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1

Bingler, Arnold, Sandor Bilicz, Mark Csornyei, and Zsolt Badics. "Thin-Wire Integral Equation Formulation With Quasistatic Darwin Approximation." IEEE Transactions on Magnetics 57, no. 6 (June 2021): 1–4. http://dx.doi.org/10.1109/tmag.2021.3064912.

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2

K. Choong, Y., P. Sewell, and C. Christopoulos. "New thin wire formulation for time-domain differential-equation models." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 15, no. 5-6 (2002): 489–501. http://dx.doi.org/10.1002/jnm.474.

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3

Chen, Yi Ping, Ying Ying Cai, Q. Ni, and G. Y. Zhao. "Simulation of Torsion of Thin FCC Single Crystal Wires by Mechanism-Based Strain Gradient Crystal Plasticity." Key Engineering Materials 626 (August 2014): 139–44. http://dx.doi.org/10.4028/www.scientific.net/kem.626.139.

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The size effects observed in the torsion of thin FCC single crystal wires is modelled by the employment of mechanism-based strain gradient crystal plasticity (MSG-CP). In the formulation the total slip resistance in each active slip system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. The MSG-CP constitutive model is implemented into the Abaqus/Standard FE platform by developing the User MATerial subroutine UMAT. By implementing the formulation, the relationship between the non-dimensional torque and the surface strain of the thin copper single crystal wires of different diameters is obtained with the [001] direction along that of the wire axis. The simulation results of torsion reveal size effects, which is in a qualitative agreement with those reported in existing literatures. An appreciable axial elongation is also found in the torsion of single crystal wires.Key words Size effect, MSG-CP model, Torsion
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4

Onyejekwe, Okey Oseloka. "Influence of Convective and Radiative Cooling on Heat Transfer for a Thin Wire with Temperature-Dependent Thermal Conductivity." WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 17 (January 2, 2022): 1–9. http://dx.doi.org/10.37394/232012.2022.17.1.

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In this study, a numerical prediction of temperature profiles in a thin wire exposed to convective, radiative and temperature-dependent thermal conductivity is carried out using a finite-difference linearization approach. The procedure involves a numerical solution of a one-dimensional nonlinear unsteady heat transfer equation with specified boundary and initial conditions. The resulting system of nonlinear equations is solved with the Newton-Raphson’s technique. However unlike the traditional approach involving an initial discretization in space then in time, a different numerical paradigm involving an Euler scheme temporal discretization is applied followed by a spatial discretization. Appropriate numerical technique involving partial derivatives are devised to handle a squared gradient nonlinear term which plays a key role in the formulation of the Jacobian matrix. Tests on the numerical results obtained herein confirm the validity of the formulation.
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5

Shahbazi, Samson, Gregg Berube, Stephanie Edwards, Ryan Persons, and Caitlin Shahbazi. "High Performance Etchable RoHS Compliant Thick Film Gold Conductor." International Symposium on Microelectronics 2018, no. 1 (October 1, 2018): 000620–27. http://dx.doi.org/10.4071/2380-4505-2018.1.000620.

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Abstract The thick film paste manufacturers are expected to produce conductors which are lead and cadmium free, yet have excellent fired film properties and the same performance and properties as the cadmium and lead containing formulations. The fired film surface of these conductors must be defect free (i.e. imperfections, pills, agglomerates) after multiple firing steps and must perform on dielectric as well as substrates from different suppliers. Typically, the thick film gold conductors are used in high reliability applications such as medical devices, military applications, and high frequency circuits, which require robust performance at high and low temperatures, in chemically aggressive environments, or extremely humid conditions. As circuits decrease in size and become more complex, the thick film gold properties become increasingly critical. The challenge is to develop an alternative gold conductor formulation, which can print and resolve fine features (down to 4 mil lines and spaces) as well as have the ability to be etched for higher density circuit designs (down to 1–2 mil lines and spaces). Gold conductors are typically used in conjunction with other high temperature thick films so good performance after multiple firings was also a targeted requirement. Heraeus has been proactive for the past decade in the development of thick film products that are both RoHS (lead and cadmium free) as well as REACH compliant. This paper discusses the experiments that were performed in order to understand the contribution of gold powder, organic and inorganic system to improve the fired film performance. These formulations were compared against existing gold conductors including the high performance gold conductor options as well as other available standard gold conductor options. Thin wire bonding trials including both gold and aluminum wire are used to compare influences of raw materials which includes high volume wire bonding reliability including failure modes and aged wire bond adhesion at elevated temperature exposures (300°C) for extended periods of time. In order to analyze fired film morphology and link this up to wire bond performance, SEM images of the conductor surface and cross sections were conducted. These studies resulted in a newly developed thick film gold conductor paste for use in a wide variety of applications. We present wire-bonding data with gold and aluminum wire and reliability results on both 96% Al2O3 ceramic substrates as well as on top of standard dielectrics.
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6

He, Xin, Fangliang Chen, and Huiming Yin. "Opening-mode micro-cracking in brittle coatings on ductile wires/rods." International Journal of Damage Mechanics 26, no. 1 (July 28, 2016): 119–46. http://dx.doi.org/10.1177/1056789516659330.

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A simplified two-dimensional model is presented to simulate periodically distributed micro-cracking in a thin coating fully bonded to an elastoplastic aluminum wire/rod. The alumina coating which is generated by anodic oxidation is treated as an elastic material, while the ductile aluminum wire substrate is characterized by a bi-linear elastoplastic hardening model. An elastoplastic shear lag model is applied to transfer the shearing stress from the substrate layer to the thin coating. When the coated structure is subjected to different applied load, the system will undergo different stress levels and exhibit different cracking stages. Accordingly, explicit solutions corresponding to different loading stages are presented based on a generalized axisymmetric formulation. Finite element simulation is employed to verify the present elastic solution when the applied load is relatively small and the whole system is in the elastic state. Experimental characterization is conducted to validate the present elastoplastic solution when the substrate or interlayer undergoes large deformation. A versatile high-fidelity optical microscope is utilized to check the micro structure of the coating and continuously monitor the fracture development in the coating layer, through which valuable detailed micro-cracking information, such as critical applied load corresponding to crack initiation, crack pattern and crack spacing, is obtained. It shows that the presented fracture model is able to accurately capture the stress and strain distribution in the coated structure and predict the fracture initiation, infilling, and saturation in the thin coating layer.
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7

Mowete, Ike, Ayotunde Ayorinde, and Adeniyi Adehola. "The Logarithmically-non-uniform Helix Antenna Mounted Above a Finite Ground Plane." ELEKTRIKA- Journal of Electrical Engineering 21, no. 1 (April 20, 2022): 25–34. http://dx.doi.org/10.11113/elektrika.v21n1.341.

