The
focus of this project is to study 1/f or 1/f2 noise of thin metal films
due to electromigration.
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| 1/f0, 1/f2 and 1/f fluctuations
The diagram on the left shows the relation between
the frequency and power (dB level) of various noise types. the 1/f0
white noise, the top horizontal line, shows a fluctuation in which
the power changes at random, irrespective of wave frequency. the 1/f2
Brownian noise, the bottom curve, shows waves which change in
very strict conformity with a certain fluctuation pattern. The 1/f,
the middle line, indicates a pattern in which the power change is
inversely proportional to the frequency. (Both power and frequency
have been converted into Fourier values)
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| Classical music and 1/f fluctuation
Analysis of wave pattern in classical music, as
well as popular songs, are shown in this diagram. Frequency is inversely
proportional to the power, a relationship which creates 1/f fluctuations.
The constant, rusty noise of a TV after broadcasting ends is displeasing.
On the contrary, wave patterns which are most soothing conform to
the 1/f fluctuation. The sounds created by classical music following
a 1/f fluctuation patterns are especially soothing to our ears.
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| Waves of electroencephalogram and 1/f function
Analysis of the relation between the alpha rhythm
and electrically stimulated pain relief is shown by the electroencephalogram
on the right coincides with 1/f fluctuation patterns seen when relaxed,
listening to music. Introduction of noise or pain while in this state
reduces the alpha rhythms, while decreasing the beta rhythms, thus
causing a shift from the 1/f fluctuation pattern to the 1/f0
fluctuation or white noise.
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| Pain relief by 1/f stimulation
The results of electrical treatment centering
on the removal of intense pains caused by cancer and other diseases
are shown above. Thirteen males and eight females were initially treated
by ordinary electric stimulation. It's effectiveness was less than
50%. When 1/f electrical stimulation was administered to five cases
which had not responded to the initial treatment, effective relief
of pain occurred in four cases.
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| Effectiveness of 1/f stimulation treatment.
The result of treatment by ordinary electric stimulation
and the 1/f electric stimulation are shown on the table on the right.
The electric stimulation was applied for about 30 minutes, and the
degree of pain reduction attributed to the treatment was evaluated.
The original pain level was established as a reference level of 10.
In 7% cases, pain almost entirely disappeared (i.e. Pain level reduced
to 0-3), by ordinary electric stimulation. In addition, 28% reported
some relief of pain. The combined results shows about 35% of patients
were satisfied with the ordinary electric treatment. When treated
by 1.f electrical stimulation, 30% of the patients reported their
pain was almost entirely gone, while about 40% felt their pain was
reduced in half. A total of 70% of patients were thus satisfied with
1/f electrical stimulation treatment.
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