Search results for: mathematical innovations

Authors: Karthiyayini Nagarajan, P. V. Ramakrishna

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Radar Imaging techniques provides extensive applications in the field of remote sensing, majorly Synthetic Aperture Radar (SAR) that provide high resolution target images. This paper work puts forward the effective and realizable signal generation and processing for SAR images. The major units in the system include camera, signal generation unit, signal processing unit and display screen. The real radio channel is replaced by its mathematical model based on optical image to calculate a reflected signal model in real time. Signal generation realizes the algorithm and forms the radar reflection model. Signal processing unit provides range and azimuth resolution through matched filtering and spectrum analysis procedure to form radar image on the display screen. The restored image has the same quality as that of the optical image. This SAR imaging system has been designed and implemented using MATLAB and Quartus II tools on Stratix III device as a System (Lab Bench) that works in real time to study/investigate on radar imaging rudiments and signal processing scheme for educational and research purposes.

Keywords: synthetic aperture radar, radio reflection model, lab bench, imaging engineering

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: Karthiyayini Nagarajan, P. V. RamaKrishna

Abstract:

Radar Imaging techniques provides extensive applications in the field of remote sensing, majorly Synthetic Aperture Radar(SAR) that provide high resolution target images. This paper work puts forward the effective and realizable signal generation and processing for SAR images. The major units in the system include camera, signal generation unit, signal processing unit and display screen. The real radio channel is replaced by its mathematical model based on optical image to calculate a reflected signal model in real time. Signal generation realizes the algorithm and forms the radar reflection model. Signal processing unit provides range and azimuth resolution through matched filtering and spectrum analysis procedure to form radar image on the display screen. The restored image has the same quality as that of the optical image. This SAR imaging system has been designed and implemented using MATLAB and Quartus II tools on Stratix III device as a System(lab bench) that works in real time to study/investigate on radar imaging rudiments and signal processing scheme for educational and research purposes.

Keywords: synthetic aperture radar, radio reflection model, lab bench

Procedia PDF Downloads 456

Authors: Ed de Jong

Abstract:

Avantium is a leading technology development company and a frontrunner in renewable chemistry. Avantium develops disruptive technologies that enable the production of sustainable high value products from renewable materials and actively seek out collaborations and partnerships with like-minded companies and academic institutions globally, to speed up introductions of chemical innovations in the marketplace. In addition, Avantium helps companies to accelerate their catalysis R&D to improve efficiencies and deliver increased sustainability, growth, and profits, by providing proprietary systems and services to this regard. Many chemical building blocks and materials can be produced from biomass, nowadays mainly from 1st generation based carbohydrates, but potential for competition with the human food chain leads brand-owners to look for strategies to transition from 1st to 2nd generation feedstock. The use of non-edible lignocellulosic feedstock is an equally attractive source to produce chemical intermediates and an important part of the solution addressing these global issues (Paris targets). Avantium’s Dawn Technology™ separates the glucose, mixed sugars, and lignin available in non-food agricultural and forestry residues such as wood chips, wheat straw, bagasse, empty fruit bunches or corn stover. The resulting very pure lignin is dense in energy and can be used for energy generation. However, such a material might preferably be deployed in higher added value applications. Bitumen, which is fossil based, are mostly used for paving applications. Traditional hot mix asphalt emits large quantities of the GHG’s CO₂, CH₄, and N₂O, which is unfavorable for obvious environmental reasons. Another challenge for the bitumen industry is that the petrochemical industry is becoming more and more efficient in breaking down higher chain hydrocarbons to lower chain hydrocarbons with higher added value than bitumen. This has a negative effect on the availability of bitumen. The asphalt market, as well as governments, are looking for alternatives with higher sustainability in terms of GHG emission. The usage of alternative sustainable binders, which can (partly) replace the bitumen, contributes to reduce GHG emissions and at the same time broadens the availability of binders. As lignin is a major component (around 25-30%) of lignocellulosic material, which includes terrestrial plants (e.g., trees, bushes, and grass) and agricultural residues (e.g., empty fruit bunches, corn stover, sugarcane bagasse, straw, etc.), it is globally highly available. The chemical structure shows resemblance with the structure of bitumen and could, therefore, be used as an alternative for bitumen in applications like roofing or asphalt. Applications such as the use of lignin in asphalt need both fundamental research as well as practical proof under relevant use conditions. From a fundamental point of view, rheological aspects, as well as mixing, are key criteria. From a practical point of view, behavior in real road conditions is key (how easy can the asphalt be prepared, how easy can it be applied on the road, what is the durability, etc.). The paper will discuss the fundamentals of the use of lignin as bitumen replacement as well as the status of the different demonstration projects in Europe using lignin as a partial bitumen replacement in asphalts and will especially present the results of using Dawn Technology™ lignin as partial replacement of bitumen.

