Present Mathematical Model Research Articles

Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs

Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model with phase lag to the non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behavior of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and, subsequently, point out the role of the Kuramoto model in understanding the evolution of synchronous and asynchronous regions. We surmise that one implication of the emergence of chimera states will lead to investigation of the present and other mathematical models in detail to generate global chimera-state maps similar to global seismicity maps for earthquake forecasting studies.

Analytical buckling of slender circular concrete-filled steel tubular columns with compliant interfaces

This paper presents an efficient mathematical model for studying the global buckling behavior of concrete-filled steel tubular (CFST) columns with compliant interfaces. The present mathematical model is used to evaluate exact critical buckling loads and modes of CFST columns for the first time. The results prove that the presence of finite interface compliance may significantly reduce the critical buckling load of CFST columns. A good agreement between analytical and experimental buckling loads of circular CFST columns is obtained if at least one among longitudinal and radial interfacial stiffnesses is high. The design methods compared in the paper give conservative results in comparison with the experimental results and analytical results for almost perfectly bonded layers. The parametric study reveals that critical buckling loads of CFST columns are very much affected by the diameter-to-depth ratio and concrete elastic modulus. Moreover, a material nonlinearity has a pronounced effect for short CFST columns, and a negligible effect for slender ones.

Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas

Time delay in insulin secretion, its absorption and action is a point of consideration in artificial pancreas as it may prove fatal in the extreme situation. The present mathematical model deals with two time delays out of which one occur in insulin secretion and second in its absorption and action. The model assess the change in glucose - insulin dynamics after the induction of different values of these time delays in their respective range. Also, simulation is performed over the model to quantify the amount of two time delays to avoid diabetic comma, which has not been explored much.

Bifurcation phenomena of two self-propelled camphor disks on an annular field depending on system length.

Mode selection and bifurcation of a synchronized motion involving two symmetric self-propelled objects in a periodic one-dimensional domain were investigated numerically and experimentally by using camphor disks placed on an annular water channel. Newton's equation of motion for each camphor disk, whose driving force was the difference in surface tension, and a reaction-diffusion equation for camphor molecules on water were used in the numerical calculations. Among various dynamical behaviors found numerically, four kinds of synchronized motions (reversal oscillation, stop-and-move rotation, equally spaced rotation, and clustered rotation) were also observed in experiments by changing the diameter of the water channel. The mode bifurcation of these motions, including their coexistence, were clarified numerically and analytically in terms of the number density of the disk. These results suggest that the present mathematical model and the analysis of the equations can be worthwhile in understanding the characteristic features of motion, e.g., synchronization, collective motion, and their mode bifurcation.

Determination of the Insoluble Aluminum Content in Steel Samples by Using Laser-Induced Breakdown Spectroscopy**supported by National Key Scientific Instrument and Equipment Development Project, China (No. 2012YQ20018208)

The insoluble aluminum content in steel samples has a significant influence on the quality of the steel. In this paper, laser-induced breakdown spectroscopy (LIBS) is used to analyze the insoluble aluminum content in steel samples using a scanning mode. The average intensity plus 2.5 standard deviations was iterated and the final iteration value was taken as the threshold that distinguishes soluble and insoluble aluminum, and thus total and soluble aluminum content calibration curves were generated. Using the relevant total and soluble aluminum content calibration curves, the total and soluble aluminum contents in steel samples could be determined. The insoluble aluminum content could be determined by subtracting the soluble aluminum content from the total aluminum content. The insoluble aluminum content of standard samples and process product samples were determined using the present mathematical model; the results agreed well with the certified reference values. This method could be used to rapidly characterize the insoluble aluminum content in steel samples.

