Invariant Forms of Conservation Equations for Reactive Fields and Hydro-Thermo-Diffusive Theory of Laminar Flames

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Angular Momentum ◽  
Propagation Speed ◽  
Premixed Flame ◽  
Laminar Flames ◽  
Enskog Equation ◽  
Scale Invariant ◽  
Propagation Models ◽  
Conservation Equations ◽  
Invariant Model ◽  
Good Agreement

A scale-invariant model of statistical mechanics is described leading to invariant Enskog equation of change that is applied to derive invariant forms of conservation equations for mass, thermal energy, linear momentum, and angular momentum in chemically reactive fields. Modified hydro-thermo-diffusive theories of laminar premixed flames for (1) rigid-body and (2) Brownian-motion flame propagation models are presented and are shown to be mathematically equivalent. The predicted temperature profile, thermal thickness, and propagation speed of laminar methane–air premixed flame are found to be in good agreement with existing experimental observations.

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

2014 ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Momentum Conservation ◽  
Enskog Equation ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Scale Invariant ◽  
Spherical Droplet ◽  
Conservation Equations ◽  
Invariant Model ◽  
Cylindrically Symmetric ◽  
Tangential Forces

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solution of the conservation equations for the problems of normal shock, flow over a flat plate, and flow within a spherical droplet located at the stagnation point of opposed cylindrically-symmetric gaseous jets are presented.

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Exact Solutions ◽  
Momentum Conservation ◽  
Immiscible Fluids ◽  
Enskog Equation ◽  
Cauchy Stress ◽  
Liquid Droplets ◽  
Scale Invariant ◽  
Conservation Equations ◽  
Cylindrically Symmetric ◽  
Laminar And Turbulent Flow

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing, all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solutions of the conservation equations for the problems of normal shock, laminar, and turbulent flow over a flat plate, and flow within a single or multiple concentric spherical liquid droplets made of immiscible fluids located at the stagnation point of opposed cylindrically symmetric gaseous finite jets are presented.

scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

EXCITATION FUNCTIONS OF ALPHA INDUCED REACTIONS ON NATURAL NICKEL UP TO 50 MeV

2005 ◽  
Vol 14 (04) ◽  
pp. 611-629 ◽  
Author(s):  
N. L. SINGH ◽  
S. MUKHERJEE ◽  
M. S. GADKARI
Keyword(s):  
Angular Momentum ◽  
Alpha Particle ◽  
Gamma Ray ◽  
Level Density ◽  
The Other ◽  
Gamma Ray Spectrometry ◽  
Excitation Functions ◽  
Classical Models ◽  
Nucleon Emission ◽  
Good Agreement

Excitation functions have been measured for alpha-particle induced reactions on natural nickel leading to the production of 62 Zn , 61 Cu , 56,57 Ni and 56,58 Co radioisotopes up to 50 MeV by the activation method and gamma-ray spectrometry. Most of these radioisotopes are produced by one or two alpha-particle emissions and a few nucleon emissions. The excitation functions were compared with semi-classical models codes, like ALICE/90, which includes a shell corrected level density formulation and the COMPLET, which takes into account angular momentum removal effects. In the case of multi-nucleon emission channels, ALICE/90 gives fairly good agreement. The COMPLET code on the other hand, explains the α-particle emission channels in a more convincing manner.

scholarly journals Gauge coupling unification in a classically scale invariant model

2016 ◽  
Vol 2016 (2) ◽  
Author(s):  
Naoyuki Haba ◽  
Hiroyuki Ishida ◽  
Ryo Takahashi ◽  
Yuya Yamaguchi
Keyword(s):  
Gauge Coupling ◽  
Scale Invariant ◽  
Invariant Model

a0(980) AND f0(980) MESONS AS HADRONIC MOLECULES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 568-571 ◽  
Author(s):  
T. BRANZ ◽  
T. GUTSCHE ◽  
V. E. LYUBOVUTSKIJ
Keyword(s):  
Size Effects ◽  
Bound States ◽  
Finite Size ◽  
Finite Size Effects ◽  
Gauge Invariant ◽  
Electromagnetic Decay ◽  
Invariant Model ◽  
Scalar Mesons ◽  
Decay Properties ◽  
Good Agreement

We discuss a possible interpretation of the scalar mesons f0(980) and a0(980) as hadronic molecules - bound states of K and [Formula: see text] mesons. Using a phenomenological Lagrangian approach we calculate strong as well as the electromagnetic decay properties of both scalars. The covariant and gauge invariant model, which also allows for finite size effects of the hadronic molecule, delivers results in good agreement with experimental data.

scholarly journals EARLY UNIVERSE SOURCES FOR CMB NON-GAUSSIANITY

2002 ◽  
Vol 17 (29) ◽  
pp. 4273-4280
Author(s):  
ALEJANDRO GANGUI
Keyword(s):  
Power Spectrum ◽  
Cosmic Microwave Background ◽  
Early Universe ◽  
Microwave Background ◽  
Scale Invariant ◽  
Invariant Model ◽  
Primordial Power Spectrum ◽  
Initial States ◽  
Non Gaussian ◽  
Inflationary Models

In the framework of inflationary models with non-vacuum initial states for cosmological perturbations, we study non-Gaussian signatures on the cosmic microwave background (CMB) radiation produced by a broken-scale-invariant model which incorporates a feature at a privileged scale in the primordial power spectrum.

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