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In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move closer to the optimal ratio of protons and neutrons. As a result of this transformation, the nucleus emits two detectable beta particles, which are electrons or positrons. The literature distinguishes between two types of double beta decay: ordinary double beta decay and neutrinoless double beta decay. In ordinary double beta decay, which has been observed in several isotopes, two electrons and two electron antineutrinos are emitted from the decaying nucleus. In neutrinoless double beta decay, a hypothesized process that has never been observed, only electrons would be emitted. The idea of double beta decay was first proposed by Maria Goeppert Mayer in 1935. In 1937, Ettore Majorana demonstrated that all results of beta decay theory remain unchanged if the neutrino were its own antiparticle, now known as a Majorana particle. In 1939, Wendell H. Furry proposed that if neutrinos are Majorana particles, then double beta decay can proceed without the emission of any neutrinos, via the process now called neutrinoless double beta decay. It is not yet known whether the neutrino is a Majorana particle, and, relatedly, whether neutrinoless double beta decay exists in nature. In 1930–1940s, parity violation in weak interactions was not known, and consequently calculations showed that neutrinoless double beta decay should be much more likely to occur than ordinary double beta decay, if neutrinos were Majorana particles. The predicted half-lives were on the order of ~ years. Efforts to observe the process in laboratory date back to at least 1948 when E.L. Fireman made the first attempt to directly measure the half-life of the isotope with a Geiger counter. Radiometric experiments through about 1960 produced negative results or false positives, not confirmed by later experiments.
[2]Paolo Prandoni, [3]LCAV, EPFL
The Karplus-Strong algorithm is a simple method to generate synthetic
sounds with arbitrary pitch. In this notebook we will explore a few
variations of the method to illustrate some basic notions of
discrete-time signal processing.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
In [2]:
plt.rcParams["figure.figsize"] [2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will investigate the effect of phase on the
perceptual quality of a sound. It is often said that the human ear is
commercial-grade audio equipment takes place in the magnitude domain
only.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
from scipy.io import wavfile
In [2]:
plt.rcParams["figure.fig