On independent sets in random graphs

The independence number of a sparse random graph G(n,m) of average degree d = 2m/n is well‐known to be with high probability, with in the limit of large d. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size , i.e., about half the maximum size. Yet in spite of 30 years of extensive research no efficient algorithm has emerged to produce an independent set with size for any fixed (independent of both d and n). In this paper we prove that the combinatorial structure of the independent set problem in random graphs undergoes a phase transition as the size k of the independent sets passes the point . Roughly speaking, we prove that independent sets of size form an intricately rugged landscape, in which local search algorithms seem to get stuck. We illustrate this phenomenon by providing an exponential lower bound for the Metropolis process, a Markov chain for sampling independent sets. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 436–486, 2015     

Emergence of the sub‐THz central peak at phase transitions in artificial BaTiO3/(Ba,Sr)TiO3 superlattices

A prominent central peak in the sub‐THz frequency range was observed in the Raman spectra of BaTiO₃/(Ba,Sr)TiO₃ (BT/BST) superlattice grown on (001)MgO substrate. Both soft and central mode show an anomaly around 200 K and 280 K, which can be correlated with orthorhombic to monoclinic phase transition of BST and BT, respectively. The observed temperature dependence of the central mode enabled us to explain rather broad temperature dependence of the dielectric permittivity previously observed in BT/BST superlattices. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

GaAs pyramidal quantum dot coupled to wetting layer in an AlGaAs matrix: A strain-free system

In this contribution, the electronic and linear and nonlinear optical properties of pyramid-shaped GaAs quantum dots (QDs) coupled to wetting layer (WL) in an Al_0.3Ga_0.7As matrix have been investigated. This nanostructure is relaxed from strain effects due to very small lattice-mismatching. Three transitions of P-to-S, WL-to-P, and WL-to-S were considered and the corresponding transition dipole moments, oscillator strengths, and linear and nonlinear optical properties regarding to these transitions were investigated as a function of the QD height. The results showed that for P-to-S transition, which is a purely in-plane-polarized transition, the dependence of electronic and optical properties on the size is moderate and can be neglected. But for WL-to-P and WL-to-S transitions, which are in-plane- and z-polarized transitions, respectively, the electronic as well as optical properties are strongly size-dependent. Furthermore, a competition between WL-to-S and WL-to-P transitions was observed when the QD size changed.     

Synthesis and electrochemical characteristics of xLi2MnO3–(1−x)Li(Mn0.375Ni0.375Co0.25)O2 (0.0 ≤ x ≤ 1.0) thin film cathode for lithium rechargeable micro batteries

We have compared the structure, microstructure, and electrochemical characteristics of xLi₂MnO₃–(1−x)Li(Mn_0.375Ni_0.375Co_0.25)O₂ (0.0 ≤ x ≤ 1.0) thin films with their bulk cathode laminate counterparts of identical compositions. Pure Li(Mn_0.375Ni_0.375Co_0.25)O₂ as well as the synthesized composite films partially transform into cubic spinel structure during charge–discharge cycling. In contrast, such layered to spinel phase transformation has only been identified in bulk cathode laminates with x ≥ 0.75. At a current density 0.05 mAcm⁻², the discharge capacity of Li(Mn_0.375Ni_0.375Co_0.25)O₂ thin film was measured to be ∼60 μAhcm⁻². The discharge capacity (∼217 μAhcm⁻²) was markedly improved in x∼0.5 composite thin film. The capacity retention after 20 charge discharge cycles are improved in composite films; however, their capacity fading could not be eliminated completely.     

Synergistic Spin Transition between Spin Crossover and Spin‐Peierls‐like Singlet Formation in the Halogen‐Bonded Molecular Hybrid System: [Fe(Iqsal)2][Ni(dmit)2]⋅CH3CN⋅H2O

To introduce halogen‐bond interactions between a cation and an anion, a novel Fe^III complex from iodine‐substituted ligands involving a paramagnetic nickel dithiolene anion was prepared and characterized. The compound exhibited the synergy between a spin‐crossover transition and a spin‐Peierls‐like singlet formation. The halogen‐bond interactions between the iodine and the sulfur atoms stabilized the paramagnetic state of π‐spins and played a crucial role in the synergistic magnetic transition between d‐ and π‐spins. In addition, the compound showed the light‐induced excited spin state trapping effect.     

