scholarly journals Reduced Models of Point Vortex Systems

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 914 ◽  
Author(s):  
Jonathan Maack ◽  
Bruce Turkington
Keyword(s):  
Optimal Path ◽  
Point Vortex ◽  
Single Layer ◽  
Coarse Grained ◽  
Two Dimensional ◽  
Predictive Capacity ◽  
Reduced Models ◽  
Spatial Moments ◽  
Geostrophic Turbulence ◽  
Vortex Systems

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler equations, as well as the quasi-geostrophic equations for either single-layer or two-layer flows. Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. In the case of point vortex ensembles, the macroscopic variables describe the spatially coarse-grained vorticity. Dynamical closure in terms of those macrostates is obtained by optimizing over paths in the parameter space of the reduced model subject to the constraints imposed by conserved quantities. This optimization minimizes a cost functional that quantifies the rate of information loss due to model reduction, meaning that an optimal path represents a macroscopic evolution that is most compatible with the microscopic dynamics in an information-theoretic sense. A near-equilibrium linearization of this method is used to derive dissipative equations for the low-order spatial moments of ensembles of point vortices in the plane. These severely reduced models describe the late-stage evolution of isolated coherent structures in two-dimensional and geostrophic turbulence. For single-layer dynamics, they approximate the relaxation of initially distorted structures toward axisymmetric equilibrium states. For two-layer dynamics, they predict the rate of energy transfer in baroclinically perturbed structures returning to stable barotropic states. Comparisons against direct numerical simulations of the fully-resolved many-vortex dynamics validate the predictive capacity of these reduced models.

Geostrophic Turbulence

1998 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Large Scale ◽  
Bottom Topography ◽  
Single Layer ◽  
Two Dimensional ◽  
Homogeneous Fluid ◽  
Coriolis Parameter ◽  
Strongly Nonlinear ◽  
Geostrophic Turbulence ◽  
Large Scale Flow ◽  
Quasigeostrophic Equations

Strongly nonlinear, rapidly rotating, stably stratified flow is called geostrophic turbulence. This subject, which blends ideas from chapters 2,4, and 5, is relevant to the large-scale flow in the Earth’s oceans and atmosphere. The quasigeostrophic equations form the basis of the study of geostrophic turbulence. We view the quasigeostrophic equations as a generalization of the vorticity equation for two-dimensional turbulence to include the important effects of stratification, bottom topography, and varying Coriolis parameter. Thus the theory of geostrophic turbulence represents an extension of the theory of two dimensional turbulence. However, its richer physics and greater applicability to real geophysical flows make geostrophic turbulence a much more interesting and important subject. This chapter offers a very brief introduction to the theory of geostrophic turbulence. We illustrate the principal ideas by separately considering the effects of bottom topography, varying Coriolis parameter, and density stratification on highly nonlinear, quasigeostrophic flow. We make no attempt at a comprehensive review. In every case, the theory of geostrophic turbulence relies almost solely on two now-familiar components: a conservation principle that energy and potential vorticity are (nearly) conserved and an irreversibility principle in the form of an appealing assumption that breaks the time-reversal symmetry of the exact (inviscid) dynamics. This irreversibility assumption takes a great many superficially dissimilar forms, fostering the misleading impression of a great many competing explanations for the same phenomena. However, broadminded analysis inevitably reveals that these competing explanations are virtually equivalent. We begin by considering the quasigeostrophic flow of a single layer of homogeneous fluid over a bumpy bottom. No case better illustrates how diverse forms of the irreversibility principle lead to the same conclusions.

scholarly journals Homogeneous 2D and 3D alignment of cardiomyocyte in dilated cardiomyopathy revealed by intravital heart imaging

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kiyoshi Masuyama ◽  
Tomoaki Higo ◽  
Jong-Kook Lee ◽  
Ryohei Matsuura ◽  
Ian Jones ◽  
...  
Keyword(s):  
Heart Failure ◽  
Dilated Cardiomyopathy ◽  
Cardiac Dysfunction ◽  
Three Dimensional ◽  
Single Layer ◽  
Specific Pattern ◽  
Two Dimensional ◽  
Heart Imaging ◽  
Novel Method ◽  
2D And 3D

