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In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete…
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…
Linear scaling quantum chemical methods for Density Functional Theory are extended to the condensed phase at the $\Gamma$-point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [J.…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
Starting from microscopic $N$ particle systems, we study the derivation of Doi type models for suspensions of non-spherical particles in Stokes flows. While Doi models accurately describe the effective evolution of the spatial particle…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
Confined quantum systems involving $N$ identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear and chemical physics. In a previous series of papers, a manybody perturbation method that…
We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the…
We present a method that offers perspectives to perform fully antisymmetrized simulations for inhomogeneous bulk fermion matter. The technique bears resemblance to classical periodic boundary conditions, using localized single-particle…
We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero…
There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We formulate a method for incorporating quantum fluctuations into molecular- dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…
We present a formalism for coupling a density functional theory-based quantum simulation to a classical simulation for the treatment of simple metallic systems. The formalism is applicable to multiscale simulations in which the part of the…
This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the…