Cell rotation graphs of strongly connected orientations of plane graphs with an application

The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is defined. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of all orientations in T induce a component of D(G), denoted by T⁻, thus (T,T⁻) is called a pair of in-trees of D(G); G is Eulerian if and only if D(G) has an odd number of components (all Eulerian orientations of G induce the same component of D(G)); the width and height of T are equal to that of T⁻, respectively. Further it is shown that the pair of directed tree structures on the perfect matchings of a plane elementary bipartite graph G coincide with a pair of in-trees of D(G). Accordingly, such a pair of in-trees on the perfect matchings of any plane bipartite graph have the same width and height.     

Coloring of distance graphs with intervals as distance sets

Let D be a set of positive integers. The distance graph G(Z,D) with distance set D is the graph with vertex set Z in which two vertices x,y are adjacent if and only if |x−y|D. The fractional chromatic number, the chromatic number, and the circular chromatic number of G(Z,D) for various D have been extensively studied recently. In this paper, we investigate the fractional chromatic number, the chromatic number, and the circular chromatic number of the distance graphs with the distance sets of the form D_m,[k,k^′]={1,2,…,m}−{k,k+1,…,k^′}, where m, k, and k^′ are natural numbers with m≥k^′≥k. In particular, we completely determine the chromatic number of G(Z,D_m,[2,k^′]) for arbitrary m, and k^′.     

On quasistatic inelastic models of gradient type with convex composite constitutive equations

This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.     

双KTP内腔参量下转换产生量子相关孪生光子对

使用双ＫＴＰ晶体串接，经光学参量振荡腔内参量下转换，在３００ｍＷ泵浦功率下，获得总功率约２３ｍＷ的强度相关的孪生光束，在１．２５ＭＨｚ处其强度差噪声功率较散离噪声极限降低５０％（３ｄＢ）。     

One‐dimensional Europium(III) Coordination Polymer Based on 3‐Pyridylacrylic Acid

Under hydrothermal conditions, the reaction of racemic 3‐pyridyl‐3‐aminopropionic acid (rac‐HPAPA) with Eu(ClO₄)₃· 6H₂O affords a 1‐D chain complex, [Eu(3‐PYA)₃(H₂O)]_n ( 1 ) (3‐PYA=3‐pyridylacrylate), which represents an example of neutral 1‐D coordination polymeric material based on 3‐HPYA (HPYA= pyridylacrylic acid) ligand with strong red fluorescent emission in the solid state.     

Transformations of gamma-alumina in aqueous suspensions 1. Alumina chemical weathering studied as a function of pH

Hydration of gamma-Al2O3 is often reported to occur via the superficial transformation of the alumina surface into aluminum hydroxide-like layers. However, very little evidence has been given so far to support this hypothesis. It is demonstrated here by X-ray diffraction, TEM, electron diffraction, and solubility studies that a second process of hydration takes place that involves the dissolution of alumina and subsequent precipitation of well-shaped Al(OH)3 particles from supersaturated alumina aqueous solution. This process can be observed on a macroscopic scale (XRD, TEM) for any pH5, provided that the contact time between alumina and water exceeds 10 h. The least thermodynamically stable phase of aluminum hydroxide, bayerite, becomes favored compared with gibbsite when the pH of the solution is increased. It is assumed that the rate of formation of bayerite germs is greater than that of gibbsite due to variations in aluminum speciation in solution as a function of pH.     

Instability and mode transition analysis of a hydrogen-rich combustion in a model afterburner

Combustion instabilities were investigated experimentally for a hydrogen-rich combustion in a model afterburner installed at the end of a high-enthalpy wind tunnel. Air was supplied at 0.3 MPa and 950 K. The combustion instabilities were studied with the time-resolved measurements of a near-infrared (NIR) emission from water molecules over 780 nm using a high-speed video camera. Pressure was also measured in the combustor. The pressure and the NIR images were analyzed by data-driven approach, which include the fast Fourier transform (FFT), the wavelet transform, the dynamic mode decomposition (DMD) and the Gaussian process latent variable methods (GP-LVM). Thermoacoustic instability was observed under a rich condition, and the amplitude of the pressure oscillation was the maximum at the overall equivalence ratio of approximately 2.4 or 2.7 as a result of the FFT. The combustion dynamics were investigated in detail for an experimental run at the equivalence ratio of 2.4. A pressure spectrogram indicated a flame–vortex interaction with a Strouhal number of 0.5 (2300 Hz), thermoacoustic instability (560 Hz), and their transitions with the wavelet transform. For NIR images, the same tendency was also observed in the spectrogram of the modes obtained by the Gabor-filtered DMD, which could clearly resolve the high-order harmonic modes of the flame–vortex interaction and the thermoacoustic instability. Furthermore, NIR images were analyzed with GP-LVM to study the evolution of the combustion dynamics in a three-dimensional latent space. Recurrence plots with the Euclidean distance function were used to visualize the evolutions of the combustion dynamics. A limit cycle behavior of the flame–vortex interaction was clearly observed, whereas the limit cycle of the thermoacoustic instability showed more complicated behaviors. The transition behaviors of the instabilities were observed in the recurrence plots in detail, indicating that the flame–vortex interaction excited the fourth harmonic mode of the thermoacoustic instability, followed by the basic mode.     

Quantifying the Interactions in the Aggregation of Thermoresponsive Polymers: The Effect of Cononsolvency

The aggregation kinetics of thermoresponsive core–shell micelles with a poly(N‐isopropyl acrylamide) shell in pure water or in mixtures of water with the cosolvents methanol or ethanol at mole fractions of 5% is investigated during a temperature jump across the respective cloud point. Characteristically, these mixtures give rise to cononsolvency behavior. At the cloud point, aggregates are formed, and their growth is followed with time‐resolved small‐angle neutron scattering. Using the reversible association model, the interaction potential between the aggregates is determined from their growth rate in dependence on the cosolvents. The effect of the cosolvent is attributed to the interaction potential on the structured layer of hydration water around the aggregates. It is surmised that the latter is perturbed by the cosolvent and thus the residual repulsive hydration force between the aggregates is reduced. The larger the molar volume of the cosolvent, the more pronounced is the effect. This framework provides a molecular‐level understanding of solvent‐mediated effective interactions in polymer solutions and new opportunities for the rational control of self‐assembly in complex soft matter systems.