Search results for: homotopy perturbation

Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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Authors: Adriano Losso, Birgit Dämon, Stefan Mayr

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In vascular plants, water flows from roots to leaves in a metastable state, and even a small perturbation of the system can lead a sudden transition from the liquid to the vapor phase, resulting in xylem embolism (cavitation). Xylem embolism, induced by drought stress and/or freezing stress is caused by the aspiration of gaseous bubbles into xylem conduits from adjacent gas-filled compartments through pit membrane pores (‘air seeding’). At water potentials less negative than the threshold for air seeding, the surface tension (γ) stabilizes the air-water interface and thus prevents air from passing the pit pores. This hold is probably also true for conifers, where this effect occurs at the edge of the sealed torus. Accordingly, it was experimentally demonstrated that γ influences air seeding, but information on the relevance of this effect under field conditions is missing. In this study, we analyzed seasonal changes in γ of the xylem sap in two conifers growing at the alpine timberline (Picea abies and Pinus mugo). In addition, cut branches were perfused (40 min perfusion at 0.004 MPa) with different γ solutions (i.e. distilled and degassed water, 2, 5 and 15% (v/v) ethanol-water solution corresponding to a γ of 74, 65, 55 and 45 mN m-1, respectively) and their vulnerability to drought-induced embolism analyzed via the centrifuge technique (Cavitron). In both species, xylem sap γ changed considerably (ca. 53-67 and ca. 50-68 mN m-1 in P. abies and P. cembra, respectively) over the season. Branches perfused with low γ solutions showed reduced resistance against drought-induced embolism in both species. A significant linear relationship (P < 0.001) between P12, P50 and P88 (i.e. water potential at 12, 50 and 88% of the loss of conductivity) and xylem sap γ was found. Based on this correlation, a variation in P50 between -3.10 and -3.83 MPa (P. abies) and between -3.21 and -4.11 MPa (P. mugo) over the season could be estimated. Results demonstrate that changes in γ of the xylem sap can considerably influence a tree´s resistance to drought-induced embolism. They indicate that vulnerability analyses, normally conducted at a γ near that of pure water, might often underestimate vulnerabilities under field conditions. For studied timberline conifers, seasonal changes in γ might be especially relevant in winter, when frost drought and freezing stress can lead to an excessive embolism.

Keywords: conifers, Picea abies, Pinus mugo, timberline

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Authors: Siddharth Ahuja, T. M. Muruganandam

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An analytical investigation is performed to study the unsteady response of a one-dimensional, non-linear dynamic shock system to external downstream pressure perturbations in a supersonic flow in a varying area duct. For a given pressure ratio across a wind tunnel, the normal shock's location can be computed as per one-dimensional steady gas dynamics. Similarly, for some other pressure ratio, the location of the normal shock will change accordingly, again computed using one-dimensional gas dynamics. This investigation focuses on the small-time interval between the first steady shock location and the new steady shock location (corresponding to different pressure ratios). In essence, this study aims to shed light on the motion of the shock from one steady location to another steady location. Further, this study aims to create the foundation of the Unsteady Gas Dynamics field enabling further insight in future research work. According to the new pressure ratio, a pressure pulse, generated at the exit of the tunnel which travels and perturbs the shock from its original position, setting it into motion. During such activity, other numerous physical phenomena also happen at the same time. However, three broad phenomena have been focused on, in this study - Traversal of a Wave, Fluid Element Interactions and Wave Interactions. The above mentioned three phenomena create, alter and kill numerous waves for different conditions. The waves which are created by the above-mentioned phenomena eventually interact with the shock and set it into motion. Numerous such interactions with the shock will slowly make it settle into its final position owing to the new pressure ratio across the duct, as estimated by one-dimensional gas dynamics. This analysis will be extremely helpful in the prediction of inlet 'unstart' of the flow in a supersonic engine intake and its prominence with the incoming flow Mach number, incoming flow pressure and the external perturbation pressure is also studied to help design more efficient supersonic intakes for engines like ramjets and scramjets.

