A theoretical study of the changes in the statistical character of a polydisperse polymer system undergoing random degradation

1962 ◽  
Vol 270 (1340) ◽  
pp. 14-26 ◽  
Keyword(s):  
Theoretical Study ◽  
Laguerre Polynomials ◽  
Polymer System ◽  
Degradation Process ◽  
Initial Distribution ◽  
Statistical Information ◽  
Average Chain Length ◽  
Statistical Character ◽  
Polydisperse Polymer ◽  
Initial Distribution Function

The combinatorial procedure, employed in our earlier work in connexion with the problem of degradation of an initially monodisperse polymer system, is extended here to the polydisperse case. The results thus obtained are applied in order to study, stage by stage, the changes in the statistical character of the distribution in a number of typical cases. Next a scheme, based on an expansion of the initial distribution function in terms of the associated Laguerre polynomials, is developed in order to treat those cases in which the statistical information is confined only to a few low-order moments. Finally, we discuss the inverse problem of determining the characteristics of the initial distribution from a knowledge of the weight-average chain length at various stages of the degradation process.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

scholarly journals Reconfigurable Dual Peptide Tethered Polymer System Offers a Synergistic Solution for Next Generation Dental Adhesives

2021 ◽  
Vol 22 (12) ◽  
pp. 6552
Author(s):  
Esra Yuca ◽  
Sheng-Xue Xie ◽  
Linyong Song ◽  
Kyle Boone ◽  
Nilan Kamathewatta ◽  
...  
Keyword(s):  
Dental Materials ◽  
Polymer System ◽  
Adhesive System ◽  
Degradation Process ◽  
Peptide Sequence ◽  
Next Generation ◽  
Dental Adhesives ◽  
Tooth Structure ◽  
Low Viscosity ◽  
Restorative Dental Materials

Resin-based composite materials have been widely used in restorative dental materials due to their aesthetic, mechanical, and physical properties. However, they still encounter clinical shortcomings mainly due to recurrent decay that develops at the composite-tooth interface. The low-viscosity adhesive that bonds the composite to the tooth is intended to seal this interface, but the adhesive seal is inherently defective and readily damaged by acids, enzymes, and oral fluids. Bacteria infiltrate the resulting gaps at the composite-tooth interface and bacterial by-products demineralize the tooth and erode the adhesive. These activities lead to wider and deeper gaps that provide an ideal environment for bacteria to proliferate. This complex degradation process mediated by several biological and environmental factors damages the tooth, destroys the adhesive seal, and ultimately, leads to failure of the composite restoration. This paper describes a co-tethered dual peptide-polymer system to address composite-tooth interface vulnerability. The adhesive system incorporates an antimicrobial peptide to inhibit bacterial attack and a hydroxyapatite-binding peptide to promote remineralization of damaged tooth structure. A designer spacer sequence was incorporated into each peptide sequence to not only provide a conjugation site for methacrylate (MA) monomer but also to retain active peptide conformations and enhance the display of the peptides in the material. The resulting MA-antimicrobial peptides and MA-remineralization peptides were copolymerized into dental adhesives formulations. The results on the adhesive system composed of co-tethered peptides demonstrated both strong metabolic inhibition of S. mutans and localized calcium phosphate remineralization. Overall, the result offers a reconfigurable and tunable peptide-polymer hybrid system as next-generation adhesives to address composite-tooth interface vulnerability.

Modeling of Hardwood Pyrolysis Using the Convex Combination of the Mass Conversion Points

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Alok Dhaundiyal ◽  
Laszlo Toth
Keyword(s):  
Convex Combination ◽  
Initial Distribution ◽  
Mass Variation ◽  
Test Rig ◽  
Qualitative Aspect ◽  
Cross Sectional ◽  
Mass Conversion ◽  
Pyrolysis Reactor ◽  
Kinetics Of ◽  
Initial Distribution Function

Abstract This work investigates the kinetics of a pyrolysis reactor. Pyrolysis is demarcated as a two-step process that is the primary and the secondary decomposition of hardwood in the presence of nitrogen. The qualitative aspect of the analysis is performed by allowing the heterogeneous characteristics of the initial distribution function of volatile content. The temperature inside the reactor varies from 19 °C to 363.761 °C. The pressure of producer gas changes from 6 Pa to 26.8 Pa during the pyrolysis of hardwood, which affects the conversion of biomass with respect to temperature. The weighted fraction of the Weibull and the Rayleigh models is used for modeling the mass variation of the biomass inside the rector. The dimension of the reactor used for the experimental work has a length of 400 mm and a cross-sectional area of 9498.5 mm2. The pyrolysis test rig is programed for the cubical form of thermal history [T = (at3 + bt2 + ct − d)].