Carrera Unified Formulation for Free-Vibration Analysis of Aircraft Structures

Advanced structural models, based on variable one-, two-, and three-dimensional kinematics, are proposed in this paper and applied to the analysis of the free vibration of reinforced aircraft shell structures. The used models go beyond classical structural theories, that is, Euler–Bernoulli (for one-dimensional beams) and Kirchhoff (for two-dimensional plates) type assumptions. The order of the expansion of the displacement fields over the cross section (one-dimensional case) and along the plate thickness (two-dimensional case) is, in fact, a free parameter of the problem. In this paper, Lagrange polynomials are used to build such expansions, and as a consequence, only displacements are used as the problem unknowns (no rotations or derivatives of displacements, which are typical of one-dimensional/two-dimensional classical theories, are introduced). The finite-element method is used to provide numerical solutions. The related arrays and the governing dynamical equations are written in terms of a few fundamental nuclei according to the Carrera unified formulation. Classical three-dimensional finite-element solid models are also considered. One-, two-, and three-dimensional finite elements are easily connected to each other to make the most appropriate computational model of the reinforced shell structures. The capability to use the same fundamental nucleus to derive finite-element matrices of one-, two-, and three-dimensional elements of the present model is unique because it is usually not available in other finite-element formulations, that is, no ad hoc techniques are required in the present case to couple finite elements with different kinematics. Three main benchmarks have been analyzed: a plate stiffened by means of bidirectional I-stiffeners, a simplified model of a complete aircraft, and a fuselage–wing connection. Comparison with commercial finite-element software (MSC Nastran) is provided for most of the quoted numerical investigations. The modal assurance criterion has been used to compare the free-vibration modes of the different models. The present mathematical models appear closer to reality and cheaper, from the computational point of view, than those of other existing formulations. Carrera unified-formulation-based finite elements do not require the definition of virtual lines (beam axes) or virtual surfaces (plate reference surfaces), and only physical lines/surfaces are therefore used.

Non-Boussinesq approach for turbulent buoyant flows in enclosure with horizontal vent and forced inlet port

The effects of forced ambient velocity on thermal plume behavior in a ceiling vented square enclosure are numerically investigated. Turbulence is modeled by unsteady Favre-averaged Navier–Stokes (UFANS) equation with Lam Bremhorst low Reynolds number k−ɛ turbulence model. A non-Boussinesq variable density approach is used to model the density variations. Simplified Marker and Cell (SMAC) algorithm is used to solve the governing equations on collocated grid with high accuracy compact finite difference schemes. The pressure Poisson equation is solved by bi-conjugate gradient algorithm and time integration is performed with four stage Runge–Kutta method (Rk-4). The results are presented for Grashof number Gr = 1011 and 1012 and Gay-Lussac number Ga = 0.2 and 2. The present model is valid when buoyancy effects are significant in comparison with forced convection effects. The heat transfer characteristics are analyzed by varying forced inlet velocity, inlet port size and inlet port location. The assisting flow enhances plume discharge rate and increases convective heat loss from cavity. The opposing flow weakens thermal buoyancy and minimizes convective heat loss from cavity. The present mathematical model and numerical method are in good agreement with the existing results available in the literature.

Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment

In this article, the geometrical nonlinear free vibration behaviour of shear deformable laminated composite single/doubly curved shell panel in hygrothermal environment is investigated. A general nonlinear mathematical model of laminated composite doubly curved shallow shell panel has been developed based on the higher order shear deformation theory and Green-Lagrange geometric nonlinear kinematics. All the nonlinear higher order terms have been included in the present mathematical model to achieve a realistic case. In addition to that, the composite material properties are considered as temperature and moisture dependent through hygro-thermo-elastic constitutive relations. The governing equation of laminated composite curved panel is obtained using Hamilton’s principle and discretised using nonlinear finite element steps. The desired responses are computed numerically using a direct iterative method. The convergence behaviour of present numerical model has been checked and validated by comparing the responses with those available published results. The effect of different geometrical and/or material parameters on nonlinear vibration behaviour of laminated composite doubly curved shell panel under hygrothermal environment is computed and discussed in detail.

Rate control management of atrial fibrillation: may a mathematical model suggest an ideal heart rate?