Keywords: analytical investigation, compression and expansion waves, fluid element interactions, shock trajectory, supersonic flow, unsteady gas dynamics, varying area duct, wave interactions

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Authors: Rehin Sulay, Anandhu Krishna, Jintumol Mathew, Vibin Ipe Thomas

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N-Nitrosodimethyl amine, the simplest member of the N-Nitrosoamine family, is a carcinogenic and mutagenic agent that has gained considerable research interest owing to its toxic nature. Ozonation of industrially important hydrazines such as unsymmetrical dimethylhydrazine (UDMH) or monomethylhydrazine (MMH) has been associated with NDMA formation and accumulation in the environment. UDMH/MMH - ozonation also leads to several other transformation products such as acetaldehyde dimethyl hydrazone (ADMH), tetramethyl tetra azene (TMT), diazomethane, methyl diazene, etc, which can be either precursors or competitors for NDMA formation.In this work, we explored the formation mechanism of ADMH and TMT from UDMH-ozonation and their further oxidation to NDMA using the second-order Moller Plesset perturbation theory employing the 6-311G(d) basis set. We have also investigated how MMH selectively forms methyl diazene and diazomethane under normal conditions and NDMA in the presence of excess ozone. Our calculations indicate that the reactions proceed via an initial H abstraction from the hydrazine –NH2 group followed by the oxidation of the generated N-radical species. The formation of ADMH from the UDMH-ozone reaction involves an acetaldehyde intermediate, which then reacts with a second UDMH molecule to generate ADMH. The preferable attack of ozone molecule on N=C bond of ADMH generates DMAN intermediate, which subsequently undergoes oxidation to form NDMA. Unlike other transformation products, TMT formation occurs via the dimerization of DMAN. Though there exist a N=N bonds in the TMT, which are preferable attacking sites for ozone, experimental studies show the lower yields of NDMA formation, which corroborates with the high activation barrier required for the process(42kcal/mol).Overall, our calculated results agree well with the experimental observations and rate constants. Computational calculations bring insights into the electronic nature and kinetics of the elementary reactions of this pathway, enabled by computed energies of structures that are not possible to access experimentally.

Keywords: reaction mechanism, ozonation, substituted hydrazine, transition state

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Authors: Zia R. Tahir, P. Mandal

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This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0°/+45°/-45°/0°] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

Keywords: CFRP composite cylindrical shell, asymmetric meshing technique, primary buckling, secondary buckling, linear eigenvalue analysis, non-linear riks analysis

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Authors: E. Ormeno, C. Gutigny, J. Ruffault, J. Madrigal, M. Guijarro, C. Lecareux, C. Ballini

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Mediterranean plant species feature numerous metabolic and morpho-physiological responses crucial to survive under both, typical Mediterranean drought conditions and future aggravated drought expected by climate change. Whether these adaptive responses will, in turn, increase the ecosystem perturbation in terms of fire hazard, is an issue that needs to be addressed. The aim of this study was to test whether recurrent and aggravated drought in the Mediterranean area favors the accumulation of waxes in leaf litter, with an eventual increase of litter flammability. The study was conducted in 2017 in a garrigue in Southern France dominated by Quercus coccifera, where two drought treatments were used: a treatment with recurrent aggravated drought consisting of ten rain exclusion structures which withdraw part of the annual precipitation since January 2012, and a natural drought treatment where Q. coccifera stands are free of such structures and thus grow under natural precipitation. Waxes were extracted with organic solvent and analyzed by GC-MS and litter flammability was assessed through measurements of the ignition delay, flame residence time and flame intensity (flame height) using an epiradiator as well as the heat of combustion using an oxygen bomb calorimeter. Results show that after 5 years of rain restriction, wax content in the cuticle of leaf litter increases significantly compared to shrubs growing under natural precipitation, in accordance with the theoretical knowledge which expects increases of cuticle waxes in green leaves in order to limit water evapotranspiration. Wax concentrations were also linearly and positively correlated to litter flammability, a correlation that lies on the high flammability own to the long-chain alkanes (C25-C31) found in leaf litter waxes. This innovative investigation shows that climate change is likely to favor ecosystem fire hazard through accumulation of highly flammable waxes in litter. It also adds valuable information about the types of metabolites that are associated with increasing litter flammability, since so far, within the leaf metabolic profile, only terpene-like compounds had been related to plant flammability.

