Elementary Model Research Articles

Optimization-based global structural identifiability

Global structural identifiability determines if it is possible to uniquely estimate unknown parameters of a model from measurements. We consider two definitions for global structural identifiability - one proposed by Walter and Lecourtier in Mathematics and Computers in Simulation, 60:472-482 (1982) and the other by Glad and Ljung in the Proceedings of the 29th Conference on Decision and Control (1990). The two definitions appear distinct because of the role of the inputs. We present here a proof of the equivalence of the two definitions. We revisit the formulation of the optimization problem to analyze global structural identifiability proposed by Asprey and Mantalaris in IFAC Computer Application in Biotechnology (2001) and propose a modification to the problem formulation. We also demonstrate with the help of an elementary model that their solution algorithm can lead to erroneous conclusions. We further analyze the global structural identifiability of a simple model using the optimization-based approach.

A Modeling-Based Approach to Calculus

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and Applied Calculus, for students who will most likely take only one calculus-level course in college and who often have a weak algebraic background that suggests they would most likely not be successful in a traditional calculus course. During the first half of the course, students review precalculus ideas while learning techniques for identifying elementary functional models whose graphs correspond to the underlying shapes of data sets, refining their models in response to new data, and using the method of least squares to find “best possible” models of a given type. During the second half of the course, these functional models are analyzed using the tools of calculus. Mathematical Modeling and Applied Calculus focuses on real-life contexts and data sets, uses RStudio to study large data sets, and explores big picture conceptual understandings in order to develop the insights and skills needed to describe, model, and analyze many aspects of our world.

The architrave a tasselli

The architrave a tasselli is a peculiar design shape of the traditional stone lintels, which are widespread in Abruzzo, Italy: stone lintels are not usually monolithic elements, being formed by three pieces, the block spanning the opening and the tasselli, two small rectangular pieces. In the current paper, by means of an elementary Wrinkler-type beam model, it has been attempted to capture the behaviour of stone lintels, chasing the mechanical reasons supporting this traditional construction technique.

Application of elementary hydrology model for the assesment of watershed health at Progo Hulu watershed

This study aimed to test the reliability of hidrology Model with MUSLE Method in predicting the hydrology indicators in assesment of watershed condition. The indicators were maximum discharge, minimum discharege, river regime coefficient, runoff coefficient, erosion and sedimentation. NRECA Hydrology Model compared to Mock Model to get a better Hydrology Model to apply in this area. The result showed that NRECA Model was better than Mock Model in predicting some hydrologic indicators and MUSLE Model was sensitive enough in predicting the other indicators which was shown by the result of good accuracy test. In this study, NRECA Model and MUSLE model performs well in predicting the hydrologic indicators in assessing Progo Hulu watershed condition.

From quantum dots to quantum dashes: Excitonic spectra of highly elongated InAs/InP nanostructures

A transition from a cylindrical quantum dot to a highly elongated quantum dash is theoretically studied here with an atomistic approach combining empirical tight binding for single particle states and configuration interaction method for excitonic properties. Large nanostructure shape anisotropy leads to a peculiar trend of the bright exciton splitting, which at certain point is quenched with further shape elongation, contradicting predictions of simplified models. Moreover strong shape elongation promotes pronounced optical activity of the dark exciton, that can reach substantial $1\%$ fraction of the bright exciton intensity without application of any external fields. An atomistic calculation is augmented with a elementary phenomenological model expressed in terms of light-hole exciton add-mixture increasing with the shape deformation. Finally, exctionic complexes $X^-$, $X^+$, and $XX$ are studied as well and the correlations due to presence of higher excited states are identified as a key-factor affecting excitonic binding energies and the fine structure.

Effect of Charge-Transfer State Energy on Charge Generation Efficiency via Singlet Fission in Pentacene-Fullerene Solar Cells.

