The elimination of fast variables in complex chemical reactions. II. Mesoscopic level (reducible case)

The master equation for chemical reactions that proceed through a number of steps (complex reactions) is considered. Examples are studied in which the reaction constant of one of the steps is much larger than the others, and a reduced master equation is derived by means of a projection operator formalism. This reduction amounts to an elimination of intermediates. The consistency of the scheme is shown by means of the-expansion.     

Fluctuations in diffusion reaction systems. I: Adiabatic elimination of transport modes from a mesoscopicN-body system and the Ω-expansion

We develop a concise method to compute the corrections to the master equation for chemically reacting systems in particle number space that arise if the system is not a well-stirred tank reactor, but the transport occurs by diffusion. Starting from the master equation in theR ^N space of all reactant particle positions, we expand in inverse powers of the diffusion constant and eliminate all transport modes adiabatically. It is found that the overall effect of spatially nonuniform fluctuations cannot be treated as a mere renormalization of the reaction rate constants. From second order on there appear correction terms with a new structure that corresponds formally to additional virtual reaction paths. An intuitive interpretation along this line is impeded, however, by the formal occurrence of negative reaction rate constants in these terms, i.e., the reaction rate may depend on the concentrations of the final products of the virtual reaction rather than on the ingoing products. We also identify Avogadro's constant as the suitable parameter and extend van Kampen's-expansion systematically, to spatially continuous systems. This secondary expansion then serves to interpret the corrections to the rate equation, and the average and autocorrelation of the density in the stationary state. It is seen that the limitsD and do not commute. The relevant length and time scales are discussed.     

Higher Conformal Multifractality

We derive, from conformal invariance and quantum gravity, the multifractal spectrum f() of the harmonic measure (i.e., electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions. It gives the Hausdorff dimension of the set of points where the potential varies with distance r to the fractal frontier as r . First examples are a random walk, i.e., a Brownian motion, a self-avoiding walk, or a critical percolation cluster. The generalized dimensions D(n) as well as the multifractal functions f() are derived, and are all identical for these three cases. The external frontiers of a Brownian motion and of a percolation cluster are thus identical to a self-avoiding walk in the scaling limit. The multifractal (MF) function f(,c) of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is given as a function of the central charge c of the associated conformal field theory. The dimensions D _EP of the external perimeter and D _H of the hull of a critical scaling curve or cluster obey the superuniversal duality equation . Finally, for a conformally invariant scaling curve which is simple, i.e., without double points, we derive higher multifractal functions, like the universal function f ₂(,) which gives the Hausdorff dimension of the points where the potential varies jointly with distance r as r on one side of the curve, and as r on the other. The general case of the potential distribution between the branches of a star made of an arbitrary number of scaling paths is also treated. The results apply to critical O(N) loops, Potts clusters, and to the SLE process. We present a duality between external perimeters of Potts clusters and O(N) loops at their critical point, as well as the corresponding duality in the SLE process for =16.     

Hollow nanoparticles of <Emphasis Type="Italic">β</Emphasis>-iron oxide synthesized by chemical vapor condensation

Hollow nanoparticles of -Fe₂O₃ were synthesized by chemical vapor condensation (CVC). A structural study revealed that the nanoparticles, 10–20 nm in diameter, consisted of hollow structures with several shells 3–5 nm in thickness. TEM observation indicated that the shells of the -Fe₂O₃ nanoparticles consist of several grain structures having different crystal orientations. This feature of the crystallinity enables us to infer the formation mechanism of the hollow structure of the -Fe₂O₃ nanoparticles during CVC process.     

Discrete fluctuations and their influence on kinetics of reactions

We study the fluctuations arising from the discrete particle nature of the reactants in chemical processes, which we termdiscrete fluctuations. It is shown how the magnitude of discrete fluctuations is formally obtained from the Van Kampen-expansion of the master equation for the process in question. It is claimed that discrete fluctuations are, at times, an important factor in determining the anomalous kinetics of reaction systems. We specialize to diffusionlimited reactions in systems below their upper critical dimensionality. Some variations of the two-species annihilation process A + B inert, as well as some other examples, are presented and analyzed. Many of these examples prove our point about the dramatic influence of discrete fluctuations on the reaction kinetics. Our theoretical scaling predictions are backed by extensive Monte Carlo simulations.     

Statistical mechanics of polymer networks of any topology

The statistical mechanics is considered of any polymer network with a prescribed topology, in dimensiond, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made toO(²), whered=4–, of the basic critical dimensions _L associated with anyL-leg vertex (L1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent _G of any networkG toO(²), includingL-leg star polymers. The infinite sets of contact critical exponents between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents ₀, ₁, ₂ calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimensiond=4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constitutingL-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents _L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled.     

