Quasi-analytical Approach Research Articles

Satellite-derived bathymetry based on machine learning models and an updated quasi-analytical algorithm approach.

Retrieving the water depth by satellite is a rapid and effective method for obtaining underwater terrain. In the optical shallow waters, the bottom signal has a great impact on the radiation from the water which related to water depth. In the optical shallow waters, the spatial distribution characteristic of water quality parameters derived by the updated quasi analysis algorithm (UQAA) is highly correlated with the bottom brightness. Because the bottom reflection signal is strongly correlated with the spatial distribution of water depth, the derived water quality parameters may helpful and applicable for optical remote sensing based satellite derived bathymetry. Therefore, the influence on bathymetry retrieval of the UQAA IOPs is worth discussing. In this article, different machine learning algorithms using a UQAA were tested and remote sensing reflectance at water depth in situ points and their detection accuracy were evaluated by using Worldwiew-2 multispectral remote sensing images and laser measurement data. A backpropagation (BP) neural network, extreme value learning machine (ELM), random forest (RF), Adaboost, and support vector regression (SVR) machine models were utilized to compute the water depth retrieval of Ganquan Island in the South China Sea. According to the obtained results, bathymetry using the UQAA and remote sensing reflectance is better than that computed using only remote sensing reflectance, in which the overall improvements in the root mean square error (RMSE) were 1 cm to 5 cm and the overall improvement in the mean relative error (MRE) was 1% to 5%. The results showed that the results of the UQAA could be used as a main water depth estimation eigenvalue to increase water depth estimation accuracy.

Investment Decisions with Two-Factor Uncertainty

This paper considers investment problems in real options with non-homogeneous two-factor uncertainty. We derive some analytical properties of the resulting optimal stopping problem and present a finite difference algorithm to approximate the firm’s value function and optimal exercise boundary. An important message in our paper is that the frequently applied quasi-analytical approach underestimates the impact of uncertainty. This is caused by the fact that the quasi-analytical solution does not satisfy the partial differential equation that governs the value function. As a result, the quasi-analytical approach may wrongly advise to invest in a substantial part of the state space.

Patterns, Trends and Drivers of Water Transparency in Sri Lanka Using Landsat 8 Observations and Google Earth Engine

Addressing inland water transparency and driver effects to ensure the sustainability and provision of good quality water in Sri Lanka has been a timely prerequisite, especially under the Sustainable Development Goals 2030 agenda. Natural and anthropogenic changes lead to significant variations in water quality in the country. Therefore, an urgent need has emerged to understand the variability, spatiotemporal patterns, changing trends and impact of drivers on transparency, which are unclear to date. This study used all available Landsat 8 images from 2013 to 2020 and a quasi-analytical approach to assess the spatiotemporal Secchi disk depth (ZSD) variability of 550 reservoirs and its relationship with natural (precipitation, wind and temperature) and anthropogenic (human activity and population density) drivers. ZSD varied from 9.68 cm to 199.47 with an average of 64.71 cm and 93% of reservoirs had transparency below 100 cm. Overall, slightly increasing trends were shown in the annual mean ZSD. Notable intra-annual variations were also indicating the highest and lowest ZSD during the north-east monsoon and south-west monsoon, respectively. The highest ZSD was found in wet zone reservoirs, while dry zone showed the least. All of the drivers were significantly affecting the water transparency in the entire island. The combined impact of natural factors on ZSD changes was more significant (77.70%) than anthropogenic variables, whereas, specifically, human activity accounted for the highest variability across all climatic zones. The findings of this study provide the first comprehensive estimation of the ZSD of entire reservoirs and driver contribution and also provides essential information for future sustainable water management and conservation strategies.

