Completely geometric theory II: basics of quantum mechanics

The geometrical approach suggested earlier, makes it possible to investigate the regions both in mega-and micro worlds that cannot be accessed by the direct observation. This makes it possible not only to interpret the basic experiments of quantum mechanics in a new way but also to escape the paradoxes stemming from the wave function introduction. It also gives perspectives to adjust the quantum mechanics and the relativity theory.

Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

Use of Different Metal Oxide Coatings in Stainless Steel Based ECDs for Smart Textiles

Electrochromism is the ability of a material to selectively change its coloration under the influence of an external electric current/potential and maintain it even after the power source has been disconnected. Devices that use such a mechanism are known as electrochromic devices (ECDs). Over the years, significant effort has been invested into the development of flexible ECDs. Such electrochromic tapes or fibers can be used as smart textiles. Recently, we utilized a novel geometrical approach in assembling electrochromic tapes which does not require the use of optically transparent electrodes. The so-called inverted sandwich ECD configuration can employ various color-changing mechanisms, e.g., intercalation, redox reactions of electrolytes or reactions on electrode surfaces. One of the most frequently used electrochromic metal oxides is WO3. However, other metal oxides with different coloration responses also exist. In this paper, we explore the use of V2O5 and TiO2 in metal-tape-based ECDs in the inverted sandwich configuration and compare their performance with WO3-based devices. Morphological features of metal oxide thin layers were investigated with scanning electron microscopy (SEM), and the performance of the tapes was investigated electrochemically and spectroscopically. We demonstrate that well-established preparation techniques (e.g., sol–gel synthesis) along with coating approaches (e.g., dipping) are adequate to prepare optically nontransparent fiber electrodes. Depending on the metal oxide, flexible electrochromic fiber devices exhibiting different coloration patterns can be assembled. Devices with TiO2 showed little coloration response, while much better performance was achieved in the case of V2O5 and WO3 ECDs.

Geometrical prediction of cleavage planes in crystal structures

Cleavage is the ability of single crystals to split easily along specifically oriented planes. This phenomenon is of great interest for materials' scientists. Acquiring the data regarding cleavage is essential for the understanding of brittle fracture, plasticity and strength, as well as for the prevention of catastrophic device failures. Unfortunately, theoretical calculations of cleavage energy are demanding and often unsuitable for high-throughput searches of cleavage planes in arbitrary crystal structures. A simplified geometrical approach (GALOCS = gaps locations in crystal structures) is suggested for predicting the most promising cleavage planes. GALOCS enumerates all the possible reticular lattice planes and calculates the plane-average electron density as a function of the position of the planes in the unit cell. The assessment of the cleavage ability of the planes is based on the width and depth of planar gaps in crystal structures, which appear when observing the planes lengthwise. The method is demonstrated on two-dimensional graphene and three-dimensional silicon, quartz and LiNbO3 structures. A summary of planar gaps in a few more inorganic crystal structures is also presented.

Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as thermodynamic geometry; (iv) the Poincaré method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $$2/3\le S\le 1$$ 2 / 3 ≤ S ≤ 1 , whereas thermodynamic geometry suggests that, at $$S=1$$ S = 1 , there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincaré method (iv) that black holes whose entropy is $$S < 4/3$$ S < 4 / 3 are stable or in a saddle-point, whereas when $$S>4/3$$ S > 4 / 3 they are always unstable, hence there is no definite answer on whether such transition occurs. Since thermodynamics geometry takes the view that the entropy is an extensive quantity, while the Poincaré method does not require extensiveness, it is valuable to present here the analysis based on both approaches, and so we do.