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Crystals, as quantum objects typically much larger than their lattice spacing, are counterexamples to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.

We find approximate solutions for the two-dimensional nonlinear $\mathrm{\Sigma }$-model with Dzyalioshinkii–Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has a fundamental rack which contains more information than the fundamental group. Racks provide an elegant and complete algebraic framework in which to study links and knots in 3–manifolds, and also for the 3–manifolds themselves. Racks have been studied by several previous authors and have been called a variety of names. In this first paper of a series we consolidate the algebra of racks and show that the fundamental rack is a complete invariant for irreducible framed links in a 3–manifold and for the 3–manifold itself. We give some examples of computable link invariants derived from the fundamental rack and explain the connection of the theory of racks with that of braids.

Numerical study is performed on the thermal fluid-flow transport phenomena in a disk-shape cavity. Consideration is given to the movement and growth of the crystal in solution layer. Here the lysozyme is employed as the crystal. The mechanism is numerically investigated by solving the two-dimensional governing equations through discretization by means of a finite-difference technique and simultaneously the crystal movement is predicted by the Basset–Boussinesq–Oseen (BBO) equation. It is found that (i) the crystal circulates in the cavity with fluid current and shows the circulation pattern of a donut shape, like the flow in a typical Benard cell, (ii) when the particle makes the second circulation with a larger loop, it falls on to the bottom near the vertical side-wall, and (iii) the size of the falling particle becomes larger as the Rayleigh number, i.e. the temperature difference between the heat sink and the vertical side-wall is increased.

The synthesis of a new self-assembled porphyrin macrostructure based on disulfide bonds, is presented. This constitutes a new way to directly connect porphyrins in macromolecular arrays, to complement the usual methods of intermolecular hydrogen bonds and metal coordination bonding.

A 4f-3d heterometallic porphyrin, [TbCo(TPPS)H₃O]_n (1) (H₂TPPS = tetra(4-sulfonatophenyl)porphyrin), has been synthesized via a hydrothermal reaction and structurally characterized by single crystal X-ray diffraction analysis. The structure of 1 consists of [TbCo(TPPS)H₃O]_n molecules. The Tb³⁺ ions are coordinated by eight oxygen atoms from eight sulfonic groups, yielding a distorted square anti-prism geometry. Compound 1 is characterized by a three-dimensional (3-D) porous open framework that is thermally stable up to 350°C. Compound 1 displays a fluorescent emission band in the ultraviolet region and its fluorescence lifetime is 1.14 ms. A slow scan CV curve of compound 1 reveals one reversible wave with E_1/2 being equal to -0.78 V, which is close to the value -0.74 V of DPV diagram.

Using a hydrothermal reaction of SmCl₃•6H₂O, ZnBr₂ and TPPS, a crystalline metalloporphyrinic compound (MPC), [SmZn(TPPS)H₃O]${}_n$•2$n$H₂O (1), was synthesized. The crystal structure of the MPC exhibits a condensed and robust 3-D porous open framework. We studied the adsorption and desorption isotherms for N₂, H₂ and CO₂ conducted at 77 K and 273 K. They show different isotherms such as Type I, II and III isotherm behaviors. We found that low temperature is propitious for the title complex to adsorb more H₂, but less N₂. Compound 1 showed remarkably high selectivity for CO₂–N₂ separation, and good thermal stability. The temperature dependent magnetic susceptibility shows an antiferromagnetic-like behavior for 1.

A novel subphthalocyanine containing bulky substituents placed at its peripheral sites (i.e. 2,3,9,10,16,17-hexa(2′,6′-di-iso-propylphenoxy)boron subphthalocyanine) was prepared and assessed for supramolecular binding with C${}_{60}$, through crystallisation and fluorescence studies. Three different crystal polymorphs of the subphthalocyanine were obtained that showed inclusion of a single aromatic solvent molecule within the well-defined cavity of the molecule but complete exclusion of C${}_{60}$. Analysis of the crystal structures indicated that the bowl-shaped cavity of the subphthalocyanine molecule was only accessible to small molecules due to the steric congestion surrounding the macrocycle, which results in hindered rotation of the substituents on the NMR timescale. Enhanced solubility, up to 42.0 g/L in common organic solvents, was demonstrated consistent with the crystal structures which are dominated by relatively weak intermolecular interactions, which allow solvent molecules to play a role in crystallisation.

A novel 5,10,15,20-tetrakis-(4-(triazol-1-yl)phenyl)porphyridine compound, namely, Zn[5,10,15,20-tetrakis-(4-(triazol-1-yl)phenyl)porphyridine] (hereafter tagged as 1) was synthesized through a solvothermal reaction with mixed solvents at 413 K. The X-ray single-crystal structure of compound 1 is featured as a two-dimensional (2D) layer-like structure with the zinc ion located at the center of the 5,10,15,20-tetrakis-(4-(triazol-1-yl)phenyl)porphyridine. The macrocycle of the 5,10,15,20-tetrakis-(4-(triazol-1-yl)phenyl)porphyridine is coplanar. The zinc ion has six coordination and coordinates with three porphyridines. The photoluminescence spectra of compound 1 with DMF solution reveal that it shows upconversion red photoluminescence. The time-dependent density functional theory (TDDFT) calculation confirms that this upconversion red photoluminescence originated from the MLCT process (metal to ligand charge transfer). The CCT (Correlated Color Temperature) is 2200 K and the CIE (Commission Internationale de I’Éclairage) chromaticity coordinate is (0.6311, 0.3595) for compound 1. The UV-vis diffuse reflectance curve measured with a solid state sample reveals that compound 1 possesses a 2.75 eV band gap.

In our previous study, with the dissipation of quartz crystal through material viscosity is being considered in vibrations of piezoelectric plates, we have the opportunity to obtain electrical parameters from vibration solutions of a crystal plate representing an ideal resonator, in which both full and partial electrodes are considered. In fact, the electrodes of resonators are not symmetrically arranged due to the mounting points of crystal blanks are only in one side. As a result, the study of asymmetric electrodes is necessary for practical applications. Different from previous ones, the vibration solutions will contain both symmetric and anti-symmetric thickness-shear vibrations in the electroded area, which will introduce new boundary conditions. We start with the first-order Mindlin plate equations of a piezoelectric plate for the thickness-shear vibration analysis of a resonator with asymmetric electrodes. The electrical parameters are derived with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity. With this approach we can further analyze the actual resonator vibration influenced by the electrode position.

Knot and link diagrams are used to represent nonstandard sets, and to represent the formalism of combinatory logic (lambda calculus). These diagrammatics create a two-way street between the topology of knots and links in three dimensional space and key considerations in the foundations of mathematics.

On beam tests were carried out on PbWO₄ crystals. One of the aims of this work was to evaluate the contribution of the Čerenkov component to the total light yield. The difference in the timing characteristics of the fast Čerenkov signals with respect to the scintillation ones, which are emitted with a decay time of about 10 ns, can be exploited in order to separate the two proportions. In this paper we present the results of an analysis performed on the time structure of signals, showing how it is possible to detect and assess the presence and the amount of Čerenkov light. Since Čerenkov light is emitted only by the electromagnetic component of a hadronic shower, its precise measurement would allow to account for one of the dominant sources of fluctuations in hadronic showers and to achieve an improvement in the energy resolution of a hadronic calorimeter.