Stochastic synchronization of interacting pathways in testosterone model

We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscillators depends on various parameters namely fluctuating factor, coupling constants ϵ, and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by ϵ ∼ AV^−γ, where γ = 1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V→ ∞, molecular population, N→ ∞ but $\frac{N}{V}\to \mathit{finite}$, to see the role of noise in information processing and found the destructive role in the rate of synchronization.     

The V state of ethylene: valence bond theory takes up the challenge

The ground state and first singlet excited state of ethylene, so-called N and V states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the N state and four structures for the V state, provide an N → V transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the N → V transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the V state wave function, 19.14 a ₀ ² , is in the range of accepted values obtained by large-scale state-of-the-art molecular orbital-based methods. The σ response to the fluctuations of the π electrons in the V state, known to be a crucial feature of the V state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the N state and 14 for the V state, confirm the results of the minimal structure set, yielding an N → V transition energy of 7.97 eV and a spatial extension of 19.16 a ₀ ² for the V state. Both types of valence bond calculations show that the V state of ethylene is not fully ionic as usually assumed, but involving also a symmetry-adapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the V state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the V state, known to be ca. 50 % larger than the V state.     

Die thermische Zersetzung von Bariumazid-Einkristallen, 5. Mitt.: Der Einfluß der Korngröße auf die thermische Zersetzung von Bariumazid

Decomposition studies on ground samples of anhydrous Ba(N₃)₂ with defined particle size are described. The kinetic equations derived for single crystals hold for the decomposition of powders too. The far faster decomposition of powders is caused both by the increased numberN ₀ of potential nuclei forming sites and the larger specific surfaceF ₀/V ₀, whereas the rate constantsk ₁ andk ₂ for nucleation and linear nucleus growth, resp., and their respective activation energies coincide with the data for single crystals. The proportionality between the rate of decomposition and the specific surface is confirmed experimentally and thereby a further proof of the geometric decomposition model is established. Independent of particle size and temperture always 75% of the azide are transformed into nitride during thermal decomposition, this value corresponding exactly to the theoretical one. It is shown experimentally that with decomposition conditions no reaction takes place between metallic Ba and N₂ in its electronic ground state and therefore the mechanism proposed for nitride formation is confirmed.     

OH rotational quantum state distributions and relaxation efficiencies for the reaction system O(1D) + H2O → 2OH

The OH rotational distribution from O(¹D) + H₂O → 2OH is presented. The v' = 0 distribution corresponds to two Boltzmann distributions. ≈500 K (k = 1–6) and ≈2500 K (k ? 6). Rotational relaxation efficiencies for N₂, He, O₂ were ?0.1, ?0.1, ?0.4. More limited data are presented for the v' = 1 and 2 levels.     

Seeded dispersion polymerization of MMA using submicron PMMA particles as seed: a mechanistic study

Micron-size poly(methyl methacrylate) (PMMA) particles having a narrow particle size distribution were prepared by seeded dispersion polymerization of methyl methacrylate (MMA) using submicron PMMA particles as seed. The processes of particle aggregation and nucleation were controlled by the initial seed size, initial seed number, and initiator concentration, determining the formation of the mature particles and the number (N _(final)) and size of the final particles. It was found that N _(final) was equal to the number of particles produced in the absence of seed (N _{(ab initio)}) when the initial number of seed particles (N _(initial)) was less than N _{(ab initio)}. When N _(initial) was greater than N _{(ab initio)}, N _(final) was equal to k?×?N _(initial), where the value of k was a function of seed size and initiator concentration. k increased with seed size and was less than 1 at high initiator concentrations (0.52 and 1.00 %), while at low initiator concentrations (0.23 and 0.30 %), a maximum value of k was found for a 198 nm seed size. k could be greater than unity in some cases.     