BackgroundDespite the routine prescription of rate control therapy for atrial fibrillation (AF), clinical evidence demonstrating a heart rate target is lacking. Aim of the present study was to run a mathematical model simulating AF episodes with a different heart rate (HR) to predict hemodynamic parameters for each situation.MethodsThe lumped model, representing the pumping heart together with systemic and pulmonary circuits, was run to simulate AF with HR of 50, 70, 90, 110 and 130 bpm, respectively.ResultsLeft ventricular pressure increased by 57%, from 33.92±37.56 mmHg to 53.15±47.56 mmHg, and mean systemic arterial pressure increased by 27%, from 82.66±14.04 mmHg to 105.3±7.6 mmHg, at the 50 and 130 bpm simulations, respectively. Stroke volume (from 77.45±8.50 to 39.09±8.08 mL), ejection fraction (from 61.10±4.40 to 39.32±5.42%) and stroke work (SW, from 0.88±0.04 to 0.58±0.09 J) decreased by 50, 36 and 34%, at the 50 and 130 bpm simulations, respectively. In addition, oxygen consumption indexes (rate pressure product – RPP, tension time index per minute – TTI/min, and pressure volume area per minute – PVA/min) increased from the 50 to the 130 bpm simulation, respectively, by 186% (from 5598±1939 to 15995±3219 mmHg/min), 56% (from 2094±265 to 3257±301 mmHg s/min) and 102% (from 57.99±17.90 to 117.4±26.0 J/min). In fact, left ventricular efficiency (SW/PVA) decreased from 80.91±2.91% at 50 bpm to 66.43±3.72% at the 130 bpm HR simulation.ConclusionAwaiting compulsory direct clinical evidences, the present mathematical model suggests that lower HRs during permanent AF relates to improved hemodynamic parameters, cardiac efficiency, and lower oxygen consumption.

MATHEMATICAL MODELING OF BUBBLE MODE MODELING IN CASE OF BOTTOM BLOWING-THROUGH OF LADLE-FURNACE. REPORT III

Formation and movement of gas bubbles in the melt affect the heat interchange and the kinetics of chemical transformations in the course of copper fire refining in a ladle-furnace. The present mathematical model considers changing the bubble speed and volume and surface of moving gas bubble through the melt height.

Bioheat transfer analysis of biological tissues induced by laser irradiation

This paper develops an analytical solution for a generalized dual phase lag (DPL) model based on the nonequilibrium heat transfer in biological tissues during laser irradiation achieved by performing volume average to the local instantaneous energy equation for blood and tissue. The obtained energy equation is solved by employing the separation of variables and Duhamel's integral method for both absorbing and scattering tissues. The generalized DPL model anticipates different results than that of the predicted by the classical DPL and Pennes bioheat transfer (parabolic) models. It is found that the generalized DPL model calculates lower temperature than that of obtained by the classical DPL model due to considering heat convection between blood vessels and tissue. The obtained analytical results are also compared with existing numerical and experimental data to verify the accuracy of the analytical solution. The results indicate that the generalized DPL model reduces to Pennes bioheat transfer model when both thermal lag times are zero. It is shown that effects of blood perfusion rate, coupling factor and the lag time τT on the temperature response of tissue are similar. Furthermore, the comparison between the analytical results and existed experimental data shows that the present mathematical model is an efficient tool for evaluation of bioheat transfer in biological tissues.

2A11 Influence of damping and rail stress on parametric instability of a wheel(Boundary)

Parametric instability of a wheel moving at a constant speed on a railway track is discussed. For this purpose, this paper presents an analytical formulation in which the damping is considered in rail supports. Since the dynamic behavior of a railway track depends on the rail axial load arising from the temperature change, this effect is also taken into account in the present mathematical model. Through numerical analyses, it is found that the eigenvalue which characterizes the quasi-steady-state dynamic reaction of the moving wheel and track is translated toward the positive imaginary number under the existence of damping. The range of unstable velocity is then narrowed by the introduction of dissipation into the track structure. Moreover, the critical damping at which the instability zone vanishes is obtained. Although the compressional rail stress reduces the instability speed, its contribution to the critical damping is insignificant.

Comparison between Mathematical Models for Roughness Obtained in Test Machine and in Industrial Machine in Semifinish Honing Processes

In the present work second order mathematical models for semifinish honing are presented for average roughness Ra as a function of abrasive stone characteristics and honing parameters. Several tests were performed in both a test machine and in an industrial machine. Results from both machines were compared. Although roughness depends on the five variables studied (grain size, density, pressure, linear speed and tangential speed) in both cases, most important factors are grain size and pressure. It is possible to use the model for the test machine in the industrial machine, in a way that only a few tests will be performed in the industrial machine in order to translate the model.

