Search results for: multifractal exponent

Authors: Johnson Audu, Faisal Fairag

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In a bounded subset of R^d, d=2 or 3, we consider the Darcy-Forchheimer power model with the exponent 1 < m ≤ 2 for a single-phase strong-inertia fluid flow in a porous medium. Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence and uniqueness of solution (u, p) in L^(m+1 ) (Ω)^d X (W^(1,(m+1)/m) (Ω)^d ⋂L_0^2 (Ω)^d) and its stability.

Keywords: porous media, power law, strong inertia, nonlinear, monotone type

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: taylor rule, monetary system, chaos theory, lyapunov exponent, GMM estimator

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Authors: T. K. Dutta, K. K. Das, N. Dutta

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The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.

Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions

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Authors: Valeria Bondarenko

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In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

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In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: memristor, chaotic circuit, dynamical behavior, chaotic system

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Xin-Yan Ji, Jing Wang, Chang Liu, Yan-Qiang Bi, Zhong-Xu Xu, Xi-Yuan Li

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Thermal tests of electronic units are critically important for the reliability validation and performance demonstration of the spacecraft hard-wares. The tailoring equation in MIL-STD-1540 is based on fatigue of solder date. In the present paper, a new test condition tailoring expression is proposed to fit different thermo-mechanical fatigue and different subsystems, by introducing an integrated evaluating method for the fatigue acceleration exponent. The validate test has been accomplished and the data has been analyzed and compared with that from the MIL-STD-1540 tailoring equations. The results are encouraging and reasonable.

Keywords: thermal cycling test, thermal fatigue, tailoring equation, test condition planning

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: R. Sadeghzadegan, S. A. Naeini, A. Mirzaii

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In this article, the results of a series of carefully conducted laboratory test program were represented to determine the small strain shear modulus of sand mixed with a range of kaolinite including zero to 30%. This was experimentally achieved using a triaxial cell equipped with bender element. Results indicate that small shear modulus tends to increase, while clay content decreases and effective confining pressure increases. The exponent of stress in the power model regression analysis was not sensitive to the amount of clay content for all sand clay mixtures, while coefficient A was directly affected by change in clay content.

Keywords: small shear modulus, bender element test, plastic fines, sand

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Authors: Kotbi Lakhdar, Hachi Mostefa

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We show that a simple transformation between the regular lattices (the square, the triangular, and the honeycomb) belonging to the same dimensionality can explain in a natural way the universality of the critical exponents found in phase transitions and critical phenomena. It suffices that the Hamiltonian and the lattice present similar writing forms. In addition, it appears that if a property can be calculated for a given lattice then it can be extrapolated simply to any other lattice belonging to the same dimensionality. In this study, we have restricted ourselves on the spectral power amplification (SPA), we note that the SPA does not have an effect on the critical exponents but does have an effect by the criticality temperature of the lattice; the generalisation to other lattice could be shown according to the containment principle.

Keywords: ising model, phase transitions, critical temperature, critical exponent, spectral power amplification

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Authors: Olga I. Moskalenko, Vladislav A. Khanadeev, Anastasya D. Koloskova, Alexey A. Koronovskii, Anatoly A. Pivovarov