Kinetics of O(1D) interactions with the atmospheric gases N2, N2O,H2O,H2, CO2, and O3

Rate coefficients for collisional removal of O(¹D) by six atmospheric gases have been measured by monitoring the appearance of O(³P) following photolytic production of O(¹D). The measured values, k_M±2σ, in units of 10^?11 cm^?3 molecule ^?1 s^?1 are k_O3 = 22.8±2.3, k_N2 = 2.52 ± 0.25, k_CO2 = 10.4 ± 1.0,k_H2O 195± 2.0, k_N2O = 11.7 ± 1.2, and k_H2, = 11.8±1.2.     

Rate of the reaction I2 + F2 → products

The rate coefficient, k1, for the reaction I2+F2k1→ products has been measured at room temperature to be k1 = (1.9 = 0.4) × 10?15 cm3/molecule s. The macroscopic rate is compared to microscopic cross-section data obtained from molecular beam experiments and is found to be consistent with the bimolecular reaction I2 + F2→ I2F + F.DG|National Research Council/Resident Research Associate.     

First normal stress difference-temperature dependence for polystyrene and high-impact polystyrene melts

The method of reduced variables or superposition is applied to investigate the first normal stress difference (N₁)-temperature dependence over the shear rate (γ) range 10–1000 s^?1 for polystyrene (PS) and high-impact polystyrene (HIPS) melts, at temperatures of 180 C and above. These conditions are similar to those for industrial polymer processing. For PS, the first normal stress differences are obtained using Tanner's equation, leading to good agreement with values obtained by other authors and methods. For HIPS we have not found data in the literature for N₁ at shear rates above 10s^?1. In our case N₁ was obtained by measurements of entrance pressure losses. Correlations, based on master curves, are found for first normal stress difference in terms of shear rate and temperature. All samples follow the power law equation $\text{N}{}_1\text{= k}\text{γ}\text{?}{}^{\mathrm{m}}$, with values of m ranging from 0.50 to 0.64.     

Vibrational energy exchange of the DF (ν=2) state with DF (ν=0)

The energy transfer rate for the reaction DF (ν=1) + DF (ν=1)^k_νν→ DF (ν=0) + DF (ν=2) + ΔE=91.6 cm^?1 has been studied in a combined shock-tube laser-induced fluorescence experiment at temperatures from 295 to 720°K. The rate coefficient k_νν for the exothermic reaction was found to vary as T^?1 when expressed in units of cm³/mole sec. At T=295°K, the probability of the reaction is approximately 0.2 per collision.     

Kinetics and Mechanism of the Reduction of Chromium(VI) and Chromium(V) by D‐Glucitol and D‐Mannitol

The oxidation of D ‐glucitol and D ‐mannitol by Cr^VI yields the aldonic acid (and/or the aldonolactone) and Cr^III as final products when an excess of alditol over Cr^VI is used. The redox reaction occurs through a Cr^VI→Cr^V→Cr^III path, the Cr^VI→Cr^V reduction being the slow redox step. The complete rate laws for the redox reactions are expressed by: a) −d[Cr^VI]/dt {k_{M2 H} [H⁺]²+k_MH [H⁺]}[mannitol][Cr^VI], where k_{M2 H} (6.7±0.3)⋅10 M s⁻¹ and k_MH (9±2)⋅10 M s⁻¹; b) −d[Cr^VI]/dt {k_{G2 H} [H⁺]²+k_GH [H⁺]}[glucitol][Cr^VI], where k_{G2 H} (8.5±0.2)⋅10 M s⁻¹ and k_GH (1.8±0.1)⋅10 M s⁻¹, at 33°. The slow redox steps are preceded by the formation of a Cr^VI oxy ester with λ_max 371 nm, at pH 4.5. In acid medium, intermediate Cr^V reacts with the substrate faster than Cr^VI does. The EPR spectra show that five‐ and six‐coordinate oxo‐Cr^V intermediates are formed, with the alditol or the aldonic acid acting as bidentate ligands. Pentacoordinate oxo‐Cr^V species are present at any [H⁺], whereas hexacoordinate ones are observed only at pH<2 and become the dominant species under stronger acidic conditions where rapid decomposition to the redox products occurs. At higher pH, where hexacoordinate oxo‐Cr^V species are not observed, Cr^V complexes are stable enough to remain in solution for several days to months.     