Subsurface transport of nuclear wastes in the Indian subcontinent

Given the diminishing non-renewable energy resources and limited progresses achieved in the renewable energy sectors in India, the existing data projects that nuclear power can play a significant role in sharing the burden of meeting the growing energy demand. Low-, medium-, and high-level radioactive wastes generated from such nuclear power plants are to be disposed safely in the subsurface geological formation with the least environmental impact. In this context, a mathematical model for describing the spatial and temporal distribution of concentration of a radionuclide chain in a saturated subsurface system is presented. The transport of radionuclides occurs by advection and hydrodynamic dispersion, while diffusive transport of radionuclides takes place from mobile into immobile water zone, in a direction, normal to the direction of fluid flow. For decay of radioactive species within fracture and rock matrix, the ingrowth of daughters is considered. In addition, unlike earlier models, the present mathematical model also takes into account precipitation and dissolution of radionuclides within high-permeable fractures and low-permeable rock matrix using first-order reaction kinetics. Further, it is also proposed that unlike dispersive-dominant sub-surface disposal of radionuclides, molecular-level surface and Knudsen diffusion play a critical role for diffusive-dominant deep geological disposal.

Community-based Early Warning and Adaptive Response System (EWARS) for mosquito borne diseases: An open source/open community approach

Abstract. A variety of studies around the world have evaluated the use of remote sensing with and without GIS in communicable diseases. The ongoing Ebola epidemic has highlighted the risks that can arise for the global community from rapidly spreading diseases which may outpace attempts at control and eradication. This paper presents an approach to the development, deployment, validation and wide-spread adoption of a GIS-based temporo-spatial decision support system which is being collaboratively developed in open source/open community mode by an international group that came together under UN auspices. The group believes in an open source/open community approach to make the fruits of knowledge as widely accessible as possible. A core initiative of the groups is the EWARS project. It proposes to strengthen existing public health systems by the development and validation a model for a community based surveillance and response system which will initially address mosquito borne diseases in the developing world. At present mathematical modeling to support EWARS is at an advanced state, and it planned to embark on a pilot project

On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions

This paper studies a Caginalp phase-field transition system endowed with a general regular potential, as well as a general class, in both unknown functions, of nonlinear and non-homogeneous (depending on time and space variables) boundary conditions. We first prove the existence, uniqueness and regularity of solutions to the Allen–Cahn equation, subject to the nonlinear and non-homogeneous dynamic boundary conditions. The existence, uniqueness and regularity of solutions to the Caginalp system in this new formulation are also proved. This extends previous works concerned with regular potential and nonlinear boundary conditions, allowing the present mathematical model to better approximate the real physical phenomena, especially phase transitions.

Mathematical Model Based on DSMC Method for Particulate Drying in a Coaxial Impinging Stream Dryer

An impinging stream dryer (ISD) belongs to a unique class of dryers that has proved to be an excellent alternative to flash dryers for removing surface moisture of particulate materials due to the collision of streams and particles in the dryer. However, the performance analysis of such devices, from a viewpoint of mathematical modeling, has not been investigated extensively. In this study, a mathematical model based on the direct simulation Monte Carlo (DSMC) method is proposed to describe the drying process of particulate materials in a coaxial ISD. The collisions between particles and the heat exchange between impacting particles are included in the present mathematical model. The predicted results were in good agreement with the experimental data, which indicates the validity of the present model. The drying process and the effects of various parameters, including the feeding mode and impinging distance, on the drying performance of the dryer were then numerically investigated and discussed.