Keywords: biorefinery, wood fractionation, lignin, asphalt, bitumen, sustainability

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Authors: M. Orefice, V. Di Vito

Abstract:

This paper provides a description of a Collision Avoidance algorithm that has been developed starting from the mathematical modeling of the flight of insects, in terms of spirals and conchospirals geometric paths. It is able to calculate a proper avoidance manoeuver aimed to prevent the infringement of a predefined distance threshold between ownship and the considered intruder, while minimizing the ownship trajectory deviation from the original path and in compliance with the aircraft performance limitations and dynamic constraints. The algorithm is designed in order to be suitable for real-time applications, so that it can be considered for the implementation in the most recent airborne automatic collision avoidance systems using the traffic data received through an ADS-B IN device. The presented approach is able to take into account the rules-of-the-air, due to the possibility to select, through specifically designed decision making logic based on the consideration of the encounter geometry, the direction of the calculated collision avoidance manoeuver that allows complying with the rules-of-the-air, as for instance the fundamental right of way rule. In the paper, the proposed collision avoidance algorithm is presented and its preliminary design and software implementation is described. The applicability of this method has been proved through preliminary simulation tests performed in a 2D environment considering single intruder encounter geometries, as reported and discussed in the paper.

Keywords: ADS-B Based Application, Collision Avoidance, RPAS, Spiral Geometry.

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Authors: Partha P. Gopmandal, Somnath Bhattacharyya, Naren Bag

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In this article, we have studied the effect of pH-regulated surface charge on the electroosmotic flow (EOF) through nanochannel filled with binary symmetric electrolyte solution. The channel wall possesses either an acidic or a basic functional group. Going beyond the widely employed Debye-Huckel linearization, we develop a mathematical model based on Nernst-Planck equation for the charged species, Poisson equation for the induced potential, Stokes equation for fluid flow. A finite volume based numerical algorithm is adopted to study the effect of key parameters on the EOF. We have computed the coupled governing equations through the finite volume method and our results found to be in good agreement with the analytical solution obtained from the corresponding linear model based on low surface charge condition or strong electrolyte solution. The influence of the surface charge density, reaction constant of the functional groups, bulk pH, and concentration of the electrolyte solution on the overall flow rate is studied extensively. We find the effect of surface charge diminishes with the increase in electrolyte concentration. In addition for strong electrolyte, the surface charge becomes independent of pH due to complete dissociation of the functional groups.

Keywords: electroosmosis, finite volume method, functional group, surface charge

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Authors: R. Di Lorenzo, S. Laneri, A. Sacchi

