Related papers: Hydrostatic Newton-Cartan Membranes
In this paper we study global existence of weak solutions for the Quantum Hydrodynamics System in 2-D in the space of energy. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
We construct the first analytic examples of non-homogeneous condensates in the Georgi-Glashow model at finite density in $(2+1)$ dimensions. The non-homogeneous condensates, which live within a cylinder of finite spatial volume, possess a…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
We review an approach towards a covariant formulation of Matrix theory based on a discretization of the 11d membrane. Higher dimensional algebraic structures, such as the quantum triple Nambu bracket, naturally appear in this approach. We…
We present a method to solve the Helmholtz equation for a non-homogeneous membrane with Dirichlet boundary conditions at the border of arbitrary two-dimensional domains. The method uses a collocation approach based on a set of localized…
In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…
Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super…
The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of…
Cell membranes are anchored to the cytoskeleton via immobile inclusions. We investigate the effect of such anchors on the in-plane dynamics of a fluid membrane and mobile inclusions (proteins) embedded in it. The immobile particles lead to…
We construct a generally-covariant formulation of non-equilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding non-conservation of the energy…
The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that,…
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air…
It is well known that couplings occur among the scalar-, vector-, and tensor-type perturbations of Friedmann world model in the second perturbational order. Here, we prove that, except for the gravitational wave contribution, the…
The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding article of this series is developed by construction of the relevant 4-dimensional stress energy tensor whose conservation in the…
It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property…
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact…
This study develops an equation for describing three-dimensional membrane transformation through proliferation of its component cells regulated by morphogen density distributions on the membrane. The equation is developed in a…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…