Surface roughening for two-dimensional percolation abovep c

The surfaces of large clusters above the critical concentrationp _c were Monte Carlo-simulated on a 2-dimensional square lattice. We study the widthW of the interface separating the interior of very large clusters from the outside region. The results show clearly surface roughening (at least in the simulated range). Even in the high concentration limitp→1 the interface widthW increases with the lengthL of the simulated interface, following (presumably) a square root law.     

Fabrication and low threshold current density CW operation of GaInAsP/InP multiple-reflector microcavity laser

We report CW operation of a GaInAsP/InP multiple-reflector microcavity (MRMC) laser operated at fairly low threshold current density. The threshold current density with broad contact (stripe widthW=240 m, cavity lengthL=60 m) under pulsed operation was 180 A cm^–2 (l _th=20 mA), and was 230 A cm^–2 under CW operation at room temperature operating at 1.52 m wavelength.     

Surface structure for three-dimensional percolation clusters abovep c

We study the surface behaviour of very large percolation clusters above the critical concentrationp _c by considering the width and the analogue of surface tension of the interface separating the interior of the cluster from the outside region. Our Monte Carlo simulation techniques, which are described in detail, are applied to a quadraticL ×L surface layer on the simple cubic lattice, withL up to 200. They give clearly a rough surface even for the highest concentrationsp. The data forp=1 suggest a logarithmic divergence for the interface width in the thermodynamic limitL.     

Analyticity properties and power law estimates of functions in percolation theory

We consider percolation on the sites of a graphG, e.g., a regulard-dimensional lattice. All sites ofG are occupied (vacant) with probabilityp (respectively,q=1–p), independently of each other.W denotes the cluster of occupied sites containing a fixed site (which will usually be taken to be the origin) andW the cardinality ofW. The percolation probability is the probability that #W=, i.e.,(p)=P _p{# W=}. Some critical values ofp,p _H andp _T, are defined, respectively, as the smallest value ofp for which(p)> 0, and for which the expectation of #W is infinite. Formally,p _H=inf {p(p)>0} andp _T=inf{p E _p{#W}=}. We show for fairly general graphsGthat ifp _T, thenP _P{#W n} decreases exponentially inn. For the special casesG =G ₀= the simple quadratic lattice andG ₁= the graph which corresponds to bond-percolation on ², we obtain upper and lower bounds for(p) of the formC¦p¦-P _H¦, and bounds forEp{#W} of the formC¦p–p _H¦^–. We also investigate smoothness properties of (p)=E _p{number of clusters per site} =E _p {(#W)^–1; (#W) 1}. This function was introduced by Sykes and Essam, who assumed that (·) has exactly one singularity, namely, atp=p _H. For the graphsG ₀ andG ₁, (i.e., site or bond percolation on ²) we show that (p) is analytic atp p _H and has two continuous derivatives atp=p _H. The emphasis is on rigorous proofs.Research supported by the NSF through a grant to Cornell University.     

Design considerations and scaling laws for high power convective cooled CW CO2 lasers

Various criteria for designing high power convective cooled CO₂ lasers have been discussed. Considering the saturation intensity, optical damage threshold of the optical resonator components and the small-signal gain, the scaling laws for designing high power CW CO₂ lasers have been established. In transverse flow CO₂ lasers having discharge of square cross-section, the discharge lengthL and its widthW for a specific laser powerP (Watt) and gas flow velocityV (cm/s) can be given byL = 1.4 x 10⁴ p ^1/2 V ^-1 cms andW = 0.04P ^1/2 cms. The optimum transmitivity of the output coupler is found to be almost constant (about 60%), independent of the small signal gain and laser power. In fast axial flow CO₂ lasers the gas flow should be divided into several discharge tubes to maintain the flow velocity within sonic limit. The discharge length in this type of laser does not depend explicitly on the laser power, instead it depends on the input power density in the discharge and the gas flow velocity. Various considerations for ensuring better laser beam quality are also discussed.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

q-deformed W-algebras and elliptic algebras

The elliptic algebra A _q,p {sl}(N _c) at the critical level c = –N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W _N algebra, are constructed. The operators t(z) also close an exchange algebra when (–p ^1/2) ^NM = q ^–c–N for M . It becomes Abelian when in addition p = q ^Nh where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W _N algebras depending on the parity of h, characterizing the exchange structures at p q ^Nh as new W _q,p(sl(N)) algebras.     

Monte Carlo studies of percolation phenomena for a simple cubic lattice

The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forp _c (0.3115±0.0005), (0.41±0.01), (1.6±0.1), and(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average surface area for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP <p _c. Forp >p _c there is too much scatter in the data to draw firm conclusions about the size distribution.Work supported in part by USAFOSR Grant #73-2430B and by ERDA #E(11-1)-3077.     