Singlet fission in pentacene creates two triplet excitons per absorbed photon. In a solar cell, each triplet can generate an electron–hole pair, and hence, external quantum efficiencies exceeding 100% have been reported for pentacene–fullerene solar cells. The energetics of this process are intriguing because the minimum photon energy loss, defined as the energy difference between the (triplet) exciton state and the open-circuit voltage, is less than 0.5 eV and distinctively smaller than that in most organic donor–acceptor solar cells. To investigate the energetics of this process, we analyze the effect of the energy of the lowest unoccupied molecular orbital (LUMO) for different fullerene derivatives. With the LUMO energy becoming less negative, the open-circuit voltage increases and charge generation decreases. For all but one of the fullerenes tested, the charge-transfer state energy is distinctively higher than the pentacene triplet energy, revealing that charge generation via singlet fission is actually endergonic. An elementary Marcus model for the rate of electron transfer provides a qualitative description of the experimental trends, in accordance with an endergonic charge transfer. Considering that charge generation from triplet states is endergonic, involvement of pentacene singlet states, either from direct photoexcitation or via triplet–triplet annihilation, cannot be excluded.

Torsion Processes for Cylindrical Samples Made of Incompressible Viscoelastic Materials of the Maxwell Type

Analytical solutions are obtained for the problem of torsion of incompressible cylinders, whose materials are described by the constitutive relations of viscoelastic media, generalizing the relations of the elementary Maxwell model for the case of finite deformations. Constitutive relations differ from each other in the value of the parameter specifying the type of an objective derivative used from the Gordon-Showalter family, including the Oldroyd, Cotter-Rivlin, and Jaumann derivatives. It is shown that a longitudinal compressive force (the Poynting effect) is generated when twisting a cylinder with a constant length, whose material is described by any constitutive relation from the one-parameter family under consideration. For stepwise deformation processes, a qualitative description of a number of available experimental data are also obtained.

An elementary model for fast detonations in tubular charges

The paper is concerned with the experimentally known phenomenon that the detonation velocity of a tubular charge may markedly exceed that of a homogeneous charge of the same explosive. It is shown that the effect may be successfully reproduced using a simple quasi-one-dimensional two-layer model assuming the gas–solid system to be isothermal and the volumetric fraction of the solid phase to be small. In view of a considerable drop of the burned gas pressure/density, compared to the Chapman–Jouguet case, fast detonation may be perceived as a variety of weak (undercompressed) detonation.

Evaluation of empathy and biopsychosocial approaches of medical faculty assistant doctors.

INTRODUCTION AND AIM:Biopsychosocial approach suggests that the individual's health condition is partly influenced by the interactions of biological, psychological, and social processes. It also concludes that the clinical method should be patient-centered, which is based on the physician's involvement in the patient's world and the physician's ability to see the illness from the patient's view. In this study, we aimed to determine the extent to which medical faculty assistant doctors use the biopsychosocial approach in their clinical practice.MATERIALS AND METHODS:Our study is a cross-sectional type, descriptive, and analytical research. The sample size consisted of assistant doctors who met the inclusion criteria which were accepted to participate in the study between December 1, 2017, and March 1, 2018, at the medical faculty hospital of Dicle University. Two hundred and three physicians participated in our study. The Patient–Physician Orientation Scale (PPOS), The Jefferson Scale of Physician Empathy (JSPE), and a survey study including questions in relation with sociodemographic characteristics were conducted in our study. The reliability of the Patient–Physician Orientation Scale (PPOS) and JSPE used in our study was tested with Cronbach's alpha and found to be 0.878 and 0.931, respectively. Questionnaires were administered by a face-to-face interview method during interview. Information on the purpose and method of the study was given.RESULTS:A total of 203 physicians participated in our study. One hundred and forty-three (70%) participants were male and 60 (30%) were female. According to medical disciplines, eight physicians (3, 9%) from psychiatry, 21 (10, 3%) from family medicine, 104 (51, 2%) from other internal medical disciplines, and 70 (34, 5%) from surgical medical disciplines participated in the study. In the first subgroup of the PPOS, which is used in our study, the average score of psychiatry physicians was 3.67 ± 0.99, family medicine assistant doctors 3.92 ± 0.67, other internal medical disciplines 3.98 ± 0.65, and surgical medical discipline 3.83 ± 0.61. In the second subgroup, which is defined as the care in the same scale, the average score of psychiatry assistant doctors was found to be 3.20 ± 0.45, family medicine assistant doctors 3.68 ± 0.54, other internal medical disciplines 3.49 ± 0.60, and surgical medical discipline 3.68 ± 0.58. The results of the Jefferson Scale used to determine the level of empathy in our study are found as psychiatry 78.25 ± 14.78, family physician 67.71 ± 14.69, other internal medical disciplines 72.03 ± 13.46, and surgical medical discipline 70.87 ± 15.24.CONCLUSIONS:The biopsychosocial approach is primarily an elementary approach model in medical discipline such as family medicine and should be applied to other internal and surgical medical disciplines as well. With conducting this study, the awareness of this area will be increased and related issues in the literature will be enriched.

