Kinetic evolutionary behavior of catalysis-select migration

We propose a catalysis-select migration driven evolution model of two-species(A-and B-species) aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K(k;i,j) = Kkij and D species catalysis-select migration rate kernel J(k;i,j) = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0(D0 and C0 are the initial numbers of the monomers of species D and C,respectively).When JD0 KC0 > 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 < 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 > 0 case.     

Dynamics and sedimentation velocity in charge-stabilized colloidal suspensions

Summary Charge-stabilized suspensions are characterized by the strong electrostatic interactions between the particles so that rather dilute systems may exhibit strong correlation resulting in a well-developed short-range order. This microstructure, quantitatively described by the pair distribution functiong(r), is rather different from that of (uncharged) hard spheres. It is shown how this difference affects the ?hydrodynamic function?H(k), which appears in the expression for the first cumulant Γ(k)=k ² D _eff(k)=k ² H(k)/S(k) of the dynamic autocorrelation function. Without hydrodynamic interaction,H(k)=D ⁰, which is the free-diffusion coefficient. Using pairwise additive hydrodynamic interaction and the lowest-order many-body theory of hydrodynamic interaction, it is found thatH(k) can deviate considerably fromD ⁰ even for systems of volume fractions ϕ as low as 10⁻³. These effects are more pronounced for collective diffusion than for self-diffusion. SinceH(k=0) is closely related to the sedimentation velocity, we have studied this quantity as a function of volume fraction. It is found that (H(0)/D ⁰) −1 scales asφ ^1/3 at low ϕ in salt-free suspensions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.     

Exact solutions for electromagnetic waves in inhomogeneous media

Exact solutions of the wave equation for the propagation of electromagnetic waves in some inhomogeneous media are found. The first solution corresponds to the barometric model of the atmosphere, whose index of refraction can be expressed by the formulaN ²(z)=1+(N ₀ ² -1) exp (–z/z ₀). The other cases correspond toN ²(z)=1+(N ₀ ² -1) ch^–2(z) andN ²(z)=a-b. [1+exp(z/L)]^–1.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.     

Hyperfine structure measurements in the4 I 9/2 ground state of141Pr

Using the atomic beam magnetic resonance method, the five hyperfine structure separations in the 4f ³ 6s ^{2 4}I_9/2 ground state of ₅₉ ¹⁴¹ Pr have been measured. The results are:F F′ E _FF′ ^* /h (MHz) 7 6 6477.913423(17) 6 5 5556.359848 (6) 5 4 4633.023306 (2) 4 3 3708.201146 (5) 3 2 2782.190601(15) From these quantities, the multipole interaction constantsA _k,k=1, 2, 3, 4 between the nucleus and the electron shell have been calculated.A ₄ especially then served to give the following limit for the intrinsic hexadecapole moment: ¦Q ₄₀¦<0.4eb ². Furthermore, theg _J -factors of the⁴ I multiplet have been measured at magnetic fields of 300 Oe. The results are:g _J(⁴ I _9/2)=0.7310371(15)g _J(⁴ I _11/2)=0.9651476(20)g _J(⁴ I _13/2)=1.1063197(40)g _J(⁴ I _15/2)=1.197963 (30) Small corrections due to perturbations by neighbouring fine structure levels are included.     

Measurement of the nuclear magnetic dipole moment of Au197 and hyperfine structure measurements in the ground states of Au197, Ag107, Ag109 and K39

Using an atomic beam magnetic resonance apparatus the nuclear magnetic dipole momentμ _I of the stable isotope Au¹⁹⁷ was measured directly with the doublet method. The result isμ _I(Au¹⁹⁷)=0.143491 (9)μ _n, uncorrected for atomic diamagnetism. Further hyperfine structure measurements were performed in the ground states of K³⁹, Ag¹⁰⁷, Ag¹⁰⁹ and Au¹⁹⁷ with the following results:Δv(K³⁹)=461.719723 (38) MHzΔv(Ag¹⁰⁷)=1712.512111 (18) MHzΔv(Ag¹⁰⁹)=1976.932075 (17) MHzΔv(Au¹⁹⁷)=6099.320184 (13) MHzg _J(Ag¹⁰⁷)/g _J(K39)=1.0000260 (20)g _J(Au¹⁹⁷)/g _J(K39)=1.0005076 (20).     