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Generalized synchronization is one of the most intricate phenomena in nonlinear science. It can be observed both in systems with a unidirectional and mutual type of coupling including the complex networks. Such a phenomenon has a number of practical applications, for example, for the secure information transmission through the communication channel with a high level of noise. Known methods for the secure information transmission needs in the increase of the privacy of data transmission that arises a question about the observation of such phenomenon in systems with a complex topology of chaotic attractor possessing two or more positive Lyapunov exponents. The present report is devoted to the study of such phenomenon in two unidirectionally and mutually coupled dynamical systems being in chaotic (with one positive Lyapunov exponent) and hyperchaotic (with two or more positive Lyapunov exponents) regimes, respectively. As the systems under study, we have used two mutually coupled modified Lorenz oscillators and two unidirectionally coupled time-delayed generators. We have shown that in both cases the generalized synchronization regime can be detected by means of the calculation of Lyapunov exponents and phase tube approach whereas due to the complex topology of attractor the nearest neighbor method is misleading. Moreover, the auxiliary system approaches being the standard method for the synchronous regime observation, for the mutual type of coupling results in incorrect results. To calculate the Lyapunov exponents in time-delayed systems we have proposed an approach based on the modification of Gram-Schmidt orthogonalization procedure in the context of the time-delayed system. We have studied in detail the mechanisms resulting in the generalized synchronization regime onset paying a great attention to the field where one positive Lyapunov exponent has already been become negative whereas the second one is a positive yet. We have found the intermittency here and studied its characteristics. To detect the laminar phase lengths the method based on a calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been verified using the example of two unidirectionally coupled Rössler systems being in the band chaos regime. We have revealed the main characteristics of intermittency, i.e. the distribution of the laminar phase lengths and dependence of the mean length of the laminar phases on the criticality parameter, for all systems studied in the report. This work has been supported by the Russian President's Council grant for the state support of young Russian scientists (project MK-531.2018.2).

Keywords: complex topology of attractor, generalized synchronization, hyperchaos, Lyapunov exponents

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Authors: Md Kamruzzaman, Lyazid Djenidi, R. A. Antonia

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This paper reports an experimental investigation of the energy spectrum of turbulent velocity fields at low Reynolds numbers ( Rλ ) in grid turbulence. Hot wire measurements are carried out in grid turbulence with subjected to a 1.36:1 contraction of the wind tunnel. Three different grids are used: (i) large square perforated grid (mesh size 43.75 mm), (ii) small square perforated grid (mesh size 14 and (iii) woven mesh grid (mesh size 5mm). The results indicate that the energy spectrum at small Rλ does not follow Kolmogorov’s universal scaling. It is further found that the critical Reynolds number,Rλ,ϲ below which the scaling breaks down is around 25.

Keywords: energy spectrum, Taylor microscale, Reynolds number, turbulent kinetic energy, decay exponent

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Authors: A. Kraiem, A. Ayadi

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The squeeze flow tests were studied by many authors to measure the rheological properties of fluid. Experimental squeezing flow test with constant area between two parallel disks of bitumen is investigated in the present work. The effect of the temperature, the process of preparing the sample and the gap between the discs were discussed. The obtained results were compared with the theoretical models. The behavior of bitumen depends on the viscosity and the yield stress. Thus, the bitumen was presented as a power law for a small power law exponent and as a biviscous fluid when the viscosity ratio was smaller than one. Also, the influence of the ambient temperature is required for the compression test. Therefore, for a high temperature the yield stress decrease.

Keywords: bitumen, biviscous fluid, squeeze flow, viscosity, yield stress

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Authors: Sania Ashraf

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The paper focuses on the prevalence of informational efficiency and integration of GCC Shariah Equity market for the period of 01st January 2010 to 31st June 2015 with daily equity returns of Kuwait, Oman, Qatar, Bahrain, Saudi Arabia and United Arab Emirates. The study employs traditional as well as the modern approach of tracing out the efficiency and integration in the return series. From the results of efficiency it was observed that the market lacked efficiency in terms of its past information. The results of integration test clearly indicates that there was a long memory in the returns of GCC Shariah during the study period. Hence it was concluded and proved that the returns of all GCC Equity Shariah were not informationally efficient but fractionally integrated during the study period.

Keywords: efficiency, Fama, GCC shariah, hurst exponent, integration, serial correlation

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Authors: Jitendra Kumar Quamara, Sohan Lal, Pushkar Raj

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Electrical conduction behavior of liquid crystalline polyurethane (LCPU) has been investigated under transient conditions in the operating temperature range 50-220°C at various electric fields of 4.35-43.45 kV/cm. The transient currents show the hyperbolic decay character and the decay exponent ∆t (one tenth decay time) dependent on field as well as on temperature. The increase in I0/Is values (where I0 represents the current observed immediately after applying the voltage and Is represents the steady state current) and the variation of mobility at high operating temperatures shows the appearance of mesophase. The origin of transient currents has been attributed to the dipolar nature of carbonyl (C＝O) groups in the main chain of LCPU and the trapping charge carriers.

