相关论文: The Golden Ratio and Hydrodynamics
The golden ratio is usually shrouded in mystique and mystery, however, showing its emergence from a familiar geometric setting makes it a more natural phenomenon. In this work, we present a new theorem connecting the Tangent Secant theorem…
On each nonorientable surface of odd genus $g \geq 5$, we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.
Most hydrodynamical calculations used in heavy-ion physics ignore the effect of freeze-out matter carrying energy and momentum away from the expanding fluid. In a simple one-dimensional model we compare calculated energy density and…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
We establish some new constructions of the golden ratio in an arbitrary triangle using symmedians and nine-point circle.
Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More…
The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…
It is demonstrated that iterative repeating of some simple geometric construction leads unavoidably in the limit to the golden ratio. The procedure appears to be quickly convergent regardless of a ratio of initial elements sizes. This could…
The "unreasonable effectiveness" of relativistic fluid dynamics in describing high energy heavy-ion and even proton-proton collisions are demonstrated and discussed. Several recent ideas of optimizing relativistic fluid dynamics for the…
We introduce an effective theory which extends hydrodynamics into a regime where the critical slowing down would otherwise make hydrodynamics inapplicable.
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an…
Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high…
The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as…
Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in…
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between…
We consider a variational formalism to describe black holes solution in higher dimensions. Our procedure clarifies the arbitrariness of the radius parameter and, in particular, the meaning of the event horizon of a black hole. Moreover, our…
The current observational evidences suggest there are about hundred billion galaxies in the observable universe and within each, on an average, about hundred billion stars. But no cosmological model indicates as to why there are these many…
Motivated by the study of the crossing number of graphs, it is shown that, for trees, the sum of the products of the degrees of the end-vertices of all edges has an upper bound in terms of the sum of all vertex degrees to the power of…
The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After…