The Numerical Solution of the Exterior Impedance (Robin) Problem for the Helmholtz’s Equation via Modified Galerkin Method: Superllipsoid

This thesis focuses on finding the solution for the exterior Robin Problem for the Helmholtz Equation and therefore, determines how a convergent smooth surface depending on its outer shape, in this case the superellipsoid, responds to different outer waves. The primary purpose is to calculate the possibility of a certain object, acquiring sufficient conditions, to either submerge under respectively high water pressure or maintain in outer space; if applicable, this approach can be used for a new efficient design of a portion of a submarine or part of a space craft, the second of more interest to NASA, one of my sponsors. In this thesis, I analyze the numerical solution for the Helmholtz equation in 3 Dimensions, for the superellipsoid for the Robin Boundary Condition and answer the question of how a surface reacts to incoming waves approaching from various directions. Would the object tend to the extremes of either absorbing or reflecting everything with which it comes into contact, or would it obtain a neutral combination of the two

Numerical Solution of the Helmholtz Equation for the Superellipsoid via the Galerkin Method for the Dirichlet Problem

The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation fora smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: x = cos(x)sin(y)n;y = sin(x)sin(y)n; z = cos(y) where n varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green’s theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala [9], Warnapala and Morgan [10]

Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method

The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: $x=cos(x)sin(y)^{n},y=sin(x)sin(y)^{n},z=cos(y)$ where $n$ varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala , Warnapala and Morgan

Molecular cloning gene and nucleotide sequence of the gene encoding an endo-1,4-β-glucanase from Bacillus sp VLSH08 strain applying to biomass hydrolysis: Research article

Bacillus sp VLSH08 screened from sea wetland in Nam Dinh province produces an extracellular endo-1,4-beta-glucanase. According to the results of the classified Kit API 50/CHB as well as sequence of 1500 bp fragment coding for 16S rRNA gene of the Bacillus sp VLSH 08 strain showed that the taxonomical characteristics between the strain VLSH 08 and Bacillus amyloliquefaciene JN999857 are similar of 98%. Culture supernatant of this strain showed optimal cellulase activity at pH 5.8 and 60 Celsius degree and that was enhanced 2.03 times in the presence of 5 mM Co2+. Moreover, the gene encoding endo-1,4-beta-glucanase from this strain was cloned in Escherichia coli using pCR2.1 vector. The entire gene for the enzyme contained a 1500-bp single open reading frame encoding 500 amino acids, including a 29-amino acid signal peptide. The amino acid sequence of this enzyme is very close to that of an EG of Bacillus subtilis (EU022560.1) and an EG of Bacillus amyloliquefaciene (EU022559.1) which all belong to the cellulase family E2. A cocktail of enzyme containing this endo-1,4-beta-glucanase used for biomass hydrolysis indicated that the cellulose conversion attained to 72.76% cellulose after 48 hours.Chủng vi khuẩn Bacillus sp VLSH08 được tuyển chọn từ tập hợp chủng vi khuẩn phân lập ở vùng ngập mặn tỉnh Nam Định có khả năng sinh tổng hợp enzyme endo-1,4-beta-glucanase ngoại bào. Kết quả phân loại chủng vi khuẩn Bacillus sp VLSH08 bằng Kit hóa sinh API 50/CHB cũng như trình tự gen mã hóa 16S rRNA cho thấy độ tương đồng của chủng Bacillus sp VLSH08 và chủng Bacillus amyloliquefaciene JN999857 đạt 98%. Dịch lên men của chủng được sử dụng làm nguồn enzyme thô để nghiên cứu hoạt độ tối ưu của enzyme ở pH 5,8 và nhiệt đô 60oC. Hoạt tính enzyme tăng 2,03 lần khi có mặt 5 mM ion Co2+. Đồng thời, gen mã hóa cho enzyme endo-1,4-betaglucanase cũng được tách dòng trong tế bào Escherichia coli sử dụng vector pCR 2.1. Gen mã hóa cho enzyme này có chiều dài 1500 bp, mã hóa cho 500 axit amin, bao gồm 29 axit amin của chuỗi peptid tín hiệu. So sánh cho thấy trình tự gen endo-1,4-beta-glucanase của chủng Bacillus sp VLSH08 có độ tương đồng cao với enzyme này của chủng Bacillus subtilis (EU022560.1) và của chủng Bacillus amyloliquefaciene (EU022559.1). Tất cả các enzyme nhóm này đều thuộc họ cellulase E2. Enzyme của chủng này cũng đã được phối trộn với các enzyme khác tạo thành cocktail để thủy phân sinh khối cho kết quả cellulose bị thủy phân 72,76% sau 48 giờ

Microwave-assisted noncatalytic esterification of fatty acid for biodiesel production: A kinetic study

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This study developed a microwave-mediated noncatalytic esterification of oleic acid for producing ethyl biodiesel. The microwave irradiation process outperformed conventional heating methods for the reaction. A highest reaction conversion, 97.62%, was achieved by performing esterification with microwave irradiation at a microwave power of 150 W, 2:1 ethanol:oleic acid molar ratio, reaction time of 6 h, and temperature of 473 K. A second-order reaction model (R2 of up to 0.997) was established to describe esterification. The reaction rate constants were promoted with increasing microwave power and temperature. A strong linear relation of microwave power to pre-exponential factors was also established, and microwave power greatly influenced the reaction due to nonthermal effects. This study suggested that microwave-assisted noncatalytic esterification is an efficient approach for biodiesel synthesis

Surface-enhanced Raman spectroscopy study of 4-ATP on gold nanoparticles for basal cell carcinoma fingerprint detection

The surface-enhanced Raman signals of 4-aminothiophenol (4-ATP) attached to the surface of colloidal gold nanoparticles with size distribution of 2 to 5 nm were used as a labeling agent to detect basal cell carcinoma (BCC) of the skin. The enhanced Raman band at 1075 cm-1 corresponding to the C-S stretching vibration in 4-ATP was observed during attachment to the surface of the gold nanoparticles. The frequency and intensity of this band did not change when the colloids were conjugated with BerEP4 antibody, which specifically binds to BCC. We show the feasibility of imaging BCC by surface-enhanced Raman spectroscopy, scanning the 1075 cm-1 band to detect the distribution of 4ATP-coated gold nanoparticles attached to skin tissue ex vivo

Absence of N-terminal acetyltransferase diversification during evolution of eukaryotic organisms

Protein N-terminal acetylation is an ancient and ubiquitous co-translational modification catalyzed by a highly conserved family of N-terminal acetyltransferases (NATs). Prokaryotes have at least 3 NATs, whereas humans have six distinct but highly conserved NATs, suggesting an increase in regulatory complexity of this modification during eukaryotic evolution. Despite this, and against our initial expectations, we determined that NAT diversification did not occur in the eukaryotes, as all six major human NATs were most likely present in the Last Eukaryotic Common Ancestor (LECA). Furthermore, we also observed that some NATs were actually secondarily lost during evolution of major eukaryotic lineages; therefore, the increased complexity of the higher eukaryotic proteome occurred without a concomitant diversification of NAT complexes

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe