Knotted Paths in Percolation

We study the topology of doubly-infinite paths in the bond percolation model on the three-dimensional cubic lattice. We propose a natural definition of a knotted doubly-infinite path. We prove the existence of a critical probability p _k satisfying p _c < p _k < 1 (where p _c is the usual percolation critical probability), such that for p _c < p < p _k , all doubly-infinite open paths are knotted, while for p > p _k there are unknotted doubly-infinite paths.     

Study of Scintillation for Infrared Laser Beam Propagating in Atmospheric Turbulence on Earth-Space Paths

On earth-space paths, by applying a modification of the Rytov method that incorporates spatial frequency filter function under strong atmosphere fluctuation conditions, a tractable model is developed for the scintillation index of infrared laser Gaussian beam wave that is valid under moderate-to-strong irradiance fluctuations. At Infrared band, based on ITU-R C ² _n model, the scintillation indexes for collimation laser beam are predicted by this analytic model. The results agree with theoretic expected scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on earth-space paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C ² _n.     

Analysis of Inner-Scale Effect on Atmosphere Scintillation for Infrared Laser Beam Propagating on Earth-Space Paths

On Earth-space paths, based on ITU-R C_n² (h) model, by means of a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, considering atmospheric turbulence inner-scale, an expression is developed for the scintillation index of a visible or a near and middle infrared laser beam wave that is valid under moderate to strong irradiance fluctuations. The quantitative analyses of scintillation index are done by this analytic model for laser Gaussian collimated beam wave at visible or near and middle infrared wave band. The results agree with theoretic analysis scintillation. This scintillation model can be converted into a Gaussian beam wave model with finite inner-scale on horizontal sight paths of invariable C_n².     

Autoionization spectra of Sm atom

Spectra of autoionizing states of the Sm atom in an energy region between 45948.9 cm-1 and 46943.6 cm-1 are systematically investigated by a three-color multi-step resonant excitation scheme with three different excitation paths.The three intermediate states,4f 66s7s 7F3,4f 66s7s 7F4,and 4f 66s7s 9F5 are employed for the three paths,respectively.Based on precise calibration of wavelength,the level energies of 112 autoionizing states are determined with the line widths and the relative line intensities of the related transitions.The possible influence of configuration interaction on the line shape of autoionizing state is also discussed.In addition,a unique value of J,the total angular momentum,is assigned to all detected states by comparing the three spectra obtained with the different excitation paths.     

Quantum Yang-Mills on a Riemann surface

We obtain the quantum expectations of gauge-invariant functions of the connection on aG=SU(N) product bundle over a Riemann surface of genusg. We show that the spaceA/G _m of connections modulo those gauge transformations which are the identity at one point is itself a principal bundle with affine linear fiber. The base space Path^2g G consists of 2g-tuples of paths inG subject to a relation on their endpoint values. Quantum expectations are iterated path integrals over first the fiber then over Path^2g G, each with respect to the push-forward toA/G _m of the measuree ^–S(A) D A. Here,S(A) denotes the Yang-Mills action onA. We exhibit a global section ofA/G _m to define a choice of origin in each fiber, relative to which the measure on the fiber is Gaussian. The induced measure on Path^2g G is the product of Wiener measures on the component paths, conditioned to preserve the endopoint relation. Conformal transformations of the metric onM act by reparametrizing these paths. We explicitly compute the partition function in the general case and the expectations of functions of certain products of Wilson loops in the caseg=1.Research supported in part by DOE grant DE-FGO2-88ER25066     

Charge transport in low-concentration MEH-PPV conjugated polymer/fullerene composites

Charge transport was studied in composites of poly[2-methoxy-5-(2′-ethyl-hexyloxy)-p-phenylene-vinylene] (MEH-PPV) conjugate polymer and low-concentration fullerenes (C₆₀) below the percolation threshold. The electron mobility showed a linear increase with the fullerene concentration, to which the hole mobility was insensitive. Our results indicate that fullerene–polymer networks provide a conduction path to the electrons, whereas the holes are transported through the polymer-only paths. The microscopic environments of the two distinct conduction paths in the composites as revealed by the electric field dependence of the mobilities are also discussed.     

Q-Systems, Heaps, Paths and Cluster Positivity

We consider the cluster algebra associated to the Q-system for A _r as a tool for relating Q-system solutions to all possible sets of initial data. Considered as a discrete integrable dynamical system, we show that the conserved quantities are partition functions of hard particles on certain weighted graphs determined by the choice of initial data. This allows us to interpret the solutions of the system as partition functions of Viennot’s heaps on these graphs, or as partition functions of weighted paths on dual graphs. The generating functions take the form of finite continued fractions. In this setting, the cluster mutations correspond to local rearrangements of the fractions which leave their final value unchanged. Finally, the general solutions of the Q-system are interpreted as partition functions for strongly non-intersecting families of lattice paths on target lattices. This expresses all cluster variables as manifestly positive Laurent polynomials of any initial data, thus proving the cluster positivity conjecture for the A _r Q-system. We also give the relation to domino tilings of deformed Aztec diamonds with defects.     

