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Analytical solution for the Feynman ratchet
Physical Review E, 2002A search for an analytical, closed form solution of the Fokker-Planck equation with periodic, asymmetric potentials (ratchets) is presented. It is found that logarithmic-type potential functions (related to "entropic" ratchets) allow for an approximate solution within a certain range of parameters. An expression for the net current is calculated and it
Karol, Pesz +2 more
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Analytic solution of a chaotic inflaton
Physical Review D, 1989We directly solve the Langevin equation of motion for a scalar field in theslow-roll limit for a lambda/phi//sup 4//4 potential. The probabilitydistribution for the inflaton and several moments of the distribution are alsocalculated. An upper bound to the percentage deviation of the mean of thedistribution from the classical value is also derived.
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Analytical Solutions for Catenary Domes
Journal of Engineering Mechanics, 2015A new concept for designing a dome is introduced. The dome is inverted from a basket made of catenary strips, thereby maintaining the optimal properties of the catenary. Four kinds of domes are considered: the polygonal catenary dome, the catenary dome of uniform thickness, the catenary dome of uniform stress, and a dome supporting a uniform platform ...
Wang, C. Y., Wang, C. M.
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Rational Interpolation: Analytical Solution
Siberian Mathematical Journal, 2001Summary: The classical problem of interpolation by rational functions is well known to be reduced to a system of linear algebraic equations, but the resultant system is usually complicated for qualitative analysis and numerical implementation. We propose a new approach which generalizes the polynomial interpolation to the rational interpolation both in
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This chapter introduces analytical solutions for SCL design, highlighting their role in early-stage analysis, rapid sensitivity checks, and validation of numerical models. It explains benefits, limitations, and applications for simple geometries and ground conditions.
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An Analytical Solution of the Inverted Pendulum
American Journal of Physics, 1965A rigorous solution of the inverted pendulum requires several mathematical techniques which are not in the repetoire of the typical student of classical mechanics at the senior level. However, the problem is tractable by Lagrange's equations and the physics of the situation is sufficiently simple so that it is an excellent example to use to extend the ...
Phelps, F. M. III, Hunter, J. H. jun.
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An Analytic Solution of the Warehouse Problem
Management Science, 1957In a recent paper, [Bellman, Richard. 1956. On the theory of dynamic programming—a warehousing problem. Management Sci. 2 (3, April) 272.], Bellman uses dynamic programming to establish a computational algorithm for the solution of the “warehouse” problem.
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