Bead-spring model of a polymer chain: A transient solution

With the Rouse-Zimm differential equation of the spring-bead model, the distribution function ofN + 1 beads(x, y, z,t) [here x denotes x₀, x₁,..., x_N, and similarly for y and z] is explicitly solved with the two different initial conditions: the Gaussian and delta distribution functions. We find that although the mean end-to-end distances obtained from the two initial conditions are the same, the expressions of the mean square end-to-end distances are different. We also obtain the expression for the mean and mean square end-to-end distances analytically from the Langevin equation with the delta initial distribution function. With this analytic expression, we show that the statistical quantities obtained from the Monte Carlo calculation are consistent with those obtained from the Rouse-Zimm differential equation if a suitable length is chosen for the time increment.NIH-Special Fellow (1F03GM43885-01) with a partial support by USPHS GM11916.     

Preparation, Luminescence Properties, and Application of Scintillators Based on Lu3Al5O12:Ce Single‐Crystal Films

The possibility of obtaining scintillators with a high effective atomic number of the element Z _ef based on Lu₃Al₅O₁₂:Ce³⁺ singlecrystal films (SCF) on doping with La³⁺ and Sc³⁺ ions on Y₃Al₅O₁₂ substrates has been investigated. It is established that the SCF of (LuLaY)₃Al₅O₁₂:Ce³⁺ (Z _ef = 58.9 and = 6.67 g/cm²) does not rank below those of Y₃Al₅O₁₂:Ce³⁺ (Z _ef = 29 and = 4.52 g/cm²) in the conversion efficiency of radiation at the band with _max = 515 nm. This allows their use as screens of xray images with a space resolution of 0.75–1.00 m. It is suggested that in the SCF of Lu₃Al₅O₁₂ the isoelectronic impurities of lanthanum and scandium form radiative recombination centers of the type La_Lu, Sc_Lu, and ScAl as well as the centers Lu as a consequence of the effect of replacement of some Lu³⁺ ions by the La³⁺ ions to octanodes of the garnet lattice. The low efficiency of Ce³⁺ radiation in the SCF of (LuSc)₃(AlSc)₅O₁₂:Ce is explained by substantial losses due to excitation of the recombination luminescence in the UV region of the centers formed by the isoelectronic impurities of scandium and to the possible existence of the channel of energy excitation dissipation related to the transitions between extrema of the allowed energy bands and activator levels.     

Ω-Expansion of van Kampen through functional integrals

We give a functional integral version of the van Kampen-expansion method for the master equation. Explicit expressions are given for the generating functional of correlation functions.     

Collective structures of the <Superscript>131</Superscript>Cs nucleus

The collective structures of ¹³¹Cs have been investigated by in-beam -ray spectroscopic techniques following the ¹²⁴Sn (^11B , 4n) reaction at a beam energy E_lab = 57MeV. The previously established rotational bands, built on g_7/2, d_5/2 and the unique-parity h_11/2 orbitals, have been extended and evolve into new bands involving rotationally aligned (h_11/2)² and (h_11/2)² quasiparticles. In addition, a new multiquasiparticle band based on the g_7/2 g_7/2 h_11/2 configuration has also been observed. Theoretical interpretations for the assigned configurations are discussed in the framework of Total Routhian Surface (TRS) and Tilted Axis Cranking (TAC) model calculations. TAC model calculations predict a decrease in the B(M1) values with increasing rotational frequency for the g_7/2/d_5/2 (h_11/2)² and h_11/2 (h_11/2)² bands, thus indicating a magnetic rotation character for these bands.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

Fluctuations in coagulating systems

Time-dependent fluctuations in a system of coagulating particles are studied, using the master equation for the probability distributionsP(m,t) for the occupation numbersm={m _k} (k=1,2,...) of thek-cluster states. Van Kampen's-expansion is used to determine the deterministic (order ⁰) and fluctuating part (order ^–1/2) of the solution. We calculate the time-dependent behavior of the fluctuations in the cluster size distribution. The model under consideration is of special interest since it exhibits a phase transition (gelation). For monodisperse initial states we give explicit expressions for the probability distribution of the fluctuations and for the equal-time and two-time correlation functions also near the phase transition. For general initial conditions we study the fluctuations (1) for large cluster sizes, (2) in the scaling limit (near the critical point), and (3) for large times. Our results show that the deterministic approach to coagulation processes (Smoluchowski theory) is invalid very close to the gelpointt _c and at large times (tt _M), where the distance from the gelpoint and the timet _M depend upon the size of the system.     