The relation between crystal structure and the formation and mobility of protonic charge carriers in perovskite-type oxides: A case study of Y-doped BaCeO3 and SrCeO3

Proton conductivity phenomena in 10% Y-doped barium and strontium cerate are investigated experimentally and by quantum molecular dynamics simulations. In particular the impact of deviations from the cubic perovskite structure on the formation and mobility of protonic charge carriers is investigated. For Y: SrCeO₃, which shows a larger deviation from the ideal cubic perovskite structure, the concentration and mobility of protonic defects is significantly lower than for Y: BaCeO₃. The first is due to the decay of the oxygen position into two sites, only one of which is involved in the formation of protonic defects. The symmetry reduction also leads to the formation of different one-dimensional proton diffusion paths, and unfavourable jumps between such paths are supposed to control the macroscopic proton diffusion coefficient in Y: SrCeO₃. The analysis suggests the formation of strong but transient hydrogen bonds and inter-octa-hedra proton transfer between vertices for SrCeO₃ in contrast to just intra-octahedra proton transfer for BaCeO₃. Whereas for BaCeO₃ the proton transfer step is identified to be rate-limiting at T= 1000 K, for SrCeO₃ both proton transfer and reorientation are found to be of similar magnitude.     

级联型四能级原子相干介质中的光学双稳态和多稳态

主要研究了在一单向环形腔内的级联型四能级原子被三个光场驱动的光学双稳态和多稳态行为. 三个单模光场通过三个光子跃迁路径与原子系统耦合. 在这种情况下,中间两能级间所加的耦合场Ω_B变得非常重要. 研究显示耦合场Ω_B的增加会使光学双稳态的阈值减小,同时也会导致光学多稳态的产生.对上面两能级间所加的耦合场的作用也进行了讨论,同时还讨论了探测场失谐和合作参数对光学双稳态及多稳态的影响. 关键词： 原子相干 光学双稳态和多稳态 四能级原子     

Stereodynamics of the O(3P) with H2 (D2) (v=0, j=0) reaction

Quasi-classical trajectory theory is used to study the reaction of O(³P) with H₂ (D₂) based on the ground ³A' potential energy surface (PES). The reaction cross section of the reaction O+H₂ → OH+H is in excellent agreement with the previous result. Vector correlations, product rotational alignment parameters 〈P₂ (j'·k)〉 and several polarized-dependent differential cross sections are further calculated for the reaction. The product polarization distribution exhibits different characteristics that can be ascribed to different motion paths on the PES, arising from various collision energies or mass factors.     

Degenerate thermal isomerizations of bicyclo[3.1.1]hept‐2‐ene: strategy and analysis

Bicyclo[3.1.1]hept‐2‐ene was first prepared and well identified in 1972. In 1974, the degenerate thermal isomerization involving 1‐d‐ and 3‐d‐bicyclo[3.1.1]hept‐2‐ene was approached successfully, as one of the two deuterium‐labeled structures was selected, heated, and equilibrated. There has been no further study of this degenerate isomerization. Here, a detailed outline of reaction trajectories for d₂‐labeled bicyclo[3.1.1]hept‐2‐enes is given that will establish the four independent kinetic parameters needed for 20 linking paths between six d₂‐species. The use of racemates, eliminating chiral separations and dissections, provides degenerate isomerization paths providing this method with general utility. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparing long-range corrected functionals in the cis–trans isomerisation of the retinal chromophore

Earlier results for the 11-cis to all-trans isomerisation of the retinal chromophore after photoexcitation, studied using time-dependent density functional theory with the hybrid CAM-B3LYP functional, are compared with new results using other long-range corrected DFT functionals. The TDDFT S₀ and S₁ minimum energy paths have been compared with the approximate coupled-cluster method RI-CC2. All calculations were consistent in producing an additional avoided crossing minimum on the S ₁ minimum energy path lying approximately halfway between the 11-cis and all-trans S₁ minima. In this minimum on the S₁ potential energy surface, the retinal chromophore has inverted bond order in its carbon chain and lower energy than it has in both the 11-cis and all-trans S₁ minima.     

