The fundamental “two-fluid” model for describing plasma dynamics is given by the EulerMaxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to globa...

The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop EulerHeisenberg effective Lagrangian for QED in a self-dual background field is naturally ex...

In this paper the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordström’s scalar theory of gravity. The evolution of the fluid is determined by a quasilinear hyperbolic system of PDEs, and a cosmological constant is introduced in order to ensure the existence of non-zero constant solutions. Accordingly, the initial value problem for a compact pe...

We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing flocking behaviors of large animal groups. establish local well-posedness theory for well global small initial data. also show asymptotic behavior, where solutions converge to constant steady state exponentially in time.

This article develops methods for studying the topology of submanifolds of constant positive curvature in Euclidean space. It proves that if Mn is an n-dimensional compact connected Riemannian submanifold of constant positive curvature in E2n−1, then Mn must be simply connected. It also gives a conformal version of this theorem.

We prove that small smooth irrotational but charged perturbations of a constant background are global and go back to equilibrium in the 3D electron Euler-Poissson equation.

We consider a model for atmospheric circulation based on the Euler equations for a compressible gas. We consider two hydrostatic base solutions depending on height, one with constant temperature and one isentropic with constant temperature gradient or lapse rate. We argue that these solutions represent solutions with maximal and minimal turbulent dissipation with the observed real lapse rate so...

We define the generalized-Euler-constant function γ(z) = ∑∞ n=1 z n−1 ( 1 n − log n+1 n ) when |z| ≤ 1. Its values include both Euler’s constant γ = γ(1) and the “alternating Euler constant” log 4 π = γ(−1). We extend Euler’s two zeta-function series for γ to polylogarithm series for γ(z). Integrals for γ(z) provide its analytic continuation to C − [1,∞). We prove several other formulas for γ(z...

We study cluster algebras with principal and arbitrary coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of certain paths on a triangulation of the surface. As an immediate consequence, we prove the positivity conjecture of Fomin and Zelevinsky for these cluster a...

We develop a formalism for computing one-loop gravitational corrections to the effective action of D-branes. In particular, we study bulk to brane mediation of supersymmetry breaking in models where supersymmetry is broken at the tree-level in the closed string sector (bulk) by Scherk-Schwarz boundary conditions, while it is realized on a collection of D-branes in a linear or non-linear way. We...