Experimental study and optimization of damping properties of epoxy-based nanocomposite: Effect of using nanosilica and high-impact polystyrene by mixture design approach

In current study the influence of weight percentage of high impact polystyrene (HIPS), nanosilica and also hardener content on damping mode properties of epoxy/HIPS/SiO2 hybrid nanocomposite has been investigated. Mixture design has been employed to present mathematical models for predicting first and second damping mode of new mentioned hybrid nanocomposite as function of physical factors and optimizing mentioned mechanical properties. Totally 10 experiments were generated according to simplex centroid mixture design and 10 samples were prepared and tested based on portions of mixture components. The maximum and minimum values of first mode of damping occurred in run numbers 10 and 1 that were 3.74% and 1.71% respectively, also the maximum and minimum value of second mode of damping occurred in coded levels 6 and 1 with the values of 4.61% and 1.02% respectively. Results of analysis of variance showed that all of selected input variables had linear effect on both of the studied responses, two component interactions among HIPS and hardener (X1∗X3) and interaction among silica and hardener (X2∗X3) affected damping 1st and 2nd modes while interaction among HIPS and silica (X1∗X2) only affected on the second mode of damping and did not have any clear effect on damping 1st mode due to its P-value. Moreover optimization was done using response optimizer part of Minitab software and the values of target and allowable minimum responses were defined for the software and finally it calculated the maximum achievable values for both of the responses and also corresponding coded values of mixture components. Optimization results described that the highest value for damping 1st and 2nd modes were 3.80% and 4.65% respectively with coded values of HIPS=0, SiO2=0.37 and hardener=0.62 and corresponding mixture components were HIPS=2wt%, SiO2=4.33wt% and hardener=27.1phr respectively.

Using response surface methodology for modeling and optimizing tensile and impact strength properties of fiber orientated quaternary hybrid nano composite

In current study, weight percentage of nano silica and nano clay and also fiber orientation have been chosen as independent variables and the affect of these variables on tensile and izod impact strength of epoxy/glass fiber/SiO2/clay hybrid laminate composite has been investigated. Central composite design (CCD) which is subset of response surface methodology has been employed to present mathematical models as function of physical factors to predict tensile and impact behavior of new mentioned hybrid nano composite and also optimizing mentioned mechanical properties. Totally 20 experiments were designed with 6 replicates at center point. The maximum and minimum value of tensile strength were 450.90MPa and 158.16MPa which occurred in design levels 1 and 14 respectively, also the maximum and minimum of izod impact strength were 10.47kJ/m2 and 2.56kJ/m2 which occurred in design levels 13 and 14 respectively. The optimization results using optimization part of Minitab software showed that the best tensile strength was obtained 488.53MPa and occurred in 3.5wt% of nano silica, 1.1wt% of nano clay and 9° of fiber orientation and after preparing and testing five samples average value of tensile strength was obtained about 480MPa. Also the results showed that the best impact strength obtained from software was 11.35kJ/m2 and occurred in 4.03wt% of nano clay, 5wt% of nano silica and 0° of fiber orientation. The optimization results also showed that tensile and impact strength at optimum values improved up to 6.4% and 203.5% compared to level 1 and 14 and 6.02% and 303.6% compared to level 13 and 14 respectively. In addition, the fracture surface morphologies of the quaternary nano composites were investigated by scanning electron microscopy (SEM).

Development of a deflector-jet electrohydraulic servovalve using a giant magnetostrictive material

Giant magnetostrictive actuators (GMAs) have received considerable attention in recent years and are becoming increasingly important in the exploitation of a new type electrohydraulic servovalve. In this paper, a deflector-jet servovalve (DJSV) using a giant magnetostrictive material (GMM) is developed for the first time, and the servovalve is mechanically less complex than a conventional DJSV. Next, a mathematical model of the GMM-based DJSV is built, which involves five submodels: a dynamic model of the power amplifier; a dynamic magnetization model of the GMM rod; a magnetoelastic model of the GMM rod; a kinetic model of the GMA; and a deflector-jet amplifier model. The experimental platform used for measuring the performance of the GMM-based DJSV is established, the prototype valve is fabricated, and the related unknown parameters are identified by experimental data from the GMA. Finally, a simulation and experimental research are performed on the GMM-based DJSV; the results indicate that the present GMM-based DJSV has a large output-pressure range, a rapid response, and a high bandwidth, which provides a competitive way to develop a new type of high-frequency and high-flow-rate electrohydraulic servovalve. Additionally, the measured characteristics of the prototype valve are in good agreement with the predicted results and demonstrate that the operational concept is viable, and the present mathematical model is reliable.