Academic literature on the topic 'Spherical many-electron systems'
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Journal articles on the topic "Spherical many-electron systems"
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TOURIGNY, DAVID S. "THE THEORY OF AN ELECTRON ON A LOXODROME." Modern Physics Letters B 26, no. 08 (March 30, 2012): 1250052. http://dx.doi.org/10.1142/s0217984912500522.
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Single-electron models are regularly used in molecular physics to obtain information on the quantum properties of many-atom systems. Examples include applications of a particle contained on a ring to benzene, and an electron on a helix to helical polymers. Here it is shown that the model of an electron on a spherical helix (a loxodrome) is also amenable to such investigation, and may be used to describe an emerging class of molecules known as "molecular apple peels". Moreover, the Schrödinger equation that arises during consideration of this model is solved exactly.
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Shao, Zhifeng. "Probe size and 5th-order aberration." Proceedings, annual meeting, Electron Microscopy Society of America 45 (August 1987): 134–35. http://dx.doi.org/10.1017/s0424820100125609.
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A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.
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Hussein, Abbas Ibrahim, Zuryati Ab-Ghani, Ahmad Nazeer Che Mat, Nur Atikah Ab Ghani, Adam Husein, and Ismail Ab. Rahman. "Synthesis and Characterization of Spherical Calcium Carbonate Nanoparticles Derived from Cockle Shells." Applied Sciences 10, no. 20 (October 14, 2020): 7170. http://dx.doi.org/10.3390/app10207170.
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Cockle shells are a natural reservoir of calcium carbonate (CaCO3), which is widely used in bone repair, tissue scaffolds, and the development of advanced drug delivery systems. Although many studies report on the preparation of CaCO3, the development of a nanosized spherical CaCO3 precursor for calcium oxide (CaO) that is suitable to be incorporated in dental material was scarce. Therefore, this study aimed to synthesize a nanosized spherical CaCO3 precursor for CaO derived from cockle shells using a sol–gel method. Cockle shells were crushed to powder form and mixed with hydrochloric acid, forming calcium chloride (CaCl2). Potassium carbonate (K2CO3) was then fed to the diluted CaCl2 to obtain CaCO3. The effect of experimental parameters on the morphology of CaCO3, such as volume of water, type of solvents, feeding rate of K2CO3, and drying method, were investigated using field-emission scanning electron microscopy, energy-dispersive X-ray spectroscopy, X-ray diffractometry (XRD), Brunauer–Emmett–Teller surface area analysis, and thermogravimetric analysis. Optimized CaCO3 was then calcined to form CaO. XRD analysis of CaCO3 nanoparticles was indicative of the formation of a calcite phase. The well-structured spherical shape of CaCO3 was obtained by the optimum condition of the addition of 50 mL of water into CaCl2 in ethanolic solution with a 1 h feeding rate of K2CO3. Less agglomeration of CaCO3 was obtained using a freeze-drying technique with the surface area of 26 m2/g and average particle size of 39 nm. Spherical shaped nanosized CaO (22–70 nm) was also synthesized. The reproducibility, low cost, and simplicity of the method suggest its potential applications in the large-scale synthesis of the nanoparticles, with spherical morphology in an industrial setting.
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Almgren, Mats. "Alexander Lecture 2003: Cubosomes, Vesicles, and Perforated Bilayers in Aqueous Systems of Lipids, Polymers, and Surfactants." Australian Journal of Chemistry 56, no. 10 (2003): 959. http://dx.doi.org/10.1071/ch03049.