scholarly journals The Role of the Ostensives in Understanding Quantitative Statistical Variables

2021 ◽  
Vol 23 (4) ◽  
pp. 16-51
Author(s):  
Irene Mauricio Cazorla ◽  
Afonso Henriques ◽  
Gleidson Santos Correia ◽  
Cláudio Vitor Santana
Keyword(s):  
Data Collection ◽  
Basic Education ◽  
Theoretical Study ◽  
Statistical Information ◽  
Fundamental Aspect ◽  
Related Research ◽  
Anthropological Theory ◽  
Data Collection And Analysis ◽  
Concrete Materials

Background: One of the main challenges of teaching statistics in basic education is the treatment of quantitative statistical variables because, besides the calculations involved in the abstract measures, understanding the behaviour of these variables and the meaning of their statistics is complex by their very nature. In this sense, using manipulable concrete materials and the student’s action as ostensive mathematical objects in the management and representation of this type of variable can help understand them. Objectives: this research investigates how the concrete manipulable materials and the student’s action contribute to understanding and representing quantitative statistical variables in different registers. Design: we make theoretical reflections on the active use of the ostensive objects in the representation and transformation of data into statistics – tables, graphs, and summary measures – in basic education based on the anthropological theory of the didactic and the theory of registers of semiotic representation. Data collection and analysis: this is a theoretical study that uses results already published in related research. Results: the analyses point out that the use of the ostensive objects helps students’ understand the statistical concepts and that from this point on, they represent and transform the representations of statistical information in different registers more fluidly. Conclusions: the study reveals that using the ostensives and the students’ actions in managing statistical concepts is a fundamental aspect of learning.

Investigation of irradiation-induced nucleation processes in silicon and germanium

1995 ◽  
Vol 53 ◽  
pp. 224-225
Author(s):  
Harry A. Atwater ◽  
C.M. Yang ◽  
K.V. Shcheglov
Keyword(s):  
Room Temperature ◽  
Crystal Size ◽  
Initial Distribution ◽  
Engineering Control ◽  
Size Evolution ◽  
Silicon And Germanium ◽  
Ge Quantum Dot ◽  
And Control ◽  
Germanium Quantum Dots ◽  
Kinetics Of

Studies of the initial stages of nucleation of silicon and germanium have yielded insights that point the way to achievement of engineering control over crystal size evolution at the nanometer scale. In addition to their importance in understanding fundamental issues in nucleation, these studies are relevant to efforts to (i) control the size distributions of silicon and germanium “quantum dots𠇍, which will in turn enable control of the optical properties of these materials, (ii) and control the kinetics of crystallization of amorphous silicon and germanium films on amorphous insulating substrates so as to, e.g., produce crystalline grains of essentially arbitrary size.Ge quantum dot nanocrystals with average sizes between 2 nm and 9 nm were formed by room temperature ion implantation into SiO2, followed by precipitation during thermal anneals at temperatures between 30°C and 1200°C[1]. Surprisingly, it was found that Ge nanocrystal nucleation occurs at room temperature as shown in Fig. 1, and that subsequent microstructural evolution occurred via coarsening of the initial distribution.

Techniques For The Preparation of Tissue Samples Containing Injectable Polymer Microcapsules

1985 ◽  
Vol 43 ◽  
pp. 710-711
Author(s):  
G.E. Visscher ◽  
R. L. Robison ◽  
G. J. Argentieri
Keyword(s):  
Drug Delivery ◽  
Drug Delivery Systems ◽  
Gastrocnemius Muscle ◽  
Degradation Process ◽  
Delivery Systems ◽  
Tissue Reaction ◽  
Electron Microscopic ◽  
Tissue Samples ◽  
Injectable Polymer ◽  
Microscopic Techniques

The use of various bioerodable polymers as drug delivery systems has gained considerable interest in recent years. Among some of the shapes used as delivery systems are films, rods and microcapsules. The work presented here will deal with the techniques we have utilized for the analysis of the tissue reaction to and actual biodegradation of injectable microcapsules. This work has utilized light microscopic (LM), transmission (TEM) and scanning (SEM) electron microscopic techniques. The design of our studies has utilized methodology that would; 1. best characterize the actual degradation process without artifacts introduced by fixation procedures and 2. allow for reproducible results.In our studies, the gastrocnemius muscle of the rat was chosen as the injection site. Prior to the injection of microcapsules the skin above the sites was shaved and tattooed for later recognition and recovery. 1.0 cc syringes were loaded with the desired quantity of microcapsules and the vehicle (0.5% hydroxypropylmethycellulose) drawn up. The syringes were agitated to suspend the microcapsules in the injection vehicle.

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