An elementary multistage discrete model of soil organic matter transformations with a continuous scale of stability

The proposed elementary mathematical model of formation and decomposition of soil organic matter (SOM) is based on using equations of chemical kinetics to describe the multistage process of SOM transformation. The model both describes each step of transformation in accordance with the law of mass action and postulates the trend of increasing stability of the matter towards further transformation, which is common for all steps. Analysis of the model demonstrates that it is extremely difficult to construct a realistic model of SOM dynamics by assembling elementary models of the type presented in this study into the full description of SOM transformation processes.

Short-run momentum, long-run mean reversion and excess volatility: An elementary housing model

We propose an elementary housing model that replicates the key properties of housing bubbles, namely short-run momentum, long-run mean reversion, and excess volatility. We analytically proof that such dynamics can only emerge if homebuyers place sufficient weight on extrapolative expectations.

Decays of Unstable Quantum Systems

This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their description beyond the exponential approximation is the source of technical and conceptual challenges. In this article, we present both general methods that can be adapted to a large class of problems, and specific elementary models to describe phenomena like photo-emission, beta emission and tunneling-induced decays. We pay particular attention to the emergence of exponential decay; we analyze the approximations that justify it, and we present criteria for its breakdown. We also present a detailed model for non-exponential decays due to resonance, and an elementary model describing decays in terms of particle-detection probabilities. We argue that the traditional methods for treating decays face significant problems outside the regime of exponential decay, and that the exploration of novel regimes of current interest requires new tools.

Research on the novel explicit model for photovoltaic I-V characteristic of the single diode model under different splitting spectrum

Abstract Photovoltaic (PV) panel has been widely used in many spectrum splitting systems. However the spectrum splitting normally discussed only with photocurrent. In this paper, the relationship between the current-voltage (I-V) curve and the irradiation spectrum is discussed by combining the single diode model. An explicit elementary analytical model with two defined shape parameters is improved with three approximations and second order Taylor expansion. The relationship between the physical parameters and the condition parameters is applied to extract the shape parameters at different scenarios. Considering the aging effect, the process of calculation to predict I-V curve is simplified as follow: (1) two shape parameters are gotten from I-V data at measurement reference conditions (MRC); (2) short circuit current, open circuit voltage and shape parameters under any splitting spectrum can be calculated based on the relationship provided in article; (3) the performance of PV panel can be predicted with parameters. The validation of this model was experimentally proven leveraging monocrystalline silicon photovoltaic module with different splitting films. Moreover, the presented model performs superior compared to other investigated models when looking at accuracy and simplicity.