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Cryo-Transmission Electron Microscopy (cryoTEM) is a method allowing visualization of many of the delicate structures that form by self-assembly of amphiphilic molecules in aqueous environments. The amphiphiles may be surfactants, lipids, or polymers, alone or in various mixtures. The distinctive feature of the method is that the objects are examined without staining or dehydration: This is achieved by capturing the structures in very thin aqueous films, that are subsequently vitrified at liquid nitrogen temperatures and examined using a microscope. Objects in the size range from 5 to 500 nm are well suited for the method. This includes various emulsion particles, such as liposomes, and more exotic cubosomes and hexasomes. In cryoTEM investigations perforated vesicles were found, an observation that triggered extensive studies of the nature and occurrence of such structures. As a complement to scattering methods, cryoTEM has proven its value in investigations of the size and morphology of various liposomal and vesicular systems. The microscopy studies show what type of structures that are present in the sample: uni- or multilamellar vesicles, open structures or closed defect-free vesicles, whether the form is spherical, tubular, or oblate, and so on. The scattering methods give good measures of size and polydispersity for defined systems.Three main themes are presented here. (a) Morphology of cubosomes and other emulsion particles from dispersed liquid-crystalline phases. (b) Perforated bilayers, their structure, nature, occurrence, and formation. (c) Spontaneous catanionic vesicles and their relationship to vesicles of zwitterionic lipids plus ionic surfactants.
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Jayakodi, Santhoshkumar, Hyunjin Kim, Soumya Menon, Venkat Kumar Shanmugam, Inho Choi, Medidi Raja Sekhar, Rakesh Bhaskar, and Sung Soo Han. "Preparation of Novel Nanoformulation to Enhance Efficacy in the Treatment of Cardiovascular Disease." Biomimetics 7, no. 4 (November 4, 2022): 189. http://dx.doi.org/10.3390/biomimetics7040189.
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Despite many efforts over the last few decades, cardiac-based drug delivery systems are experiencing major problems, such as the effective delivery of the precise amount of a drug. In the current study, an effort has been made to prepare a nano-herbformulation (NHF) to overcome the major problem of conventional intervention. Copper oxide-based NHF was prepared using plant extract of Alternanthera sessilis and characterized using physicochemical techniques such as Transmission electron microscopy (TEM), X-ray powder diffraction (XRD), Dynamic light scattering (DLS), UV-Vis spectroscopy, and Fourier-transform infrared spectroscopy (FTIR). TEM analysis revealed that spherical NHF obtained of size 20–50 nm. In addition, XRD and FTIR confirmed the presence of phytochemicals with biological properties over the surface of copper oxide-based NHF. It was demonstrated that dose-dependent antiapoptotic activity was shown against DOX-induced cardiomyocytes, where ROS levels were significantly reduced to 0.29% from 37.99%. The results of the flow cytometry analysis using PI and Annexin staining further confirmed the antiapoptotic activity of NHF against DOX-induced cardiomyocytes by ROS scavenging. Thus, NHF might be used for cardiovascular disease treatment.
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Carapeto, A. P., A. M. Ferraria, P. A. Carvalho, P. Brogueira, S. Boufi, and A. M. Botelho do Rego. "Hybrid systems of gold and silver nanoparticles generated on cellulose surfaces." Microscopy and Microanalysis 19, S4 (August 2013): 119–20. http://dx.doi.org/10.1017/s1431927613001219.
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Developing methods for immobilizing metallic nanoparticles (NP) onto different surfaces is a subject of fundamental interest, as nanometric structures enable the appearance of novel properties, absent in bulk or even in micrometric dimensions. In fact, the presence of NP with different size and shape on surfaces can induce substantial modifications on their electronic, optical, magnetic, physical or chemical proprieties. This will be very useful for many applications in different areas ranging from electronics to biomedicine.In this work, we use a simple, reproducible and economic method to grow metallic gold and silver NP directly on cellulose surfaces. A prior chemical activation of the alcohol groups on the cellulose surface is needed for grafting amino functions, which will complex silver and gold ions. Therefore, NP nucleation is only allowed and selectively accomplished on these seed coordination sites. The growth of NP is achieved by the interaction of aqueous dilute solutions of AgNO3 or NaAuCl4 with the cellulose surface. The procedure limits the generation of NP only to the cellulose surface, keeping the dispersion medium completely exempt of them. The resulting NP are, consequently chemically immobilized on the cellulose surface. The chemical anchoring of the NP to the surface avoids particle desorption and extends the lifetime of the resulting hybrid materials. Following this procedure, silver and gold NP could be successfully created on cellulose and this was supported by transmission electron microscopy (TEM), scanning electron microscopy (SEM) and atomic force microscopy (AFM).The present AFM (Figure 1) study enabled to characterize the size and shape of silver NP: they are spherical and have a diameter of ~15 nm. SEM image of Ag NP (Figure 2) display the existence of NP agglomerates. Comparison of the two images suggests size and spatial distributions strongly non- uniform. It is now a challenge to deposit nanoparticles in an organized manner, achieving a regular surface functionalization of cellulose. In TEM (Figure 3) we see a sample where Ag and Au salts interacted simultaneously with the cellulose surface. Crossing the images with other information from analytical techniques, it seems that Ag NP and Au NP form mainly separately instead of presenting a core-shell structure. Also, there is evidence that larger NP are the ones made of silver which suggests that the final result is kinetically (and not thermodynamically) controlled.The authors acknowledge FCT for A.M. Ferraria Grant SFRH/BPD/26239/2006, for A. P. Carapeto Grant SFRH/BD/75734/2011 and strategic projects PEst-OE/CTM/LA0024/2011 and PEst-OE/CTM-UI0084/2011.