Phase Transition of [2,2]‐Paracyclophane – An End to an Apparently Endless Story

In this contribution, the solid‐state low‐temperature phase structure of [2,2]‐paracyclophane is unambiguously characterised by single‐crystal X‐ray analysis. Additionally, a heat capacity measurement was undertaken, which proves the existence of a λ‐type phase transition at 45 K, a transition that is connected with the formation of a secondary C_p/T feature at 60 K. The low‐temperature phase (<45 K) crystallises in the lower symmetry space group P$\bar 4$ n2, whereas the high‐temperature phase (>60 K) crystallises in space group P4₂/mnm. This proves what has been postulated both by experimental and theoretical chemists but has repeatedly been dismissed as speculation many times.     

Systematic Tuning and Switching of Neutral and Ionic Phases in a Donor–Acceptor Chain Compound by Doping with Less‐Active Donors and by Pressure Application

The temperature‐induced stepwise neutral–ionic (N–I) phase transition in the covalently bonded donor–acceptor chain compound [Ru₂(2,3,5,6‐F₄PhCO₂)₄DMDCNQI] ? 2(p‐xylene) (2,3,5,6‐F₄PhCO₂^?=2,3,5,6‐tetrafluorobenzoate; DMDCNQI=2,5‐dimethyl‐N,N′‐dicyanoquinodiimine) was systematically tuned over a wide temperature range using two techniques: 1) A chemical technique based on doping with a less‐active donor unit [Ru₂^II,II(F₅PhCO₂)₄] (F₅PhCO₂^?=pentafluorobenzoate), thereby providing an isostructural doped series [{Ru₂^II,II(2,3,5,6‐F₄PhCO₂)₄}_1?x{Ru₂^II,II(F₅PhCO₂)₄}_xDMDCNQI] ? 2(p‐xylene), with x=0.06, 0.10, 0.21, and 0.24; and 2) a physical technique, which was the application of hydrostatic pressure to the doped compounds. The stepwise N–I transition observed in the original compound was systematically varied in terms of the viewpoints of both transition temperature and transition features (stepwise or monotonic) dependent on the amount of dopants x. Application of pressure efficiently tuned the N–I transitions, with the oxidation phases being dramatically modified by applying only weak pressure up to 4 kbar. Even in cases that led to N–I transitions in small domains of the chains at ambient pressure, the application of pressure caused an expansion of the domains that enabled N–I transitions, finally leading to a complete change in the oxidation state of the chains, from neutral to ionic, accompanied by a change from a paramagnetic state to a ferrimagnetically ordered state.     

Superelastic Organic Crystals

Superelastic materials (crystal‐to‐crystal transformation pseudo elasticity) that consist of organic components have not been observed since superelasticity was discovered in a Au‐Cd alloy in 1932. Superelastic materials have been exclusively developed in metallic or inorganic covalent solids, as represented by Ti‐Ni alloys. Organosuperelasticity is now revealed in a pure organic crystal of terephthalamide, which precisely produces a large motion with high repetition and high energy storage efficiency. This process is driven by a small shear stress owing to the low density of strain energy related to the low lattice energy.     

Anomalous High Temperature Structural Behavior of Potential Multifunctional Material SmCo0.5Cr0.5O3

Crystal structure parameters of the mixed cobaltite–chromite SmCo_0.5Cr_0.5O₃ in the temperature range of 298–1173 K were derived from in situ high-resolution X-ray synchrotron powder diffraction data. Similar to the parent SmCoO₃ compound, SmCo_0.5Cr_0.5O₃ reveals anomalous thermal expansion reflected in abnormal temperature dependence of the unit cell dimensions and the selected interatomic distances and angles. These anomalies are associated with temperature induced changes of spin state of Co³⁺ ions and coupled insulator-metal transition. Observed decreasing behavior of the bandwidth W points on the increasing population of the exited spin states of Co³⁺ ions in SmCo_0.5Cr_0.5O₃ with increasing temperature. First principle calculations revealed antiferromagnetic ground state of SmCo_0.5Cr_0.5O₃ as the most stable.