Lp estimates on a time-inhomogeneous diffusion process

2005 ◽  
Vol 46 (8) ◽  
pp. 083513 ◽  
Author(s):  
Litan Yan ◽  
Ligang Lu ◽  
Zhiqiang Xu
Keyword(s):  
Diffusion Process ◽  
Lp Estimates ◽  
Inhomogeneous Diffusion

scholarly journals Inhomogeneous diffusion process in elongated rooms: An interpretation based on the dynamics of sound particles

2021 ◽  
Vol 1 (5) ◽  
pp. 051601
Author(s):  
Cédric Foy ◽  
Vincent Valeau ◽  
Christian Prax ◽  
Judicaël Picaut ◽  
Anas Sakout
Keyword(s):  
Diffusion Process ◽  
Inhomogeneous Diffusion

scholarly journals On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

2021 ◽  
Author(s):  
Swagatam Sen ◽  
Anindya Sen ◽  
Ye Liu ◽  
Bisakha Pia Sen
Keyword(s):  
Diffusion Process ◽  
Spatial Variations ◽  
State Regulations ◽  
Diffusive Process ◽  
Firearm Violence ◽  
Cross Border ◽  
Flow Parameters ◽  
Diffusive Flow ◽  
Inhomogeneous Diffusion ◽  
The Impact

Objectives : Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state groups that are especially vulnerable to cross-border firearm violence. Methods : Incidence of firearm violence (2000 to 2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results : Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant. Conclusion : The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence : Source states, Transitive states, Destination states, Isolated issue states and Stable . It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighbouring Source and Transitive States.

scholarly journals On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

2021 ◽  
Author(s):  
Swagatam Sen ◽  
Anindya Sen ◽  
Ye Liu ◽  
Bisakha Sen
Keyword(s):  
Diffusion Process ◽  
Stable States ◽  
State Regulations ◽  
Diffusive Process ◽  
Firearm Violence ◽  
Cross Border ◽  
Flow Parameters ◽  
Diffusive Flow ◽  
Inhomogeneous Diffusion ◽  
The Impact

Abstract Objectives – Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state-groups that are especially vulnerable to cross-border firearm violence.Methods – Incidence of firearm violence (2000-2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results – Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant.Conclusion – The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence – Source states, Transitive states, Destination states, Isolated issue states and Stable states. It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighboring Source and Transitive States.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

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