相关论文: Unfolding-based corrector estimates for a reaction…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…
Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
Multiphase flows through reservoir rocks are a universal and complex phenomenon. Relative permeability is one of the primary determinants in reservoir performance calculations. Accurate estimation of the relative permeability is crucial for…
A receding-front model for drying of porous material is proposed that explains their drying-rate curves based on the dynamics of the evaporation front. The falling-rate regime is attributed to the slowing down of the front's propagation…
The unfolding problem in particle physics is to make inferences about the true particle spectrum based on smeared observations from a detector. This is an ill-posed inverse problem, where small changes in the smeared distribution can lead…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
Compressed sensing Synthetic Aperture Radar (SAR) image formation, formulated as an inverse problem and solved with traditional iterative optimization methods can be very computationally expensive. We investigate the use of denoising…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
Downscaling, or super-resolution, provides decision-makers with detailed, high-resolution information about the potential risks and impacts of climate change, based on climate model output. Machine learning algorithms are proving themselves…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
In this work we propose upscaling method for nonlinear Forchheimer flow in highly heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and slightly-compressible single-phase flows. We use recently…
Diffusion inversion aims to recover the initial noise corresponding to a given image such that this noise can reconstruct the original image through the denoising diffusion process. The key component of diffusion inversion is to minimize…