The HYDROP experiment: an empirical method for the determination of the continuum limit in rain

2001 ◽  
Vol 59-60 ◽  
pp. 163-197 ◽  
Author(s):  
Nicolas Desaulniers-Soucy ◽  
Shaun Lovejoy ◽  
Daniel Schertzer
Keyword(s):  
Continuum Limit ◽  
Empirical Method ◽  
The Continuum

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Coupled dynamics of populations supported by discrete sites and their continuum limit

2010 ◽  
Vol 466 (2121) ◽  
pp. 2561-2586 ◽  
Author(s):  
Timothy R. Field ◽  
Robert J. A. Tough
Keyword(s):  
Evolution Equation ◽  
Closed Form ◽  
Generating Function ◽  
Rate Equation ◽  
Continuum Limit ◽  
Infinite Chain ◽  
Migration Process ◽  
The Mean ◽  
The Continuum ◽  
Birth Death

The illumination of single population behaviour subject to the processes of birth, death and immigration has provided a basis for the discussion of the non-Gaussian statistical and temporal correlation properties of scattered radiation. As a first step towards the modelling of its spatial correlations, we consider the populations supported by an infinite chain of discrete sites, each subject to birth, death and immigration and coupled by migration between adjacent sites. To provide some motivation, and illustrate the techniques we will use, the migration process for a single particle on an infinite chain of sites is introduced and its diffusion dynamics derived. A certain continuum limit is identified and its properties studied via asymptotic analysis. This forms the basis of the multi-particle model of a coupled population subject to single site birth, death and immigration processes, in addition to inter-site migration. A discrete rate equation is formulated and its generating function dynamics derived. This facilitates derivation of the equations of motion for the first- and second-order cumulants, thus generalizing the earlier results of Bailey through the incorporation of immigration at each site. We present a novel matrix formalism operating in the time domain that enables solution of these equations yielding the mean occupancy and inter-site variances in the closed form. The results for the first two moments at a single time are used to derive expressions for the asymptotic time-delayed correlation functions, which relates to Glauber’s analysis of an Ising model. The paper concludes with an analysis of the continuum limit of the birth–death–immigration–migration process in terms of a path integral formalism. The continuum rate equation and evolution equation for the generating function are developed, from which the evolution equation of the mean occupancy is derived, in this limit. Its solution is provided in closed form.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

scholarly journals Lithium Observations in the Sun

1968 ◽  
Vol 1 ◽  
pp. 243-246
Author(s):  
Edith A. Müller
Keyword(s):  
Unknown Origin ◽  
Absorption Feature ◽  
The Sun ◽  
Degree Of Ionization ◽  
Lithium Abundance ◽  
Resonance Doublet ◽  
Lower Temperature ◽  
Central Depth ◽  
The Continuum

The determination of the lithium abundance in the solar atmosphere is essentially based on the LiI resonance doublet at λ 6707·761 and 6707·912 Å. These two lines form a very faint absorption feature, the central depth of the stronger component being of the order of 1% of the continuum. The violet component, which is also the stronger of the two, occurs near the red wing of a faint solar line of unknown origin, and the lines appear to be blended with other faint lines including possibly the doublet of the Li6 isotope (the isotopic shift being 0·160 Å). No other line of LiI has been detected in the Fraunhofer spectum of the undisturbed solar disk. This is nothing surprising, because practically all lithium is expected to be ionized in the photosphere on account of its low ionization potential (Xion = 5·37 e.v.). In sunspot spectra the lower temperature reduces the degree of ionization of lithium and causes a strengthening of the LiI lines. In fact, the LiI resonance lines which appear as a very faint absorption feature on disk spectra are about 50 times stronger in spot spectra. Furthermore, the very weak feature at λ 6103·6 Å was identified by Dubov (1964) and by Schmahl and Schröter (1965) as due to the 2s 2S–3d 2D transition of LiI. Both the resonance doublet and the faint feature at 6103·6 Å have been used by the above-mentioned authors to derive the lithium abundance in spots.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

scholarly journals The Empirical and Theoretical Miscible Characterization Method in Gas-Enhanced Oil Recovery

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wang Chengjun ◽  
Li Xiaorui
Keyword(s):  
Oil Recovery ◽  
Research Result ◽  
Empirical Method ◽  
Reservoir Engineering ◽  
Forecasting Accuracy ◽  
Factors Affecting ◽  
Development Scheme ◽  
Gas Flooding ◽  
New Ideas

The determination of miscible characteristic is one of the key technologies for enhancing oil recovery of gas flooding. If the miscible characteristic at each development period of gas flooding can be known in real time, it will be helpful to guide gas flooding development scheme. The minimum miscible pressure (MMP) is mostly used to describe miscible characteristic. Currently, the MMP forecasting methods can be classified into two categories—the empirical method and theoretical calculation method. In this paper, the main controlling factors affecting MMP are analyzed combined with reservoir engineering method, phase equilibrium theory, reservoir numerical simulation technology, and so on. Based on this, new empirical and theoretical MMP forecasting model was built. Meanwhile, new ideas for improving forecasting accuracy through modifying miscible criterion were proposed. The calculation accuracies of the two MMP forecasting models can be improved to over 90% that is more accurate and adapted than other methods. This research result can supply new ideas for gas flooding MMP forecasting.

High-resolution spectroscopy near the continuum limit: the microwave spectrum of trans-3-bromo-1,1,1,2,2-pentafluoropropane

2018 ◽  
Vol 117 (9-12) ◽  
pp. 1351-1359 ◽  
Author(s):  
Frank E. Marshall ◽  
Nicole Moon ◽  
Thomas D. Persinger ◽  
David J. Gillcrist ◽  
Nelson E. Shreve ◽  
...  
Keyword(s):  
High Resolution ◽  
Continuum Limit ◽  
Microwave Spectrum ◽  
High Resolution Spectroscopy ◽  
The Continuum

scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

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