On independent degrees of freedom of turbulent mixing: The one-dimensional formulation

2021 ◽  
Vol 33 (10) ◽  
pp. 105125
Author(s):  
Sotiris Kioroglou
Keyword(s):  
Turbulent Mixing ◽  
Degrees Of Freedom ◽  
One Dimensional ◽  
The One

scholarly journals Analysis of one-dimensional models for exchange flows under strong stratification

2019 ◽  
Vol 70 (1) ◽  
pp. 41-56
Author(s):  
Steven J. Kaptein ◽  
Koen J. van de Wal ◽  
Leon P. J. Kamp ◽  
Vincenzo Armenio ◽  
Herman J. H. Clercx ◽  
...  
Keyword(s):  
Density Gradient ◽  
Turbulent Mixing ◽  
Schmidt Number ◽  
Density Gradients ◽  
One Dimensional ◽  
Exchange Flows ◽  
Dimensional Models ◽  
The One ◽  
Horizontal Density Gradient ◽  
Classical Constant

AbstractOne-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Reg, the Schmidt number Sc, and the aspect ratio of the channel Γ. For small values of RegΓ, when diffusion dominates, all models perform well. However, as RegΓ increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.

scholarly journals Channelization of plumes beneath ice shelves

2015 ◽  
Vol 785 ◽  
pp. 109-134 ◽  
Author(s):  
M. C. Dallaston ◽  
I. J. Hewitt ◽  
A. J. Wells
Keyword(s):  
Turbulent Mixing ◽  
Simplified Model ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ice Shelves ◽  
Narrow Channels ◽  
One Dimensional ◽  
Grounding Line ◽  
The One

We study a simplified model of ice–ocean interaction beneath a floating ice shelf, and investigate the possibility for channels to form in the ice shelf base due to spatial variations in conditions at the grounding line. The model combines an extensional thin-film description of viscous ice flow in the shelf, with melting at its base driven by a turbulent ocean plume. Small transverse perturbations to the one-dimensional steady state are considered, driven either by ice thickness or subglacial discharge variations across the grounding line. Either forcing leads to the growth of channels downstream, with melting driven by locally enhanced ocean velocities, and thus heat transfer. Narrow channels are smoothed out due to turbulent mixing in the ocean plume, leading to a preferred wavelength for channel growth. In the absence of perturbations at the grounding line, linear stability analysis suggests that the one-dimensional state is stable to initial perturbations, chiefly due to the background ice advection.

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

Static and energy dependent nucleus–nucleus potential for description of near and sub-barrier fusion data

2015 ◽  
Vol 93 (11) ◽  
pp. 1343-1351 ◽  
Author(s):  
Manjeet Singh Gautam
Keyword(s):  
Degrees Of Freedom ◽  
Saxon Potential ◽  
Model Calculations ◽  
One Dimensional ◽  
A Value ◽  
Fusion Data ◽  
The One ◽  
Energy Dependent ◽  
Coupled Channel

This article analyzes the validity of static Woods–Saxon potential and the energy-dependent Woods–Saxon potential (EDWSP) to explore the specific features of fusion dynamics of [Formula: see text] and [Formula: see text] systems. The intrinsic degrees of freedom, such as inelastic surface excitations, play a crucial role in the enhancement of sub-barrier fusion excitation functions over the expectations of the one-dimensional barrier penetration model. Role of dominant intrinsic degrees of freedom of collision partners are entertained within the context of coupled channel calculations. Furthermore, the one-dimensional Wong formula using static Woods–Saxon potential fails miserably to describe the fusion enhancement of [Formula: see text] and [Formula: see text] systems. However, the Wong formula along with the EDWSP model accurately explains the observed fusion enhancement of [Formula: see text] reactions. In the fusion of [Formula: see text] reaction, the above-barrier fusion data are suppressed by a factor of 0.66 with reference to the EDWSP model calculations while the below-barrier fusion data are adequately addressed by the EDWSP model and the coupled channel calculations. Therefore, the coupled channel calculations and the EDWSP model calculations reasonably describe the observed fusion mechanism of [Formula: see text] and [Formula: see text] reactions. This suggests that the energy dependence in the Woods–Saxon potential model introduces similar kinds of barrier modification effects (barrier height, barrier position, and barrier curvature) as reflected from the coupled channel calculations. In the EDWSP model calculations, significantly larger values of diffuseness ranging from a = 0.86 to 0.94 fm, which is much larger than a value extracted from the elastic scattering analysis, are needed to address the sub-barrier fusion data.

scholarly journals One-Dimensional Alternating Extended Hubbard Model at Quarter-Filling and Its Applications to Structural Instabilities of Organic Conductors

Crystals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 942
Author(s):  
M. Ménard ◽  
C. Bourbonnais
Keyword(s):  
Hubbard Model ◽  
Degrees Of Freedom ◽  
Organic Conductors ◽  
Group Method ◽  
Extended Hubbard Model ◽  
Bechgaard Salts ◽  
One Dimensional ◽  
Ordered Alloys ◽  
The One ◽  
Structural Instabilities

The one-dimensional extended Hubbard model with lattice dimerization and alternated site potentials is analyzed using the renormalization group method. The coupling of electrons to structural degrees of freedom such as the anion lattice and acoustic phonons is investigated to obtain the possible instabilities against the formation of lattice superstructures. Applications of the theory to anionic and spin-Peierls instabilities in the Fabre and Bechgaard salts series of organic conductors and ordered alloys are presented and discussed.

LOW-LYING EXCITATIONS IN SPIN-PEIERLS SYSTEM WITH QUANTUM LATTICE DYNAMICAL EFFECT

2006 ◽  
Vol 20 (09) ◽  
pp. 1037-1048
Author(s):  
JING XU ◽  
ZHI-GUO WANG ◽  
YUN-LONG SHI ◽  
YU-GUANG CHEN ◽  
HONG CHEN
Keyword(s):  
Excitation Spectrum ◽  
Degrees Of Freedom ◽  
Chain Model ◽  
Heisenberg Chain ◽  
Phonon Coupling ◽  
Quantum Lattice ◽  
One Dimensional ◽  
The One ◽  
Magnon Excitation ◽  
The Continuum

In the continuum limit, we map a Heisenberg chain model, in which the spins are explicitly coupled to the lattice degrees of freedom, to one-dimensional quantum sine-Gorden model, and obtain the phase diagram and excitation spectrum of the system. The effect of quantum lattice fluctuation on the ground-state properties of the system is discussed in detail. The results show that a quantum phase transition from a gapless state to gapped dimerized phase occurs at nonzero value of the spin-phonon coupling. Moreover, our results indicate that the two-magnon excitation spectrum is more sensitive to the spin-phonon coupling than the one-magnon excitation spectrum.

GROUND-STATE PROPERTIES AND ELEMENTARY EXCITATIONS OF THE ONE-DIMENSIONAL HUBBARD MODEL

1988 ◽  
Vol 02 (05) ◽  
pp. 1013-1019 ◽  
Author(s):  
J. Carmelo ◽  
D. Baeriswyl
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Distribution Functions ◽  
Electron Hole ◽  
Elementary Excitations ◽  
One Dimensional ◽  
Fermion Systems ◽  
Weakly Coupled ◽  
Bethe Ansatz Solution ◽  
The One

The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.

Electronic Systems

2019 ◽  
pp. 585-630
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Degrees Of Freedom ◽  
Electronic Systems ◽  
One Dimensional ◽  
Kondo Resonance ◽  
Nested Bethe Ansatz ◽  
Component Systems ◽  
Metallic Ring ◽  
The One ◽  
Internal Degrees Of Freedom

The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ‎-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.

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