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.

Free Vibration Studies on Stress-Free Three-Dimensional Elastic Solids

1995 ◽  
Vol 62 (1) ◽  
pp. 159-165 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Free Vibration ◽  
Three Dimensional ◽  
Energy Functional ◽  
Mode Shapes ◽  
Elastic Solids ◽  
Displacement Fields ◽  
Short Columns ◽  
Cartesian Coordinate ◽  
Three Dimensional Elasticity ◽  
The Continuum

A comprehensive investigation on free vibration of three-dimensional elastic solids of rectangular planform is reported. The continuum is considered to be free from normal and in-plane stresses on the facets. Functions representing the spatial displacement fields of the continuum in a complete Cartesian coordinate system are expressed in terms of sets of orthogonal polynomial functions in the x, y, and z directions. The energy functional derived based on the three-dimensional elasticity theory is minimized to arrive at the governing eigenvalue equation. In this paper, the vibration of stress-free elastic solids in the forms of short columns, thick plates, and solid cubes are studied. Frequency parameters and the first known three-dimensional deformed mode shapes have been generated for these stress-free elastic solids.

Application of high-resolution field-emission LVSEM, backscatter imaging, immunogold staining to definition of the spatial distributions of two human neutrophil adherence receptors

1993 ◽  
Vol 51 ◽  
pp. 36-37
Author(s):  
Robert D. Nelson ◽  
Sharon R. Hasslen ◽  
Stanley L. Erlandsen
Keyword(s):  
Cell Surface ◽  
Surface Membrane ◽  
Three Dimensional ◽  
Human Neutrophils ◽  
Spatial Distributions ◽  
Immunogold Staining ◽  
Functional Control ◽  
Neutrophil Adherence ◽  
Definition Of ◽  
Mode Of Attachment

Receptors are commonly defined in terms of number per cell, affinity for ligand, chemical structure, mode of attachment to the cell surface, and mechanism of signal transduction. We propose to show that knowledge of spatial distribution of receptors on the cell surface can provide additional clues to their function and components of functional control.L-selectin and Mac-1 denote two receptor populations on the neutrophil surface that mediate neutrophil-endothelial cell adherence interactions and provide for targeting of neutrophil recruitment to sites of inflammation. We have studied the spatial distributions of these receptors using LVSEM and backscatter imaging of isolated human neutrophils stained with mouse anti-receptor (primary) antibody and goat anti-mouse (secondary) antibody conjugated to 12 nm colloidal gold. This combination of techniques provides for three-dimensional analysis of the expression of these receptors on different surface membrane domains of the neutrophil: the ruffles and microvilli that project from the cell surface, and the cell body between these projecting structures.

ГЕРМЕНЕВТИКА ЛИЧНОСТИ КАК МЕТОД СОВРЕМЕННОЙ ПЕРСОНОЛОГИИ

1970 ◽  
Vol 6 (1) ◽  
pp. 32-42
Author(s):  
Елена Старовойтенко
Keyword(s):  
Text Setting ◽  
Research Setting ◽  
Textual Representations ◽  
General Scientific ◽  
Definition Of ◽  
The Individual ◽  
The Continuum

Персонологическая интерпретация текстов предполагает реализацию общенаучных, а также специфических для персонологии, герменевтических установок, к которым относятся: установка на интерпретацию текста как исследование, установка на разнообразие герменевтических действий с текстом, установка на выявление неисследованных содержаний текста, установка на творческое постижение тайн текста, установка на целостное отношение к личности и "Я" автора текста, установка на выявление способности автора быть "практикующим феноменологом", установка на определение места изучаемого текста в континууме текстовых репрезентаций "личности", установка на соотнесение своего понимания текста с другими интерпретациями и их интеграцию, установка на раскрытие сущности авторской "идеи личности", возможное только в единстве интерпретаций, установка на построение и применение герменевтической модели, определяющей процедуру интерпретации как исследования и творчества, установка на определение места проделанного герменевтического поиска в культуре познания и жизни личности, установка на интерпретацию различных видов "текстов личности". Personological interpretation of texts suggests the implementation of the general scientific and also hermeneutical settings specific for Personology which include the setting of the interpretation of the text as a research, setting of a variety of hermeneutical actions with the text, setting to identify unexplored contents of the text, setting of the creative comprehension of the mysteries of the text, setting of the integrity of the attitude of the individual and the "I" of the author of the text, setting to reveal the author's ability to be "practicing phenomenologist", setting of the definition of the place in the text in the continuum of textual representations of the "personality", setting in the correlation of the understanding of the text with other interpretations and their integration, setting of the disclosure of the author's "ideas person" is possible only in the unity of interpretation, setting of the construction and usage of hermeneutical models defining the procedure for the interpretation of both studies and work, the setting to determine the place of hermeneutical research in culture and knowledge of a person's life, setting of the interpretation of various types of "texts of the individual."

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Proposing 3D Thermal Technology for Heritage Building Energy Monitoring

2021 ◽  
Vol 13 (8) ◽  
pp. 1537
Author(s):  
Antonio Adán ◽  
Víctor Pérez ◽  
José-Luis Vivancos ◽  
Carolina Aparicio-Fernández ◽  
Samuel A. Prieto
Keyword(s):  
Computer Vision ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Building Energy ◽  
Energy Monitoring ◽  
3D Computer Vision ◽  
Building Monitoring ◽  
Heritage Buildings ◽  
Heritage Building ◽  
Definition Of

The energy monitoring of heritage buildings has, to date, been governed by methodologies and standards that have been defined in terms of sensors that record scalar magnitudes and that are placed in specific positions in the scene, thus recording only some of the values sampled in that space. In this paper, however, we present an alternative to the aforementioned technologies in the form of new sensors based on 3D computer vision that are able to record dense thermal information in a three-dimensional space. These thermal computer vision-based technologies (3D-TCV) entail a revision and updating of the current building energy monitoring methodologies. This paper provides a detailed definition of the most significant aspects of this new extended methodology and presents a case study showing the potential of 3D-TCV techniques and how they may complement current techniques. The results obtained lead us to believe that 3D computer vision can provide the field of building monitoring with a decisive boost, particularly in the case of heritage buildings.

Anion packing density: a universal quantity for both dense and porous crystalline inorganic phases

2002 ◽  
Vol 58 (3) ◽  
pp. 457-462 ◽  
Author(s):  
F. Liebau ◽  
H. Küppers
Keyword(s):  
High Pressure ◽  
Packing Density ◽  
Three Dimensional ◽  
Ionic Radii ◽  
Generalized Framework ◽  
Molal Volumes ◽  
Definition Of ◽  
Anion Packing ◽  
Very High ◽  
Framework Density

To compare densities of inorganic high-pressure phases their molal volumes or specific gravities are usually employed, whereas for zeolites and other microporous materials the so-called framework density, FD, is applied. The definition of FD, which refers only to phases with three-dimensional tetrahedron frameworks, is extended to a `generalized framework density' d f, which is independent of the dimensionality of the framework and the coordination number(s) of the framework cations. In this paper the anion packing density, d ap, is introduced as a new quantity which is not only applicable to any inorganic phase but, in contrast to FD and d f, also allows quantitative comparisons to be made for crystalline inorganic phases of any kind. The anion packing density can readily be calculated if the volume and content of the unit cell and the radii of the anions of a phase are known. From d ap values calculated for high-pressure silica polymorphs studied under very high pressure, it is concluded that Shannon–Prewitt effective ionic radii do not sufficiently take into account the compressibility of the anions.

