Isomorphism criterion for monomial graphs

Let q be a prime power, ??_q be the field of q elements, and k, m be positive integers. A bipartite graph G = G_q(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over ??_q, with two vertices (p₁, p₂) ∈ P and [ l₁, l₂] ∈ L being adjacent if and only if p₂ + l₂ = pl. We prove that graphs G_q(k, m) and G_q′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q ? 1), gcd (m, q ? 1)} = {gcd (k′, q ? 1),gcd (m′, q ? 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005     

Modeling microstructure evolution of binary systems subjected to irradiation and mechanical loading

We study a change in mechanical properties of binary systems subjected to irradiation influence described by ballistic flux of atomic mixing having regular and stochastic contributions. By using numerical modeling based on the phase field approach we study dynamics of deformation fields in a previously irradiated system and in the binary system deformed during irradiation. An influence of both deterministic and stochastic components of ballistic flux onto both yield strength and ultimate strength is studied. We have found that degradation of mechanical properties relates to the formation of percolating clusters of shear bands. Considering a hardening coefficient we analyze stages of plastic deformation of both initially irradiated alloy and alloy subjected to sustained irradiation. Stability of binary alloy under mechanical loading in the form of shear strain with a constant rate and cyclic deformation is discussed.     

Phase field modeling precipitation of β-phase and mechanical properties change in Zr–Nb alloys under neutron irradiation

ABSTRACT

We study microstructure transformation in Zr–Nb system under neutron irradiation and its mechanical properties change under mechanical loads in a form of shear deformation by using phase field methodology. The developed phase field approach takes into account defects dynamics based on reaction rate theory and elastic contribution to study mechanical properties change. A numerical modeling is provided in three stages: sample preparation, irradiation of the prepared sample and mechanical loading of the irradiated sample. A precipitation of β-Niobium particles of the size of several nanometers is discussed. Results of phase field modeling indicate that β-Niobium particles grow slowly during irradiation due to point defects rearrangement. Statistical analysis of dynamics of radiation-induced microstructure transformations is provided. Simulation results of shear deformation of pre-irradiated and post-irradiated alloys are discussed. Maps of local distribution of strain and stress and strain–stress curves are obtained. Results are verified with experimental data.     

Infinite Gold Zig‐Zag Chains as Structural Motif in Ca3Au3In – A Ternary Ordered Variant of the Ni4B3 Type

New auride Ca₃Au₃In was synthesized from the elements in a sealed tantalum tube in a high‐frequency furnace. Ca₃Au₃In was investigated by X‐ray powder and single crystal diffraction: ordered Ni₄B₃ type, Pnma, a = 1664.1(6), b = 457.3(2), c = 895.0(3) pm, wR2 = 0.0488, 1361 F² values, and 44 variables. The three crystallographically independent boron positions of the Ni₄B₃ type are occupied by the gold atoms, while the four nickel sites are occupied by calcium and indium in an ordered manner. All gold atoms have trigonal prismatic coordination, i.e. Ca₆ prisms for Au1 and Au2 and Ca₄In₂ prisms for Au3. While the Au3 atoms are isolated, we observe Au1–Au1 and Au2–Au2 zig‐zag chains at Au–Au distances of 292 and 284 pm. These slabs resemble the CrB type structure of CaAu. Consequently Ca₃Au₃In can be considered as a ternary auride. Together the Au2, Au3 and indium atoms build up a three‐dimensional [Au₂In] polyanionic network (281–293 pm Au–In) in which the chains of Au1 centered trigonal prisms are embedded. The crystal chemical similarities with the structures of Ni₄B₃, CaAuIn, and CaAu are discussed.     

A study of void size growth in nonequilibrium stochastic systems of point defects

We study properties of voids growth dynamics in a stochastic system of point defects insolids under nonequilibrium conditions (sustained irradiation). It is shown thatfluctuations of defect production rate (external noise) increase the critical void radiuscomparing to a deterministic system. An automodel regime of void size growth in astochastic system is studied in detail. Considering a homogeneous system, it is found thatexternal noise does not change the universality of the void size distribution function;the mean void size evolves according to classical nucleation theory. The noise increasesthe mean void size and spreads the void size distribution. Studying dynamics of spatiallyextended systems it was shown that vacancies remaining in a matrix phase are able toorganize into vacancy enriched domains due to an instability caused by an elastic latticedeformation. It is shown that dynamics of voids growth is defined by void sinks strengthwith void size growth exponent varying from 1/3 up to 1/2.     

