Constant Branching Research Articles

Ozonolysis of 2-Methyl-2-pentenal: New Insights from Master Equation Modeling.

Experimental and theoretical studies were carried out to investigate the ozonolysis of trans-2-methyl-2-pentenal. The experiments were conducted in atmospheric simulation chambers coupled to a Fourier transform infrared (FTIR) spectrometer and a gas chromatograph-mass spectrometer at room temperature and atmospheric pressure in the presence of an excess of cyclohexane in dry conditions (RH < 1%). The ozonolysis reaction was investigated theoretically from the results of accurate density functional (M06-2X) and ab initio [CCSD(T)] computations, employing the AVTZ basis set. The sequence of reaction steps was established, and the system of kinetics equations was modeled using MESMER. In the first step, a primary ozonide is formed, which then decomposes along two pathways. The principal ozonolysis products are propanal, methylglyoxal, ethylformate, and a secondary ozonide. An interesting competition between sequential reaction steps and well-skipping is found, which leads to an inversion of the expected methylglyoxal/propanal product ratio at temperatures below 210 K. The mechanism of the "hot ester" reaction channel of the Criegee intermediate was revisited. The computed ozonolysis rate constant and product branching ratio are in excellent agreement with the experimental data that are also reported in the present work.

Kinetics and thermodynamics of unimolecular dissociation of n-C3H7I

Abstract The present work expands previous studies on the kinetics of the n-C3H7I unimolecular decomposition and the thermodynamic properties of n-C3H7I and i-C3H7I molecules, by providing combined experimental and theoretical data on the rate constant for reaction of n-C3H7I + Ar ⇌ n-C3H7 + I + Ar, as well as thermodynamic data for iodopropane isomers, calculated based on the density functional theory. The n-C3H7I dissociation rate constant has been precisely determined in shock-tube experiments by applying atomic resonance absorption spectrometry (ARAS) at the resonance transition wavelength of atomic iodine (183.0 nm) in a temperature range from 830 to 1230 K at a pressure of 3–4 bar. The resulting expression is presented in the Arrhenius form: k 1st = 1.17 × 1013exp(−191.4 kJ mol−1/RT) (s−1). Theoretical RRKM/ME calculation of the temperature- and pressure-dependent rate constant and channel branching ratio have been based on quantum chemical calculations and were performed over a wide range of thermodynamic conditions (T = 300–2000 K, p = 10−4 to 102 bar). Additionally, the thermochemistry of the reactions of n-C3H7I dissociation and isomerization has been calculated on B3LYP/cc-pVTZ-PP level of theory. Thermodynamic data, which are provided in NASA polynomial format, are in a better agreement with the available experimental data and previous theoretical estimates.

Pressure and temperature dependent kinetics and the reaction mechanism of Criegee intermediates with vinyl alcohol: a theoretical study.

Criegee intermediates (CIs), the key intermediates in the ozonolysis of olefins in atmosphere, have received much attention due to their high activity. The reaction mechanism of the most simple Criegee intermediate CH2OO with vinyl alcohol (VA) was investigated by using the HL//M06-2X/def2TZVP method. The temperature and pressure dependent rate constant and product branching ratio were calculated using the master equation method. For CH2OO + syn-VA, 1,4-insertion is the main reaction channel while for the CH2OO + anti-VA, cycloaddition and 1,2-insertion into the O-H bond are more favorable than the 1,4-insertion reaction. The 1,4-insertion or cycloaddition intermediates are stabilized collisionally at 300 K and 760 torr, and the dissociation products involving OH are formed at higher temperature and lower pressure. The rate constants of the CH2OO reaction with syn-VA and anti-VA both show negative temperature effects, and they are 2.95 × 10-11 and 2.07 × 10-13 cm3 molecule-1 s-1 at 300 K, respectively, and the former is agreement with the prediction in the literature.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment.