Optimizing Emitters’ Density and Water Supplies in Trickle Irrigation Systems

The usual approaches for designing trickle irrigation systems are based upon empirical estimation of the emitters’ density and the moistened soil volume. The objective of this paper is to implement a quasi-analytical approach that allows the inference of these two parameters. The emitters’ density is determined so that the rooted soil volume would be moistened even at the peak period. The proposed approach enables to adjust the irrigation time in order to replenish the rooted soil volume up to a threshold for an optimal plant growth. The required inputs are: the water retention curve, the hydraulic conductivity at the wetting front, the radius of the moistened spot at the soil surface, and the rooted soil depth. The method is assessed with respect to study cases for sandy and silty soils. The used emitters’ discharge were 2 l/h and 4 l/h. The present approach has the advantage of preserving the mass conservation as well as the dynamic aspect of irrigation management. For design purpose, the irrigation time is set equal to the time required to attain a quasi-state flow conditions within the rooted zone. Nevertheless, irrigation time should vary so that design errors are adjusted for irrigation scheduling needs.

Quasi-analytical homogenization approach for the non-linear analysis of in-plane loaded masonry panels

A simple holonomic compatible homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented.The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar joints. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how the homogenized stress-strain behaviour can be evaluated semi-analytically. At a structural level, it is therefore not necessary to solve a FE homogenization problem at each load step in each Gauss point.Non-linear structural analyses are carried out on a windowed shear wall, for which experimental and numerical data are available in the literature, with the aim of showing how quite reliable results may be obtained with a limited computational effort.

Quasi-analytical solution of two-dimensional Helmholtz equation

• Formulation of transformed Helmholtz equation. • Illustration of conformal mapping to solve the Helmholtz equation. • Illustration of quasi-analytical solution of Helmholtz equation for non-trivial shapes. The two-dimensional Helmholtz differential equation governs vibrational problems for a thin membrane and is therefore well studied. Analytical solutions are limited to particular domain shapes, so that in general numerical methods are used when an arbitrary domain is considered. In this paper, a quasi-analytical solution is proposed, suitable to be applied to an arbitrary domain shape. Concretely, the Helmholtz equation is transformed to account for a conformal map between the shape of the physical domain and the unit disk as canonical domain. This way, the transformed Helmholtz equation is solved exploiting well known analytical solutions for a circular domain and the solution in the physical domain is obtained by applying the conformal map. The quasi-analytical approach is compared to analytical solutions for the case of a circular, elliptic and squared domain.

Nuclear-relaxed elastic and piezoelectric constants of materials: Computational aspects of two quantum-mechanical approaches.

Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi-analytical approach based on the evaluation of the force- and displacement-response internal-strain tensors as combined with the interatomic force-constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi-Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc.

Transformation Optics Approach to Plasmon-Exciton Strong Coupling in Nanocavities.

We investigate the conditions yielding plasmon-exciton strong coupling at the single emitter level in the gap between two metal nanoparticles. Inspired by transformation optics ideas, a quasianalytical approach is developed that makes possible a thorough exploration of this hybrid system incorporating the full richness of its plasmonic spectrum. This allows us to reveal that by placing the emitter away from the cavity center, its coupling to multipolar dark modes of both even and odd parity increases remarkably. This way, reversible dynamics in the population of the quantum emitter takes place in feasible implementations of this archetypal nanocavity.

Quasi-Analytical Approach for Modeling of Surface-Enhanced Raman Scattering

Surface-enhanced Raman scattering has become a powerful analytical tool for the characterization of molecules adsorbed on metal surfaces. The lack of reliable computational methods to accurately assign the complicated Raman spectra has hampered its practical applications. We propose here a quasi-analytical method that allows for the effective evaluation of Raman tensors in periodic systems based on density functional perturbation theory and the finite-difference approach. Its applicability has been validated by simulating Raman spectra of 4,4′-bipyridine (4,4′-bpy) in various conditions. The calculated Raman spectra of isolated 4,4′-bpy as well as its adsorption on flat gold surfaces nicely reproduce their experimental counterparts. The same method has also been successfully applied to a more complicated system, namely 4,4′-bpy inside gold nano junctions. By comparing with the in situ experimental spectra, four interfacial configurations are identified, which are further verified by the good agreement between the simulated charge transfer properties and the experimental measurements. These results indicate that the proposed low-cost quasi-analytical method can provide accurate interpretation for the experimentally measured surface-enhanced Raman spectra and unambiguously determine the structures of the molecules on metal surfaces.

