scholarly journals On the recovery of the doping profile in an time-dependent drift-diffusion model

2014 ◽  
Vol 22 (2) ◽  
pp. 253-274
Author(s):  
Bin Wu ◽  
Zewen Wang
Keyword(s):  
Inverse Problem ◽  
Diffusion Model ◽  
Electric Potential ◽  
Parabolic Equations ◽  
Time Dependent ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
System Of Parabolic Equations ◽  
Theoretical Results

AbstractWe consider an inverse problem arising from an time-dependent drift-diffusion model in semiconductor devices, which is formulated in terms of a system of parabolic equations for the electron and hole densities and the Poisson equation for the electric potential. This inverse problem aims to identify the doping profile from the final overdetermination data of the electric potential. By using the Schauder’s fixed point theorem in suitable Sobolev space, the existence of this inverse problem are obtained. Moreover by means of Gronwall inequality, we prove the uniqueness of this inverse problem for small measurement time. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model.

scholarly journals Bayesian confidence for drift diffusion observers in dynamic stimuli tasks

2020 ◽  
Author(s):  
Joshua Calder-Travis ◽  
Rafal Bogacz ◽  
Nick Yeung
Keyword(s):  
Diffusion Model ◽  
Drift Rate ◽  
Response Times ◽  
Time Dependent ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Dynamic Stimuli ◽  
Computationally Expensive ◽  
Insight Into ◽  
Confidence Data

AbstractMuch work has explored the possibility that the drift diffusion model, a model of response times and choices, could be extended to account for confidence reports. Many methods for making predictions from such models exist, although these methods either assume that stimuli are static over the course of a trial, or are computationally expensive, making it difficult to capitalise on trial-by-trial variability in dynamic stimuli. Using the framework of the drift diffusion model with time-dependent thresholds, and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of “pipeline” evidence which has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli which change over the course of a trial with normally distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions only contain a small number of standard functions, and only require evaluating once per trial, making trial-by-trial modelling of confidence data in dynamic stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

The Multidimensional Bipolar Quantum Drift-diffusion Model

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Xiuqing Chen ◽  
Yingchun Guo
Keyword(s):  
Weak Solution ◽  
Diffusion Model ◽  
Semiclassical Limit ◽  
Global Weak Solution ◽  
Mean Value ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
New Methods ◽  
Fourth Order Parabolic System

AbstractWe investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.

scholarly journals Informing cognitive abstractions through neuroimaging: The neural drift diffusion model.

2015 ◽  
Vol 122 (2) ◽  
pp. 312-336 ◽  
Author(s):  
Brandon M. Turner ◽  
Leendert van Maanen ◽  
Birte U. Forstmann
Keyword(s):  
Diffusion Model ◽  
Drift Diffusion Model ◽  
Drift Diffusion

Incorporating photon recycling into the analytical drift-diffusion model of high efficiency solar cells

2014 ◽  
Vol 116 (19) ◽  
pp. 194504 ◽  
Author(s):  
Matthew P. Lumb ◽  
Myles A. Steiner ◽  
John F. Geisz ◽  
Robert J. Walters
Keyword(s):  
Solar Cells ◽  
Diffusion Model ◽  
High Efficiency ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
High Efficiency Solar Cells ◽  
Photon Recycling
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