Related papers: Optimal velocity fields for instantaneous magnetic…
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…
A compact version of the variation evolving method (VEM) is developed in the primal variable space for optimal control computation. Following the idea that originates from the Lyapunov continuous-time dynamics stability theory in the…
We investigate pointwise estimation of the function-valued velocity field of a second-order linear SPDE. Based on multiple spatially localised measurements, we construct a weighted augmented MLE and study its convergence properties as the…
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the…
The magnetic Rayleigh-Taylor instability has been shown to play a key role in many astrophysical systems. The equation for the growth rate of this instability in the incompressible limit, and the most-unstable mode that can be derived from…
Recently we have presented a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in phase spaces . The maximal proper-acceleration bound is $a = c^2/…
We derive and assess the sharpness of analytic upper bounds for the instantaneous growth rate and finite-time amplification of palinstrophy in solutions of the two-dimensional incompressible Navier-Stokes equations. A family of optimal…
An exact analytic solution is obtained for a uniformly expanding, neutral, highly conducting plasma sphere in an ambient dipole magnetic field with an arbitrary orientation of the dipole moment in the space. Based on this solution the…
In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev.…
I argue that ideal MHD relativistic winds are always limited in practice to asymptotic 4-velocity $\gamma_\infty \approx \sigma_0^{1/3}$ and asymptotic magnetization $\sigma \sim \sigma_0^{2/3} \gg 1$, where $\sigma_0$ is the wind…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
Dynamical extra dimensions break the conformal invariance of Maxwell's equations in four dimensions. A higher dimensional background with $n$ contracting extra dimensions and four expanding dimensions is matched to an effectively four…
An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A…
The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of…
We study the problem of optimal mixing of a passive scalar $\rho$ advected by an incompressible flow on the two dimensional unit square. The scalar $\rho$ solves the continuity equation with a divergence-free velocity field $u$ with…
We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the…