By Alexander Mielke,Tomáš Roubíček
This monograph offers either an advent to and an intensive exposition of the speculation of rate-independent platforms, which the authors were engaged on with loads of collaborators over 15 years. the focal point is usually on absolutely rate-independent platforms, first on an summary point both with or perhaps with no linear constitution, discussing a variety of ideas of strategies with complete mathematical rigor. Then, usefulness of the summary options is proven at the point of assorted purposes essentially in continuum mechanics of solids, together with appropriate approximation innovations with assured numerical balance and convergence. specific purposes difficulty inelastic approaches reminiscent of plasticity, harm, part variations, or adhesive-type contacts either at small traces and at finite traces. a number of different actual platforms, e.g. magnetic or ferroelectric fabrics, and couplings to rate-dependent thermodynamic versions are regarded as good. chosen purposes are observed by way of numerical simulations illustrating either the types and the potency of computational algorithms.
In this e-book, the mathematical framework for a rigorous mathematical remedy of "rate-independent platforms" is gifted in a accomplished shape for the 1st time. Researchers and graduate scholars in utilized arithmetic, engineering, and computational physics will locate this well timed and good written booklet useful.
Read Online or Download Rate-Independent Systems: Theory and Application (Applied Mathematical Sciences) PDF
Best differential equations books
The 1st modern textbook on traditional differential equations (ODEs) to incorporate directions on MATLAB®, Mathematica®, and Maple™, A path in usual Differential Equations specializes in purposes and strategies of analytical and numerical ideas, emphasizing techniques utilized in the common engineering, physics, or arithmetic student's box of analysis.
Remark Fatou et Julia ont inventé ce que l’on appelle aujourd’hui les ensembles de Julia, avant, pendant et après los angeles première guerre mondiale? L’histoire est racontée, avec ses mathématiques, ses conflits, ses personnalités. Elle est traitée à partir de assets nouvelles, et avec rigueur. On pourra s’y initier à l’itération des fractions rationnelles et à l. a. dynamique complexe (ensembles de Julia, de Mandelbrot, ensembles-limites).
This ebook offers a entire creation to numerical tools and research of stochastic techniques, random fields and stochastic differential equations, and provides graduate scholars and researchers strong instruments for figuring out uncertainty quantification for probability research. insurance comprises conventional stochastic ODEs with white noise forcing, powerful and vulnerable approximation, and the multi-level Monte Carlo process.
Those lecture notes supply an advent to the functions of Brownian movement to research and extra quite often, connections among Brownian movement and research. Brownian movement is a well-suited version for quite a lot of genuine random phenomena, from chaotic oscillations of microscopic items, akin to flower pollen in water, to inventory marketplace fluctuations.
Additional resources for Rate-Independent Systems: Theory and Application (Applied Mathematical Sciences)
Rate-Independent Systems: Theory and Application (Applied Mathematical Sciences) by Alexander Mielke,Tomáš Roubíček