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Mohamed, HudaElslam, Unal Camdali, Atilla Biyikoglu, and Metin Aktas. "Enhancing the Performance of a Vapour Compression Refrigerator System Using R134a with a CuO/CeO2 Nano-refrigerant." Strojniški vestnik - Journal of Mechanical Engineering 68, no. 6 (June 22, 2022): 395–410. http://dx.doi.org/10.5545/sv-jme.2021.7454.
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Most studies report that dispersing nanoparticles into refrigerants and lubricating oils leads to performance improvements in refrigeration systems, due to improvements in the thermal physics properties of a pure refrigerant, which leads to reduced energy consumption. Using nanoparticles in a refrigeration system is associated with many difficulties, such as the cost of preparing and obtaining a stable and homogeneous mixture with less agglomeration and sedimentation. Most current studies focus on the use of metals, metal oxides, and a hybrid of oxides as nanoparticles in refrigeration systems. In this research, nanoparticles were prepared in an inexpensive and easy way as a single oxide and as a mixture consisting of copper and cerium oxides. The results of nanoparticle preparation using X-ray diffraction and scanning electron microscopy prove that the particles of the samples were spherical in shape, with suitable average diameters ranging from 78.95 nm, 79.9 nm, 44.15 nm and 63.3 nm for copper oxide, cerium oxide, the first mixture, and the second mixture, respectively. Cerium oxide has not been used in a refrigeration system; this study preferred the implementation of a theoretical study using Ansys Fluent software to verify the possibility of improving the performance of the refrigeration system. The results confirmed that copper oxide enhanced the coefficient of performance of the refrigeration system by 25 %, and cerium oxide succeeded in improving the performance of the. system by a lesser value. The mixture containing a higher percentage of copper oxide yielded better results.
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Ali, Muna, Kareem Mosa, Ali El-Keblawy, and Hussain Alawadhi. "Exogenous Production of Silver Nanoparticles by Tephrosia apollinea Living Plants under Drought Stress and Their Antimicrobial Activities." Nanomaterials 9, no. 12 (December 1, 2019): 1716. http://dx.doi.org/10.3390/nano9121716.
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Nanoparticle (NP) synthesis by biological systems is more cost-effective, safe, and environmentally friendly when compared to currently used chemical and physical methods. Although many studies have utilized different plant extracts to synthesize NPs, few studies have incorporated living plants. In this study, silver nanoparticles (AgNPs) were synthesized exogenously by Tephrosia apollinea living plant system under the combined stresses of silver nitrate and different levels of drought stress simulated by Polyethylene glycol (PEG) (0, −0.1, −0.2, and −0.4 MPa for three and six days). Biomass, cell death, and H2O2 content were evaluated to determine the toxicological effect of the treatments on the plant. More severe effects were detected in day 6 plants compared to day 3 plants, and at higher drought levels. UV-visible spectrum, energy dispersive X-ray spectroscopy, X-ray diffraction, scanning electron microscope, and Fourier transform infrared spectroscopy were used to detect and characterize the T. apollinea synthesized NPs. The shapes of the NPs were spherical and cubic with different phytochemicals being the possible capping agents. Broth microdilution was used to determine the antimicrobial activity of the NPs against Escherichia coli and Staphylococcus aureus. In this case, antimicrobial activity increased at higher PEG concentrations. Bactericidal effects were observed against E. coli, while only bacteriostatic effects were detected against S. aureus.
