The Products of Molecules and Clusters on Polytopes of Higher Dimension

2021 ◽  
pp. 144-181
Keyword(s):  
Arbitrary Dimension ◽  
Higher Dimension ◽  
Living Matter ◽  
One Dimensional ◽  
Face To Face ◽  
Different Dimensions

The molecules and clusters given in the previous chapters are multiplied by polytopes of different dimensions and types: from a one-dimensional segment to polytopes of arbitrary dimension n. The structure of their products is analytically determined. Due to the presence in the products of polytopes of several families of parallel edges, these polytopes can become the basis of parallelohedrons, dividing the space of higher dimension face to face. The products of polytopes can simulate continuous areas of living matter of finite sizes.

Optimization of synthetic jet actuation by analytical modeling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Max Huber ◽  
Andreas Zienert ◽  
Perez Weigel ◽  
Martin Schüller ◽  
Hans-Reinhard Berger ◽  
...  
Keyword(s):  
High Performance ◽  
Synthetic Jet ◽  
Parameter Study ◽  
Content Type ◽  
One Dimensional ◽  
Wide Range ◽  
Jet Actuators ◽  
Different Dimensions ◽  
Oscillation Correction ◽  
Good Agreement

Purpose The purpose of this paper is to analyze and optimize synthetic jet actuators (SJAs) by means of a literature-known one-dimensional analytical model. Design/methodology/approach The model was fit to a wide range of experimental data from in-house built SJAs with different dimensions. A comprehensive parameter study was performed to identify coupling between parameters of the model and to find optimal dimensions of SJAs. Findings The coupling of two important parameters, the diaphragm resonance frequency and the cavity volume, can be described by a power law. Optimal orifice length and diameter can be calculated from cavity height in good agreement with literature. A transient oscillation correction is required to get correct simulation outcomes. Originality/value Based on these findings, SJA devices can be optimized for maximum jet velocity and, therefore, high performance.

scholarly journals Crystal structures of 4-chloropyridine-2-carbonitrile and 6-chloropyridine-2-carbonitrile exhibit different intermolecular π-stacking, C—H...Nnitrileand C—H...Npyridineinteractions

2015 ◽  
Vol 71 (7) ◽  
pp. 852-856 ◽  
Author(s):  
Matthew J. Montgomery ◽  
Thomas J. O'Connor ◽  
Joseph M. Tanski
Keyword(s):  
Solid State ◽  
Crystal Structures ◽  
Pyridine Ring ◽  
Nitrile Group ◽  
Two Dimensional ◽  
One Dimensional ◽  
Face To Face ◽  
Π Stacking

The two title compounds are isomers of C6H3ClN2containing a pyridine ring, a nitrile group, and a chloro substituent. The molecules of each compound pack together in the solid state with offset face-to-face π-stacking, and intermolecular C—H...Nnitrileand C—H...Npyridineinteractions. 4-Chloropyridine-2-carbonitrile, (I), exhibits pairwise centrosymmetric head-to-head C—H...Nnitrileand C—H...Npyridineinteractions, forming one-dimensional chains, which are π-stacked in an offset face-to-face fashion. The intermolecular packing of the isomeric 6-chloropyridine-2-carbonitrile, (II), which differs only in the position of the chloro substituent on the pyridine ring, exhibits head-to-tail C—H...Nnitrileand C—H...Npyridineinteractions, forming two-dimensional sheets which are π-stacked in an offset face-to-face fashion. In contrast to (I), the offset face-to-face π-stacking in (II) is formed between molecules with alternating orientations of the chloro and nitrile substituents.

scholarly journals Estimating Differential Entropy using Recursive Copula Splitting

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 236 ◽  
Author(s):  
Gil Ariel ◽  
Yoram Louzoun
Keyword(s):  
Compact Support ◽  
Mixed Type ◽  
Random Variables ◽  
Differential Entropy ◽  
High Dimensions ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Different Dimensions

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.

Applicability of One-Dimensional Transient Solutions for Ground-Coupled Heat Transfer in Buildings

2013 ◽  
Vol 361-363 ◽  
pp. 386-390 ◽  
Author(s):  
J Daniel Mena Baladés ◽  
Ismael Rodríguez Maestre ◽  
Pascual Álvarez Gómez ◽  
J. Luis Foncubierta Blázquez
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Finite Element Software ◽  
Coupled Heat Transfer ◽  
Transient Solutions ◽  
Detailed Simulation ◽  
Different Dimensions ◽  
Multidimensional Effects

The ground-coupled heat transfer in buildings is a complex, transient and multidimensional problem. There have been many studies focused to obtain the heat flux in slab and basement foundations. Most of them include the multidimensional effects occur at the perimeter however there are situations in which the heat transfer is mainly one-dimensional. This paper presents a study that aims to establish the accurate of an analytical one-dimensional solution to estimate the ground-coupled heat transfer. Detailed simulation by using finite element software is used to obtain the total heat flux at indoor surface of the building for a whole year. Typical slabs and basements foundations for different dimensions have been analyzed. A correlation to estimate the relative error is proposed.

