Related papers: Deterministic Partial Differential Equation Model …
A new type of disorder-driven electronic percolation transition is found for two-dimensional electron gas (2DEG), based on a quantum cellular automaton model. This transition is shown to be accompanied with a metal-insulator transition, as…
Fully differential cross sections are calculated for the ionization of H$_2$ by fast charged projectiles using a semiclassical model developed previously for the ionization of atoms. The method is tested in case of 4 keV electron and 6 MeV…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a…
An early phase clinical trial is the first step in evaluating the effects in humans of a potential new anti-disease agent or combination of agents. Usually called "phase I" or "phase I/II" trials, these experiments typically have the…
Identifying the mutations that drive cancer growth is key in clinical decision making and precision oncology. As driver mutations confer selective advantage and thus have an increased likelihood of occurrence, frequency-based statistical…
Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density $\rho_A(E)$ and to particle-hole densities. We use exact…
A classical description of electron emission differential ionization cross sections for highly-charged high-velocity ions ($\sim$ 10 a.u.) impinging on water molecules is presented. We investigate the validity of the classical statistical…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
The level density is among the most important statistical nuclear properties. It appears in Fermi's golden rule for transition rates and is an important input to the Hauser-Feshbach theory of compound nucleus reactions. We discuss empirical…
Skin dose in radiotherapy is a key issue for reducing patient side effects, but dose calculations in this high-gradient region remains a challenge. To support radiation therapists and medical physicist in their decisions, a computational…
Radiotherapy can effectively kill malignant cells, but the doses required to cure cancer patients may inflict severe collateral damage to adjacent healthy tissues. Hyperthermia (HT) is a promising option to improve the outcome of radiation…
Fully relativistic approach to evaluate the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in $1/Z$ are treated rigorously within the framework of…
Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule.…
With the increased affordability and availability of whole-genome sequencing, large-scale and high-throughput gene expression is widely used to characterize diseases, including cancers. However, establishing specificity in cancer diagnosis…
Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual…
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D…
We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
We present a multi-layer mathematical model to describe the the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describe the basic convection-diffusion process, with the electric potential obtained by…