Isotropic and nematic phase N.M.R. spectra of tellurophen

In molecular beam experiments the preferred spatial orientation or polarization of the rotational angular momentum of reactively scattered molecules can be determined by deflection in an inhomogeneous electric field. The apparatus, experimental method, and analysis procedure are described and illustrated with data obtained for the K + HBr, Cs + HBr, and Cs + HI reactions. The experiments employ a new field design which eliminates the non-adiabatic change of quantization axis that handicapped a previous polarization study. A simple normalization procedure provides ‘reduced deflection profiles’ which are very insensitive to substantial variations in the experimental parameters, including the deflection field strength, beam position in the field, collimating slit widths, dipole moment, and distributions of rotational and translational energy. These reduced profiles yield 2 x> and 4 x>, the first two moments of the probability distribution of polarization, where x is the angle between the rotational angular momentum and the initial relative velocity vector. The experimental results indicate marked polarization, corresponding to 2 x> < 0·10, and agree well with theoretical moments calculated from a statistical phase-space treatment.     

Sulphidation-induced changes in the metallic phase of Fe-Cr alloys

The influence of sulphidation on the metallic phase in a series of Fe_100–x Cr _x alloys (x<15) was investigated by means of⁵⁷Fe Mössbauer spectroscopy. The results obtained gave evidence that the sulphidation at 1073 K is selective in the atmosphere of H₂/H₂S, with the partial pressure of sulphur ranging from 10^–7 to 10^–9 atm. Atx _cr=5.0(1) at.%, a change of the sulphidation preference occurs. Forx<5.0 at.%, the sulphidation results in an enrichment of the metallic phase in chromium, while forx> 5.0 at.%, in iron.     

Chiral-invariant phase space model

The masses of the SU(3)×SU(6) hadrons are calculated in the chiral-invariant phase space (CHIPS) model as a sum of the mean energies of the quarks at a constant temperature T _c with the color-magnetic splitting and the color-electric shift. The masses of hadrons are parametrized by four constants: T _c, m_s, E _CE and A _CM. With the same number of parameters the CHIPS model fits the masses of hadrons better than the classic bag model. The small mass of the d-quark ( m _d = 2.7MeV) is used to prove that the isotopic shifts of hadrons can be explained by the mass difference between the d- and u-quarks. The dibaryon mass is estimated in CHIPS to be 200MeV higher than in the bag model. The prediction for the mass of the α^* cluster is about the same in both models. It is close to 4 ^. m _Δ. Received: 12 December 2001 / Accepted: 23 May 2002     

A one-dimensional model with phase transition

Two repellent particles are bound to occupy two among thek _n +1 adjacent sites 0=x ₀ ⁽ⁿ⁾ <x ₁ ⁽ⁿ⁾ <...<x _kn ⁽ⁿ⁾ =1, sayx _q ⁽ⁿ⁾ ,x _q+1 ⁽ⁿ⁾ . Define the Hamiltonian _q ⁽ⁿ⁾ =–ln(x _q+1 ⁽ⁿ⁾ –x _q ⁽ⁿ⁾ ) and the partition function     

A second-order phase transition in the complete graph stochastic epidemic model

A stochastic model for epidemic spread in a set of individuals placed upon the sites of a complete graph of relations is investigated. The model is defined by three parameters: the number of individuals or sites, N, the probability that an infected site transmits the disease to a susceptible site, α, and the probability of recovery of infected sites, β, both referred to the unit of time.We show that this system evolves towards a, approximately Gaussian, stationary distribution of infected sites whose mean and variance can be analytically estimated. Also, we find that the average fraction of infected sites, x, is zero for transmission probabilities below the critical value α_c=1-e^-β/N and grows linearly with α for 0<α-α_c1. A sharp peak observed in Monte Carlo simulations of the variance of the number of infected sites as a function of α allows us to classify this dynamical phase transition as second order with x playing the role of an order parameter. Some consequences of this model to the dynamics of highly connected complex systems, such as the brain cortex, are also discussed.     