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In this paper the influence of ground plane size on the performance characteristics of a thin-wire helical antenna characterized by a logarithmically varying turns spacing, and mounted above a circular ground plane of finite extent, is systematically investigated. The moment-method formulation utilized in the paper involves a wire-grid model for the ground plane as well as explicit expressions, deriving from a vector potential approach, for the radiation fields of this ‘loghelix’. Subsequent computational results obtained for a candidate 8-turn ‘loghelix’ axial-mode ˀantenna using various combinations of ‘logarithmic variation factor’ and ground plane size, very clearly reveal that limiting the size of the ground plane to finite dimensions significantly improves antenna performance. Maximum gain obtainable, for example, emerged as 16.45dBi when a finite ground plane is utilized, as against 13.55dBi for the corresponding antenna, backed by an infinite ground plane. The associated axial ratio performance is characterized by for the finite ground case, and , for the infinite ground plane case. A notable finding of the investigations is that the dip that typically features in the power gain profiles of antenna structures backed by finite ground planes will be eliminated, when ground plane size, relative to antenna size exceeds a certain minimum.
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8

Mowete, Ike, Ayotunde Ayorinde, and Adeniyi Adehola. "The Logarithmically-non-uniform Helix Antenna Mounted Above a Finite Ground Plane." ELEKTRIKA- Journal of Electrical Engineering 21, no. 1 (April 20, 2022): 25–34. http://dx.doi.org/10.11113/elektrika.v21n1.341.

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In this paper the influence of ground plane size on the performance characteristics of a thin-wire helical antenna characterized by a logarithmically varying turns spacing, and mounted above a circular ground plane of finite extent, is systematically investigated. The moment-method formulation utilized in the paper involves a wire-grid model for the ground plane as well as explicit expressions, deriving from a vector potential approach, for the radiation fields of this ‘loghelix’. Subsequent computational results obtained for a candidate 8-turn ‘loghelix’ axial-mode ˀantenna using various combinations of ‘logarithmic variation factor’ and ground plane size, very clearly reveal that limiting the size of the ground plane to finite dimensions significantly improves antenna performance. Maximum gain obtainable, for example, emerged as 16.45dBi when a finite ground plane is utilized, as against 13.55dBi for the corresponding antenna, backed by an infinite ground plane. The associated axial ratio performance is characterized by for the finite ground case, and , for the infinite ground plane case. A notable finding of the investigations is that the dip that typically features in the power gain profiles of antenna structures backed by finite ground planes will be eliminated, when ground plane size, relative to antenna size exceeds a certain minimum.
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9

Mowete, Ike, Ayotunde Ayorinde, and Adeniyi Adehola. "The Logarithmically-non-uniform Helix Antenna Mounted Above a Finite Ground Plane." ELEKTRIKA- Journal of Electrical Engineering 21, no. 1 (April 20, 2022): 25–34. http://dx.doi.org/10.11113/elektrika.v21n1.341.

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In this paper the influence of ground plane size on the performance characteristics of a thin-wire helical antenna characterized by a logarithmically varying turns spacing, and mounted above a circular ground plane of finite extent, is systematically investigated. The moment-method formulation utilized in the paper involves a wire-grid model for the ground plane as well as explicit expressions, deriving from a vector potential approach, for the radiation fields of this ‘loghelix’. Subsequent computational results obtained for a candidate 8-turn ‘loghelix’ axial-mode ˀantenna using various combinations of ‘logarithmic variation factor’ and ground plane size, very clearly reveal that limiting the size of the ground plane to finite dimensions significantly improves antenna performance. Maximum gain obtainable, for example, emerged as 16.45dBi when a finite ground plane is utilized, as against 13.55dBi for the corresponding antenna, backed by an infinite ground plane. The associated axial ratio performance is characterized by for the finite ground case, and , for the infinite ground plane case. A notable finding of the investigations is that the dip that typically features in the power gain profiles of antenna structures backed by finite ground planes will be eliminated, when ground plane size, relative to antenna size exceeds a certain minimum.
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10

Lemke, L. A., R. L. Knight, and J. B. Kissam. "Evaluation of Boric Acid Formulations for Control of Red Imported Fire Ants, 1984." Insecticide and Acaricide Tests 10, no. 1 (January 1, 1985): 345–46. http://dx.doi.org/10.1093/iat/10.1.345.

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Abstract Five numbered compounds containing boric acid were evaluated for use as mound drenches for control of red imported fire ants in South Carolina. These studies were conducted in 2 pastures, 1 in Boykin and the second in Santee. In the first pasture 14 circular plots (100 ft diam) were delineated with the location of fire ant mounds in each plot mapped. A minimum of 5 mounds were present in each plot. The activity of each mound was also determined by slightly prodding the mound with a thin metal wire and then estimated by the number of ants coming to the surface using the following scale: 0 = inactive mound, 1 = 1-100 ants, 2 = 101-1000 ants and 3 = greater than 1000 ants. To each of the 14 plots, 1 of 7 treatments was assigned randomly. The concentration of each EI formulation was determined by adding 70 ml of compound to 1 gal of water as instructed by the company. One gal of solution was applied to each mound. Treatments in field 1 were applied on 18 Jun 84. In the second study conducted at Santee, the same procedure was followed except that EI formulations were doubled, 140 ml in 1 gal of water. Treatments in field 2 were applied on 13 Oct 84.
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11

Al-Marouf, Mohamad, and Ravi Samtaney. "A Multi-Fluid Investigation of the Membrane Supporting Grid Effects on the Richtmyer-Meshkov Instability." Defect and Diffusion Forum 390 (January 2019): 1–7. http://dx.doi.org/10.4028/www.scientific.net/ddf.390.1.

