Related papers: Deterministic Partial Differential Equation Model …
We present a novel method to improve pharmacokinetics modeling, an essential step of drug development. Conventional models frequently fail to fully represent the intricacies of drug absorption and distribution, which limits their predictive…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We propose a method of simulation that is based on the averaging of formal solutions of the transfer equation by taking the integral by the Monte Carlo method. This method is used to compute two models, which correspond to the limiting…
Utilizing the Pauli equation based multislice method, introduced in Phys. Rev. Lett. 116, 127203 (2016), we study the atomic resolution differential phase contrast (DPC) imaging on an example of a hard magnet FePt with in-plane…
We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the…
For the first time, we report a theoretical methodology to predict charge state distribution of projectile ions inside a solid-target. The method utilizes either a simple Fermi gas model or an ab initio theoretical method and a certain…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
The present paper deals with the study of the fluence rate over both healthy and tumor tissues in the presence of focal laser ablation (FLA). We propose new analytical solutions for the coupled partial differential equations (PDE) system,…
Radiotherapy is one of the main methods in the successful treatment of cancer. The tumor is irradiated with photons or charged particles (e.g. protons), and in the case of massive charged particles, the treatment results in less unnecessary…
The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting…
We present a state-space-based path integral method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. We employ an exact path integral in discrete electronic states and continuous…
We consider a simple neural field model in which the state variable is dendritic voltage, and in which somas form a continuous one-dimensional layer. This neural field model with dendritic processing is formulated as an integro-differential…
We introduce a novel learning framework for accelerated Monte Carlo (MC) dose calculation termed Energy-Shifting. This approach leverages deep learning to synthesize highly complex polyenergetic dose distributions directly from simple…
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees…
We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we…
Starting from a general equation for organism (or cell system) growth and attributing additional cell death rate (besides the natural rate) to therapy, we derive an equation for cell response to {\alpha} radiation. Different from previous…