scholarly journals Radial symmetry on three-dimensional shells in the Landau–de Gennes theory

2016 ◽  
Vol 314 ◽  
pp. 18-34 ◽  
Author(s):  
Giacomo Canevari ◽  
Mythily Ramaswamy ◽  
Apala Majumdar
Keyword(s):  
Three Dimensional ◽  
Radial Symmetry ◽  
Gennes Theory

Theory and Simulation of Texture Transformations in Chiral Systems: Applications to Biological Fibrous Composites

2001 ◽  
Vol 709 ◽  
Author(s):  
Gino De Luca ◽  
Alejandro D. Rey
Keyword(s):  
Three Dimensional ◽  
Front Propagation ◽  
Fibrous Composites ◽  
Propagation Process ◽  
Chiral Nematic ◽  
New Information ◽  
Biological Structures ◽  
Planar Film ◽  
Chiral Systems ◽  
Gennes Theory

ABSTRACTNumerous studies [1-3] have shown that chiral biological structures share common properties with liquids crystals, in particular a tendency to assemble in three-dimensional lattices very similar to that of chiral nematics. Biological fibrous composites are usually found in planar (film) and cylindrical (fibber) twist geometries. In this work, the formation process of the planar twist architecture is numerically investigated using a mesoscopic model based on the Landau-de Gennes theory of chiral nematic liquid crystals. The simulations and visualizations of the computed textures provide new information on some of the principles that govern the formation of chiral biological structures. It is found that a defect-free planar twist architecture arises from a chiral front propagation process with a fully relaxed wake.

Simplified Triped Robot for Analysis of Three-Dimensional Gait Generation

2017 ◽  
Vol 29 (3) ◽  
pp. 528-535
Author(s):  
Yoichi Masuda ◽  
◽  
Masato Ishikawa
Keyword(s):  
High Speed ◽  
Force Feedback ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
The Body ◽  
Walking Robots ◽  
Body Structure ◽  
Gait Patterns ◽  
Gait Generation ◽  
Proposed Model

[abstFig src='/00290003/08.jpg' width='230' text='The tripedal robot “Martian petit”' ] Significant efforts to simplify the body structure of multi-legged walking robots have been made over the years. Of these, the Spring-Loaded-Inverted-Pendulum (SLIP) model has been very popular, therefore widely employed in the design of walking robots. In this paper, we develop a SLIP-based tripedal walking robot with a focus on the geometric symmetry of the body structure. The proposed robot possesses a compact, light-weight, and compliant leg modules. These modules are controlled by a distributed control law that consists of decoupled oscillators with only local force feedback. As demonstrated through experiments, the simplified design of the robot makes possible the generation of high-speed dynamic locomotion. Despite the structural simplicity of the proposed model, the generation of several gait-patterns is demonstrated. The proposed minimalistic design approach with radial symmetry simplifies the function of each limb in the three-dimensional gait generation of the robot.

Molecular Ion Channels; Electrodiffusion in R3

2010 ◽  
Vol 297-301 ◽  
pp. 1469-1474 ◽  
Author(s):  
Bogusław Bożek ◽  
Bartek Wierzba ◽  
Marek Danielewski
Keyword(s):  
Ion Channels ◽  
Ion Transport ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
Clear Understanding ◽  
Three Dimensional Model ◽  
Molecular Ion ◽  
Channel Interactions ◽  
Molecular Channel

Ion transport across the membrane of the living cell (molecular ion channels) is a critical process, e.g., the triggering of nerve cells and heart muscle cells is coupled with mechanisms controlled by ion diffusion (electrodiffusion). Although the process is described by the century old Nernst- Planck-Poisson system of equations, it is not well understood and a clear understanding of how the interaction between channel and ions affects the flow is still missing. We present a three-dimensional model of the molecular channel. An appropriate quantitative description of the ion transport process allows proper explanation of molecule channel interactions (e.g. the ions flow for a given concentration gradient should depend on the potential and other parameters describing the interaction, i.e. asymmetric transport). We show the simulation of the stationary electrodiffusion in the ion channel showing radial symmetry.

scholarly journals Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory

2010 ◽  
Vol 21 (2) ◽  
pp. 181-203 ◽  
Author(s):  
APALA MAJUMDAR
Keyword(s):  
Three Dimensional ◽  
Energy Functional ◽  
Order Parameters ◽  
Tensor Order ◽  
Temperature Regimes ◽  
Explicit Bounds ◽  
Scalar Order ◽  
Definition Of ◽  
Gennes Theory ◽  
The Continuum

We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.

Plane‐wave decomposition of seismograms

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1375-1401 ◽  
Author(s):  
Sven Treitel ◽  
P. R. Gutowski ◽  
D. E. Wagner
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
Angle Of Incidence ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Predictive Deconvolution ◽  
Seismic Recording ◽  
Wave Decomposition ◽  
Slant Stacking

A point‐source seismic recording can be decomposed into a set of plane‐wave seismograms for arbitrary angles of incidence. Such plane‐wave seismograms possess an inherently simple structure that make them amenable to existing inversion methods such as predictive deconvolution. Implementation of plane‐wave decomposition (PWD) takes place in the frequency‐wavenumber domain under the assumption of radial symmetry. This version of PWD is equivalent to slant stacking if allowance is made for the customary use of linear recording arrays on the surface of a three‐dimensional medium. An imaging principle embodying both kinematic as well as dynamic characteristics allows us to perform time migration of the plane‐wave seismograms. The imaging procedure is implementable as a two‐dimensional filter whose independent variables are traveltime and angle of incidence.

Improved Fluid Circulation and Heat Transfer in Geothermal Reservoirs due to Superior Fracture Network in Hot Dry Rocks (HDR)

2012 ◽  
Author(s):  
Mir Akbar Hessami ◽  
Justine White
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
Fracture Network ◽  
Radial Symmetry ◽  
Fracture Pattern ◽  
Two Dimensions ◽  
Working Fluid ◽  
Geothermal Reservoirs ◽  
Hot Dry Rocks ◽  
Adjacent Fractures

As the reduction of carbon emissions becomes an increasingly pressing issue, a larger emphasis is being placed on the need for the development of renewable energy. One such option is geothermal energy which utilizes the heat from the earth’s crust; it presents a vast potential for the production of commercial scale base-load power generation. However, the conventional techniques used in the stimulation of hot dry rocks (HDR) geothermal wells are not very effective in producing a permeable reservoir for heat exchange between the rock mass and the working fluid. To increase the permeability of geothermal reservoirs, a new stimulation technique (developed by CSIRO - Commonwealth Scientific and Industrial Research Organisation) which involves isolating sections of the well for controlled planar fracture growth can be used. However, if these notches/fractures are placed too closely together they will interact with one another, resulting in a deviated fracture path. A two dimensional numerical model has thus been developed to study conditions under which adjacent fractures will interact with one another. This study aims to verify the numerical model through stimulating a number of granite blocks, and drawing comparisons between the observed fracture pattern and that predicted by the model. To achieve this goal, the stimulated and fractured granite blocks were sectioned and their fracture patterns were extracted using a MATLAB code, before being reconstructed in their respective positions. Stimulation was carried out firstly using conventional techniques, and then by trialling the method proposed by CSIRO. Observation of the reconstructed images showed good agreement between the model predictions and the observed fracturing patterns in two-dimensions. However, the three-dimensional pattern in the notched, perpendicular well-bore was observed as a ‘half cylinder’. This was counter intuitive as it was expected that radial symmetry of the fractures would be observed resulting in a ‘bowl’ shape. It was therefore concluded that while the model was unable to accurately predict the three-dimensional geometry of an array of fractures, stimulation through a notched perpendicular wellbore was very effective in the production of a controlled system of fractures with an improved fluid flow and heat exchanging surface area of the reservoir in comparison to the conventional techniques.

scholarly journals On the Disclination Lines of Nematic Liquid Crystals

2016 ◽  
Vol 19 (2) ◽  
pp. 354-379 ◽  
Author(s):  
Yucheng Hu ◽  
Yang Qu ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Practical Importance ◽  
Three Dimensional ◽  
Defect Structures ◽  
Static Structure ◽  
Spherical Droplet ◽  
Topological Constraint ◽  
Defects In Liquid Crystals ◽  
Gennes Theory

AbstractDefects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a challenge. We investigate defect patterns of nematic liquid crystals confined in three-dimensional spherical droplet and two-dimensional disk under different boundary conditions, within the Landau-de Gennes model. We implement a spectral method that numerically solves the Landau-de Gennes model with high accuracy, which allows us to study the detailed static structure of defects. We observe five types of defect structures. Among them the 1/2-disclination lines are the most stable structure at low temperature. Inspired by numerical results, we obtain the profile of disclination lines analytically. Moreover, the connection and difference between defect patterns under the Landau-de Gennes model and the Oseen-Frank model are discussed. Finally, three conjectures are made to summarize some important characteristics of defects in the Landau-de Gennes theory. This work is a continuing effort to deepen our understanding on defect patterns in nematic liquid crystals.

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