Keywords: electrical conduction, transient current, liquid crystalline polymers, mesophase

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Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay

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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.

Keywords: autocorrelation function, density fluctuation, GEMC, simulation

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Authors: Hacer Yeldan, Erhan Akamca, Sedat Gündogdu

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Length-Weight and Length-length relationship were estimated of 14 species Sparidae (Boops boops, Diplodus annularis, Diplodus cervinus, Dipladus puntazzo, Diplodus sargus, Diplodus vulgaris, Lithognathus mormyrus, Oblada melanura, Pagellus acarne, Pagellus erythrinus, Pagrus auriga, Pagrus caeruleostictus, Sarpa salpa, Sparus aurata) sampled from in the Northeastern Mediterranean Sea coast of Turkey, Iskenderun Bay. Samples were collected from July 2014 to June 2015, using bottom trawl and trammel net into three different depth; 0-10 m, 10-20 m, 20-50m. Length-length relationships were determined size measurements: standard length (SL) and fork length (FL) to total length (TL) for fish species. The relationships between TL, FL and TL, SL were all linear. The values of the exponent b of the length-weight relationships ranged between 2.685 and 3.473. The type of growth for fish species was algometric growth.

Keywords: Sparidae, Iskenderun bay, length-length, length-weight relationships

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Muhammad Naeem, Abdus Salam, Sumera Yasmin, Abir Ishtiaq

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In the present study, eighty-three wild Oreochromis aureus of different body size ranging 5.3-14.6 cm in total length were collected from the River Chenab, District Muzzafer Garh, Pakistan to investigate the parameters of length –weight, length-length relationships and condition factor in relation to size. Each fish was measured and weighed on arrival at laboratory. Log transformed regressions were used to test the allometric growth. Length-weight relationship was found highly significant (r = 0.964; P < 0.01). The values of exponent “ b” in Length–weight regression (W=aL^b), deviated from 3, showing isometric growth (b = 2.75). Results for LLRs indicated that these are highly correlated (P < 0.001). Condition factor (K) found constant with increasing body weight, however, showed negative influence with increasing total length.

Keywords: lenght-weight, Oreochromis aureus, morphometric study

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Authors: Tejeet Singh, Harmanjit Singh

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Creep behavior of thick-walled functionally graded cylinder consisting of AlSiC and subjected to internal pressure and high temperature has been analyzed. The functional relationship between strain rate with stress can be described by the well-known threshold stress based creep law with a stress exponent of five. The effect of imposing non-linear particle gradient on the distribution of creep stresses in the thick-walled functionally graded composite cylinder has been investigated. The study revealed that for the assumed non-linear particle distribution, the radial stress decreases throughout the cylinder, whereas the tangential, axial and effective stresses have averaging effect. The strain rates in the functionally graded composite cylinder could be reduced to significant extent by employing non-linear gradient in the distribution of reinforcement.

Keywords: functionally graded material, pressure, steady state creep, thick-cylinder

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Authors: Cesar Hernández, Diego Giral, Ingrid Páez

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This article proposes a hybrid algorithm for spectrum allocation in cognitive radio networks based on the algorithms Analytical Hierarchical Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to improve the performance of the spectrum mobility of secondary users in cognitive radio networks. To calculate the level of performance of the proposed algorithm a comparative analysis between the proposed AHP-TOPSIS, Grey Relational Analysis (GRA) and Multiplicative Exponent Weighting (MEW) algorithm is performed. Four evaluation metrics is used. These metrics are the accumulative average of failed handoffs, the accumulative average of handoffs performed, the accumulative average of transmission bandwidth, and the accumulative average of the transmission delay. The results of the comparison show that AHP-TOPSIS Algorithm provides 2.4 times better performance compared to a GRA Algorithm and, 1.5 times better than the MEW Algorithm.

