MOND reveals the thermodynamics of gravity

We show that treating gravitation as a thermodynamical theory leads to the modified Newton dynamics (MOND) equations if one takes into account the Hubble's expansion. Then the universal MOND acceleration a0 is exactly twice the product of the light velocity c and the Hubble constant H. No dark matter is needed for the description of the galaxy rotational curves as well as for the accounting for the additional gravitational lensing at large distances.Comment: 7 pages, 0 figures, 16 reference

Exact solutions for the dispersion relation of Bogoliubov modes localized near a topological defect - a hard wall - in Bose-Einstein condensate

We consider a Bose-Einstein condensate of bosons with repulsion, described by the Gross-Pitaevskii equation and restricted by an impenetrable "hard wall" (either rigid or flexible) which is intended to suppress the "snake instability" inherent for dark solitons. We solve analytically the Bogoliubov - de Gennes equations to find the spectra of gapless Bogoliubov excitations localized near the "domain wall" and therefore split from the bulk excitation spectrum of the Bose-Einstein condensate. The "domain wall" may model either the surface of liquid helium or of a strongly trapped Bose-Einstein condensate. The dispersion relations for the surface excitations are found for all wavenumbers $k$ along the surface up to the "free-particle" behavior $k \rightarrow \infty$, the latter was shown to be bound to the "hard wall" with some "universal" energy $\Delta$.Comment: 6 pages, 2 figure

Mutually touching infinite cylinders in the 3D world of lines

Recently we gave arguments that only two unique topologically different configurations of 7 equal all mutually touching round cylinders (the configurations being mirror reflections of each other) are possible in 3D, although a whole world of configurations is possible already for round cylinders of arbitrary radii. It was found that as many as 9 round cylinders (all mutually touching) are possible in 3D while the upper bound for arbitrary cylinders was estimated to be not more than 14 under plausible arguments. Now by using the chirality and Ring matrices that we introduced earlier for the topological classification of line configurations, we have given arguments that the maximal number of mutually touching straight infinite cylinders of arbitrary cross-section (provided that its boundary is a smooth curve) in 3D cannot exceed 10. We generated numerically several configurations of 10 cylinders, restricting ourselves with elliptic cylinders. Configurations of 8 and 9 equal elliptic cylinders (all in mutually touching) are generated numerically as well. A possibility and restriction of continuous transformations from elliptic into round cylinder configurations are discussed. Some curious results concerning the properties of the chirality matrix (which coincides with Seidel's adjacency matrix important for the Graph theory) are presented.Comment: 27 pages, 10 figure

Symmetry, topology and the maximum number of mutually pairwise touching infinite cylinders: complete configuration classification

We provide a complete classification of possible configurations of mutually pairwise touching infinite cylinders in Euclidian 3D space. It turns out that there is a maximum number of such cylinders possible in 3D independently on the shape of the cylinder cross-sections. We give the explanation of the uniqueness of the non-trivial configuration of seven equal mutually touching round infinite cylinders found earlier. Some results obtained for the chirality matrix which is equivalent to the Seidel adjacency matrix may be found useful for the theory of graphs.Comment: 120 pages (23 pages of text and 5 Appendices), 11 Figures in the tex

Discrete geometry and topology of entanglement of straight lines in 3-space

We propose an unexpected twist to description of the geometry and topology of configurations of n straight lines considered as a whole 3D entity (because the lines are inseparably linked pairwise while having linking numbers 1/2 or -1/2) and named n-cross. Our theory stems from our work on configurations of mutually touching straight cylinders but, along with the previously introduced Ring matrix (that controls the encaging of each line by other lines), we now introduce fundamental direction 3D matrices (whose entries 0, 1, and -1 are signs of mixed products of line orientation vector triples). Discrete motion/connection combination principle established in the space of Ring and direction matrices (forming a groupoid and resembling moves in Loyd 15-puzzle game or Khovanov homology) allows one to discern topologically different configurations of lines with elementary methods and without link diagrams of knot theory. However, with the help of so-called projection 3D matrix we also integrated our matrix approach into the knot theory and established topological invariants for line entanglement in both approaches thus connecting 2D projections with 3D configurations. With Jones polynomials we show that an n-cross is a link of pairwise connected n unknots in a topological sense. The known results of the knot theory for rigid isotopy of 6 and 7 lines are reproduced and a novel result for 8 lines is given. With our approach we reach nuances of the geometry of lines never investigated before. It may find applications in Algebra, Discrete Geometry and Topology, and Quantum Physics.Comment: 33 pages, 8 figures, 4 table