Wn (n= 1–6)团簇吸附CO的密度泛函研究

采用密度泛函理论(density functional theory, DFT) 在B3LYP/LANL2DZ基组水平上对钨团簇吸附CO分子进行了系统研究. 结果表明, W_nCO团簇的基态结构是在W_n团簇中性或阴离子基态结构的基础上吸附CO生长而成; CO的吸附以端位吸附为主,桥位吸附为辅; CO分子在W_n团簇表面发生的是非解离性吸附. 与优化的CO键长(0.116 nm)相比,吸附后C-O键长变长(0.120–0.123 nm), 表明吸附后C-O键被削弱, CO分子被活化了.稳定性分析表明,在所研究的团簇中, W₃CO和W₅CO团簇的稳定性较强;自然键轨道(NBO)分析表明, W原子与CO分子相互作用的本质是CO分子内的杂化轨道与W原子6s, 5d, 6p和6d轨道相互作用的结果. 关键词： nCO (n= 1–6)团簇')" href="#">W_nCO (n= 1–6)团簇 基态构型 稳定性 电子性质     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

A percolation approach to the Kauffman model

A study is made of the spreading of damage in the random but deterministic Kauffman model on the square lattice with the spreading from one edge of the lattice. The critical value of the parameterp _c above which the system becomes chaotic is found to bep _c0.298. The possibility of suppression of the chaotic phase by noise is also studied. It is found that forpp _c, an extremely large noise levelg>0.99 is required, if possible at all.On leave from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Typical cluster size for two-dimensional percolation processes

The typical cluster size for two-dimensional percolation models is discussed. It is shown that, forW ₀={xZ ²0x}, [–lim _n(1/n) logP _p (W ₀=n)]^–1p–p _c ^– aspp _c , provided thatE _p (W ₀²)/E _p (W ₀)p–P _c ^– aspp _c . Furthermore, we introduce a new quantityf _s (p), which may be thought of as the singular part of the free energy, and show thatf _s (p)¦p–p _c ¦^2v provided that the correlation length ¦p–p _c ¦^–v aspp _c .     

Non-linear structures in the non-critical NSR string

We investigate the Ward identities of theW symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge . The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from theq–1 gravitational primaries by one of the ring generators in the R-sector acting on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of theusual W _q algebra constraints as in the bosonic case:W _n ^(k+1) ,=0, (k=1,...,q–1;nZ1–k), where the equations for even and oddn come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles ofp andq. Then we get theW _p algebra constraints.     

Spectral properties and scaling relations in off diagonally disordered chains

We obtain the localization lengthL as a function of the energyE and the disorder widthW for an off-diagonally disordered chain. This is done performing numerical simulations involving the continued fraction representations of the transfer matrix. The scaling relationL=W ^s is obtained with values of the exponents in agreement with calculations of other authors. We also obtain the relationL|E| ^v forE0, and use it in the Herbert-Spencer-Thouless formula forL to describe the singularity of the density of states nearE=0. We show that the slightest diagonal disorder obliterates this singularity. A practical method is presented to calculate the Green function by exploiting its continued fraction expansion.     

Possible generalization of Boltzmann-Gibbs statistics

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS _q k [1 – _i=1 ^W p _i ^q ]/(q-1), whereq characterizes the generalization andp _i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

Uncertainty principle and uncertainty relations

It is generally believed that the uncertainty relation q p1/2, where q and p are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW and the mean peak width w of a general wave function and show that the productW w is bounded from below if is the Fourier transform of . It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments.     

Moyal Deformations of Gravity via SU(∞) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

Moyal noncommutative star-product deformations of higher-dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(), W gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional knots have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W symmetries which are very relevant in the study of W Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix models and Gravity needs to be investigated further within the framework of W Gauge theories.     

Self-avoiding walks on percolation clusters at criticality and lattice animals

We use the real-space renormalization group method to study the critical behavior of self-avoiding walks (SAWs) on both site percolation clusters at percolation threshold and site lattice animals in a square lattice. The correlation length exponents of SAWs are found to be on the percolation clusters atp _c and _SAW ^LA =0.804 on lattice animals. These results are compared with Kremer's suggestion of modified Flory formula where is the fractal dimension of the fractal object.     

WnNim(n+m=8)团簇的极性和光谱性质的理论研究

采用密度泛函理论(DFT)中的B3LYP方法,在LANL2DZ基组水平上对WnNim(n+m=8)团簇的各种可能构型进行了几何参数全优化,得到了它们的基态构型;并对基态构型的偶极距、极化率、红外光谱和拉曼光谱性质进行了分析,结果表明:团簇WnNim(n+m=8)都具有极性,富W团簇非线性光学效应强,容易被外加场极化;振动频率主要分布在0-350 cm-1范围内,团簇W4Ni4因其振动方式的特殊性,红外光谱和拉曼光谱在频率421.971 cm-1处,都有明显强峰;团簇W5Ni3因其结构的高对称性在振动光谱中出现多处共振现象.