The Use of Photogrammetry in Piping Design

1983 ◽  
Vol 197 (2) ◽  
pp. 125-138 ◽  
Author(s):  
P A Bracewell ◽  
U R Klement
Keyword(s):  
Information Retrieval ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cost Effective ◽  
Process Industry ◽  
Process Plant ◽  
Definition Of ◽  
High Degree ◽  
Positional Data

Piping design for ‘revamp’ projects in the process industry requires the retrieval of large amounts of ‘as-built’ data from existing process plant installations. Positional data with a high degree of accuracy are required. Photogrammetry, the science of measurement from photographs, was identified in Imperial Chemical Industries plc (ICI) as a suitable tool for information retrieval. The mathematical formulation enabling the definition of three-dimensional positions from photographic information is described. The process of using ICI's photogrammetric system for the definition of complete objects such as structures and pipes is illustrated. The need for specialized photogrammetric software for design purposes is explained. A case study describing how the photogrammetric system has been applied is described and graphical outputs from this exercise are shown. It is concluded that this particular photogrammetric system has proved to be a cost effective and accurate tool for the retrieval of ‘as-built’ information.

scholarly journals Three-dimensional quantification of twisting in the Arabidopsis petiole

2021 ◽  
Author(s):  
Yuta Otsuka ◽  
Hirokazu Tsukaya
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Light Sheet ◽  
Underlying Mechanism ◽  
Two Dimensions ◽  
Observation Angle ◽  
Differential Growth ◽  
Light Sheet Microscopy ◽  
Definition Of ◽  
Twisting Angle

AbstractOrganisms have a variety of three-dimensional (3D) structures that change over time. These changes include twisting, which is 3D deformation that cannot happen in two dimensions. Twisting is linked to important adaptive functions of organs, such as adjusting the orientation of leaves and flowers in plants to align with environmental stimuli (e.g. light, gravity). Despite its importance, the underlying mechanism for twisting remains to be determined, partly because there is no rigorous method for quantifying the twisting of plant organs. Conventional studies have relied on approximate measurements of the twisting angle in 2D, with arbitrary choices of observation angle. Here, we present the first rigorous quantification of the 3D twisting angles of Arabidopsis petioles based on light sheet microscopy. Mathematical separation of bending and twisting with strict definition of petiole cross-sections were implemented; differences in the spatial distribution of bending and twisting were detected via the quantification of angles along the petiole. Based on the measured values, we discuss that minute degrees of differential growth can result in pronounced twisting in petioles.

Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

Numerical exploration on snap buckling of a pre-stressed hemispherical gridshell

2021 ◽  
pp. 1-11
Author(s):  
Weicheng Huang ◽  
Longhui Qin ◽  
Qiang Chen
Keyword(s):  
Three Dimensional ◽  
Energy Functional ◽  
Elastic Rods ◽  
Geometrically Nonlinear ◽  
Local Response ◽  
Micro Electro Mechanical Systems ◽  
One Dimensional ◽  
Numerical Exploration ◽  
Planar Grid ◽  
Fundamental Understanding

Abstract Motivated by the observations of snap-through phenomena in pre-stressed strips and curved shells, we numerically investigate the snapping of a pre-buckled hemispherical gridshell under apex load indentation. Our experimentally validated numerical framework on elastic gridshell simulation combines two components: (i) Discrete Elastic Rods method, for the geometrically nonlinear description of one dimensional rods; and (ii) a naive penalty-based energy functional, to perform the non-deviation condition between two rods at joint. An initially planar grid of slender rods can be actuated into a three dimensional hemispherical shape by loading its extremities through a prescribed path, known as buckling induced assembly; next, this pre-buckled structure can suddenly change its bending direction at some threshold points when compressing its apex to the other side. We find that the hemispherical gridshell can undergo snap-through buckling through two different paths based on two different apex loading conditions. The first critical snap-through point slightly increases as the number of rods in gridshell structure becomes denser, which emphasizes the mechanically nonlocal property in hollow grids, in contrast to the local response of continuum shells. The findings may bridge the gap among rods, grids, knits, and shells, for a fundamental understanding of a group of thin elastic structures, and inspire the design of novel micro-electro-mechanical systems and functional metamaterials.

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