Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.     

Asymptotics in ASEP with Step Initial Condition

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribution function F ₂ arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial condition.     

Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition

In this paper we give the distribution of the position of a particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find ℙ(X _m (t)≤x) where X _m (t) is the position of the particle at time t which was at m=2k−1, k∈ℤ at t=0. As in the ASEP with step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand of the integral formula for ℙ(X _m (t)≤x) to a determinantal form together with an extra product.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

Large Deviation Functional of the Weakly Asymmetric Exclusion Process

We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like _L ¹ . We recover as limiting cases the expressions derived recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP limit, the nonlinear differential equation one needs to solve can be analysed by a method which resembles the WKB method.     

Shock profiles for the asymmetric simple exclusion process in one dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation; the latter has shock solutions with a discontinuous jump from left density ρ- to right density ρ+, ρ-< ρ +, which travel with velocity (2p−1 )(1−ρ₊−p ₋). In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time-invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice siten, measured from this particle, approachesp _± at an exponential rate asn→ ±∞, witha characteristic length which becomes independent ofp when . For a special value of the asymmetry, given byp/(1−p)=p ₊(1−p ₋)/p ₋(1−p ₊), the measure is Bernoulli, with densityρ ₋ on the left andp ₊ on the right. In the weakly asymmetric limit, 2p−1 → 0, the microscopic width of the shock diverges as (2p+1)^-1. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.     

A Fredholm Determinant Representation in ASEP

In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers ℤ⁺ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.     

Inverse resonance scattering for Jacobi operators

The Jacobi operator (Jf) _n = a _n−1 f _n−1 +a _n f _n+1 + b _n f _n on ℤ with real finitely supported sequences (a _n − 1) _n∈ℤ and (b _n ) _n∈ℤ is considered. The inverse problem for two mappings (including their characterization): (a _n , b _n , n ∈ ℤ) → {the zeros of the reflection coefficient} and (a _n , b _n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.     

On the Law of Addition of Random Matrices

Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices A _n and B _n rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix U _n (i.e. A _n +U _n ^* B _n U _n ) is studied in the limit of large matrix order n. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of A _n and B _n is obtained and studied. Received: 27 October 1999/ Accepted: 22 March 2000     

Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances

As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process(ASEP) has been widely used to study many physical, chemical, and biological systems. The ASEP shows a range of nontrivial macroscopic phenomena, among which, the spontaneous symmetry breaking has gained a great deal of attention. Nevertheless,as a basic problem, it has been controversial whether there exist one or two symmetry-broken phases in the ASEP. Based on the mean field analysis and current minimization principle, this paper demonstrates that one of the broken-symmetry phases does not exist in a bidirectional two-lane ASEP with narrow entrances. Moreover, an exponential decay feature is observed,which has been used to predict the phase boundary in the thermodynamic limit. Our findings might be generalized to other ASEP models and thus deepen the understanding of the spontaneous symmetry breaking in non-equilibrium systems.     

Effect of postgrafted alkyl chains on the wettability of hydrophilic poly(amidoamine)-grafted nano-sized silica

In order to control the surface wettability of hyperbranched hydrophilic poly(amidoamine) (PAMAM)-grafted nano-sized silica, hydrophilic alkyl chain (C _n H_2n+1) with different chain lengths (n = 4, 8, 15) were postgrafted onto PAMAM-grafted silica by the reaction of terminal amino groups of PAMAM grafted on the silica surface with alkyl acid chlorides (C _n H_2n+1-COCl). The postgrafting of C _n H_2n+1-COCl increased with increasing PAMAM grafting and alkyl chain length of C _n H_2n+1-COCl. However, the terminal amino groups of PAMAM-grafted silica used for the postgrafting of C _n H_2n+1-COCl decreased with increasing chain length. This may be due to the steric hindrance between terminal amino groups of PAMAM-grafted silica and C _n H_2n+1-COCl: the steric hindrance is considered to increase with increasing chain length of C _n H_2n+1-COCl. The surface wettability was estimated by contact angle measurement for water and methanol wettability. As a result, it was found that contact angle and methanol wettability increased with increasing alkyl chain length of postgrafted C _n H_2n+1-COCl. The hyperbranched PAMAM-grafted silica readily dispersed in water and methanol because of the hydrophilic nature of grafted PAMAM, but it lost dispersibility in water and methanol due to postgrafting of hydrophobic chains.     

