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1
Jander, Kai, Lars Braubach, and Alexander Pokahr. "Practical Defense-in-depth Solution for Microservice Systems." Journal of Ubiquitous Systems and Pervasive Networks 11, no. 1 (May 1, 2019): 17–25. http://dx.doi.org/10.5383/juspn.11.01.003.
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Gojic, Gorana, Radovan Turovic, Dinu Dragan, Dusan Gajic, and Veljko Petrovic. "Automatic corrections of human body depth maps using deep neural networks." Serbian Journal of Electrical Engineering 17, no. 3 (2020): 285–96. http://dx.doi.org/10.2298/sjee2003285g.
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This paper presents an approach to correcting misclassified pixels in depth maps representing parts of the human body. A misclassified pixel is a pixel of a depth map which, incorrectly, has the ?background? value and does not accurately reflect the distance from the sensor to the body being scanned. A completely automatic, deep learning based solution for depth map correction is proposed. As an input, the solution requires a color image and a corresponding erroneous depth map. The input color image is segmented using deep neural network for human body segmentation. The extracted segments are further used as guidance to find and amend the misclassified pixels on the depth map using a simple average based filter. Unlike other depth map refinement solutions, this paper designs a method for the improvement of the input depth map in terms of completeness instead of precision. The proposed method does not exclude the application of other refinement methods. Instead, it can be used as the first step in a depth map enhancement pipeline to determine approximate depths for erroneous pixels, while other refinement methods can be applied in a second step to improve the accuracy of the recovered depths.
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Al‐Chalabi, M. "Parameter nonuniqueness in velocity versus depth functions." GEOPHYSICS 62, no. 3 (May 1997): 970–79. http://dx.doi.org/10.1190/1.1444203.
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Except for hypothetical cases that are never encountered in practice, the solution for the parameters of analytic velocity versus depth functions is inherently nonunique. This nonuniqueness means that there is no particular parameter combination that represents “the” solution. The average discrepancy between the observed velocity‐depth (or time‐depth) curve and the calculated function curve gives a measure of the degree of fit between the two curves. In the parameter space, within a given degree of fit that may be considered as the margin of tolerance for the particular problem in hand, every parameter combination provides a valid solution. The solution trough is defined as the region in the parameter space containing these solutions. The shape of the solution trough depends on the relationship between the parameters and, therefore, on the form of the function being used. If the parameters are related linearly or if the relation is linearized then the axis of the solution trough is a straight line. The slope of the axis corresponds to a point close to the average depth of the interval to which the observed data pertain. The intercept corresponds to a velocity value that is quite close to the average velocity over the interval. These properties are extremely useful for understanding the nature of the solution trough in parameter space. Hence, composite displays of solution troughs pertaining to a number of wells can be interpreted to provide information on whether the unit to which the function corresponds has undergone any lateral changes. Such displays also illustrate how current practices that assume the existence of a unique or “true” solution need to be critically revised.
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Caliskaner, Onder, and George Tchobanoglous. "Development and Solution of Depth Filtration Equation." Proceedings of the Water Environment Federation 2008, no. 13 (January 1, 2008): 3335–47. http://dx.doi.org/10.2175/193864708788732892.
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Acree, Steven D., Jill R. Acree, and Pradeep Talwani. "The Lake Keowee, South Carolina Earthquakes of February through July 1986." Seismological Research Letters 59, no. 2 (April 1987): 63–70. http://dx.doi.org/10.1785/gssrl.59.2.63.
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Abstract In the early morning of 13 February 1986, an earthquake with a duration magnitude (MD) of 3.2 rumbled through northwestern South Carolina. The event was centered near Lake Keowee in Oconee County in a region of prior low level seismicity. Approximately eighty aftershocks with magnitudes ranging from −1.0 to 2.0 were recorded during the next six days. The locations of five aftershocks were accurately determined, utilizing data from portable seismographs deployed in the epicentral area. Depths of the two earthquakes with a location quality of B or better were between 3 and 4 km. First motion focal mechanism solutions for the mainshock suggest oblique slip along a plane striking northeast or northwest. The P axis was oriented northeast-southwest in support of the directions obtained from mechanisms of other local earthquakes and from direct measurements of the maximum horizontal stress in the regions. A second mainshock (MD = 2.8) occurred in the vicinity of Lake Keowee on 11 June 1986 and was followed by over sixty earthquakes during the next five weeks. Focal mechanism solutions from first motion data obtained for the mainshock resemble those of the 13 February event and suggest oblique slip along a northeast or northwest striking plane. Depths of the best located aftershocks were approximately 1 km. Two tests were applied to the data to assess the reliability of the depth estimates. These involve the determination that the plot of RMS travel time residual versus fixed solution depth exhibits a single, sharp RMS minimum at the depth obtained from a free solution (depth uniqueness) and that the final free solution depth is not dependent upon the choice of starting depth (depth stability). Free solution depths obtained for the majority of the better located aftershocks were found to be unique and stable at depths between 1 and 4 km. A northeast trending anomaly is prominent in the geophysical data for this area. This anomaly is interpreted to result from an abrupt, lateral change in lithology along a shallow, northeast striking plane. The earthquakes do not appear to be associated with this feature. Instead, these earthquakes appear to be associated with a shallow body and may represent slip along northeast or northwest striking joints. The proximity of these earthquakes to Lake Keowee suggests the possibility of reservoir triggering. No correlation between seismicity and reservoir level is evident prior to the February events. Rapid fluctuations in water level did precede the events in June and July, providing possible triggering mechanisms.
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Hocking, G. C. "Bow flows with smooth separation in water of finite depth." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 35, no. 1 (July 1993): 114–26. http://dx.doi.org/10.1017/s033427000000730x.
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AbstractThe bow flow generated by a wide flat-bottomed ship moving in water of finite depth is examined. Solutions obtained using an integral equation technique are presented for a range of different depths and for a range of angles of the front of the bow. The solution for the limiting case of infinite Froude number is obtained as an integral, and numerical solutions are found for the nonlinear problem in which the Froude number is finite. Solutions with smooth separation are shown to exist for all values of Froude number greater than unity, for any bow slope.
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Kovač, Žarko, Trevor Platt, and Shubha Sathyendranath. "Sverdrup meets Lambert: analytical solution for Sverdrup’s critical depth." ICES Journal of Marine Science 78, no. 4 (March 10, 2021): 1398–408. http://dx.doi.org/10.1093/icesjms/fsab013.
