Exact solutions for network rewiring models

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.     

Stop coannihilation in the CMSSM and SubGUT models

Stop coannihilation may bring the relic density of heavy supersymmetric dark matter particles into the range allowed by cosmology. The efficiency of this process is enhanced by stop-antistop annihilations into the longitudinal (Goldstone) modes of the W and Z bosons, as well as by Sommerfeld enhancement of stop annihilations and the effects of bound states. Since the couplings of the stops to the Goldstone modes are proportional to the trilinear soft supersymmetry-breaking A-terms, these annihilations are enhanced when the A-terms are large. However, the Higgs mass may be reduced below the measured value if the A-terms are too large. Unfortunately, the interpretation of this constraint on the stop coannihilation strip is clouded by differences between the available Higgs mass calculators. For our study, we use as our default calculator FeynHiggs 2.13.0, the most recent publicly available version of this code. Exploring the CMSSM parameter space, we find that along the stop coannihilation strip the masses of the stops are severely split by the large A-terms. This suppresses the Higgs mass drastically for \(\mu \) and \(A_0 > 0\), whilst the extent of the stop coannihilation strip is limited for \(A_0 < 0\) and either sign of \(\mu \). However, in sub-GUT models, reduced renormalization-group running mitigates the effect of the large A-terms, allowing larger LSP masses to be consistent with the Higgs mass calculation. We give examples where the dark matter particle mass may reach \(\gtrsim 8\) TeV.     

Dilations of dynamical semi-groups

We prove the existence of isometric and unitary dilations of a class of semi-groups of completely positive maps on an algebra of operators on a Hilbert space. The result has relevance to the problem of embedding an open quantum mechanical system in a closed one.     

Vowel normalization for accent: an investigation of best exemplar locations in northern and southern British English sentences

Two experiments investigated whether listeners change their vowel categorization decisions to adjust to different accents of British English. Listeners from different regions of England gave goodness ratings on synthesized vowels embedded in natural carrier sentences that were spoken with either a northern or southern English accent. A computer minimization algorithm adjusted F1, F2, F3, and duration on successive trials according to listeners' goodness ratings, until the best exemplar of each vowel was found. The results demonstrated that most listeners adjusted their vowel categorization decisions based on the accent of the carrier sentence. The patterns of perceptual normalization were affected by individual differences in language background (e.g., whether the individuals grew up in the north or south of England), and were linked to the changes in production that speakers typically make due to sociolinguistic factors when living in multidialectal environments.     

Highly Enantioselective,Organocatalytic, and Scalable Synthesis of a Rare cis,cis-Tricyclic Diterpenoid

A highly enantioselective, organocatalytic, and scalable synthesis of a very unusual cis-decalin-cis-hydrindane tricyclic diterpenoid system has been achieved. Despite the prevalent pharmacological space that the related trans,trans and trans,cis-systems occupy, there have been no reports of an asymmetric synthesis of the cis,cis systems in the literature until now. We demonstrate the flexibility of our approach not only through access to a diverse range of products, all of which are attained in exceptionally high selectivities, but also by showing their easy conversion to the corresponding trans,cis-system and other derivatives.     

Four-space formulation of Dirac's equation

Dirac's equation is reviewed and found to be based on nonrelativistic ideas of probability. A 4-space formulation is proposed that is completely Lorentzinvariant, using probability distributions in space-time with the particle's proper time as a parameter for the evolution of the wave function. This leads to a new wave equation which implies that the proper mass of a particle is an observable, and is sharp only in stationary states. The model has a built-in arrow of time, which is associated with a restriction to positive-energy solutions. The usual solution for a Coulomb field is retained, though it now implies a slightly different charge distribution. The conventional nonstationary solutions become invalid. The new formulation appears to offer a resolution of difficulties that have been associated with Dirac's equation. It also predicts the occurrence of virtual pairs at a level that may be experimentally testable, and suggests a mechanism for self-cancellation of the vacuum energy.     

Photophysics and Electrochemistry of some Thione Far-Red/Near-IR Triplet Emitters

The photophysics and cyclic voltammetry of two novel phosphorescent thiones, 2,2-dimethyl-indan-1-one-3-thione (DMIKT) and 2,2-dimethyl-indan-1,3-dithione (DMIDT), and three known phosphorescent thiones, 4H-pyran-4-thione (PT), 4H-1-benzopyran-4-thione (BPT) and 2,2-dimethylindan-1-thione (DMIT), have been characterised and compared. The phosphorescence emission of DMIT, DMIKT and DMIDT extends from the red into the near-IR spectral region. The additional carbonyl or thione group of DMIKT and DMIDT causes a significant shift in the emission maxima to 680 nm compared to that of DMIT, at 637 nm, in perfluorinated hydrocarbons. In acetonitrile the emission maxima of DMIKT and DMIDT are at 696 and 706 nm, respectively, and the spectra show vibronic bands which extend out beyond 850 nm. There is a significant reduction in triplet lifetime along this series (from 44 (±2) μs (DMIT) to 10 ((±0.8) μs (DMIKT) in perfluorinated solvents, and 8.6 (±0.5) (DMIT), 1.3 (±0.5) (DMIKT) and 0.35 (±0.07) μs (DMIDT) in acetonitrile), as well as a reduction in the rate constant for ground-state quenching of the triplet, (from 9.8 ((±0.9) to 3.5 ((±0.6) and 1.3 ((±0.2) × 10⁹ mol⁻¹ dm³ s⁻¹ for the same compounds). The addition of the C=O or C=S groups also causes a decrease in phosphorescence quantum yield with the highest emission quantum yield obtained for DMIT (Φ _P = 0.149 (±0.015)). Electrochemical studies show that while PT and BPT exhibit irreversible redox behaviour, DMIT, DMIKT and DMIDT all show at least one reversible reduction wave attributed to a one-electron process centred on the C=S moiety. The suitability of these lumophores for use in OLEDs is discussed.     

The characterization of the iron content of industrially cast aluminium

Pure intermetallic phases Al₁₃Fe₄, Al₆Fe, Al_mFe and Al_xFe have been extracted from Bridgman grown model aluminium–iron binary alloys by dissolving the aluminium matrix in butanol. Each phase has a distinct Mössbauer spectrum and variable temperature ⁵⁷Fe Mössbauer studies have enabled the Debye temperature of each phase to be determined. Hence, the variation of the recoilfree fraction f with temperature is determined for each phase. From this information it is possible to measure the proportion of each phase, either when the phases are extracted or in situ in aluminium. The results obtained can be used in the characterisation of industrially cast aluminium.     

The conjugate-pairing rule for non-Hamiltonian systems

In systems that satisfy the Conjugate Pairing Rule (CPR), the spectrum of Lyapunov exponents is symmetric. The sum of each conjugate pair of exponents is identical. Since in dissipative systems the sum of all the exponents is the entropy production divided by Boltzmann's constant, the calculation of transport coefficients from the Lyapunov exponents is greatly simplified in systems that satisfy CPR. Sufficient conditions for CPR are well known: the underlying adiabatic dynamics should be symplectic. However, the necessary conditions for CPR are not known. In this paper we report on the results of computer simulations which shed light on the necessary conditions for the CPR to hold. We provide, for the first time, convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the CPR, even in the thermodynamic limit. In spite of this it appears that the sum of the maximal exponents is equal to the entropy production per degree of freedom. Thus it appears that the shear viscosity can still be calculated using the standard viscosity algorithm by summing the maximal pair of exponents.(c) 1998 American Institute of Physics.