Fast and numerically stable Mie solution of EM near field and absorption for stratified spheres

Purpose The purpose of this paper is the development of an analytic computational model for electromagnetic (EM) wave scattering from spherical objects. The main application field is the modeling of electrically large objects, where the standard numerical techniques require huge computational resources. An example is full-wave modeling of the human head in the millimeter-wave regime. Hence, an approximate model or analytical approach is used. Design/methodology/approach The Mie–Debye theorem is used for calculating the EM scattering from a layered dielectric sphere. The evaluation of the analytical expressions involved in the infinite sum has several numerical instabilities, which makes the precise calculation a challenge. The model is validated through an application example with comparing results to numerical calculations (finite element method). The human head model is used with the approximation of a two-layer sphere, where the brain tissues and the cranial bones are represented by homogeneous materials. Findings A significant improvement is introduced for the stable calculation of the Mie coefficients of a core–shell stratified sphere illuminated by a linearly polarized EM plane wave. Using this technique, a semi-analytical expression is derived for the power loss in the sphere resulting in quick and accurate calculations. Originality/value Two methods are introduced in this work with the main objective of estimating the final precision of the results. This is an important aspect for potentially unstable calculations, and the existing implementations have not included this feature so far.

A Class of Three-Dimensional Subspace Conjugate Gradient Algorithms for Unconstrained Optimization

In this paper, a three-parameter subspace conjugate gradient method is proposed for solving large-scale unconstrained optimization problems. By minimizing the quadratic approximate model of the objective function on a new special three-dimensional subspace, the embedded parameters are determined and the corresponding algorithm is obtained. The global convergence result of a given method for general nonlinear functions is established under mild assumptions. In numerical experiments, the proposed algorithm is compared with SMCG_NLS and SMCG_Conic, which shows that the given algorithm is robust and efficient.

Approximate Models of Microbiological Processes in a Biofilm Formed on Fine Spherical Particles

This paper concerns the dynamical modeling of the microbiological processes that occur in the biofilms that are formed on fine inert particles. Such biofilm forms e.g. in fluidized-bed bio-reactors, expanded bed biofilm reactors and biofilm air-lift suspension reactors. An approximate model that is based on the Laplace–Carson transform and a family of approximate models that are based on the concept of the pseudo-stationary substrate concentration profile in the biofilm were proposed. The applicability of the models to the microbiological processes was evaluated following Monod or Haldane kinetics in the conditions of dynamical biofilm growth. The use of approximate models significantly simplifies the computations compared to the exact one. Moreover, the stiffness that was present in the exact model, which was solved numerically by the method of lines, was eliminated. Good accuracy was obtained even for large internal mass transfer resistances in the biofilm. It was shown that significantly higher accuracy was obtained using one of the proposed models than that which was obtained using the previously published approximate model that was derived using the homotopy analysis method.

Robust Adaptive Self-Structuring Neural Network Bounded Target Tracking Control of Underactuated Surface Vessels

This paper studies the target-tracking problem of underactuated surface vessels with model uncertainties and external unknown disturbances. A composite robust adaptive self-structuring neural-network-bounded controller is proposed to improve system performance and avoid input saturation. An extended state observer is proposed to estimate the uncertain nonlinear term, including the unknown velocity of the tracking target, when only the measurement values of the line-of-sight range and angle can be obtained. An adaptive self-structuring neural network is developed to approximate model uncertainties and external unknown disturbances, which can effectively optimize the structure of the neural network to reduce the computational burden by adjusting the number of neurons online. The input-to-state stability of the total closed-loop system is analyzed by the cascade stability theorem. The simulation results verify the effectiveness of the proposed method.

Stabilization of a class of underactuated Euler Lagrange system using an approximate model

The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the underactuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear and nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of underactuated EL systems. To develop this method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. Hence, the assignable potential energy function and the controlled inertia matrix both are constructed as a common solution of these PDEs. Subsequently, the gyroscopic and dissipative forces are determined as the solution for kinetic energy matching condition. Conclusively, the control rule is constructed by adding energy shaping rule and additional dissipation injection to provide asymptotic stability. The stability analysis of the closed-loop system which used the control rule derived with the proposed method is also provided. To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.

A generic hidden Markov model for multi-parent populations

A common step in the analysis of multi-parent populations is genotype reconstruction: identifying the founder origin of haplotypes from dense marker data. This process often makes use of a probability model for the pattern of founder alleles along chromosomes, including the relative frequency of founder alleles and the probability of exchanges among them, which depend on a model for meiotic recombination and on the mating design for the population. While the precise experimental design used to generate the population may be used to derive a precise characterization of the model for exchanges among founder alleles, this can be tedious, particularly given the great variety of experimental designs that have been proposed. We describe an approximate model that can be applied for a variety of multi-parent populations. We have implemented the approach in the R/qtl2 software, and we illustrate its use in applications to publicly-available data on Diversity Outbred and Collaborative Cross mice.

Dynamic Fit Index Cutoffs for One-Factor Models

Assessing unidimensionality of a scale is a frequent interest in behavioral research. Often, this is done with approximate model fit indices in a factor analysis framework such as RMSEA, CFI, or SRMR. These fit indices are continuous measures, so values indicating acceptable fit are up to interpretation. Cutoffs suggested by Hu and Bentler (1999) are a common guideline used in empirical research. However, these cutoffs were derived with intent to detect omitted cross-loadings or omitted factor covariances in three-factor models. These types of misspecifications cannot exist in one-factor models, so the appropriateness of using these guidelines in one-factor models is uncertain. This paper uses a simulation study to address whether traditional fit index cutoffs are sensitive to the types of misspecifications that can occur in one-factor models. The results showed that traditional cutoffs have very poor sensitivity to misspecification in one-factor models and that the traditional cutoffs generalize poorly to one-factor contexts. As an alternative, we investigate the accuracy and stability of the recently introduced dynamic fit cutoff approach for creating fit index cutoffs for one-factor models. Simulation results indicated excellent performance of dynamic fit index cutoffs to classify correct or misspecified one-factor models and that dynamic fit index cutoffs are a promising approach for more accurate assessment of unidimensionality.

Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Decrease of Leidenfrost temperature at quenching in subcooled liquids

Cooling of high-temperature bodies in liquids largely depends on its subcooling to the saturation temperature. An increase in subcooling leads to an increase in the surface temperature, at which the vapor film loses its stability and an intensive cooling regime begins. This temperature depends on a number of parameters, such as the properties of a liquid and a solid, the composition and topology of the surface, the value of subcooling. Within the framework of this work, it was possible to achieve a significant decrease in the temperature of the onset of an intensive cooling mode in subcooled water and ethanol by using as working sections of metal samples with a high of thermal effusivity, low roughness and a protective coating from oxidation. The obtained experimental results confirm the approximate model of the appearance of an intense cooling regime