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Abstract In his 1953 paper, Harald Sverdrup argued that the development of a spring bloom in the ocean depends on the juxtaposition of two depth horizons: the mixed-layer depth and the critical depth. Mixed-layer depth shallower than the critical depth favours phytoplankton growth in the layer and vice versa. However, mathematically, Sverdrup left the problem unsolved in the form of a transcendental equation. In spite of the high number of citations that this paper has garnered, the solution to this equation has not been found, until now. In this work, we present an analytical solution for the critical depth, as originally defined by Sverdrup. The paper opens with the definition of the critical depth and the description of the Lambert W function. The analytical solution for critical depth follows. Sverdrup’s original model is extended to include the effect of light attenuation by phytoplankton and the analytical solution for steady-state biomass in the mixed layer is derived. The expression for mixed-layer production at steady state is also presented. Two novel variants of the critical depth are defined: the optically uncoupled critical depth and the optically coupled critical depth. It is demonstrated that at steady state the optically coupled critical depth equals the mixed-layer depth and that the irradiance at the base of the mixed layer equals the irradiance at the optically uncoupled critical depth. Competitive exclusion is demonstrated to hold and the optically uncoupled critical depth is linked to the critical light intensity in multi-species competition. Finally, a conservation principle for the critical depth is found.
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Shang, Haixin, Song Xu, Kuandi Zhang, and Luyou Zhao. "Explicit Solution for Critical Depth in Closed Conduits Flowing Partly Full." Water 11, no. 10 (October 13, 2019): 2124. http://dx.doi.org/10.3390/w11102124.
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Critical depth is an essential parameter for the design, operation, and maintenance of conduits. Circular, arched, and egg-shaped sections are often used in non-pressure conduits in hydraulic engineering, irrigation, and sewerage works. However, equations governing the critical depth in various sections are complicated implicit transcendental equations. The function model is established for the geometric features of multiple sections using the mathematical transform method and while considering non-dimensional parameters. Then, revised PSO algorithms are implemented in MATLAB, and the right solution’s formula for the critical depths in various non-pressure conduit sections is established through optimization. The error analysis results show that the established formula has broad applicability. The maximum relative errors of the formula for critical depths are less than 0.182%, 0.0629%, and 0.170% in circular, arched, and egg-shaped sections, respectively, which are more accurate than those of existing formulas; the form of the formula proposed in this work is also more compact than that of the existing formulas. The results of this research may be useful in design, operation, and maintenance in conduit engineering.
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Dey, Subhasish. "CHEBYSHEV SOLUTION FOR CRITICAL DEPTH IN OPEN CHANNELS." ISH Journal of Hydraulic Engineering 6, no. 1 (January 2000): 20–24. http://dx.doi.org/10.1080/09715010.2000.10514661.
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Li, Jiaxing, Yongxin Yang, Bin Jia, Hui Huang, Biao Li, and Tao Wang. "GFRP erosion depth model under alkaline solution erosion." IOP Conference Series: Earth and Environmental Science 783, no. 1 (May 1, 2021): 012031. http://dx.doi.org/10.1088/1755-1315/783/1/012031.
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Schajer, Gary S., and Michael B. Prime. "Residual Stress Solution Extrapolation for the Slitting Method Using Equilibrium Constraints." Journal of Engineering Materials and Technology 129, no. 2 (July 20, 2006): 227–32. http://dx.doi.org/10.1115/1.2400281.
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Established methods for calculating residual stresses from the strains measured when using the slitting method give results for the stresses that exist within the depth range of the slit. Practical considerations typically limit this range to about 90–95% of the specimen thickness. Force and moment equilibrium can provide additional information that may be used to estimate the residual stresses in the “no-data” region within the remaining ligament beyond the maximum slit depth. Three different numerical methods to calculate the residual stress profile over the entire specimen thickness are investigated. They are truncated Legendre series, regularized Legendre series, and regularized unit pulses. In tests with simulated strain data and with strain data measured on a cold compressed 7050-T7452 Aluminum hand forging, the three methods gave generally similar stress results in the central region of the specimen. At small depths, where the strain sensitivity to the residual stresses is low, the two regularized calculation methods tended to give more stable results. In the area of very large depth beyond the maximum depth of the slit, the regularized Legendre series solution generally gave the most realistic stress results.
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Szmidt, Kazimierz, and Benedykt Hedzielski. "Nonlinear Interactions between Gravity Waves in Water of Constant Depth." Archives of Hydro-Engineering and Environmental Mechanics 62, no. 1-2 (June 1, 2015): 3–25. http://dx.doi.org/10.1515/heem-2015-0016.
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AbstractThe paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.
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Lu, Yan, Ryland B. Edwards, Shane Nho, Brian J. Cole, and Mark D. Markel. "Lavage Solution Temperature Influences Depth of Chondrocyte Death and Surface Contouring during Thermal Chondroplasty with Temperature-Controlled Monopolar Radiofrequency Energy." American Journal of Sports Medicine 30, no. 5 (September 2002): 667–73. http://dx.doi.org/10.1177/03635465020300050601.
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Background: Although radiofrequency energy can smooth and contour cartilage surface, it has deleterious effects on chondrocyte viability. Hypothesis: Monopolar thermal chondroplasty in a 37°C lavage solution, as compared with a 22° lavage solution, will reduce chondrocyte death and result in greater smoothing of the articular cartilage surface. Study Design: Controlled laboratory study. Methods: Sixteen chondromalacic samples from patients undergoing total knee arthroplasty were divided into two groups: 22°C and 37°C lavage solution. Each sample was divided into two equal parts and half of each group was treated for 10 seconds and the other half for 15 seconds. Results: Confocal laser microscopy demonstrated that the depth of chondrocyte death in the 37°C lavage solution group was significantly less (range, 200 to 340 μm) than that in the 22°C solution group for both 10- and 15-second treatment times. Scanning electron microscopy demonstrated that the cartilage surface in the 37°C lavage solution group was smoother than that in the 22°C solution group for the 10-second treatment time. Energy delivery power in the 37°C lavage solution group was significantly lower than in the 22°C solution group for both treatment times. Conclusions: Thermal chondroplasty with 37°C lavage solution resulted in less depth of chondrocyte death and produced smoother surfaces than with 22°C solution for 10 seconds of treatment. Clinical Relevance: Less chondrocyte death would permit increased use of thermal chondroplasty.
