The scalar complex potential and the Aharonov-Bohm effect

The Aharonov-Bohm effect is traditionally attributed to the effect of the electromagnetic 4-potential $A$, even in regions where both the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ are zero. The AB effect reveals that multiple-valued functions play a crucial role in the description of an electromagnetic field. We argue that the quantity measured by AB experiments is a difference in values of a multiple-valued complex function, which we call a complex potential or {pre-potential. We show that any electromagnetic field can be described by this pre-potential, and give an explicit expression for the electromagnetic field tensor through this potential. The pre-potential is a modification of the two scalar potential functions.Comment: 10 pages 2 figure

A simple 5-DOF walking robot for space station application

Robots on the NASA space station have a potential range of applications from assisting astronauts during EVA (extravehicular activity), to replacing astronauts in the performance of simple, dangerous, and tedious tasks; and to performing routine tasks such as inspections of structures and utilities. To provide a vehicle for demonstrating the pertinent technologies, a simple robot is being developed for locomotion and basic manipulation on the proposed space station. In addition to the robot, an experimental testbed was developed, including a 1/3 scale (1.67 meter modules) truss and a gravity compensation system to simulate a zero-gravity environment. The robot comprises two flexible links connected by a rotary joint, with a 2 degree of freedom wrist joints and grippers at each end. The grippers screw into threaded holes in the nodes of the space station truss, and enable it to walk by alternately shifting the base of support from one foot (gripper) to the other. Present efforts are focused on mechanical design, application of sensors, and development of control algorithms for lightweight, flexible structures. Long-range research will emphasize development of human interfaces to permit a range of control modes from teleoperated to semiautonomous, and coordination of robot/astronaut and multiple-robot teams

Fixed subgroups are compressed in surface groups

For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\operatorname{Fix} B$, of any family $B$ of endomorphisms of $\pi_1(\Sigma)$ is compressed in $\pi_1(\Sigma)$ i.e., $\operatorname{rk}((\operatorname{Fix} B)\cap H)\leq \operatorname{rk}(H)$ for any subgroup $\operatorname{Fix} B \leq H \leq \pi_1(\Sigma)$. On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, $G$, of finitely many free and surface groups, and give a characterization of when $G$ satisfies that $\operatorname{rk}(\operatorname{Fix} \phi) \leq \operatorname{rk}(G)$ for every $\phi \in Aut(G)$

Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics

We study reactions between end-functionalized chains at a polymer-polymer interface. For small chemical reactivities (the typical case) the number of diblocks formed, $R_t$, obeys 2nd order chemically controlled kinetics, $R_t \sim t$, until interfacial saturation. For high reactivities (e.g. radicals) a transition occurs at short times to 2nd order diffusion-controlled kinetics, with $R_t \sim t/\ln t$ for unentangled chains while $t/\ln t$ and $t^{1/2}$ regimes occur for entangled chains. Long time kinetics are 1st order and controlled by diffusion of the more dilute species to the interface: $R_t \sim t^{1/4}$ for unentangled cases, while $R_t \sim t^{1/4}$ and $t^{1/8}$ regimes arise for entangled systems. The final 1st order regime is governed by center of gravity diffusion, $R_t \sim t^{1/2}$.Comment: 11 pages, 3 figures, uses poliface.sty, minor changes, to appear in Europhysics Letter

Occurrence of normal and anomalous diffusion in polygonal billiard channels

From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e. when no particle can travel arbitrarily far without colliding. For the infinite horizon case we present numerical tests showing that the mean squared displacement instead grows asymptotically as t log t. When the unit cell contains accessible parallel scatterers, however, we always find anomalous super-diffusion, i.e. power-law growth with an exponent larger than 1. This behavior cannot be accounted for quantitatively by a simple continuous-time random walk model. Instead, we argue that anomalous diffusion correlates with the existence of families of propagating periodic orbits. Finally we show that when a configuration with parallel scatterers is approached there is a crossover from normal to anomalous diffusion, with the diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures, additional comments. Some higher quality figures available at http://www.fis.unam.mx/~dsander

Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability

Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce misleading and verbose results if the model is too complex, especially w.r.t. feature interactions. To quantify the complexity of arbitrary machine learning models, we propose model-agnostic complexity measures based on functional decomposition: number of features used, interaction strength and main effect complexity. We show that post-hoc interpretation of models that minimize the three measures is more reliable and compact. Furthermore, we demonstrate the application of these measures in a multi-objective optimization approach which simultaneously minimizes loss and complexity

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering from this instability decrease to around 100Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000

On wormholes with arbitrarily small quantities of exotic matter

Recently several models of traversable wormholes have been proposed which require only arbitrarily small amounts of negative energy to hold them open against self-collapse. If the exotic matter is assumed to be provided by quantum fields, then quantum inequalities can be used to place constraints on the negative energy densities required. In this paper, we introduce an alternative method for obtaining constraints on wormhole geometries, using a recently derived quantum inequality bound on the null-contracted stress-energy averaged over a timelike worldline. The bound allows us to perform a simplified analysis of general wormhole models, not just those with small quantities of exotic matter. We then use it to study, in particular, the models of Visser, Kar, and Dadhich (VKD) and the models of Kuhfittig. The VKD models are constrained to be either submicroscopic or to have a large discrepancy between throat size and curvature radius. A recent model of Kuhfittig is shown to be non-traversable. This is due to the fact that the throat of his wormhole flares outward so slowly that light rays and particles, starting from outside the throat, require an infinite lapse of affine parameter to reach the throat.Comment: 30 pages, 2 figure

On attributes of a Rotating Neutron star with a Hyperon core

We study the effect of rotation on global properties of neutron star with a hyperon core in an effective chiral model with varying nucleon effective mass within a mean field approach. The resulting gross properties of the rotating compact star sequences are then compared and analyzed with other theoretical predictions and observations from neutron stars. The maximum mass of the compact star predicted by the model lies in the range $(1.4-2.4) ~M_{\odot}$ at Kepler frequency $\Omega_K$, which is consistant with recent observation of high mass stars thereby reflecting the sensitivity of the underlying nucleon effective mass in the dense matter EoS. We also discuss the implications of the experimental constraints from the flow data from heavy-ion collisions on the global properties of the rotating neutron stars.Comment: 11 Pages, 10 Figures and 2 Table