scholarly journals Multiple Twisted Chiral Nematic Structures in Cylindrical Confinement

Crystals ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 576
Author(s):  
Milan Ambrožič ◽  
Apparao Gudimalla ◽  
Charles Rosenblatt ◽  
Samo Kralj
Keyword(s):  
Liquid Crystal ◽  
Elastic Constant ◽  
Model Parameters ◽  
Free Energies ◽  
Type Analysis ◽  
Chiral Nematic ◽  
The Stability ◽  
Stability Of Structures ◽  
The Impact ◽  
Insight Into

In this article, we theoretically and numerically study the chirality and saddle-splay elastic constant ( K 24 ) -enabled stability of multiple twist-like nematic liquid crystal (LC) structures in cylindrical confinement. We focus on the so-called radially z-twisted (RZT) and radially twisted (RT) configurations, which simultaneously exhibit twists in different spatial directions. We express the free energies of the structures in terms of dimensionless wave vectors, which characterise the structures and play the roles of order parameters. The impact of different confinement anchoring conditions is explored. A simple Landau-type analysis provides an insight into how different model parameters influence the stability of structures. We determine conditions for which the structures are stable in chiral and also nonchiral LCs. In particular, we find that the RZT structure could exhibit macroscopic chirality inversion upon varying the relevant parameters. This phenomenon could be exploited for the measurement of   K 24 .

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals Computational Insight into the Rope-Skipping Isomerization of Diarylether Cyclophanes

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2127
Author(s):  
Thomas J. Summers ◽  
Hrishikesh Tupkar ◽  
Tyler M. Ozvat ◽  
Zoë Tregillus ◽  
Kenneth A. Miller ◽  
...  
Keyword(s):  
Asymmetric Catalysis ◽  
Room Temperature ◽  
Chemical Bonds ◽  
Chiral Molecules ◽  
Free Energies ◽  
Design And Synthesis ◽  
The Impact ◽  
Rope Skipping ◽  
Temperature Factors ◽  
Insight Into

The restricted rotation of chemical bonds may lead to the formation of stable, conformationally chiral molecules. While the asymmetry in chiral molecules is generally observed in the presence of one or more stereocenters, asymmetry exhibited by conformational chirality in compounds lacking stereocenters, called atropisomerism, depends on structural and temperature factors that are still not fully understood. This atropisomerism is observed in natural diarylether heptanoids where the length of the intramolecular tether constrains the compounds to isolable enantiomers at room temperature. In this work, we examine the impact tether length has on the activation free energies to isomerization of a diarylether cyclophane substructure with a tether ranging from 6 to 14 carbons. Racemization activation energies are observed to decay from 48 kcal/mol for a 7-carbon tether to 9.2 kcal/mol for a 14-carbon tether. Synthetic efforts to experimentally test these constraints are also presented. This work will likely guide the design and synthesis of novel asymmetric cyclophanes that will be of interest in the catalysis community given the importance of atropisomeric ligands in the field of asymmetric catalysis.

scholarly journals Using the LIST model to Estimate the Effects of Contact Tracing on COVID-19 Endemic Equilibria in England and its Regions

2020 ◽  
Author(s):  
Rosalyn J. Moran ◽  
Alexander J. Billig ◽  
Maell Cullen ◽  
Adeel Razi ◽  
Jean Daunizeau ◽  
...  
Keyword(s):  
Endemic Equilibrium ◽  
Contact Tracing ◽  
Model Parameters ◽  
Infection Rates ◽  
Stable States ◽  
Medium Term ◽  
The Stability ◽  
Lower Death Rate ◽  
The Impact ◽  
List Model