Estimation of the Directions of Alpha Rhythm Elementary Sources Using the Method of Human Brain Functional Tomography Based On the Magnetic Encephalography Data

New method for the magnetic encephalography data analysis was proposed. The method transforms multichannel time series into the spatial structure of the human brain activity. In this paper we further develop this method to determine the dominant direction of the electrical sources of brain activity at each node of the calculation grid. We have considered the experimental data, obtained with three 275-channel magnetic encephalographs in New York University, McGill University and Montreal University. The human alpha rhythm phenomenon was selected as a model object. Magnetic encephalograms of the brain spontaneous activity were registered for 5-7 minutes in magnetically shielded room. Detailed multichannel spectra were obtained by the Fourier transform of the whole time series. For all spectral components, the inverse problem was solved in elementary current dipole model and the functional structure of the brain activity was calculated in the frequency band 8-12 Hz. In order to estimate the local activity direction, at the each node of calculation grid the vector of the inverse problem solution was selected, having the maximal spectral power. So, the 3D-map of the brain activity vector field was produced – the directional functional tomogram. Such maps were generated for 15 subjects and some common patterns were revealed in the directions of the alpha rhythm elementary sources. The proposed method can be used to study the local properties of the brain activity in any spectral band and in any brain compartment.

Evaluation of creep models for frozen soils

To model the creep behavior of frozen soils, three creep stages have to be reasonably described(i.e., primary, secondary and tertiary stages). Based on a series of uniaxial creep test results, three creep models were evaluated. It was shown that hypoplastic creep model has high prediction accuracy for both creep strain and strain rate in a wide stress range. The elementary rheological creep model can only be used for creep strains at low stress levels, because of the restraints of its mathematical construction. For the soft soil creep model, the progressive change from the primary to secondary and tertiary stages cannot be captured at high stress levels. Therefore, the elementary rheological and soft soil creep models can only be used for low stress levels without a tertiary stage; while the hypoplastic creep model is applicable at high stress levels with the three creep stages.

Inconsistency evaluation of the curriculum logical structure

Purpose of the study. The main purpose of creating a curriculum is to regulate academic disciplines in accordance with the logic of the learning process, defined by the relationship between the basic concepts of the disciplines. Violation of this logic becomes apparent only directly during the training sessions.A large variety of quantitative methods uses indicators that do not reveal structural deficiencies in the curriculum. This makes it difficult to improve the curriculum.The purpose of this work is to demonstrate the application of a general approach to the assessment of the structural inconsistency of systems in relation to the evaluation of the logical structure of the curriculum.Materials and methods. The paper applies a general approach to the assessment of structural integrity, developed on the basis of the provisions of the general theory of systems and graph theory. The approach involves the construction of three interrelated structural models of the system and using them to determine the initial data for calculating the index of inconsistency of the system structure.Results. The overall approach to the assessment of structural integrity is adapted to assess the logical structure of the curriculum. Three models of curriculum structure are developed:Elementary model of interdisciplinary communication;Curriculum network model;Hierarchical curriculum model.Based on the parameters of the hierarchical curriculum model, using three adapted algorithms, the value of the inconsistency index of the curriculum structure in the direction of preparation “Applied Informatics” is calculated. Recommendations on changing the structure of the studied curriculum to reduce the degree of its structural inconsistency are proposed. Conclusion. As a result of the research, the methods were proposed that allow identifying possible contradictions in the structure of the curriculum and evaluating its inconsistency. As the experiments have shown, it is extremely difficult to study the curricula in a manual manner, the number of disciplines in which exceeds 50. In this regard, the development of a complex of computer programs that will automate the assessment of the inconsistency of large curricula is being completed.