The quasi-equilibrium phase of nonlinear chains

We show that time evolution initiated via kinetic energy perturbations in conservative, discrete, spring-mass chains with purely nonlinear, non-integrable, algebraic potentials of the formV(x _i − x _i +1) ∼ (x _i − x _i+1 ) ²ⁿ ,n ≥ 2 and an integer, occurs via discrete solitary waves (DSWs) and discrete antisolitary waves (DASWs). Presence of reflecting and periodic boundaries in the system leads to collisions between the DSWs and DASWs. Such collisions lead to the breakage and subsequent reformation of (different) DSWs and DASWs. Our calculations show that the system eventually reaches a stable ‘quasi-equilibrium’ phase that appears to be independent of initial conditions, possesses Gaussian velocity distribution, and has a higher mean kinetic energy and larger range of kinetic energy fluctuations as compared to the pure harmonic system withn = 1; the latter indicates possible violation of equipartition.     

Incorporation of Sn into epitaxial GaAs grown from the liquid phase

The incorporation of Sn into LPE GaAs was studied as a function of the atomic fractionx _Sn ^l of Sn in the liquid (1.6×10⁻⁴≤x _Sn ^l ≤0.54), the growth temperatureT _K and the cooling rate α. The diffusion coefficient of As in Ga for moderate Sn-doping was deduced from the growth velocities to beD _As (760° C)=(3.3±1.0)×10⁻⁵ cm²/s. The epitaxial layers were analyzed after van der Pauw with special emphasis on the sources of experimental error. With the aid of current mobility theories the concentrations of the ionized donors and acceptors were derived. From their dependence onx _Sn ^l , on α and onT _K combined with the Schottky-barrier model of Sn incorporation it can be concluded that the melt and the growing crystal surface were in thermal equilibrium. The diffusion coefficient of Sn in GaAs is about 8×10⁻¹⁴ cm²/s at 760° C. The distribution coefficient for Sn increases from 4.4×10⁻⁵ to 12.3×10⁻⁵ in the temperature range from 690 to 800° C. The total Sn incorporationx _Sn ^s was measured using the atomic absorption spectroscopy for the first time down tox _Sn ^s =10¹⁷/cm³. From these data it can be concluded that up tox _Sn ^l =0.54 the dopant Sn is incorporated as donor and as acceptor only and that within the experimental scatter there is no indication of incorporation as a neutral species.     

Hadron production ine +e− annihilation and μ-p collisions under the assumption of longitudinal phase space dominance

Rapidity and multiplicity distributions are calculated for the hadrons produced ine ⁺e^? annihilation and deep inelastic muon-proton collisions for c.m. energies of 10 to 40 GeV. The hypothesis of longitudinal phase space dominance leads to a probability distribution which is identical to that of a grand canonical ensemble of non-interacting particles. We successfully describe experimental rapidity distributions, domains of Feynman-x scaling and scaling violations and the rapidity dependence of the mean transverse momentum. Multiplicity distributions are derived to be close to negative binomial distributions even for finite rapidity intervals. The plateau in the rapidity distribution is the origin for the negative binomial distribution in multiplicity. The mean number of hadrons of each species and the mean overall transverse momentum are the main input parameters in our calculation and are taken from experiment.     

Si含量对高锰硅化合物相组成及热电性能的影响研究

采用高频感应熔融、退火结合放电等离子烧结方法制备高锰硅(HMS)化合物MnSi1.70+x(x=0,0.05,0.1,0.15),系统研究了Si含量变化对材料相组成、微结构和热电性能的影响规律.结果表明,当x0.1时,样品由HMS和贫Si的MnSi金属相两相组成,随着Si含量x的增加,MnSi相相对含量减小;当x=0.1时,所得样品为单相HMS化合物;当x0.1时,样品由HMS和过量Si两相组成.随着x的增加,由于样品中高电导的金属相MnSi含量逐渐减少,样品的电导率逐渐下降,而Seebeck系数随之增加.室温下样品载流子浓度和有效质量随x增大逐渐减小,而迁移率逐渐增加.MnSi和Si杂相与HMS相比均为高热导相,因此当x=0.1时,由于样品为单相HMS,从而表现出最低热导率和最高ZT值.MnSi1.80样品在800K时热导率最小值达到2.25W·m-1K-1,并在850K处获得最大ZT值(0.45).     