A dynamic program for valuing corporate securities

We design and implement a dynamic program for valuing corporate securities, seen as derivatives on a firm’s assets, and computing the term structure of yield spreads and default probabilities. Our setting is flexible for it accommodates an extended balance-sheet equality, arbitrary corporate debts, multiple seniority classes, and a reorganization process. This flexibility comes at the expense of a minor loss of efficiency. The analytical approach proposed in the literature is exchanged here for a quasi-analytical approach based on dynamic programming coupled with finite elements. To assess our construction, which shows flexibility and efficiency, we carry out a numerical investigation along with a complete sensitivity analysis.

Evaluation of VOC fluxes at the soil-air interface using different flux chambers and a quasi-analytical approach

Dense nonaqueous-phase liquids (DNAPLs) spilled on the soil migrate vertically depending upon gravity and capillary forces through the unsaturated zone of the porous aquifer, forming a vapour plume. These volatile organic compounds (VOCs) can be transferred by advection-diffusion to the groundwater or to the atmosphere. Evaluating DNAPL vapour fluxes at the soil-air interface is one of the key challenges in the remediation of contaminated sites. This work discusses the results of a large-scale vapour plume experiment with a well-defined trichloroethylene (TCE) spill, including a sequential raising and lowering of the water table, where the TCE vapour fluxes at the soil surface were experimentally quantified in two ways: (i) directly, with measurements at the soil-air interface using different flux chambers at various operational modes under both transient and steady-state conditions of the vapour plume, and (ii) indirectly, using a quasi-analytical approach based on soil gas measurements. It was shown that upward displacement of the water-air front during the controlled raising of the water table (approximately 10 cm h−1) increased the TCE vapour flux measured at the soil surface by factors of 4 to 10. Under steady-state transport conditions, TCE vapour fluxes measured using five types of flux chambers and three operational modes were similar. The effects of the flux chamber geometry, the accumulation of TCE vapours in the chamber headspace or the air recirculation at a low flow rate on the measured TCE vapour fluxes were low. At steady-state transport conditions, TCE vapour fluxes measured with the flux chambers and estimated using the quasi-analytical approach were of the same order of magnitude. However, under transient conditions of the vapour plume, the TCE vapour flux predicted by the quasi-analytical approach greatly underestimated or overestimated the real TCE vapour flux at the soil-air interface.

A quasi-analytical approach to the advection–diffusion–reaction problem, using operator splitting

Solutions of the combined advection–diffusion–reaction (ADR) transport equation are generally restricted to numerical methods. However, each subprocess, advection, diffusion and reaction can all be solved individually using analytical techniques for a variety of situations. We present a simple numerical technique that uses the split operator method, and the Semi-Lagrangian scheme, to combine these analytical solutions. The result is a coherent, quasi-analytical solution to the combined ADR transport equation.

Time-Dependent Debye–Mie Series Solutions for Electromagnetic Scattering

Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analog is a challenge, as it involves an inverse Fourier transform of the spherical Hankel functions (and their derivatives) that are convolved with inverse Fourier transforms of spherical Bessel functions (and their derivatives). Series expansion of these convolutions is highly oscillatory (therefore, poorly convergent) and unstable. Indeed, the literature on numerical computation of this convolution is very sparse. In this paper, we present a novel quasi-analytical approach to compute transient Mie scattering that is both stable and rapidly convergent. The approach espoused here is to use vector tesseral harmonics as basis function for the currents in time-domain integral equations (TDIEs) together with a novel addition theorem for the Green's functions that render these expansions stable. This procedure results in an orthogonal, spatially meshfree, and singularity-free system, giving us a set of one-dimensional (1-D) Volterra Integral equations. Time-dependent multipole coefficients for each mode are obtained via a time-marching procedure. Finally, several numerical examples are presented to show the accuracy and stability of the proposed method.

Relativistic quantum dynamics of a spinless particle in the Som-Raychaudhuri spacetime

The Klein-Gordon equation under the influence of the gravitational field produced by a topology such as the Som-Raychaudhuri spacetime and the Klein-Gordon oscillator in the presence of a uniform magnetic field as well as without magnetic field are investigated. Moreover, the Klein-Gordon equation with a cylindrically symmetric scalar potential in the background spacetime is also studied. By using the quasi-analytical ansatz approach, we obtain the energy eigenvalues and corresponding wave functions of these systems. They show that the energy levels of the considered physical systems depend explicitly on the angular deficit α and the vorticity parameter Ω which characterize the global structure of the metric in the Som-Raychaudhuri spacetime.

Remote sensing of shelf sea optical properties: Evaluation of a quasi-analytical approach for the Irish Sea

A quasi-analytical approach to deriving the coefficients of absorption, a(λ), backscattering, bb(λ), and the attenuation of planar irradiance, Kd(λ), from sub-surface remote sensing reflectance, rrs(λ), was investigated for the optically complex (Case 2) waters of the Irish Sea. The algorithms of Lee et al. (2005b, Journal of Geophysical Research Oceans, 110, C02017) were tuned for this region using radiative transfer calculations which incorporated locally determined specific inherent optical properties and constituent concentrations. The optimised algorithms were then applied to rrs spectra derived from profiling radiometry for 145 stations in the Irish Sea and adjacent waters, and their outputs compared with inherent optical property measurements for these stations. For the modelled data, recoveries of, a(λ), bb(λ) and Kd(λ) in six wavebands between 412nm and 667nm had mean percentage errors below 3% and standard deviations of around 6%. For in situ data, the algorithms tended to over-estimate a(λ) and under estimate bb(λ) relative to measured values, but a contributing factor could be the difficulty of measuring optical properties accurately in turbid waters. Retrieved values of Kd(λ) were highly correlated with those measured in situ, with regression slopes in the best-performing bands of 1.05 at 442nm (r2=0.91) and 0.92 at 488nm (r2=0.96). Three previously published relationships between satellite-derived optical properties at 490nm and euphotic depth, z1%PAR, produced roughly equivalent results with root mean square percentage errors, relative to in situ measurements, of around 20%. On the logarithmic scales usually employed in remote sensing, values of a(488), bb(488), Kd(488) and z1%PAR recovered using the optimised algorithms bore strong linear relationships to in situ measurements, with least square regression slopes in the range 0.89 to 1.03 and r2 values from 0.87 to 0.94. Application of these algorithms to a MODIS image of the Irish Sea in early summer (25th May 2013) revealed marked spatial variations in optical properties which were well correlated with known patterns of tidal stirring in the region.

Valuation of Perpetual Strangles: A Quasi-Analytical Approach

A strangle is the simultaneous purchase of an out-of-the-money call and an out-of-the-money put with the same expiration dates. If the options are both European, only one can be in the money at expiration, and the strangle is valued simply as the sum of the call and the put. An American call on a non-dividend-paying stock should not be exercised before maturity, so as maturity extends to infinity, the call value asymptotically approaches the value of the underlying stock. An infinitely lived European put should have zero value, but a perpetual American put can and should be exercised early. In practice, however, a perpetual strangle contract is not just the sum of a perpetual American call and put, because it entails the restriction that exercise of one of the options cancels the other. This obviously reduces the strangle value and makes the early exercise decision of some interest. In this article, Chuang develops a quasi-analytical approach for pricing a perpetual strangle based on the properties of the perpetual case’s early exercise frontier.

Quantifying cyanobacterial phycocyanin concentration in turbid productive waters: A quasi-analytical approach

In this research, we present a novel technique to monitor cyanobacterial bloom using remote sensing measurements. We have used a multi-band quasi analytical algorithm that determines phytoplankton absorption coefficients, aϕ(λ), from above surface remote sensing reflectance, Rrs(λ). In situ data including remote sensing reflectance, phytoplankton pigment concentration, and absorption coefficients of optically active constituents in the water were collected from highly turbid and productive aquaculture ponds. These shallow (<1.5m) ponds in northwestern Mississippi, USA, were used for channel catfish Ictalurus punctatus aquaculture and had high nitrogen and phosphorus loading rates from manufactured feeds added to ponds to promote rapid fish growth. These practices resulted in high phytoplankton biomass (chlorophyll-a concentrations=59.4–1376.6mgm−3) with communities dominated by filamentous, gas-vacuolate cyanobacteria. A novel technique was developed to further decompose the aϕ to obtain phycocyanin absorption coefficient, aPC, at 620nm, a primary peak of phycocyanin absorption spectrum. Validation of the model produced mean and median absolute relative errors of 36.2% and 22.0%. Overall, the model performance was higher in the higher range of PC concentration (>150μgl−1). Results demonstrate that the new approach will be suitable for quantifying phycocyanin concentration in cyanobacteria dominated turbid productive waters.

