scholarly journals Reanalysis of Rate Data for the Reaction CH3 + CH3 → C2H6 Using Revised Cross Sections and a Linearized Second-Order Master Equation

2015 ◽  
Vol 119 (28) ◽  
pp. 7668-7682 ◽  
Author(s):  
M. A. Blitz ◽  
N. J. B. Green ◽  
R. J. Shannon ◽  
M. J. Pilling ◽  
P. W. Seakins ◽  
...  
Keyword(s):  
Master Equation ◽  
Cross Sections ◽  
Second Order ◽  
Rate Data

Determination of absolute two-photon excitation cross sections by in situ second-order autocorrelation

1995 ◽  
Vol 20 (23) ◽  
pp. 2372 ◽  
Author(s):  
Chris Xu ◽  
Winfried Denk ◽  
Jeffrey Guild ◽  
Watt W. Webb
Keyword(s):  
Cross Sections ◽  
Second Order ◽  
Two Photon ◽  
Photon Excitation ◽  
Excitation Cross Sections ◽  
Two Photon Excitation

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Mechanisms of Nucleophilic Attack at Carbon - Nitrogen Double Bonds: Reactions of Benzohydrazonoyl Halides with Secondary Amines in Benzene

1997 ◽  
Vol 50 (8) ◽  
pp. 849 ◽  
Author(s):  
Jeffrey E. Rowe ◽  
Kam Lee
Keyword(s):  
Second Order ◽  
Secondary Amines ◽  
Nucleophilic Attack ◽  
Rate Equations ◽  
Rate Data ◽  
Double Bonds ◽  
Effect Data ◽  
First Order ◽  
Amine Molecule

The reactions of a series of substituted benzohydrazonoyl halides with cyclic secondary amines in benzene as solvent are investigated. The rate equations for these reactions were complex and the derived rate data are reported. The element effect data showed that the fluoro compounds only reacted when a second amine molecule was available to assist the reaction, whereas the chloro and bromo compounds reacted by reactions which were both first order and second order in amine (k′′Br : k′′Cl = 9·5 : 1 and k′′′Br :k′′′Cl : k′′′F = 4·7 : 1 : 0·65). The mechanism of these reactions is discussed.

Second-Order Diffraction Loads on Plural Vertical Cylinder With Arbitrary Cross Sections

1987 ◽  
Vol 109 (4) ◽  
pp. 314-319
Author(s):  
K. Masuda ◽  
W. Kato ◽  
H. Ishizuka
Keyword(s):  
Boundary Value Problem ◽  
Cross Sections ◽  
Present Method ◽  
Boundary Value ◽  
Vertical Cylinder ◽  
Wave Force ◽  
Second Order ◽  
Wave Forces ◽  
Order Diffraction ◽  
Rectangular Cylinders

The purpose of the present study is development of a powerful numerical method for calculating second-order diffraction loads on plural vertical cylinder with arbitrary cross sections. According to the present method, second-order wave force can be obtained from a linear radiation potential without solving second-order boundary value problem. The boundary value problem for the radiation potential is solved with the hybrid boundary element method. The computations for circular and rectangular cylinders were carried out and compared with the experiments. In addition, second-order wave forces on twin circular cylinder are calculated with the present method.

scholarly journals Reviving the local second-order boundary approach within the two-relaxation-time lattice Boltzmann modelling

2020 ◽  
Vol 378 (2175) ◽  
pp. 20190404 ◽  
Author(s):  
Goncalo Silva ◽  
Irina Ginzburg
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Cross Sections ◽  
Lattice Boltzmann ◽  
Soft Matter ◽  
Second Order ◽  
Unknown Boundary ◽  
Single Node ◽  
Finite Difference Approximations ◽  
Problem Class

This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB within the two-relaxation-time (TRT) framework, which achieves a more standardized and easy to use algorithm due to the pivotal parametrization TRT properties. The LSOB explicitly reconstructs the unknown boundary populations in the form of a Chapman–Enskog expansion, where not only first- but also second-order momentum derivatives are locally extracted with the TRT symmetry argument, through a simple local linear algebra procedure, with no need to compute their non-local finite-difference approximations. Here, two LSOB strategies are considered to realize the wall boundary condition, the original one called Lwall and a novel one Lnode, which operate with the wall and node variables, roughly speaking. These two approaches are worked out for both plane and curved walls, including the corners. Their performance is assessed against well-established LBM boundary schemes such as the bounce-back, the local second-order accurate CLI scheme and two different parabolic multi-reflection (MR) schemes. They are all evaluated for 3D duct flows with rectangular, triangular, circular and annular cross-sections, mimicking the geometrical challenges of real porous structures. Numerical tests confirm that LSOB competes with the parabolic MR accuracy in this problem class, requiring only a single node to operate. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Slenderness Influence on the Behavior of Composite Columns

2016 ◽  
Vol 691 ◽  
pp. 40-50
Author(s):  
Štefan Gramblička ◽  
Andrea Hrusovska
Keyword(s):  
Cross Sections ◽  
Design Method ◽  
Tall Buildings ◽  
Concrete Columns ◽  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Composite Columns ◽  
Steel Members ◽  
Composite Steel

Composite steel and concrete columns have been used in the tall buildings due theirs high-resistance and the possibility to reduce cross sections when we compered composite columns with reinforced concrete columns. There are a lot of types of composite columns. We are concerned with columns, which are completely or partially concrete-encased steel members. In practice, a lot of composite columns are relatively slender and in design the second - order effects will usually need to be included. A partially concrete encased steel cross-section was selected for laboratory tests of composite columns. According to the results of the experiments (total of 18 columns were tested in two series), we analyzed the effects of the second - order theory. The experimental results were compared with theoretical results obtained from the model developed in the non-linear software. The evaluation of the results is also shown in comparison with the general design method according to Eurocode 4, Design of composite steel and concrete structures - Part 1.1 General rules and rules for buildings.

W, Z PLUS JET PRODUCTION AT $p\bar p$ COLLIDERS

1991 ◽  
Vol 06 (22) ◽  
pp. 3973-3988 ◽  
Author(s):  
F.T. BRANDT ◽  
G. KRAMER ◽  
SU-LONG NYEO
Keyword(s):  
Cross Sections ◽  
Z Bosons ◽  
Second Order ◽  
Jet Production ◽  
Two Jets

We have calculated cross sections for the production of W± and Z bosons in association with one and two jets at [Formula: see text] collider energies. The rates for these processes in second-order QCD are compared with jet rates measured by UA1 and CDF.

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