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Lancioni, G., R. Bernetti, E. Quagliarini, and L. Tonti. "Effects of Underground Cavities on the Frequency Spectrum of Seismic Shear Waves." Advances in Civil Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/934284.
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A numerical method is proposed to study the scattering of seismic shear waves induced by the presence of underground cavities in homogeneous soils. The method is based on the superposition of two solutions: the solution of the free-wave propagation problem in a uniform half-space, easily determined analytically, and the solution of the wave scattering problem due to the cave presence, evaluated numerically by means of an ad hoc code implemented by using the ANSYS Parametric Design Language. In the two-dimensional setting, this technique is applied to the case of a single cave, placed at a certain depth from the ground level. The frequency spectrum of the seismic shear oscillation on the ground surface is determined for different dimensions and depths of the cave and compared with the spectrum registered without caves. The influence of the cave dimensions and depth on the spectrum amplification is analyzed and discussed.
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Hoang Nam, Binh. "An approximate formula to calculate the critical depth in circular culvert." Transport and Communications Science Journal 71, no. 7 (September 30, 2020): 840–52. http://dx.doi.org/10.47869/tcsj.71.7.9.
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Critical depth is a depth of flow where a specific energy section is at a minimum value with a flow rate. Critical depth is an essential parameter in computing gradually varied flow profiles in open channels and in designing culverts. If cross-sections are rectangular or triangular, the critical depth can be computed by the governing equation. However, for other geometries such as trapezoidal, circular, it is totally difficult to find a solution, because the governing equations are implicit. Therefore, the approximate solution could be determined by trial, numerical or graphical methods. These methods tend to take a long time to find an approximate solution, so a simple formula will be more convenient for consultant hydraulic design engineers. The existing formulas are simple, but the relative error between the approximate solutions and true values can reach 9% or greater. This article presents new explicit regression equations for the critical depth in a partially full circular culvert. The proposed formula is quite simple, and the relative maximum error is 3.03%. It would be very useful as a reference for design in conduit engineering
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Hoang Nam, Binh. "An approximate formula to calculate the critical depth in circular culvert." Transport and Communications Science Journal 71, no. 7 (September 30, 2020): 840–52. http://dx.doi.org/10.25073/tcsj.71.7.9.
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Critical depth is a depth of flow where a specific energy section is at a minimum value with a flow rate. Critical depth is an essential parameter in computing gradually varied flow profiles in open channels and in designing culverts. If cross-sections are rectangular or triangular, the critical depth can be computed by the governing equation. However, for other geometries such as trapezoidal, circular, it is totally difficult to find a solution, because the governing equations are implicit. Therefore, the approximate solution could be determined by trial, numerical or graphical methods. These methods tend to take a long time to find an approximate solution, so a simple formula will be more convenient for consultant hydraulic design engineers. The existing formulas are simple, but the relative error between the approximate solutions and true values can reach 9% or greater. This article presents new explicit regression equations for the critical depth in a partially full circular culvert. The proposed formula is quite simple, and the relative maximum error is 3.03%. It would be very useful as a reference for design in conduit engineering
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Jia, Peng. "Research on Critical Cut Depth of Glass BK7 in Diamond Cutting." Materials Science Forum 770 (October 2013): 230–33. http://dx.doi.org/10.4028/www.scientific.net/msf.770.230.
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In diamond cutting of optical glasses, the magnitude of critical depth of cut for brittle-ductile transition is an important factor affecting the machinability of the work material in terms of production rate and surface quality. In this work, scratching tests with increasing depths of cut were conducted on glass BK7 to evaluate the influence of the cutting fluid properties on the critical depth of cut. Boric acid solutions of different concentrations were selected as cutting fluids in the tests. The resulting scratches were examined utilizing a white light interferometer and the values of the critical depth of cut were determined based on the observations of the micro-morphology of the scratch surfaces produced. Experimental results indicated that compared with the process without cutting fluid action, the critical depth of cut in diamond cutting of glass BK7 can be increased by using boric acid solution as the cutting fluid.
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Jia, Peng. "Influence of Cutting Compound on Critical Cut Depth of Glass BK7." Key Engineering Materials 579-580 (September 2013): 97–100. http://dx.doi.org/10.4028/www.scientific.net/kem.579-580.97.
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In diamond cutting of optical glasses, the magnitude of critical depth of cut for brittle-ductile transition is an important factor affecting the machinability of the work material in terms of production rate and surface quality. In this work, scratching tests with increasing depths of cut were conducted on glass BK7 to evaluate the influence of the cutting fluid properties on the critical depth of cut. Boric acid solutions of different concentrations were selected as cutting fluids in the tests. The resulting scratches were examined utilizing a white light interferometer and the values of the critical depth of cut were determined based on the observations of the micro-morphology of the scratch surfaces produced. Experimental results indicated that compared with the process without cutting fluid action, the critical depth of cut in diamond cutting of glass BK7 can be increased by using boric acid solution as the cutting fluid.
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Jia, Peng. "Indentation and Scratching Experimental Research on Brittle-Ductile Transition of Optical Glass SF6." Key Engineering Materials 589-590 (October 2013): 480–84. http://dx.doi.org/10.4028/www.scientific.net/kem.589-590.480.
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In diamond cutting of optical glasses, the magnitude of critical depth of cut for brittle-ductile transition is an important factor affecting the machinability of the work material in terms of production rate and surface quality. In this work, scratching tests with increasing depths of cut were conducted on glass BK7 to evaluate the influence of the cutting fluid properties on the critical depth of cut. Boric acid solutions of different concentrations were selected as cutting fluids in the tests. The resulting scratches were examined utilizing a white light interferometer and the values of the critical depth of cut were determined based on the observations of the micro-morphology of the scratch surfaces produced. Experimental results indicated that compared with the process without cutting fluid action, the critical depth of cut in diamond cutting of glass BK7 can be increased by using boric acid solution as the cutting fluid.
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Zhou, Ming, Peng Jia, and Min Li. "Research on the Influence of Cutting Fluids on the Critical Depth of Cut in Diamond Cutting of Optical Glass BK7." Key Engineering Materials 431-432 (March 2010): 126–29. http://dx.doi.org/10.4028/www.scientific.net/kem.431-432.126.