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Hair surface properties affect hair texture and shine, whereas the healthy state of the hair cortex sways hair ends. Even if cosmetic treatments are intrinsically safe, there is potentially damaging action on the hair fibers. Loss of luster, frizz, split ends, and other hair problems are particularly prevalent among people who repeatedly alter the natural style of their hair or among people with intrinsically weak hair. Technological and scientific innovations in hair care thus become invaluable allies to preserve their natural well-being and shine. The study evaluated restoring keratin-like ingredients that improve hair fibers' structural integrity, increase tensile strength, improve hair manageability and moisturizing. The hair shaft is composed of 65 - 95% of keratin. It gives the hair resistance, elasticity, and plastic properties and also contributes to their waterproofing. Providing exogenous keratin is, therefore, a practical approach to protect and nourish the hair. By analyzing the amino acid composition of keratin, we find a high frequency of hydrophobic amino acids. It confirms the critical role interactions, mainly hydrophobic, between cosmetic products and hair. The active ingredient analyzed comes from vegetable proteins through an enzymatic cut process that selected only oligo- and polypeptides (> 3500 KDa) rich in amino acids with hydrocarbon side chains apolar or sulfur. These chemical components are the most expressed amino acids at the level of the capillary keratin structure, and it determines the most significant possible compatibility with the target substrate. Given the biological variability of the sources, it isn't easy to define a constant and reproducible molecular formula of the product. Still, it consists of hydroxypropiltrimonium vegetable peptides with keratin-like performances. 20 natural hair tresses (30 cm in length and 0.50 g weight) were treated with the investigated products (5 % v/v aqueous solution) following a specific protocol and compared with non-treated (Control) and benchmark-keratin-treated strands (Benchmark). Their brightness, moisture content, cortical and surface integrity, and tensile strength were evaluated and statistically compared. Keratin-like treated hair tresses showed better results than the other two groups (Control and Benchmark). The product improves the surface with significant regularization of the cuticle closure, improves the cortex and the peri-medullar area filling, gives a highly organized and tidy structure, delivers a significant amount of sulfur on the hair, and is more efficient moisturization and imbibition power, increases hair brightness. The hydroxypropyltrimonium quaternized group added to the C-terminal end interacts with the negative charges that form on the hair after washing when disheveled and tangled. The interactions anchor the product to the hair surface, keeping the cuticles adhered to the shaft. The small size allows the peptides to penetrate and give body to the hair, together with a conditioning effect that gives an image of healthy hair. Results suggest that the product is a valid ally in numerous restructuring/conditioning, shaft protection, straightener/dryer-damage prevention hair care product.

Keywords: conditioning, hair damage, hair, keratin, polarized light microscopy, scanning electron microscope, thermogravimetric analysis

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Authors: Chen Zhang, Bernhard Schwarz-Röhr, Alexander Härting

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To acquire accurate ship motions at the center of gravity, a single low-cost inertial sensor is utilized and applied on board to measure ship oscillating motions. As observations, the three axes accelerations and three axes rotational rates provided by the sensor are used. The mathematical model of processing the observation data includes determination of the distance vector between the sensor and the center of gravity in x, y, and z directions. After setting up the transfer matrix from sensor’s own coordinate system to the ship’s body frame, an extended Kalman filter is applied to deal with nonlinearities between the ship motion in the body frame and the observation information in the sensor’s frame. As a side effect, the method eliminates sensor noise and other unwanted errors. Results are not only roll and pitch, but also linear motions, in particular heave and surge at the center of gravity. For testing, we resort to measurements recorded on a small vessel in a well-defined sea state. With response amplitude operators computed numerically by a commercial software (Seaway), motion characteristics are estimated. These agree well with the measurements after processing with the suggested method.

Keywords: extended Kalman filter, nonlinear estimation, sea trial, ship motion estimation

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Authors: Eldho Paul, Brijesh Paul

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This work proposes an auction mechanism based solution methodology for the optimum scheduling of trucks in a cross-docking centre. The cross-docking centre is an important element of lean supply chain. It reduces the amount of storage and transportation costs in the distribution system compared to an ordinary warehouse. Better scheduling of trucks in a cross-docking center is the best way to reduce storage and transportation costs. Auction mechanism is commonly used for allocation of limited resources in different real-life applications. Here, we try to schedule inbound trucks by integrating auction mechanism with the functioning of a cross-docking centre. A mathematical model is developed for the optimal scheduling of inbound trucks based on the auction methodology. The determination of exact solution for problems involving large number of trucks was found to be computationally difficult, and hence a genetic algorithm based heuristic methodology is proposed in this work. A comparative study of exact and heuristic solutions is done using five classes of data sets. It is observed from the study that the auction-based mechanism is capable of providing good solutions to scheduling problem in cross-docking centres.

Keywords: auction mechanism, cross-docking centre, genetic algorithm, scheduling of trucks

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: Munoz A. Tatiana, Solano R. Brandon, Montes C. Juan, Cierco G. Javier

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The hydrodynamic cavitation is a process in which the energy that the fluids have in the phase changes is used. From this energy, local temperatures greater than 5000 °C are obtained where thermal cracking of the fluid molecules takes place. The process applied to heavy oil affects variables such as viscosity, density, and composition, which constitutes an important improvement in the quality of crude oil. In this study, the need to design a software through mathematical integration models of mixing, cavitation, kinetics, and reactor, allows modeling changes in density, viscosity, and composition of a heavy oil crude, when the fluid passes through a hydrodynamic cavitation reactor. In order to evaluate the viability of this technique in the industry, a heavy oil of 18° API gravity, was simulated using naphtha as a hydrogen donor at concentrations of 1, 2 and 5% vol, where the simulation results showed an API gravity increase to 0.77, 1.21 and 1.93° respectively and a reduction viscosity by 9.9, 12.9 and 15.8%. The obtained results allow to have a favorable panorama on this technological development, an appropriate visualization on the generation of innovative knowledge of this technique and the technical-economic opportunity that benefits the development of the hydrocarbon sector related to heavy crude oil that includes the largest world oil production.