Keywords: cuticular waxes, drought, flammability, litter

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Authors: Sharmin Sultana, Reinhard Schlickeiser

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A degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, degenerate/non-degenerate light nuclei, and non-degenerate heavy nuclei) is considered to investigate the propagation characteristics of electrostatic solitary waves (in the ionic scale length) theoretically and numerically. The ion-acoustic solitons are found to be associated with the modified ion-acoustic waves (MIAWs) in which inertia (restoring force) is provided by mass density of the light or heavy nuclei (degenerate pressure of the cold electrons). A mechanical-motion analog (Sagdeev-type) pseudo-potential approach is adopted to study the properties of large amplitude solitary waves. The basic properties of the large amplitude MIAWs and their existence domain in terms of soliton speed (Mach number) are examined. On the other hand, a multi-scale perturbation approach, leading to an evolution equation for the envelope dynamics, is adopted to derive the cubic nonlinear Schrödinger equation (NLSE). The criteria for the occurrence of modulational instability (MI) of the MIAWs are analyzed via the nonlinear dispersion relation of the NLSE. The possibility for the formation of highly energetic localized modes (e.g. peregrine solitons, rogue waves, etc.) is predicted in such DRQP medium. Peregrine solitons or rogue waves with amplitudes of several times of the background are observed to form in DRQP. The basic features of these modulated waves (e.g. envelope solitons, peregrine solitons, and rogue waves), which are found to form in DRQP, and their MI criteria (on the basis of different intrinsic plasma parameters), are investigated. It is emphasized that our results should be useful in understanding the propagation characteristics of localized disturbances and the modulation dynamics of envelope solitons, and their instability criteria in astrophysical DRQP system (e.g. white dwarfs, neutron stars, etc., where matters under extreme conditions are assumed to exist) and also in ultra-high density experimental plasmas.

Keywords: degenerate plasma, envelope solitons, modified ion-acoustic waves, modulational instability, rogue waves

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

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The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Green–Naghdi equations, nonlinearity, numerical prediction, sloshing waves, solitary waves

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Authors: Agnieszka Krzemińska, Katarzyna Świderek, Vicente Molinier, Piotr Paneth

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In order to understand in details the interactions between ligands and the enzyme isotope effects were studied between clinically used drugs that bind in the active site of Human Immunodeficiency Virus Reverse Transcriptase, HIV-1 RT, as well as triazole-based inhibitor that binds in the allosteric pocket of this enzyme. The magnitudes and origins of the resulting binding isotope effects were analyzed. Subsequently, binding isotope effect of the same triazole-based inhibitor bound in the active site were analyzed and compared. Together, these results show differences in binding origins in two sites of the enzyme and allow to analyze binding mode and place of newly synthesized inhibitors. Typical protocol is described below on the example of triazole ligand in the allosteric pocket. Triazole was docked into allosteric cavity of HIV-1 RT with Glide using extra-precision mode as implemented in Schroedinger software. The structure of HIV-1 RT was obtained from Protein Data Bank as structure of PDB ID 2RKI. The pKa for titratable amino acids was calculated using PROPKA software, and in order to neutralize the system 15 Cl- were added using tLEaP package implemented in AMBERTools ver.1.5. Also N-terminals and C-terminals were build using tLEaP. The system was placed in 144x160x144Å3 orthorhombic box of water molecules using NAMD program. Missing parameters for triazole were obtained at the AM1 level using Antechamber software implemented in AMBERTools. The energy minimizations were carried out by means of a conjugate gradient algorithm using NAMD. Then system was heated from 0 to 300 K with temperature increment 0.001 K. Subsequently 2 ns Langevin−Verlet (NVT) MM MD simulation with AMBER force field implemented in NAMD was carried out. Periodic Boundary Conditions and cut-offs for the nonbonding interactions, range radius from 14.5 to 16 Å, are used. After 2 ns relaxation 200 ps of QM/MM MD at 300 K were simulated. The triazole was treated quantum mechanically at the AM1 level, protein was described using AMBER and water molecules were described using TIP3P, as implemented in fDynamo library. Molecules 20 Å apart from the triazole were kept frozen, with cut-offs established on range radius from 14.5 to 16 Å. In order to describe interactions between triazole and RT free energy of binding using Free Energy Perturbation method was done. The change in frequencies from ligand in solution to ligand bounded in enzyme was used to calculate binding isotope effects.

Keywords: binding isotope effects, molecular dynamics, HIV, reverse transcriptase

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Authors: Amit Kumar, Archana Gupta, Poonam Tandon, E. D. D’Silva

