Electric charge in the field of a magnetic event in three-dimensional spacetime

We analyze the motion of an electric charge in the field of a magnetically charged event in three-dimensional spacetime. We start by exhibiting a first integral of the equations of motion in terms of the three conserved components of the spacetime angular momentum, and then proceed numerically. After crossing the light cone of the event, an electric charge initially at rest starts rotating and slowing down. There are two lengths appearing in the problem: (i) the characteristic length $\frac{q g}{2 \pi m}$, where $q$ and $m$ are the electric charge and mass of the particle, and $g$ is the magnetic charge of the event; and (ii) the spacetime impact parameter $r_0$. For $r_0 \gg \frac{q g}{2 \pi m}$, after a time of order $r_0$, the particle makes sharply a quarter of a turn and comes to rest at the same spatial position at which the event happened in the past. This jump is the main signature of the presence of the magnetic event as felt by an electric charge. A derivation of the expression for the angular momentum that uses Noether's theorem in the magnetic representation is given in the Appendix.Comment: Version to appear in Phys. Rev.

Is Sustainable Development of Deserts Feasible?

Hot deserts that presently cover about one-fifth of the land area of our planet are rapidly devouring more and more arable lands mostly due to anthropogenic causes. We propose an interdisciplinary approach to revitalizing and commercializing hot deserts, which is based on systems thinking and Russian and NASA space technology experience in designing life-support systems for long-duration flights. We formulate ten principles for the design of sustainable life support systems in deserts, which can make the development of the deserts feasible. It is discussed how the principles can be employed to design and operate desert’s eco-industrial parks with greenhouses in which the transpired and evaporated moisture is collected and condensed. The potential benefits of setting up the eco-industrial parks in deserts include the slowdown and eventual reversal of the desertification trend, the migration of many industrial production facilities from mild-climate regions to deserts, the increased availability of potable water and food in deserts, the development of poor African countries, and the emergence of new investment markets

Fluid Dynamics of NSR Strings

We show that the renormalization group flows of the massless superstring modes in the presence of fluctuating D-branes satisfy the equations of fluid dynamics.In particular, we show that the D-brane's U(1) field is related to the velocity function in the Navier-Stokes equation while the dilaton plays the role of the passive scalar advected by the turbulent flow. This leads us to suggest a possible isomorphism between the off-shell superstring theory in the presence of fluctuating branes and the fluid mechanical degrees of freedom.Comment: 24 pages Dedicated to the memory of Ian Koga

Extra ZZ bosons and low-energy tests of unification

If there is an extra U(1) gauge symmetry broken at low energies, then it may be possible from the charges of the known quarks and leptons under this U(1) to make inferences about how much gauge unification occurs at high scales and about the unification group. (For instance, there are certain observed properties of an extra $U(1)'$ that would be inconsistent with unification in four dimensions at high scales.) A general analysis is presented. Two criteria used in this analysis are (1) the degree to which the generator of the extra U(1) mixes with hypercharge, and (2) the ratio of the extra U(1) charge of the "10" and the "$\bar{5}$" of quarks and leptons.Comment: 27 pages, LaTex, no figures. Changed content. References added. Typos correcte

Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology

We study a surface model with a self-avoiding (SA) interaction using the canonical Monte Carlo simulation technique on fixed-connectivity (FC) triangulated lattices of sphere topology. The model is defined by an area energy, a deficit angle energy, and the SA potential. A pressure term is also included in the Hamiltonian. The volume enclosed by the surface is well defined because of the self-avoidance. We focus on whether or not the interaction influences the phase structure of the FC model under two different conditions of pressure ${\it \Delta} p$; zero and small negative. The results are compared with the previous results of the self-intersecting model, which has a rich variety of phases; the smooth spherical phase, the tubular phase, the linear phase, and the collapsed phase. We find that the influence of the SA interaction on the multitude of phases is almost negligible except for the evidence that no crumpled surface appears under {\it \Delta} p\=\0 at least even in the limit of zero bending rigidity \alpha\to \0. The Hausdorff dimension is obtained in the limit of \alpha\to \0 and compared with previous results of SA models, which are different from the one in this paper.Comment: 9 figure

Moduli Spaces of Lumps on Real Projective Space

Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge three lumps is a D2-symmetric 7-dimensional manifold of cohomogeneity one. In this paper, we discuss the charge three moduli spaces of lumps from two perspectives: discrete symmetries of lumps and the Riemann-Hurwitz formula. We then calculate the metric and find explicit formula for various geometric quantities. We also discuss the implications for lump decay

Numerical Investigation of Monopole Chains

We present numerical results for chains of SU(2) BPS monopoles constructed from Nahm data. The long chain limit reveals an asymmetric behavior transverse to the periodic direction, with the asymmetry becoming more pronounced at shorter separations. This analysis is motivated by a search for semiclassical finite temperature instantons in the 3D SU(2) Georgi-Glashow model, but it appears that in the periodic limit the instanton chains either have logarithmically divergent action or wash themselves out.Comment: 14 pages, 6 figures; v2 minor changes, published versio