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In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…
Torque-driven microscale swimming robots, or microrotors, hold significant potential in biomedical applications such as targeted drug delivery, minimally invasive surgery, and micromanipulation. This paper addresses the challenge of…
The charge transported when a quantum pump is adiabatically driven by time-dependent external forces in presence of dissipation is given by the line integral of a pumping field $\mathbf{F}$. We give a general expression of $\mathbf{F}$ in…
The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an…
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…
We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses and is advected by the suspending fluid. Beyond a certain emission/absorption rate (characterized by a…
Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenomena by combining hydrophobicity and roughness to trap gas bubbles in microscopic textures. Recent works in this area have focused on specific…
Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
Smoothed Particle Hydrodynamics (SPH) is a unique numerical method widely used for astrophysical problems since it involves no spatial grid. Rather, fluid quantities are carried by a set of Lagrangian `particles' which move with the flow,…
We develop a simulational methodology allowing for simulation of the pressure-driven flow in the pore with flat and polymer-modified walls. Our approach is based on dissipative particle dynamics and we combine earlier ideas of fluid-like…
The mobility of externally-driven phoretic propulsion of particles is evaluated by simultaneously solving the solute conservation equation, interaction potential equation, and the modified Stokes equation. While accurate, this approach is…
We study the particle-scale motion of highly polydisperse hard disks flowing in a two-dimensional bent channel. We use various size distributions of particles, in which the largest particles are up to five times larger than the smallest.…
Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction, such as the venous and the lymphatic system. We investigate here a certain class of models where the fluid is driven by peristaltic…
Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves…
We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…
A magnetic field rotating on the free surface of a ferrofluid layer is shown to induce considerable fluid motion toward the direction the field is rolling. The measured flow velocity i) increases with the square of the magnetic field…
We derive from first principles a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of…
Pebble accretion offers an efficient pathway to form planets, driven by a constant supply of inward drifting mass and an accretion efficiency enhanced by gas drag. While most studies assume a single pebble size (monodisperse), real discs…