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In diamond cutting of optical glasses, the magnitude of critical depth of cut for brittle-ductile transition is an important factor affecting the machinability of the work material in terms of production rate and surface quality. In this work, scratching tests with increasing depths of cut were conducted on glass BK7 to evaluate the influence of the cutting fluid properties on the critical depth of cut. Boric acid solutions of different concentrations were selected as cutting fluids in the tests. The resulting scratches were examined utilizing a white light interferometer and the values of the critical depth of cut were determined based on the observations of the micro-morphology of the scratch surfaces produced. Experimental results indicated that compared with the process without cutting fluid action, the critical depth of cut in diamond cutting of glass BK7 can be increased by using boric acid solution as the cutting fluid.
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Abdelrahman, El‐Sayed M., and Hamdy I. Hassanein. "Shape and depth solutions from magnetic data using a parametric relationship." GEOPHYSICS 65, no. 1 (January 2000): 126–31. http://dx.doi.org/10.1190/1.1444703.
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We have developed a simple method to simultaneously determine the shape (shape factor) and the depth of a buried structure from magnetic data. The method is similar to Euler deconvolution, but it solves for shape and depth independently. The method involves using a relationship between the shape factor, the depth to the source, and a combination of observations at symmetric points with respect to the coordinate of the source center with a free parameter (graticule spacing). The relationship represents a parametric family of curves. For a fixed free parameter, the depth is determined for each shape factor. The computed depths are plotted against the shape factors representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the parametric curves. The parametric curves method is applied to two theoretical magnetic anomaly profiles due to a thin dike and a horizontal cylinder. The method is also tested on a field example from Brazil. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones.
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Tissot, Héloise, Giorgia Olivieri, Jean-Jacques Gallet, Fabrice Bournel, Mathieu G. Silly, Fausto Sirotti, and François Rochet. "Cation Depth-Distribution at Alkali Halide Aqueous Solution Surfaces." Journal of Physical Chemistry C 119, no. 17 (April 17, 2015): 9253–59. http://dx.doi.org/10.1021/jp512695c.
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Vatankhah, Ali R. "General Solution of Conjugate Depth Ratio (Power-Law Channels)." Journal of Irrigation and Drainage Engineering 143, no. 9 (September 2017): 06017009. http://dx.doi.org/10.1061/(asce)ir.1943-4774.0001224.
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Kontsevich, Leonid L. "Pairwise comparison technique: a simple solution for depth reconstruction." Journal of the Optical Society of America A 10, no. 6 (June 1, 1993): 1129. http://dx.doi.org/10.1364/josaa.10.001129.
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Wheeler, DM, and DC Edmeades. "Effect of depth and lime or phosphorus-fertilizer applications on the soil solution chemistry of some New Zealand pastoral soils." Soil Research 33, no. 3 (1995): 461. http://dx.doi.org/10.1071/sr9950461.
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Thirteen trails were sampled to investigate the effects of depth, or the surface application of lime and phosphorus (P) fertilizer, on solution composition. Soil solutions were extracted by centrifuge from field moist soils within 24 h of sampling. Solution Ca, Mg, Na and K, Al, Mn and Fe concentrations generally decreased and Al, Mn and Fe concentrations generally increased with depth; although exceptions occurred. The largest decrease occurred in the first 25-50 mm of soil. Higher solution Al concentrations occurred in a band at a depth of between 50 and 100 mm in some soils. Lime generally increased solution pH and solution Ca, Mg and HCO3 concentrations, and reduced solution Al, Fe and Mn concentrations in the topsoils. In one soil (Matapiro silt loam) 2 years after lime was applied, lime increased solution pH down to a depth of 100 mm, Ca and HCO3 down to 75 mm and Mg down to 50 mm. Lime also decreased solution Al and Mn down to 75 mm and Fe down to 50 mm. In one series of trials, lime increased solution Ca concentrations at a depth of 50-100 mm 4 years after application in six out of the eight sites. In the same trial series, the application of P fertilizer increased solution P concentrations at 0-50 mm from a mean of 5 �M in the no-added P plots up to a mean of 56 �M at the highest P rate. The highest solution P concentration recorded was 194 �M. The increase in solution P concentrations for a given application of fertilizer P varied from 0.05 to 1.03 �M P per kg P ha-1 applied. Maximum pasture yield and 90% maximum yield occurred when solution P concentrations were about 28 and 14 �M respectively. Solution P concentrations determined from P adsorption isotherms were not a good indicator of solution P concentrations measured in soil. Solution pH was higher than soil pH (1:2.5 soil:water ratio, 2 h equilibration) with a solution pH of 6.0 corresponding to a soil pH in water of about 5.2.
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Rajab, M. D., and Akram Zahoor. "Tearing Modulus Analysis for Pipes Containing Constant Depth Internal Flaw." Journal of Engineering Materials and Technology 113, no. 1 (January 1, 1991): 156–61. http://dx.doi.org/10.1115/1.2903372.
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The pipe displacement and tearing modulus solutions are derived for pipes containing a uniform depth internal flaw under bending moment or axial loading. The tearing modulus solution is derived for both load control and displacement control conditions. These solutions are then used to construct critical stress curves for various flaw sizes for a carbon steel pipe. These curves are useful in predicting the onset of flaw growth instability. Critical stress curves can be similarly constructed for other materials and pipe geometries.
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Jensen, Elin A., Will Hansen, and Rune Brincker. "Engineering Solution for the Uniform Strength of Partially Cracked Concrete." Transportation Research Record: Journal of the Transportation Research Board 1919, no. 1 (January 2005): 16–22. http://dx.doi.org/10.1177/0361198105191900102.
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Significant computational resources are required to predict the remaining strength from numerical fracture analysis of a jointed plain concrete pavement that contains a partial depth crack. It is, therefore, advantageous when the failure strength can be adequately predicted with an engineering solution. Current engineering or closed-form solutions are based on the elastic effective crack approach with the fracture parameters toughness and critical crack tip opening of concrete. The solutions do not directly consider the effect of the distance to the boundary conditions (restrained slab length) and the cracking process caused by stress softening across the crack. A proposed engineering solution methodology includes these latter variables. The application of the solution is demonstrated on a slab containing a partial depth midslab crack and subjected to in-plane tension. The solution captures the effects of material fracture properties and structural size in terms of crack length and distance from boundary to the crack. The model assumes a bilinear stress–crack width relationship for the fracture process zone. The concrete characteristic length, determined from the fracture energy represented by the first part of the stress–crack width relationship, controls the failure load of a partially cracked concrete slab. A unique master curve between slab strength and crack depth was developed using the results from the numerical analysis. The master curve was verified with results from laboratory testing of large-scale slabs subjected to in-plane tension. The solution methodology can readily be extended to other loading cases.
