Semi-infinite Models Research Articles

Data-driven contract design for supply chain coordination with algorithm sharing and algorithm competition

Supply chain members can intelligently learn their decisions based on historical data by using Machine-Learning (ML) algorithms. To coordinate the supply chain, the data-driven contract design problems for three contracts—buyback, quantity flexibility, and combined quantity flexibility and rebate—were investigated for a supply chain with one manufacturer and multiple retailers under algorithm sharing and algorithm competition. The problems were formulated as bi-level optimization models by introducing nonlinear mapping from historical demand data to ordering decisions and using ML algorithms to learn the mapping parameters. The bi-level optimization models were transformed into semi-infinite programming models and solved using the (nested) cutting plane methods. Empirical studies using data from two databases showed that algorithm sharing or algorithm competition, the type of contract used, and learning algorithms were the three factors influencing the performance of supply chain coordination when using a data-driven contract design. Algorithm sharing was found to be more beneficial to the supply chain members than algorithm competition in promoting supply chain coordination. An effective incentive mechanism, such as an individualized buyback ratio and a rebate from the manufacturer to the retailers with a good forecast performance, can encourage the retailers to participate in algorithm sharing and improvement.

Quantification of blood flow index in diffuse correlation spectroscopy using a robust deep learning method.

Diffuse correlation spectroscopy (DCS) is a powerful, noninvasive optical technique for measuring blood flow. Traditionally the blood flow index (BFi) is derived through nonlinear least-square fitting the measured intensity autocorrelation function (ACF). However, the fitting process is computationally intensive, susceptible to measurement noise, and easily influenced by optical properties (absorption coefficient and reduced scattering coefficient ) and scalp and skull thicknesses. We aim to develop a data-driven method that enables rapid and robust analysis of multiple-scattered light's temporal ACFs. Moreover, the proposed method can be applied to a range of source-detector distances instead of being limited to a specific source-detector distance. We present a deep learning architecture with one-dimensional convolution neural networks, called DCS neural network (DCS-NET), for BFi and coherent factor () estimation. This DCS-NET was performed using simulated DCS data based on a three-layer brain model. We quantified the impact from physiologically relevant optical property variations, layer thicknesses, realistic noise levels, and multiple source-detector distances (5, 10, 15, 20, 25, and 30mm) on BFi and estimations among DCS-NET, semi-infinite, and three-layer fitting models. DCS-NET shows a much faster analysis speed, around 17,000-fold and 32-fold faster than the traditional three-layer and semi-infinite models, respectively. It offers higher intrinsic sensitivity to deep tissues compared with fitting methods. DCS-NET shows excellent anti-noise features and is less sensitive to variations of and at a source-detector separation of 30mm. Also, we have demonstrated that relative BFi (rBFi) can be extracted by DCS-NET with a much lower error of 8.35%. By contrast, the semi-infinite and three-layer fitting models result in significant errors in rBFi of 43.76% and 19.66%, respectively. DCS-NET can robustly quantify blood flow measurements at considerable source-detector distances, corresponding to much deeper biological tissues. It has excellent potential for hardware implementation, promising continuous real-time blood flow measurements.

CO2 solubility and diffusivity in 1-ethyl-3-methylimidazolium cation-based ionic liquids; isochoric pressure drop approach