Be9(d,p),(d,t),(d,a)反应研究

本文在E_d=0.1—2.5MeV能量范围内,研究了Be⁹(d,p₀)Be¹⁰(0),Be⁹(d,p₁)Be¹⁰(3.368MeV),Be⁹(d,t₀)Be⁸(0),Be⁹(d,α₀)Li⁷(0)及Be⁹(d,α₁)Li⁷(0.478MeV)诸反应。在E_d=0.150,0.220,0.401,0.706,1.005,1.301,1.484,1.750,2.000,2.250和2.500MeV共十一个能量上分别测量了这五群出射粒子在θ_L=10—155°区间的角分布。在θ_L=135°,E_d=0.1—2.5MeV,在θ_L=95°,E_d=0.1—2.2MeV,和在θ_L=112.5°,E_d=0.5—2.5MeV测量了Be⁹(d,p₀)Be¹⁰的激发函数。在θ_L=135°和112.5°,E_d=1.2MeV,用较厚靶(100—300μg/cm²)测量了Be⁹(d,p₀)Be¹⁰(0)反应的截面绝对值,结果为σ_(p0)(θ_L=135°)=1.60mb/sr,σ_(p0)(θ_L=112.5°)=1.55mb/sr。这样就得到了在此能区内,这五群出射粒子的截面情况。对所得结果进行了一些讨论。     

Conformal blocks and generalized theta functions

LetSU _X r be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical isomorphism of the space of global sections ofL ^k with the space of conformal blocks defined in terms of representations of the Lie algebrasl _r (C((z))). It follows in particular that the dimension ofH ⁰(SU _X r,L ^k ) is given by the Verlinde formula.Both authors were partially supported by the European Science Project Geometry of Algebraic Varieties, Contract no. SCI-0398-C(A)     

Level crossing investigation of the 6p 2 P 3/2 and 7p 2 P 3/2 levels of Cs133, Cs135, and Cs137

The level crossing method has been used for the investigation of the hyperfine structure of the 6p²P_3/2 and 7p²P_3/2 levels of the isotopes Cs¹³³, Cs¹³⁵, and Cs¹³⁷. For the hyperfine coupling constants a and b and for the lifetimes Τ we find: a(6p Cs¹³³)=50.72(3) g_J/?1.345, b(6p Cs¹³³)=?0.38(18) g_J/?1.345 a(7p Cs¹³³)=16.610(6) g_J/?1.3349, b(7p Cs¹³³)=?0.15(3) g_J/?1.3349 a(6p Cs¹³⁵)=53.64(4) g_J/?1.345, b(6p Cs¹³⁵)=7.41(32) g_J/?1.345 a(7p Cs¹³⁵)=17.570(6) g_J/?1.3349, b(7p Cs¹³⁵)=2.35(7) g_J/?1.3349 a(6p Cs¹³⁷)=55.80(4) g_J/?1.345, b(6p Cs¹³⁷)=7.54(20) g_J/?1.345 a(7p Cs¹³⁷)=18.274(6) g_J/?1.3349, b(7p Cs¹³⁷)=2.37(4) g_J/?1.3349 (MHz), Τ(6p²P_3/2)=29.7(2) ?1.345/g_J ns, Τ(7p²P_3/2)=135(1) ?1.3349_Jns. From a comparison with double resonance results the g_J factor of the 7p²P_3/2 level was deduced: g_J(7p²P_3/2=?1.3349(10). Level crossing measurements in the 8p²P_3/2 state of Cs¹³³ give for the g_J factor and the lifetime the following results: g_J(8p²P_3/2)=?1.3353(14), Τ(8p²P_3/2)=310(15) ns. Using recently calculated relativistic correction factors and applying corrections for core polarization and the Sternheimer effect, we obtain for the quadrupole moments: Q(Cs¹³³)=?0.0030 b, Q(Cs¹³⁵)=+0.052 b, Q(Cs¹³⁷)=+0.052 b.     

