Deterministic Methods in Systems Hydrology

Dooge, J. C. I.; O'Kane, Philip

doi:10.1201/9781315275123

Cited by 6 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The function Lγk (ℓ, t) u H (t) can then be approximated by A k δ (t − τ kg ) where A k and τ kg are, respectively, its area and its centre of gravity. Since Lγk (ℓ, t) u H (t) is the inverse Fourier transform of K (ℓ, Ω) = 1 − H (ℓ, Ω), we have A k = 1 − H (ℓ, 0) = 1 − e −L and, by an expansion of ln [K (ℓ, Ω)] in cumulants [38], τ kg = L/ γ e L − 1 > 0. Injecting these results in Eq.…”

Section: Long Pulse or Adiabatic Limitmentioning

confidence: 99%

“…When the intensity of the secondary lobes is weak enough, the distortion of the transmitted pulse mainly consists in a narrowing. This simply results from the negative value of the second cumulant of H (ℓ, Ω) and the additivity of the cumulants [38]. The narrowing of t/τ p Figure 10: Effect on the transmitted intensity of a frequency detuning of the incident pulse for e(0, t) = e2(0, t).…”

Section: Optimization Of the Fractional Pulse-advancementioning

confidence: 99%

“…Second, the mean time of h (ℓ, t), i.e. the group delay τ g , equals the first cumulant κ 1 of H (ℓ, Ω) [38]. Quite generally the cumulants κ n are given by the following expansion of ln [H (ℓ, Ω)] :…”

Section: General Analysismentioning

confidence: 99%

See 2 more Smart Citations

On-resonance material fast light

Macke

Ségard

2018

Phys. Rev. A

View full text Add to dashboard Cite

We theoretically revisit the problem of the propagation of coherent light pulses through a linear medium when the carrier frequency of the pulses coincides with the minimum of a narrow dip in the medium transmission. Considering realistic contrasts between the maximum and minimum transmission of the medium and incident pulses of strictly finite duration, we combine temporal and spectral approaches to obtain analytical expressions of the transmitted pulse that reproduce the main features of the exact numerical solutions derived by fast Fourier transform. A special attention is paid to the advance of the pulse maximum over that of a pulse covering the same distance in vacuum and the ratio of this advance to the pulse duration (fractional advance) is optimized.

show abstract

Section: Long Pulse or Adiabatic Limitmentioning

confidence: 99%

Section: Optimization Of the Fractional Pulse-advancementioning

confidence: 99%

See 1 more Smart Citation

On-resonance material fast light

Macke

Ségard

2018

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…where F −1 designates inverse Fourier transforms. General characteristics of ∆I(L, t) and ∆N (L, t) can be derived by exploiting the remarkable properties of the cumulants [4,50]. The cumulants κ n of the Fourier transform G(Ω) of a real function g(t) are given by the expansion…”

Section: Case Of Weak Modulation Depthsmentioning

confidence: 99%

Slow light in saturable absorbers: Progress in the resolution of a controversy

2017

View full text Add to dashboard Cite

There are two opposing models in the analysis of the slow transmission of light pulses through saturable absorbers. The canonical incoherent bleaching model simply explains the slow transmission by combined effects of saturation and of non-instantaneous response of the medium resulting in absorption of the front part of the incident pulse larger than that of its rear. The second model, referred to as the coherent-population-oscillations (CPO) model, considers light beams whose intensity is slightly pulse modulated and attributes the time delay of the transmitted pulse to a reduction of the group velocity. We point out some inconsistencies in the CPO model and show that the two models lie in reality on the same hypotheses, the equations derived in the duly rectified CPO model being local expressions of the integral equations obtained in the incoherent bleaching model. When intense pulses without background are used, the CPO model, based on linearized equations, breaks down. The incoherent bleaching model then predicts that the transmitted light should vanish when the intensity of the incident light is strictly zero. This point is confirmed by the experiments that we have performed on ruby with square-wave incident pulses and we show that the whole shape of the observed pulses agrees with that derived analytically by means of the incoherent bleaching model. We also determine in this model the corresponding evolution of the fluorescence light, which seems to have been evidenced in other experiments.

show abstract

“…Further, many of the hydrologic routing methods, such as the Muskingum model, and lag and route model (Dooge and O'Kane, 2003) were developed in the pre-computer era for their use in the context of design flood studies required for many river valley projects and these models served their intended purpose by accounting the translation and attenuation characteristics of a flood wave in a lumped manner which are, however, intrinsically accounted in a distributed manner in hydraulic routing methods, such as the four-point finite difference method (NERC, 1975). Therefore, the VPMM method characterized by two parameters, accounting for translation and attenuation of flood wave in a lumped manner at any given instant of time, the linkage of these parameters with the channel and flow characteristics based on hydrodynamic principles, is more desirable than the multi parameter nonlinear routing models developed based on the NLM model of Gill (1977Gill ( , 1978 or its latter variants with more than three parameters.…”

mentioning

confidence: 99%

Reply to comment on “Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods” by Reza Barati

Perumal

Tayfur

Chintalacheruvu

et al. 2017

Journal of Hydrology

View full text Add to dashboard Cite

The writers thank the discusser for his interest in the study of Perumal et al. (2017) and welcome the opportunity to address the issues raised by the discusser. The discusser has mainly raised four issues on the comparative study carried out by Perumal et al. (2017) in evaluating the performances of the VPMM model and the NLM based models, which was initiated by Gill (1977Gill ( , 1978. These four issues are addressed by these writers in the following pages:As a first issue, the discusser has raised a question about the appropriateness of using the VPMM model (Perumal and Price, 2013), which he considers as the much improved routing model of the Muskingum-Cunge family approach, and the original nonlinear Muskingum model of Gill (1978), which he, perhaps, considers as a initial version of the NLM models. These writers perceive that the discusser intends to convey that the performance evaluation study presented by Perumal et al. (2017) based on a latest improved model and a initial version of the NLM models is inappropriate. Before discussing straightaway on this issue, the writer would like to clarify on the misconception of the discusser in categorizing the VPMM method and the Muskingum-Cunge method under one family approach.In developing the storage equation of the classical Muskingum method, McCarthy (1938) used the heuristic assumption that the storage of the routing reach can be considered to consist of a combination of prism and wedge storages resulting in the storage equation expressed in terms of linear weighted discharge of inflow and outflow of the reach. However, Cunge (1969) interpreted the Muskingum model by discarding the heuristic assumption employed by McCarthy (1938) for describing the storage equation as discussed above, and argued that the Muskingum model developed based on a one-to-one relationship between stage and discharge in a channel reach is not theoretically capable of exhibiting attenuation, but attributed the attenuation exhibited by it to the numerical diffusion of its routing equation. To quote herein in words of Cunge (1969):

show abstract

Deterministic Methods in Systems Hydrology

Cited by 6 publications

References 0 publications

On-resonance material fast light

On-resonance material fast light

Slow light in saturable absorbers: Progress in the resolution of a controversy

Reply to comment on “Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods” by Reza Barati

Contact Info

Product

Resources

About