A Levenberg–Marquardt method based on Sobolev gradients

Kazemi, Parimah; Renka, Robert J.

doi:10.1016/j.na.2012.06.022

Cited by 24 publications

(10 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the kinetic models from biodegradation processes, Eqns (2) to (4) were used as the first zero‐order, first‐order, and second‐order kinetic models, respectively, in this study. Equations (2) to (4) could be solved by the Levenberg–Marguardt method:

M_{C H_{4}} = M_{0} - K_{0} t

M_{C H_{4}} = M_{0} e^{- K_{1} t}

\frac{1}{M_{C H_{4}}} = \frac{1}{M_{0}} + \frac{1}{K_{2} \times t}

…”

Section: Methodsmentioning

confidence: 99%

Impact of external carbon source addition on methane emissions from a vertical subsurface‐flow constructed wetland

Liu¹,

et al. 2019

Greenhouse Gases

View full text Add to dashboard Cite

In this study, different concentrations of urea (0, 12.1, 30, 45, 61 and 80 mmol·L−1) were added separately, as external carbon sources, to a two‐stage vertical subsurface‐flow constructed wetland (VSSF CW) where Cyperus alternifolius L. was planted, with the aim of understanding methane (CH4) emissions driven by urea. Results indicate that the average CH4 emissions from a two‐stage VSSF CW were 6.88, 7.11, 6.22, 7.45, 5.06 and 2.80 mol·m−2·day−1, corresponding to urea concentrations of 0, 12.1, 30, 45, 61 and 80 mmol·L−1 added in the VSSF CW, respectively. Urea as a carbon source had an average of 31.57% of influent total organic carbon (TOC). It was transformed into CH4‐C, of which CH4‐C/TOCinfluent may be be considered as an important component when anthropogenic methanogenesis from treatment wetlands was driven by carbon sources or carbon loading. Methane emissions were at their lowest when the C/N ratio was 5.89, at a urea concentration of 80 mmol·L−1. Principal component analysis (PCA) indicates that CH4 correlated positively with temperature and redox conditions (Eh). Methane emissions driven by urea in the two‐stage VSSF CW were found to be in accordance with the second‐rate dynamics kinetic model (kinetic constant = 22.94 mg CH4·h−1, R2 = 0.99), which can be considered as a high level of CH4 emissions. It indicates that external carbon sources can influence CH4 emissions from two‐stage VSSF CW significantly. © 2019 Society of Chemical Industry and John Wiley & Sons, Ltd.

show abstract

M_{C H_{4}} = M_{0} - K_{0} t

M_{C H_{4}} = M_{0} e^{- K_{1} t}

\frac{1}{M_{C H_{4}}} = \frac{1}{M_{0}} + \frac{1}{K_{2} \times t}

…”

Section: Methodsmentioning

confidence: 99%

Impact of external carbon source addition on methane emissions from a vertical subsurface‐flow constructed wetland

Liu¹,

et al. 2019

Greenhouse Gases

View full text Add to dashboard Cite

show abstract

“…Immobilization of enzymes on the external or internal (pore) membrane surfaces is widely used in biotechnology industries [7,8], where immobilization is generally achieved by establishing non-covalent interactions between protein and polymeric surfaces without chemical modifications of membranes and enzymes [9]. As a result, non-covalent adsorption is an interesting research topic, and computational methodologies able to optimize and control this process on a larger scale [10,11] are highly desirable. However, due to some process limitations, several aspects need to be improved to increase the immobilized enzyme activity and re-usability.…”

Section: Introductionmentioning

confidence: 99%

Enzyme Immobilization on Polymer Membranes: A Quantum and Molecular Mechanics Study

et al. 2019

View full text Add to dashboard Cite

Adsorption of the phosphotriesterase on a polysulfone membrane surface was investigated in this paper through a double-scale computational approach. Surface charges of the enzyme, as well as membrane, were calculated at sub and nanoscale while protein adsorption was simulated at larger scale. Adsorption energies were calculated as a function of the enzyme–surface distance, and for each distance, several protein rotations were tested to find the most stable orientations of the macromolecule. The results of this model were useful in obtaining information about the adhesion of the enzyme and to give indications on the orientations of its binding site. Adsorption energies agreed with the literature data. Furthermore, the binding site of the immobilized phosphotriesterase was less accessible with respect to native enzymes due to the steric hindrance of the polymer surface; thus, a reduction of its efficiency is expected. The proposed methodology made use of fundamental quantities, calculated without resorting to adjustable or empirical parameters, providing basic outputs useful for ascertaining enzymatic catalysis rate.

show abstract

“…This is similar to a Riemannian manifold in which inner products are assigned to tangent spaces in a differentiable fashion. We have made a start toward extending the theory of Sobolev gradients to variable metric methods in [17], but much work remains to be done.…”

Section: Resultsmentioning

confidence: 99%

Minimization of the Ginzburg–Landau energy functional by a Sobolev gradient trust-region method

Kazemi

Renka

2013

Applied Mathematics and Computation

View full text Add to dashboard Cite

We describe a generalized Levenberg-Marquardt method for computing critical points of the Ginzburg-Landau energy functional which models superconductivity. The algorithm is a blend of a Newton iteration with a Sobolev gradient descent method, and is equivalent to a trust-region method in which the trustregion radius is defined by a Sobolev metric. Numerical test results demonstrate the method to be remarkably effective.

show abstract

A Levenberg–Marquardt method based on Sobolev gradients

Cited by 24 publications

References 7 publications

Impact of external carbon source addition on methane emissions from a vertical subsurface‐flow constructed wetland

Impact of external carbon source addition on methane emissions from a vertical subsurface‐flow constructed wetland

Enzyme Immobilization on Polymer Membranes: A Quantum and Molecular Mechanics Study

Minimization of the Ginzburg–Landau energy functional by a Sobolev gradient trust-region method

Contact Info

Product

Resources

About