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We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…
Scanning Tunneling Spectroscopy (STS) is a unique technique to probe the local density of states (LDOS) at the atomic scale by measuring the tunneling conductance between a sharp tip and a sample surface. However, the technique suffers of…
We have developed a lab work module where we teach undergraduate students how to quantify the dynamics of a suspension of microscopic particles, measuring and analyzing the motion of those particles at the individual level or as a group.…
Single-detector 3D dynamic light scattering (3D-DLS) emerges as a reliable technique to determine the drift velocity of out-of-equilibrium colloidal particles. In particular, our investigation reveals the appearance of oscillations of a…
Laboratory experiments and theoretical modelling are conducted to determine the raindrop size distribution (DSD) resulting from distinct fragmentation processes under various upward airstreams. Since weather radar echoes are proportional to…
Simulating high-resolution Synthetic Aperture Radar (SAR) images in complex scenes has consistently presented a significant research challenge. The development of a microwave-domain surface scattering model and its reversibility are poised…
Wireless devices need spectrum to communicate. With the increase in the number of devices competing for the same spectrum, it has become nearly impossible to support the throughput requirements of all the devices through current spectrum…
A continuous time random walk (CTRW) model with waiting times following the Levy-stable distribution with exponential cut-off in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian diffusion. The distribution…
Oscillating-gradient spin-echo diffusion-weighted magnetic resonance imaging (OGSE-DWI) has been promoted as a promising technique for studying the microstructure of complex hydrated matter in the frequency domain. The target of the…
Plastic scintillation detectors are increasingly used to measure dose distributions in the context of radiotherapy treatments. Their water-equivalence, real-time response and high spatial resolution distinguish them from traditional…
A phase shift and sum (PSAS) algorithm to image objects in dispersive media is presented. The algorithm compensates the phase shift of the scattered field from the receiver to the source for each frequency component in an ultrawideband…
We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at position $\x$…
To estimate the diffusion constant $D$ of particles in a plasma, we develop a method that is based on the mean free path $\lambda$ for scatterings with momentum transfer $q >~ T$. Using this method, we estimate $\lambda$ and $D$ for squarks…
This work introduces Differential Wavelet Amplifier (DWA), a drop-in module for wavelet-based image Super-Resolution (SR). DWA invigorates an approach recently receiving less attention, namely Discrete Wavelet Transformation (DWT). DWT…
Dissipationless hydrodynamics regularized by dispersion describe a number of physical media including water waves, nonlinear optics, and Bose-Einstein condensates. As in the classical theory of hyperbolic equations where a non-convex flux…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
The viscously dominated, low Reynolds' number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behavior when viewed appropriately. In these systems, nonlinear self-steepening competes with wave…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
We present a comprehensive investigation of polymer diffusion in the semidilute regime by fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Using single-labeled polystyrene chains, FCS leads to the…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…