Keywords: cognitive radio, decision making, hybrid algorithm, spectrum handoff, wireless networks

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Authors: Muhammad Naeem, Amina Zubari, Abdus Salam, Summera Yasmeen, Syed Ali Ayub Bukhari, Abir Ishtiaq

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In the present study, eighty three wild Oreochromis aureus of different body size ranging 5.3-14.6 cm in total length were collected from the River Chenab, District Muzzafer Garh, Pakistan to investigate the parameters of length –weight, length-length relationships and condition factor in relation to size. Each fish was measured and weighed on arrival at laboratory. Log transformed regressions were used to test the allometric growth. Length-weight relationship was found highly significant (r = 0.964; P < 0.01). The values of exponent “ b” in Length–weight regression (W=aLb), deviated from 3, showing isometric growth (b = 2.75). Results for LLRs indicated that these are highly correlated (P< 0.001). Condition factor (K) found constant with increasing body weight, however, showed negative influence with increasing total length.

Keywords: Oreochromis aureus, weight-length relationship, condition factor, predictive equations

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Authors: Gülşen Akın Evingür, Önder Pekcan

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The fractal analysis is a bridge between the microstructure and macroscopic properties of gels. Fractal structure is usually provided to define the complexity of crosslinked molecules. The complexity in gel systems is described by the fractal dimension (Df). In this study, polyacrylamide- graphene oxide (GO) composite gels were prepared by free radical crosslinking copolymerization. The fractal analysis of polyacrylamide- graphene oxide (GO) composite gels were analyzed in various GO contents during gelation and were investigated by using Fluorescence Technique. The analysis was applied to estimate Df s of the composite gels. Fractal dimension of the polymer composite gels were estimated based on the power law exponent values using scaling models. In addition, here we aimed to present the geometrical distribution of GO during gelation. And we observed that as gelation proceeded GO plates first organized themselves into 3D percolation cluster with Df=2.52, then goes to diffusion limited clusters with Df =1.4 and then lines up to Von Koch curve with random interval with Df=1.14. Here, our goal is to try to interpret the low conductivity and/or broad forbidden gap of GO doped PAAm gels, by the distribution of GO in the final form of the produced gel.

Keywords: composite gels, fluorescence, fractal, scaling

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Authors: Chaudhuri Manoj Kumar Swain, Susmita Das

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This paper explores a detailed procedure of predicting a path loss (PL) model and its application in estimating the coverage probability in a WiMAX network. For this a hybrid approach is followed in predicting an empirical PL model of a 2.65 GHz WiMAX network deployed in a suburban environment. Data collection, statistical analysis, and regression analysis are the phases of operations incorporated in this approach and the importance of each of these phases has been discussed properly. The procedure of collecting data such as received signal strength indicator (RSSI) through experimental set up is demonstrated. From the collected data set, empirical PL and RSSI models are predicted with regression technique. Furthermore, with the aid of the predicted PL model, essential parameters such as PL exponent as well as the coverage probability of the network are evaluated. This research work may assist in the process of deployment and optimisation of any cellular network significantly.

Keywords: WiMAX, RSSI, path loss, coverage probability, regression analysis

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Authors: Tibor Ajtai, Máté Pintér, Noémi Utry, Gergely Kiss-Albert, Andrea Palágyi, László Manczinger, Csaba Vágvölgyi, Gábor Szabó, Zoltán Bozóki