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Ghanimati, G. R., and P. M. Naghdi. "Oscillations over basins of variable depth." Journal of Fluid Mechanics 164 (March 1986): 359–81. http://dx.doi.org/10.1017/s0022112086002598.
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This paper is concerned with oscillations of a body of water in basins of variable depth, employing a system of linearized equations which can be obtained from the theory of a directed fluid sheet for an incompressible, homogeneous, inviscid fluid (Green & Naghdi 1976a, 1977). For free oscillations over a level bottom, an assessment of the range of validity of the linearized theory is made by an appropriate comparison with a corresponding well-known exact solution (Lamb 1932). This assessment indicates an ‘intermediate’ range of validity for the linearized theory not covered by usual classical approximations for long waves. Encouraged by this assessment, we apply the linear theory of a directed fluid sheet to basins of variable depth; and, in particular, consider a class of basin profiles whose equilibrium depth (along its width) varies in one direction only. By a method of asymptotic integration, a general solution is obtained which is relatively simple and accounts for the effect of vertical inertia. The solution is sinusoidal in time, periodic along the breadth direction and involves Bessel functions of the first order in the width direction. For two special basin profiles, detailed comparisons are made between the predictions of the asymptotic solution (i.e. the frequencies in the lowest modes of oscillations) with corresponding results obtained by other procedures.
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Bhupinderpal-Singh, M. J. Hedley, and S. Saggar. "In situ dynamics of recently allocated 14C in pasture soil and soil solution collected with Rhizon Soil Moisture Samplers." Soil Research 43, no. 5 (2005): 659. http://dx.doi.org/10.1071/sr04107.
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Information on the dynamics of recently photo-assimilated carbon (C) allocated to roots and root-derived exudates in soils is scarce and experimentally difficult to obtain. We used Rhizon Soil Moisture SamplersTM (RSMS) placed at different depths in soil (20, 40, 80, 120 mm) to monitor short-term dynamics of root and root-derived C at the root–soil interface after 14CO2 pulse-labelling of pasture cores. At the 20 mm depth, 14C activity in soil solution peaked within 2 h of 14CO2 application. The peak of 14C activity took longer to appear and slower to disappear with increased depth. Negligible amounts of 14C as soluble exudates were found in the soil solution. The pattern of initial 14C activity in soil solution, allocation of recently assimilated 14C in roots, and root mass distribution with depth were closely related to each other. This suggested that the rapid appearance of 14CO2 in soil solution is more closely linked to root respiration of recent 14C-assimilates (transferred via shoots to roots) and/or to microbial decomposition of root-released 14C-assimilates than to transfer by diffusion of atmospheric 14CO2 through open soil surface to different depths in soil. The use of RSMS was an effective, simple, and non-destructive method to monitor the dynamics of root-derived 14C by in situ sampling of soil solution.
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Jiang, Li, Jianzhong Zhang, and Zhibing Feng. "A versatile solution for the gravity anomaly of 3D prism-meshed bodies with depth-dependent density contrast." GEOPHYSICS 82, no. 4 (July 1, 2017): G77—G86. http://dx.doi.org/10.1190/geo2016-0394.1.
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We have developed a generalized solution for computing the gravity anomalies of 3D irregular-mass bodies with complicated density-contrast variation. The 3D irregular-shaped bodies can be approximated flexibly by a collection of finite-juxtaposed right-rectangular prisms. The complicated density-contrast variation of each prism can be well-represented by a depth-dependent polynomial function. A novel analytic solution of gravity anomalies due to a right-rectangular prism with an arbitrary order of polynomial density-contrast function of depth is then derived. The solution is singularity free in the upper half-space over the prism, and its singularity in the lower half-space containing the prism is resolved by assigning their limit values to the singular terms. The numerical stability of the solution is also evaluated through numerical tests. Hence, the solution can be used to compute the gravity anomalies of 3D irregular bodies with variable density contrasts without singularities when computation points are within the numerical stability range. Based on synthetic models with variable density contrast, our solution is validated by using other solutions in the literature. We also simulated the gravity anomalies of the Los Angeles basin and compared them with the observed anomalies and with those computed using the analytic solutions of other workers. These tests confirm the accuracy and efficiency of our analytic solution.
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Abdelrahman, El-Sayed M., and Khalid S. Essa. "Magnetic interpretation using a least-squares, depth-shape curves method." GEOPHYSICS 70, no. 3 (May 2005): L23—L30. http://dx.doi.org/10.1190/1.1926575.
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We have developed a least-squares approach to depth determination from residual magnetic anomalies caused by simple geologic structures. By normalizing the residual magnetic anomaly using three characteristic points and their corresponding distances on the anomaly profile, the problem of determining depth from residual magnetic anomalies has been transformed into finding a solution to a nonlinear equation of the form z = f(z). Formulas have been derived for spheres, horizontal cylinders, thin dikes, and contacts. The method is applied to synthetic data with and without random noise. We have also developed a method using depth-shape curves to simultaneously define the shape and depth of a buried structure from a residual magnetic anomaly profile. The method is based on determining the depth from the normalized residual anomaly for each shape factor using the least-squares method mentioned above. The computed depths are plotted against the shape factors on a graph. The solution for the shape and depth of the buried structure is read at the common intersection of the depth-shape curves. The depth-shape curves method was successfully tested on theoretical data with and without random noise and applied to a known field example from Ontario.
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Samelson, R. M. "Time-Dependent Adjustment in a Simple Model of the Mid-Depth Meridional Overturning Cell." Journal of Physical Oceanography 41, no. 5 (May 1, 2011): 1009–25. http://dx.doi.org/10.1175/2010jpo4562.1.