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We present results of numerical experiments performed to evaluate the effects of the material interface supporting wire grid on the Richtmyer-Meshkov instability (RMI). An air-SF6 interface initially perturbed sinusoidally supported on a number of solid circular cylinders. These cylinders are introduced along the interface to mimic the presence of the grid thin wires. The resulted mixing and growth rate of the perturbation in the presence and absence of the supporting grid were analyzed and validated with experimental measurements. The small scales perturbation imposed by the cylinders are around two orders of magnitude smaller than the interface sinusoidal perturbation wavelength requiring the adaptive mesh refinement (AMR) to adequately resolve small scale features. Furthermore, an embedded boundary technique is used to handle the complex geometry stemming from the presence of these multiple. A multi-fluid formulation is utilized to form a multi-gas species interface and compute the gas mixture properties.
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12

Poljak, Dragan, Mario Cvetković, Vicko Dorić, Ivana Zulim, Zoran Đogaš, Maja Rogić Vidaković, Jens Haueisen, and Khalil El Khamlichi Drissi. "Integral Equation Formulations and Related Numerical Solution Methods in Some Biomedical Applications of Electromagnetic Fields." International Journal of E-Health and Medical Communications 9, no. 1 (January 2018): 65–84. http://dx.doi.org/10.4018/ijehmc.2018010105.

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The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.
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13

Hyun, Seung-Yeup. "Improved Discrete-Time Boundary Condition for the Thin-Wire FDTD Analysis of Lossy Insulated Cylindrical Antennas Located in Lossy Media." Journal of Electromagnetic Engineering and Science 21, no. 1 (January 31, 2021): 60–63. http://dx.doi.org/10.26866/jees.2021.21.1.60.

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For the thin-wire (TW) finite-difference time-domain (FDTD) analysis of lossy insulated antennas surrounded by lossy media, an improved discrete-time boundary condition (DTBC) at the interface is proposed here. In previous TW-FDTD techniques, the DTBC formulations on the material discontinuity between the lossy insulation and lossy surrounding media were derived from the dielectric constitutive relation under the uniform field approximation (UFA) over each time step. In this paper, to achieve higher accuracy, an improved DTBC is formulated from Maxwell’s equations under the linear field approximation (LFA) and subsequently corrected in the TW-FDTD update equation. By comparing the input impedances of Teflon-insulated cylindrical monopole antennas located in wet soils, we show that the proposed approach provides higher accuracy than previous techniques.
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14

Shen, Zhenzhen, and Aleksey Reiderman. "High-Temperature Reliability of Wire Bonds on Thick Film." International Symposium on Microelectronics 2017, no. 1 (October 1, 2017): 000531–35. http://dx.doi.org/10.4071/isom-2017-tha23_086.

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Abstract In a harsh environment, wire-bonded interconnects are critical for overall reliability of microelectronic assemblies. Aluminum is the dominating metallization of the die wire bonding pads and aluminum wires are used to achieve monometallic bonding system on die side. On the substrate side, a monometallic connection is not readily available and typically involves expensive aluminum thin-film deposition or labor-intensive bonding tabs. Nickel-palladium-gold galvanic or electro-less plating stacks are also used to improve bondability and reliability of non-monometallic Al wire bonds on the substrate side. However, these plating stacks do not perform well after excursions above 330°C that are needed for the attachment of die and passives prior to wire bonding. At these temperatures, both palladium and nickel diffuse through the gold and form surface oxides that degrade wire bondability. In monometallic wire-bonding schemes, in addition to aluminum wires gold wires within same assembly are often also needed, for example, when some die is only available with gold-plated bond pads, or to connect substrates to gold-plated pins of hybrid housings. A universal substrate metallization, compatible with aluminum wire and gold wire, is therefore desirable. Thin-film substrates produced by sequential deposition and etching of gold metal, barrier metals, then aluminum metal is a good working solution, but it can be as much as ten times more expensive than other types of substrates. Printed thick-film metallization, a well-established technology, have been widely used for hybrid substrates. Silver-based thick films are inexpensive and capable of accepting aluminum and gold bonds. However, the silver-aluminum bonds are seldom used because of intermetallic formation and subsequent degradation triggered by multiple factors like temperature, humidity, and the presence of halogens. Pd and Pt are often added to the Ag thick films to decrease this effect, but potential usability and the reliability of these formulations in extreme temperature environments is not well researched. For this study, samples of Pt/Ag thick-film metallization were printed on Al2O3 substrates, and 25-um and 250-um aluminum wires and 50-um gold wires were wedge bonded in daisy chain to the substrate. The test vehicles were subjected to high-temperature testing at 260°C and 280°C. Thermal cycling tests from −20°C to 280°C were also performed. Mechanical and electrical characterizations of the wire bonds were conducted periodically. These tests included resistance and pull-strength measurements. Failure analysis of the bond joints was performed to understand the results of the tests. The 250-um Al wire and 25-um Al wire showed no significant changes until a critical time-at-temperature was reached. After reaching this temperature, the wire/substrate interface resistance rapidly increased to values as high as 40 Ohms for the 25-um Al wires. However, the pull strength remained within standard throughout the tests of up to 1200 hours. The relationship between time to failure and the temperature is presented in the paper. There was a four times life increase of bonds with every 20°C. With gold wires, no dramatic increase of bond resistance was observed, only a slight increase with time. The pull strength of Au wires remained stable throughout the time at high temperature. The tested Ag/Pt thick film metallization was found to be compatible with bonding of the gold wires and the aluminum wires for high-temperature applications up to an Arrhenius equivalent of 800 hours at 260°C. Additionally, Parylene HT coating was vapor-deposited on one set of 250-um Al wire-bonding samples. This set of samples demonstrated doubling of its useful life as compared to the uncoated samples.
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15

Al-Talqany, Faris J. "Effect of Number of Wire Mesh Layers and Depth Ratio on Ultimate Shear Force for Monopanel Beam Specimens." Journal of University of Babylon for Engineering Sciences 26, no. 1 (December 21, 2017): 407–13. http://dx.doi.org/10.29196/jub.v26i1.379.