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Vu, Tri Thien, Dung Thi Nguyen, Tran Hung Nguyen, Huu Thanh Le, Dinh Duc Nguyen, and Duong Duc La. "One-Step Solution Plasma-Mediated Preparation of Se Nanoplarticles and Evaluating Their Acute Oral Toxicity in Mice." Sustainability 14, no. 16 (August 18, 2022): 10294. http://dx.doi.org/10.3390/su141610294.
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Selenium element is considered as one of the most important micronutrients for many biological systems. It has been well demonstrated that Se nanoparticles (Se NPs) express greater bioavailability, biocompatability, and less toxicity than that of Se in ion form. In this work, the Se NPs were facilely fabricated by a one-step plasma process in the ethanol–water solution mixture. The as-prepared Se NPs were well characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), UV-vis spectroscopy, Raman spectroscopy, and energy dispersive X-ray spectroscopy (EDX). The prepared Se NPs were a light red color with a spherical shape and particle size in the range of 100–200 nm. The average diameter of the Se NPs calculated from the ImageJ software and TEM image was approximately 154 nm. The EDX results showed that the Se NPs prepared by the plasma process in the solution were highly pure and stable. The acute oral toxicity of the obtained Se NPs toward mice was also studied, which revealed that the Se NPs were safe for the human body. The mechanism for the formation of Se NPs from the Se ions under the solution plasma condition was also studied and discussed.
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Elbialy, Nihal S. "Preparation and Characterization of Curcumin Loaded Dextrin Sulfate- Chitosan Nanoparticles for Promoting Curcumin Anticancer Activity." JOURNAL OF ADVANCES IN PHYSICS 16, no. 1 (June 5, 2019): 185–95. http://dx.doi.org/10.24297/jap.v16i1.8276.
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Curcumin as a natural medicinal agent has been proved to kill cancer cells effectively. However, its biomedical applications have been hindered owing to its poor bioavailability. Many nanoparticulate systems have been introduced to overcome this problem. Among this types polymeric-based nanoparticles which exhibit unique properties allowing their use as a efficient drug carrier. Developing a polymeric- blend nanoparticles will offer a promising nanocarrier with excellent biocompatibility, biodegradability and low immunogencity.
In this study, curcumin nano-vehicle has been made up by combining dextren sulfate and chitosan (DSCSNPs). DSCSNPs have been characterized using different techniques. Transmission electron microscopy (TEM) which revealed the spherical, smooth surface of the nano-formulation. Dynamic light scattering (DLS) for measuring DSCSNPs hydrodynamic- diameter. Zeta potential measurements showed nanoparticles high stability. Fourier transform infrared spectroscopy (FTIR) confirmed successful combination between the two polymers and curcumin loading on naoparticles surface. Curcumin release profile out of DSCSNPs showed high drug release in tumor acidic microenvironment. In vitro cytotoxicity measurements demonstrated that curcumin loaded polymeric nanoparticles (DSCSNPs-Cur) have high therapeutic efficacy against colon (HCT-116) and breast (MCF-7) cancer cells compared with free curcumin. DSCSNPs as a combined biopolymers is an excellent candidate for improving curcumin bioavailability allowing its use as anticancer agent.
Dissertations / Theses on the topic "Spherical many-electron systems"
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Gould, Timothy John, and n/a. "Correlation and Response in Spherical Many-Electron Systems." Griffith University. School of Science, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20030818.125106.
