Related papers: The exact solution of the diffusion trapping model…
An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice…
Modelling of colloidal and nano-suspension transport in porous media has garnered significant attention due to the prevalence of these processes in many engineering applications. A number of experimental studies have reported retention…
We introduce a new attack paradigm that embeds hidden adversarial capabilities directly into diffusion models via fine-tuning, without altering their observable behavior or requiring modifications during inference. Unlike prior approaches…
This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…
We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field…
We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we focus on the so-called unipolar case, a system of PDE's derived…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Material properties strongly depend on the nature and concentration of defects. Characterizing these features may require nano- to atomic-scale resolution to establish structure-property relationships. 4D-STEM, a technique where diffraction…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
There is a need for numerical models capable of predicting local accumulation of hydrogen near stress concentrators and crack tips to prevent and mitigate hydrogen assisted fracture in steels. The experimental characterisation of trapping…
Positron emission tomography (PET) is an advanced medical imaging technique that plays a crucial role in non-invasive clinical diagnosis. However, while reducing radiation exposure through low-dose PET scans is beneficial for patient…
A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an…
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…
We examine the applicability of various model profiles for the liquid/vapor interface by X-ray reflectivities on water and ethanol and their mixtures at room temperature. Analysis of the X-ray reflecivities using various density profiles…
Upon impact, the free surface of a solid metal may eject a cloud of fast and fine particles. Photon Doppler Velocimetry (PDV) is one of the optical diagnostics used to characterize these ejecta. Although the technique provides a direct way…
Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp…
Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality,…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
A precise comparison of the cross sections for the elastic scattering of electrons and positrons on protons was performed recently at the VEPP-3 storage ring in Novosibirsk, Russia. To provide the proposed accuracy, the energies of the…
Background: Positronium lifetime imaging extends conventional positron emission tomography by using the time interval between positron emission and annihilation as an additional contrast mechanism. Voxel-wise lifetime estimation in fully…