相关论文: The control of particles in the Stokes limit

In this paper we present a finite element analysis for a Dirichlet boundary control problem governed by the Stokes equation. The Dirichlet control is considered in a convex closed subset of the energy space $\mathbf{H}^1(\Omega).$ Most of…

Contactless manipulation of small objects is essential for biomedical and chemical applications, such as cell analysis, assisted fertilisation, and precision chemistry. Established methods, including optical, acoustic, and magnetic…

This work develops scientific computing techniques to further the exploration of using boundary control alone to optimize mixing in Stokes flows. The theoretical foundation including mathematical model and the optimality conditions for…

Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has been almost no theoretical investigation into the associated…

As in arXiv: math. 0809.2365 we consider classical system of interacting particles $\mathcal{P}_1, ..., \mathcal{P}_n$ on the line with only neighboring particles involved in interaction. On the contrast to arXiv: math. 0809.2365 now {\it…

Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…

With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…

Accessing the ballistic regime of single particles in liquids remains an experimental challenge that shrouds our understanding of the particle-liquid interactions on exceedingly short time scales. We demonstrate the ballistic measurements…

Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can…

PDE-constrained optimization is a field of numerical analysis that combines the theory of PDEs, nonlinear optimization and numerical linear algebra. Optimization problems of this kind arise in many physical applications, prominently in…

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…

This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…

It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the dynamics are described in a four dimensional phase space and thus…

We study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus…

We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek-Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological…

Particles suspended in a viscous fluid circle in optical vortices generated by holographic optical-tweezer techniques [Curtis J E and Grier D G 2003 Phys. Rev. Lett. 90 133901]. We model this system and show that hydrodynamic interactions…

Droplet coalescence is essential in a host of biological and industrial processes, involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of…

In this work, a combination of experiments and theory is used to investigate three-body, normal collisions between solid particles with a liquid coating (i.e., "wetted" particles). Experiments are carried out using a Stokes' cradle, an…

Current optical manipulation techniques rely on carefully engineered setups and samples. Although similar conditions are routinely met in research laboratories, it is still a challenge to manipulate microparticles when the environment is…