Keywords: hydrodynamic cavitation, thermal cracking, hydrogen donor, heavy oil upgrading, simulator

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Authors: Aakansha Gupta, Neha Vadnere, Tapasvi Soni, M. Anbarsi

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Protein secondary structure prediction is one of the most important goals pursued by bioinformatics and theoretical chemistry; it is highly important in medicine and biotechnology. Some aspects of protein functions and genome analysis can be predicted by secondary structure prediction. This is used to help annotate sequences, classify proteins, identify domains, and recognize functional motifs. In this paper, we represent protein secondary structure as a mathematical model. To extract and predict the protein secondary structure from the primary structure, we require a set of parameters. Any constants appearing in the model are specified by these parameters, which also provide a mechanism for efficient and accurate use of data. To estimate these model parameters there are many algorithms out of which the most popular one is the EM algorithm or called the Expectation Maximization Algorithm. These model parameters are estimated with the use of protein datasets like RS126 by using the Bayesian Probabilistic method (data set being categorical). This paper can then be extended into comparing the efficiency of EM algorithm to the other algorithms for estimating the model parameters, which will in turn lead to an efficient component for the Protein Secondary Structure Prediction. Further this paper provides a scope to use these parameters for predicting secondary structure of proteins using machine learning techniques like neural networks and fuzzy logic. The ultimate objective will be to obtain greater accuracy better than the previously achieved.

Keywords: model parameters, expectation maximization algorithm, protein secondary structure prediction, bioinformatics

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Authors: Reynaldo Esquivel, Pedro Hernandez, Aaron Martinez-Higareda, Sergio Tena-Cano, Enrique Alvarez-Ramos, Armando Lucero-Acuna

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Stimuli-responsive nanomaterials play an essential role in loading, transporting and well-distribution of anti-cancer compounds in the cellular surroundings. The outstanding properties as the Lower Critical Solution Temperature (LCST), hydrolytic cleavage and protonation/deprotonation cycle, govern the release and delivery mechanisms of payloads. In this contribution, we experimentally determine the load efficiency and release of antineoplastic Vincristine Sulfate into PNIPAM-Interpenetrated-Chitosan (PIntC) nanoparticles. Structural analysis was performed by Fourier Transform Infrared Spectroscopy (FT-IR) and Proton Nuclear Magnetic Resonance (1HNMR). ζ-Potential (ζ) and Hydrodynamic diameter (DH) measurements were monitored by Electrophoretic Mobility (EM) and Dynamic Light scattering (DLS) respectively. Mathematical analysis of the release pharmacokinetics reveals a three-phase model above LCST, while a monophasic of Vincristine release model was observed at 32 °C. Cytotoxic essays reveal a noticeable enhancement of Vincristine effectiveness at low drug concentration on HeLa cervix cancer and MDA-MB-231 breast cancer.

Keywords: nanoparticles, vincristine, drug delivery, PNIPAM

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Authors: Raj K. Gupta, X. Gary Tan, Andrzej Przekwas

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Bomb blasts from Improvised Explosive Devices (IEDs) account for vast majority of terrorist attacks worldwide. Injuries caused by IEDs result from a combination of the primary blast wave, penetrating fragments, and human body accelerations and impacts. This paper presents a multiscale computational model of coupled blast physics, whole human body biodynamics and injury biomechanics of sensitive organs. The disparity of the involved space- and time-scales is used to conduct sequential modeling of an IED explosion event, CFD simulation of blast loads on the human body and FEM modeling of body biodynamics and injury biomechanics. The paper presents simulation results for blast-induced brain injury coupling macro-scale brain biomechanics and micro-scale response of sensitive neuro-axonal structures. Validation results on animal models and physical surrogates are discussed. Results of our model can be used to 'replicate' filed blast loadings in laboratory controlled experiments using animal models and in vitro neuro-cultures.