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

12C+12C reactions for Nuclear Astrophysics

12C fusion reactions are among the most important in stellar evolution since they determine the destiny of massive stars. Over the past fifty years, massive efforts have been done to measure these reactions at low energies. However, existing data present several discrepancies between sets and large uncertainties specially at the lowest energies. Factors such as beam/environmental backgrounds, extremely low cross sections and insufficient knowledge of the reaction mechanism contribute to these problems. Recently, the ERNA collaboration measured the 12C+12C reactions at Ec.m. = 2.51 - 4.36 MeV with energy steps between 10 and 25 keV in the centre of mass. Representing the smallest energy steps to date. In these measurements, beam induced background was minimised and S-factors for the proton and alpha channels were calculated. Results indicate that a possible explanation for the discrepancies between data sets is the wrongly assumed constant branching ratios and isotropical angular distributions. Given the excellent performance of the detectors for low energy measurements, a collaboration with the LUNA group (LNGS) has started. Background measurements underground are being performed and results indicate it could be possible to measure the 12C+12C reactions directly into the Gamow Window.

Modeling and Analysis of Root Branching Plasticity Based on Parrondo's Game

Abstract For different kinds of plants, the distribution of lateral roots is highly plastic in different growth environments. In particular, the branching distance of the roots plays a decisive role in the formation of the root system architecture. In many root-system architecture models, constant branching distances of different branching orders usually are used to simulate the dynamics of a root system architecture. However, little is known about the formation of lateral roots, and branching distances for different branching orders are variable in the actual root system. The resource allocation model for predicting the lateral root distribution in individual plants has been established based on Parrondo's game. The root branching data predicted by the model is compared with the actual root branching data. The results show that the proposed method can cause serious changes in the spacing and distribution of lateral root formation. A parameter called development window can be used to override interbranch distance in the root-system architecture models.

Direct dynamics simulation of the thermal O(3P) + dimethylamine reaction in the triplet surface. I. Rate constant and product branching

AbstractIn order to provide atomistic details for the mechanism of the collisional dynamics of O(3P) and dimethylamine (DMA) in the triplet electronic surface, direct dynamics simulations are reported herein. The simulations are performed at the U‐HSE06/aug‐cc‐pVDZ level of theory. The results are reported for the relative collision energy of 7.8 kcal/mol. For the vibrational and rotational excitations, following temperature regimes have been considered: 200 and 10 K, respectively. Simulations reveal that the reaction can lead to two product channels in the considered energy regime: (1) 2OH + 2CH3NHCH2 and (2) 2OH + 2CH3NCH3. The computed reaction cross section for pathways 1 and 2 are as follows: 17.89 0.20 Å2 and 3.28 0.03 Å2, whereas the computed microcanonical reaction rate constants for pathways 1 and 2 are as follows: (4.21 0.05)*10−10 and (7.72 0.07)*10−11 cm3/(molecule sec). Both pathways follow direct and indirect H abstraction processes. Among the direct pathways, stripping and rebound mechanisms have been observed, whereas the indirect pathway involves formation of a post‐reaction complex having lifetime ~0.4–0.5 ps. The velocity scattering angle distribution for the reaction is dominated by scattering in the sideways (60–120 ) and backward (120–180 ) directions with some contribution from the scattering in the forward direction (0–60 ).

Theoretical studies on the initial reaction kinetics and mechanisms of p-, m- and o-nitrotoluene

The potential energy surfaces (PESs) of three nitrotoluene isomers, such as p-nitrotoluene, m-nitrotoluene, and o-nitrotoluene, have been theoretically built at the CCSD(T)/CBS level. The geometries of reactants, transition states (TSs) and products are optimized at the B3LYP/6-311++G(d,p) level. Results show that reactions of -NO2 isomerizing to ONO, and C-NO2 bond dissociation play important roles among all of the initial channels for p-nitrotoluene and m-nitrotoluene, and that the H atom migration and C-NO2 bond dissociation are dominant reactions for o-nitrotoluene. In addition, there exist pathways for three isomer conversions, but with high energy barriers. Rate constant calculations and branching ratio analyses further demonstrate that the isomerization reactions of O transfer are prominent at low to intermediate temperatures, whereas the direct C-NO2 bond dissociation reactions prevail at high temperatures for p-nitrotoluene and m-nitrotoluene, and that H atom migration is a predominant reaction for o-nitrotoluene, while C-NO2 bond dissociation becomes important by increasing the temperature.

