Related papers: Elastic displacements and viscous hydrodynamic flo…
Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this…
Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force…
A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…
Elastic channels are an important component of many soft matter systems, in which hydrodynamic interactions with confining membranes determine the behavior of particles in flow. In this work, we derive analytical expressions for the Green's…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
We study classical binary fluid mixtures in which densities vary on very short time (ps) and length (nm) scales, such that hydrodynamics does not apply. In a pure fluid with a localized heat pulse the breakdown of hydrodynamics was overcome…
We compile a list of 2-D and axisymmetric Green's functions for isotropic full and half spaces, to complement our letter "Linear elasticity of incompressible solids". We also extend the isotropic exactly incompressible linear theory from…
Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified during the past. Prime example systems are given by functionalized elastic…
This paper develops a comprehensive mathematical framework for modeling the coupled hydroelastic dynamics of sea-ice floes of arbitrary shape and non-uniform thickness under linear ocean wave forcing. We simultaneously incorporate four…
The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…
A problem on propagation of waves in deformable shells with flowing liquid is very urgent in connection with wide use of liquid transportation systems in living organisms and technology. It is necessary to consider shell motion equations…
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the…
A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of the homogeneous reference state is studied in detail using methods of non-equilibrium statistical mechanics. A…
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…
Non-equilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early time pre-equilibrium stage of high-energy heavy ion collisions. Besides their practical relevance they also…
We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
Understanding the hydrodynamics of out-of-equilibrium dense viscous fluids is of key importance to accurate descriptions of physical systems such as compact stars, particularly their mergers. We consider a near-equilibrium relativistic…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…