Isotropic Properties of Platelet-Reinforced Media

1979 ◽  
Vol 101 (3) ◽  
pp. 299-303 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Composite Material ◽  
Edge Effects ◽  
Volume Fraction ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Effective Moduli ◽  
Dilute Suspension ◽  
Stiffening Effect ◽  
Special Case ◽  
Three Dimensional Space

The effective moduli are derived for a composite material containing platelet-type inclusions. The platelets are taken to be randomly oriented in three-dimensional space and to have so large a diameter-to-thickness ratio that edge effects can be neglected. The effective moduli that are derived reduce to known results in the special case of a dilute suspension. Comparisons are made with the corresponding type of composite medium that involves randomly oriented fibers. For the same volume fraction of reinforcing phase, the platelet case provides a stiffening effect about three times greater than the fiber case.

Generalized Euler-Venn Diagrams for Fuzzy Sets

2020 ◽  
Vol 7 (4) ◽  
pp. 34-43
Author(s):  
Yu. Mironova
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Venn Diagram ◽  
Linguistic Variables ◽  
Venn Diagrams ◽  
Time Of Year ◽  
Special Case ◽  
Three Dimensional Space

The fuzzy set concept is often used in solution of problems in which the initial data is difficult or impossible to represent in the form of specific numbers or sets. Geo-information objects are distinguished by their uncertainty, their characteristics are often vague and have some error. Therefore, in the study of such objects is introduced the concept of "fuzziness" — fuzzy sets, fuzzy logic, linguistic variables, etc. The fuzzy set concept is given in the form of membership function. An ordinary set is a special case of a fuzzy one. If we consider a fuzzy object on the map, for example, a lake that changes its shape depending on the time of year, we can build up for it a characteristic function from two variables (the object’s points coordinates) and put a certain number in accordance with each point of the object. That is, we can describe a fuzzy set using its two-dimensional graphical image. Thus, we obtain an approximate view of a surface z = μ(x, y) in three-dimensional space. Let us now draw planes parallel to the plane. We’ll obtain intersections of our surface with these planes at 0 ≤ z ≤ 1. Let's call them as isolines. By projecting these isolines on the OXY plane, we’ll obtain an image of our fuzzy set with an indication of intermediate values μ(x, y) linked to the set’s points coordinates. So we’ll construct generalized Euler — Venn diagrams which are a generalization of well-known Euler — Venn diagrams for ordinary sets. Let's consider representations of operations on fuzzy sets A a n d B. Th e y u s u a l l y t a k e : μA B = min (μA,μB ), μA B = max (μA,μB ), μA = 1 − μA. Algebraic operations on fuzzy sets are defined as follows: μ A B x μ A x μ B x ( ) = ( ) + ( ) − −μ A (x)μ B (x), μ A B x μ A x μ B x ( ) = ( ) ( ), μ A (x) = 1 − μ A (x). Let's construct for a particular problem a generalized Euler — Venn diagram corresponding to it, and solve subtasks graphically, using operations on fuzzy sets, operations of intersection and integrating of the diagram’s bars.

A General Model for Thermal Conductivity and Electric Conductivity of Nanofluids

2012 ◽  
Vol 614-615 ◽  
pp. 529-535 ◽  
Author(s):  
Wei Ting Jiang
Keyword(s):  
Electric Conductivity ◽  
Volume Fraction ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Simulation Method ◽  
Space Structure ◽  
Liquid Molecule ◽  
Nanoparticle Clusters ◽  
Network Method ◽  
Three Dimensional Space

Nanoparticles in nanofluids are in the form of nanoparticle clusters caused by aggregation. In order to calculate the thermal and electric conductivity of the nanofluids, the growth process and three-dimensional space structure of the nanoparticle cluster in the host fluid is simulated, and then the thermal and electric conductivity of the cluster are calculated with the resistance network method. The thermal and electric conductivity of the nanofluid are calculated based on the simulated thermal and electric conductivity of nanoparticle clusters, the volume fraction of nanoparticle clusters to the nanofluid as well as the liquid molecule adsorption layer of the nanoparticle. The simulation method is validated by experimental data.

