Experimental observation of the geostrophic turbulence regime of rapidly rotating convection

2021 ◽  
Vol 118 (44) ◽  
pp. e2105015118
Author(s):  
Vincent Bouillaut ◽  
Benjamin Miquel ◽  
Keith Julien ◽  
Sébastien Aumaître ◽  
Basile Gallet
Keyword(s):  
Heat Transport ◽  
Scaling Law ◽  
Quantitative Agreement ◽  
Scaling Exponent ◽  
Magnetic Field Generation ◽  
Rotating Convection ◽  
Turbulence Regime ◽  
Dynamical Regimes ◽  
Geostrophic Turbulence ◽  
The One

The competition between turbulent convection and global rotation in planetary and stellar interiors governs the transport of heat and tracers, as well as magnetic field generation. These objects operate in dynamical regimes ranging from weakly rotating convection to the “geostrophic turbulence” regime of rapidly rotating convection. However, the latter regime has remained elusive in the laboratory, despite a worldwide effort to design ever-taller rotating convection cells over the last decade. Building on a recent experimental approach where convection is driven radiatively, we report heat transport measurements in quantitative agreement with this scaling regime, the experimental scaling law being validated against direct numerical simulations (DNS) of the idealized setup. The scaling exponent from both experiments and DNS agrees well with the geostrophic turbulence prediction. The prefactor of the scaling law is greater than the one diagnosed in previous idealized numerical studies, pointing to an unexpected sensitivity of the heat transport efficiency to the precise distribution of heat sources and sinks, which greatly varies from planets to stars.

scholarly journals Rigorous bounds on the heat transport of rotating convection with Ekman pumping

2020 ◽  
Vol 61 (2) ◽  
pp. 023101
Author(s):  
B. Pachev ◽  
J. P. Whitehead ◽  
G. Fantuzzi ◽  
I. Grooms
Keyword(s):  
Heat Transport ◽  
Ekman Pumping ◽  
Rotating Convection ◽  
Rigorous Bounds

REACTION-FRONT DYNAMICS IN A+B→C WITH INITIALLY-SEPARATED REACTANTS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 405-415 ◽  
Author(s):  
S. HAVLIN ◽  
M. ARAUJO ◽  
H. LARRALDE ◽  
A. SHEHTER ◽  
H.E. STANLEY
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction System ◽  
Diffusion Reaction ◽  
Dimensional System ◽  
Scaling Exponent ◽  
One Dimensional ◽  
Recent Developments ◽  
The One ◽  
Front Dynamics

We review recent developments in the study of the diffusion reaction system of the type A+B→C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x>0 and x<0 respectively. We find that whereas for d≥2 a single scaling exponent characterizes the width of the reaction zone, a multiscaling approach is needed to describe the one-dimensional system. We also present analytical and numerical results for the reaction rate on fractals and percolation systems.

scholarly journals Scaling properties of gravity-driven sediments

1995 ◽  
Vol 2 (3/4) ◽  
pp. 178-185 ◽  
Author(s):  
D. H. Rothman ◽  
J. P. Grotzinger
Keyword(s):  
Critical Thickness ◽  
Sedimentary Basin ◽  
Scaling Law ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Scaling Properties ◽  
Number Of Layers ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
Open Question

Abstract. Recent field observations of the statistical distribution of turbidite and debris flow deposits are discussed. In some cases one finds a good fit over 1.5-2 orders of magnitude to the scaling law N(h) α h-B, where N(h) is the number of layers thicker than h. Observations show that the scaling exponent B varies widely from deposit to deposit, ranging from about 1/2 to 2. Moreover, one case is characterized by a sharp crossover in which B increases by a factor of two as h increases past a critical thickness. We propose that the variations in B, either regional or within the same deposit, are indicative of the geometry of the sedimentary basin and the rheological properties of the original gravity-driven flow. The origin of the power-law distribution remains an open question.

scholarly journals Universal evaporation dynamics of ordered arrays of sessile droplets

2019 ◽  
Vol 866 ◽  
pp. 61-81 ◽  
Author(s):  
Sandeep Hatte ◽  
Keshav Pandey ◽  
Khushboo Pandey ◽  
Suman Chakraborty ◽  
Saptarshi Basu
Keyword(s):  
Near Field ◽  
Scaling Law ◽  
Present Theory ◽  
Solid Substrate ◽  
Local Concentration ◽  
Sessile Droplet ◽  
Droplet Array ◽  
Ordered Array ◽  
The One ◽  
Evaporation Dynamics