密度泛函理论对ZrnPd团簇结构和性质的研究

用B3LYP/LANL2DZ方法对Zr_nPd(n =1—13)团簇的平衡几何结构、能量、频率、电子性质和磁性进行了计算.研究表明,Pd原子位于表面的异构体更为稳定,其中Zr₇Pd,Zr₁₂Pd团簇稳定性高,是幻数团簇,此外,相对于Zr_nCo与Zr_nFe团簇,Zr_nPd团簇参与化学反应的能力较弱,化学稳定性更     

Cross-section measurements of (n, 2n) and (n, p) reactions on 124,126,128,130,131,132Xe in the 14 MeV region and theoretical calculations of their excitation functions

The reaction cross-sections of ¹²⁴Xe(n, 2n)¹²³Xe, ¹²⁶Xe(n, 2n)¹²⁵Xe, ¹²⁸Xe(n, 2n)¹²⁷Xe, ¹³⁰Xe(n, 2n)^129mXe, ¹³²Xe(n, 2n)^131mXe, ¹³⁰Xe(n, p)¹³⁰I, ¹³¹Xe(n, p)¹³¹I, and ¹³²Xe(n, p)¹³²I were measured at the 13.5, 13.8, 14.1, 14.4, and 14.8 MeV neutron energies. The monoenergetic neutrons were generated via the ³H(d,n)⁴He reaction at the China Academy of Engineering Physics using the K-400 Neutron Generator with a solid ³H-Ti target. A high-purity germanium detector was employed to measure the activities of the product. The reactions ⁹³Nb(n, 2n)^92mNb and ²⁷Al(n, α)²⁴Na were adopted for neutron flux calibration. The cross sections of the (n, 2n) and (n, p) reactions of the xenon isotopes were obtained within the 13–15 MeV neutron energy range. These cross-sections were then compared with the IAEA-exchange format (EXFOR) database-derived experimental data, together with the evaluation results of the CENDL-3, ENDF/B-VIII.0, JENDL-4.0, RUSFOND, and JEFF-3.3 data libraries, as well as the theoretical excitation function obtained using the TALYS-1.95 code. The cross-sections of the reactions (except for the ¹²⁴Xe(n, 2n)¹²³Xe and ¹³²Xe(n, p)¹³²I) at 13.5, 13.8, and 14.1 MeV are reported for the first time in this study. The obtained results are beneficial in providing better cross-section constraints for the reactions in the 13–15 MeV region, thus improving the quality of the corresponding database. Meanwhile, these data can also be used for the verification of relevant nuclear reaction model parameters.     

A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs

Characteristic polynomial coefficients of three classes of graph, namely L_n + n(p), C_n + n(p) and K _1,n-1 + n(p), which are known to have reciprocal pairs of eigenvalues, have been shown to be generated by simple manipulation of the Pascal's triangle.     

Lagrangian instanton for the Kraichnan model

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scaling exponents ζ_n of the structure functions S _n for n≫1 under the additional condition dζ₂≫1 (where d is the dimensionality of space).At n<n _c (where n _c =dζ₂/[2(2−ζ₂)]) the exponents are ζ_n=(ζ ₂/4)(2n−n ²/n _c ), while at n>n _c they are n-independent: ζ _n=ζ₂ n _c /4. We also estimate the n-dependent factors in S _n . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 588–593 (10 October 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fractional Super-Multi-Virasoro Algebra

An n-dimensional fractional supersymmetry theory is algebraically constructedon the n-dimensional multicomplex space M _n. By emphasizing its appearanceas a special case of generalized Clifford algebra (GCA), we formulate the fractional superspace FM _n through a generalized Grassmann algebra (GGA) and constructthe generators and the covariant derivative of FSUSY on FM _n . The generatorsof FSUSY are extended to get n copies of the fractional centerlesssuper-Virasoro algebra.     

Initiation of the (<Emphasis Type="Italic">γ, n</Emphasis>) and (<Emphasis Type="Italic">p,n</Emphasis>) nuclear reactions in the picosecond laser plasma at a laser intensity of 2 × 10<Superscript>18</Superscript> W/cm<Superscript>2</Superscript>

The experimental results on the initiation of various (γ, n) and (p, n) nuclear reactions in the picosecond laser plasma are presented. It is demonstrated that the following (γ, n) and (p, n) nuclear reactions can be initiated at a laser intensity of 2 × 10¹⁸ W/cm² with the threshold energies of γ-quanta ranging from 1.67 to 7.56 MeV and the threshold energies of protons ranging from 1.88 to 5 MeV: ⁹Be(γ, n)2α, ¹⁸¹Ta(γ, n)¹⁸⁰Ta, ⁷Li(p, n)⁷Be, ⁶³Cu(p, n)⁶³Zn, ⁴⁸Ti(p, n)⁴⁸V. The method based on the detection of fast neutrons using the 3He counters is employed for the measurement of the number of the initiated (γ, n) and (p, n) nuclear reactions. The measured yield of the (γ, n) and (p, n) nuclear reactions ranges from 5 × 10¹ to 10⁵ reactions per laser pulse.     

