Self-similar curling of a naturally curved elastica.
نویسندگان
چکیده
We consider the curling of an initially flat but naturally curved elastica on a hard, nonadhesive surface. Combining theory, simulations, and experiments, we find novel behavior, including a constant front velocity and a self-similar shape of the curl that scales in size as t(1/3) at long times after the release of one end of the elastica. The front velocity is selected by matching the self-similar solution with a roll of nearly constant curvature located near the free end.
منابع مشابه
Curling and rolling dynamics of naturally curved ribbons.
When a straight rod is bent and suddenly released on one end, a burst of dispersive flexural waves propagates down the material as predicted by linear beam theories. However, we show that for ribbons with a longitudinal natural radius of curvature a0, geometrical constraints lead to strain localization which controls the dynamics. This localized region of deformation selects a specific curling ...
متن کاملDeformation by Discrete Elastica
Modeling a physically plausible deformation of a flexible object from its naturally planar (curved) state is a fundamental and challenging topic in digital surface processing with applications to computer animation and game design. We propose a new variational model for detail preserving surface-based deformation of a body based on total curvature energy. We demonstrate the efficacy of the mode...
متن کاملEvaluation and mitigation of potential errors in radiochromic film dosimetry due to film curvature at scanning
This work considers a previously overlooked uncertainty present in film dosimetry which results from moderate curvature of films during the scanning process. Small film samples are particularly susceptible to film curling which may be undetected or deemed insignificant. In this study, we consider test cases with controlled induced curvature of film and with film raised horizontally above the sc...
متن کاملTwirling elastica: kinks, viscous drag, and torsional stress.
Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain ...
متن کاملA comparative study on egoism and love to the self
Egoism is regarded one of the basic schools in moral philosophy. On egoism, one should act in such a way that his or her most benefits be prepared. The roots of this school can be found in Epicurean school or hedonism. The school, however, was supported later by such philosophers as Schopenhauer, Nietzsche and Fraud in various ways. On this basis Nietzsche presented the theory of Super man a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review letters
دوره 108 17 شماره
صفحات -
تاریخ انتشار 2012