Steric control of the excited-state intramolecular proton transfer in 3-hydroxyquinolones: steady-state and time-resolved fluorescence study

3-Hydroxyquinolones (3HQs), similarly to their 3-hydroxychromone analogs, undergo excited state intramolecular proton transfer (ESIPT) resulting in dual emission. In the ground state, 2-phenyl-3HQ derivatives are not flat due to a steric hindrance between the 2-phenyl group and the 3-OH group that participates in the ESIPT reaction. To study the effect of this steric hindrance on the ESIPT reaction, a number of 3HQ derivatives have been synthesized and characterized in different organic solvents by steady-state and time-resolved fluorescence techniques. According to our results, 2-phenyl-3HQ derivatives undergo much faster ESIPT (by nearly 1 order of magnitude) than their 2-methyl-3HQ analogs. Moreover, 1-methyl-2-phenyl-3HQ having a strongly twisted 2-phenyl group undergoes a two- to three-fold slower ESIPT compared to 2-phenyl-3HQ. These results suggest that the flatter conformation of 2-phenyl-3HQ, which allows a close proximity of the 2-phenyl and 3-OH groups, favors a fast ESIPT reaction. The absorption and fluorescence spectra of the 3HQ derivatives additionally confirm that the steric rather than the electronic effect of the 2-phenyl group is responsible for the faster ESIPT reaction. Based on the spectroscopic studies and quantum chemical calculations, we suggest that the 2-phenyl group decreases the rotational freedom of its proximal 3-OH group in the more planar conformation of 2-phenyl-3HQ. As a result, the conformations of 3HQ, where the 3-OH group orients to form an intramolecular H-bond with the 4-carbonyl group, are favored over those with a disrupted intramolecular H-bond. Therefore, the 2-phenyl group sterically favors the intramolecular H-bond and thus accelerates the ESIPT reaction. This conclusion provides a new understanding of the ESIPT process in 3-hydroxyquinolones and related systems and suggests new possibilities for the design of ESIPT based molecular sensors and switchers.     

Modulation of excited-state intramolecular proton transfer by viscosity in protic media

3-Hydroxyquinolones undergo excited-state intramolecular proton transfer (ESIPT), resulting in a dual emission highly sensitive to H-bonding perturbations. Here, we report on the strong effect of viscosity on the dual emission of 2-(2-thienyl)-3-hydroxyquinolone in protic solvents. An increase in viscosity significantly decreases the formation of the ESIPT product, thus changing dramatically the ratio of the two emission bands. Time-resolved studies suggest the presence of solvated species characterized by decay times close to the solvent relaxation times in viscous media. The intramolecular H bond in this species is probably disrupted by the solvent, and therefore, its ESIPT requires a reorganization of the solvation shell for restoring this intramolecular H bond. Thus, the ESIPT reaction of this dye and its dual emission depend on solvent relaxation rates and, therefore, on viscosity. The present results suggest a new physical principle for the fluorescence ratiometric measurement of local viscosity.     

Solution 1H NMR characterization of the axial bonding of the two His in oxidized human cytoglobin

Solution 1H NMR spectroscopy has been used to determine the relative strengths (covalency) of the two axial His-Fe bonds in paramagnetic, S = 1/2, human met-cytoglobin. The sequence specific assignments of crucial portions of the proximal and distal helices, together with the magnitude of hyperfine shifts and paramagnetic relaxation, establish that His81 and His113, at the canonical positions E7 and F8 in the myoglobin fold, respectively, are ligated to the iron. The characterized complex (approximately 90%) in solution has protohemin oriented as in crystals, with the remaining approximately 10% exhibiting the hemin orientation rotated 180 degrees about the alpha-, gamma-meso axis. No evidence could be obtained for any five-coordinate complex (<1%) in equilibrium with the six-coordinate complexes. Extensive sequence-specific assignments on other dipolar shifted helical fragments and loops, together with available alternate crystal coordinates for the complex, allowed the robust determination of the orientation and anisotropies of the paramagnetic susceptibility tensor. The tilt of the major axis is controlled by the His-Fe-His vector, and the rhombic axes are controlled by the mean of the imidazole orientations for the two His. The anisotropy of the paramagnetic susceptibility tensor allowed the quantitative factoring of the hyperfine shifts for the two axial His to reveal an indistinguishable pattern and magnitudes of the contact shifts or pi spin densities, and hence, indistinguishable Fe-imidazole covalency for both Fe-His bonds.     

Electron-impact-induced asparagine molecule fragmentation

The fragmentation of the hydrated and anhydrous asparagine molecule (C₄H₈N₂O₃) under a low-energy electron impact was studied both experimentally and theoretically. The main emphasis was given to the mechanisms of the fragment production of these molecules. A special attention was paid to the energy characteristics of the ionic fragment yield. The geometrical parameters of the initial molecule rearrangement were also analyzed.