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Exponential growth
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===Physics=== * [[Avalanche breakdown]] within a [[dielectric]] material. A free [[electron]] becomes sufficiently accelerated by an externally applied [[electrical field]] that it frees up additional electrons as it collides with [[atom]]s or [[molecule]]s of the dielectric media. These ''secondary'' electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete [[dielectric breakdown]] of the material. * [[Nuclear chain reaction]] (the concept behind [[nuclear reactors]] and [[nuclear weapons]]). Each [[uranium]] [[atomic nucleus|nucleus]] that undergoes [[Nuclear fission|fission]] produces multiple [[neutron]]s, each of which can be [[absorption (chemistry)|absorbed]] by adjacent uranium atoms, causing them to fission in turn. If the [[probability]] of neutron absorption exceeds the probability of neutron escape (a [[function (mathematics)|function]] of the [[shape]] and [[mass]] of the uranium), the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction. "Due to the exponential rate of increase, at any point in the chain reaction 99% of the energy will have been released in the last 4.6 generations. It is a reasonable approximation to think of the first 53 generations as a latency period leading up to the actual explosion, which only takes 3β4 generations."<ref>{{cite web|url=http://nuclearweaponarchive.org/Nwfaq/Nfaq2.html| title=Introduction to Nuclear Weapon Physics and Design|publisher=Nuclear Weapons Archive|last=Sublette|first=Carey|access-date=26 May 2009}}</ref> * [[Positive feedback]] within the linear range of electrical or electroacoustic [[Amplifier|amplification]] can result in the exponential growth of the amplified signal, although [[resonance]] effects may favor some [[component frequency|component frequencies]] of the signal over others.
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