AbstractGovernments across Europe are preparing for the emergence from lockdown, in phases, to prevent a resurgence in cases of COVID-19. Along with social distancing (SD) measures, contact tracing – find, track, trace and isolate (FTTI) policies are also being implemented. Here, we investigate FTTI policies in terms of their impact on the endemic equilibrium. We used a generative model – the dynamic causal ‘Location’, ‘Infection’, ‘Symptom’ and ‘Testing’ (LIST) model to identify testing, tracing, and quarantine requirements. We optimised LIST model parameters based on time series of daily reported cases and deaths of COVID-19 in England— and based upon reported cases in the nine regions of England and in all 150 upper tier local authorities. Using these optimised parameters, we forecasted infection rates and the impact of FTTI for each area—national, regional, and local. Predicting data from early June 2020, we find that under conditions of medium-term immunity, a ‘40%’ FTTI policy (or greater), could reach a distinct endemic equilibrium that produces a significantly lower death rate and a decrease in ICU occupancy. Considering regions of England in isolation, some regions could substantially reduce death rates with 20% efficacy. We characterise the accompanying endemic equilibria in terms of dynamical stability, observing bifurcation patterns whereby relatively small increases in FTTI efficacy result in stable states with reduced overall morbidity and mortality. These analyses suggest that FTTI will not only save lives, even if only partially effective, and could underwrite the stability of any endemic steady-state we manage to attain.

scholarly journals Mathematical analysis of an age structured epidemic model with a quarantine class

2021 ◽  
Author(s):  
Bedreddine AINSEBA ◽  
Tarik Touaoula ◽  
Zakia Sari
Keyword(s):  
Reproduction Number ◽  
Asymptotic Behavior Of Solutions ◽  
Model Parameters ◽  
Qualitative Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
The Impact

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave their class of quarantine before being completely recovered and thus will participate again to the transmission of the disease. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give the explicit expression of the epidemic reproduction number $R_{0}.$ This number is a combination of the classical epidemic reproduction number for the SIQR model and a new epidemic reproduction number corresponding to the individuals infected by a relapsed person from the R-class. It is shown that, if $R_{0}\leq 1$, the disease free equilibrium is globally asymptotically stable and becomes unstable for $R_{0}>1$. Secondly, while $R_{0}>1$, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset $\Omega_{0}.$

The impact of flexibility of polyimides backbones on the stability of liquid crystal vertical alignment

RSC Advances ◽  
2016 ◽  
Vol 6 (60) ◽  
pp. 55479-55489 ◽  
Author(s):  
Xinyuan Che ◽  
Shiming Gong ◽  
Leishan Shao ◽  
Tian Lan ◽  
Fei Wang ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
The Other ◽  
Side Chain ◽  
Vertical Alignment ◽  
The Stability ◽  
The Impact ◽  
Chain Type

Two side-chain-type polyimides (RPI and SPI) containing different backbones induced vertical alignments of liquid crystals, after rubbing, one maintained stable vertical, while the other transformed from vertical into parallel.

Predicting the Benefits of Adding Ternary Elements to Al-Sc Alloys

2006 ◽  
Vol 979 ◽  
Author(s):  
Darko Simonovic ◽  
Marcel H. F. Sluiter
Keyword(s):  
Aging Temperature ◽  
Density Functional ◽  
Enthalpy Of Mixing ◽  
Miscibility Gap ◽  
Zero Temperature ◽  
Electronic Density ◽  
Environment Type ◽  
The Stability ◽  
Stability Of Structures ◽  
Insight Into

AbstractWe seek to explain 1) the effectiveness of substituting Sc with Dy, Er, Y and 2) the loss of properties when Sc is replaced with Yb, Gd and Sm [1]. For a preliminary insight into the stability of structures we utilize the concept of Atomic Environment Type (AET) as pertaining to trialuminides. Electronic density functional total energy calculations at zero temperature are performed to obtain the enthalpy of mixing of quasi-binary Al-Sc-X structures. Estimates of the entropy are used to compute the stability regions of Al3Sc1-αXα L12 phase. We show that Sc is completely miscible with X=Dy, Er, Y and that there is a miscibility gap for X=Yb, Gd and Sm at temperatures near the aging temperature of Al-Sc alloys.