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Abstract A recently proposed reduced-gravity model of the warm-water branch of the middepth meridional overturning circulation in a rectangular basin with a circumpolar connection is extended to include time dependence. The model describes the balance between gain of warm water through northward Ekman advection across the circumpolar current, loss of warm water through eddy fluxes southward across the current, net gain or loss of warm water through diabatic processes north of the current, and changes in the thickness of the warm-water layer. The steady solutions are the same as those found previously, when the previous parameterization of diabatic fluxes is used. Time-dependent solutions are considered for the approach of the solution to a new equilibrium when the forcing or parameters are abruptly changed and then held fixed. An initial adjustment occurs through a combination of boundary and equatorial adjustment, followed by planetary wave propagation. The longer-term adjustment to equilibrium consists primarily of the slow change in eastern boundary thickness of the warm layer, which controls the mean depth of the entire layer. An approximate analytical solution of the time-dependent equations yields an explicit expression for the intrinsic time scale of the long-term adjustment, which depends on the eddy and diabatic flux parameters and on the equilibrium solution toward which the time-dependent solution adjusts. Numerical solutions are also considered with a second, advective–diffusive diabatic flux parameterization. These solutions differ quantitatively but not qualitatively from those with the original parameterization. For the range of parameter values considered, the adjustment time scale has dimensional values of several decades to more than a century, but the meridional flux of warm water may respond to changes in external parameters or forcing much more rapidly than this time scale for equilibration of the eastern boundary thickness and thermocline structure.
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Dinvay, E., and N. Kuznetsov. "Modified Babenko’s Equation For Periodic Gravity Waves On Water Of Finite Depth." Quarterly Journal of Mechanics and Applied Mathematics 72, no. 4 (July 13, 2019): 415–28. http://dx.doi.org/10.1093/qjmam/hbz011.
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Summary A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko’s equation considered in Kuznetsov and Dinvay (Water Waves, 1, 2019). Both operators in the proposed equation are nonlinear and depend on the parameter equal to the mean depth of water, whereas each solution defines a parametric representation for a symmetric free surface profile. The latter is a component of a solution of the two-dimensional, nonlinear problem describing steady waves propagating in the absence of surface tension. Bifurcation curves (including a branching one) are obtained numerically for solutions of the new equation; they are compared with known results.
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Abdelrahman, El‐Sayed M., Tarek M. El‐Araby, Hesham M. El‐Araby, and Eid R. Abo‐Ezz. "A new method for shape and depth determinations from gravity data." GEOPHYSICS 66, no. 6 (November 2001): 1774–80. http://dx.doi.org/10.1190/1.1487119.
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We have developed a simple method to determine simultaneously the shape and depth of a buried structure from residualized gravity data using filters of successive window lengths. The method is similar to Euler deconvolution, but it solves for shape and depth independently. The method involves using a relationship between the shape factor and the depth to the source and a combination of windowed observations. The relationship represents a parametric family of curves (window curves). For a fixed window length, the depth is determined for each shape factor. The computed depths are plotted against the shape factors, representing a continuous, monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. This method can be applied to residuals as well as to the Bouguer gravity data of a short or long profile length. The method is applied to theoretical data with and without random errors and is tested on a known field example from the United States. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones.
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Mittet, Rune. "Perturbation approach to depth extrapolation." GEOPHYSICS 70, no. 1 (January 2005): S18—S29. http://dx.doi.org/10.1190/1.1852786.
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The Born-series solution of the Lippmann-Schwinger equation does not necessarily converge properly for depth-extrapolation problems. Even more seriously, the Lippmann-Schwinger equation is not necessarily self-consistent for depth extrapolation, unless it is interpreted correctly. A solution is proposed by using the generalized Lippmann-Schwinger equation that includes boundary value contributions that normally are ignored. A modified version of the Lippmann-Schwinger equation for depth extrapolation is obtained. The corrections to the Born-series expansion for depth extrapolation are demonstrated. The new system has the desired convergence and self-consistency properties. Explicit depth extrapolation is discussed in the context of the Lippmann-Schwinger equation. A partial explanation for why explicit depth extrapolation works reasonably well in laterally inhomogeneous media may be that the contribution from the perturbation term in the Lippmann-Schwinger equation for that problem is small for a wide variety of velocity models.
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Liu, Yang, Wen Jing Shang, Hong Fang Liu, and Zhi Gang Huang. "Effect of Annealing Temperature on Corrosion Resistance of Cold-Rolled Strip of Complex Brass." Applied Mechanics and Materials 184-185 (June 2012): 959–62. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.959.
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Using weight-loss method combined with metallographic to analysis the effect of annealing temperature (600°C, 640°C, 680°C) on the corrosion resistance of cold rolled strip of complex brass HAl72-2.5Al-1.0Ni alloy. Corrosive solutions for testing the corrosion velocity were 3.5% of the neutral sodium chloride solution, artificial acid rain (3.5% NaCl+H2SO4 solution) and artificial sweat solution. The research results show that the corrosion of cold rolled strip occurs easily because grains stretched along the direction of deformation and the existence of residual stress. The maximum corrosion depth of cold-rolled strip is 94.8μm. Annealing treatment can effectively reduce the corrosion depth of alloy. Corrosion resistance of alloy rises with the increase of annealing temperature, because the recrystallization degree of alloy goes on more sufficient. The corrosion depth of samples annealed at 600°C and 680°C drops from 64.45μm to 56.32μm respectively. Aluminum content in the alloy also affects the corrosion resistance of the alloy, because oxygen oxidizes aluminum to density Al2O3 film which prevents the further corrosion of the alloy. The corrosion velocity of samples in the solution of artificial acid rain is fastest and lowest in artificial perspiration solution.
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Осадчук, С. А., Л. И. Ныркова, and Ю. Ф. Фатеев. "ОСОБЕННОСТИ КАТОДНЫХ И АНОДНЫХ РЕАКЦИЙ НА УГЛЕРОДИСТОЙ СТАЛИ В ЗАВИСИМОСТИ ОТ ГЛУБИНЫ ПОГРУЖЕНИЯ В НЕЙТРАЛЬНЫЙ РАСТВОР." Bulletin of the Kyiv National University of Technologies and Design. Technical Science Series 138, no. 5 (February 3, 2020): 87–96. http://dx.doi.org/10.30857/1813-6796.2019.5.10.