Keywords: blast waves, improvised explosive devices, injury biomechanics, mathematical models, traumatic brain injury

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Authors: Imene Skhakhfa, Lahbaci Ouerdachi

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To ensure the overall coherence of simulated results, it is necessary to develop a robust validation process. In many applications, it is no longer content to calibrate and validate the model only in relation to the hydro graph measured at the outlet, but we try to better simulate the functioning of the watershed in space. Therefore the timing also performs compared to other variables such as water level measurements in intermediate stations or groundwater levels. As part of this work, we limit ourselves to modeling flood of short duration for which the process of evapotranspiration is negligible. The main parameters to identify the models are related to the method of unit hydro graph (HU). Three different models were tested: SNYDER, CLARK and SCS. These models differ in their mathematical structure and parameters to be calibrated while hydrological data are the same, the initial water content and precipitation. The models are compared on the basis of their performance in terms six objective criteria, three global criteria and three criteria representing volume, peak flow, and the mean square error. The first type of criteria gives more weight to strong events whereas the second considers all events to be of equal weight. The results show that the calibrated parameter values are dependent and also highlight the problems associated with the simulation of low flow events and intermittent precipitation.

Keywords: model calibration, intensity, runoff, hydrograph

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Authors: Sharad Singh, Ajay Kumar Sinha

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Coupled dampers like viscoelastic-frictional dampers for supplemental damping are a newer technique. In this paper, innovative Visco-frictional damping models have been presented and investigated. This paper attempts to couple frictional and fluid viscous dampers into a single unit of supplemental dampers. Visco-frictional damping model is developed by series and parallel coupling of frictional and fluid viscous dampers using Maxwell and Kelvin-Voigat models. The time analysis has been performed using numerical simulation on an SDOF system with varying fundamental periods, subject to a set of 12 ground motions. The simulation was performed using the direct time integration method. MATLAB programming tool was used to carry out the numerical simulation. The response behavior has been analyzed for the varying time period and added damping. This paper compares the response reduction behavior of the two modes of coupling. This paper highlights the performance efficiency of the suggested damping models. It also presents a mathematical modeling approach to visco-frictional dampers and simultaneously suggests the suitable mode of coupling between the two sub-units.

Keywords: hysteretic damping, Kelvin model, Maxwell model, parallel coupling, series coupling, viscous damping

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Authors: Nancy Mackin

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Historically, architects from Aalto to Gaudi to Wright have looked to the architectural knowledge of long-resident peoples for forms and structural principles specifically adapted to the regional climate, geology, materials availability, and culture. In this research, structures traditionally built by Inuit peoples in a remote region of the Canadian high Arctic provides a folio of architectural ideas that are increasingly relevant during these times of escalating carbon emissions and climate change. ‘Green architecture from the Thawing Arctic’ researches, draws, models, and reconstructs traditional buildings of Inuit (Eskimo) peoples in three remote, often inaccessible Arctic communities. Structures verified in pre-contact oral history and early written history are first recorded in architectural drawings, then modeled and, with the participation of Inuit young people, local scientists, and Elders, reconstructed as emergency shelters. Three full-sized building types are constructed: a driftwood and turf-clad A-frame (spring/summer); a stone/bone/turf house with inwardly spiraling walls and a fan-shaped floor plan (autumn); and a parabolic/catenary arch-shaped dome from willow, turf, and skins (autumn/winter). Each reconstruction is filmed and featured in a short video. Communities found that the reconstructed buildings and the method of involving young people and Elders in the reconstructions have on-going usefulness, as follows: 1) The reconstructions provide emergency shelters, particularly needed as climate change worsens storms, floods, and freeze-thaw cycles and scientists and food harvesters who must work out of the land become stranded more frequently; 2) People from the communities re-learned from their Elders how to use materials from close at hand to construct impromptu shelters; 3) Forms from tradition, such as windbreaks at entrances and using levels to trap warmth within winter buildings, can be adapted and used in modern community buildings and housing; and 4) The project initiates much-needed educational and employment opportunities in the applied sciences (engineering and architecture), construction, and climate change monitoring, all offered in a culturally-responsive way. Elders, architects, scientists, and young people added innovations to the traditions as they worked, thereby suggesting new sustainable, culturally-meaningful building forms and materials combinations that can be used for modern buildings. Adding to the growing interest in bio-mimicry, participants looked at properties of Arctic and subarctic materials such as moss (insulation), shrub bark (waterproofing), and willow withes (parabolic and catenary arched forms). ‘Green Architecture from the Thawing Arctic’ demonstrates the effective, useful architectural oeuvre of a resilient northern people. The research parallels efforts elsewhere in the world to revitalize long-resident peoples’ architectural knowledge, in the interests of designing sustainable buildings that reflect culture, heritage, and identity.