Time-dependent branching processes: a model of oscillating neuronal avalanches

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results.

Initial charm program on direct measurements of weak decay constant fDs and branching fraction B(Ds → μνμ) and prospect with high-precision

First direct measurements of the weak decay constant [Formula: see text] and the [Formula: see text] branching fractions to [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] at the BES experiments in 1990s are reviewed. Referring to the BESIII results of [Formula: see text] and branching fraction [Formula: see text] with best precision1 to date, prospect for challenge on precision measurements of [Formula: see text] and [Formula: see text] at BESIII is presented.

On the spectrum of finite, rooted homogeneous trees

In this paper we study the adjacency spectrum of families of finite rooted trees with regular branching properties. In particular, we show that in the case of constant branching, the eigenvalues are realized as the roots of a family of generalized Fibonacci polynomials and produce a limiting distribution for the eigenvalues as the tree depth goes to infinity. We indicate how these results can be extended to periodic branching patterns and also provide a generalization to higher order simplicial complexes.

Structure–property relationships of the thermal gelation of partially hydrolyzed polyacrylamide/polyethylenimine mixtures in a semidilute regime

In this work, the structure–property relationships of the thermal gelation of partially hydrolyzed polyacrylamide (PHPA) and polyethylenimine (PEI) mixtures were investigated under realistic conditions of temperature (80 °C) and salinity (total dissolved solids = 3.4 g/l) of the Algerian reservoir (Tin Fouye Tabankort) prior to a conformance control application. The reactants were characterized with regard to their hydrolysis degree or branching degree using 13C-nuclear magnetic resonance, and viscosity–average molecular weights ($$ \bar{M}_{\text{v}} $$) were estimated using the Mark–Houwink equation and intrinsic viscosities measurements. The polymers had molecular weights that varied from 5 to 10 × 106 g/mol for PHPAs with initial hydrolysis degrees between 6 and 20 mol%, while the molecular weights of the PEI were between 2 and 67 × 104 g/mol with a constant branching degree of 57–59. Consequently, the effect of steady shear on the gelation time was investigated followed by the effect of reactant concentrations, the polymer and cross-linker molecular weights, the polymer’s hydrolysis degree, the temperature and the initial pH. All experiments were conducted in a semidilute concentration regime while maintaining practical initial gelant viscosities. As a result, the gelation time was found to decrease with reactant concentrations, molecular weights and temperature (Ea = 62 kJ/mol) and to increase with hydrolysis degree.

An investigation of atropisomerism in ortho‐imide substituted 1,3‐benzoxazine by experimental NMR and DFT calculations

AbstractA new type of atropisomerism in ortho‐imide functional 1,3‐benzoxazine compound was evident from nuclear magnetic resonance (NMR) spectra, which showed constant branching ratio of the two products at different measurement temperatures of NMR. Density functional theory calculations were performed to obtain molecular‐level insights into the atropisomerism, which suggested that the reaction intermediate, ortho‐imide phenol, determines the branching ratio of the products. Our calculations showed a large energy barrier after deprotonation of this molecule, which prevents any configurational switch in the follow‐on reactions. Potentially, the atropisomerization mechanism discovered in this work can be used as a generic design principle for improving drug development, organic catalysts, molecular electronics, and other fields wherever atropisomers can play important and prevalent roles.

Direct Dynamics Simulation of the Thermal 3CH2 + 3O2 Reaction. Rate Constant and Product Branching Ratios.