Influence of calcium substitution on the phase transition and ionic conductivity in BICAVOX oxide ion conductor

Samples of Bi₄Ca _x V_{2? x} O_{11?(3 x /2)?δ} in the composition range 0.07 ≤ x ≤ 0.30 were prepared by conventional solid state reactions. The stability of different phases as a function of composition was analysed by X-ray powder diffraction, FT-IR spectra, differential thermal analysis and AC impedance spectroscopy. For the compositions x ≤ 0.10, monoclinic α-phase structure is retained at room temperature. For x = 0.13, orthorhombic β-phase is observed, whereas for x ≥ 0.17, high O^2?conducting tetragonal γ-phase is stabilised. However, the highest ionic conductivity σ_300°C = 3.27 × 10^?4 S cm^?1 was observed for x = 0.17. This higher value of conductivity of the substituted compound as compared to the parent compound can be attributed to the increased oxygen ion vacancies generated as a result of cation doping. AC impedance spectroscopy reveals the fact that this ionic conductivity is mainly due to the grain contribution.     

The “transition probability” in the state space of a 1-algebra

Let ω,? be two states of a 1-algebra and let us consider representations of this algebra R for which ω and ? are realized as vector states by vectors x and y. The transition probability P(ω,?) is the spectrum of all the numbers |(x,y)|² taken over all such realizations. We derive properties of this straightforward generalization of the quantum mechanical transition probability and give, in some important cases, an explicit expression for this quantity.     

Kinetics of phase transitions with singular multiplicative noise

The behavior of the most probable values of the order parameter x and the amplitude p of conjugate force fluctuations is studied for a stochastic system with a noise amplitude depending on x as |x|^a. It is shown that the phase half-plane x>0 for the canonical pair x, p is divided into isolated regions of large, intermediate, and small values of x. In the first region, the trajectories converge to values of x, p → ∞ as the time t → ∞, and the probability of their realization is negligibly small. In the intermediate region, the configuration point tends to the attraction center corresponding to a stationary ordered state. In the region , the trajectories converge to the point x=p=0 for 0<a<1/2 and to x=0, p → ∞ for 1/2<a≤1. In the former case, the probability of realization of trajectories is finite, while, in the latter case, it is negligibly small, and an absorbing state can be formed.     

Energy levels of the Schrödinger equation for some rational potentials in two-dimensional space using the inner product technique

The energy levels of a two-dimensional system are calculated for the rational potential,V(x, y; λ, g)=x ²+y ²+λ[x ²/(1+gx ²)+y ²/(1+gy ²)+a _xxx⁴+a _xyx² y ²+a _yyy⁴] using the inner product technique over a wide range of values of the perturbation parameters (g, λ) and for various eigenstates.     

On the n-p phase transitions in Mn1-x Cu x Cr2S4

The Seebeck coefficient for polycrystalline samples of: 1. Mn_1-x Cu _x Cr₂S₄ (0.0 ≤ x < 1.00) at 313 K and 2. MnCr₂S₄ between 313–393 K is presented. The electrical resistivity of Mn_1-x Cu _x Cr₂S₄ as a function of x at the room temperature is also presented. The n-p phase transition is observed in two cases: 1. on changing x at constant temperature (313 K) for 0.0 ≤ x ≤ 0.1 and 2. on changing temperature for MnCr₂S₄ at about 326 K. The first case is probably connected with the noncollinear ferromagnetic interaction of the chromium 3+ and 4+ ions. The second case follows from the strong ferrimagnetic interaction of the Mn²⁺ and Cr³⁺ ions in pure MnCr₂S₄.     