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A monopanel is the system building witch consists of two thin ferrocement block as a faces and between them a bushy layer of low strength, density and cost as a core made from lightweight material for example from polystyrene foam as using in this investigation or any material as an insulation . The simple structural idealization of a monopanel system is that the core provides transverse trusses between the faces that prevent flexural ,shear force and compression. Transverse trusses made of steel bars having a diameter of 3.2 mm, which make available as tie reinforcement to prevent the thin ferrocement skins from local buckling, have been used in the present work. These transfer system consist of two longitudinal bars connected by inclined steel bar forming trusses shape making an angle equals to 60o with the longitudinal bars. The main object of this research is to present an experimental investigation on the behavior and load carrying capacity of monopanel beams. The experimental work includes testing six groups of monopanel beams, and has been investigated the effect of a different depths of monopanel beams and number of layer of wire mesh of skin faces (one or two layers ) on the behavior and the ultimate load capacity. Also comparison of these results with the ACI code 318M-08 formulations have been made.
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16

ROGER, MICHEL. "On broadband jet–ring interaction noise and aerofoil turbulence-interaction noise predictions." Journal of Fluid Mechanics 653 (May 5, 2010): 337–64. http://dx.doi.org/10.1017/s0022112010000285.

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The aerodynamic noise of a thin rigid annulus (referred to as the ring here) placed in the mixing layer of a subsonic circular jet is investigated in the paper, both theoretically and experimentally. From the experimental point of view, the jet–ring configuration is understood as an axisymmetric alternative to more usual ones involving a rectangular aerofoil held between parallel side plates, dedicated to the study of the noise due to the impingement of upstream turbulence. The main advantages of the circular geometry are a minimum background noise, the absence of tip effects and more specifically the account for all radiation angles from the surface in the far-field acoustic signature. The circular set-up is well suited for the study of pure broadband interaction noise only if the flow remains free of self-sustained oscillations. This is ensured by keeping a sufficient interaction distance between the nozzle and the ring, and by shaping serrations on the nozzle lip. From the theoretical point of view, an analytical model is derived as a straightforward extension of existing formulations. The induced unsteady lift forces on the ring are first inferred from a linearized unsteady aerodynamic theory and the far field is calculated in a second step by a radiation integral. This relates the far-field acoustic pressure power spectral density (PSD) to the two-wavenumber spectrum of the radial turbulent velocity at the ring location, by means of an aeroacoustic transfer function. The latter is shown asymptotically identical to the one detailed in the Appendix for a rectangular aerofoil, in the limit of relatively high frequencies. The analytical acoustic predictions are found to agree well with the measurements over an extended frequency range, provided that the model is fed with turbulent velocity input data measured by a hot-wire probe. Indirectly, this agreement validates the transfer function for a rectangular aerofoil at oblique radiation angles, which is not achievable in a set-up involving side plates and a rectangular nozzle.
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17

Hussain Mian, Abrar. "Isolation And Characterization Of Biosurfactant Producing Bacteria From Different Environmental Soil Samples." Journal of Toxicology and Environmental Sciences 1, no. 1 (November 2, 2021): 36–47. http://dx.doi.org/10.55124/jtes.v1i1.133.

