Related papers: Bending of Sparklers
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
Several of the inconsistencies plaguing the field of novae are resolved once we consider novae to be steady state super-Eddington objects. In particular, we show that the super-Eddington shell burning state is a natural consequence of the…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus.…
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a…
In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…
We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, and are also more…
In this paper we examine more deeply about the bending mechanism of rod-shaped fireworks which burned from the free end. We derived new analytic equations. Surprisingly, we obtained the bending patterns are similar to the cornu spiral. With…
Fluid elements deform in turbulence by stretching and folding. In this work, by projecting the material deformation tensor onto the largest stretching direction, the dynamics of folding is depicted through the evolution of the material…
Because of the mass density-dependence, an extra term should be added to the expression of pressure. However, it should not appear in that of energy according to both the general ensemble theory and basic thermodynamic principle. We give a…
This article introduces a new geophysical theory, in the form of a single simple partial integro-differential equation, to explain how frictional abrasion alone of a stone on a planar beach can lead to the oval shapes observed empirically.…
Thermodynamic formulas for investigating systems with density and/or temperature dependent particle masses are generally derived from the fundamental derivation equality of thermodynamics. Various problems in the previous treatments are…
Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens…
A liquid drop impacting a dry solid surface with sufficient kinetic energy will splash, breaking apart into numerous secondary droplets. This phenomenon shows many similarities to forced wetting, including the entrainment of air at the…
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…
The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with…
From geometry and conservation we derive two nonlinear evolution equations for sand ripples. In the case of a strong wind leading to a net erosion of the sand bed, ripples obey the Benney equation. This leads either to order or disorder…
The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in…
String theory predicts that the couplings of Nature descend from dynamical fields. All known string-motivated particle physics models also come with a wide range of possible extra sectors. It is common to posit that such moduli are frozen…