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Nonlinear optical (NLO) materials are the key materials for the fast processing of information and optical data storage applications. In the last decade, materials showing nonlinear optical properties have been the object of increasing attention by both experimental and computational points of view. Chalcones are one of the most important classes of cross conjugated NLO chromophores that are reported to exhibit good SHG efficiency, ultra fast optical nonlinearities and are easily crystallizable. The basic structure of chalcones is based on the π-conjugated system in which two aromatic rings are connected by a three-carbon α, β-unsaturated carbonyl system. Due to the overlap of π orbitals, delocalization of electronic charge distribution leads to a high mobility of the electron density. On a molecular scale, the extent of charge transfer across the NLO chromophore determines the level of SHG output. Hence, the functionalization of both ends of the π-bond system with appropriate electron donor and acceptor groups can enhance the asymmetric electronic distribution in either or both ground and excited states, leading to an increased optical nonlinearity. In this research, the experimental and theoretical study on the structure and vibrations of (2E)-3-[4-(methylsulfanyl) phenyl]-1-(3-bromophenyl) prop-2-en-1-one (3Br4MSP) is presented. The FT-IR and FT-Raman spectra of the NLO material in the solid phase have been recorded. Density functional theory (DFT) calculations at B3LYP with 6-311++G(d,p) basis set were carried out to study the equilibrium geometry, vibrational wavenumbers, infrared absorbance and Raman scattering activities. The interpretation of vibrational features (normal mode assignments, for instance) has an invaluable aid from DFT calculations that provide a quantum-mechanical description of the electronic energies and forces involved. Perturbation theory allows one to obtain the vibrational normal modes by estimating the derivatives of the Kohn−Sham energy with respect to atomic displacements. The molecular hyperpolarizability β plays a chief role in the NLO properties, and a systematical study on β has been carried out. Furthermore, the first order hyperpolarizability (β) and the related properties such as dipole moment (μ) and polarizability (α) of the title molecule are evaluated by Finite Field (FF) approach. The electronic α and β of the studied molecule are 41.907×10-24 and 79.035×10-24 e.s.u. respectively, indicating that 3Br4MSP can be used as a good nonlinear optical material.

Keywords: DFT, MEP, NLO, vibrational spectra

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Authors: Shenghong Huang, Weirong Wang, Xisheng Luo, Xinzhu Li, Xinwen Zhao

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Understanding of material mixing induced by Richtmyer-Meshkov instability (RMI) at extreme shock compressing conditions (high energy density environment: P >> 100GPa, T >> 10000k) is of great significance in engineering and science, such as inertial confinement fusion(ICF), supersonic combustion, etc. Turbulent mixing induced by RMI is a kind of complex fluid dynamics, which is closely related with hydrodynamic conditions, thermodynamic states, material physical properties such as compressibility, strength, surface tension and viscosity, etc. as well as initial perturbation on interface. For phenomena in ordinary thermodynamic conditions (low energy density environment), many investigations have been conducted and many progresses have been reported, while for mixing in extreme thermodynamic conditions, the evolution may be very different due to ionization as well as large difference of material physical properties, which is full of scientific problems and academic interests. In this investigation, the first principle based molecular dynamic method is applied to study metal Lithium and gas Hydrogen (Li-H2) interface mixing in micro/meso scale regime at different shock compressing loading speed ranging from 3 km/s to 30 km/s. It's found that, 1) Different from low-speed shock compressing cases, in high-speed shock compresing (>9km/s) cases, a strong acceleration of metal/gas interface after strong shock compression is observed numerically, leading to a strong phase inverse and spike growing with a relative larger linear rate. And more specially, the spike growing rate is observed to be increased with shock loading speed, presenting large discrepancy with available empirical RMI models; 2) Ionization is happened in shock font zone at high-speed loading cases(>9km/s). An additional local electric field induced by the inhomogeneous diffusion of electrons and nuclei after shock font is observed to occur near the metal/gas interface, leading to a large acceleration of nuclei in this zone; 3) In conclusion, the work of additional electric field contributes to a mechanism of RMI in micro/meso scale regime at extreme shock compressing conditions, i.e., a Rayleigh-Taylor instability(RTI) is induced by additional electric field during RMI mixing process and thus a larger linear growing rate of interface spike.

Keywords: ionization, micro/meso scale, material mixing, shock

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Authors: A. C. Blaga, A. Cârlescu, M. Turnea, A. I. Galaction, D. Caşcaval

