Related papers: Tuned Finite-Difference Diffusion Operators
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…
Dynamical downscaling is crucial for deriving high-resolution meteorological fields from coarse-scale simulations, enabling detailed analysis for critical applications such as weather forecasting and renewable energy modeling. Generative…
The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…
The sharing of microdata, such as fund holdings and derivative instruments, by regulatory institutions presents a unique challenge due to strict data confidentiality and privacy regulations. These challenges often hinder the ability of both…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
Magnetised turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the…
Virtual fixtures assist human operators in teleoperation settings by constraining their actions. This extended abstract introduces a novel virtual fixture formulation \emph{on surfaces} for tactile robotics tasks. Unlike existing methods,…
Seismic data processing involves techniques to deal with undesired effects that occur during acquisition and pre-processing. These effects mainly comprise coherent artefacts such as multiples, non-coherent signals such as electrical noise,…
Numerical underflow and overflow are major hurdles for rolling-out the modeling and simulation infrastructure for temperatures below about 50 K. Extending the numeric precision is computationally intensive and thus best avoided. The root…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
Accurate long-term traffic forecasting remains a critical challenge in intelligent transportation systems, particularly when predicting high-frequency traffic phenomena such as shock waves and congestion boundaries over extended rollout…
Redundant manipulators, with their higher Degrees of Freedom (DoFs), offer enhanced kinematic performance and versatility, making them suitable for applications like manufacturing, surgical robotics, and human-robot collaboration. However,…
Conditional diffusion models have demonstrated impressive performance in image manipulation tasks. The general pipeline involves adding noise to the image and then denoising it. However, this method faces a trade-off problem: adding too…