Mathematical Methods in Physics

Blanchard, Philippe; Brüning, Erwin

doi:10.1007/978-3-319-14045-2

Cited by 42 publications

(22 citation statements)

References 1 publication

(1 reference statement)

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“…In this paper, the SERS of 101 strawberry samples based on AuNPs enhancement were obtained and pretreated by standard normal variation (SNV), multiplicative scatter correction (MSC), de-trending (DT), and first-derivative (1st-Der). Meanwhile, considering that the Raman peaks of deltamethrin were mainly distributed in the range of 500–1800 cm −1 , the original SERS of deltamethrin in strawberry were preprocessed and then modeled by partial least squares (PLS) [ 28 ] and backward interval partial least squares (BIPLS) [ 29 ].…”

Section: Resultsmentioning

confidence: 99%

“…Partial least squares (PLS) is a most widely-used regression modeling method in spectral data analysis for its flexibility and reliability in dealing with the redundant spectral data. When PLS is applied to dealing with the spectral data, the spectral matrix is decomposed first and the main principal component variables are obtained, then the contribution rate of each principal component is calculated [ 28 ]. The flexibility of PLS makes it possible to establish a regression model in the case where the number of samples is less than the number of variables.…”

Section: Methodsmentioning

confidence: 99%

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Density Functional Theory Analysis of Deltamethrin and Its Determination in Strawberry by Surface Enhanced Raman Spectroscopy

Dong

Lin

et al. 2018

Molecules

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Deltamethrin is widely used in pest prevention and control such as red spiders, aphids, and grubs in strawberry. It is important to accurately monitor whether the deltamethrin residue in strawberry exceeds the standard. In this paper, density functional theory (DFT) was used to theoretically analyze the molecular structure of deltamethrin, gold nanoparticles (AuNPs) and silver nanoparticles (AgNPs) were used to enhance the surface enhanced Raman spectroscopy (SERS) detection signal. As a result, the theoretical Raman peaks of deltamethrin calculated by DFT were basically similar to the measured results, and the enhancing effects based on AuNPs was better than that of AgNPs. Moreover, 554, 736, 776, 964, 1000, 1166, 1206, 1593, 1613, and 1735 cm−1 could be determined as deltamethrin characteristic peaks, among which only three Raman peaks (736, 1000, and 1166 cm−1) could be used as the deltamethrin characteristic peaks in strawberry when the detection limit reached 0.1 mg/L. In addition, the 500–1800 cm−1 SERS of deltamethrin were analyzed by the partial least squares (PLS) and backward interval partial least squares (BIPLS). The prediction accuracy of deltamethrin in strawberry (Rp2 = 0.93, RMSEp = 4.66 mg/L, RPD = 3.59) was the highest when the original spectra were pretreated by multiplicative scatter correction (MSC) and then modeled by BIPLS. In conclusion, the deltamethrin in strawberry could be qualitatively analyzed and quantitatively determined by SERS based on AuNPs enhancement, which provides a new detection scheme for deltamethrin residue determination in strawberry.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Density Functional Theory Analysis of Deltamethrin and Its Determination in Strawberry by Surface Enhanced Raman Spectroscopy

Dong

Lin

et al. 2018

Molecules

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“…Density Functional Theory (DFT), as a tool for calculating molecular energy and analyzing properties, has been widely used in the field of physics and chemistry. It provides the computational strategies for obtaining information about the energetics, structure, and properties of atoms and molecules [ 28 , 29 ]. Based on the idea that the electron density is the fundamental quantity for describing atomic and molecular ground states, Parr et al [ 30 ] gave sharp definitions for chemical concepts in various branches of chemistry.…”

Section: Methodsmentioning

confidence: 99%

Rapid Determination of Thiabendazole Pesticides in Rape by Surface Enhanced Raman Spectroscopy

Lin

Dong

Nie

et al. 2018

Sensors

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Thiabendazole is widely used in sclerotium blight, downy mildew and black rot prevention and treatment in rape. Accurate monitoring of thiabendazole pesticides in plants will prevent potential adverse effects to the Environment and human health. Surface Enhanced Raman Spectroscopy (SERS) is a highly sensitive fingerprint with the advantages of simple operation, convenient portability and high detection efficiency. In this paper, a rapid determination method of thiabendazole pesticides in rape was conducted combining SERS with chemometric methods. The original SERS were pretreated and the partial least squares (PLS) was applied to establish the prediction model between SERS and thiabendazole pesticides in rape. As a result, the SERS enhancing effect based on silver Nano-substrate was better than that of gold Nano-substrate, where the detection limit of thiabendazole pesticides in rape could reach 0.1 mg/L. Moreover, 782, 1007 and 1576 cm−1 could be determined as thiabendazole pesticides Raman characteristic peaks in rape. The prediction effect of thiabendazole pesticides in rape was the best (Rp2 = 0.94, RMSEP = 3.17 mg/L) after the original spectra preprocessed with 1st-Derivative, and the linear relevance between thiabendazole pesticides concentration and Raman peak intensity at 782 cm−1 was the highest (R2 = 0.91). Furthermore, five rape samples with unknown thiabendazole pesticides concentration were used to verify the accuracy and reliability of this method. It was showed that prediction relative standard deviation was 0.70–9.85%, recovery rate was 94.71–118.92% and t value was −1.489. In conclusion, the thiabendazole pesticides in rape could be rapidly and accurately detected by SERS, which was beneficial to provide a rapid, accurate and reliable scheme for the detection of pesticides residues in agriculture products.