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The performance of an aerobic stirred bioreactor for fungal fermentation was analyzed on the basis of mixing time and oxygen mass transfer coefficient, by quantifying the influence of some specific geometrical and operational parameters of the bioreactor, as well as the rheological behavior of Penicillium chrysogenum broth (free mycelia and mycelia aggregates). The rheological properties of the fungus broth, controlled by the biomass concentration, its growth rate, and morphology strongly affect the performance of the bioreactor. Experimental data showed that for both morphological structures the accumulation of fungus biomass induces a significant increase of broths viscosity and modifies the rheological behavior. For lower P. chrysogenum concentrations (both morphological conformations), the mixing time initially increases with aeration rate, reaches a maximum value and decreases. This variation can be explained by the formation of small bubbles, due to the presence of solid phase which hinders the bubbles coalescence, the rising velocity of bubbles being reduced by the high apparent viscosity of fungus broths. By biomass accumulation, the variation of mixing time with aeration rate is gradually changed, the continuous reduction of mixing time with air input flow increase being obtained for 33.5 g/l d.w. P. chrysogenum. Owing to the superior apparent viscosity, which reduces considerably the relative contribution of mechanical agitation to the broths mixing, these phenomena are more pronounced for P. chrysogenum free mycelia. Due to the increase of broth apparent viscosity, the biomass accumulation induces two significant effects on oxygen transfer rate: the diminution of turbulence and perturbation of bubbles dispersion - coalescence equilibrium. The increase of P. chrysogenum free mycelia concentration leads to the decrease of kla values. Thus, for the considered variation domain of the main parameters taken into account, namely air superficial velocity from 8.36 10-4 to 5.02 10-3 m/s and specific power input from 100 to 500 W/m3, kla was reduced for 3.7 times for biomass concentration increase from 4 to 36.5 g/l d.w. The broth containing P. crysogenum mycelia aggregates exhibits a particular behavior from the point of view of oxygen transfer. Regardless of bioreactor operating conditions, the increase of biomass concentration leads initially to the increase of oxygen mass transfer rate, the phenomenon that can be explained by the interaction of pellets with bubbles. The results are in relation with the increase of apparent viscosity of broths corresponding to the variation of biomass concentration between the mentioned limits. Thus, the apparent viscosity of the suspension of fungus mycelia aggregates increased for 44.2 times and fungus free mycelia for 63.9 times for CX increase from 4 to 36.5 g/l d.w. By means of the experimental data, some mathematical correlations describing the influences of the considered factors on mixing time and kla have been proposed. The proposed correlations can be used in bioreactor performance evaluation, optimization, and scaling-up.

Keywords: biomass concentration, mixing time, oxygen mass transfer, P. chrysogenum broth, stirred bioreactor

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Authors: Lalita, Niladri Sarkar, Subhasis Ghosh

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Since the discovery of high temperature superconductivity (HTSC) in cuprates, several aspects of this phenomena have fascinated physics community. The most debated one is the linear temperature dependence of normal state resistivity over wide range of temperature in violation of with Fermi liquid theory. The linear-in-T resistivity (LITR) is the indication of strongly correlated metallic, known as “strange metal”, attributed to non Fermi liquid theory (NFL). The proximity of superconductivity to LITR suggests that there may be underlying common origin. The LITR has been shown to be due to unknown dissipative phenomena, restricted by quantum mechanics and commonly known as ‘‘Planckian dissipation” , the term first coined by Zaanen and the associated inelastic scattering time τ and given by 1/τ=αkBT/ℏ, where ℏ, kB and α are reduced Planck’s constant, Boltzmann constant and a dimensionless constant of order of unity, respectively. Since the first report, experimental support for α ~ 1 is appearing in literature. There are several striking issues which remain to be resolved if we desire to find out or at least get a clue towards microscopic origin of maximal dissipation in cuprates. (i) Universality of α ~ 1, recently some doubts have been raised in some cases. (ii) So far, Planckian dissipation has been demonstrated in overdoped Cuprates, but if the proximity to quantum criticality is important, then Planckian dissipation should be observed in optimally doped and marginally underdoped cuprates. The link between Planckian dissipation and quantum criticality still remains an open problem. (iii) Validity of Planckian dissipation in all cuprates is an important issue. Here, we report reversible change in the superconducting behavior of high temperature superconductor Bi2Sr2Ca2Cu3O10+δ (Bi-2223) under dynamic doping induced by photo-excitation. Two doped Bi-223 samples, which are x = 0.16 (optimal-doped), x = 0.145 (marginal-doped) have been used for this investigation. It is realized that steady state photo-excitation converts magnetic Cu2+ ions to nonmagnetic Cu1+ ions which reduces superconducting transition temperature (Tc) by killing superfluid density. In Bi-2223, one would expect the maximum of suppression of Tc should be at charge transfer gap. We have observed suppression of Tc starts at 2eV, which is the charge transfer gap in Bi-2223. We attribute this transition due to Cu-3d9(Cu2+) to Cu-3d10(Cu+), known as d9 − d10 L transition, photoexcitation makes some Cu ions in CuO2 planes as spinless non-magnetic potential perturbation as Zn2+ does in CuO2 plane in case Zn-doped cuprates. The resistivity varies linearly with temperature with or without photo-excitation. Tc can be varied by almost by 40K be photoexcitation. Superconductivity can be destroyed completely by introducing ≈ 2% of Cu1+ ions for this range of doping. With this controlled variation of Tc and resistivity, detailed investigation has been carried out to reveal Planckian dissipation underdoped to optimally doped Bi-2223. The most important aspect of this investigation is that we could vary Tc dynamically and reversibly, so that LITR and associated Planckian dissipation can be studied over wide ranges of Tc without changing the doping chemically.