Finitely Generated Free Orthomodular Lattices. III

The finitely generated free algebras F _V(Lk)(n) (k 2, n 3) in the varieties V(L _k )of orthomodular lattices generated by the ortholattices L _k which are horizontalsums of one block 2³ and k – 1 blocks 2² are described as abstract algebras. Thisis a continuation of earlier work and indicates the complexity one must expectwhen describing the finitely generated free algebras in finitely generated varietiesof orthomodular lattices generated by ortholattices containing Boolean blockslarger than 2².     

Bestimmung derg J-Faktoren in den Zuständen 62 P 3/2 und 82 P 3/2 von133Cs

The hyperfine structures of the 6² P _3/2- and 8² P _3/2-states of¹³³Cs have been investigated by optical double resonance in a strong magnetic field. The Landé-g-factors and the hfs coupling constants were found to be:g _J(6² P _3/2)=1.3340(3)g _J(8² P _3/2)=1.3342(2)a(6² P _3/2)=50.02(25) MHza(8² P _3/2)=7.644(25) MHz. Contrarily to recent measurements, theg _J-factors agree well with the value calculated from the Landé formula.     

Absence of continuous symmetry breaking in a one-dimensional n−2 model

For a one-dimensional array ofS ^N–1 spins (N 2) with isotropic pair interactions (and more general systems) with J(j–i) obeying sup_n[n^–1 ₁ ⁿ j ²|J(j)|]<, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n ^–2.Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Vortices and Magnetization in Kac’s Model

We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential J _γ(i)=γ ² J(γ i), J with compact support. The system is subject to boundary conditions with vorticity. Using a gradient-flow dynamics, we compute minimizers of the free energy functional at low temperature, i.e. in the regime of phase transition. We have the numerical evidence of a vortex structure for minimizers, which present many common features with those of the Ginzburg-Landau functional. We extend the results to spins valued in S ² and compare with the celebrated Belavin and Polyakov model.     

Nonisotropic L-conversion-electron — X-ray directional correlations in160Dy

The directional correlations betweenL-conversion electrons andL x-rays have been measured. The electrons were emitted in the 86.78keV 2⁺→0⁺ transition in¹⁶⁰Dy, in the decay of¹⁶⁰Tb. The experimental results areA ₂₂(e _L -x _Li )=0.085 (22),A ₂₂(e _L -x _Lα )=0.0066 (29),A ₂₂(e _L -x _Lβ )=0.0000 (27), andA ₂₂(e _L -x _Lγ )=0.0096 78). These results are in disagreement with published theoretical values. It is suggested that the discrepancy is due to a phase inconsistency in the internal conversion matrix elements and there is good agreement withA ₂₂ values calculated in this work.     

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution function also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^−1/2f(h_m L^−1/2) for all L>0 where the function f(x) is the Airy distribution function. This result is valid for both the Edwards–Wilkinson (EW) and the Kardar–Parisi–Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^−1/2F(h_m L^−1/2), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the EW interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [S.N. Majumdar and A. Comtet, Phys. Rev. Lett. 92: 225501 (2004)].     

The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

Precision measurement of theg J factors of metastable atomic states of88Sr and138Ba using the atomic beam magnetic resonance method

Theg _J factors of the metastable states³ P ₂ of⁸⁸Sr and³ D ₁,³ D ₂,³ D ₃, and¹ D ₂ of¹³⁸Ba have been measured using the atomic-beam magnetic resonance method. The metastable states were populated by an electric discharge within the atomic-beam source. From the measurements of rf transitions between the Zeeman levels (m _J =+1)?(m _J =?1) we obtained:⁸⁸Sr:g _J (³ P ₂) =1.501124(10)¹³⁸Ba:g _J (³ D ₃)=1.3340823 (10)g _J (³ D′₂)=1.1637406(11)g _J (³ D ₁)=0.4985751(13)g _J (¹ D′₂)=1.003 1449(10). The relativistic and diamagnetic corrections for theg _J factor of the³ P ₂ state of Sr have been calculated. With these and the Schwinger correction included we getg _J (³ P ₂)=1.501119(12).