Analytical description of the effects of modifiers and of enzyme multivalency upon the steady state catalyzed reaction rate

1953 ◽  
Vol 49 ◽  
pp. 696 ◽  
Author(s):  
Jean Botts ◽  
Manuel Morales
Keyword(s):  
Steady State ◽  
Reaction Rate ◽  
Analytical Description

Optimizing Nephelometric Measurement of Specific Serum Proteins: Evaluation of Three Diluents

1974 ◽  
Vol 20 (12) ◽  
pp. 1548-1552 ◽  
Author(s):  
Lawrence M Killingsworth ◽  
Gregory J Buffone ◽  
Meena B Sonawane ◽  
Glennie C Lunsford
Keyword(s):  
Steady State ◽  
Continuous Flow ◽  
Reaction Rate ◽  
Serum Proteins ◽  
Physiological Saline ◽  
Rate Analysis ◽  
Specific Serum ◽  
State Approximation ◽  
Α2 Macroglobulin ◽  
Steady State Approximation

Abstract Three diluents were studied, to determine which is the best for the automated immunochemical measurement of specific serum proteins. Nine serum proteins (orosomucoid, α1-antitrypsin, α2-macroglobulin, haptoglobin, transferrin, C3, IgG, IgA, and IgM) were measured in physiological saline (9 g NaCI/liter), tris(hydroxymethyl)aminomethane buffer (0.01 mol/liter; pH 7.4), and physiological saline containing polyethylene glycol ("PEG 6000," 40 g/liter). Criteria were: reaction rate, analysis rate, carryover between samples, steady-state approximation, precision, and correlation with other methods. Saline containing polyethylene giycol is the best of the three diluents for use in continuous-flow nephelometric analysis of serum proteins.

scholarly journals The Role Of Chemical Reaction In Waste-Form Performance

1987 ◽  
Vol 112 ◽  
Author(s):  
P. L. Chambré ◽  
C. H. Kang ◽  
W. W.-L. Lee ◽  
T. H. Pigford
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Dissolution Rate ◽  
Chemical Reaction ◽  
Borosilicate Glass ◽  
Reaction Rate ◽  
Waste Form ◽  
Spent Fuel ◽  
Wide Range ◽  
Chemical Reaction Rate

AbstractThe dissolution rate of waste solids in a geologic repository is a complex function of waste form geometry, chemical reaction rate, exterior flow field, and chemical environment. We present here an analysis to determine the steady-state mass transfer rate, over the entire range of flow conditions relevant to geologic disposal of nuclear waste. The equations for steady-state mass transfer with a chemical-reaction-rate boundary condition are solved by three different mathematical techniques which supplement each other. This theory is illustrated with laboratory leach data for borosilicate-glass and a spherical spent-fuel waste form under typical repository conditions. For borosilicate glass waste in the temperature range of 57°C to 250°C, dissolution rate in a repository is determined for a wide range of chemical reaction rates and for Peclet numbers from zero to well over 100, far beyond any Peclet values expected in a repository. Spent-fuel dissolution in a repository is also investigated, based on the limited leach data now available.

Effect of the potential-energy surface on the diatom dissociation rate constant for F 2 in Ar at 3000 K

1987 ◽  
Vol 414 (1847) ◽  
pp. 297-314
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Rate Constants ◽  
Reaction Rate ◽  
Energy Surface ◽  
Rate Coefficient ◽  
Classical Mechanics ◽  
Rate Coefficients ◽  
Steady State Rate ◽  
State Rate

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.

Uncertainties in Chi analysis: implications for drainage network and divide stability

2020 ◽  
Author(s):  
Jens Turowski ◽  
Wolfgang Schwanghart ◽  
Kim Huppert ◽  
Claire Masteller
Keyword(s):  
Steady State ◽  
Differential Cross ◽  
Analytical Description ◽  
Drainage Area ◽  
River Networks ◽  
Drainage Network ◽  
Visual Interpretation ◽  
Topographic Data ◽  
Sources Of Error ◽  
Source Of Error

<p>In recent years, Chi analysis has become an important tool for tectonic and geomorphic analyses of longitudinal and planform patterns of river networks. Predicated on the commonly observed inverse scaling between drainage area and slope in rivers and integrating drainage area, the metric Chi has several advantages over other topographic metrics used to describe river long profiles. For a steady state river, Chi scales linearly with elevation, simplifying visual interpretation and further analysis. As an integral property, it also reduces scatter in noisy topographic data. In addition, comparison of computed Chi values to the steady state assumption are a popular tool to determine the stability of river networks and mobility of drainage divides. In this application it is thought that the drainage divide is mobile when Chi values are unequal at adjacent channel heads when integrated from a common base level. These differences in Chi are now frequently used to map mobile and stationary divides and to interpret their spatial patterns in terms of tectonic forcing.</p><p> </p><p>As the interpretation of divide mobility relies on a difference in Chi values across the divide, the question arises: how magnitude of cross-divide differences in Chi is necessary for a statistically significant result, given inherent uncertainty in calculations of Chi and the topographic data from which they are derived? Currently, uncertainties in Chi have not been formally evaluated. As such, it remains unclear how robust measurements of differential cross-divide Chi are as a proxy for interpreting drainage divide mobility. Here, we argue that uncertainties in differential cross-divide Chi depend on the location and length of the drainage divide. In a discrete representation of topography, we identify two sources of error. The first source of error can arise if a pixel is incorrectly assigned to a catchment on one side of the divide due either to error in the topographic data or uncertainty in the delineation of drainage area from a digital elevation model (DEM). The second source of error arises because the divide is a linear feature, which cuts across individual pixels in a gridded DEM. Thus, a pixel at the boundary of one designated catchment typically contains area that should drain to its neighboring catchment. We develop an analytical description of these sources of error and show that uncertainties in differential cross-divide Chi can be of the same order as the cross-divide difference in Chi itself. The results from the analytical solution are consistent with a numerical assessment of Chi uncertainties from flow routing on DEMs using multiple flow directions. We discuss scaling with drainage area, and the implications for drainage network mobility using type examples.</p>

