Related papers: A note on fractional derivative modeling of broadb…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution…
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
This paper presents a paraxial modeling approach for vibro-acoustography, a high-frequency ultrasound imaging technique that makes use of the excited low-frequency field to achieve a higher resolution while avoiding speckles. We start from…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
Recent studies have developed tunable topological elastic metamaterials to maximize performance in the presence of varying external conditions, adapt to changing operating requirements, and enable new functionalities such as a programmable…
THis work is a survey of a few nonlinear PDE based models in image restoring.
We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that…
The effect of structural defects on the critical ultrasound attenuation and ultrasound velocity dispersion in Ising-like three-dimensional systems is studied. A field-theoretical description of the dynamic effects of acoustic-wave…
We consider deep learning strategies in ultrasound systems, from the front-end to advanced applications. Our goal is to provide the reader with a broad understanding of the possible impact of deep learning methodologies on many aspects of…
In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\rho(\cdot)$ typically scales poorly…
Single-shot ultrafast absorbance spectroscopy based on the frequency encoding of the kinetics is analyzed theoretically and implemented experimentally. In Part II of the series, arbitrary thickness sample is analysed theroretically. The…
Spreading uniform and dense layers is of paramount importance to creating high-quality components using powder bed additive manufacturing (AM). Blade-like tools are often employed for spreading powder metal feedstocks, especially in laser…
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop for our analysis are: (i) a new density result in $GSBV^{p}$ of functions satisfying a…
The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse…
In MR elastography it is common to use an elastic model for the tissue's response in order to properly interpret the results. More complex models such as viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic ones are also…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…