New insight into the reaction mechanism of carbon disulfide hydrolysis and the impact of H2S with density functional modeling

2019 ◽  
Vol 43 (5) ◽  
pp. 2347-2352 ◽  
Author(s):  
Xin Song ◽  
Chi Wang ◽  
Khaled A. M. Gasem ◽  
Kai Li ◽  
Xin Sun ◽  
...  
Keyword(s):  
Reaction Mechanism ◽  
Carbon Disulfide ◽  
Density Functional ◽  
Functional Modeling ◽  
One Step ◽  
The Stability ◽  
The Impact ◽  
Insight Into

One-step hydrolysis can easily take place without a catalyst. H2S is beneficial in maintaining the stability of the intermediates.

The Research of Warning Model of Hidden Failure Based on Data Mining

2016 ◽  
Vol 693 ◽  
pp. 1844-1848
Author(s):  
Jing Liu ◽  
Qing Xiang Zhu ◽  
Xin Yu ◽  
Jing Xin Wang ◽  
Yi Ge Huang
Keyword(s):  
Data Mining ◽  
Normal Operation ◽  
Model Parameters ◽  
National Defense ◽  
Hidden Failure ◽  
Complex Equipment ◽  
The Stability ◽  
Hidden Failures ◽  
Warning Model ◽  
The Impact

Complex equipment is mainly used in important areas of national defense, health care, banking, etc. Consequences of failure are relatively severe, while the hidden failures are contained in the most complex devices as the process is running. Hidden failures in the normal operation of the device is difficult to find, and only under certain conditions will be triggered, while other faults may be led. The stability of the running system will be undermined. In order to monitor the occurrence and development of hidden failure of complex equipment, a hidden failure warning model based on data mining has been put forward, and the theory of the model has been analyzed, the selection gist of the model parameters has been given. The result shows that the accuracy of hidden failure impact value forecast by the model is 93.33%, the impact degree of the hidden failure effect on the dominant failure can be effectively monitored, and the model makes a good preventative effect against the sudden failure caused by the hidden failure.

scholarly journals Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.

2020 ◽  
Vol 51 (4) ◽  
pp. 261-287
Author(s):  
Shaibu Osman ◽  
Oluwole Daniel Makinde ◽  
David Mwangi Theuri
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Model Problem ◽  
Control Strategies ◽  
Model Parameters ◽  
Contaminated Food ◽  
Serious Disease ◽  
The Stability ◽  
The Impact ◽  
Disease Free

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.

Dietary Vitamin and Stability of Oral Anticoagulation: Proposal of a Diet with Constant Vitamin K1 Content

1997 ◽  
Vol 77 (03) ◽  
pp. 504-509 ◽  
Author(s):  
Sarah L Booth ◽  
Jacqueline M Charnley ◽  
James A Sadowski ◽  
Edward Saltzman ◽  
Edwin G Bovill ◽  
...  
Keyword(s):  
Dietary Intake ◽  
Vitamin K ◽  
High Performance ◽  
Case Reports ◽  
Food Composition ◽  
Dietary Guidelines ◽  
Dietary Vitamin ◽  
Vitamin K1 ◽  
The Stability ◽  
The Impact

SummaryCase reports cited in Medline or Biological Abstracts (1966-1996) were reviewed to evaluate the impact of vitamin K1 dietary intake on the stability of anticoagulant control in patients using coumarin derivatives. Reported nutrient-drug interactions cannot always be explained by the vitamin K1 content of the food items. However, metabolic data indicate that a consistent dietary intake of vitamin K is important to attain a daily equilibrium in vitamin K status. We report a diet that provides a stable intake of vitamin K1, equivalent to the current U.S. Recommended Dietary Allowance, using food composition data derived from high-performance liquid chromatography. Inconsistencies in the published literature indicate that prospective clinical studies should be undertaken to clarify the putative dietary vitamin K1-coumarin interaction. The dietary guidelines reported here may be used in such studies.

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