A computational approach to non-smooth optimization by diffusion equations

2021 ◽  
Vol 384 ◽  
pp. 113166
Author(s):  
Jinghao Zhu
Author(s):  
S. Nakahara ◽  
D. M. Maher

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.


Author(s):  
Elizabeth S Baranowski ◽  
Sreejita Ghosh ◽  
Cedric HL Shackleton ◽  
Angela E Taylor ◽  
Beverly A Hughes ◽  
...  

2020 ◽  
Author(s):  
Francisco Andújar-Vera ◽  
Cristina García-Fontana ◽  
Sheila González-Salvatierra ◽  
Manuel Muñoz-Torres ◽  
Beatriz García-Fontana

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.


2019 ◽  
Author(s):  
Sayan Mondal ◽  
Gary Tresadern ◽  
Jeremy Greenwood ◽  
Byungchan Kim ◽  
Joe Kaus ◽  
...  

<p>Optimizing the solubility of small molecules is important in a wide variety of contexts, including in drug discovery where the optimization of aqueous solubility is often crucial to achieve oral bioavailability. In such a context, solubility optimization cannot be successfully pursued by indiscriminate increases in polarity, which would likely reduce permeability and potency. Moreover, increasing polarity may not even improve solubility itself in many cases, if it stabilizes the solid-state form. Here we present a novel physics-based approach to predict the solubility of small molecules, that takes into account three-dimensional solid-state characteristics in addition to polarity. The calculated solubilities are in good agreement with experimental solubilities taken both from the literature as well as from several active pharmaceutical discovery projects. This computational approach enables strategies to optimize solubility by disrupting the three-dimensional solid-state packing of novel chemical matter, illustrated here for an active medicinal chemistry campaign.</p>


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