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The investigation of the depth immersion of the specimens on corrosion rate of steel St3 in 3 % NaCl solution. Simulation of atmospheric corrosion (humid and wet) was performed by immersing of a steel sample by the size of (50×10×2) mm in a neutral solution of 3% NaCl at different depths. By leading the lower boundary of the working surface of the sample to the level of the solution (about 0 mm), humid corrosion was simulated, submerged to a depth of 2 mm (up to the upper boundary), wet corrosion, and 10 mm from the upper boundary - the electrolyte volume. The developed method allowed to carry out electrochemical researches by the method of polarization curves. The polarization curves were measured in the potentiodynamic mode with the potential scanning rate of 5∙10-4 V/s .The working electrode was a sample of steel St3 by the size (10×50×2) mm. A work surface (10×2) mm was separated on the sample, the rest of the surface was isolated with a non-conductive varnish. The results of the investigation of the effect of depth immersion of samples into electrolyte solution on corrosion rate of St3 steel are presented. The conditions of “humid” and “wet” atmospheric corrosion of the metal were simulated by the immersion of samples on a depth from 0 to 10 mm into 3% sodium chloride solution. It was found, that on the base on determination of the rate of particular electrode reactions occurring on the electrode at various depths of its immersion into the solution, the corrosion rate of steel St3 was determined by the value of the limiting diffusion current.It was shown that the value of limiting current increases from 0.51 to 2 A/m2 with decreasing of the film thickness. It has been established that the cathodic process rate depends both on the concentration of oxygen in the layers of the solution, which are at different distances from the solution/air boundary, and on the speed of its diffusion to the metal surface. Because the method of polarization resistance allows to measure the currents smaller than the currents of oxygen reduction in thin films of the solution, it can be used to estimate the rate of atmospheric corrosion of steel. Based on simulation of humid and wet atmospheric corrosion the effect of immersion depth of the specimens on the cathodic reaction rate of steel St3 in 3 % NaCl solution was established. The cathodic current density (limit diffusion current) is raised from 0,51 to 2 A/m2 under decreasing of immersion depth. The suggested method of simulation of atmospheric corrosion may be used for electrochemical investigations in thin films of moisture of different thickness which are form on the metals and sensors surfaces. The possibility of application of polarization resistance method for atmospheric conditions was presented.
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CLAMOND, DIDIER. "Steady finite-amplitude waves on a horizontal seabed of arbitrary depth." Journal of Fluid Mechanics 398 (November 10, 1999): 45–60. http://dx.doi.org/10.1017/s0022112099006151.
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From shallow-water gravity wave theories it is shown that the velocity field in the whole fluid domain can be reconstructed using an analytic transformation (a renormalization). The resulting velocity field satisfies the Laplace equation exactly, which is not the case for shallow-water approximations. Applying the renormalization to the first-order shallow-water solution of limited accuracy, gives accurate simple solutions for both long and short waves, even for large amplitudes. The KdV and Airy solutions are special limiting cases.
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Kim, J. W., K. J. Bai, R. C. Ertekin, and W. C. Webster. "A Strongly-Nonlinear Model for Water Waves in Water of Variable Depth—The Irrotational Green-Naghdi Model." Journal of Offshore Mechanics and Arctic Engineering 125, no. 1 (February 1, 2003): 25–32. http://dx.doi.org/10.1115/1.1537722.
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Recently, the authors have derived a new approximate model for the nonlinear water waves, the Irrotational Green-Naghdi (IGN) model. In this paper, we first derive the IGN equations applicable to variable water depth, and then perform numerical tests to show whether and how fast the solution of the IGN model converges to the true solution as its level increases. The first example given is the steady solution of progressive waves of permanent form, which includes the small-amplitude sinusoidal wave, the solitary wave and the nonlinear Stokes wave. The second example is the run-up of a solitary wave on a vertical wall. The last example is the shoaling of a wave train over a sloping beach. In each numerical test, the self-convergence of the IGN model is shown first. Then the converged solution is compared to the known analytic solutions and/or solutions of other approximate models such as the KdV and the Boussinesq equations.
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An, Sangkyum, Keunhwa Lee, and Woojae Seong. "Optimal Operating Depth Search for Active Towed Array Sonar using Simulated Annealing." Defence Science Journal 69, no. 4 (July 15, 2019): 415–19. http://dx.doi.org/10.14429/dsj.69.13693.
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In an active towed array sonar, it is important to find the optimal operation depth. Generally, the optimal depth can be chosen via numerical simulations for all sonar depths and this imposes great burdens of time and cost.In this paper, an efficient approach is proposed to find the optimal depth using the optimisation technique. First, the sonar performance function is newly defined as a measure of how well the active sonar might perform. This function depends on the properties of the ocean environment and the positions of sonar and underwater target. Then, the simulated annealing to find an optimal solution for maximising sonar performance is used. The optimised depth agrees well with the depth obtained from direct searching for all depths of source and receiver combinations, but its computational time is largely reduced.
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Bulatov, Vitaly, and Yury Vladimirov. "Generation of Internal Gravity Waves Far from Moving Non-Local Source." Symmetry 12, no. 11 (November 19, 2020): 1899. http://dx.doi.org/10.3390/sym12111899.
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We consider analytical solutions describing the generation of internal gravity waves far from a non-local source of disturbances. We suppose that the source moves on the surface of stratified medium of a finite depth. A model distribution of the non-local source shape with radial symmetry is used. This approximation correctly describes (qualitatively) the main spatiotemporal characteristics of natural sources of generation of internal gravity waves in the ocean. The resulting solution is the sum of wave modes. The solution is presented as a series of eigenfunctions of the spectral problem of internal gravity waves. The results of numerical calculations of internal gravity waves components at different depths are presented and discussed.
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Shakhvorostov, D., W. N. Lennard, and P. R. Norton. "Analytical solution for depth scale calculations in Rutherford backscattering spectrometry." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 272 (February 2012): 18–22. http://dx.doi.org/10.1016/j.nimb.2011.01.024.
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Guo, Junke. "Exact Solution for Depth of Impact Crater into Granular Bed." Journal of Engineering Mechanics 144, no. 1 (January 2018): 06017018. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001393.
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Jagielska-Wiaderek, Karina, Henryk Bala, and Tadeusz Wierzchon. "Corrosion depth profiles of nitrided titanium alloy in acidified sulphate solution." Open Chemistry 11, no. 12 (December 1, 2013): 2005–11. http://dx.doi.org/10.2478/s11532-013-0342-0.