The reaction of 3CH2 with 3O2 is of fundamental importance in combustion, and the reaction is complex as a result of multiple extremely exothermic product channels. In the present study, direct dynamics simulations were performed to study the reaction on both the singlet and triplet potential energy surfaces (PESs). The simulations were performed at the UM06/6-311++G(d,p) level of theory. Trajectories were calculated at a temperature of 300 K, and all reactive trajectories proceeded through the carbonyl oxide Criegee intermediate, CH2OO, on both the singlet and triplet PESs. The triplet surface leads to only one product channel, H2CO + O(3P), while the singlet surface leads to eight product channels with their relative importance as CO + H2O > CO + OH + H ∼ H2CO + O(1D) > HCO + OH ∼ CO2 + H2 ∼ CO + H2 + O(1D) > CO2 + H + H > HCO + O(1D) + H. The reaction on the singlet PES is barrierless, consistent with experiment, and the total rate constant on the singlet surface is (0.93 ± 0.22) × 10-12 cm3 molecule-1 s-1 in comparison to the recommended experimental rate constant of 3.3 × 10-12 cm3 molecule-1 s-1. The simulation product yields for the singlet PES are compared with experiment, and the most significant differences are for H, CO2, and H2O. The reaction on the triplet surface is also barrierless, inconsistent with experiment. A discussion is given of the need for future calculations to address (1) the barrier on the triplet PES for 3CH2 + 3O2 → 3CH2OO, (2) the temperature dependence of the 3CH2 + 3O2 reaction rate constant and product branching ratios, and (3) the possible non-RRKM dynamics of the 1CH2OO Criegee intermediate.

Chain-Walking Polymerization of Linear Internal Octenes Catalyzed by α-Diimine Nickel Complexes

The chain-walking polymerization of linear internal alkenes (i.e., trans-2-, 3-, and 4-octenes) using α-diimine nickel catalysts activated with modified methylaluminoxane (MMAO) was studied in comparison with the corresponding terminal alkene polymerization. The rates of polymerization were found to decrease in the following order: 1-octene > 4-octene ≥ 2-octene ≫ 3-octene. The obtained branched poly(2-octene)s and poly(4-octene)s with high molecular weight and Mw/Mn less than 2 were amorphous polymers with low glass transition temperature (Tg) of approximately −66 °C. At 0 °C, 4-octene polymerized in a living/controlled manner. The NMR analyses of the polymers showed that the chain-walking polymerization of 4-octene gave periodically branched polymers with the constant branching density, while that of 2-octene gave the polymer possessing fewer branches than the expected value due to monomer-isomerization. The (n+2),(n+3)- and (n+3),(n+2)-insertions of the internal (n+2)-alkene [CH3(CH2)nCH═CH(CH2)mCH3] f...

Intermittency for branching walks with heavy tails

Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the particles inside of the front are distributed very non-uniformly. The particles exhibit intermittent behavior in a large part of the region behind the front (i.e. the particles are concentrated only in very sparse spots there). The zone of non-intermittency (were particles are distributed relatively uniformly) extends with a power rate. This rate is found.

Reactivity from excited state (4)FeO(+) + CO sampled through reaction of ground state (4)FeCO(+) + N2O.

The kinetics of the FeCO(+) + N2O reaction have been studied at thermal energies (300-600 K) using a variable temperature selected ion flow tube apparatus. Rate constants and product branching fractions are reported. The reaction is modestly inefficient, proceeding with a rate constant of 6.2 × 10(-11) cm(3) s(-1) at 300 K, with a small negative temperature dependence, declining to 4.4 × 10(-11) cm(3) s(-1) at 600 K. Both Fe(+) and FeO(+) products are observed, with a constant branching ratio of approximately 40:60 at all temperatures. Calculation of the stationary points along the reaction coordinate shows that only the ground state quartet surface is initially sampled resulting in N2 elimination; a submerged barrier along this portion of the surface dictates the magnitude and temperature dependence of the total rate constant. The product branching fractions are determined by the behavior of the remaining (4)OFeCO(+) fragment, and this behavior is compared to that found in the reaction of FeO(+) + CO, which initially forms (6)OFeCO(+). Thermodynamic and kinetic arguments are used to show that the spin-forbidden surface crossing in this region is efficient, proceeding with an average rate constant of greater than 10(12) s(-1).