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“…This chapter is based on the presentation of Density Functional Theory in Ref. [13][14][15][16]. Structural and electronic properties of crystalline materials are a key interest not only in many fields of solid state physics but also in quantum chemistry and material sciences in general.…”

Section: Density Functional Theorymentioning

confidence: 99%

“…In this section we lay the foundation for the Two-Particle Self-Consistent approach (TPSC) following the many-body physics script of A.-M. Tremblay [110] and the textbook of A. L. Fetter and J. D. Walecka [30] while the mathematical motivation for Green's function follows Ref. [15]. Apart from the basic notion of many-body theory where the Green's function formalism and linear response theory are important tools to describe single-and two-particle properties [30,[111][112][113] we will need to introduce the language of functional derivatives [114] to find approximate expressions for those two objects.…”

Section: Green's Functionsmentioning

confidence: 99%

The two-particle self-consistent approach and its application to real materials

Zantout¹

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Diese Thesis befasst sich mit dem Problem korrelierter Elektronensysteme in realen Materialien. Ausgangspunkt hierbei ist die quantenmechanische Beschreibung dieser Systeme im Rahmen der sogenannten Kohn-Scham Dichtefunktionaltheorie, welche die Elektronen der Kristallsysteme als effektiv nicht-wechselwirkende Teilchen beschreibt. Während diese Modellierung im Falle vieler Materialklassen erfolgreich ist, unterscheiden sich die korrelierten Elektronensysteme dadurch, dass der kollektive Charakter der Elektronendynamik nicht zu vernachlässigen ist. Um diese Korrelationseffekte genauer zu untersuchen, verwenden wir in dieser Arbeit das Hubbard-Modell, welches mit der projektiven Wannierfunktionsmethode aus der Kohn-Scham Dichtefunktionaltheorie konstruiert werden kann. Das Hubbard-Modell umfasst hierbei nur die lokale Elektron-Elektron-Wechselwirkung auf einem Gitter. Auch wenn das Modell augenscheinlich sehr simpel ist, existieren exakte Lösungen nur in bestimmten Grenzfällen. Dies macht die Entwicklung approximativer Ansätze erforderlich, wobei die Weiterentwicklung der sogenannten Two-Particle Self-Consistent Methode (TPSC) eine zentrale Rolle dieser Arbeit einnimmt. Bei TPSC handelt es sich um eine Vielteilchenmethode, die in der Sprache funktionaler Ableitungen und sogenannter conserving approximations hergeleitet werden kann. Der zentrale Gedanke dabei ist, den effektiven Wechselwirkungsvertex als statisch und lokal zu approximieren. Dies wiederum erlaubt die Bewegungsgleichung des Systems erheblich zu vereinfachen, sodass eine numerische approximative Lösung des Hubbard-Modells möglich wird. Vorsetzung hierbei ist nur, dass sich das System in der normalleitenden Phase befindet und die bei Phasenübergängen entstehenden Fluktuationen nicht zu groß sind. Während diese Methode ursprünglich von Y. M. Vilk und A.-M. Tremblay für das Ein-Orbital Hubbard-Modell entwickelt wurde, stellen wir in dieser Arbeit eine Erweiterung auf Viel-Orbital-Systeme vor. Im Falle mehrerer Orbitale treten in der TPSC-Herleitung einzelne Komplikationen auf, die mit weiteren Approximationen behandelt werden müssen. Diese werden anhand eines einfachen Zwei-Orbital Modell-Systems diskutiert und die TPSC-Ergebnisse werden darüber hinaus mit den Ergebnissen der etablierten dynamischen Molekularfeldnährung verglichen. In diesem Zusammenhang werden auch mögliche zukünftige Erweiterungen bzw. Verbesserungen von TPSC diskutiert. Ein weiterer wichtiger Aspekt ist die Anwendung von TPSC auf reale Materialien. In diesem Zusammenhang werden in dieser Arbeit die supraleitenden Eigenschaften der organischen K-(ET)2X Systeme untersucht. Hierbei lassen die TPSC-Resultate darauf schließen, dass das populäre Dimer-Modell, welches zur Beschreibung dieser Materialien herangezogen wird, nicht genügt um die experimentell bestimmten kritischen Temperaturen zu erklären und dass das komplexere Molekülmodell weitere exotische supraleitende Lösungen zulässt. Schließlich untersuchen wir außerdem die elektronischen Eigenschaften des eisenbasierten Supraleiters LiFeAs und diskutieren inwieweit nicht-lokale Korrelationseffekte, welche durch TPSC aufgelöst werden können, die experimentellen Daten reproduzieren.

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Mathematical Methods in Physics

Cited by 42 publications

References 1 publication

Density Functional Theory Analysis of Deltamethrin and Its Determination in Strawberry by Surface Enhanced Raman Spectroscopy

Density Functional Theory Analysis of Deltamethrin and Its Determination in Strawberry by Surface Enhanced Raman Spectroscopy

Rapid Determination of Thiabendazole Pesticides in Rape by Surface Enhanced Raman Spectroscopy

The two-particle self-consistent approach and its application to real materials

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