Bandgap engineering of three-dimensional phononic crystals in a simple cubic lattice

2018 ◽  
Vol 113 (20) ◽  
pp. 201902 ◽  
Author(s):  
Frieder Lucklum ◽  
Michael J. Vellekoop
Keyword(s):  
Three Dimensional ◽  
Phononic Crystals ◽  
Bandgap Engineering ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

scholarly journals Effect of Anisotropy on the Critical Behaviour of Three- Dimensional Heisenberg Ferromagnets

1976 ◽  
Vol 31 (1) ◽  
pp. 34-40 ◽  
Author(s):  
R. Shanker ◽  
R. A. Singh
Keyword(s):  
Three Dimensional ◽  
Experimental Investigations ◽  
Isotropic Case ◽  
Zero Field ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Anisotropic System ◽  
Critical Temperature Tc

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

CRITICAL TEMPERATURES AND MEAN-FIELD CRITICAL COEFFICIENTS FOR THE HEISENBERG MODEL BASED ON CVM

1992 ◽  
Vol 06 (13) ◽  
pp. 2363-2374
Author(s):  
GIICHI TANAKA ◽  
MINORU KIMURA
Keyword(s):  
Heisenberg Model ◽  
Mean Field ◽  
Three Dimensional ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Cluster Variation

Critical temperatures T c and mean-field critical coefficients [Formula: see text] for susceptibilities are calculated by a cluster-variation method (CVM) for a three-dimensional Heisenberg model on a simple cubic lattice. Both the full CVM based on a 4-spin cluster and the SCVM are applied and the same values for T c and [Formula: see text] are obtained by three different approximation in the SCVM. The results are compared with those obtained by the same approach for the three-dimensional Ising model on the simple cubic lattice.

Waves in three-dimensional simple cubic lattice

2006 ◽  
Vol 30 (4) ◽  
pp. 909-919 ◽  
Author(s):  
Xiao-yun Wang ◽  
Wen-shan Duan ◽  
Mai-mai Lin ◽  
Gui-xin Wan
Keyword(s):  
Three Dimensional ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

Statistical mechanics and the partition of numbers II. The form of crystal surfaces

1952 ◽  
Vol 48 (4) ◽  
pp. 683-697 ◽  
Author(s):  
H. N. V. Temperley
Keyword(s):  
Surface Energy ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Crystal Surfaces ◽  
Cubic Crystal ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
First Approximation ◽  
Equilibrium Profile

AbstractThe classical theory of partition of numbers is applied to the problem of determining the equilibrium profile of a simple cubic crystal. It is concluded that it may be thermo-dynamically profitable for the surface to be ‘saw-toothed’ rather than flat, the extra entropy associated with such an arrangement compensating for the additional surface energy. For both a two- and a three-dimensional ‘saw-tooth’ the extra entropy varies, to a first approximation, in the same way as the surface energy, i.e. is proportional to or respectively, where N is the number of molecules in a ‘tooth’. For the simple cubic lattice, the entropy associated with the formation of a tooth containing N atoms is estimated to be 3.3 It is also possible to estimate the variation of the ‘equilibrium roughness’ of a crystal with temperature, if its surface energy is known.

VARIATIONAL STUDY ON INSTABILITY OF NAGAOKA STATE IN A THERMODYNAMIC LIMIT

1993 ◽  
Vol 07 (24n25) ◽  
pp. 1619-1625
Author(s):  
SHUN-QING SHEN ◽  
ZHAO-MING QIU
Keyword(s):  
Thermodynamic Limit ◽  
Ground State ◽  
State Energy ◽  
Three Dimensional ◽  
Critical Value ◽  
Square Lattice ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Variational Study

In this paper, we have rigorously shown that, in a thermodynamic limit, there always exists a one-spin-flipped state degenerate with the Nagaoka state in one-band Hubbard model on a two and three-dimensional simple cubic lattice when the number of holes [Formula: see text] (with 0≤α<1, N∧ and N e are the numbers of sites and electrons respectively) for all U (including U=∞). It is also shown that there does not exist a finite critical value U c for which, when U>U c , the Nagaoka state has the ground-state energy of the system for a two-dimensional square lattice when ρ→0.

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