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We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
Video virtual try-on aims to transfer a clothing item onto the video of a target person. Directly applying the technique of image-based try-on to the video domain in a frame-wise manner will cause temporal-inconsistent outcomes while…
We study a continuum model of the lipid bilayer based on minimizing the free energy of a mixture of water and lipid molecules. This paper extends previous work by Blom & Peletier (2004) in the following ways. (a) It formulates a more…
To synthesize diffusion MR measurements from Monte-Carlo simulation using tissue models with sizes comparable to those of scan voxels. Larger regions enable restricting structures to be modeled in greater detail and improve accuracy and…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
This study introduces a novel approach for image reconstruction based on a diffusion model conditioned on the native data domain. Our method is applied to multi-coil MRI and quantitative MRI reconstruction, leveraging the domain-conditioned…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
Diffusion Probabilistic Models (DPMs) have demonstrated significant potential in 3D medical image segmentation tasks. However, their high computational cost and inability to fully capture global 3D contextual information limit their…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
This work introduces a new latent diffusion model to generate high-quality 3D chest CT scans conditioned on 3D anatomical masks. The method synthesizes volumetric images of size 256x256x256 at 1 mm isotropic resolution using a single…
We have studied the dynamics of spreading of viscous non-volatile fluids on surfaces by MC simulations of SOS models. We have concentrated on the complete wetting regime, with surface diffusion barriers neglected for simplicity. First, we…
The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical…
While the availability of open 3D medical shape datasets is increasing, offering substantial benefits to the research community, we have found that many of these datasets are, unfortunately, disorganized and contain artifacts. These issues…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…