Keywords: linear resistivity, HTSC, Planckian dissipation, strange metal

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Authors: Lamia Bouzgarrou, Amira Omrane, Leila Mrabet, Taoufik Khalfallah

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Background and aims: School accidents are one of the leading causes of morbidity and mortality among pupils and students. Indeed, they may induce an elevated number of lost school days, heavy emotional and physical disabilities, and financial costs on the victims and their families. This study aims to evaluate the annual incidence of school accidents in the central Tunisian governorate of Mahdia and to identify the epidemiological profile of victims and risk factors of these accidents. Methods: A retrospective study was conducted over the period of 5 school years, focusing on school accidents that occurred in public educational institutions (primary, basic, secondary and university) in the governorate of Mahdia (area = 2 966 km² and number of inhabitants in 2014 = 410 812). All accidents declared near the only official insurance of this type of injuries (MASU: Mutual School and University Accidents), and initially taken in charge at the University Hospital of Mahdia were included. Data was collected from the MASU reporting forms and the medical records of emergency and other specialized hospital departments. Results: With 3248 identified victims, the annual incidence of school accidents was equal to 0.69 per 100 pupils and students per year. The average age of victims was 14.51 ± 0.059 years and the sex ratio was 1.58. Pupils aged between 12 and 15 years, were concerned by 46.7% of the identified accidents. The practice of sports was the most relevant circumstances of these accidents (76.2 %). In 56.58 % of cases, falls were the leading mechanism. Bruises and fractures were the most frequent lesions (32.43 % and 30.51 %). Serious school accidents were noted in 28% of cases with hospitalization in 2.27 % of them. The average lost school days, was 12.23±1.73 days. Accidents occurring during sports or leisure activities were significantly more serious (p= 0.021). Furthermore, the frequency of hospitalization was significantly higher among boys (2.81% vs. 1.43%; p= 0.035), students ≤11 years (p= 0.008), and following crush trauma (p= 0.000). In addition, the surgical interventions were statistically more frequent among male victims (p=0.00), accidents occurring during physical education sessions (p=0.000); those associated to falls (p=0.000) and to crushes mechanisms (p=0.002), and injuries affecting lower limbs (p=0.000). Following this Multi-varied analysis concluded that the severity of school accident is correlated to the activity practiced during the trauma and the geographical location of the school. Conclusion: Children and adolescents are one of the most vulnerable groups against incidents with the risk of permanent disability, mainly related to the perturbation of the growth process and physiological limitations. Our five-year study, objectified a real elevate incidence of school accident among children and adolescents, with a considerable rate of severe injuries. In any community, the promotion of adolescents and children’s health is an important indicator of the public health level. Thus, it’s important to develop a multidisciplinary prevention strategy of school accident, based on safety and security rules and adapted to the specificity of our context.

Keywords: children and adolescents, children health, injuries and disability, school accident

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Authors: Samuele Viaro, Pierre Ricco

