Effects of additive noise on the stability of glacial cycles

It is well acknowledged that the sequence of glacial-interglacial cycles is paced by the astronomical forcing. However, how much is the sequence robust against natural fluctuations associated, for example, with the chaotic motions of atmosphere and oceans? In this article, the stability of the glacial-interglacial cycles is investigated on the basis of simple conceptual models. Specifically, we study the influence of additive white Gaussian noise on the sequence of the glacial cycles generated by stochastic versions of several low-order dynamical system models proposed in the literature. In the original deterministic case, the models exhibit different types of attractors: a quasiperiodic attractor, a piecewise continuous attractor, strange nonchaotic attractors, and a chaotic attractor. We show that the combination of the quasiperiodic astronomical forcing and additive fluctuations induce a form of temporarily quantised instability. More precisely, climate trajectories corresponding to different noise realizations generally cluster around a small number of stable or transiently stable trajectories present in the deterministic system. Furthermore, these stochastic trajectories may show sensitive dependence on very small amounts of perturbations at key times. Consistently with the complexity of each attractor, the number of trajectories leaking from the clusters may range from almost zero (the model with a quasiperiodic attractor) to a significant fraction of the total (the model with a chaotic attractor), the models with strange nonchaotic attractors being intermediate. Finally, we discuss the implications of this investigation for research programmes based on numerical simulators. }Comment: Parlty based on a lecture given by M. Crucifix at workshop held in Rome in 2013 as a part of Mathematics of Planet Earth 201

Range fluctuations of high energy muons passing through matter

The information about energy spectrum of sea level muons at high energies beyond magnetic spectrographs can be obtained from the underground intensity measurements if the fluctuations problems are solved. The correction factor R for the range fluctuations of high energy muons were calculated by analytical method of Zatsepin, where most probable energy loss parameter are used. It is shown that by using the R at great depth together with the slope, lambda, of the vertical depth-intensity (D-I) curve in the form of exp(-t/lambda), the spectral index, gamma, in the power law energy spectrum of muons at sea level can be obtained

Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles

Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\sim$40 kyr before the so-called middle Pleistocene transition between $\sim$1.2 and $\sim$0.7 Myr ago, and it is $\sim$100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.Comment: 25 pages, 9 figure

A small tabletop experiment for a direct measurement of the speed of light

A small tabletop experiment for a direct measurement of the speed of light to an accuracy of few percent is described. The experiment is accessible to a wide spectrum of undergraduate students, in particular to students not majoring in science or engineering. The experiment may further include a measurement of the index of refraction of a sample. Details of the setup and equipment are given. Results and limitations of the experiment are analyzed, partly based on our experience in employing the experiment in our student laboratories. Safety considerations are also discussed.Comment: 4pages, 5fig

Sustainability, Debt Management, and Public Debt Policy in Japan

The purpose of this paper is to analyze sustainability issues of Japan's fiscal policy and then to discuss the debt management policy using theoretical models and numerical studies. We also investigate the desirable coordination of fiscal and monetary authorities toward fiscal reconstruction. We include a potential possibilities of the government bonds in our theoretical model The public bonds, therefore, cannot be sold when the issuance leads the amount of debt outstanding to be more than a certain level. In this respect, the fiscal authority has to take into account the upper limit of stocks of public debt. This possibility of debt default provides the fiscal authority to issue public bonds strategically in an earlier period. A strategic behavior of fiscal authority induces the monetary authority, in a later period, to boost output and raise seigniorage revenues to eliminate the distortion of resource allocation due to the limitation on debt issuance. Therefore, the monetary policy in a later period suffers from an inflation bias from the ax ante point of view. There are two ways to eliminate this distortion toward successful fiscal reconstruction. One of them is to make the monetary authority more conservative than society in the sense that the price stability weight of monetary authority is higher than that of society. The other way of eliminating the distortion of the resource allocation is to design an institutional ceiling on the debt issuance. The direct ceiling can provide a binding constraint of the public bond issuance for the fiscal authority of Japan because it has accumulated the debt outstanding much more than other countries.