel analysis of the instanton amplitudes. To this end, we introduce a differential operator th…
In this paper, we theoretically and numerically study the minimizers for the Cahn-Hilliard energy with the Flory-Huggins potential under the strong anchoring condition, i.e., the Dirichlet boundary co…
Very-low-Earth orbit drag uncertainty quantification in the rarefied/transitional Knudsen-number regime requires estimating not only the mean drag coefficient but also higher-order moments under atmos…
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artifici…
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