Keywords: architectural culture and identity, climate change, forms from nature, Inuit architecture, locally sourced biodegradable materials, traditional architectural knowledge, traditional Inuit knowledge

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: P. A. Broodryk, A. F. Van Der Merwe, H. W. J. P. Neomagus

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The production of the clear liquid fertilizer ammonium polyphosphate (APP) is best achieved by the pyrolysis of urea phosphate, as it produces a product that is free from any of the impurities present in the raw phosphoric acid it was made from. This is a multiphase, multi-step reaction that produces carbon dioxide and ammonia as gasses and ammonium polyphosphate as liquid products. The polyphosphate chain length affects the solubility and thus the applicability of the product as liquid fertiliser, thus proper control of the reaction conditions is thus required for the use of this reaction in the production of fertilisers. This study investigates the reaction kinetics of the aforementioned reaction, describing a mathematical model for the kinetics of the reaction along with the accompanying rate constants. The reaction is initially exothermic, producing only carbon dioxide as a gas product and ammonium diphosphate, at higher temperatures the reaction becomes endothermic, producing ammonia gas as an additional by-product and longer chain polyphosphates, which when condensed too far becomes highly water insoluble. The aim of this study was to (i) characterise the pyrolysis reaction of urea phosphate by determining the mechanisms and the associated kinetic constants, and (ii) to determine the optimum conditions for ammonium diphosphate production. A qualitative investigation was also done to find the rate of hydrolysis of APP as this provides an estimate of the shelf life of an APP clear liquid fertiliser solution.

Keywords: ammonium polyphosphate, kinetics, pyrolysis, urea phosphate

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Authors: D. Srinivasacharya, G. Madhava Rao

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In this article, the pulsatile flow of blood flow in bifurcated artery with mild stenosis is investigated. Blood is treated to be a micropolar fluid with constant density. The arteries forming bifurcation are assumed to be symmetric about its axes and straight cylinders of restricted length. As the geometry of the stenosed bifurcated artery is irregular, it is changed to regular geometry utilizing the appropriate transformations. The numerical solutions, using the finite difference method, are computed for the flow rate, the shear stress, and the impedance. The influence of time, coupling number, half of the bifurcated angle and Womersley number on shear stress, flow rate and impedance (resistance to the flow) on both sides of the flow divider is shown graphically. It has been observed that the shear stress and flow rate are increasing with increase in the values of Womersley number and bifurcation angle on both sides of the apex. The shear stress is increasing along the inner wall and decreasing along the outer wall of the daughter artery with an increase in the value of coupling number. Further, it has been noticed that the shear stress, flow rate, and impedance are perturbed largely near to the apex in the parent artery due to the presence of backflow near the apex.

Keywords: micropolar fluid, bifurcated artery, stenosis, back flow, secondary flow, pulsatile flow, Womersley number

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: M. Gobinath, S. Balaji

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Assumptions in model inputs: Grade of concrete=40 N/mm2 (for slab), Grade of concrete=40 N/mm2 (for shear wall), Grade of Structural steel (plate girder)=350 N/mm2 (yield strength), Ultimate strength of structural steel=490 N/mm2, Grade of rebar=500 N/mm2 (yield strength), Applied Load=1716 kN (un-factored). Following assumptions are made for the mathematical modelling of RCC with steel embedment: (1) The bond between the structural steel and concrete is neglected. (2) The stiffener is provided with shear studs to transfer the shear force. Hence nodal connectivity is established between solid nodes (concrete) and shell elements (stiffener) at those locations. (3) As the end reinforcements transfer either tension/compression, it is modeled as line element and connected to solid nodes. (4) In order to capture the bearing of bottom flange on to the concrete, the line element of plan size of solid equal to the cross section of line elements is connected between solid and shell elements below for bottom flange and above for top flange. (5) As the concrete cannot resist tension at the interface (i.e., between structural steel and RCC), the tensile stiffness is assigned as zero and only compressive stiffness is enabled to take. Hence, non-linear static analysis option is invoked.