AbstractIn contrast to hypertrophic cardiomyopathy, there has been reported no specific pattern of cardiomyocyte array in dilated cardiomyopathy (DCM), partially because lack of alignment assessment in a three-dimensional (3D) manner. Here we have established a novel method to evaluate cardiomyocyte alignment in 3D using intravital heart imaging and demonstrated homogeneous alignment in DCM mice. Whilst cardiomyocytes of control mice changed their alignment by every layer in 3D and position twistedly even in a single layer, termed myocyte twist, cardiomyocytes of DCM mice aligned homogeneously both in two-dimensional (2D) and in 3D and lost myocyte twist. Manipulation of cultured cardiomyocyte toward homogeneously aligned increased their contractility, suggesting that homogeneous alignment in DCM mice is due to a sort of alignment remodelling as a way to compensate cardiac dysfunction. Our findings provide the first intravital evidence of cardiomyocyte alignment and will bring new insights into understanding the mechanism of heart failure.

A simple point vortex model for two‐dimensional decaying turbulence

1992 ◽  
Vol 4 (5) ◽  
pp. 1036-1039 ◽  
Author(s):  
R. Benzi ◽  
M. Colella ◽  
M. Briscolini ◽  
P. Santangelo
Keyword(s):  
Point Vortex ◽  
Two Dimensional ◽  
Simple Point ◽  
Vortex Model ◽  
Decaying Turbulence ◽  
Point Vortex Model

First principles studies on electronic and contact properties of Single layer 2H-MoS2/1T'-MX2 heterojunctions

2022 ◽  
Author(s):  
Jiao Yu ◽  
Caijuan Xia ◽  
Zhengyang Hu ◽  
jianping Sun ◽  
Xiaopeng Hao ◽  
...  
Keyword(s):  
Transition Metal ◽  
First Principles ◽  
Field Effect ◽  
Field Effect Transistors ◽  
Single Layer ◽  
Metal Chalcogenides ◽  
Two Dimensional ◽  
Transition Metal Chalcogenides

With in-plane heterojunction contacts between semiconducting 2H phase (as channel) and the metallic 1T' phase (as electrode), the two-dimensional (2D) transition metal chalcogenides (TMDs) field-effect transistors (FETs) have received much...

Controllable Fabrication and Photocatalytic Performance of Nanoscale Single-layer MoSe2 with Substantial Edges on Ag(111)

Nanoscale ◽  
2021 ◽  
Author(s):  
Jianchen Lu ◽  
Gefei Niu ◽  
Xiao Ren ◽  
De-Liang Bao ◽  
Hui Chen ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Transition Metal ◽  
Photocatalytic Performance ◽  
Transition Metal Dichalcogenides ◽  
Single Layer ◽  
Two Dimensional ◽  
Metal Dichalcogenides ◽  
Controllable Fabrication

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are emerging as new electrocatalysts and photocatalysts, in which edge sites of 2D TMDs are highly catalytic activity and are thus favored at the...

scholarly journals A structure hierarchy for silicate minerals: sheet silicates

2018 ◽  
Vol 83 (1) ◽  
pp. 3-55 ◽  
Author(s):  
Frank C. Hawthorne ◽  
Yulia A. Uvarova ◽  
Elena Sokolova
Keyword(s):  
Double Layer ◽  
Structural Connectivity ◽  
Single Layer ◽  
Common Species ◽  
Two Dimensional ◽  
Structural Units ◽  
Coordination Polyhedra ◽  
Silicate Minerals ◽  
Sheet Silicates ◽  
Sheet Silicate

AbstractThe structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerisation of coordination polyhedra of higher bond-valence. A hierarchical structural classification is developed for sheet-silicate minerals based on the connectedness of the two-dimensional polymerisations of (TO4) tetrahedra, where T = Si4+ plus As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Two-dimensional nets and oikodoméic operations are used to generate the silicate (sensu lato) structural units of single-layer, double-layer and higher-layer sheet-silicate minerals, and the interstitial complexes (cation identity, coordination number and ligancy, and the types and amounts of interstitial (H2O) groups) are recorded. Key aspects of the silicate structural unit include: (1) the type of plane net on which the sheet (or parent sheet) is based; (2) the u (up) and d (down) directions of the constituent tetrahedra relative to the plane of the sheet; (3) the planar or folded nature of the sheet; (4) the layer multiplicity of the sheet (single, double or higher); and (5) the details of the oikodoméic operations for multiple-layer sheets. Simple 3-connected plane nets (such as 63, 4.82 and 4.6.12) have the stoichiometry (T2O5)n (Si:O = 1:2.5) and are the basis of most of the common rock-forming sheet-silicate minerals as well as many less-common species. Oikodoméic operations, e.g. insertion of 2- or 4-connected vertices into 3-connected plane nets, formation of double-layer sheet-structures by (topological) reflection or rotation operations, affect the connectedness of the resulting sheets and lead to both positive and negative deviations from Si:O = 1:2.5 stoichiometry. Following description of the structural units in all sheet-silicate minerals, the minerals are arranged into decreasing Si:O ratio from 3.0 to 2.0, an arrangement that reflects their increasing structural connectivity. Considering the silicate component of minerals, the range of composition of the sheet silicates completely overlaps the compositional ranges of framework silicates and most of the chain-ribbon-tube silicates.