Micro-CT scan reveals an unexpected high-volume and interconnected pore network in a Cretaceous Sanagasta dinosaur eggshell.

The Cretaceous Sanagasta neosauropod nesting site (La Rioja, Argentina) was the first confirmed instance of extinct dinosaurs using geothermal-generated heat to incubate their eggs. The nesting strategy and hydrothermal activities at this site led to the conclusion that the surprisingly 7 mm thick-shelled eggs were adapted to harsh hydrothermal microenvironments. We used micro-CT scans in this study to obtain the first three-dimensional microcharacterization of these eggshells. Micro-CT-based analyses provide a robust assessment of gas conductance in fossil dinosaur eggshells with complex pore canal systems, allowing calculation, for the first time, of the shell conductance through its thickness. This novel approach suggests that the shell conductance could have risen during incubation to seven times more than previously estimated as the eggshell erodes. In addition, micro-CT observations reveal that the constant widening and branching of pore canals form a complex funnel-like pore canal system. Furthermore, the high density of pore canals and the presence of a lateral canal network in the shell reduce the risks of pore obstruction during the extended incubation of these eggs in a relatively highly humid and muddy nesting environment.

Energy flow along the medium-induced parton cascade

We discuss the dynamics of parton cascades that develop in dense QCD matter, and contrast their properties with those of similar cascades of gluon radiation in vacuum. We argue that such cascades belong to two distinct classes that are characterized respectively by an increasing or a constant (or decreasing) branching rate along the cascade. In the former class, of which the BDMPS, medium-induced, cascade constitutes a typical example, it takes a finite time to transport a finite amount of energy to very soft quanta, while this time is essentially infinite in the latter case, to which the DGLAP cascade belongs. The medium induced cascade is accompanied by a constant flow of energy towards arbitrary soft modes, leading eventually to the accumulation of the initial energy of the leading particle at zero energy. It also exhibits scaling properties akin to wave turbulence. These properties do not show up in the cascade that develops in vacuum. There, the energy accumulates in the spectrum at smaller and smaller energy as the cascade develops, but the energy never flows all the way down to zero energy. Our analysis suggests that the way the energy is shared among the offsprings of a splitting gluon has little impact on the qualitative properties of the cascades, provided the kernel that governs the splittings is not too singular.

Developmental Programming of Branching Morphogenesis in the Kidney.

The kidney developmental program encodes the intricate branching and organization of approximately 1 million functional units (nephrons). Branching regulation is poorly understood, as is the source of a 10-fold variation in nephron number. Notably, low nephron count increases the risk for developing hypertension and renal failure. To better understand the source of this variation, we analyzed the complete gestational trajectory of mouse kidney development. We constructed a computerized architectural map of the branching process throughout fetal life and found that organogenesis is composed of two distinct developmental phases, each with stage-specific rate and morphologic parameters. The early phase is characterized by a rapid acceleration in branching rate and by branching divisions that repeat with relatively reproducible morphology. The latter phase, however, is notable for a significantly decreased yet constant branching rate and the presence of nonstereotyped branching events that generate progressive variability in tree morphology until birth. Our map identifies and quantitates the contribution of four developmental mechanisms that guide organogenesis: growth, patterning, branching rate, and nephron induction. When applied to organs that developed under conditions of malnutrition or in the setting of growth factor mutation, our normative map provided an essential link between kidney architecture and the fundamental morphogenetic mechanisms that guide development. This morphogenetic map is expected to find widespread applications and help identify modifiable targets to prevent developmental programming of common diseases.