Manipulation of an array of surface droplets organised in an ordered structure turns out to be of immense consequence in a wide variety of applications ranging from photonics, near field imaging and inkjet printing on the one hand to bio-molecular analysis and DNA sequencing on the other. While evaporation of a single isolated sessile droplet has been well studied, the collective evaporative dynamics of an ordered array of droplets on a solid substrate remains elusive. Physically, the closed region between the centre and side droplets in the ordered array reduces the mobility of the diffusing vapour, resulting in its accumulation along with enhanced local concentration and a consequent increment in the lifetime of the centre droplet. Here, we present a theoretical model to account for evaporation lifetime scaling in closely placed ordered linear droplet arrays. In addition, the present theory predicts the limiting cases of droplet interaction; namely, critical droplet separation for which interfacial interaction ceases to exist and minimum possible droplet separation (droplets on the verge of coalescence) for which the droplet system achieves maximum lifetime scaling. Further experimental evidence demonstrates the applicability of the present scaling theory to extended dimensions of the droplet array, generalising our physical conjecture. It is also worth noting that the theoretical time scale is applicable across a wide variety of drop–substrate combinations and initial droplet volumes. We also highlight that the scaling law proposed here can be extended seamlessly to other forms of confinement such as an evaporating droplet inside a mini-channel, as encountered in countless applications ranging from biomedical engineering to surface patterning.

scholarly journals COMPLEX NETWORK ANALYSIS OF LITERARY AND SCIENTIFIC TEXTS

2012 ◽  
Vol 23 (07) ◽  
pp. 1250051 ◽  
Author(s):  
IWONA GRABSKA-GRADZIŃSKA ◽  
ANDRZEJ KULIG ◽  
JAROSŁAW KWAPIEŃ ◽  
STANISŁAW DROŻDŻ
Keyword(s):  
English Language ◽  
Quantitative Difference ◽  
Clustering Coefficient ◽  
Literary Texts ◽  
Scaling Exponent ◽  
Scientific Texts ◽  
Scale Free ◽  
Network Properties ◽  
The One ◽  
Zipf Law

We present results from our quantitative study of statistical and network properties of literary and scientific texts written in two languages: English and Polish. We show that Polish texts are described by the Zipf law with the scaling exponent smaller than the one for the English language. We also show that the scientific texts are typically characterized by the rank-frequency plots with relatively short range of power-law behavior as compared to the literary texts. We then transform the texts into their word-adjacency network representations and find another difference between the languages. For the majority of the literary texts in both languages, the corresponding networks revealed the scale-free structure, while this was not always the case for the scientific texts. However, all the network representations of texts were hierarchical. We do not observe any qualitative and quantitative difference between the languages. However, if we look at other network statistics like the clustering coefficient and the average shortest path length, the English texts occur to possess more clustered structure than do the Polish ones. This result was attributed to differences in grammar of both languages, which was also indicated in the Zipf plots. All the texts, however, show network structure that differs from any of the Watts–Strögatz, the Barabási–Albert, and the Erdös–Rényi architectures.

A neutron scattering study of spin dynamics in the one-dimensional paramagnet CsMnBr3

1984 ◽  
Vol 62 (11) ◽  
pp. 1132-1138 ◽  
Author(s):  
B. D. Gaulin ◽  
M. F. Collins
Keyword(s):  
Neutron Scattering ◽  
Spin Wave ◽  
Spin Dynamics ◽  
Quantitative Agreement ◽  
Generalized Langevin Equation ◽  
Heisenberg Antiferromagnet ◽  
One Dimensional ◽  
Truncation Scheme ◽  
Zone Centre ◽  
The One

CsMnBr3 is a quasi-one-dimensional Heisenberg antiferromagnet. We present results of the magnetic inelastic response of CsMnBr3 across the magnetic Brillouin zone by neutron scattering techniques. Well-defined spin-wave modes, characteristic of one-dimensional magnetic insulators, are found over most of the zone in the paramagnetic phase at 15 K. The zone centre response is not sharp, but peaks in the scattering function S(k, ω) are found. No excitation branch going to zero energy at zero wavevector is found. At small wavevectors there is a mode with energy 1.7 ± 0.2 meV and we use it to identify planar anisotropy in this system. The mid-zone response as a function of temperature is analyzed in terms of a generalized Langevin equation approach (Mori formulation) to the dynamics of the one-dimensional Heisenberg antiferromagnet. The theory contains no adjustable parameters. Our results are compared with two truncation schemes of the theory. We report qualitative agreement with the theories, including the observation of upwards renormalization of spin-wave energy with temperature. Quantitative agreement is less than good for either truncation scheme.