A master equation investigation of coagulation reactions: Sol-gel transition

The kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration-dependent reaction kernels, K_ij = (ij)^ω, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol-gel transition.     

Absolute Rate constants for O + No + N2 → NO2 + N2 from 217–500 K

Flash photolysis of NO coupled with time resolved detection of O via resonance fluorescence has been used to obtain rate constants for the reaction O + NO + N₂ → NO₂ + N₂ at temperatures from 217 to 500 K. The measured rate constants obey the Arrhenius equation k = (15.5 ± 2.0) × 10^?33 exp(1160 ± 70)/1.987 T] cm⁶ molecule^?2 s^?1. An equally acceptable equation describing the temperature dependence of k is k = 3.80 × 10^?27/T^1.82 cm⁶ molecule^?2 s^?1. These results are discussed and compared with previous work.     

Der potentialverlauf galvanischer sensoren bei pulsförmiger probenaufgabe

It has been shown that by sample application as a pulse the voltage—time relation of a galvanic sensor can generally be described by the equation

where U_a is the voltage output change, U_o the maximum voltage change at open circuit, R_a and R the external and total resistance, k₁ and k₂=1/RC the rate constants of charging and discharging and C the total capacity of the cell (→condenser model). k₁ is related to the over-all reaction of charging and gives no immediate indication to the rate determining step. For instance k₁ can be the rate constant of chemisorption or an other first order reaction. In the case of a diffusion controlled reaction it is

where K is the partition and D the diffusion coefficient in the electrolyte, S the electrode surface, d the mean thickness of the electrolyte film, V₀ the cell and V_L the electrolyte volume above the catalyst. The deduced equation can also be extended to a quite chemical reaction, for instance when the measuring electrode is depolarized by oxygen. k₂ has then analogous meanings to k₁. The mentioned formulas give some indication to the optimalisation of the cell geometry and the preparation of the electrodes. The experimental treatment includes the response of an alcohol sensor, also the determination of k₁ is described and its kinetic meaning is discussed.     

Cascades of energy among the vibrational levels of diatomic molecules trapped in a rare gas matrix: With application to 12C16O(ν) in Ar

Energy stored in vibrational level ν = 1 of several individual dipolar diatomic molecules AB which are trapped in a rare gas matrix M is automatically accumulated in a higher level ν > 1 of a single molecule AB. This remarkable cascade of energy upwards competes with a cascade of energy downwards. the radiative decay. The interplay of both cascades, first observed by Dubost and Charneau, is explained a simple model. The model incorporates three processes into a master equation for the relative populations P_ν(t) of levels ν: (a) migration of single quanta by resonance energy transfer, AB(1) + AB(0) ? AB(0) + AB(1); (b) phonon assisted excitation of upper levels, AB(1) + AB(ν) → AB(0) + AB(ν+1); and (c) radiative decay, AB(ν) → AB(ν-1). The model assumes that there is only one isotopic species AB which has a small but nonzero vibrational anharmonicity, that the temperature is low, T → 0 K, the concentration ratio ?_M/?_AB is large and that, initially, at time t = 0, a small fraction p₁ of molecules AB is excited to level ν = 1. The master equation has only two parameters, the radiative lifetime t_rad and k  2/[?_AB?₁k(1,1 → 0,2)t_rad], where k(1,1 → 0,2) is the reference rate constant of process (b). The master equation is solved in closed form for the Pν(t). For t_rad = 14 ms and k = 0.2, very satisfactory qualitative agreement is found for the theoretical P_ν(t) and the experimental time evolution of the relative population of vibrational levels of ¹²C¹⁶O in an argon matrix, for ?_M/?_AB = 2000 at T = 9 K. In agreement with experimental results it is concluded that the risetime of the fluorescence signals decreases whereas population inversion increases for decreasing values of ?_M/?AB. At long times, t > t_rad, any population inversion should disappear.     

Reversible intersystem crossing,fluorescence lifetime lengthening and collisionally induced phosphorescence in biacetyl

The emissions of biacetyl excited at 4200 Å were studied at pressures down to 10^?3 torr. Apart from the well-known nanosecond fluorescence, a new emission of the same spectral composition was found with a non-exponential decay in the microsecond range. Furthermore the phosphorescence, as defined by its spectral composition, was found to be collisionally induced.The results imply that after excitation, the molecule rapidly transfers (rate constant k_S→T) to the triplet state, giving rise to the nanosecond decay time; and can then transfer back to the singlet state (rate constant k_T→S), giving rise to the microsecond emission. At the same time internal conversion can occur (k_S→S0). From an analysis of the data we find for k_S→S0 = 2.4 × 10⁷ sec^?1, k_S→T = 7.6 × 10⁷ sec^?1, k_T→S = 1.9 × 10⁵ sec^?1. The kinetic treatment can be transformed to a quantum mechanical one, yielding values for the triplet level density (?_T), the coupling element V_ST and the number of triplet states (N) coupled to the singlet excited. At 4200 Å we find ?_T = 6.3 × 10⁵cm, V_ST = 1.0 × 10^?5 cm^?1, N = 400.Phosphorescence occurs only when the molecule is deactivated by collisions to a vibronic triplet state below the vibrationless excited singlet state. The efficiency of biacetyl collisions is 0.54.     

Electrochemical production of NH2• radicals by the system Cu2+/VO2+/NH2OH and their reactions with benzene and toluene

Electroinitiated production of NH₂^. radicals was demonstrated to occur in aqueous acid solution when in the system Cu²⁺/VO²⁺/NH₂OH Cu²⁺ is reduced to metallic copper on a mercury cathode. The first stage of this process involves the reduction of vanadyl to V³⁺ by metallic copper. The electrochemical system Cu²⁺/VO²⁺ was demonstrated to follow a depolarization scheme of the type of the catalyzed electrode process.For the reaction Cu+2 VO²⁺k₁→Cu²⁺+2 V³⁺ a k₁ value of 32 M^?1 s^?1 at 50°C was calculated.The second stage of the process is the reduction of NH₂OH by V³⁺ to give aminyl radicals. In presence of benzene and toluene these radicals add to the aromatic ring to give new radicals which are oxidized by Cu²⁺ to the corresponding amines.The cuzrent yield of this process attains values as high as 70%. The yield dependence on H₂SO₄ concentration, electrolytic current and dioxane concentration is discussed.     

硅酸及其盐的研究——ⅩⅤⅢ.硅溶胶胶粒的生长速度

为弄清各种影响因素对硅溶胶胶粒生长的作用,实验测定了胶粒自发生长速度与温度、pH和胶粒粒径等之间的关系,得到了复杂的胶粒生长过程的一些信息。并根据本实验室提出的硅酸聚合理论推导了胶粒生长速度公式,用该式推出的结果与实验所得结果基本符合,说明该式能较正确地反映胶粒生长规律,因而在哇溶胶实际生产中有一定的参考价值。     

Dissolution kinetics of silver metal nanoparticles in their reaction with nitric acid in an reverse micelle solution of AOT

The dissolution of silver nanoparticles in their reaction with aqueous HNO₃ solubilized to an reverse micelle solution of sodium bis(2-ethylhexyl)sulfosuccinate in decane is studied spectrophotometrically. A physicochemical model is advanced for quantifying the process kinetics on th basis of the following autocatalytic scheme: Ag⁰ + H⁺ + NO ₃ ^? → Ag⁺ + products (k ₁), and Ag⁰ + Ag⁺ + NO ₃ ^? → 2Ag⁺ + products (k ₂). The effective rate constant k ₂ decreases with decreasing solubilization capacity V _S/V _O (where V _S is the volume of the solubilized dispersed aqueous phase and V _O is the volume of the micelle solution); the solubilization capacity determines the size of the micelle cavities in which the reaction between Ag⁰ and HNO₃ occurs: k ₂ = 74 (V _S/V _O) · 100% ≈ 3.8%), 41 (2.9), and 35 (2.0) L/(mol s). The effective constant k ₁ is determined with a high uncertainty; the effect of V _S/V _O on k ₁ has the opposite tendency.