Suspension and levitation in nonlinear theories

I investigate stable equilibria of bodies in potential fields satisfying a generalized Poisson equation: divergence[m(grad phi) grad phi]= source density. This describes diverse systems such as nonlinear dielectrics, certain flow problems, magnets, and superconductors in nonlinear magnetic media; equilibria of forced soap films; and equilibria in certain nonlinear field theories such as Born-Infeld electromagnetism. Earnshaw's theorem, totally barring stable equilibria in the linear case, breaks down. While it is still impossible to suspend a test, point charge or dipole, one can suspend point bodies of finite charge, or extended test-charge bodies. I examine circumstances under which this can be done, using limits and special cases. I also consider the analogue of magnetic trapping of neutral (dipolar) particles.Comment: Five pages, Revtex, to appear in Physics Letters

BFFT quantization with nonlinear constraints

We consider the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) that makes the conversion of second-class constraints into first-class ones for the case of nonlinear theories. We first present a general analysis of an attempt to simplify the method, showing the conditions that must be fulfilled in order to have first-class constraints for nonlinear theories but that are linear in the auxiliary variables. There are cases where this simplification cannot be done and the full BFFT method has to be used. However, in the way the method is formulated, we show with details that it is not practicable to be done. Finally, we speculate on a solution for these problems.Comment: 19 pages, Late

Practically linear analogs of the Born-Infeld and other nonlinear theories

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear theories of special interest, for which they can serve as approximations. The idea can be applied to a large class of nonlinear theories, exemplified here with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics. The general class of such PL theories of electromagnetism are governed by a Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples to currents in the standard way, while Qmn is an auxiliary field, derived from a vector potential that does not couple directly to currents. By picking a special form of S(Q_mn), we can make such a theory similar in some regards to a given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A particularly felicitous choice is to take S as the Legendre transform of U. For the BI theory, this Legendre transform has the same form as the BI Lagrangian itself. Various matter-of-principle questions remain to be answered regarding such theories. As a specific example, I discuss BI electrostatics in more detail. As an aside, for BI, I derive an exact expression for the short-distance force between two arbitrary point charges of the same sign, in any dimension.Comment: 20 pages, Version published in Phys. Rev.

Inflation-Produced Magnetic Fields in Nonlinear Electrodynamics

We study the generation of primeval magnetic fields during inflation era in nonlinear theories of electrodynamics. Although the intensity of the produced fields strongly depends on characteristics of inflation and on the form of electromagnetic Lagrangian, our results do not exclude the possibility that these fields could be astrophysically interesting.Comment: 6 page

Experimental Investigations of Elastic Tail Propulsion at Low Reynolds Number

A simple way to generate propulsion at low Reynolds number is to periodically oscillate a passive flexible filament. Here we present a macroscopic experimental investigation of such a propulsive mechanism. A robotic swimmer is constructed and both tail shape and propulsive force are measured. Filament characteristics and the actuation are varied and resulting data are quantitatively compared with existing linear and nonlinear theories

A Note on the Linear and Nonlinear Theories for Fully Cavitated Hydrofoils

The lifting problem of fully cavitated hydrofoils has recently received some attention. The nonlinear problem of two-dimensional fully cavitated hydrofoils has been treated by the author, using a generalized free streamline theory. The hydrofoils investigated in Ref. 1 were those with sharp leading and trailing edges which are assumed to be the separation points of the cavity streamlines. Except for this limitation, the nonlinear theory is applicable to hydrofoils of arbitrary geometric profile, operating at any cavitation number, and for almost all angles of attack as long as the cavity wake is fully developed. By using an elegant linear theory, Tulin has treated the problem of a fully cavitated flat plate set at a small angle of attack and operated at arbitrary cavitation number. In the case of hydrofoils of arbitrary profile operating at zero cavitation number, some interesting simple relationships are given by Tulin for the connection between the lift, drag and moment of a supercavitating hydrofoil and the lift, moment and the third moment of an equivalent airfoil (unstalled). In the present investigation, Tulin's linear theory is first extended to calculate the hydrodynamic lift and drag on a fully cavitated hydrofoil of arbitrary camber at arbitrary cavitation number. A numerical example is given for a circular hydrofoil subtending an arc angle of 160, for which the corresponding nonlinear solution is available. A direct comparison between these two theories is made explicitly for the flat plate and the circular arc hydrofoil. Some important aspects of the results are discussed subsequently

Exactly solvable models of nonlinear extensions of the Schr\"odinger equation

A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger equations and exactly solvable nonlinear theories. We provide several examples illustrating the method. We rederive well-known soliton solutions and find new exactly solvable nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.Comment: 14 pages, 7 figure

Lower bound to limiting fields in nonlinear electrodynamics

In view of new high-precision experiments in atomic physics it seems necessary to reexamine nonlinear theories of electrodynamics. The precise calculation of electronic and muonic atomic energies has been used to determine the possible size of the upper limit Emax to the electric field strength, which has been assumed to be a parameter. This is opposed to Born's idea of a purely electromagnetic origin of the electron's mass which determines Emax. We find Emax≥1.7×1020 V/cm