Quasianalytical modal approach for computing Casimir interactions in periodic nanostructures

We present an almost fully analytical technique for computing Casimir interactions between periodic lamellar gratings based on a modal approach. Our method improves on previous work on Casimir modal approaches for nanostructures by using the exact form of the eigenvectors of such structures, and computing eigenvalues by solving numerically a simple transcendental equation. In some cases eigenvalues can be solved for exactly, such as the zero frequency limit of gratings modeled by a Drude permittivity. Our technique also allows us to predict analytically the behavior of the Casimir interaction in limiting cases, such as the large separation asymptotics. The method can be generalized to more complex grating structures, and may provide a deeper understanding of the geometry-composition-temperature interplay in Casimir forces between nanostructures.

Prediction of Vertical DNAPL Vapour Fluxes in Soils Using Quasi-Analytical Approaches: Bias Related to Density-Driven and Pressure-Gradient-Induced Advection

This study focuses on a detailed analysis of the errors introduced by two quasi-analytical approaches based on either Fick’s first law or a combination of Fick’s and Darcy’s laws to evaluate the vapour flux of chlorinated solvents from a source zone located in the unsaturated zone towards the atmosphere. A coupled one-dimensional numerical flow and transport model was developed and applied to three case studies characterised by different water content profiles in the vadose zone and under different levels of maximum dense nonaqueous-phase liquid vapour concentrations and vapour pressure conditions of the source zone. The steady-state concentration and pressure profiles obtained were then used in the two quasi-analytical approaches to estimate the flux towards the atmosphere. When mass fluxes due to density-driven advection become dominant and the vertical advective mass fluxes are increased due to strong pressure gradients in the soil air, the error was observed to increase when using the pure diffusion approach in the quantification of the surface flux calculated by the numerical model with increasing dimensionless Rayleigh numbers. Without taking into account the advective transport in the approach, the relative error calculated with only Fick’s law overestimates the real vapour flux when density-driven advection is dominant and underestimates it when pressure-gradient-driven advection dominates. The more advanced advective–diffusive quasi-analytical approach fits reasonably well with the numerically obtained mass fluxes except near soil layer discontinuities, where the evaluation of both the concentration gradient and pressure gradient in the porous media as well as the determination of the average effective diffusion coefficients are rendered more difficult.

High Intensity Drying in Porous Materials

High intensity drying is used to characterize those situations for which the drying medium is sufficiently above the saturation temperature of water to preclude the existence of a two-phase zone. In the present work, three models are applied to high intensity drying of porous materials. The three models are: (1) a traditional one-equation model that assumes local thermal equilibrium (LTE); (2) a two-equation model that utilizes lumped capacitance assumption to predict the heat transfer to the solid phase; and (3) a two-equation model that utilizes a more precise quasi-analytical approach to more accurately characterize the conduction in the solid phase. In addition, the relationship between pressure and the drying conditions and material properties is examined since elevated pressure that can occur during high intensity drying is potentially destructive. An implicit finite difference scheme is utilized to determine the drying rate in a porous medium saturated with water and undergoing the phase change process. The case for low local Reynolds number is considered, hence Nusselt number is assumed constant. Results illustrate that the one-equation model does not yield accurate results when the thermophysical properties characterized by the volume weighted ratio of thermal diffusivities, C &gt; 10 (within 5% error). Hence, a two-equation model is suggested. In addition, consistent with the established “rule of thumb,” for Biot number, Biv &lt; 0.1, the traditional two-equation model which makes the lumped capacitance assumption for the solid phase compares well with a two-equation model that more accurately predicts the time dependent diffusion in the solid phase using Duhamel’s theorem. The peak pressures observed during drying for a range of Darcy number and surface heat flux are presented.