scholarly journals On regular and random two-dimensional packing of crosses

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ralf Stannarius ◽  
Jonas Schulze
Keyword(s):  
Correlation Functions ◽  
Short Range ◽  
Orientational Order ◽  
Simple Relation ◽  
Random Packing ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Packing Problems ◽  
Aspect Ratios ◽  
Local Correlations

AbstractPacking problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packing structures are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. There is no simple relation between the geometries of the crosses and the peaks in the spatial correlation functions, but some features of the orientational correlations can be traced to typical local configurations.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Antiferromagnetic Short Range Order in a Two-Dimensional Manganite Exhibiting Giant Magnetoresistance

1997 ◽  
Vol 78 (16) ◽  
pp. 3197-3200 ◽  
Author(s):  
T. G. Perring ◽  
G. Aeppli ◽  
Y. Moritomo ◽  
Y. Tokura
Keyword(s):  
Short Range ◽  
Giant Magnetoresistance ◽  
Short Range Order ◽  
Range Order ◽  
Two Dimensional

scholarly journals CFD Analysis of Urban Canopy Flows Employing the V2F Model: Impact of Different Aspect Ratios and Relative Heights

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Fabio Nardecchia ◽  
Annalisa Di Bernardino ◽  
Francesca Pagliaro ◽  
Paolo Monti ◽  
Giovanni Leuzzi ◽  
...  
Keyword(s):  
Flow Field ◽  
Water Channel ◽  
Flow Regimes ◽  
Two Dimensional ◽  
Mean Flow ◽  
Ansys Fluent ◽  
Practical Applications ◽  
Aspect Ratios ◽  
Starting Point ◽  
Step Down

Computational fluid dynamics (CFD) is currently used in the environmental field to simulate flow and dispersion of pollutants around buildings. However, the closure assumptions of the turbulence usually employed in CFD codes are not always physically based and adequate for all the flow regimes relating to practical applications. The starting point of this work is the performance assessment of the V2F (i.e., v2¯ − f) model implemented in Ansys Fluent for simulating the flow field in an idealized array of two-dimensional canyons. The V2F model has been used in the past to predict low-speed and wall-bounded flows, but it has never been used to simulate airflows in urban street canyons. The numerical results are validated against experimental data collected in the water channel and compared with other turbulence models incorporated in Ansys Fluent (i.e., variations of both k-ε and k-ω models and the Reynolds stress model). The results show that the V2F model provides the best prediction of the flow field for two flow regimes commonly found in urban canopies. The V2F model is also employed to quantify the air-exchange rate (ACH) for a series of two-dimensional building arrangements, such as step-up and step-down configurations, having different aspect ratios and relative heights of the buildings. The results show a clear dependence of the ACH on the latter two parameters and highlight the role played by the turbulence in the exchange of air mass, particularly important for the step-down configurations, when the ventilation associated with the mean flow is generally poor.

Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Glass Transition ◽  
Intermediate Phase ◽  
Orientational Order ◽  
Finite Size ◽  
Two Dimensions ◽  
Size Difference ◽  
Two Dimensional ◽  
Atomic Size ◽  
Bond Orientational Order ◽  
Dynamics Simulations

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

scholarly journals Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

2018 ◽  
Vol 173 ◽  
pp. 06008 ◽  
Author(s):  
Eugene A. Koval ◽  
Oksana A. Koval
Keyword(s):  
Cross Section ◽  
Short Range ◽  
Strong Dependence ◽  
Dipolar Interaction ◽  
Two Dimensional ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Interaction Radius ◽  
Ultracold Polar Molecules ◽  
Spatial Dimensions

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

Spin–Spin Correlations in Site Disordered ±J 2D Ising Spin Glasses

1998 ◽  
Vol 09 (05) ◽  
pp. 685-691
Author(s):  
B. Kawecka-Magiera ◽  
A. Z. Maksymowicz ◽  
M. Kowal ◽  
K. Kulakowski
Keyword(s):  
Correlation Functions ◽  
Spin Glasses ◽  
Interatomic Distance ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Spin Correlations ◽  
Ising Spin ◽  
Bond System ◽  
Random Site

Spin–spin correlation functions <S(0)S(R)> as dependent on interatomic distance R are studied in the random-site two-dimensional Ising S=1/2 ±J system. Oscillations of the correlation functions are found, which is not a case in the random-bond system.

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