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We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and…
We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
This work considers the {\em gravitational} $N$-body problem and introduces global time-renormalization {\em functions} that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence…
A shadow of a numerical solution to a chaotic system is an_exact_ solution to the equations of motion that remains close to the numerical solution for a long time. In a collisionless n-body system, we know that particle motion is governed…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
The evolution of a many-particle system on a one-dimensional lattice, subjected to a quantum walk can cause spatial entanglement in the lattice position, which can be exploited for quantum information/communication purposes. We demonstrate…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states…
Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian…
Elegant integration schemes of second and fourth order for simulations of rigid body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact…
Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…
We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…