Microfabrication of FeMnPt films involving magnetic phase change due to structural transformation caused by ion irradiation

Correlations between crystal structures and magnetic properties of Fe_1–xMn_x Pt films were studied. The disordered films with x ≥ 0.44 had paramagnetic properties and the ordered films with x ≥ 0.46 had antiferromagnetic properties, viz. a difference of 0.02 in the x ‐value (i.e., 1.0 at%) was found. At x = 0.44 with the ordered structure, the uniaxial magnetocrystalline anisotropy was about 2.1 × 10⁷ erg cm^–3. A microfabrication process involving the slight composition difference of 0.02, which results in ferromagnetic–paramagnetic phase change due to the structural transformation caused by ion irradiation, was investigated. Only the area irradiated by Mn ions changed from ferromagnetic to paramagnetic phase. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Chiral invariant phase space event generator

The Geant4 quark level CHIPS (CHiral Invariant Phase Space) model simulates nuclear reactions assuming asymptotic freedom of massless quarks uniformly distributed over invariant phase space. Electro-nuclear reactions are simulated generating low-Q² equivalent photons. In this paper generalisation of the model for high Q² is made to describe neutrino-nuclear reactions, where the low-Q² contribution is suppressed by the W -boson mass. The proposed non-perturbative approximation of structure functions fits high-energy lepto-nucleon reactions with high-Q² and neutrino-nucleon reactions starting from the threshold.     

NiS2-xSex在x=1.00附近的反铁磁量子相变

针对NiS_2-xSe_x系统在x=1.0０附近发生的反铁磁量子相变,制备了一系列NiS_2-xSe_x(x=0.96, 0.98, 1.00, 1.05, 1.10和1.20)多晶样品,对其结构、磁性质和电阻率进行了系统的观测.结果发现：样品磁化率-温度关系呈现典型的强关联电子系统特征;与铜氧化物超导体相类似,它们的电阻率-温度关系在很宽的温 关键词： 量子相变 反铁磁自旋涨落 2-xSe_x体系')" href="#">NiS_2-xSe_x体系     

A microscopic calculation of dynamic critical exponents for displacive phase transitions

For anO(n)-isotropic lattice dynamicalQ ⁴-model describing displacive phase transitions ind dimensions, we employ a microscopic 1/n-expansion in order to show that over-damped soft-phonon behavior emerges for frequencies smaller than those of the characteristic orderv _c =O(n ^–x ). This is concluded from the fact that the displacement propagatorD(q, v) assumes the time-dependent Ginzburg-Landau (TDGL) form with a damping coefficient=O(n ^–x ), whenv becomes smaller thanv _c . The exponentx is found to bex=4–d for 2<d<3,x=(d–1)/2 for 3<d<5, andx=2 ford>5. The dynamic critical exponents forv _c (q) and forD(0,v) are derived atT=T _c 0 and toO(1/n). Their values are nontrivial for 2<d<4 and, within the TDGL-region, agree with the those appearing already for frequencies ofO(n ⁰) in TDGL-models with nonconserved order parameter andO(n ⁰)-damping coefficient. The latter case was studied by Halperin, Hohenberg, and Ma in 1972. Even in the TDGL-region, the energy conservation does not affect the dynamic exponents for largen(>2, since the specific heat is finite), but an energy diffusion singularity appears in theQ ²-response function which is related to the basic quantity of the 1/n-method, the effective interactionU _eff. By an estimate of order we find that the damping coefficients resulting from the coupling between the relaxation modes contained inU _eff and the critical modes inD are of ordern ^–w withw>x, such that the coupling between weakly damped critical modes is responsible for the crossover to the TDGL-behavior for largen. The exponentz=d/2, known to be generated by the coupling between order parameter and conservedO(n)-densities in TDGL-models, cannot be seen up to the order calculated. We also point out problems of a microscopic-expansion and comment upon differences between microscopic treatments for displacive transitions and those for the Bose condensation.     

Co(S1-xSex)2系统中的铁磁量子相变

针对Co(S_1-xSe_x)₂系统在x=0.11附近发生的铁磁金属到顺磁金属相变,制备了一系列不同Se替代浓度的多晶样品.通过对其结构和电阻率-温度ρ(T)关系的系统观测,结果发现,样品铁磁相变温度T_C随着Se替代浓度x值的增加,以(1-x)^1/2关系单调下降,其二级铁磁相变转变为一级相变 关键词： 量子相变 自旋量子涨落 1-xSe_x)₂')" href="#">Co(S_1-xSe_x)₂