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Ab initio prediction of the electronic properties of solids is traditionally performed using groundstate Density Functional Theory. These methods are unreliable however, for a class of important problems involving weak attractive forces. These problems include (i) the energetics of hydrogen storage and metal interactions in graphene, (ii) cohesion properties of some polymer systems and (iii) possibly, the weak hydrophobic forces in biomolecules. For these cases a more powerful method than groundstate DFT are timedependent DFT (tdDFT) methods related to the Random-Phase Approximation (RPA). All of these methods proceed by looking at the dynamic density-density response function, whose long-ranged properties naturally lead to the weak forces referred to above. In this thesis we have tested these ideas by investigating electronic response and correlation on the predicted properties of spherical atoms. We have developed and tested a variety of approximations to the timedependent response function through approximations of the tdDFT class and a new method involving greater self-consistency in the screening equation, the inhomogenous STLS approach. Through the development of new methods and computer code, we have solved the response equation allowing us to test our approximations on atoms. Calculation of certain dynamic and static properties of a variety of atoms within our approximations generally agree well with known results. In this thesis we have calculated excitation energies of Helium, dipole polarisabilities and C6 van der Waals (vdW) coefficients of a variety of atoms, and groundstate correlation energies Ec of some atoms. The excitation spectra of Helium generated in our new PGG+c approximation are in good agreement with experiment. The dipole polarisabilities are generally in good agreement with known results, with the exception of Magnesium, Beryllium and Sodium. The C6 coefficients are a little poorer with the exception of Helium where they are nearly exact. Correlation energies are generally reasonable in the PGG+c approximation although they are considerably less accurate than the other properties we have calculated for all atoms other than He. The ISTLS correlation energy of Helium is within 5% suggesting that this method may perform well for larger atoms where our present numerical techniques require improvement. These generally positive results suggest that the approximations we have developed may be applied to more complicated systems such as those described above with good results.
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Gould, Timothy John. "Correlation and Response in Spherical Many-Electron Systems." Thesis, Griffith University, 2003. http://hdl.handle.net/10072/366874.
Full textAbstract:
Ab initio prediction of the electronic properties of solids is traditionally performed using groundstate Density Functional Theory. These methods are unreliable however, for a class of important problems involving weak attractive forces. These problems include (i) the energetics of hydrogen storage and metal interactions in graphene, (ii) cohesion properties of some polymer systems and (iii) possibly, the weak hydrophobic forces in biomolecules. For these cases a more powerful method than groundstate DFT are timedependent DFT (tdDFT) methods related to the Random-Phase Approximation (RPA). All of these methods proceed by looking at the dynamic density-density response function, whose long-ranged properties naturally lead to the weak forces referred to above. In this thesis we have tested these ideas by investigating electronic response and correlation on the predicted properties of spherical atoms. We have developed and tested a variety of approximations to the timedependent response function through approximations of the tdDFT class and a new method involving greater self-consistency in the screening equation, the inhomogenous STLS approach. Through the development of new methods and computer code, we have solved the response equation allowing us to test our approximations on atoms. Calculation of certain dynamic and static properties of a variety of atoms within our approximations generally agree well with known results. In this thesis we have calculated excitation energies of Helium, dipole polarisabilities and C6 van der Waals (vdW) coefficients of a variety of atoms, and groundstate correlation energies Ec of some atoms. The excitation spectra of Helium generated in our new PGG+c approximation are in good agreement with experiment. The dipole polarisabilities are generally in good agreement with known results, with the exception of Magnesium, Beryllium and Sodium. The C6 coefficients are a little poorer with the exception of Helium where they are nearly exact. Correlation energies are generally reasonable in the PGG+c approximation although they are considerably less accurate than the other properties we have calculated for all atoms other than He. The ISTLS correlation energy of Helium is within 5% suggesting that this method may perform well for larger atoms where our present numerical techniques require improvement. These generally positive results suggest that the approximations we have developed may be applied to more complicated systems such as those described above with good results.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Science
Faculty of Science
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Book chapters on the topic "Spherical many-electron systems"
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Autschbach, Jochen. "Electron Spin and General Angular Momenta." In Quantum Theory for Chemical Applications, 356–76. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190920807.003.0019.
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The historical background of the discovery of the electron spin is provided. The Stern-Gerlach and Einstein-de Haas experiments are discussed. The operators for a single electron spin are defined, along with the formulation in terms of the 2x2 Pauli matrices. The discussion then moves on to the definition of the spin for many-electron systems and explains how the famous Hund rule (or Hund’s first rule) arises from considering the energy of an open-shell spin singlet vs. triplet state. Next, the generalized angular momentum, ladder operators, and spherical vector operators are defined, and the rules for the addition of angular momenta are derived. The chapter concludes with a discussion of the total spin, orbital, and total angular momentum for open-shell atoms, term symbols, and Hund’s second and third rule.
