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A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large…
We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids…
We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction…
Existing approaches to solving the Vlasov equation treat the system as a partial differential equation on a phase space grid, and track in either an Eulerian, Lagrangian, or semi-Lagrangian picture. We present an alternative approach, which…
We study constrained nonconvex optimization problems in machine learning, signal processing, and stochastic control. It is well-known that these problems can be rewritten to a minimax problem in a Lagrangian form. However, due to the lack…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…
Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…
Curved fluid interfaces are investigated on the nanometre length scale by molecular dynamics simulation. Thereby, droplets surrounded by a metastable vapour phase are stabilized in the canonical ensemble. Analogous simulations are conducted…
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,'' and can they be derived by an application of these laws? We…
Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…
Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…
We propose a $\tau$-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional $\tau$-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures…
Aims. This work presents a new hydrodynamical algorithm to study astrophysical detonations. A prime motivation of this development is the description of a carbon detonation in conditions relevant to superbursts, which are thought to result…
We investigate through numerical simulations the hydrodynamic interactions between two rigid spherical particles suspended on the axis of a cylindrical tube filled with an elastoviscoplastic fluid subjected to pressure-driven flow. The…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
We propose unified data structures and algorithms for free-surface fluid simulations based on partial optimal transport, such as the Power Particles method or Gallou\"et-M\'erigot's scheme. Such methods previously relied on a discretization…