Keywords: structure, construction, signature tower, embedment design concept

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Authors: Meng Koon Lee, Mohammad Hosseini Fouladi, Satesh Narayana Namasivayam

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Research is focused on the response of soundboards of Classical guitars at frequencies up to 5 kHz as the soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. A thin rectangular plate of variable thickness that is simply-supported on all sides is used as an analytical model of the research. This model is used to study the response of the guitar soundboard as the latter can be considered as a modified form of a rectangular plate. Homotopy Perturbation Method (HPM) is selected as a mathematical method to obtain an analytical solution of the 4th-order parabolic partial differential equation of motion of the rectangular plate of constant thickness viewed as a linear problem. This procedure is generalized to the nonlinear problem of the rectangular plate with variable thickness and an analytical solution can also be obtained. Sound power is used as a parameter to investigate the acoustic radiation of soundboards made from spruce using various bracing patterns. The sound power of soundboards made from Malaysian softwood such as damar minyak, sempilor or podo are investigated to determine the viability of replacing spruce as future materials for soundboards of Classical guitars.

Keywords: rectangular plates, analytical solution, homotopy perturbation, natural frequencies

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Authors: Sethu Lekshmi, Shahanas, Prettha P.

Abstract:

All existing protocols in wireless networks are mainly based on Carrier Sense Multiple Access with Collision avoidance. By applying collision detection in wireless networks, the time spent on collision can be reduced and thus improves system throughput. However in a real WLAN scenario due to the use of nonlinear modulation techniques only receiver can decided whether a packet loss take place, even there are multiple transmissions. In this proposed method, the receiver or Access Point detects the collision when multiple data packets are transmitted from different wireless stations. Whenever the receiver detects a collision, it transmits a jamming signal to all the transmitting stations so that they can immediately stop their on-going transmissions. We also provide preferential access to all collided packet to reduce unfairness and to increase system throughput by reducing contention. However, this preferential access will not block the channel for the long time. Here, an in-band transmission is considered in which both the data frames and control frames are transmitted in the same channel. We also provide a simple mathematical model for the proposed protocol and give the simulation result of WLAN scenario under various capture thresholds.

Keywords: 802.11, WLAN, capture effect, collision detection, collision resolution, receiver initiated

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Authors: Y. D. Lim, K. S. Yap, K. T. Ooi

Abstract:

Cross Vane Expander Compressor (CVEC) is a newly invented expander-compressor combined unit, where it is introduced to replace the compressor and the expansion valve in traditional refrigeration system. The mathematical model of CVEC has been developed to examine its performance, and it was found that the energy consumption of a conventional refrigeration system was reduced by as much as 18%. It is believed that energy consumption can be further reduced by optimizing the device. In this study, the coefficient of performance (COP) of CVEC has been optimized under predetermined operational parameters and constrained main design parameters. Several main design parameters of CVEC were selected to be the variables, and the optimization was done with theoretical model in a simulation program. The theoretical model consists of geometrical model, dynamic model, heat transfer model and valve dynamics model. Complex optimization method, which is a constrained, direct search and multi-variables method was used in the study. As a result, the optimization study suggested that with an appropriate combination of design parameters, a 58% COP improvement in CVEC R134a refrigeration system is possible.

Keywords: COP, cross vane expander-compressor, CVEC, design, simulation, refrigeration system, air-conditioning, R134a, multi variables

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Authors: K. I. M. Guerra, L. A. P. Silva, J. C. Leal

Abstract:

This study aims to understand with more amplitude and clarity the behavior of a porous medium where a pressure wave travels, translated into relative displacements inside the material, using mathematical tools derived from topology and symplectic geometry. The paper starts with a given partial differential equation based on the continuity and conservation theorems to describe the traveling wave through the porous body. A solution for this equation is proposed after all boundary, and initial conditions are fixed, and it’s accepted that the solution lies in a manifold U of purely spatial dimensions and that is embedded in the Real n-dimensional manifold, with spatial and kinetic dimensions. It’s shown that the U manifold of lower dimensions than IRna, where it is embedded, inherits properties of the vector spaces existing inside the topology it lies on. Then, a second manifold (U*), embedded in another space called IRnb of stress dimensions, is proposed and there’s a non-degenerative function that maps it into the U manifold. This relation is proved as a transformation in between two corresponding admissible solutions of the differential equation in distinct dimensions and properties, leading to a more visual and intuitive understanding of the whole dynamic process of a stress wave through a porous medium and also highlighting the dimensional invariance of Terzaghi’s theory for any coordinate system.