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Abdulwahab Alfahad, Maadh. "The Activity of New Bio-Agent to Control Cucumovirus Cucumber Mosaic Virus (CMV)." In Studies on Cucumber (Cucumis sativus L.) [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96587.
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CMV virus is worldwide, especially in temperate regions, where it can infect more than 800 plant species belonging to about 40 families. Although the main factor that the plant takes in order not to be infected is because it has preventive means that inhibit the direction of pathogens so that the infection occurs under conditions that suit it and suit its success. Cucumber Mosaic Virus belongs to the group of plant viruses to the genus Cucumovirus, as the virus particles are symmetrically spherical, not enveloped, with a diameter of 29 nm, and the virus has several strains that differ among themselves in terms of factors, symptoms of infection and methods of transmission. The stimulation of induced systemic resistance (ISR) leads to the interest of many researchers. Many types of research and studies have been conducted in the field of biochemical changes in the form of modulating the host’s cell wall. The production of phytoalexin. And the manufacture of pathogen-related proteins (Pathogenesis Related Protein). It has been indicated that treatment with various factors, for example (non-pathogenic organisms, weak pathogens, chemical and industrial compounds, plant extracts, nutritional supplements) has the ability to activate plant defense mechanisms and induce systemic resistance against pathogens. In the field of biological control, bacterial types have been used on many pathogens, including fluorescens Pseudomonas and Bacillus subtillus, as they have proven effective in controlling many different fungal and bacterial pathogens as well as viral, and the reason is due to the ability of the bacteria to produce many growth regulators and thus stimulate resistance The systemic plant and the production of phytotoxins are in addition to being one of the most important growth stimuli. New methods have been used to resist viruses by using natural nutritional supplements with effective effect, because plants have defensive means, and for this reason, the use of these supplements can be stimulated in addition to the preventive aspect, a decrease in infection parameters, and an increase in growth indicators and outcome. Several methods have been relied upon to diagnose viruses, the first being the symptoms of reagents, and they are of basic methods. After that, serological tests were adopted, which are highly specialized and accurate in diagnosing viruses, and electron microscopy was used as a method to detect the size and shape of viruses. Polymerase Chain Reaction (PCR) technology is a fast and accurate way to detect plant viruses compared to other tests, such as the ELISA test and plant reagents.
Conference papers on the topic "Spherical many-electron systems"
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Sripada, Srinivas S., P. S. Ayyaswamy, and I. M. Cohen. "Numerical Computation of the Heat Transfer to a Spherical-Tip Anode During an Electronic Flame Off Process." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0831.
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Abstract In the ball-wedge bonding process employed in microelectronic packaging, the first step is the formation of a spherical tip by the melting and roll-up of a segment of a cylindrical wire. The heat transfer for the melting and roll-up to a spherical-tip shape is provided by a plasma are that is struck between the wire tip (anode) and a flat plate cathode (wand). Eventually, the spherical tip becomes part of a ball. The ball so formed is bonded on the bond pad of a chip, and the unmelted segment of the wire is looped to form a second (wedge) bond on the lead frame. This provides the interconnection between the chip and the external world. The plasma arc provides heat energy to the wire causing it to melt. A portion of the energy generated by the arc is lost by conduction up the wire, while another portion is lost to the surroundings by radiation and convection. A portion is also lost to the cathode plate. In order to estimate the various heat transport quantities, a numerical simulation of the plasma arc process is required. Here, we provide results of such a numerical simulation. A set of continuum conservation equations for the charged particle densities and the temperatures in the discharge gap are solved, along with Poisson’s equation for the self-consistent electric potential. The equipotential contours, the electron number density and temperature variation in the discharge gap, and the results for the heat transfer to the spherical tip of the wire are presented. Once the heat transfer is evaluated in this manner, subsequent calculations for melting and the ultimate shape and size of the ball may be made. These calculations in turn may be used to develop optimal characteristics for bonding which consist of near-spherical balls with minimal porosity. These are known to be the best candidates for a secure interconnection between the chip and the lead-frame. Although in the past we have published many results for related situations, this is the first time when the anode geometry is completely taken into account. The numerical calculations involve adaptive grid generation based on a body-fitted coordinate system. Results provided here are of immediate application value to the microelectronic packaging industry.