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AbstractThick (400 µm) glow-discharge nitrided layers, TiN+Ti2N + αTi(N) type, have been produced on the Ti-1Al-1Mn titanium alloy. Using a progressive thinning method, the polarization characteristics at different depths of nitrided layers have been measured. From the plots of obtained potentiodynamic polarization curves the depth profiles of characteristic anodic and cathodic currents (at potentials corresponding to (a) hydride formation, (b) hydrogen evolution, (c) primary passivation, (d) oxygen evolution and (e) secondary passivation) as well as polarization resistance have been determined in 0.5 M Na2SO4 solution acidified to pH = 2. The anomalously high slope of the polarization curves in the cathodic region has been ascribed to the formation of titanium hydride. It has been shown that outer nitrided layers (up to 25 µm) exhibit excellent acid corrosion resistance owing to strong inhibition of the anodic process by TiN phase. Corrosion resistance of deeper situated layers gradually decreases and at depths of 250–370 µm the corrosion process is accelerated by presence of TiO2 precipitations. Nitrided layers, unlike the alloy core, allow oxygen evolution on the oxy-nitrided surface at potential of +1.6 V and at more positive potentials gradual transformation of the surfacial film into TiO2 takes place. Secondary passivation on nitrided titanium is less efficient than that in the absence of Ti-N species.
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Sun, J. G. "Analysis of Pulsed Thermography Methods for Defect Depth Prediction." Journal of Heat Transfer 128, no. 4 (October 24, 2005): 329–38. http://dx.doi.org/10.1115/1.2165211.
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Pulsed thermography is an effective technique for quantitative prediction of defect depth within a specimen. Several methods have been reported in the literature. In this paper, using an analysis based on a theoretical one-dimensional solution of pulsed thermography, we analyzed four representative methods. We show that all of the methods are accurate and converge to the theoretical solution under ideal conditions. Three methods can be directly used to predict defect depth. However, because defect features that appear on the surface during a pulsed thermography test are always affected by three-dimensional heat conduction within the test specimen, the performance and accuracy of these methods differs for defects of various sizes and depths. This difference is demonstrated and evaluated from a set of pulsed thermography data obtained from a specimen with several flat-bottom holes as simulated defects.
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Li, Dao Xi. "The Role of Dissolved CH4 in Soil Solution in the CH4 Emission from Water-Saving Irrigated Rice Fields." Applied Mechanics and Materials 148-149 (December 2011): 977–82. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.977.
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To examine how the dissolved CH4 in soil solution would affect the CH4 emission from rice field, fluxes of CH4 emission were measured by using a manually closed static chamber-gas chromatography method, and the dissolved CH4 in soil solution was obtained through shaking soil solutions, which were extracted from different paddy soil layers by a soil solution sampler with suction and pressure. The results show that the CH4 fluxes from rice fields and the concentration of dissolved CH4 in soil solution are both reduced significantly under the water-saving irrigation as compared to the traditional flooded irrigation. Under the water-saving irrigation, naturally receding water-layer during the early stage leads to an earlier peak of CH4 flux, but dramatically reduces the concentration of dissolved CH4 in soil solution. The maximum concentration is shifted to about 20-cm depth soil layers, and the relationship between CH4 emissions and dissolved CH4 in soil solution can be estimated using an exponential function of dissolved CH4 in soil solution at the depth of about 20 cm (R2＝0.89, p4 in soil solution plays a more dominant role in CH4 emission under the water-saving irrigation than that under continuously flooded irrigation.
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Soudki, Khaled A., Md Safiuddin, Paul Jeffs, Gary Macdonald, and Marcos Kroker. "CHLORIDE PENETRATION RESISTANCE OF CONCRETE SEALER AND COATING SYSTEMS." Journal of Civil Engineering and Management 21, no. 4 (March 30, 2015): 492–502. http://dx.doi.org/10.3846/13923730.2014.890659.
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This study investigated the chloride penetration resistance of a silane-based sealer (SS1), an acrylic-based coating (AC1), and two cementitious coatings (CC1 and CC2) when applied on concrete surface. Concrete powder samples were collected from 15, 30 and 45 mm depths of sealer and coating treated concrete prism specimens, which were exposed to H2O and de-icing solutions of NaCl, Geomelt S30, MgCl2 and CaCl2 for 100 freeze-thaw cycles followed by 25 wet-dry cycles. Chloride analysis was carried out to determine the total water-soluble chlorides of concrete. Test results revealed that the chloride penetration for exposure to the de-icing chemicals occurred at a depth of 15 mm from the concrete surface. The highest chloride penetration occurred for the non-treated concrete. The sealer ‘SS1’ exhibited good performance except with exposure to NaCl solution. Among the three different coating products, the acrylic-based coating ‘AC1’ was the best-performing coating, whereas the cementitious coating ‘CC1’ had the worst performance. The amount of penetrated water-soluble chlorides was greater than the maximum recommended value of 0.025% (by concrete weight) at 15 mm depth for the sealer ‘SS1’ when exposed to NaCl de-icing solution, and for the coating ‘CC1’ when exposed to NaCl, CaCl2 and MgCl2 solutions.
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Jin, Jian Ming. "Solutions for Axisymmetric Problems of Layered Generalized Gibson Subgrade." Applied Mechanics and Materials 574 (July 2014): 53–57. http://dx.doi.org/10.4028/www.scientific.net/amm.574.53.
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This article presents the solutions for displacements and stress of layered generalized Gibson subgrade subjected to an axisymmetric surface load. We assume that the material has constant Poisson’s ratios (μ=0.5), and its shear moduli varies linearly with depth. During the solutions, the Hankel transform in a cylindrical co-ordinate system is employed. The relationship between the solution and half-space solution is also examined and discussed. At last, the analysis flow is presented .
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Zhu, Guofu, and Jian-Hua Yin. "Consolidation of soil under depth-dependent ramp load." Canadian Geotechnical Journal 35, no. 2 (April 1, 1998): 344–50. http://dx.doi.org/10.1139/t97-092.
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This technical note presents a mathematical solution for the consolidation analysis of a soil layer with a change in vertical total stress that varies linearly with depth and time and then remains unchanged after a certain period of time. The solution is described in detail. Results are presented as figures and tables for practical applications.Key words: consolidation, pore-water pressure, average degree of consolidation, total stress, clay, soil.
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Dorodnitsyn, A. V. "Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem." Highlights of Astronomy 11, no. 1 (1998): 381. http://dx.doi.org/10.1017/s1539299600021316.
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We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.