In this study, an experimental approach based on the isochoric pressure drop principle was implemented to measure (at low equilibrium pressure, 1.3–3.6 bar) the solubility and binary diffusivity of CO2 (constant and variable) in four imidazolium-based room-temperature ionic liquids (RTILs), namely, 1-ethyl-3-methylimidazolium acetate ([emim][Ac]), 1-ethyl-3-methylimidazolium dicyanamide ([emim][DCA]), 1-ethyl-3-methylimidazolium methyl sulfate ([emim][MeSO4]) and 1-ethyl-3-methylimidazolium ethyl sulfate ([emim][EtSO4]). The molar fraction of the dissolved CO2 and Henry's law constant were measured from experimental data. Constant binary diffusion coefficients were measured from the transient thin-film and semi-infinite volume models. In the original approach, the variable diffusivity coefficient model was used to measure the concentration-based variable diffusion coefficient. Anion interaction of the RTILs was found to have a strong influence on the CO2 solubility, and Henry's law constant and the studied anions were ranked as [Ac]− >> [EtSO4]− > [DCA]− > [MeSO4]−. Increasing temperature is not likely for CO2 solubility while it favors CO2 diffusivity. Thin-film model diffusivity measurements were found to be more suitable for [emim][MeSO4] and [emim][EtSO4], while semi-infinite volume model was suitable for [emim][Ac] and [emim][DCA]. Variable diffusion coefficients were found not to be a monotonous function of time, which increased in early stages and decreased after a certain time. Gibbs free energy, enthalpy, and entropy values indicate the strength of the favorable interaction between CO2 and RTILs, mildly exothermic in nature and falling in the range of physisorption.

A MODEL OF WELDING THERMAL PROCESSES WITH A LIMITED NUMBER OF FICTITIOUS POINT SOURCES

Analytical methods of calculation of thermal processes at welding enable to estimate operatively the influence of welding modes on parameters of a temperature field and to predict structural changes in a zone of thermal influence. In the mid-twentieth century it was suggested to calculate the heat processes in welded products with parallel boundary planes by summing up the temperature fields of the main and infinite number of fictitious point sources using thereflection method. However, due to computational difficulties, this method could not be brought to a state of wide practical application. Furthermore, since the schematization of heated bodies is conditional, the choice of the body scheme (plate, flat layer, semi-infinite body) and therefore the thermal calculation model is performed intuitively based on the accumulated experience. This uncertainty inevitably leads to discrepancy between the calculated and actual parameters of the thermal welding process. The purpose of this work is to adapt a model of thermal processes with a limited number of fictitious fast moving point sources to the calculation of thermal welding processes. The proposed model, solvable in Mathcad software, contains the equations of temperature field and temperature rate of change with account of the number
 of fictitious heat sources involved in the calculation. This model allows a reasonable limitation of the number of fictitious heat sources for providing the required accuracy of calculations, since as the fictitious heat sources move away from the product and their influence on the product heating decreases. In most cases for practical calculations 2 pairs of fictitious sources are enough for welding of 2 cm thick steel products, of 0.5 cm thick products ‒ 5 pairs, of 0.2 cm thick products ‒ 12 pairs. Comparison of the calculated values of the proposed model with actual temperature field measurements and known effects of cooling rate in the plate, plane layer and semi-infinite body within the accepted limits have confirmed its adequacy. The presented comparative results demonstrate versatility of the proposed model with a limited number of fictitious fast moving point sources, which can be applied sufficiently and successfully for analysis of the thermal welding processes of real industrial products of arbitrary thickness without discriminating into plate, plane layer and semi-infinite body models.

Influence of conductive porous electrodes on the apparent electrode kinetics of fenitrothion

• FT’s cyclic voltammetry response at planar and porous modified electrode is simulated. • Simulations reveal the occurrence of thin-layer effects at porous modified electrode. • Cyclic voltammetry experiment validates the simulation results. Planar bare electrodes fabricated with surface-modified multiwalled carbon nanotubes (MWCNT) are used to detect organophosphate (OP) compounds, which are used as herbicides and fungicides but are harmful to human health. Deposition of carbon nanotubes on the surfaces of bare electrodes enhances electrocatalysis, increasing the electrode to analyte current response and narrowing peak-to-peak potential separation during cyclic voltammetry (CV). We hypothesize that, as the thickness of the deposited MWCNT layer decreases, Fenitrothion (FT, an OP) mass transport between the layers of porous multiwalled carbon nanotubes changes from semi-infinite to thin-layer diffusion. This influences the electrode electrochemical response to the analyte. Using simulations and experiments, we show that when porous MWCNT are deposited on a conductive glassy carbon electrode the mass transport of FT changes from semi-infinite to thin-layer diffusion during CV. This alters the electrochemical response of the electrode and reduces peak-to-peak potential separation. To simulate CV response to multi-step and multi-electron electrochemical reactions of FT, both the semi-infinite and thin-layer diffusion models are employed for the planar bare and modified porous surface electrodes. The transition from thin layer to semi-infinite diffusion is clear when the nanotube layer thickness on the bare electrode increases. The model is applicable to other toxic chemicals, such as 4-nitrophenol, parathion, or methyl parathion that have similar electrode kinetics.