The probability of intersection of independent random walks in four dimensions

LetS ₁ andS ₂ be independent simple random walks of lengthn inZ ⁴ starting at 0 andx ₀ respectively. If |x ₀|₂n, it is shown that the probability that the paths intersect is of order (logn)^–1. Ifx ₀=0, it is shown that the probability of no intersection of the paths decays no faster than (logn)^–1 and no slower than (logn)^–1/2. It is conjectured that (logn)^–1/2 is the actual decay rate.Research supported by National Science Foundation grant MCS-8002758     

Even-parity states of the Sm atom with stepwise excitation

Two-colour stepwise excitation and photoionization schemes are adopted to study the spectra of high-lying states of the Sm atom. These bound even-parity states are excited with three different excitation paths from the 4f66s6p7DJ (J = 1, 2, 3) intermediate states, respectively. They are probed by photoionization process with an extra photon driving them to the continuum states. In this experiment, 270 states are detected in an energy range from 36160 cm-1 to 42250 cm-1, 109 of which are newly discovered, while the rest of them are confirmed to be the energy levels reported previously. Furthermore, based on the J-momentum selection rules of three excitation paths, a unique assignment of J-momentum for all observed states is determined, eliminating all remaining ambiguities in the literature. Finally, 53 single-colour transitions originating from the scanning laser are also identified. For all the relevant transitions, the information about their relative intensities is also given in the paper.     

Plasma Processes in Activated Thin Film Deposition

This paper deals with plasma aspects in physical and chemical vapour deposition processes. A systematic representation of deposition methods is given and possibilities of plasma diagnostic are summerized. Characteristic parameters of electron kinetics (mean free paths, collision frequencies, energy distribution functions) and rate equations for calculation of particle densities are discussed for a plasma in plasma activated physical vapour deposition device. Theoretical results are compared with measurements (T_e, N_e, E_z) in the plasma of a TiN_x-deposition device with hollow cathode arc evaporator. Mechanism of plasma polymerisation is discussed. Results of experimental investigations of the plasma in an Ar-hexamethyldisiloxane D.C. low pressure glow discharge are presented and compared with results of modelling of this plasma taking into account direct-, stepwise- and Penning-ionization. The necessivity of knowledge of reactive cross sections for understanding of plasma assisted thin film formation processes is accentuated.     

Mass and stability of rigidly rotating relativistic polytropes by energy method

The energy of a rigidly rotating star is written in the first and second post-Newtonian approximation. Conditions for equilibrium and stability are derived, as well as evolutionary paths for stars shedding angular momentum or mass. For polytropic index n > 1, these analytic results agree with exact numerical results to within a few percent as long as the general relativity index (P/c²)_c < 0.1. The energy method is applied to low mass white dwarfs, to semirelativistic neutron stars and to supermassive stars.     

Linear concentration dependence of vibrational width and vibrational dephasing paths in aqueous nitrate solutions

A theoretical model of vibrational dephasing of Raman active ions in aqueous electrolyte solutions is presented in which a probe ion is coupled to the bath by direct ion-solvent and ion-ion interactions. Expression for the vibrational width in terms of concentrations and efficiencies of the vibrational frequency modulation by ion-perturber interactions is given in the fast modulation scheme. The observed linear concentration dependence of the vibrational dephasing width of the v ₁(A'₁) mode of NO₃ ^- in aqueous solutions is reasonably well explained from this model, and efficiencies of the dephasing paths through NO₃ ^--water hydrogen bonding interaction and contact NO₃ ^--cation pair formation interaction are estimated. Anions in the solution give only a secondary effect to nitrate vibrational dephasing because of interionic repulsive forces.     

Reactive scattering of alkali dimers: chemi-ionization

Measurements of total cross sections Q_i for chemi-ionization in scattering of a K₂ dimer beam by a range of halogen containing molecules, at translational energies E ～ 7–11 kcal mol^-1, are reported. Substantial cross sections, Q_i ～ 2–10 Ų are exhibited by the halogen molecules Br₂, ICl, IBr, I₂. Distinctly lower values Q_i ～ 0·1–0.2 Ų are exhibited by BrCN and the mercuric and stannic halides, HgX₂, SnX₄. The results show a close correlation with the chemi-ionization exoergicities, particularly for formation of a K⁺,X^- ion pair. These chemi-ionization data and results from previous reactive scattering studies are compared, in order to estimate relative reaction yields for different reaction paths. The reaction dynamics for K₂ with halogen molecules and cyanohalides are rationalized in terms of the electronic structure of the potential surface, where the orientation of the K₂ dimer plays a crucial role.     

Residual two-body matrix elements for pre-equilibrium calculations

The effective matrix elements which appear in pre-equilibrium calculations in the rate expressions for the residual two-body interactions have been evaluated from analyses of emitted particle energy spectra. Probably because of details in the model formulation, the results are found to depend on the nature of the projectile. They are, however, of reasonable magnitude and show a mass number and excitation energy dependence consistent with predictions based on calculations of mean free paths in nuclear matter. The square of the empirical effective matrix element is found to approximately obey the relation M² = K_aA⁻³E⁻¹ with the values of K_a = 95 MeV³ and 725 MeV³ applying to proton and α-particle induced reactions respectively. The quantities A and E are the mass number and excitation energy of the system respectively.