Related papers: Plumbing bijections
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
The interaction of electrical fields and liquids can lead to phenomena that defies intuition. Some famous examples can be found in Electrohydrodynamics as Taylor cones, whipping jets or non-coalescing drops. A less famous example is the…
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high…
We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes…
A little known property of free-fall motion is the elliptic locus of the maximum heights attained by coplanar projectiles launched from a single point in different directions with the same initial speed. Another, less known and perhaps…
We study the following question dating back to J.E. Littlewood (1885-1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to be points moving with at most unit speed. That the…
In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there…
The XY-model shows in two dimensions in the strong coupling regime a universal distribution, named BHP, which in turn also describes other models of criticality and self-organized criticality and even describes natural data as river level…
More than five hundred years ago Leonardo Da Vinci found a pattern in the growth of trees nowadays known as the Leonardo's rule. This rule relates the thickness of the stem with the thickness of the branches at different bifurcation stages…
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…
We present a variation of the water puzzle, which is related to a simple model of marginal utility. The problem has an intriguing solution and can be extended in several directions.
We consider a symmetric 0-pi Josephson junction of length $L$, which classically can be in one of two degenerate ground states up or down, corresponding to supercurrents circulating clockwise or counterclockwise around the 0-pi boundary.…
Liquids generally become more ordered upon cooling. However, it has been a long-standing debate on whether such structural ordering in liquid water takes place continuously or discontinuosly: continuum vs. mixture models. Here, by computer…
We consider a system of two semifluxons of opposite polarity in a 0-pi-0 long Josephson junction, which classically can be in one of two degenerate states: up-down or down-up. When the distance $a$ between the 0-pi boundaries (semifluxon's…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
The bottle-flip challenge -- the upright landing of a partially filled bottle after tossing and flipping it in the air -- unexpectedly became a viral mechanics exercise. Through high-speed visualization, we evidence that fluid content…
A detailed experimental and theoretical study has been performed about a phenomenon, not previously reported in the literature, occurring in highly viscous liquids: the formation of a definite pipe structure induced by the passage of a…
Simple ideas that shed new light on the physics of rotation as it concerns two famous experiments: The Wilson and Wilson, and the Michelson and Morley experiments.
Robust and precise localization is essential for the autonomous system with navigation requirements. Light detection and ranging (LiDAR) odometry is extensively studied in the past decades to achieve this goal. Satisfactory accuracy can be…
In the shallow water approximation, the cross-sectional profiles of laboratory rivers satisfy a differential equation here shown to be formally the Friedmann equation of cosmology ruling the evolution of Anti-de Sitter universe. The ensuing…