Related papers: Geometric flows and the Swampland
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation.…
For certain terms in the action, supersymmetry can forbid an infinite number of possible contributions. We study whether such protection can occur in quantum gravity even without sufficient supersymmetry. We focus on whether the…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the…
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…
Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary…
Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory. Such F- and W-functionals were introduced in the Ricci flow theory of…
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…
In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
Recall that a vector field on an n-dimensional differentiable manifold M is a mapping X defined on M with values in the tangent bundle TM that assigns to each point $x\in M$ a vector X(x) in the tangent space $T_x M$. A vector field may be…
An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
We develop techniques for calculating the ground state wave functional and the geometric entropy for some simple field theories. Special attention is devoted to fermions, which present special technical difficulties in this regard. Explicit…
The new formal analogy between superfluid systems and cosmology, which emerges by taking into account the back-reaction of the vacuum to the quanta of sound waves \cite{noi}, enables us to put forward some common features between these two…