Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks.

Whether there exist finite-time blow-up solutions for the 2D Boussinesq and the 3D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new numerical framework, employing physics-informed neural networks, that discover, for the first time, a smooth self-similar blow-up profile for both equations. The solution itself could form the basis of a future computer-assisted proof of blow-up for both equations. In addition, we demonstrate physics-informed neural networks could be successfully applied to find unstable self-similar solutions to fluid equations by constructing the first example of an unstable self-similar solution to the Córdoba-Córdoba-Fontelos equation. We show that our numerical framework is both robust and adaptable to various other equations.

Direct Verification of the Kinetic Description of Wave Turbulence for Finite-Size Systems Dominated by Interactions among Groups of Six Waves.

The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schrödinger equation. Specific parameter regimes in which ensemble-averaged dynamics of such systems with finite size are accurately described by a wave kinetic equation, as used in wave turbulence theory, are theoretically predicted. In addition, the underlying reasons that the wave kinetic equation may be a poor predictor of wave dynamics outside these regimes are also discussed. These theoretical predictions are directly verified by comparing ensemble averages of solutions to the dynamical equation with corresponding solutions of the wave kinetic equation.

Evidence that macrophages are programmed to die after activating autologous, cloned, antigen-specific, CD4+ T cells.

The bone marrow produces large numbers of monocytes daily, but the mechanisms balancing production and elimination are unknown. In this report we demonstrate that macrophages (M phi) undergo apoptosis after activating autologous CD4+ cells. Since apoptosis is a genetically programmed response, these results argue that M phi death can be part of a normal immune response. This event may have relevance to monocyte/M phi homeostasis, as well as immune response regulation and host defenses to intracellular organisms.