Related papers: Geometrically incompatible confinement of solids
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
We review the circumstances under which test particles can be localized around a spacetime section \Sigma_0 smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, \Sigma_0 is said to be totally…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave…
We study equilibrium configurations for the Euler-Plateau energy with elastic modulus, which couples an energy functional of Euler-Plateau type with a total curvature term often present in models for the free energy of biomembranes. It is…
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface $(M,g)$ isometrically embedded in $\mathbb{R}^3$, we…
The Euler characteristic is an invariant of a topological space that in a precise sense captures its canonical notion of size, akin to the cardinality of a set. The Euler characteristic is closely related to the homology of a space, as it…
Topological matter in 3D is characterized by the presence of a topological BF term in its long-distance effective action. We show that, in 3D, there is another marginal term that must be added to the action in order to fully determine the…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
The Euler buckling of rods is a long-studied mechanical instability, and it remains relevant to this day, as the constituent components in many biological and physical systems are linear polymers, such as microtubules or carbon nanotubes.…
In this paper, we establish a mathematical theory on statement and validation of the hypersonic similarity law within the framework of Radon measure solutions of steady compressible Euler equations. We consider two scenarios: (1)…
Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates -- what is a petty frustration when placing a sticky bandage onto an elbow or knee is a more serious matter in the coating and…
We establish two Phragm\'en--Lindel\"{o}f theorems for a fully nonlinear elliptic equation. We consider a dynamic boundary condition that includes both spatial variable and time derivative terms. As a spatial term, we consider a non-linear…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem…
We consider a wavefunction of large $N$ matrices supported close to an emergent classical fuzzy sphere geometry. The $SU(N)$ Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric…
We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density $\rho$, shear modulus $\mu$, put in a rigid cylindrical dish of depth $h$. When turned…
Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…