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Görtler instabilities generate in boundary layers from an unbalance between pressure and centrifugal forces caused by concave surfaces. Their spatial streamwise evolution influences transition to turbulence. It is therefore important to understand even the early stages where perturbations, still small, grow linearly and could be controlled more easily. This work presents a rigorous theoretical framework for compressible flows using the linearized unsteady boundary region equations, where only the streamwise pressure gradient and streamwise diffusion terms are neglected from the full governing equations of fluid motion. Boundary and initial conditions are imposed through an asymptotic analysis in order to account for the interaction of the boundary layer with free-stream turbulence. The resulting parabolic system is discretize with a second-order finite difference scheme. Realistic flow parameters are chosen from wind tunnel studies performed at supersonic and subsonic conditions. The Mach number ranges from 0.5 to 8, with two different radii of curvature, 5 m and 10 m, frequencies up to 2000 Hz, and vortex spanwise wavelengths from 5 mm to 20 mm. The evolution of the perturbation flow is shown through velocity, temperature, pressure profiles relatively close to the leading edge, where non-linear effects can still be neglected, and growth rate. Results show that a global stabilizing effect exists with the increase of Mach number, frequency, spanwise wavenumber and radius of curvature. In particular, at high Mach numbers curvature effects are less pronounced and thermal streaks become stronger than velocity streaks. This increase of temperature perturbations saturates at approximately Mach 4 flows, and is limited in the early stage of growth, near the leading edge. In general, Görtler vortices evolve closer to the surface with respect to a flat plate scenario but their location shifts toward the edge of the boundary layer as the Mach number increases. In fact, a jet-like behavior appears for steady vortices having small spanwise wavelengths (less than 10 mm) at Mach 8, creating a region of unperturbed flow close to the wall. A similar response is also found at the highest frequency considered for a Mach 3 flow. Larger vortices are found to have a higher growth rate but are less influenced by the Mach number. An eigenvalue approach is also employed to study the amplification of the perturbations sufficiently downstream from the leading edge. These eigenvalue results are compared with the ones obtained through the initial value approach with inhomogeneous free-stream boundary conditions. All of the parameters here studied have a significant influence on the evolution of the instabilities for the Görtler problem which is indeed highly dependent on initial conditions.

Keywords: compressible boundary layers, Görtler instabilities, receptivity, turbulence transition

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Authors: Pawel Martynowicz

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Vibrations are a crucial problem for slender structures such as towers, masts, chimneys, wind turbines, bridges, high buildings, etc., that is why most of them are equipped with vibration attenuation or fatigue reduction solutions. In this work, a slender structure (i.e., wind turbine tower-nacelle model) equipped with nonlinear, semiactive tuned vibration absorber(s) is analyzed. For this study purposes, magnetorheological (MR) dampers are used as semiactive actuators. Several optimal-based approaches to structural vibration attenuation are investigated against the standard ‘ground-hook’ law and passive tuned vibration absorber(s) implementations. The common approach to optimal control of nonlinear systems is offline computation of the optimal solution, however, so determined open loop control suffers from lack of robustness to uncertainties (e.g., unmodelled dynamics, perturbations of external forces or initial conditions), and thus perturbation control techniques are often used. However, proper linearization may be an issue for highly nonlinear systems with implicit relations between state, co-state, and control. The main contribution of the author is the development as well as numerical and experimental verification of the Pontriagin maximum-principle-based vibration control concepts that produce directly actuator control input (not the demanded force), thus force tracking algorithm that results in control inaccuracy is entirely omitted. These concepts, including one-step optimal control, quasi-optimal control, and optimal-based modified ‘ground-hook’ law, can be directly implemented in online and real-time feedback control for periodic (or semi-periodic) disturbances with invariant or time-varying parameters, as well as for non-periodic, transient or random disturbances, what is a limitation for some other known solutions. No offline calculation, excitations/disturbances assumption or vibration frequency determination is necessary, moreover, all of the nonlinear actuator (MR damper) force constraints, i.e., no active forces, lower and upper saturation limits, hysteresis-type dynamics, etc., are embedded in the control technique, thus the solution is optimal or suboptimal for the assumed actuator, respecting its limitations. Depending on the selected method variant, a moderate or decisive reduction in the computational load is possible compared to other methods of nonlinear optimal control, while assuring the quality and robustness of the vibration reduction system, as well as considering multi-pronged operational aspects, such as possible minimization of the amplitude of the deflection and acceleration of the vibrating structure, its potential and/or kinetic energy, required actuator force, control input (e.g. electric current in the MR damper coil) and/or stroke amplitude. The developed solutions are characterized by high vibration reduction efficiency – the obtained maximum values of the dynamic amplification factor are close to 2.0, while for the best of the passive systems, these values exceed 3.5.

