Related papers: Hyperinstantons, the Beltrami Equation, and Trihol…
The hydrodynamic escape problem (HEP), which is characterized by a free boundary value problem of Euler equation with gravity and heat, is crucial for investigating the evolution of planetary atmospheres. In this paper, the global existence…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…
Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the long-wavelength and slow-time fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to…
We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry,…
Recently, the existence of an Amplituhedron for tree level amplitudes in the bi-adjoint scalar field theory has been proved by Arkhani-Hamed et al. We argue that hyperbolic geometry constitutes a natural framework to address the study of…
Some of the most interesting results on the global dynamics of solutions of the vacuum Einstein equations concern the Gowdy spacetimes whose spatial topology is that of a three-dimensional torus. In this paper certain of these ideas are…
We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…
Magnetic monopoles in hyperbolic space are in correspondence with certain algebraic curves in mini-twistor space, known as spectral curves, which are in turn in correspondence with rational maps between Riemann spheres. Hyperbolic monopoles…
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with…
In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami type, that can…
We examine the anomalies arising in instanton calculus as detailed by Damiano Anslemi in 1994. Whereas Anselmi uses BRST theory, we use the ADHM construction to arrive at the same conclusions from a differential-geometric way. We observe…
In the present work the local form of certain Calabi-Yau metrics possessing a local Hamiltonian Killing vector is described in terms of a single non linear equation. The main assumptions are that the complex $(3,0)$-form is of the form…
This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and…
We exactly solve the relaxation-time approximation Boltzmann equation for a system which is transversely homogeneous and undergoing boost-invariant longitudinal expansion. We compare the resulting exact numerical solution with approximate…
We present a new ray bending approach, referred to as the Eigenray method, for solving two-point boundary-value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are…
The technique of generating new solutions to 4D gravity/matter systems by dimensional reduction to a sigma-model is extended to supersymmetric configurations of supergravity. The conditions required for the preservation of supersymmetry…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…