scholarly journals Staggered flux state for rectangular-lattice spin- 12 Heisenberg antiferromagnets

2020 ◽  
Vol 102 (21) ◽  
Author(s):  
N. E. Shaik ◽  
B. Dalla Piazza ◽  
D. A. Ivanov ◽  
H. M. Rønnow
Keyword(s):  
Rectangular Lattice ◽  
Lattice Spin ◽  
Heisenberg Antiferromagnets ◽  
Flux State

Cryo-Electron Microscopy and Correlation Averaging of Frozen-Hydrated, Polymorphic 2D Crystals of the Mitochondrial Outer Membrane Channel

1990 ◽  
Vol 48 (1) ◽  
pp. 100-101
Author(s):  
Xiao-Wei Guo
Keyword(s):  
Outer Membrane ◽  
Hexagonal Lattice ◽  
Mitochondrial Outer Membrane ◽  
Rectangular Lattice ◽  
Electron Microscopic ◽  
Cryo Electron Microscopy ◽  
Voltage Dependent ◽  
Outer Membrane Channel ◽  
2D Crystals ◽  
Vdac Channel

Voltage-dependent, anion-selective channels (VDAC) are formed in the mitochondrial outer membrane (mitOM) by a 30-kDa polypeptide. These channels form ordered 2D arrays when mitOMs from Neurospora crassa are treated with soluble phospholipase A2. We obtain low-dose electron microscopic images of unstained specimens of VDAC crystals preserved in vitreous ice, using a Philips EM420 equipped with a Gatan cryo-transfer stage. We then use correlation analysis to compute average projections of the channel crystals. The procedure involves Fourier-filtration of a region within a crystal field to obtain a preliminary average that is subsequently cross-correlated with the entire crystal. Subregions are windowed from the crystal image at coordinates of peaks in the cross-correlation function (CCF, see Figures 1 and 2) and summed to form averages (Figure 3).The VDAC channel forms several different types of crystalline arrays in mitOMs. The polymorph first observed during phospholipase treatment is a parallelogram array (a=13 run, b=11.5 run, θ==109°) containing 6 water-filled pores per unit cell. Figure 1 shows the CCF of a sub-field of such an “oblique” array used to compute the correlation average of Figure 3A. With increased phospholipase treatment, other polymorphs are observed, often co-existing within the same crystal. For example, two distinct (but closely related) types of lattices occur in the field corresponding to the CCF of Figure 2: a “contracted” version of the parallelogram lattice (a=13 run, b=10 run, θ=99°), and a near-rectangular lattice (a=8.5 run, b=5 nm). The pattern of maxima in this CCF suggests that a third, near-hexagonal lattice (a=4.5 nm) may also be present. The correlation averages of Figures 3B-D were computed from polycrystalline fields, using peak coordinates in regions of CCFs corresponding to each of the three lattice types.

The size of the region occupied by one type in an invasion process

1976 ◽  
Vol 13 (02) ◽  
pp. 355-356 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Rectangular Lattice ◽  
Invasion Process

Particles are situated on a rectangular lattice and proceed to invade each other's territory. When they are equally competitive this creates larger and larger blocks of one type as time goes by. It is shown that the expected size of such blocks is equal to the expected range of a simple random walk.

scholarly journals Approximate Tensorization of the Relative Entropy for Noncommuting Conditional Expectations

2021 ◽  
Author(s):  
Ivan Bardet ◽  
Ángela Capel ◽  
Cambyse Rouzé
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Logarithmic Sobolev Inequality ◽  
Spin Systems ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Finite Dimensional ◽  
Lattice Spin ◽  
Lattice Spin Systems ◽  
Conditional Expectations

AbstractIn this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. This generalisation, referred to as approximate tensorization of the relative entropy, consists in a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

scholarly journals Geometric criterion for solvability of lattice spin systems

2020 ◽  
Vol 102 (24) ◽  
Author(s):  
Masahiro Ogura ◽  
Yukihisa Imamura ◽  
Naruhiko Kameyama ◽  
Kazuhiko Minami ◽  
Masatoshi Sato
Keyword(s):  
Spin Systems ◽  
Geometric Criterion ◽  
Lattice Spin ◽  
Lattice Spin Systems

scholarly journals Reflections on iridescent neck and breast feathers of the peacock, Pavo cristatus

2018 ◽  
Vol 9 (1) ◽  
pp. 20180043 ◽  
Author(s):  
Pascal Freyer ◽  
Bodo D. Wilts ◽  
Doekele G. Stavenga
Keyword(s):  
Three Dimensional ◽  
Refractive Indices ◽  
Rectangular Lattice ◽  
Pavo Cristatus ◽  
Feather Coloration ◽  
Air Channels ◽  
Difference Time ◽  
Modelling Methods ◽  
Reflection Characteristics ◽  
Reflectance Measurements

The blue neck and breast feathers of the peacock are structurally coloured due to an intricate photonic crystal structure in the barbules consisting of a two-dimensionally ordered rectangular lattice of melanosomes (melanin rodlets) and air channels embedded in a keratin matrix. We here investigate the feather coloration by performing microspectrophotometry, imaging scatterometry and angle-dependent reflectance measurements. Using previously determined wavelength-dependent refractive indices of melanin and keratin, we interpret the spectral and spatial reflection characteristics by comparing the measured spectra to calculated spectra by effective-medium multilayer and full three-dimensional finite-difference time-domain modelling. Both modelling methods yield similar reflectance spectra indicating that simple multilayer modelling is adequate for a direct understanding of the brilliant coloration of peacock feathers.

Existence of N�el order in some spin-1/2 Heisenberg antiferromagnets

1988 ◽  
Vol 53 (5-6) ◽  
pp. 1019-1030 ◽  
Author(s):  
Tom Kennedy ◽  
Elliott H. Lieb ◽  
B. Sriram Shastry
Keyword(s):  
Heisenberg Antiferromagnets

scholarly journals Double-cladding rectangular-lattice birefringence photonic crystal fiber with elliptical air holes

2015 ◽  
Vol 47 (8) ◽  
pp. 2649-2657 ◽  
Author(s):  
Wan Zhang ◽  
Shu-guang Li ◽  
Guo-Wen An ◽  
Zhen-Kai Fan ◽  
Ya-Jie Bao
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Rectangular Lattice ◽  
Crystal Fiber

scholarly journals Thermal Conductivity of Cage-Like Structures

2011 ◽  
Author(s):  
Mona Zebarjadi ◽  
Keivan Esfarjani ◽  
Gang Chen
Keyword(s):  
Thermal Conductivity ◽  
Atomic Displacement ◽  
Rectangular Lattice ◽  
Local Minima ◽  
Atomic Displacement Parameter ◽  
Band Dispersion ◽  
Dynamics Simulations ◽  
Filler Mass ◽  
The Right ◽  
Double Well Potential

A two dimensional toy model is developed to study thermal transport in cage like structures such a skutterudites and clathrates. The model consists of host atoms on a rectangular lattice with fillers in the center of each rectangle. The thermal conductivity is calculated by using Green-Kubo equilibrium molecular dynamics simulations. It is generally believed that the smaller and the heavier the filler, the lower is the thermal conductivity. We show that the thermal conductivity decreases with atomic displacement parameter while it has local minima versus filler mass. Our study shows that it is very important to include the correct band dispersion to get the right features of the thermal conductivity. We show that by having a double well potential one can further reduce the thermal conductivity.

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