Related papers: An Anti-Perfect Dynamo Result
We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative and the fluid distribution…
The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through…
It is known that in order for a supersymmetric gauge theory to be dynamically broken a necessary but not sufficient condition is that the Witten index $(-1)^F=n_b^0-n_f^0$ is zero. In the case the Witten index is zero it is in general hard…
In this paper, we study in detail a perfect fluid cosmological model with time-varying "constants" using dimensional analysis and the symmetry method. We examine the case of variable "constants" in detail without considering the perfect…
The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…
A differentiable function is pseudoconvex if and only if its restrictions over straight lines are pseudoconvex. A differentiable function depending on one variable, defined on some closed interval $[a,b]$ is pseudoconvex if and only if…
We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to…
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…
We present a new general method to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations of the theory relative to a diffeomorphic flow of curvilinear coordinates which…
In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of "integral action" for proportional(-derivative)-controlled systems whose…
The dynamics of a liquid dielectric attracted by a vertical cylindrical capacitor is studied. Contrary to what might be expected from the standard calculation of the force exerted by the capacitor, the motion of the dielectric is different…
We continue our investigation of the Gauss variational problem for infinite dimensional vector measures associated with a condenser $(A_i)_{i\in I}$. It has been shown in Potential Anal., DOI:10.1007/s11118-012-9279-8 that, if some of the…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
A new analysis of basic Couette flow, is based on an Action Principle for compressible fluids, with a Hamiltonian as well as a kinetic potential. An effective criterion for stability recognizes the tensile strength of water. This…
State-of-the-art approaches to optimal control use smooth approximations of value and policy functions and gradient-based algorithms for improving approximator parameters. Unfortunately, we show that value and policy functions that arise in…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
A sequence of exact relations is found which connect one- and many-particle time-dependent distribution functions of low-density gas with their derivatives in respect to mean density. It is shown that, at least in the context of spatially…
Irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analysed for the purpose of application to superfluid layers in neutron stars. Asymptotic solutions are found by…
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a…