Review Article<i>The Roman Inscriptions of Britain</i>. R. G. Collingwood , R. P. Wright

Gordon, Arthur E.

doi:10.1086/365347

Cited by 50 publications

(80 citation statements)

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“…[42] This procedure is known as the product difference algorithm. [43] Once the weights and abscissas are known the transport equations for the moments can be solved.…”

Section: Population Balance Modellingmentioning

confidence: 99%

CFD simulation and comparison of industrial crystallizers

et al. 2014

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Simulation of flow patterns in eleven industrial crystallizers (standard Messo, Cerny direct contact, Swenson draft tube baffled, Swenson walker, Swenson evaporative, Oslo cooling, Oslo Krystal, APV Kestner, Batch Vacuum, stirred tank with disc turbine, and stirred tank with pitched blade impeller) have been carried out using computational fluid dynamics (CFD). Population balance modelling (PBM) is coupled with CFD to obtain better results. In all the cases, the crystallizer volume was 100 liter and the power consumption per unit volume was 1 kW/m 3 . The simulation results have been presented in terms of mean velocity components, turbulent kinetic energy and dissipation rate. On the basis of the flow patterns, these eleven crystallizers have been compared for crystal size distribution (CSD). It was found that Swenson Evaporative, Krystal and Batch Vacuum provide relatively low CSD.

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“…[42] This procedure is known as the product difference algorithm. [43] Once the weights and abscissas are known the transport equations for the moments can be solved.…”

Section: Population Balance Modellingmentioning

confidence: 99%

CFD simulation and comparison of industrial crystallizers

et al. 2014

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“…Masses are measured in units of m, lengths in units of a (see Fig. 1 Of particular importance are the CFs C l0 tY C 0l t, and C lYÀl t with l = 1, 2, since all the spectroscopic observables are completely determined by the first and second rank orientational CFs 54) . For the system under study, (all the other components of the Christoffel symbol are identically zero).…”

Section: Illustrative Calculationmentioning

confidence: 99%

“…Third, inertial effects are necessary to ensure a correct description of the relaxation dynamics at a short enough time interval. It is well known that correlation functions (CF) of any dynamic variable, A (t), under equilibrium conditions must exhibit the following short time behavior 8,54) :…”

Section: Introductionmentioning

confidence: 99%

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Inertial effects in the Brownian dynamics with rigid constraints

Gelin¹

1999

Macromol. Theory Simul.

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SUMMARY: To investigate the influence of inertial effects on the dynamics of an assembly of beads subjected to rigid constraints and placed in a buffer medium, a convenient method to introduce suitable generalized coordinates is presented. Without any restriction on the nature of the soft forces involved (both stochastic and deterministic), pertinent Langevin equations are derived. Provided that the Brownian forces are Gaussian and Markovian, the corresponding Fokker-Planck equation (FPE) is obtained in the complete phase space of generalized coordinates and momenta. The correct short time behavior for correlation functions (CFs) of generalized coordinates is established, and the diffusion equation with memory (DEM) is deduced from the FPE in the high friction limit. The DEM is invoked to perform illustrative calculations in two dimensions of the orientational CFs for once broken nonrigid rods immobilized on a surface. These calculations reveal that the CFs under certain conditions exhibit an oscillatory behavior, which is irreproducible within the standard diffusion equation. Several methods are considered for the approximate solution of the DEM, and their application to three dimensional DEMs is discussed.

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“…First, if classical dynamics are assumed, then the lineshapes must be symmetrical. 17 Hence any observed Boltzmann asymmetry implies that quantum mechanical corrections are important. Second, as shown in Appendix A, for molecules with Ca.…”

Section: C{vr(t) = (Ai(t)ai(o) )+4/3c;hvr(t)mentioning

confidence: 99%

Raman line shapes in liquid CH3I and CD3I

Goldberg

Pershan

1973

The Journal of Chemical Physics

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The six fundamental bands of CH3I and CD3I, both as pure liquids and in solution with CS2, have been studied in order to obtain information about the molecular rotational and vibrational dynamics. Emphasis was placed on the features of the spectra that can be interpreted independent of a particular model. An examination for Boltzmann asymmetry in the A1 and E bands indicates that the former, being symmetric, are amenable to classical description, while the latter, being asymmetric, definitely require quantum mechanical interpretations. With respect to the validity of the assumption that rotation-vibration coupling can be ignored, we give evidence of substantial coupling effects in a nondegenerate A1 mode (v1) as well as in the doubly degenerate E modes. We emphasize that, in attempting to obtain dynamical information, several bands of any given liquid must be studied and compared in order to decide which can be used with confidence in a detailed analysis. The consistency of the rotational diffusion model for describing the tumbling motion of the methyl iodide molecules has been confirmed.

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Review ArticleThe Roman Inscriptions of Britain. R. G. Collingwood , R. P. Wright

Cited by 50 publications

References 0 publications

CFD simulation and comparison of industrial crystallizers

CFD simulation and comparison of industrial crystallizers

Inertial effects in the Brownian dynamics with rigid constraints

Raman line shapes in liquid CH3I and CD3I

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