On Controlled P Systems

We introduce and brie y investigate P systems with controlled computations. First, P systems with label restricted transitions are considered (in each step, all rules used have either the same label, or, possibly, the empty label, ), then P systems with the computations controlled by languages (as in context-free controlled grammars). The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies (characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework). A series of open problems and research topics are formulated

ZJ-theorems for fusion systems

For p an odd prime, we generalise the Glauberman-Thompson p-nilpotency theorem [5, Ch. 8, Theorem 3.1] to arbitrary fusion systems. We define a notion of Qd(p)- free fusion systems and show that if F is a Qd(p)-free fusion system on some finite p-group P then F is controlled by W(P) for any Glauberman functor W, generalising Glauberman’s ZJ-theorem [3] to arbitrary fusion systems

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

Controlling Multiparticle System on the Line, II - Periodic case

As in arXiv: math. 0809.2365 we consider classical system of interacting particles $\mathcal{P}_1, ..., \mathcal{P}_n$ on the line with only neighboring particles involved in interaction. On the contrast to arXiv: math. 0809.2365 now {\it periodic boundary conditions} are imposed onto the system, i.e. $\mathcal{P}_1$ and $\mathcal{P}_n$ are considered neighboring. Periodic Toda lattice would be a typical example. We study possibility to control periodic multiparticle systems by means of forces applied to just few of its particles; mainly we study system controlled by single force. The free dynamics of multiparticle systems in periodic and nonperiodic case differ substantially. We see that also the controlled periodic multiparticle system does not mimic its non-periodic counterpart. Main result established is global controllability by means of single controlling force of the multiparticle system with ageneric potential of interaction. We study the nongeneric potentials for which controllability and accessibility properties may lack. Results are formulated and proven in Sections~2,3.Comment: 15 page

Spontaneous surface magnetization and chiral Majorana modes

Majorana fermions are often proposed to be realized by first singling out a single non-degenerate Fermi surface in spin-orbit coupled systems, and then imposing boundaries or defects. In this work, we take a different route starting with two degenerate Fermi surfaces without spin-orbit coupling, and show that by the method of "kink on boundary", the dispersive chiral Majorana fermions can be realized in superconducting systems with $p\pm is$ pairings. The surfaces of these systems develop spontaneous magnetizations whose directions are determined by the boundary orientations and the phase difference between the $p$ and $s$-component gap functions. Along the magnetic domain walls on the surface, there exist chiral Majorana fermions propagating unidirectionally, which can be conveniently dragged and controlled by external magnetic fields. Furthermore, the surface magnetization is shown to be a magnetoelectric effect based on a Ginzburg-Landau free energy analysis. We also discuss how to use the proximity effects to realize chiral Majorana fermions by performing the "kink on boundary" method

Regularity for Lorentz Metrics under Curvature Bounds

Let (M, g) be an (n+1) dimensional space-time, with bounded curvature with respect to a bounded framing. If (M, g) is vacuum or satisfies a mild condition on the stress-energy tensor, then we show that (M, g) locally admits coordinate systems in which the Lorentz metric is well-controlled in the (space-time) Sobolev space L^{2,p}, for any finite p.Comment: 18p

Sources for Chern-Simons theories

The coupling between Chern-Simons theories and matter sources defined by branes of different dimensionalities is examined. It is shown that the standard coupling to membranes, such as the one found in supergravity or in string theory, does not operate in the same way for CS theories; the only p-branes that naturally couple seem to be those with p=2n; these p-branes break the gauge symmetry (and supersymmetry) in a controlled and sensible manner.Comment: 17 pages, Dedicated to Claudio Bunster on the occasion of his 60th birthday. To appear in Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicit