scholarly journals A General Theory of Polymer Ejection Tested in a Quasi Two-Dimensional Space

2021 ◽  
Author(s):  
Pai-Yi Hsiao ◽  
Wei-Yei Chen
Keyword(s):  
Volume Fraction ◽  
Dimensional Space ◽  
Outer Space ◽  
Three Dimensional ◽  
Pore Channel ◽  
Escape Time ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Polymer Translocation ◽  
Dynamics Simulations

Abstract A general ejection theory of polymer is developed in a two- and three-dimensional space.A polymer is confined initially in a cavity and ejects spontaneously to the outer space through a nanopore channel without the help of any external stimulus. A reflective wall boundary is set at the pore entrance to prevent the falling of the head monomer of chain into the cavity. Three stages are distinguished in a process: (1) the entering stage, in which the head monomer enters the pore to search for a way to traverse the pore channel, (2) the main ejection stage, in which the chain body is transported from the cavity to the outer space, (3) the leaving stage, in which the tail monomer passes through and leaves the pore channel. Depending on the number of the monomers remaining in the cavity, the main ejection stage can be divided into the confined and the non-confined stages. The non-confined stage can be further split into the thermal escape and the entropic pulling stages. The Onsager's variational principle is used to derive the kinetics equation of ejection. The escape time is calculated from the corresponding Kramers' escape problem.Extensive molecular dynamics simulations are then performed in a quasi two-dimensional space to verify the theory. The variation of the ejection speed is carefully examined in a process. The decreasing behavior of the number of monomers in the cavity is studied in details. The scaling properties of the spending time at each processing stage are investigated systematically by varying the chain length, the cavity diameter, and the initial volume fraction of chain. The results of simulation support firmly the predictions of the theory, cross-checked in the studies of various topics. Together with the previous investigations in the three-dimensional space, the generalized theory is very robust able to explain the two seemly different phenomena, polymer ejection and polymer translocation, under the same theoretical framework in the two space dimensions.

scholarly journals A general theory of polymer ejection tested in a quasi two-dimensional space

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pai-Yi Hsiao ◽  
Wei-Yei Chen
Keyword(s):  
Volume Fraction ◽  
Dimensional Space ◽  
Outer Space ◽  
Three Dimensional ◽  
Pore Channel ◽  
Escape Time ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Dynamics Simulations ◽  
Three Dimensional Space

AbstractA general ejection theory of polymer is developed in a two- and three-dimensional space. A polymer is confined initially in a cavity and ejects spontaneously to the outer space through a nanopore channel without the help of any external stimulus. A reflective wall boundary is set at the pore entrance to prevent the falling of the head monomer of chain into the cavity. Three stages are distinguished in a process: (1) an entering stage, in which the head monomer enters the pore to search for a way to traverse the pore channel, (2) a main ejection stage, in which the chain body is transported from the cavity to the outer space, (3) a leaving stage, in which the tail monomer passes through and leaves the pore channel. Depending on the number of the monomers remaining in the cavity, the main ejection stage can be divided into the confined and the non-confined stages. The non-confined stage can be further split into the thermal escape and the entropic pulling stages. The Onsager’s variational principle is applied to derive the kinetics equation of ejection. The escape time is calculated from the corresponding Kramers’ escape problem. Extensive molecular dynamics simulations are then performed in a quasi two-dimensional space to verify the theory. The variation of the ejection speed is carefully examined. The decreasing behavior of the number of monomers in the cavity is studied in details. The scaling properties of the spending time at each processing stage are investigated systematically by varying the chain length, the cavity diameter, and the initial volume fraction of chain. The results of simulation support firmly the predictions of the theory, cross-checked in the studies of various topics. In combining with the previous investigations in the three-dimensional space, the generalized theory is very robust, able to explain the two seemly different phenomena, polymer ejection and polymer translocation, together under the same theoretical framework in the two space dimensions.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

Symbol recognition system based on 3D stereo vision

2020 ◽  
pp. 1-10
Author(s):  
Linlin Wang
Keyword(s):  
Camera Calibration ◽  
Stereo Vision ◽  
Stereo Matching ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Recognition System ◽  
Symbol Recognition ◽  
Two Dimensional ◽  
Measuring Machine ◽  
Left And Right

With the continuous development of computer science and technology, symbol recognition systems may be converted from two-dimensional space to three-dimensional space. Therefore, this article mainly introduces the symbol recognition system based on 3D stereo vision. The three-dimensional image is taken by the visual coordinate measuring machine in two places on the left and right. Perform binocular stereo matching on the edge of the feature points of the two images. A corner detection algorithm combining SUSAN and Harris is used to detect the left and right camera calibration templates. The two-dimensional coordinate points of the object are determined by the image stereo matching module, and the three-dimensional discrete coordinate points of the object space can be obtained according to the transformation relationship between the image coordinates and the actual object coordinates. Then draw the three-dimensional model of the object through the three-dimensional drawing software. Experimental data shows that the logic resources and memory resources occupied by image preprocessing account for 30.4% and 27.4% of the entire system, respectively. The results show that the system can calibrate the internal and external parameters of the camera. In this way, the camera calibration result will be more accurate and the range will be wider. At the same time, it can effectively make up for the shortcomings of traditional modeling techniques to ensure the measurement accuracy of the detection system.

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals Capacity of Inhomogeneous Hybrid Wireless Networks in Three-Dimensional Space

2015 ◽  
Vol 11 (9) ◽  
pp. 47
Author(s):  
Feng Wu ◽  
Jiang Zhu ◽  
Yilong Tian ◽  
Zhipeng Xi
Keyword(s):  
Sensor Node ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Capacity ◽  
Throughput Capacity ◽  
Two Dimensional ◽  
Hybrid Wireless Networks ◽  
Node Distribution ◽  
Analytical Expressions ◽  
Three Dimensional Space

Network capacity has been widely studied in recent years. However, most of the literatures focus on the networks where nodes are distributed in a two-dimensional space. In this paper, we propose a 3D hybrid sensor network model. By setting different sensor node distribution probabilities for cells, we divide all the cells in the network into dense cells and sparse cells. Analytical expressions of the aggregate throughput capacity are obtained. We also find that suitable inhomogeneity can increase the network throughput capacity.

Map fragmentation in two- and three-dimensional environments

2013 ◽  
Vol 36 (5) ◽  
pp. 569-570 ◽  
Author(s):  
Homare Yamahachi ◽  
May-Britt Moser ◽  
Edvard I. Moser
Keyword(s):  
Small Area ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Brain Circuits ◽  
Three Dimensional Space

AbstractThe suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in complex two-dimensional environments. How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.

Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

2011 ◽  
Vol 137 ◽  
pp. 1-6
Author(s):  
Qing Li ◽  
Xiao Xiang Yang
Keyword(s):  
Carbon Black ◽  
Mechanical Behavior ◽  
Plane Stress ◽  
Volume Fraction ◽  
Filler Particle ◽  
Three Dimensional ◽  
Rubber Matrix ◽  
Two Dimensional ◽  
Rubber Composites ◽  
Dimensional Plane

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

Sign in / Sign up

Export Citation Format

Share Document