Differing perceptions on the landing of the rod into the slot

In the usual rod and slot paradox, the rod, if it falls, was expected to fall into the slot due to gravity. Many thought experiments have been conducted where the presence of gravity is eliminated with the rod and slot approaching each other along a line joining their centers, whereby the considerations come strictly under Special Relativity. In these experiments the line of motion is not parallel to either the axis of the rod or the slot. In this paper we consider in detail the two cases when the rod does fall into the slot and when the rod does not fall into the slot, each from the perspective of the co-moving frames of the rod and the slot. We show that whether the rod falls into the slot as determined by Galilean kinematics is also valid under relativistic kinematics; this determination does not depend upon the magnitude of the velocity, but only on the proper lengths and the proper angles of the rod and slot with the line of motion. Our conclusion emphasizes the fact that the passing (or crashing) of the rod as a wholesome event is unaffected by relativistic kinematics. We also provide a simple formula to determine whether or not the rod passes through the slot.Comment: 9 pages, 6 figure

Moving Signals and Their Measured Frequencies

In determining the classical Doppler Effect, two assumptions are used for computing the difference in distance travelled by consecutive signals: (a) the receptor is stationary, and (b) the emitter is stationary. The calculated Doppler Effect under the two assumptions are identical, provided the velocity of propagation with respect to source and the velocity of propagation with respect to the receptor differ exactly by the velocity of relative motion. We show that, in the case of light, the ratio of the two calculated classical Doppler Effects, with propagation speed c in the source and receptor inertial frames respectively, remains constant in all geometries and orientations. Furthermore, the observed Doppler Effect, as predicted by special relativity, is the geometric mean of the two expected classical Doppler Effects in all geometries and orientations. This leads to two simultaneous conclusions: (1) by the receptor that the clock associated with the emitter runs slow, and (2) by the emitter that the clock associated with the receptor runs slow. These differences can be resolved if we theorize that light travels at speed c with respect to the emitter as it leaves the emitter and travels at speed c with respect to the receptor as it approaches the receptor.Comment: Revised in accordance with peer review process; Published August 2013 in Int. J. Engg. Res. & Sci & Tech 2(3) pp 24-3

Relaxation Behavior by Time-Salt and Time-Temperature Superpositions of Polyelectrolyte Complexes from Coacervate to Precipitate

Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different salt types. We find that the complexes exhibit time-temperature superposition (TTS) at all salt concentrations, while the range of overlapped-frequencies for time-temperature-salt superposition (TTSS) strongly depends on the salt concentration (Cs) and gradually shifts to higher frequencies as Cs is decreased. The sticky-Rouse model describes the relaxation behavior at all Cs. However, collective relaxation of polyelectrolyte complexes gradually approaches a rubbery regime and eventually exhibits a gel-like response as Cs is decreased and limits the validity of TTSS.Comment: 12 pages, 5 figures, Follow Gels journal link for latest versio

Fields and fluids on curved non-relativistic spacetimes

We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example we write down the most general theory of dissipative fluids consistent with the second law in curved non-relativistic geometries and find significant differences in the allowed transport coefficients from those found previously. Kubo formulas for all response coefficients are presented. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its relation to non-relativistic limits may be found in a companion paper [arXiv:1503.02682].Comment: Reference added. 44 page

Comprehensive learning incorporating Ako: A tertiary education approach at Wintec

This article outlines the design and implementation of a scenario-based approach to teaching and learning in tertiary education, inspired from Ako, adopted at the Waikato Institute of Technology (Wintec). This learning approach, titled ‘Comprehensive Learning (CL)’, aligns with the holistic objective of enabling students with an active, flexible, personalised, authentic and practical approach to learning that builds upon students’ interests and experiences. The article explains the motivation and the process used in creating and applying this approach to teach some of the IT and Business modules. The main reason to implement this approach is to encourage/enable critical thinking while learning in a continuous and personalised manner. CL allows students to specialize in a context of their choice, which in turn induces learning. In addition, students are less motivated to plagiarize due to the unique nature of their scenarios, and inherent safeguards present within the approach

Physical stress, mass, and energy for non-relativistic matter

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.Comment: 31 pages, one appendix. Minor clarifications added and typos fixe

A Variational Principle for the Axisymmetric Stability of Rotating Relativistic Stars

It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar-Friedman-Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh-Ritz type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.Comment: v2: updated some text and references; published in CQG v1: 36 page