Time-Dependent Fluorescence in Nanoconfined Solvents. A Smoluchowski Equation Model Study

2010 ◽  
Vol 114 (10) ◽  
pp. 4279-4290 ◽  
Author(s):  
Xiaobing Feng ◽  
Ward H. Thompson
Keyword(s):  
Equation Model ◽  
Smoluchowski Equation ◽  
Time Dependent ◽  
Model Study

scholarly journals Finite Element Analysis of the Time-Dependent Smoluchowski Equation for Acetylcholinesterase Reaction Rate Calculations

2007 ◽  
Vol 92 (10) ◽  
pp. 3397-3406 ◽  
Author(s):  
Yuhui Cheng ◽  
Jason K. Suen ◽  
Deqiang Zhang ◽  
Stephen D. Bond ◽  
Yongjie Zhang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Reaction Rate ◽  
Smoluchowski Equation ◽  
Time Dependent ◽  
Element Analysis ◽  
Acetylcholinesterase Reaction

MODELING OF GOLD DISPERSION IN GLASSY POLYMERS BY SMOLUCHOWSKI EQUATION

2002 ◽  
Vol 13 (09) ◽  
pp. 1301-1312 ◽  
Author(s):  
ZBIGNIEW J. GRZYWNA ◽  
JACEK STOLARCZYK
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Partial Differential Equation ◽  
Smoluchowski Equation ◽  
Glassy Polymers ◽  
Time Dependent ◽  
Acetone Vapor ◽  
Induced Stress ◽  
Theoretical Predictions ◽  
Good Agreement

A unidimensional diffusion in a potential field of induced stress is considered. The way from random walk (RW) to limiting partial differential equation (Smoluchowski equation) for standard and time dependent RW is shown. A technologically important case of gold dispersion in crystallizing polymer swollen by acetone vapor is analyzed. Theoretical predictions based on Smoluchowski equation with time dependent coefficients are found to be in very good agreement with experimental data.

scholarly journals Disappearing Errors in a Conversion Model

2021 ◽  
pp. 341-358
Author(s):  
David P. Fan
Keyword(s):  
Public Opinion ◽  
Diffusion Of Innovations ◽  
Measurement Errors ◽  
Equation Model ◽  
Bad News ◽  
Time Dependent ◽  
Bass Model ◽  
Persuasive Messages ◽  
Conversion Model ◽  
Basic Differential Equation

The same basic differential equation model has been adapted for time-dependent conversions of members of a population among different states. The conversion model has been applied in different contexts such as epidemiological infections, the Bass model for the diffusion of innovations, and the ideodynamic model for public opinion. For example, the ideodynamic version of the model predicts changes in public opinions in response to persuasive messages extending back to an indefinite past. All messages are measured with error, and this chapter discusses how errors in message measurements disappear with time so that predicted opinion values gradually become unaffected by past measurement errors. Prediction uncertainty is discussed using formal statistics, sensitivity analysis, and bootstrap variance calculations. This chapter presents ideodynamic predictions for opinion time series about the Toyota car manufacturer calculated from daily Twitter scores over two-and-a-half years. During this time, there was a sudden onslaught of bad news for Toyota, and the model was able to accurately predict the accompanying drop in favourable public opinion towards Toyota and rise in unfavourable opinion.

scholarly journals CoVID-19 prediction for India from the existing data and SIR(D) model study

2020 ◽  
Author(s):  
Aditya Rajesh ◽  
Haidas Pai ◽  
Victor Roy ◽  
Subhasis Samanta ◽  
Sabyasachi Ghosh
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Strategic Decision ◽  
Time Dependent ◽  
Strategic Decision Making ◽  
Model Study ◽  
The World ◽  
The Future ◽  
D Model ◽  
Existing Data

CoVID-19 is spreading throughout the world at an alarming rate. So far it has spread over 200 countries in the whole world. Mathematical modelling of an epidemic like CoVID-19 is always useful for strategic decision making, especially it is very useful to gain some understanding of the future of the epidemic in densely populous countries like India. We use a simple yet effective mathematical model SIR(D) to predict the future of the epidemic in India by using the existing data. We also estimate the effect of lock-down/social isolation via a time-dependent coefficient of the model. The model study with realistic parameters set shows that the epidemic will be at its peak around the end of June or the first week of July with almost 108 Indians most likely being infected if the lock-down relaxed after May 3, 2020. However, the total number of infected population will become one-third of what predicted here if we consider that people only in the red zones (approximately one-third of India's population) are susceptible to the infection. Even in a very optimistic scenario we expect that at least the infected numbers of people will be of the order of 107.

scholarly journals Dust Evolution in Protoplanetary Accretion Disks

1997 ◽  
Vol 163 ◽  
pp. 721-722 ◽  
Author(s):  
Th. Henning ◽  
W. Schmitt ◽  
R. Mucha
Keyword(s):  
Accretion Disk ◽  
Accretion Disks ◽  
Smoluchowski Equation ◽  
Time Dependent ◽  
One Dimensional ◽  
Coagulation Of Particles ◽  
Non Linear ◽  
Disk Evolution ◽  
Dust Evolution

AbstractWe have numerically investigated the dust evolution in a protoplanetary accretion disk which is described by a time-dependent one-dimensional (radial) α-model. The coagulation of particles due to cohesive collisions is calculated by solving the non-linear Smoluchowski equation. The feedback of the dust evolution and the related opacity changes to the disk evolution is explicitly treated. Three different regimes during the evolution of the grain population can be identified.

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