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According to the best knowledge of the authors, here we experimentally demonstrate first, a quantified correlation between the real-time measured optical feature of the ambient and the off-line measured toxicity data. Finally, using these correlations we are presenting a novel methodology for real time characterisation of ambient toxicity based on the multi wavelength aerosol phase photoacoustic measurement. Ambient carbonaceous particulate matter is one of the most intensively studied atmospheric constituent in climate science nowadays. Beyond their climatic impact, atmospheric soot also plays an important role as an air pollutant that harms human health. Moreover, according to the latest scientific assessments ambient soot is the second most important anthropogenic emission source, while in health aspect its being one of the most harmful atmospheric constituents as well. Despite of its importance, generally accepted standard methodology for the quantitative determination of ambient toxicology is not available yet. Dominantly, ambient toxicology measurement is based on the posterior analysis of filter accumulated aerosol with limited time resolution. Most of the toxicological studies are based on operational definitions using different measurement protocols therefore the comprehensive analysis of the existing data set is really limited in many cases. The situation is further complicated by the fact that even during its relatively short residence time the physicochemical features of the aerosol can be masked significantly by the actual ambient factors. Therefore, decreasing the time resolution of the existing methodology and developing real-time methodology for air quality monitoring are really actual issues in the air pollution research. During the last decades many experimental studies have verified that there is a relation between the chemical composition and the absorption feature quantified by Absorption Angström Exponent (AAE) of the carbonaceous particulate matter. Although the scientific community are in the common platform that the PhotoAcoustic Spectroscopy (PAS) is the only methodology that can measure the light absorption by aerosol with accurate and reliable way so far, the multi-wavelength PAS which are able to selectively characterise the wavelength dependency of absorption has become only available in the last decade. In this study, the first results of the intensive measurement campaign focusing the physicochemical and toxicological characterisation of ambient particulate matter are presented. Here we demonstrate the complete microphysical characterisation of winter time urban ambient including optical absorption and scattering as well as size distribution using our recently developed state of the art multi-wavelength photoacoustic instrument (4λ-PAS), integrating nephelometer (Aurora 3000) as well as single mobility particle sizer and optical particle counter (SMPS+C). Beyond this on-line characterisation of the ambient, we also demonstrate the results of the eco-, cyto- and genotoxicity measurements of ambient aerosol based on the posterior analysis of filter accumulated aerosol with 6h time resolution. We demonstrate a diurnal variation of toxicities and AAE data deduced directly from the multi-wavelength absorption measurement results.

Keywords: photoacoustic spectroscopy, absorption Angström exponent, toxicity, Ames-test

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Authors: T. T. Naas, Y. Lasbet, C. Kezrane

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The thermal control in many systems is widely accomplished applying mixed convection process due to its low cost, reliability and easy maintenance. Typical applications include the aircraft electronic equipment, rotating-disc heat exchangers, turbo machinery, and nuclear reactors, etc. Natural convection in an inclined square enclosure heated via wall heater has been studied numerically. Finite volume method is used for solving momentum and energy equations in the form of stream function–vorticity. The right and left walls are kept at a constant temperature, while the other parts are adiabatic. The range of the inclination angle covers a whole revolution. The method is validated for a vertical cavity. A general power law dependence of the Nusselt number with respect to the Rayleigh number with the coefficient and exponent as functions of the inclination angle is presented. For a fixed Rayleigh number, the inclination angle increases or decreases is found.

Keywords: natural convection in enclosure, inclined enclosure, Nusselt number, entropy generation analyze

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Authors: Daniel Rowe, Christopher R. Vogel, Richard H. J. Willden

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The University of Oxford’s recirculating water flume is a combined wave and current test tank with a 1 m depth, 1.1 m width, and 10 m long working section, and is capable of flow speeds up to 1 ms−1 . This study documents the hydrodynamic characteristics of the facility in preparation for experimental testing of horizontal axis tidal stream turbine models. The turbine to be tested has a rotor diameter of 0.6 m and is a modified version of one of two model-scale turbines tested in previous experimental campaigns. An Acoustic Doppler Velocimeter (ADV) was used to measure the flow at high temporal resolution at various locations throughout the flume, enabling the spatial uniformity and turbulence flow parameters to be investigated. The mean velocity profiles exhibited high levels of spatial uniformity at the design speed of the flume, 0.6 ms−1 , with variations in the three-dimensional velocity components on the order of ±1% at the 95% confidence level, along with a modest streamwise acceleration through the measurement domain, a target 5 m working section of the flume. A high degree of uniformity was also apparent for the turbulence intensity, with values ranging between 1-2% across the intended swept area of the turbine rotor. The integral scales of turbulence exhibited a far higher degree of variation throughout the water column, particularly in the streamwise and vertical scales. This behaviour is believed to be due to the high signal noise content leading to decorrelation in the sampling records. To achieve more realistic levels of vertical velocity shear in the flume, a simple procedure to practically generate target vertical shear profiles in open-channel flows is described. Here, the authors arranged a series of non-uniformly spaced parallel bars placed across the width of the flume and normal to the onset flow. By adjusting the resistance grading across the height of the working section, the downstream profiles could be modified accordingly, characterised by changes in the velocity profile power law exponent, 1/n. Considering the significant temporal variation in a tidal channel, the choice of the exponent denominator, n = 6 and n = 9, effectively provides an achievable range around the much-cited value of n = 7 observed at many tidal sites. The resulting flow profiles, which we intend to use in future turbine tests, have been characterised in detail. The results indicate non-uniform vertical shear across the survey area and reveal substantial corner flows, arising from the differential shear between the target vertical and cross-stream shear profiles throughout the measurement domain. In vertically sheared flow, the rotor-equivalent turbulence intensity ranges between 3.0-3.8% throughout the measurement domain for both bar arrangements, while the streamwise integral length scale grows from a characteristic dimension on the order of the bar width, similar to the flow downstream of a turbulence-generating grid. The experimental tests are well-defined and repeatable and serve as a reference for other researchers who wish to undertake similar investigations.