scholarly journals Stone–Wales defects preserve hyperuniformity in amorphous two-dimensional networks

2021 ◽  
Vol 118 (3) ◽  
pp. e2016862118
Author(s):  
Duyu Chen ◽  
Yu Zheng ◽  
Lei Liu ◽  
Ge Zhang ◽  
Mohan Chen ◽  
...  
Keyword(s):  
2D Materials ◽  
Single Layer ◽  
Salient Feature ◽  
Density Fluctuations ◽  
Wave Number ◽  
Static Structure Factor ◽  
Two Dimensional ◽  
Static Structure ◽  
Topological Transformation ◽  
Amorphous Graphene

Disordered hyperuniformity (DHU) is a recently discovered novel state of many-body systems that possesses vanishing normalized infinite-wavelength density fluctuations similar to a perfect crystal and an amorphous structure like a liquid or glass. Here, we discover a hyperuniformity-preserving topological transformation in two-dimensional (2D) network structures that involves continuous introduction of Stone–Wales (SW) defects. Specifically, the static structure factor S(k) of the resulting defected networks possesses the scaling S(k)∼kα for small wave number k, where 1≤α(p)≤2 monotonically decreases as the SW defect concentration p increases, reaches α≈1 at p≈0.12, and remains almost flat beyond this p. Our findings have important implications for amorphous 2D materials since the SW defects are well known to capture the salient feature of disorder in these materials. Verified by recently synthesized single-layer amorphous graphene, our network models reveal unique electronic transport mechanisms and mechanical behaviors associated with distinct classes of disorder in 2D materials.

scholarly journals Graphene-Based Nanosystems: Versatile Nanotools for Theranostics and Bioremediation

2021 ◽  
Author(s):  
Marlene Lúcio ◽  
Eduarda Fernandes ◽  
Hugo Gonçalves ◽  
Sofia Machado ◽  
Andreia C. Gomes ◽  
...  
Keyword(s):  
Biomedical Applications ◽  
Quantum Physics ◽  
Single Layer ◽  
The Body ◽  
Diagnostic Tools ◽  
Honeycomb Lattice ◽  
Two Dimensional ◽  
Advantages And Disadvantages ◽  
Broad Variety ◽  
Imaging Strategy

Since its revolutionary discovery in 2004, graphene— a two-dimensional (2D) nanomaterial consisting of single-layer carbon atoms packed in a honeycomb lattice— was thoroughly discussed for a broad variety of applications including quantum physics, nanoelectronics, energy efficiency, and catalysis. Graphene and graphene-based nanomaterials (GBNs) have also captivated the interest of researchers for innovative biomedical applications since the first publication on the use of graphene as a nanocarrier for the delivery of anticancer drugs in 2008. Today, GBNs have evolved into hybrid combinations of graphene and other elements (e.g., drugs or other bioactive compounds, polymers, lipids, and nanoparticles). In the context of developing theranostic (therapeutic + diagnostic) tools, which combine multiple therapies with imaging strategies to track the distribution of therapeutic agents in the body, the multipurpose character of the GBNs hybrid systems has been further explored. Because each therapy and imaging strategy has inherent advantages and disadvantages, a mixture of complementary strategies is interesting as it will result in a synergistic theranostic effect. The flexibility of GBNs cannot be limited to their biomedical applications and, these nanosystems emerge as a viable choice for an indirect effect on health by their future use as environmental cleaners. Indeed, GBNs can be used in bioremediation approaches alone or combined with other techniques such as phytoremediation. In summary, without ignoring the difficulties that GBNs still present before being deemed translatable to clinical and environmental applications, the purpose of this chapter is to provide an overview of the remarkable potential of GBNs on health by presenting examples of their versatility as nanotools for theranostics and bioremediation.

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

Sign in / Sign up

Export Citation Format

Share Document