Analysis of equivalent thickness of geological media for lab-scale study of radon exhalation.

Geological media are omnipresent in nature. Lab-scale tests are frequently employed in radon exhalation measurements for these media. Thus, it is critical to find the thickness of the medium at an experimental scale that is equivalent to the medium thickness in a real geological system. Based on the diffusion-advection transport of radon, theoretical models of the surface radon exhalation rate for homogeneous semi-infinite and finite-thickness systems were derived (denoted as Jse and Jfi, respectively). Analysis of the equivalency of Jse and Jfi was subsequently carried out by introducing several dimensionless parameters, including the ratio of the exhalation rates for the semi-infinite and finite-thickness models, ε, and the number of diffusion lengths required to achieve a desired ε value, n. The results showed that when radon transport in geological media is dominantly driven by diffusion effect, if n > 3.6626, then ε > 95%; if n > 5.9790, then ε > 99.5%. When radon migration is dominantly driven by advection effect, if n > 2.5002, then ε > 95%; if n > 4.0152, then ε > 99.5%. Therefore, if the thickness of the geological media (x0) is greater than a certain n times the radon diffusion length of the media (L), the media can be modeled as semi-infinite. To validate the model, a pure radon diffusion experiment (no advection) was developed using uranium mill tailings, laterite, and radium-bearing rocklike material with different thicknesses (x0). The theoretical model was demonstrated to be reliable and valid. This study provides a basis for determining the appropriate thickness of geological media in lab-scale radon exhalation measurement experiments with open bottom.

Noninvasive continuous optical monitoring of absolute cerebral blood flow in critically ill adults.

.We investigate a scheme for noninvasive continuous monitoring of absolute cerebral blood flow (CBF) in adult human patients based on a combination of time-resolved dynamic contrast-enhanced near-infrared spectroscopy (DCE-NIRS) and diffuse correlation spectroscopy (DCS) with semi-infinite head model of photon propogation. Continuous CBF is obtained via calibration of the DCS blood flow index (BFI) with absolute CBF obtained by intermittent intravenous injections of the optical contrast agent indocyanine green. A calibration coefficient () for the CBF is thus determined, permitting conversion of DCS BFI to absolute blood flow units at all other times. A study of patients with acute brain injury () is carried out to ascertain the stability of . The patient-averaged DCS calibration coefficient across multiple monitoring days and multiple patients was determined, and good agreement between the two calibration coefficients measured at different times during single monitoring days was found. The patient-averaged calibration coefficient of was applied to previously measured DCS BFI from similar brain-injured patients; in this case, absolute CBF was underestimated compared with XeCT, an effect we show is primarily due to use of semi-infinite homogeneous models of the head.

Exact solution of the Linear Parabolic Approximation for flow-depth based diffusive flow routing

The Linearized Parabolic Approximation of the Saint Venant Equations is often used for flood routing, but the corresponding analytic solutions usually neglect the downstream boundary conditions. This is an issue because the presence of hydraulic structures at the end of a river reach, or natural morphologic conditions, may influence the wave propagation. In order to take into account realistic boundary conditions, namely a stage-hydrograph upstream and a stage-discharge relationship downstream, a new set of exact solutions of the Linearized Parabolic Approximation of the Saint Venant Equations with uniformly distributed lateral inflows is presented. This exact solution is demonstrated by using it as a building block in a simplified flood routing model, whose numerical results are compared with those supplied by laboratory experiments from literature. Finally, the new solutions are used to analyze the range of validity of semi-infinite channel models. The comparison shows that semi-infinite channel models are accurate when convective effects are prevailing on diffusive effects, and the downstream boundary condition corresponds to uniform flow conditions. In addition, the results show that semi-infinite channel models based on the knowledge of the upstream stage-hydrograph can predict flow depths better than those making use of a flow hydrograph, while being practically equivalent in predicting flow rates.

