Related papers: Brachistochronous motion of a flat plate parallel …
The brachistochrone, the curve of fastest descent under gravity, is a cycloid when friction is absent. Underwater, however, buoyancy, viscous drag, and the added mass of entrained fluid fundamentally alter the problem. We formulate and…
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…
In a variety of applications, most notably microfluidic design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height…
We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
The numerical approach has been performed to study the Bingham fluid flow through an oscillatory porous plate with Ion-Slip and Hall current. Initially, at time; t = 0 both the fluid and the upper plate are at rest. At time; t > 0 the upper…
The motion of incompressible fractional Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies time-dependent shear stresses to the fluid is studied by means of integral transforms. In the special cases of…
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…
We study the problem of minimising the connection time between non-equilibrium steady states of the Brownian Gyrator. This is a paradigmatic model in non-equilibrium statistical mechanics, an overdamped Brownian particle trapped in a…
The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled the instantaneous conformation of the…
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…
We theoretically studied the optimal control, frequency lock-in, and phase lock-in phenomena due to the spatially localized periodic forcing in the flow past the inclined plate. Although frequency lock-in is evident in many fluid phenomena,…
By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then…
We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…