Perpetual floating drops

The stability of floating drops on the liquid surface of the same liquid is considered in terms of viscous drainage theory. We have expressed the minimal thickness of the air film, separating the drop from the liquid surface, and the lifetime of the drop through the Hamaker constant, characterizing the intensity of van-der-Waals forces which make the air film unstable. It is shown that a horizontally moving or just rotating drop can have an infinite lifetime when the drop surface velocity exceeds some critical value. A spectacular example of a long-living rotating paraffin droplet on a burning candle is given. Results obtained can help to control a liquid surface in situ with the use of floating/rotating drops.Comment: 4 pages, 1 figure, 1 movi

Seven, eight, and nine mutually touching infinitely long straight round cylinders: Entanglement in Euclidean space

It has been a challenge to make seven straight round cylinders mutually touch before our now 10-year old discovery [Phys. Rev. Lett. 93, 015505 (2004)] of configurations of seven mutually touching infinitely long round cylinders (then coined 7-knots). Because of the current interest in string-like objects and entanglement which occur in many fields of Physics it is useful to find a simple way to treat ensembles of straight infinite cylinders. Here we propose a treatment with a chirality matrix. By comparing 7-knot with variable radii with the one where all cylinders are of equal radii (here 7*-knot, which for the first time appeared in [phys. stat. solidi, b 246, 2098 (2009)]), we show that the reduction of 7-knot with a set of non-equal cylinder radii to 7*-knot of equal radii is possible only for one topologically unique configuration, all other 7-knots being of different topology. We found novel configurations for mutually touching infinitely long round cylinders when their numbers are eight and ultimately nine (here coined 8-knots and 9-knots). Unlike the case of 7-knot, where one angular parameter (for a given set of fixed radii) may change by sweeping a scissor angle between two chosen cylinders, in case of 8- and 9-knots their degrees of freedom are completely exhausted by mutual touching so that their configurations are "frozen" for each given set of radii. For 8-knot the radii of any six cylinders may be changeable (for example, all taken equal) while two remaining are uniquely determined by the others. We show that 9-knot makes the ultimate configuration where only three cylinders can have changeable radii and the remaining six are determined by the three. Possible generalizations and connection with Physics are mentioned.Comment: 18 pages, 9 figures, 1 tabl

Exact surface-wave spectrum of a dilute quantum liquid

We consider a dilute gas of bosons with repulsive contact interactions, described on the mean-field level by the Gross-Pitaevskii equation, and bounded by an impenetrable "hard" wall (either rigid or flexible). We solve the Bogoliubov-de Gennes equations for excitations on top of the Bose-Einstein condensate analytically, by using matrix-valued hypergeometric functions. This leads to the exact spectrum of gapless Bogoliubov excitations localized near the boundary. The dispersion relation for the surface excitations represents for small wavenumbers $k$ a ripplon mode with fractional power law dispersion for a flexible wall, and a phonon mode (linear dispersion) for a rigid wall. For both types of excitation we provide, for the first time, the exact dispersion relations of the dilute quantum liquid for all $k$ along the surface, extending to $k \rightarrow \infty$. The small wavelength excitations are shown to be bound to the surface with a maximal binding energy $\Delta= \frac18 (\sqrt{17}-3)^2 mc^2 \simeq 0.158\, mc^2$, which both types of excitation asymptotically approach, where $m$ is mass of bosons and $c$ bulk speed of sound. We demonstrate that this binding energy is close to the experimental value obtained for surface excitations of helium II confined in nanopores, reported in Phys. Rev. B 88, 014521 (2013).Comment: 9 pages of RevTex4-1, 3 figure

CO2 laser-driven reactions in pure acetylene flow

We show that multiple-photon absorption of radiation from a 10.56 {\mu}m cw CO2 laser by intermediates (ethylene, vinylidene) generated in pure acetylene flow makes them decompose to carbon dimers and excited hydrogen. The latter associates with downstream acetylene to feedback those laser absorbing intermediates thus making the reactions self-sustained in the absence of oxygen. This process is different from acetylene self-decomposition that may occur at higher temperature and pressure. The results of our work may be useful for understanding the generation of various carbon allotropes and interstellar dust from acetylene

Trapped charge driven degradation of perovskite solar cells

Perovskite solar cells have shown fast deterioration during actual operation even with encapsulation, but its mechanism has been elusive. We found the fundamental mechanism for irreversible degradation of perovskite materials in which trapped charges regardless of the polarity play a decisive role. A novel experimental setup utilizing different polarity ions revealed that the moisture induced irreversible dissociation of perovskite materials is triggered by charges trapped along grain boundaries. Our finding clearly explained the intriguing observations why light soaking induces irreversible degradation while in the dark, moisture only causes reversible hydration, and why degradation begins from different side of interface for different charge extraction layers. The deprotonation of organic cations by trapped charge induced local electric field is attributed to the initiation of irreversible decomposition