Thermal Model of Electromagnetic Skin-Equivalent Phantom at Millimeter Waves

This paper reports the first thermal model and detailed analysis of the heating of an electromagnetic (EM) skin-equivalent phantom with a finite thickness at 60 GHz. The 1-D heat transfer equation is solved analytically for homogeneous phantoms with finite thicknesses. The temperature rise dynamics and heating distribution within the phantom are calculated for several phantom thicknesses (5, 10, and 15 mm) using measured thermal properties of the phantom. Analytical results are confirmed by numerical analysis based on EM-thermal cosimulations. Furthermore, the numerical model is validated by measurements using an experimental setup based on the high-resolution infrared thermometry. The impact of uncertainty of EM and the thermal parameters of the numerical model upon heat deposition is also studied. Our results reveal that, for short exposure durations (i.e., less than 1 min), the surface temperature is well described by the semi-infinite and finite-thickness phantom models, whereas, for longer exposures (more than 1 min), finite-thickness models must be used to properly account for heating accumulation close to the phantom boundaries. While the reported results cannot be directly used for predicting temperature increase in skin, they are of importance for temperature-based dosimetric assessment in the millimeter-wave band using currently available homogeneous phantoms.

Investigation of dimensional and heat source effects in Lock-In Thermography applications in semiconductor packages

Lock-In Thermography (LIT) is a powerful non-contact and non-destructive investigating technique that has recently emerged in the semiconductor industry. The current LIT applications interpret LIT data using the semi-infinite models. However, semiconductor package has finite geometry with convective heat transfer on surface. This paper studies the accuracy of the interpretation of LIT data based on the commonly used semi-infinite models. The effects of finite dimensions, heat source configuration, convective heat transfer coefficient, thickness of material, thermal diffusivity of material, and lock-in frequency are examined. Furthermore, the effects of heat source’s shape and location, as well as the problems involving non-homogeneous materials are also investigated. It has been found that the errors in phase shift estimate using semi-infinite models may occur at lower lock-in frequency with high diffusivity material and thinner specimen. When multiple materials are involved with various scenarios of heat source locations, the phase shift may decrease with the lock-in frequency, as observed in experiment. Finite element transient heat conduction analysis is a useful tool to derive the actual z-depth of heat source based on the phase shift data from experiment.

Semi-analytical and semi-numerical method for plane strain consolidation of double-layer foundation considering stress paths

In this work, a simplified solution method is present for the elasto-plastic consolidation of a double-layer foundation under different stress paths. A double-yield surface model is introduced as the constitutive model framework for saturated clay and sand. Using a Gauss kernel function, a partial derivative coefficient sequences is obtained. Then, the model is applied to Biot’s consolidation equations and to establish incremental governing partial differential equations for the plane strain consolidation problem. By simplifying the continuity equation as a Poisson equation, the fundamental solutions are derived for double-layer foundation model. Based on it, a semi-analytical and semi-numerical method is presented which is implemented in our finite element program. Comparisons with different mesh show that the stability of the numerical method is good. Moreover, the consolidation of semi-infinite double-layer foundation models is analysed under two stress paths (conventional loading path under the condition of isotropic consolidation CTC and conventional loading path under the condition of anisotropic consolidation K0 + CTC). It is shown that the model can reflect the influence of stress path, loading distribution width and some other factors on the deformation of the soil skeleton and pore water pressure. This simplified solution appears to be more convenient than the traditional coupling stiffness matrix method.