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Biosurfactants are natural substances produced by several bacterial and fungal organisms that are amphiphilic and are extracellular (a part of the cell membrane). Biosurfactants can reduce the stress between solids and liquids on the surface and at the end. Biosurfactants have several properties, i.e. they are stable, less harmful, as well as readily degradable, and extremely eco-friendly. Biosurfactants also have a wide range of industrial uses because they are a versatile category of chemical substances. The principal justification for conducting such research was the isolation of possible biosurfactants containing bacteria. Sampling was performed for the isolation of bacteria producing biosurfactants from different oil-polluted sites That is to say, experiment for emulsification, test for oil spreading, test for drop collapse, and measure for hemolysis. The capability to produce biosurfactants was seen in 22 different isolates from polluted sites B1, B2, and B3. Through different biochemical tests and Gram staining, it was identified that isolated bacterial strains are Pseudomonas spp and that is Pseudomonas aeruginosa. The procedure used as characterizing biosurfactants was the TLC plate’s procedure, by using TLC plates process yellow dots emerged after spraying on silica gel plates with an throne and ninhydrin reagents. These yellow spots confirmed the presence and production of rhamnolipid in the biosurfactant. Hence, it was concluded that identified strains in the study can be helpful in the heavy metals, pesticides, and hydrocarbons bio-degradation and bioremediation. These may also be used as biological control agents to protect plants from various pathogens, resulting in improved crop yields. Introduction Biosurfactants are natural substances produced by several bacterial and fungal organisms that are amphiphilic and are extracellular (a part of the cell membrane) (Chen et al., 2007; Ghayyomiet al., 2012). Main purpose of the bio-surfactantsgeneration or production is a consequence of financial availability (Van Dyke et al., 1993 It is reported that almost 50 percent of the world's surfactants are used because of the need for cleaning agents as well as the rate of growth grows every day (Deleu and Paquot, 2004). Appropriate use of bio-surfactants will control environmental emissions what these are the most dangerous, constantly rising gradually and disrupting the routine maintenance of life every day. Awareness campaign initiatives have been introduced and also increase for environmental laws, various innovative approaches need to be implemented and even the issue of pollution focused entirely. Developing appropriate advanced technologies to help clear up chemicals and toxins from the ecosystem, like hydrocarbons (both inorganic and organic). Studies on biosurfactants are being launched by scholars and researchers with significant health issues like adverse environmental effects, air contamination, environmental change, and waste management (Makkar and Cameotra, 2002 Biosurfactants contribute to expanded demand for such microbial products as alternatives to chemical surfactants (Benatet al., 2000). Microbes seem to have the capability to degrade contaminants, but their biodegradation is limited leading to hydrophobicity, low solubility in water, and inadequate bioavailability, of such pollutants (Patil, et al., 2012). GhayyomiJazeh, Mishraet. al (2001) those bacteria that produce biosurfactants were isolated from the site of petroleum spills and afterward, 160 strains and as well as 59 strains were able to produce biosurfactants have shown better performance in a test for hemolysis of blood, and 45 strains with positive findings within oil spread experiment were applied in the laboratory to isolate and segregate the media cultured Banat process (Rahman et al., 2002) These were observed and researched that biosurfactants of Pseudomonas aeruginosa spp are most likely to disrupt the bonding of hydrocarbons like nonadecane, octa, Hexa, and hepta, in marine Water contaminated with oil spills up To approximately 47%, 53%, 73% and 60%(Abrar et al., 2020). Current study concluded that the isolated strain having the ability to degrade hydrocarbon as well as the ability to degrade the heavy metal. The strain also can protect the plant from various diseases. The present research found that the isolated strain is capable of degrading hydrocarbon while also being capable of degrading the heavy metal. As well as the strain does have the capability to defend plants from different diseases. Material And Methods Area of Study The investigation was conducted at HazaraUniversity(HU) Microbiology Laboratory, MansehraPakistan. Assemblage of Samples Thehomestay area of the city Mansehra Pakistan which is named as a township, where oil spills arose, oil spills soil samples were obtained as well as sampling from various Mansehra automobile workshops were also done. Sterilized bags of polythene were being used to collect samples of the soil, after thatthe sample was taken towards the Hazara University (HU) Mansehra Microbiology Laboratory to examine and extract bacterial strains that could develop biosurfactants. The soil temperature at the time of sample selection was around 30 ° C. The pH was also verified by Galvano science companies at the time of selection by pH meter, and the pH being reported was 7. Preparation of Media 15 x 100 mm Petri dishes were being used to prepare the media. Agar plates were thoroughly cleaned with water from the tap and then carefully covered in aluminum foil following cleaning then placed within autoclave at 121°C for about 15 min at 15 psi for sterilization. The nutrient agar which contains 0.5% NaCl, 0.3% beef extract, 0.5% peptone, and 1.5% agar, in 500 ml of distilled water, 14 g of the nutrient agar media (Merck) were dissolved. The nutrient level used mainly for the production of non-fastidious species. Nutrient agar is widely known as it's capable of growing a variety of bacteria types and provides nutrients required for the growth of bacteria. Upon sufficient dissolution of such nutrient agar in distilled water, these were then sterilized by autoclaving for 15 min at 15 psi in the autoclave and held at 121 °C Upon autoclaving, pouring of the media was done in laminar flow hood, and then packed and placed for yet more use in a fridge at 4°C. 2.4 Preparation of serial dilution The bacteria are isolated using the serial dilution process. During this process, 10 test tubes were taken and distilled water (9ml) was added in each tube. After that tubes were put for 15 minutes in the autoclave machine at 121°C. After that 1gm of a crude oil sample from the soil was added in a test tube containing distilled water. Further, 1 ml of the solution was taken from the first test tube and poured to the adjoining tubes for the preparation dilution as under . Afterward, 10μl of the solution was pipetted from both the dilution of and shifted for spread culture techniques, then incubated the plates at 37°C for 48hrs. Biosurfactants extraction Firstly, in nutrient broth solution theculture of bacteria was added and inoculated with oil, the bacterial colony was then incubated at the temperature of 25°C in a shaking incubator just for 7 days. Incubation after seven days of trembling. Thebacterial Crop was then taken and centrifuged at 5000rpm at temperature 4°C for 20minutes. Following centrifugation, the supernatant was collected and then mixed in the equivalent amount in Methanol: Chloroform. White sediment was then retained and collected for further use . Bacterial Colonies Isolation 1 g of the soil polluted with oil was diluted serially up to 106 dilutions.10 μl of 104 and 106 dilutions for spread culture were transferred to the MSM agar plates and nutrient agar. The plates were then incubated at 37°C for 48hrs. Twenty-two morphologically separate colonies were separated for further specific examination just after the incubation and processed by using the technique of streak plate. Screening of Isolates’ Biosurfactants Behavior To check the activity of biosurfactants produced by the bacterial species the following methods of screening were done. Hemolytic Activity of Biosurfactants for Erythrocytes Blood agar containing 5% of blood was prepared as after the fresh isolates were added and inoculated on blood agar plates, then the plates were taken and placed in the incubator at temperature 37°C for 48hrs (Rashediet al., 2005). Thereafter the observation of clear zone in the colonies indicated the existence of bacterial species that produce biosurfactants. This experiment was undertaken to control the ability of isolated bacteria to induce blood agar hemolysis. Three forms of hemolysis usually involve; alpha, beta, and hemolysis of the gamma. The agar underneath the species is dark greenish, then it is Alpha, the yellowish color produced in beta hemolysis and gamma hemolysis does not affect the bacterial sppwhichadded on the plates (Anandaraj and Thivakaran, 2010). Bio-surfactant identification with process of CTAB MSM (Mineral salt agar medium) with (2%) of glucose serving both as carbon source, (0.5 mg / ml) acetyl-tri-methyl-ammonium-bromide (CTAB), and methylene blue (MB: 0.2 mg/ml) are used to detect anionic bio-surfactants (Satpute et al., 2008). For this method, thirty microliters (30μl) of cell-free supernatant were added to each of the wells of the methylene blue agar plate that comprises of borer (4 mm in diameter). after that, the incubation of the plates was done for 48-72 hrs at 37°C. Just after incubation in each of the wells, a dark blue halo zone was being used to show the successful anionic bio-surfactant production. Table 1: Composition of MSM Media S. No Ingredients Amount (gm/L) I Potassium dihydrogen phosphate (KH2PO4) II Magnesium Sulfate (MgSO4) III Iron Sulfate (FeSO4) IV Sodium Nitrate (NaNO3) V Calcium Chloride (CaCl2) VI Ammonium Sulfate (NH4)2SO4 Technique for Spreading of Oil A sufficient number of isolated bacteria were inoculated into a solution of 100ml nutrient broth. Over 3 days, the culture was incubated at 37 ° C in a rotating shaker incubator (150 rpm). After that biosurfactants synthesis was checked in