scholarly journals Milling Dynamics and Propagation of Mechanically Activated Self-Sustaining Reactions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Alberto Cincotti ◽  
Gabriele Traversari ◽  
Giorgio Pia ◽  
Francesco Delogu
Keyword(s):  
Reaction Rate ◽  
Equations Of Motion ◽  
Analytical Description ◽  
Chemical Conversion ◽  
Mechanical Processing ◽  
Ball Mills ◽  
Operational Conditions ◽  
Powder Particles ◽  
Milling Dynamics ◽  
Individual Particles

This work focuses on the propagation of mechanically activated self-sustaining reactions during the mechanical processing of powder in ball mills. We use a numerical model to reconstruct the dynamics of a single ball and powder particles inside the reactor of a SPEX Mixer/Mill 8000 under operational conditions. Taking advantage of the analytical description of the reactor swing, the equations of motion of ball and powder particles are solved numerically. The discrete element method is used to describe contacts. Reaction is ignited in an individual particle randomly selected among those compressed during an impact between ball and reactor. A simple kinetic law and a set of rules involving degree of chemical conversion and distance between particles are used to obtain a phenomenological description of the reaction propagation. We show that the propagation is significantly affected by reaction rate in individual particles, with other factors being less influential. We observe a strong coupling between the dynamics of powder particles and the reaction propagation.

Robustness of Quantum Correlations in Entangled Two su(2) Systems Non-mutually Interacting with su(1, 1) System under Intrinsic Decoherence

2018 ◽  
Vol 25 (03) ◽  
pp. 1850015
Author(s):  
A.-B. A. Mohamed ◽  
M. S. Abdalla ◽  
A.-S. F. Obada
Keyword(s):  
Steady State ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Bell State ◽  
Analytical Description ◽  
Quantum Correlations ◽  
Total System ◽  
Intrinsic Decoherence ◽  
Geometric Quantum Discord ◽  
Phase Decoherence

Two two-level systems generated by su(2) algebra are initially prepared in a maximum nonsymmetric Bell state and having no mutual interaction. Each su(2)-system spatially interacts with two-mode cavity field in the nondegenerate parametric amplifier type cast through operators governed by su(1, 1) Lie algebra. An analytical description for the time evolution of the final state of the total system with the effect of intrinsic decoherence is found. Therefore, the robustness of the quantum correlations between the two su(2)-system is investigated by means of geometric quantum discord, measurement-induced nonlocality and negativity. We analyze in some detail the influence of initial coherence intensities, detuning and phase decoherence parameters on the steady-state correlation. We find that the steady-state correlations can be generated and enhanced by controlling the parameters of: the initial coherence intensities, the Bargmman index and the detuning. It is shown that the phenomenon of sudden death and re-birth of entanglement, and the sudden changes of the geometric quantum correlation can be controlled by these parameters. We find that the robustness of the quantum correlation can be greatly enhanced by the Bargmman index and the resonance detuning. Negativity is the measure most susceptible to phase decoherence, while geometric quantum discord and measurement-induced nonlocality are the more robust measures.

Steady-state two-dimensional detonation

1981 ◽  
Vol 108 ◽  
pp. 195-226 ◽  
Author(s):  
J. B. Bdzil
Keyword(s):  
Steady State ◽  
Detonation Velocity ◽  
Sound Speed ◽  
Reaction Rate ◽  
State Dependence ◽  
State Theory ◽  
Experimental Shock ◽  
Leading Term ◽  
High Degree ◽  
Detonation Failure

An analytical steady-state theory of the detonation ‘diameter effect’ is presented. This theory, which includes the off-axis flow, is a generalization of the Wood-Kirkwood analysis. When the state dependence of the reaction rate is stronger than that of the product of the sound speed squared and the flow divergence, detonation failure can occur. The leading term in the extrapolation of the detonation velocity to infinite charge size is quadratic in the inverse charge size and not linear as popularly believed. When calibrated to the detonation velocity vs. charge-size data, the theory reproduces the limited amount of experimental shock loci to a high degree of accuracy.

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