An upgraded camera-based imaging system for mapping venous blood oxygenation in human skin tissue

A camera-based imaging system was previously developed for mapping venous blood oxygenation in human skin. However, several limitations were realized in later applications, which could lead to either significant bias in the estimated oxygen saturation value or poor spatial resolution in the map of the oxygen saturation. To overcome these issues, an upgraded system was developed using improved modeling and image processing algorithms. In the modeling, Monte Carlo (MC) simulation was used to verify the effectiveness of the ratio-to-ratio method for semi-infinite and two-layer skin models, and then the relationship between the venous oxygen saturation and the ratio-to-ratio was determined. The improved image processing algorithms included surface curvature correction and motion compensation. The curvature correction is necessary when the imaged skin surface is uneven. The motion compensation is critical for the imaging system because surface motion is inevitable when the venous volume alteration is induced by cuff inflation. In addition to the modeling and image processing algorithms in the upgraded system, a ring light guide was used to achieve perpendicular and uniform incidence of light. Cross-polarization detection was also adopted to suppress surface specular reflection. The upgraded system was applied to mapping of venous oxygen saturation in the palm, opisthenar and forearm of human subjects. The spatial resolution of the oxygenation map achieved is much better than that of the original system. In addition, the mean values of the venous oxygen saturation for the three locations were verified with a commercial near-infrared spectroscopy system and were consistent with previously published data.

Influence of the size and skin thickness of apple varieties on the retrieval of internal optical properties using Vis/NIR spectroscopy: A Monte Carlo-based study

Visible/near-infrared spectroscopy is a well-established method to measure optical properties of tissues, assuming that a light propagation model can be used to recover absorption and reduced scattering coefficients from non-invasive probing. Spectroscopic measurements have achieved success in non-destructive assessment of apple optical properties and quality attributes. However, the spectroscopy of apples must consider the size of the fruit and the presence of the thin skin layer that surrounds the flesh, to correctly read the signals acquired on the boundary. In this research, the fruit was modelled as a two layer spherical structure with various radii and finite thickness of the upper skin layer. Monte Carlo computations were performed to generate time-resolved reflectance and spatially-resolved reflectance measurements. Simulated data were then fitted using a procedure based on Levenberg–Marquardt algorithm with specific semi-infinite models. The errors in the retrieved optical properties of the flesh (absorption coefficient μa, and reduced scattering coefficient μ′s) were studied as functions of apple radius, skin thickness, and source–detector distance, for given optical parameter sets assigned to the flesh and the skin. The results suggest that the time-resolved reflectance spectroscopy may probe optical properties of the flesh regardless of the skin layer, when a sufficient source–detector distance (15mm) is used for the measurements. Similar results were found in case of using the spatially resolved spectroscopy, because measurements extend up to 15–29mm by steps of 1mm or 2mm. The computations also show that the curvature of the boundary has noticeable effect on the errors in the retrieved optical coefficients of the flesh. However, results from time-resolved spectroscopy are more influenced by the size of apples, compared with the spatially-resolved spectroscopy.

Ion boundary conditions in semi-infinite fluid models of electron beam-plasma interaction

The modified Bohm criterion is derived for the plasma consisting of the monoenergetic electron beam and thermal electrons. This criterion allows us to define the accurate ion boundary conditions for semi-infinite collisionless fluid models of electron beam–plasma interaction. In the absence of electron beam, these boundary conditions give the classical sheath parameters. When the monoenergetic electron beam propagates through the plasma, the fluid model with proposed boundary conditions gives the results, which are in qualitative agreement with the results obtained earlier in M. Sharifian and B. Shokri, Phys. Plasmas 14, 093503 (2007). However, dynamics and parameters of the plasma sheath are different.

