Related papers: A frame energy for immersed tori and applications …
Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise…
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the…
We analyse the entrainment and energetics of equal and opposite axisymmetric turbulent air plumes in a vertically confined space at a Rayleigh number of $1.24\times 10^{7}$ using theory and direct numerical simulation. On domains of…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the…
The interaction of a magnetic dipole with a point charge leads to an apparent paradox when analyzed using the 3-vector formulation of the Lorentz force. Specifically, the dipole is subject to a torque in some frames and not in others. We…
In this paper, we propose a discrete version of O'Hara's knot energy defined on polygons embedded in the Euclid space. It is shown that values of the discrete energy of polygons inscribing the curve which has bounded O'Hara's energy…
For geodesic motion of a particle in a stationary spacetime the $U_0$ component of particle 4-velocity is constant and is considered to be a conserved mechanical energy. We show that this concept of a conserved mechanical energy can be…
We study the existence of whiskered tori in a family $f_\mu$ of conformally symplectic maps depending on parameters $\mu$. Whiskered tori are tori on which the motion is a rotation, but they have as many expanding/contracting directions as…
We investigate sufficient H\"older continuity conditions on Leray-Hopf (weak) solutions to the in unsteady Navier-Stokes equations in three dimensions guaranteeing energy conservation. Our focus is on the half-space case with homogeneous…
Onsager's conjecture, which relates the conservation of energy to the regularity of weak solutions of the Euler equations, was completely resolved in recent years. In this work, we pursue an analogue of Onsager's conjecture in the context…
The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished…
A topological classification of many classes of dynamical systems with regular dynamics in low dimensions is often reduced to combinatorial invariants. In dimension 3 combinatorial invariants are proved to be insufficient even for simplest…
The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a…
We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with…
In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM) models in fractured porous media accounting for Coulomb frictional contact at matrix fracture interfaces. The simulation of such models plays an important role in…
We prove an $\epsilon$-regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the tracefree second fundamental form from a small control…
We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free…
Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical…