scholarly journals Magneto-orientation response of ferronematic with a tilted orientation of the director and magnetization

2021 ◽  
pp. 48-58
Author(s):  
Danil A. Petrov ◽  
◽  
Rifat R. Khannanov ◽  
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Continuum Theory ◽  
Weak Magnetic Fields ◽  
Orientation Response ◽  
Analytical Expressions ◽  
Ferromagnetic Particles ◽  
Pretilt Angle ◽  
The Continuum ◽  
Orientational Transitions

The article considers orientational transitions induced by a magnetic field in a highly dispersed suspension of ferromagnetic particles in a nematic liquid crystal – ferronematic. We research the case when, in the absence of an external magnetic field between the directions of the liquid crystal director and magnetization of the impurity particles, a constant pretilt angle is maintained, and the coupling of the liquid crystal molecules to the surface of the ferroparticles is assumed to be soft and planar. An example of such an impurity is ferromagnetic carbon nanotubes magnetized at a certain angle to their long axes. On the basis of the continuum theory, the equilibrium values of the orientation angles of the liquid crystal director and magnetization are calculated for different values of the pretilt angle. The results of calculations are compared with the previously considered case of planar coupling between the director and magnetization. Analytical expressions are obtained for determining the orientational and magnetic structure of the ferronematic in the case of weak magnetic fields. The magnetization of the ferronematic is studied for different values of the pretilt angle.

scholarly journals Magnetic field induced orientational transitions in liquid crystals doped with carbon nanotubes

2017 ◽  
Vol 8 ◽  
pp. 2807-2817 ◽  
Author(s):  
Danil A Petrov ◽  
Pavel K Skokov ◽  
Alexander N Zakhlevnykh
Keyword(s):  
Magnetic Field ◽  
Carbon Nanotubes ◽  
Liquid Crystal ◽  
Continuum Theory ◽  
Weakly Coupled ◽  
Transitions In Liquid Crystals ◽  
The Matrix ◽  
Liquid Crystal Matrix ◽  
Planar Phase ◽  
Orientational Transitions

We propose a continuum theory of orientational phase transitions induced by an external magnetic field in a suspension of carbon nanotubes in a nematic liquid crystal. It is shown that in a magnetic field a non-uniform and two different uniform phases are possible in the suspension. The uniform phases of the suspension differ by the type of orientational coupling of nanotubes with the liquid crystal matrix (the planar type when the nanotubes are oriented along the matrix director, and the homeotropic type when the nanotubes are perpendicular to the director). The possibility of a redistribution of the nanotube concentration (segregation effect) is shown. The fields of orientational transitions between uniform and non-uniform phases of the suspension are found analytically. It is shown that, when the nanotubes are weakly coupled to the matrix, the magnetic field induces reentrant transitions (uniform planar phase–non-uniform phase–uniform homeotropic phase–non-uniform phase). These transitions can be of first or of second order depending on the carbon nanotubes segregation intensity.

scholarly journals EVOLVING SCALE-FREE NETWORK MODEL WITH TUNABLE CLUSTERING

2005 ◽  
Vol 19 (26) ◽  
pp. 3951-3959 ◽  
Author(s):  
BING WANG ◽  
HUANWEN TANG ◽  
ZHONGZHI ZHANG ◽  
ZHILONG XIU
Keyword(s):  
Rate Equation ◽  
Continuum Theory ◽  
Clustering Coefficient ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
Law Degree ◽  
Analytical Expressions ◽  
Good Agreement ◽  
The Continuum

The Barabási–Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability p, we add a new node with m edges which preferentially link to the nodes presented in the network; with probability 1-p, we add m edges among the present nodes. A node is preferentially selected by its degree to add an edge randomly among its neighbors. Using the continuum theory and the rate equation method we get the analytical expressions of the power-law degree distribution with exponent γ=3 and the clustering coefficient c(k)~k-1+c. The analytical expressions are in good agreement with the numerical calculations.

EVOLVING SCALE-FREE NETWORK MODEL

2008 ◽  
Vol 22 (13) ◽  
pp. 2139-2149
Author(s):  
QIONG QIN ◽  
ZHIPING WANG ◽  
FANG ZHANG ◽  
PENGYUAN XU
Keyword(s):  
Time Evolution ◽  
Preferential Attachment ◽  
Continuum Theory ◽  
Scale Free Network ◽  
Scale Free ◽  
Long Time ◽  
Free Network ◽  
Law Degree ◽  
Analytical Expressions ◽  
The Continuum

The Barabási–Albert (BA) model is extended here to include the concept of modifying the preferential attachment and combining the global preferential attachment with local preferential attachment. Our preferential attachment makes the nodes with higher degree increase less rapidly than the BA model after a long time. The maximum degree is introduced. We compare the time-evolution of the degree of the BA model and our model to illustrate that our model can control the degree of some nodes increasing dramatically with increasing time. Using the continuum theory and the rate equation method, we obtain the analytical expressions of the time-evolution of the degree and the power-law degree distribution.

Digital phase analysis in interference electron microscopy

1988 ◽  
Vol 46 ◽  
pp. 842-843
Author(s):  
S. Hasegawa ◽  
T. Kawasaki ◽  
J. Endo ◽  
M. Futamoto ◽  
A. Tonomura
Keyword(s):  
Magnetic Field ◽  
Electron Microscopy ◽  
Phase Distribution ◽  
Magnetic Recording Media ◽  
Electron Wave ◽  
Vector Potentials ◽  
Weak Magnetic Fields ◽  
Leakage Magnetic Field ◽  
Optical Reconstruction ◽  
Processing Techniques

Interference electron microscopy enables us to record the phase distribution of an electron wave on a hologram. The distribution is visualized as a fringe pattern in a micrograph by optical reconstruction. The phase is affected by electromagnetic potentials; scalar and vector potentials. Therefore, the electric and magnetic field can be reduced from the recorded phase. This study analyzes a leakage magnetic field from CoCr perpendicular magnetic recording media. Since one contour fringe interval corresponds to a magnetic flux of Φo(=h/e=4x10-15Wb), we can quantitatively measure the field by counting the number of finges. Moreover, by using phase-difference amplification techniques, the sensitivity for magnetic field detection can be improved by a factor of 30, which allows the drawing of a Φo/30 fringe. This sensitivity, however, is insufficient for quantitative analysis of very weak magnetic fields such as high-density magnetic recordings. For this reason we have adopted “fringe scanning interferometry” using digital image processing techniques at the optical reconstruction stage. This method enables us to obtain subfringe information recorded in the interference pattern.

Tuning the Magnetic Alignment of Cellulose Nanocrystals from Perpendicular to Parallel Using Lepidocrocite Nanoparticles

2019 ◽  
Author(s):  
Valentina Guccini ◽  
Sugam Kumar ◽  
Yulia Trushkina ◽  
Gergely Nagy ◽  
Christina Schütz ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Cellulose Nanocrystals ◽  
Small Angle Neutron Scattering ◽  
Lower Amount ◽  
Magnetic Alignment ◽  
Polarized Optical Microscopy ◽  
Parallel Orientation ◽  
Weak Magnetic Fields

The magnetic alignment of cellulose nanocrystals (CNC) and lepidocrocite nanorods (LpN), pristine and in hybrid suspensions has been investigated using contrast-matched small-angle neutron scattering (SANS) under in situ magnetic fields (0 – 6.8 T) and polarized optical microscopy. The pristine CNC (diamagnetic) and pristine LpN (paramagnetic) align perpendicular and parallel to the direction of field, respectively. The alignment of both the nanoparticles in their hybrid suspensions depends on the relative amount of the two components (CNC and LpN) and strength of the applied magnetic field. In the presence of 10 wt% LpN and fields < 1.0 T, the CNC align parallel to the field. In the hybrid containing lower amount of LpN (1 wt%), the ordering of CNC is partially frustrated in all range of magnetic field. At the same time, the LpN shows both perpendicular and parallel orientation, in the presence of CNC. This study highlights that the natural perpendicular ordering of CNC can be switched to parallel by weak magnetic fields and the incorporation of paramagnetic nanoparticle as LpN, as well it gives a method to influence the orientation of LpN.<br>

scholarly journals Gradient pretilt angle alignment materials with different photosensitivity for tunable polarization‐independent self‐aligned liquid crystal lens

2021 ◽  
Author(s):  
Veronika S. Bezruchenko ◽  
Alexander A. Muravsky ◽  
Anatoli A. Murauski ◽  
Alexander I. Stankevich ◽  
Uladzimir V. Mahilny
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystal Lens ◽  
Polarization Independent ◽  
Pretilt Angle
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