Exact solutions for chemical concentration waves of self-propelling camphor particles racing on a ring: A novel potential dynamics perspective

A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are derived. The bifurcation diagram describing the transition between the immobile and self-propelling modes of camphor objects is derived semi-analytically. The bifurcation is of a pitchfork type which is consistent with earlier theoretical work in which natural boundary conditions have been considered.Comment: 12 pages, 4 figure

A Simple Nested Simulation for SED-ML

This document describes a simple nested Simulation Experiment for SED-ML [1] that is easy to implement and will help to broaden what SED-ML is able to encode

Synchronization and anchoring of two non-harmonic canonical-dissipative oscillators via Smorodinsky-Winternitz potentials

Two non-harmonic canonical-dissipative limit cycle oscillators are considered that oscillate in one-dimensional Smorodinsky-Winternitz potentials. It is shown that the standard approach of the canonical-dissipative framework to introduce dissipative forces leads naturally to a coupling force between the oscillators that establishes synchronization. The non-harmonic character of the limit cycles in the context of anchoring, the phase difference between the synchronized oscillators, and the degree of synchronization are studied in detail.Comment: 7 pages, 1 figur

On the Sensitivity of Aggregate Productivity Growth Rates to Noisy Measurement

Aggregate rates of productivity growth are among the most closely watched indicators of economic performance. They are also among the most difficult to measure accurately. This paper explores the sensitivity of such rates to random measurement error using a simple generic model. The model allows for errors in the input and output components of the productivity ratio, with different variances, and for serial and cross correlation of the errors. The effects of the errors are considered from the point of view of growth rates themselves, changes in growth rates, and comparisons between rates in different countries.productivity; growth rates; measurement error

On the Sensitivity of Aggregate Productivity Growth Rates to Noisy Measurement

Aggregate rates of productivity growth are among the most closely watched indicators of economic performance. They are also among the most difficult to measure accurately. This paper explores the sensitivity of such rates to random measurement error using a simple generic model. The model allows for errors in the input and output components of the productivity ratio, with different variances, and for serial and cross correlation of the errors. The effects of the errors are considered from the point of view of growth rates themselves, changes in growth rates, and comparisons between rates in different countries.productivity; growth rates; measurement error