scholarly journals Entropic Separations of Mixtures of Aromatics by Selective Face-to-Face Molecular Stacking in One-Dimensional Channels of Metal-Organic Frameworks and Zeolites

ChemPhysChem ◽  
2014 ◽  
Vol 16 (3) ◽  
pp. 532-535 ◽  
Author(s):  
Ariana Torres-Knoop ◽  
Salvador R. G. Balestra ◽  
Rajamani Krishna ◽  
Sofía Calero ◽  
David Dubbeldam
Keyword(s):  
Metal Organic Frameworks ◽  
One Dimensional ◽  
Face To Face ◽  
Metal Organic ◽  
Molecular Stacking

Design of a New Internet of Things Storage Mailbox System

2013 ◽  
Vol 753-755 ◽  
pp. 2841-2844
Author(s):  
Ke Wang Huang
Keyword(s):  
Internet Of Things ◽  
Personal Information ◽  
The Internet ◽  
Rfid Technology ◽  
One Dimensional ◽  
Face To Face ◽  
The Internet Of Things

The paper focuses on design of the internet of things storage mailbox system. The system uses RFID technology and compatible one-dimensional barcode to shield the personal information of the sender and the recipient. It manages the authentication of the user, the parcel, the courier and the storage mailbox remotely. And sending and receiving the parcel is not face-to-face handover. The system monitors the process of sending and receiving so as to ensure that the parcel will be sent to the recipient accurately and efficiently. The use of the system will avoid malicious parcel and waste parcel appearing.

scholarly journals Multivariate Markov Families of Copulas

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Ludger Overbeck ◽  
Wolfgang M. Schmidt
Keyword(s):  
Markov Property ◽  
Dimensional Case ◽  
Dependence Structure ◽  
Multivariate Process ◽  
One Dimensional ◽  
Multivariate Case ◽  
Finite Dimensional ◽  
Different Dimensions ◽  
The One ◽  
Dimension One

AbstractFor the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.

The bis(ethylenedithio)tetrathiafulvalene-based ionic charge-transfer complex with 2,3-dichloro-5,6-dicyano-p-benzoquinone

2013 ◽  
Vol 69 (4) ◽  
pp. 400-402
Author(s):  
Yuki Nakagawa ◽  
Yukihiro Takahashi ◽  
Jun Harada ◽  
Tamotsu Inabe
Keyword(s):  
Charge Transfer ◽  
Charge Transfer Complex ◽  
Ionic Charge ◽  
One Dimensional ◽  
Face To Face ◽  
Ladder System ◽  
Donor And Acceptor ◽  
Ct Complex ◽  
Centrosymmetric Dimers ◽  
Ct Complexes

In the ionic charge-transfer (CT) complex composed of bis(ethylenedithio)tetrathiafulvalene (ET) and 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ), C10H8S8·C8Cl2N2O2, the donor and acceptor molecules both form centrosymmetric dimers associated by strong face-to-face π–π interactions. The disordered DDQ molecules form a one-dimensional π-stacked column, while the ET molecules form a two-leg ladder through additional short S...S contacts between adjacent π–π-bonded dimers. The crystal structure of ET–DDQ revealed in this study will provide a valuable example of the two-leg spin ladder system, which has rarely been reported for ET-based CT complexes.

Theoretical design of MoO3-based high-rate lithium ion battery electrodes: the effect of dimensionality reduction

2014 ◽  
Vol 2 (45) ◽  
pp. 19180-19188 ◽  
Author(s):  
Fengyu Li ◽  
Carlos R. Cabrera ◽  
Zhongfang Chen
Keyword(s):  
Density Functional ◽  
Three Dimensional ◽  
Lithium Ion ◽  
High Rate ◽  
Functional Theory ◽  
One Dimensional ◽  
Theoretical Design ◽  
Different Dimensions ◽  
Li Adsorption ◽  
And Diffusion

By means of density functional theory computations, we systematically investigated the behavior of lithium (Li) adsorption and diffusion on MoO3 with different dimensions: including three-dimensional (3D) bulk, two-dimensional (2D) double-layer, 2D monolayer and one-dimensional (1D) nanoribbons.

scholarly journals Directed Rooted Forests in Higher Dimension

10.37236/5819 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Olivier Bernardi ◽  
Caroline J. Klivans
Keyword(s):  
Generating Function ◽  
Vector Fields ◽  
Arbitrary Dimension ◽  
Graph Laplacian ◽  
Connected Components ◽  
Higher Dimension ◽  
Cell Complexes ◽  
Open Questions ◽  
Higher Dimensional ◽  
Rooted Forest

For a graph $G$, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. This requires generalizing the notion of rooted forest to higher dimension. We also introduce orientations of higher dimensional rooted trees and forests. These orientations are discrete vector fields which lead to open questions concerning expressing homological quantities combinatorially.

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