culture suspensions (Priya and Usharani, 2009; Anandaraj and Thivakaran, 2010). For this process, thirty milliliters (30ml) of distilled water was added in a Petri dish. In the middle of the distilled water, 1 milliliter (1ml) of diesel oil was added, and then a centrifuged twenty microliter (20μl) culture was introduced to the middle of a plate, which was isolated from oil spilled soil or local oily groundwater. The species producing the bio-surfactant displace the hydrocarbons and disperse it even in the water. Then it was calculated and analyzed within 1 mint (Ali et al., 2013). Technique for Drop collapse In this process, 96-wellsformed in each of the plates of nutrient agar. Afterwards, all the 96-wells of microliter plates was then filled withmineral oil of about 2ml. Then stabilized the plate at 37oC for 1 hour, after which the oil surface was filled with 5μl of supernatant culture. Therefore, the drop shape was taken to be observed on the oil surface after 1min. The drop which was collapsed, generated by the supernatant culture which is used to signify positive(+ive) outcome and the drops which stayed the same and displayed no changeindicates negative(-ive) outcome. And was taking distilled water as a control(Plaza et al., 2006). Emulsification index The emulsification index was calculated, as stated by the process followed by Cooper and Goldenberg (1981) In this process, 2 ml of kerosene oil was taken and inserted in each of the test tubes to the same amount of cell-free supernatant, and then homogenized for 2 min in a vortex at high speed and allowed for 24 hours to stand. The emulsification steadiness was then determined after the 24 hours, and the emulsification value was estimated by measuring the emulsified layer height by the total liquid layer height, then multiplied by 100. Quantification for the Dry weight of Biosurfactants The bacterial colony was inserted and inoculated in the nutrient broth medium, followed by oil and centrifuged at 5000rpm and after that, the supernatant was clutched and treated with chloroform and methanol and mixed. The white colored deposits were taken and used for the furtherprocess of dry weight. Afterwards, took the clean Petri plate and determined the empty plate weight. Next, the sediment was poured onto Petri plates. Now, for the drying process the hot air oven was used and set the 100ºC of temperature for 30minutes and the plates were put in the oven. After the drying process, the plates were weighted again. The dry weight was calculated for the biosurfactants using the formula which described below: Selected strains Identification and their characterization Instead, various basic biochemical methods were used to identify the isolated bacterial strains. Various biochemical tests, such as Gram staining, Oxidase test, Urease test.Catalase test, Methyl red test, Motility test, Indole test, Starch hydrolysis, Citrate test, Spore staining, Gelatin hydrolysis. Then afterwards, for the preliminary characterization of the biosurfactant, the thin layer chromatography process was used. Physical characterization of the strains selected Gram staining First, on the slide, using the wire loop the bacterial pure culture was taken, and smear was prepared on the slide, and then a drop of purified water was applied. Then, the sterile loop or needle was correctly mixed the bacterial colony and purified water, then mixed up until it is somewhat turbid. Then, spirit lamp was used to fixed the bacterial smear on slide and cooled to room temperature. With this glass slide was loaded with solution of crystal violet and stood for 1minute anddistilled water was applied on slide. Meanwhile the slide was submerged for 1 minute with the iodine solution, and then flushed and rinsed with water. Therefore, decolorizer of about 1 to 2 drops(5 percent acetone and 95 percent alcohol) were added to the slide’s smear and stand for 30seconds, and then treated with water. After then slide was rinsed with safranin for 60seconds, and then treated with water anddry in air. Microscopic analysis was done with 100x objective lenses using emersion oil on smear. Cell morphology The isolates of the bacterial cell were gram stained on slides and then the slides were observed under the light microscope, showing the shape and color of the cells. Biochemical characterization of the selected strains Catalase test Aim of this study is to identify, evaluate and examine that, whether or not the microbes are capable of producing catalase enzymes, while catalase is a protective enzyme, i.e. catalase has the potential to protect against the lethal chemicals known as (H2O2). In this study a bacterial culture that was clarified overnight was used. This culture has been smeared on a glass slide, and 3 percent hydrogen peroxide (H2O2) has been applied and observed on smear. Effects have been observed for bubble formation. Citrate test This study was performed to check the amount or ingest the citrate as the carbon and energy supply for growth and metabolism. Medium containing bromothymol blue and sodium citrate as pH indicator, bacterial was introduced. Ammonium chloride is also present in this medium used as a nitrogen source. Results were noted with variations of color from green to blue. Urease test The capability of urease enzyme for degrading urea was calculated in this bacterial capacity test. Bacterial culture was taken and inoculated for 48 hours at 37 ° C in urease broth, and then color was observed. Methyl red test Through using the process known as mixed acid fermentation which is used to evaluate the bacteria's acid production. The bacterial culture was taken and introduced in the broth of MR-VP and then incubated for 3days at a temperature of 37°C. Two (2) to three (3) drops of Methyl red were added in the broth medium after the incubation period. The change in broth color was observed for final results after a few seconds. Indole test Through using the process to assess the bacteria 's capability to crash indole from tryptophane molecules. After the 24 hours of incubated, taken the fresh inoculum of bacteria and then inserted into the tryptone medium, 24 hours of incubation of about 30oC, 2ml of the tryptone broth medium was added into a sterile test tube. Kovac's reagent was taken to be added (few drops) in sterile test tube and stimulated for a few minutes, and variations of color were detected. Gelatin test It is the approach assess to figure out the use of enzymes known as gelatins from bacterial organisms that precipitate the gelatin. Fresh inoculum of bacteria was taken after 24 hours, and inserted into the media of gelatin agar. This was incubated for around 24 hours, so the temperature did not exceed 30 ° C. Media was observed after incubation time. Starch hydrolysis Several of the micro-organisms that use the starch as a carbon energysource. Therefore, this method has been used to assess whether or not bacteria may use starch as a source of carbon. The bacterial fresh inoculum was spread on the petri starch agar plates, and after that the plate was incubated for 24 hours andmaintained the temperature at 30 to 35 ° C, then gradually applying the supplements of iodine to the plates to flow the change, and then examining the plates. Preliminary characterization of the strains selected Experimental characterization of the bio-surfactant was performed by using the process of TLC (Anandaraj et al., 2010). On a silica gel plate, crude portion of the rudimentary bio-surfactant was separated using Methanol: Chloroform: water (CH3OH: CHCl3: H2O) in the ratio of as an eluent with a different color producing reagents. Ninhydrin reagent (0.5 g ninhydrin in 100ml anhydrous acetone) was used to find bio-surfactant lipopeptide as red spots and anthrone reagent (1 g anthrone in 5ml sulfuric acid combined with 95ml ethanol) as yellow spots to identify rhamnolipid bio-surfactant (Yin et al., 2008). Results and Discussion Isolation of bacteria At first, twenty-two (22) strains from a polluted soil sample were isolated from nutrient agar media.Mixed culture provided by these colonies, so they were taken and smeared on the plates of nutrient agar and then fresh inoculum was collected and stored at temperature of 4oC for the further analysis. Bio-surfactants (surface-active compounds)are formed by a variety of amphiphilic bacterial and fungal organisms that are extracellular (a part of the cellular membrane) (Chen et al., 2007). Screening of Isolated strains for biosurfactant producing colonies Different experiments were carried out to identify, isolate and screen bacteria that are capable of generating bio-surfactants and that is Oil spreading technique(OST), blood hemolysis test(BHT), CTAB test, Emulsification operation. There were twenty-two distinct isolates observed in the current research. And the B1, B2 and B3culture were taken and selected from the twenty-two (22) strains isolated from the polluted spot, which were found to produce biosurfactant. And the oil spreading technique showed promising results for these strains. And strain B2 showed a greater displacement of oil and this is 4 mm. Oil spreading method is quick and often easy to handle, and this technique requires no particular equipment, only a very small amount of sample is used. This approach can be applied when the production and quantity of biosurfactant is small (Plaza et al., 2006) and (Youssef et al., 2004) Only bacterial cultures have been allocated and screened for bacterial species that can generate or use biosurfactants. Just three (3) strainsamong them presented the best results.Those 3 strain,s (B1, B2 and B3) were selected as an additional analysis. Blood hemolysis test On the petri plates of blood agar, the . Isolated bacteriaof B1, B2 and B3 were taken andstreak at the temperature about 37°C for 48 hours. Strain B1 demonstrated β (Beta) hemolysis after the incubation cycle and B2 and B3strains demonstrated γ (Gamma) hemolysis. The B1 strain had an emulsification index of about 74 percent and that was very high as compared to 70 percent for B2 and about 53 percent for B3 respectively. Around the same time, B1 strain showed β (Beta) hemolysis and γ (Gamma) hemolysis was shown bystrains B2 and B3 on the platesof bloodagar. The β