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An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in through the early s.
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- The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem.
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It discusses such problems as the nonlinear oscillator simulation, the seminal discoveries at MIT in the early s, the mathematical rediscovery of solitons in the late s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen.
No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.
Route to thermalization in the α-Fermi–Pasta–Ulam system - Europe PMC Article - Europe PMC
Read more Read less. No customer reviews. Videos matching Fermi—Pasta—Ulam—Tsingou problem. Video of the states of 32 nodes in a Fermi-Pasta-Ulam Experiment over time video This is the result of my toying around with the equations of the Experiment that launched numerical simulations in science Pasta Experiment video This video was uploaded from an Android phone.
FPU Simulation with Fourier energy video. FPU simulation 3 video. Kink antikink annihilation video. Golden age of physics video The texts in this video are taken from wikipedia.
The Genesis of Simulation in Dynamics
However, when they did the simulation, they found to their great surprise that this energy was shared by only a few other modes; the remaining modes were hardly excited. Moreover, after a long time the initial state was almost completely recovered. This result, which is known as the FPU problem or the FPU paradox, shows that nonlinearity is not sufficient to guarantee the equipartition of energy. It turns out that ergodic behavior is only observed when the magnitude of the nonlinear term is more than a certain critical value. The program uses the Verlet algorithm to solve Newton's equations of motion numerically.
The mean energy in these three modes is given when the simulation is stopped. If the system is ergodic, then all particles will see the same average environment, and the time average of any physical quantity associated with individual particles will be the same for each particle if the time t is sufficiently long.
The time average of this quantity f for particle i is defined as.