Keywords: acoustic doppler Velocimeter, experimental hydrodynamics, open-channel flow, shear profiles, tidal stream turbines

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Authors: Maor Farid, Oleg Gendelman

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The following study deals with fluid vibration of a liquid in a partially filled vessel under periodic ground excitation. This external excitation might lead to hidraulic impact applied on the vessel inner walls. In order to model these sloshing dynamic regimes, several equivalent mechanical models were suggested in the literature, such as series of pendula or mass-spring systems that are able to impact the inner tank walls. In the following study, we use the latter methodology, use parameter values documented in literature corresponding to cylindrical tanks and consider structural elasticity of the tank. The hydraulic impulses are modeled by the high-exponent potential function. Additional system parameters are found with the help of Finite-Element (FE) analysis. Model-driven stress assessment method is developed. Finally, vibration mitigation performances of both tuned mass damper (TMD) and nonlinear energy sink (NES) are examined.

Keywords: nonlinear energy sink (NES), reduced-order modelling, liquid sloshing, vibration mitigation, vibro-impact dynamics

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Authors: C. H. Shashikanth, M. J. Davidson, V. Suresh Babu

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The formability of metals depends on a number of variables such as strain, strain rate, and temperature. Though most of the metals are formable at room temperature, few are not. To evaluate the workability of such metals at elevated temperatures, thermomechanical experiments should be carried out to find out the forming temperatures and strain rates. Though a number of constitutive relations are available to correlate the material parameters and the corresponding formability at elevated temperatures, the constitutive rule proposed by Arrhenius has been used in this work. Thus, in the present work, the material constants such as A (constant), α (stress multiplier), β (constant), and n (stress exponent) of AA 2017 has been found by conducting a series of hot compression tests at different temperatures such as 400°C, 450°C, 500°C, and 550°C and at different strain rates such as 0.16, 0.18, and 0.2. True stress (σt), true strains (εt) deformation activation energy (Q), and the Zener-Hollomon parameter (Z value) were also calculated. The results indicate that the value of ln (Z) decreases as the temperature increases and it increases as the strain rate increases.

Keywords: hot compression test, aluminium alloy, flow stress, activation energy

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Authors: Riaz Ahmad, Jiazhong Zhang, Asma Farooqi

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In this study, mass transport between separation bubbles and the flow around a two-dimensional airfoil are numerically investigated using Lagrangian Coherent Structures (LCSs). Finite Time Lyapunov Exponent (FTLE) technique is used for the computation to identify invariant manifolds and LCSs. Moreover, the Characteristic Base Split (CBS) scheme combined with dual time stepping technique is applied to simulate such transient flow at low Reynolds number. We then investigate the evolution of vortex structures during the transport process with the aid of LCSs. To explore the vortex formation at the surface of the airfoil, the dynamics of separatrix is also taken into account which is formed by the combination of stable-unstable manifolds. The Lagrangian analysis gives a detailed understanding of vortex dynamics and separation bubbles which plays a significant role to explore the performance of the unsteady flow generated by the airfoil. Transport process and flow separation phenomena are studied extensively to analyze the flow pattern by Lagrangian point of view.

Keywords: transport phenomena, CBS Method, vortex formation, Lagrangian Coherent Structures

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