Related papers: Surface terms on the Nishimori line of the Gaussia…
We utilize total-internal reflection to isolate the two-dimensional `surface foam' formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly…
The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational problem of min-max type. In the absence of magnetic fields…
For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, where A is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at…
We study free boundary compressible viscous models that may include nonlinear viscosities. These are compressible/incompressible Navier-Stokes type systems for a non-Newtonian stress tensor. They describe the motion of a possibly…
The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
Rotating convection is considered on the tilted $f$-plane where gravity and rotation are not aligned. For sufficiently large rotation rates, $\Omega$, the Taylor-Proudman effect results in the gyroscopic alignment of anisotropic columnar…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash--Moser iteration…
We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in…
While the notion of isometric deformations of surfaces is straightforward for surfaces with Euclidean metric, a corresponding notion in isotropic space has been missing. By making Gauss' Theorema Egregium a necessary condition we develop a…
A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of…
I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of…
We study the effect of surface tension of the phase boundary in the dynamics of an expanding fluid. A fluid at local thermal equilibrium, but has a slowly varying temperature profile, like the plasma formed in heavy ion collisions, will…
We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which…
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
We derive a formula, useful for first-principles calculations, which relates the free energy of an oxide/metal interface to the free energies of surfaces and the work of separation of the interface. We distinguish the latter {\it…