hemolysisshowed by the strain B1 in the blood agar test, and the strain B2 and B3 showed γ (Gamma) hemolysis. It is determined that 20 percent strains that are the bestproducer of rhamnolipid have not fully lysed the blood, because the ability of the producer strains capacity not be responsible for the hemolytic activity. According to many researchers, who have shown that this is not such an effective tool for biosurfactant detection due to many bioproducts that may also induce red blood cell lysis, that is not so sufficient to be the surface-active molecule (Youssef et al., 2004). (Rashedi and others, 2005). Table2 Blood Hemolysis Test CTAB agar plate test This test confirms the anionic biosurfactants development. After plate incubation at a temperature of 37 ° C for 72 hours, dark blue hollow zone was existedaround each of the B1 strains wells, which clearly indicated the positive (+ive) development of anionic Biofactant. In addition, the B1 and B2 strains showed positive (+ I ve) results and, in the CTAB analysis, the B3 strain was found to be negative (-ive). The growing microorganisms when secreted the anionic biosurfactants on the plates of CTAB (cetyl-tri-methyl-ammonium-bromide) and methylene blue, then as a result the dark blue-purple insoluble ion pairs formed on the plates. The halo zone around each of the colonies was developed that can recognize rhamnolipid production and that was dark blue in colour, and could correlate with production of rhamnolipid (Siegmund et al., 1991). As indicated in (Fig1) Fig1: B1 positive on CTAB agar plate Oil Spreading Technique The oil was displaced by B1, B2and B3 strains in this test strain and showed a zone that was so clear. The bacterial strains capable of developing biosurfactant were tested and separated from the sample of soil which was oil spilled and brought from the District of Mansehra, Pakistan and from automobile workshops of Mansehra. As shown in (Fig.2). Fig.2: Results of Oil Spreading by B1, B2 and B3Table 3;.Test for oil spreads Bacterial culture Formation of zone (mm) Readings B,1 B,2 B,3 Drop-collapse technique During this process the drop shape was observed at the oil surface. As seen in Fig 3, the collapsed drop was provided by the supernatant culture B1 , B2 and B3.. Emulsification index Emulsification stability was measured with the use of kerosene oilin this test, and then observed the results. Since this emulsification index was calculated by dividing the height of the emulsion layer by the total height of the liquid layer and then multiplying by 100, as shown in the formulation below. Emulsification index Emulsification stability was measured with the use of kerosene oilin this test, and then observed the results. Since this emulsification index was calculated by dividing the height of the emulsion layer by the total height of the liquid layer and then multiplying by 100, as shown in the formulation below. Fig 3: Result of Drop-collapse test Table 4: The activity of Biosurfactant emulsification Dry weight of bio-surfactants In this examination, white-colored sediment was collected. Then measured the weight of the sterile Petri plate which was empty in the first step. Then, the sediment was poured into plates. The plates were taken and weighted after 30 minutes of drying on a hot air oven, following the process of drying. The weight of biosurfactants (dry weight) was measured using the following formulations: Fig 4: Dry weight of biosurfactants Table: 5: Dry weight of the biosurfactants Bacterial Culture Weight of the plate (g) biosurfactant in The plate after drying (g) Dry weight of Biosurfactant (g) B,1 B,2 B,3 Identification of selected strains and their characterization Gram staining For structural applications, and stroke analysis gram staining method was used.(Fig.5) shows findings from the process of gram staining. Fig 5: Microscopic view of Gram staining Biochemical identification of bacterial strains and their characterization Specific biochemical studies were performed to identify the species for further recognition and characterization. The bio-surfactant producing microorganism was found to be Pseudomonas aeruginosa after conducting various characterizations and the biochemical tests(Eric Deziel et al., 1996), Which can be used to further analyze and study the industrial development of the biosurfactant. Rhamnolipid is also isolated and produced from the Pseudomonas aeruginosa species on the silica gel plate (Rashedi et al., 2005), a form of biosurfactants highly recommended for processes of bioremediation. All the findings collected from biochemical testing were labeled as Berge 's Manual and it revealed that the protected microorganism was (Pseudomonas aeruginosa). Results of biochemical test were tabulated in (Table.5) Table 6: Bacterial strain identification Tests B1 B2 B3 Gram staining Negative Negative Negative Oxidases Positive e Positive Positive Catalase Positive Positive Positive Indole Positive Negative Negative Citrate Positive Negative Negative Urease Negative Positive Negative Nitrate Positive Positive Positive Motility Positive Positive Positive Gelatin hydrolysis Positive Negative Negative Lactose Negative Positive Positive Methyl red Negative Positive Positive Voges Proskauer Negative Negative Negative Fig 6: Results of biochemical tests(A) Methyl red and Voges Proskauer tests (b) catalase tests (c) oxidase tests (d) indole tests (e) citrate tests (g) lactose tests (h) urease tests Preliminary bacterial strain’s characterization The plates showed yellow dots, when sprayed with anthrone reagent. It indicated the existence of biosurfactants of rhamnolipid in the organism on the plate of TLC as seen in theFig.7 Fig 7: Biosurfactant characterization by TLC Conclusion Biosurfactant development is exciting and perceptible across industries to clean up oil waste and pollutants, particularly in the ecosystem.Compared with chemical surfactants, the biosurfactants are less harmful. It plays an important role in defining the advantages and the importance of industrial applications. Therefore, it is not possible to disregard the growing role and importance of biosurfactants in environmental sustainability.Biosurfactant formulations which can be used for bacterial, fungal, and viral organisms as growth inhibitors. Such biosurfactant inhibition properties can make them components that are applicable to Numerous illnesses that are used as medicinal agents. Therefore it was decided that the described strain could be used as a potential source for heavy metal bioremediation pesticide and hydrocarbon polluted sites. And also used as shielding the plant from different pathogens, contributing to improved crop yields. There is no doubt that the biosurfactants are a multifunctional, advanced, versatile, long-lasting and updated type not only for the twenty-first century but beyond. Conflict of interest The authors declared that they have no conflict of interest and the paper presents their own work which does not been infringe any third-party rights, especially authorship of any part of the article is an original contribution, not published before and not being under consideration for publication elsewhere. References Ali, S.R.; Chowdhury, B.R.; Mondal, P. and Rajak, S. “Screening and characterization of biosurfactants producing microorganism from natural environment (Whey spilled soil)”. Nat. Sci. Res. 2013, 3(13), 34–64. Anandaraj, B. and Thivakaran, P. “Isolation and production of biosurfactants producing organism from oil spilled soil”. Biosci. Tech. 2010, 1(3), 120–126. Banat, I.M.; Makkar, R.S. AND Cameotra, S.S. “Potential commercial Application of Microbial Surfactants”. Applied MicrobialBioethanol. 2000, 53, 495-508. Cooper, D. G, Zajic, J. E. and Denis, C. J. Am. Oil Chem. Soc. 1981, 58, 7780. Deleu, M. and Paquot, M. “From Renewable Vegetables Resources to Microorganisms: New Trends in Surfactants”C.R. 2004, 7, 641-646. Eric, Deziel.; Gilles,Pauette.; Richars, Villemur.; Francois,Lepine.; and Jean-Guy, Bisaillon. “Biosurfactants Production by a Soil Pseudomonas Strain Growing on Polycyclic Aromatic Hydrocarbons”. Applied and Environmental Microbiology. 1996, 62(6), 1908-1912. Ghayyomi, J.M.; Forghani, F.; Deog, Hwan, Oh. “Biosurfactant production by Bacillus sp. Isolated from petroleum contaminated soil of Sirri Island”. Ame. J. Appl. Sci, 2012, 9(1), 1-6. Makkar, R.; & Cameotra, S. An update on the use of unconventional substrates for biosurfactant production and their new applications. Applied microbiology and biotechnology. 2002, 58(4), 428-434. Mishra, S.; Jyot, J.; Kuhad, R. C.; & Lal, B. Evaluation of inoculum addition to stimulate in situ bioremediation of oily-sludge-contaminated soil. Environ. Microbiol. 2001, 67(4), 1675-1681. Patil, T. D.; Pawar, S.; Kamble P. N. & Thakare, S. V. “Bioremediation of complex hydrocarbons using microbial consortium isolated from diesel oil polluted soil”. Der ChemicaSinica Journal of Biotechnology. 2012, 3(4), 953-958. Plaza, G.; Zjawiony, I.; and Banat, I. “Use of different methods for detection of thermophilic biosurfactants producing bacteria from hydrocarbon contaminated bioremediation soils”. Petro. Sci. Eng. 2006, 50(1), 71–77. Priya, T.; Usharani, G. “Comparative study for bio-surfactant production by using Bacilus subtilis and Pseudomonas aeruginosa”. Res. Int. 2009, 2(4), 284–287. Rahman, K.S.M.; T.J. 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"Pseudomonas aeruginosa UG2 rhamnolipid biosurfactants structural characterization and their use in removing hydrophobic compounds from soil". J. Microbiol. 1993, 39, 1071-1078. Yin, H.; J, Qiang.; Y, Jia.; J, Ye.; H,Peng.; H, Qin.; N, Zhang. B. “Characteristics of bio-surfactant produced by Pseudomonas aeruginosa S6 isolated from oil containing water”. Process Biochemistry. 2008, 44: 302–308. Youssef, H.; Duncan, El.; Nagle, P.; Savage, N.; Knapp, M.; McInerney, J. “Comparison of methods to detect biosurfactant production by diverse microorganisms”. Microbiol Methods. 2004, 56, 339-347.
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Davidson, David B. "Convergence of the MPIE Galerkin MoM thin wire formulation." IEEE Transactions on Antennas and Propagation, 2021, 1. http://dx.doi.org/10.1109/tap.2021.3076520.