Nonlinear Field Theoretical Approaches to the Electron Density Amplitude Equation in Many-Electron Atoms and Molecules

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1693-1707 ◽  
Author(s):  
J. M. Dixon ◽  
J. A. Tuszyński ◽  
N. H. March
Keyword(s):  
Quantitative Agreement ◽  
Amplitude Equation ◽  
Classical Field ◽  
Nonlinear Field ◽  
Many Body ◽  
Energy Functionals ◽  
Theoretical Approaches ◽  
Physical Effects ◽  
The One ◽  
Made In

In this paper we have presented a comparison of the effective one-body potentials arising in Thomas–Fermi (TF) phenomenology and density function (DF) theories on the one hand and the Method of Coherent Structures (MCS) on the other. In spite of a number of assumptions made in TF and DF, particularly in connection with the exchange component of the potential, quantitative agreement has been found with the MCS. In addition we have drawn attention to several similarities in the associated energy functionals. The Saxon–Woods potential, used in diverse contexts of many-body physics, has been shown to satisfy a nonlinear differential equation which can be transformed into a equation of the class satisfied by the classical field equation in the MCS. This indicates, once more, that there are intricate connections between phenomenological approaches, which attempt to incorporate many-body physical effects, and the systematic and unifying development offered within the MCS.

scholarly journals Correlation Length in Concentrated Electrolytes: Insights from All-Atom Molecular Dynamics Simulations

2019 ◽  
Author(s):  
Samuel Coles ◽  
Chanbum Park ◽  
Rohit Nikam ◽  
Matej Kanduč ◽  
Joachim Dzubiella ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Correlation Length ◽  
Salt Concentration ◽  
Scaling Law ◽  
Solvent Mixture ◽  
Scaling Exponent ◽  
Concentrated Electrolytes ◽  
Theoretical Predictions ◽  
Dynamics Simulations

<div><p>We study the correlations length of the charge-charge pair correlations in concentrated electrolyte solutions by means of all-atom, explicit-solvent molecular dynamics simulations. We investigate LiCl and NaI in water, which constitute highly soluble, prototypical salts for experiments, as well as two more complex, molecular electrolyte systems of lithium bis(trifluoromethane)sulfonimide (LiTFSI), commonly employed in electrochemical storage systems, in water and in an organic solvent mixture of dimethoxyethane (DME) and dioxolane (DOL). Our simulations support the recent experimental observations as well as theoretical predictions of a non-monotonic behavior of the correlation length with increasing salt concentration. We observe a Debye-Hückel like regime at low concentration, followed by a minimum reached when <i>d/λ<sub>D</sub></i> = 1, where <i>λ<sub>D</sub></i> is the Debye correlation length and d the effective ionic diameter, and an increasing correlation length with salt concentration in very concentrated electrolytes. As in the experiments, we find that the screening length in the concentrated regime follows a universal scaling law as a function <i>d/λ<sub>D</sub></i> for all studied salts. However, the scaling exponent is significantly lower than the experimentally measured one, and lies in the range of the theoretical predictions based on much simpler electrolyte models.</p> </div>

scholarly journals Hydrogen Intramolecular Stretch Redshift in the Electrostatic Environment of Type II Clathrate Hydrates from Schrödinger Equation Treatment

2020 ◽  
Vol 10 (23) ◽  
pp. 8504
Author(s):  
Christian J. Burnham ◽  
Zdenek Futera ◽  
Zlatko Bacic ◽  
Niall J. English
Keyword(s):  
Molecular Dynamics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantitative Agreement ◽  
Type Ii ◽  
One Dimensional ◽  
Peak Splitting ◽  
Extended Type ◽  
Ab Initio Md ◽  
The One

The one-dimensional Schrödinger equation, applied to the H2 intramolecular stretch coordinate in singly to quadruply occupied large cages in extended Type II (sII) hydrogen clathrate hydrate, was solved numerically herein via potential-energy scans from classical molecular dynamics (MD), employing bespoke force-matched H2–water potential. For both occupation cases, the resultant H–H stretch spectra were redshifted by ~350 cm−1 vis-à-vis their classically sampled counterparts, yielding semi-quantitative agreement with experimental Raman spectra. In addition, ab initio MD was carried out systematically for different cage occupations in the extended sII hydrate to assess the effect of differing intra-cage intrinsic electric field milieux on H–H stretch frequencies; we suggest that spatial heterogeneity of the electrostatic environment is responsible for some degree of peak splitting.

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