Beta-decay studies of neutron-rich Sc- Cr nuclei

The neutron-rich nuclei ₂₁^{57, 58}Sc, ₂₂^58-60Ti, ₂₃^60-63V, ₂₄^62-66Cr have been produced at Ganil via interactions of a 61.8A MeV ⁷⁶Ge beam with a ⁵⁸Ni target. Beta-decay studies have been performed using combined - and -ray spectroscopy. Half-lives have been determined and -decay schemes are proposed for ⁵⁸Ti, ⁶¹V and ⁶²Cr. From these studies, new hints for the existence of -decaying isomers in ⁶⁰V and in ⁶²Mn are provided. These results are compared to shell model calculations. The role of the f_7/2- f_5/2 proton-neutron interaction is examined through its influence on the lifetime values.     

High-spin isomer in 93Mo

The high-spin states of ⁹³Mo have been studied by a ⁸²Se( ¹⁶O, 5n) ⁹³Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2^-) state at about 9.7 MeV. The near-yrast states in ⁹³Mo were interpreted using the weak-coupling picture of a d_5/2 neutron to a neutron magic core nucleus ⁹²Mo.     

The (2+1) Dirac Equation with a Delta Potential

In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric (r–r ₀) potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of r ₀ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.     

q-Deformation of the Double Complex Ernst Equation

From a known three-dimensional representation of the double quantum algebra su _q ((J)), a nonlinear q-deformed Ernst equation system is obtained. By using a gauge covariant form, the deformation effects are found to generate a torsion in the field and to form a gauge field with source.     

Proton-neutron configurations in 236g, mAm and its EC-decay daughter 236Pu

The EC decay of ²³⁶Am has been studied using a gas-jet coupled on-line isotope separator. A half-life analysis revealed that there are two EC-decaying states in ²³⁶Am: the 5^- state with T_1/2 = 3.6(2) min and the (1^-) state with T_1/2 = 2.9(2) min. The 1185.5 keV level in ²³⁶Pu was found to be the K isomer with K = 5^- and t_1/2 = 1.2(3) s. EC transitions from ^{236g, m}Am to the 1185.5, 1311.5, and 1340.8 keV levels in ²³⁶Pu show small log ft values of 4.9, 5.3, and 4.8, respectively, indicating that the 5/2⁺[642] 5/2⁺[633] transition largely contributes to these transitions, and thus, the populated levels should be the 5/2^-[523]5/2⁺[642] two-quasiparticle states. The K = 0^- octupole band established in ²³⁶Pu is located at higher energy than those in ^238,240Pu, which implies that the octupole correlations become weak at ²³⁶Pu.     

Role of the Carbohydrate Moiety and of α-L-Fucose in the Stabilization and the Dynamics of the Lens culinaris Agglutinin–Glycoprotein Complex. A Fluorescence Study

Interaction between the fluorescent Lens culinaris agglutinin–fluorescein complex (LCA-FITC) and two glycoproteins, lactotransferrin (LTF) and serotransferrin (STF), was studied. The two glycoproteins have the same glycan structures, with one difference: the lactotransferrin glycans contain a fucose residue -1,6-linked to the N-acetylglucosamine residue involved in the N-glycosylamine linkage. Fluorescence intensity quenching of the LCA-FITC complex shows that affinity between LCA and lactotransferrin is 50 times higher than that between LCA and serotransferrin, the fucose playing a major role in this high affinity (K _a is equal to 9.66 and 0.188 M ^–1 for the LCA–LTF complex and LCA–STF complex, respectively). Time-resolved anisotropy decay indicates that the rotational correlation time of LCA (20 ns) does not change to a large extent whether the glycoproteins are bound to LCA or not. This suggests that there is no extended physical contact between LCA and the glycoproteins. The interaction between LCA and the glycoproteins occurs likely only via the carbohydrate chains, the STF and the LTF rotating almost-freely in the vicinity of LCA, with the glycans as an anchor.     

A 3-quasiparticle isomer in neutron-rich <Superscript>183</Superscript>Ta

Excited states in neutron-rich ¹⁸³Ta have been studied using a two-neutron transfer reaction of ¹⁸¹Ta(¹⁸O,¹⁶O) . In-beam -rays were measured in coincidence with scattered ions detected by a high-resolution E -E Si telescope for reaction channel selection. Previously known 1-quasiparticle bands are extended to higher spins, and several levels including a T _1/2 = 0.9(3) μs 3-quasiparticle isomer are identified.     

Non-linear pressure dependence of A-state fluorescence lifetime of formaldehyde

Fluorescence lifetimes of formaldehyde excited at 352 nm ( A₂ – A₁ 4₀¹ band) were measured as a function of bath gas pressure. He, N₂, O₂, CO₂ and HCHO were investigated for the bath gas and the temperature dependence between 298 and 500 K for N₂ and O₂ bath gases was also examined. It was found that the non-linear pressure dependence of the lifetime is successfully reproduced by the model formula