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Ye, Weiping, Weidong Liu, Nianwen Xiang, Kejie Li, and Weijiang Chen. "Analytical Evaluation of Partial Elements in the Full-Wave PEEC Formulation for Thin-Wire Structure." IEEE Transactions on Electromagnetic Compatibility, 2023, 1–12. http://dx.doi.org/10.1109/temc.2023.3295056.

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20

Sævik, Svein, and Mats J. Thorsen. "An Analytical Treatment of Buckling and Instability of Tensile Armors in Flexible Pipes." Journal of Offshore Mechanics and Arctic Engineering 139, no. 4 (May 5, 2017). http://dx.doi.org/10.1115/1.4036205.

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Abstract:
The present paper addresses aspects related to local buckling and instability of tensile armors in flexible pipes. Analytical models for evaluating the tensile armor buckling capacity in both transverse (radial and lateral) directions are presented based on formulating the linearized differential equation describing transverse stability of the thin curved wire assuming no friction. Then analytical models for the ultimate capacity of the outer sheath and antibuckling tape are formulated and a combined criterion for radial instability is proposed based on considering radial buckling of the tensile armor, wire yield failure, and the ultimate capacity of the outer sheath and tape. Thereafter, a study is performed comparing the proposed models with test data and alternative models available in the literature.
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