scholarly journals Ideals of Herzog–Northcott type

2011 ◽  
Vol 54 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Liam O'Carroll ◽  
Francesc Planas-Vilanova
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Regular Sequence ◽  
Point Of View ◽  
Prime Ideals ◽  
Monomial Curves ◽  
Definition Of ◽  
Minimal Prime ◽  
Special Case ◽  
Three Dimensional Space

AbstractThis paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial curves in three-dimensional space, which were studied by Herzog. In the broader context studied here, these ideals are identified as Northcott ideals in the sense of Vasconcelos, and so their liaison properties are displayed. It is shown that they are set-theoretically complete intersections, revisiting the work of Bresinsky and of Valla. Even when the three elements are taken to be variables in a polynomial ring in three variables over a field, this point of view gives a larger class of ideals than just the defining ideals of monomial curves. We then characterize when the ideals in this larger class are prime, we show that they are usually radical and, using the theory of multiplicities, we give upper bounds on the number of their minimal prime ideals, one of these primes being a uniquely determined prime ideal of definition of a monomial curve. Finally, we provide examples of characteristic-dependent minimal prime and primary structures for these ideals.

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.

scholarly journals SELF-FOCUSING AND SELF-TRAPPING OF SPHERCIAL BEAMS IN A NONLINEAR MEDIUM

1994 ◽  
Vol 25 (2) ◽  
pp. 179-187
Author(s):  
KIN-CHUNG NG
Keyword(s):  
Dimensional Space ◽  
Focal Length ◽  
Three Dimensional ◽  
Spherical Waves ◽  
Self Focusing ◽  
Self Trapping ◽  
Diffraction Effects ◽  
Incident Waves ◽  
Special Case ◽  
Three Dimensional Space

Self-focusing and self-trapping of optical beams are studied by obtaining the asymptotic solution of the nonlinear reduced wave equation \[ \nabla^2 u +k^2n^2(|u|^2)u=0\] in three dimensional space where the incident waves are assumed to be spherical waves . In order to discuss diffraction effects and self-focusing effects of the beam, the concepts of diffraction length and focal length are introduced. It is shown that diffraction effects and self-focusing effects occur in different regions. This means that diffraction cannot, in general, influence self-focusing. In the special case where diffraction effects and self-focusing effects are balanced, a self-trapped beam is shown to exist.  

A Prediction Method for Thermal Conductivity and Electric Conductivity of Nanofluids Based on Particles Aggregation Theory

2007 ◽  
Author(s):  
Guo-Liang Ding ◽  
Wei-Ting Jiang ◽  
Yi-Feng Gao
Keyword(s):  
Volume Fraction ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Prediction Method ◽  
Simulation Method ◽  
Space Structure ◽  
Liquid Molecule ◽  
Nanoparticle Clusters ◽  
Network Method ◽  
Three Dimensional Space

Nanoparticles in nanofluids are in the form of nanoparticle clusters caused by aggregation. In order to calculate the thermal and electric conductivities of the nanofluids, the growth process and three-dimensional space structure of the nanoparticle cluster in the host fluid was simulated, and then the thermal and electric conductivities of the cluster were calculated with the resistance network method. The thermal and electric conductivities of the nanofluid were calculated based on the simulated thermal and electric conductivities of nanoparticle clusters, the volume fraction of nanoparticle clusters to the nanofluid as well as the liquid molecule adsorption layer of the nanoparticle. The simulation method was validated by experimental data.

Just the tip of the iceberg: The bicoded map is but one instantiation of scalable spatial representation structures

2013 ◽  
Vol 36 (5) ◽  
pp. 565-566 ◽  
Author(s):  
Holger Schultheis ◽  
Thomas Barkowsky
Keyword(s):  
Spatial Representation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Alternative Account ◽  
Interesting Candidate ◽  
Special Case ◽  
Three Dimensional Space

AbstractAlthough the bicoded map constitutes an interesting candidate representation, proposing it as the predominant representation for three-dimensional space is too restrictive. We present and argue for scalable spatial representation structures as a more comprehensive alternative account that includes the bicoded map as a special case.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

Sign in / Sign up

Export Citation Format

Share Document