A study of nuclear transmutation of Th and <Superscript>nat</Superscript>U with neutrons produced in a Pb target and U blanket irradiated by 1.6 GeV deuterons

The spallation lead target in the “Energy plus Transmutation” set-up, covered with uranium blanket, was irradiated by the 1.6GeV deuteron beam from the Nuclotron accelerator at the Joint Institute for Nuclear Research in Dubna. The neutrons generated in the subcritical uranium blanket are used to activate the radioactive uranium and thorium samples outside the blanket. Rates of the (n,g \gamma) , (n, f) and (n, 2n) reactions are determined for some residual nuclei. The ratio of the reaction rates R(n, 2n)/R(n, f) is estimated to be 27(9)%. Contributions of the neutrons with energy E _n > 20 MeV to the (n, f) reaction rate is ∼ 57% for ²³²Th and ∼ 37% for ^natU , respectively. To compare with the experimental results, the reaction rates are simulated by generating the neutron fluxes employing two different models, the beam shapes by the MCNPX 2.6.c code and making use of the appropriate libraries of cross-sections. The transmutation power of the set-up is estimated using the average (n,g \gamma) and (n, 2n) reaction rates and compared with some of the results of the TARC experiment.     

Structural,electronic and magnetic properties of Au<Subscript>n</Subscript>Pt (n = 1−12) clusters in comparison with corresponding pure Au<Subscript>n+1</Subscript> (n = 1−12) clusters

An all-electron scalar relativistic calculation on Au _n Pt (n = 1−12) clusters has been performed by using density functional theory with the generalized gradient approximation at PW91 level. Our results reveal that all the lowest energy geometries of Au _n Pt  (n = 1−12) clusters may be generated by substituting Pt atom for one gold atom of the Au _n+1 cluster at the highest coordinated site. Compared with corresponding pure Au _n+1 cluster, the lowest energy geometries of Au _n Pt clusters are distorted slightly and still keep the planar structures due to the strong scalar relativistic effect in small gold cluster. The Au-Pt bonds are stronger and most Au-Au bonds far from Pt atom are weaker than the corresponding Au-Au bonds in pure Au _n+1 cluster. By substituting Pt atom for one gold atom of Au _n+1 cluster at the highest coordinated site, the relatively stable and inactive odd-numbered Au _n+1 cluster becomes the relatively unstable and reactive odd-numbered Au _n Pt cluster, and the relatively unstable and reactive even-numbered Au _n+1 cluster becomes the relatively stable and inactive even-numbered Au _n Pt  cluster chemically and electronically. All the Au _n Pt clusters prefer low spin multiplicity. The even-numbered Au _n Pt clusters are found to exhibit zero magnetic moment and the odd-numbered Au _n Pt clusters are found to possess magnetic moment with the value of 1 μ _B. The odd-even alterations of magnetic moments and electronic configurations for Au _n Pt clusters are very obvious and may be simply understood in terms of the electron pairing effect.     

Synthesis and luminescence properties of lead-halide based organic–inorganic layered perovskite compounds (CnH2n+1NH3)2PbI4 (n=4, 5, 7, 8 and 9)

This paper describes the synthesis and characterization of organic–inorganic layered perovskite compounds, (C_nH_2n+1NH₃)₂PbI₄ (n=4, 5, 7, 8 and 9). The effect of the number of carbon atoms on luminescence properties has been examined. Thin films of microcrystalline (C_nH_2n+1NH₃)₂PbI₄ fabricated by spin-coating are highly oriented, with the c-axis perpendicular to the substrate surface. Temperature-dependent optical absorption spectra reveal that (C_nH_2n+1NH₃)₂PbI₄ films (n=4, 7, 8 and 9) show the structural phase transitions. The excitonic structures of (C_nH_2n+1NH₃)₂PbI₄ vary with the number of carbon atoms of the alkyl chain length. At low temperatures below 100 K, the lowest-energy free-exciton band of (C_nH_2n+1NH₃)₂PbI₄ (n=7, 8 and 9) split into three fine-structure levels. In contrast to (C_nH_2n+1NH₃)₂PbBr₄ films, (C_nH_2n+1NH₃)₂PbI₄ (n=7, 8 and 9) shows no triplet exciton emission, but it shows the Stokes-shifted emission from bound excitons.