Related papers: Quantum spin representation for the Navier-Stokes …
Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the…
We present a mapping between a Schr\"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential…
Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…
The search for quantum-like wave formulations of the Navier-Stokes (Schr\"odinger-Navier-Stokes, SNS for short) equations describing classical dissipative fluids has met with increasing attention in the recent years, due to the large…
Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for…
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importance, their behavior in turbulent regimes remains incompletely…
Vortex interactions are commonly observed in atmospheric turbulence, plasma dynamics, and collective behaviors in biological systems. However, accurately simulating these complex interactions is highly challenging due to the need to capture…
The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in…
A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…
In this study, we propose a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on the extended Navier-Stokes (N-S) equations. With some phenomenological observations and H. J. Kreuer's…
Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital…
We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…
Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum…
Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through…
This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with fractional operators and quantum-inspired dynamics. We propose…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is…
Physical vacuum is a special superfluid medium. Its motion is described by the Navier-Stokes equation having two slightly modified terms that relate to internal forces. They are the pressure gradient and the dissipation force because of…