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

Thermodynamic aspects of rock friction

Rate- and state-dependent friction law for velocity-step tests is analyzed from a thermodynamic point of view. A simple macroscopic non-equilibrium thermodynamic model with a single internal variable reproduces instantaneous jump and relaxation. Velocity weakening appears as a consequence of a plasticity related nonlinear coefficient. Permanent part of displacement corresponds to plastic strain, and relaxation effects are analogous to creep in thermodynamic rheology.Comment: 13 pages 3 figures. Revision: thermodynamic compatibility of velocity weakenin

Noise reduction and hyperfine level coherence in spontaneous noise spectroscopy of atomic vapor

We develop a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two in novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1\,kHz without high frequency ($\gtrsim10\,$MHz) noise. These methods are described systematically and the performance of the asurement system is examined through experimental results.Comment: 6pages. 4 figure

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