Keywords: poremechanics, soil dynamics, symplectic geometry, wave propagation

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Authors: Allouache Nadia

Abstract:

Solid adsorption cooling machines have been extensively studied recently. They constitute very attractive solutions recover important amount of industrial waste heat medium temperature and to use renewable energy sources such as solar energy. The development of the technology of these machines can be carried out by experimental studies and by mathematical modelisation. This last method allows saving time and money because it is suppler to use to simulate the variation of different parameters. The adsorption cooling machines consist essentially of an evaporator, a condenser and a reactor (object of this work) containing a porous medium, which is in our case the activated carbon reacting by adsorption with ammoniac. The principle can be described as follows: When the adsorbent (at temperature T) is in exclusive contact with vapour of adsorbate (at pressure P), an amount of adsorbate is trapped inside the micro-pores in an almost liquid state. This adsorbed mass m, is a function of T and P according to a divariant equilibrium m=f (T,P). Moreover, at constant pressure, m decreases as T increases, and at constant adsorbed mass P increases with T. This makes it possible to imagine an ideal refrigerating cycle consisting of a period of heating/desorption/condensation followed by a period of cooling/adsorption/evaporation. Effect of key parameters on the machine performances are analysed and discussed.

Keywords: activated carbon-ammoniac pair, effect of key parameters, numerical modeling, solar cooling machine

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Authors: H. D. Arora, Anjali Dhiman

Abstract:

Uncertainty is found everywhere and its understanding is central to decision making. Uncertainty emerges as one has less information than the total information required describing a system and its environment. Uncertainty and information are so closely associated that the information provided by an experiment for example, is equal to the amount of uncertainty removed. It may be pertinent to point out that uncertainty manifests itself in several forms and various kinds of uncertainties may arise from random fluctuations, incomplete information, imprecise perception, vagueness etc. For instance, one encounters uncertainty due to vagueness in communication through natural language. Uncertainty in this sense is represented by fuzziness resulting from imprecision of meaning of a concept expressed by linguistic terms. Fuzzy set concept provides an appropriate mathematical framework for dealing with the vagueness. Both information theory, proposed by Shannon (1948) and fuzzy set theory given by Zadeh (1965) plays an important role in human intelligence and various practical problems such as image segmentation, medical diagnosis etc. Numerous approaches and theories dealing with inaccuracy and uncertainty have been proposed by different researcher. In the present communication, we generalize fuzzy entropy proposed by De Luca and Termini (1972) corresponding to Shannon entropy(1948). Further, some of the basic properties of the proposed measure were examined. We also applied the proposed measure to the real life decision making problem.

Keywords: entropy, fuzzy sets, fuzzy entropy, generalized fuzzy entropy, decision making

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Authors: Muhammad Abdullah, Asma Rashid Butt, Nauman Raza

Abstract:

Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs.

Keywords: viscous fluid, magnetic particles, fractional calculus, laplace transformation

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Authors: Reyhaneh Soltanshah, Hamid R. Zarandi

Abstract:

In order to be more efficient in industries that are related to computer systems, software testing is necessary despite spending time and money. In the embedded system software test, complete knowledge of the embedded system architecture is necessary to avoid significant costs and damages. Software tests increase the price of the final product. The aim of this article is to provide a method to reduce time and cost in tests based on program structure. First, a complete review of eleven white box test methods based on ISO/IEC/IEEE 29119 2015 and 2021 versions has been done. The proposed algorithm is designed using two versions of the 29119 standards, and some white-box testing methods that are expensive or have little coverage have been removed. On each of the functions, white box test methods were applied according to the 29119 standard and then the proposed algorithm was implemented on the functions. To speed up the implementation of the proposed method, the Unity framework has been used with some changes. Unity framework can be used in embedded software testing due to its open source and ability to implement white box test methods. The test items obtained from these two approaches were evaluated using a mathematical ratio, which in various software mining reduced between 50% and 80% of the test cost and reached the desired result with the minimum number of test items.

Keywords: embedded software, reduce costs, software testing, white-box testing

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