Volumetric properties of solutions on the perspective of Voronoi tessellation

2021 ◽  
pp. 118173
Author(s):  
Evgenii D. Kadtsyn ◽  
Vladislav A. Nichiporenko ◽  
Nikolai N. Medvedev
2008 ◽  
Vol 59 (5) ◽  
Author(s):  
Viorel Feroiu ◽  
Dan Geana ◽  
Catinca Secuianu

Vapour � liquid equilibrium, thermodynamic and volumetric properties were predicted for three pure hydrofluorocarbons: difluoromethane (R32), pentafluoroethane (R125) and 1,1,1,2 � tetrafluoroethane (R134a) as well as for binary and ternary mixtures of these refrigerants. Three cubic equations of state GEOS3C, SRK (Soave � Redlich � Kwong) and PR (Peng � Robinson) were used. A wide comparison with literature experimental data was made. For the refrigerant mixtures, classical van der Waals mixing rules without interaction parameters were used. The GEOS3C equation, with three parameters estimated by matching several points on the saturation curve (vapor pressure and corresponding liquid volumes), compares favorably to other equations in literature, being simple enough for applications.


2021 ◽  
Vol 502 (3) ◽  
pp. 3942-3954
Author(s):  
D Hung ◽  
B C Lemaux ◽  
R R Gal ◽  
A R Tomczak ◽  
L M Lubin ◽  
...  

ABSTRACT We present a new mass function of galaxy clusters and groups using optical/near-infrared (NIR) wavelength spectroscopic and photometric data from the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) survey. At z ∼ 1, cluster mass function studies are rare regardless of wavelength and have never been attempted from an optical/NIR perspective. This work serves as a proof of concept that z ∼ 1 cluster mass functions are achievable without supplemental X-ray or Sunyaev-Zel’dovich data. Measurements of the cluster mass function provide important contraints on cosmological parameters and are complementary to other probes. With ORELSE, a new cluster finding technique based on Voronoi tessellation Monte Carlo (VMC) mapping, and rigorous purity and completeness testing, we have obtained ∼240 galaxy overdensity candidates in the redshift range 0.55 < z < 1.37 at a mass range of 13.6 < log (M/M⊙) < 14.8. This mass range is comparable to existing optical cluster mass function studies for the local universe. Our candidate numbers vary based on the choice of multiple input parameters related to detection and characterization in our cluster finding algorithm, which we incorporated into the mass function analysis through a Monte Carlo scheme. We find cosmological constraints on the matter density, Ωm, and the amplitude of fluctuations, σ8, of $\Omega _{m} = 0.250^{+0.104}_{-0.099}$ and $\sigma _{8} = 1.150^{+0.260}_{-0.163}$. While our Ωm value is close to concordance, our σ8 value is ∼2σ higher because of the inflated observed number densities compared to theoretical mass function models owing to how our survey targeted overdense regions. With Euclid and several other large, unbiased optical surveys on the horizon, VMC mapping will enable optical/NIR cluster cosmology at redshifts much higher than what has been possible before.


PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Rajesh Chandrasekaran ◽  
Markus Hillgärtner ◽  
Ameya Rege ◽  
Barbara Milow ◽  
Mikhail Itskov
Keyword(s):  

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.


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