Thermal mirror spectrometry: An experimental investigation of optical glasses

The Thermal mirror technique relies on measuring laser-induced nanoscale surface deformation of a solid sample. The amplitude of the effect is directly dependent on the optical absorption and linear thermal expansion coefficients, and the time evolution depends on the heat diffusion properties of the sample. Measurement of transient signals provide direct access to thermal, optical and mechanical properties of the material. The theoretical models describing this effect can be formulated for very low optical absorbing and for absorbing materials. In addition, the theories describing the effect apply for semi-infinite and finite samples. In this work, we apply the Thermal mirror technique to measure physical properties of optical glasses. The semi-infinite and finite models are used to investigate very low optical absorbing glasses. The thickness limit for which the semi-infinite model retrieves the correct values of the thermal diffusivity and amplitude of the transient is obtained using the finite description. This procedure is also employed on absorbing glasses, and the semi-infinite Beer–Lambert law model is used to analyze the experimental data. The experimental data show the need to use the finite model for samples with very low bulk absorption coefficients and thicknesses L<1.5mm. This analysis helped to establish limit values of thickness for which the semi-infinite model for absorbing materials could be used, L>1.0mm in this case. In addition, the physical properties of the samples were calculated and absolute values derived.

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.

Modeling of Urea Release from Briquettes Using Semi infinite and Shrinking Core Models

Briquetted urea is commonly used in wet agricultural soils since it has potential to reduce loss of urea occuring in the fields by various mechanisms. In the present study, commercially available uncoated urea briquettes were subjected to release in wet loam and wet silty clay soils, both maintained at 40% moisture, measured on dry basis. Adapted semi infinite model and developed shrinking core model predictions were compared with the experimentally determined concentration profiles and unreleased quantity of urea, respectively. Semi infinite model developed with the assumption of unchanging briquette size did not match well with experimental results. However, shrinking core model predicted the unreleased urea contents in briquettes reasonably well.

Numerical solutions for the elastic deformation of spherical bearing surfaces of metal-on-metalhip joint implants

On the elastohydrodynamic lubrication analysis, one of the most time-consuming issues is the calculation of surface deformation. Two methods are usually adopted to fasten the calculation: the multi-level multi-integration (MLMI) and the fast Fourier transform (FFT). However, in spherical models such as for hip joint replacements, the finite-element method has to be employed instead of analytical formulations to determine the influence coefficients. It limits the coarsest grid to 60 × 60 points to ensure numerical accuracy. This limitation prevents the MLMI to achieve high performance. Therefore, a combined MLMI and FFT method is proposed. The basic idea is to replace the direct summation on the coarse grids in the MLMI by the FFT algorithm. The combined method is validated by comparing to the individual MLMI and FFT. The combined method is found to perform fastest. In solving a quasi-static elastohydrodynamic lubrication solution, approximately 65 per cent less CPU time is required on grid 512 × 512, and the accuracy is not affected. For the usual semi-infinite plane models, sometimes a large number of levels can cause a lot of additional operations and storage space when translating data between the levels. The combined MLMI and FFT method can be an alternative way to choose the coarse grid more flexibly, reduce the number of grid levels, and optimize the computing performance.

Localization of adipose tissue embedded biliary tree vessels by use of near-infrared diffuse photon propagation models: a computational feasibility study

Biliary tree structures are embedded in adipose tissue and, therefore, cannot be visualized directly by the surgeon during cholecystectomy operations. This can lead to inadvertent injuries with serious complications for the patient. Computational studies were performed to assess the feasibility of noninvasively localizing these structures from spectrally resolved near-infrared reflectance measurements. Methodologies were developed for vessel localization, both on the adipose tissue surface and depthwise, by use of semi-infinite and two-layer models of diffuse photon propagation in tissues, respectively. The simulation results, along with some preliminary experimental measurements on tissue-simulating phantoms, prove the feasibility of these methods and show promise for their future clinical application.

Dynamic elastoplastic analysis by a hybrid BEM–FEM time-domain formulation

This study presents a hybrid BEM–FEM procedure for the dynamic analysis of elastoplastic models. In this hybrid approach, boundary node and internal point displacements are evaluated considering the time-domain BEM formulation (initial stress approach), and stresses are computed taking into account FEM techniques (domain discretization is only necessary where non-linear behaviour is expected to occur). This hybrid methodology is very appropriate to model infinite or semi-infinite elastoplastic models and, at the end of the paper, three numerical applications are presented, illustrating the potentialities of the proposed formulation.