Kinetic study of the regeneration of spent caustic via the genetic algorithm method

Background: Spent caustic contains noxious components such as sulfide species and also high chemical oxygen demand content (COD). Oxidation of these materials to caustic and sulfate species is mostly the rate-controlling step within catalytic oxidation of spent caustic. Methods: In this study, the kinetics of catalytic oxidation of spent caustic and the regeneration methodology of the sulfidic spent caustic were investigated. The kinetics of catalytic oxidation of spent caustic was studied in the presence of a heterogeneous catalyst. The developed mathematical model was verified via the batch bubble column reactor. The elementary and non-elementary models based on the genetic algorithm were used to obtain the rate coefficient and kinetic order. Results: The experiments were carried out at various conditions. The results indicated that the error of objective function of the non-elementary and elementary models was 3.01% and 134.96%, respectively. Conclusion: According to the results, the non-elementary model had rational outcome compared to the elementary one. Also, non-elemental model is more concordance with experimental results.

Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators

Networks of degrade-and-fire oscillators are elementary models of populations of synthetic gene circuits with negative feedback, which show elaborate phenomenology while being amenable to mathematical analysis. In addition to thorough investigation in various examples of interaction graphs, previous studies have obtained conditions on interaction topology and strength that ensure that asymptotic behaviors are periodic (assuming that the so-called firing sequence is itself periodic and involves all nodes). Here, we revisit and extend these conditions and we analyse the dynamics in a case of unidirectional periodic chain. This example shows in particular that the updated conditions for asymptotic periodicity are optimal. Altogether, our results provide a novel instance of direct impact of the topology of interactions in the global dynamics of a collective system.

An elementary 1-dimensional model for a solid state lithium-ion battery with a single ion conductor electrolyte and a lithium metal negative electrode

An elementary 1-dimensional model is developed for a solid state lithium-ion battery having a single ion conductor electrolyte, a lithium metal negative electrode and a composite positive electrode. The battery topology is assumed to be of the layered variety, thereby justifying the 1-dimensional formulation. The governing equations for the electrochemical kinetics at the interface between the negative electrode and the electrolyte separator are stated, as are those for ion transport in the electrolyte. The positive electrode is assumed to be a particulate composite of storage material within a matrix of electrolyte. A mixture theory is developed for the positive electrode encompassing ion transport in the electrolyte matrix and storage and unstorage of lithium in the active material subject to electrochemical kinetics at the perimeter of the storage particles. Many simplifying assumptions are made with the advantage of them leading to closed-form or semi-closed-form solutions, including linearization of the equations governing the redox kinetics at interfaces in the battery between electrolyte and active material. An approximation is given for the concentration of lithium in the positive electrode of the battery during discharge, with the details depending on a length scale parameter that depends on the competition between the rate of lithium insertion into/extraction from the storage particles and the rate at which lithium ions are transported in the electrolyte. When the conductivity of the electrolyte is high and the redox reactions are relatively sluggish, this length scale parameter is comparable to the thickness of the positive electrode or larger than it. In that case lithium insertion into/extraction from storage particles occurs everywhere within an active zone of the positive electrode, but with the rates least at the current collector of the positive electrode. If the conductivity of the electrolyte is poor and the redox reactions rapid, the length scale for the solution is small compared to the thickness of the positive electrode and insertion into/extraction from storage particles occurs only in a narrow slice of the positive electrode. This slice moved along the positive electrode and separates a region of it that is completely filled/empty from a region of it that has not yet gained or lost any of its lithium. In all cases there will usually be a region of the positive electrode near the separator that is completely filled during discharge and completely empty during battery charging. Our results also give outcomes from which the internal resistance of the battery can be estimated.

SiC power MOSFET in short-circuit operation: Electro-thermal macro-modelling combining physical and numerical approaches with circuit-type implementation

The purpose of this paper is to describe, for the first time, a global transient electrothermal model of (SiC) power MOSFETs during accidental short-circuit (SC) operations. The developed models allow to analyse an inverter-leg malfunctioning. A thermal model of the SiC MOSFET dies combined with extensive experimentations allow to develop models of the gate leakage current and of the drain saturation current during SC events. After verifying the robustness of the proposed elementary models, an original global circuit model with an easy implementation using a commercial circuit simulation tool is proposed and discussed. This circuit model can be used in order to develop protection schemes against SC faults.