Keywords: magnetorheological damper, nonlinear tuned vibration absorber, optimal control, real-time structural vibration attenuation, wind turbines

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Authors: Akanksha Agrawal, Richa Rathor, Geetha Suryakumar

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Muscle represents about ¾ of the body mass, and a healthy muscular system is required for human performance. A healthy muscular system is dynamically balanced via the catabolic and anabolic process. High altitude associated hypoxia altered this redox balance via producing reactive oxygen and nitrogen species that ultimately modulates protein structure and function, hence, disrupts proteostasis or protein homeostasis. The mechanism by which proteostasis is clinched includes regulated protein translation, protein folding, and protein degradation machinery. Perturbation in any of these mechanisms could increase proteome imbalance in the cellular processes. Altered proteostasis in skeletal muscle is likely to be responsible for contributing muscular atrophy in response to hypoxia. Therefore, we planned to elucidate the mechanism involving altered proteostasis leading to skeletal muscle atrophy under chronic hypobaric hypoxia. Material and Methods-Male Sprague Dawley rats weighing about 200-220 were divided into five groups - Control (Normoxic animals), 1d, 3d, 7d and 14d hypobaric hypoxia exposed animals. The animals were exposed to simulated hypoxia equivalent to 282 torr pressure (equivalent to an altitude of 7620m, 8% oxygen) at 25°C. On completion of chronic hypobaric hypoxia (CHH) exposure, rats were sacrificed, muscle was excised and biochemical, histopathological and protein synthesis signaling were studied. Results-A number of changes were observed with the CHH exposure time period. ROS was increased significantly on 07 and 14 days which were attributed to protein oxidation via damaging muscle protein structure by oxidation of amino acids moiety. The oxidative damage to the protein further enhanced the various protein degradation pathways. Calcium activated cysteine proteases and other intracellular proteases participate in protein turnover in muscles. Therefore, we analysed calpain and 20S proteosome activity which were noticeably increased at CHH exposure as compared to control group representing enhanced muscle protein catabolism. Since inflammatory markers (myokines) affect protein synthesis and triggers degradation machinery. So, we determined inflammatory pathway regulated under hypoxic environment. Other striking finding of the study was upregulation of Akt/PKB translational machinery that was increased on CHH exposure. Akt, p-Akt, p70 S6kinase, and GSK- 3β expression were upregulated till 7d of CHH exposure. Apoptosis related markers, caspase-3, caspase-9 and annexin V was also increased on CHH exposure. Conclusion: The present study provides evidence of disrupted proteostasis under chronic hypobaric hypoxia. A profound loss of muscle mass is accompanied by the muscle damage leading to apoptosis and cell death under CHH. These cellular stress response pathways may play a pivotal role in hypobaric hypoxia induced skeletal muscle atrophy. Further research in these signaling pathways will lead to development of therapeutic interventions for amelioration of hypoxia induced muscle atrophy.

Keywords: Akt/PKB translational machinery, chronic hypobaric hypoxia, muscle atrophy, protein degradation

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Authors: Abdul Rehman, Bo Liu

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Axial flow turbines are commonly designed with high loads that generate strong secondary flows and result in high secondary losses. These losses contribute to almost 30% to 50% of the total losses. Non-axisymmetric endwall profiling is one of the passive control technique to reduce the secondary flow loss. In this paper, the non-axisymmetric endwall profile construction and optimization for the stator endwalls are presented to improve the efficiency of a high pressure turbine. The commercial code NUMECA Fine/ Design3D coupled with Fine/Turbo was used for the numerical investigation, design of experiments and the optimization. All the flow simulations were conducted by using steady RANS and Spalart-Allmaras as a turbulence model. The non-axisymmetric endwalls of stator hub and shroud were created by using the perturbation law based on Bezier Curves. Each cut having multiple control points was supposed to be created along the virtual streamlines in the blade channel. For the design of experiments, each sample was arbitrarily generated based on values automatically chosen for the control points defined during parameterization. The Optimization was achieved by using two algorithms i.e. the stochastic algorithm and gradient-based algorithm. For the stochastic algorithm, a genetic algorithm based on the artificial neural network was used as an optimization method in order to achieve the global optimum. The evaluation of the successive design iterations was performed using artificial neural network prior to the flow solver. For the second case, the conjugate gradient algorithm with a three dimensional CFD flow solver was used to systematically vary a free-form parameterization of the endwall. This method is efficient and less time to consume as it requires derivative information of the objective function. The objective function was to maximize the isentropic efficiency of the turbine by keeping the mass flow rate as constant. The performance was quantified by using a multi-objective function. Other than these two classifications of the optimization methods, there were four optimizations cases i.e. the hub only, the shroud only, and the combination of hub and shroud. For the fourth case, the shroud endwall was optimized by using the optimized hub endwall geometry. The hub optimization resulted in an increase in the efficiency due to more homogenous inlet conditions for the rotor. The adverse pressure gradient was reduced but the total pressure loss in the vicinity of the hub was increased. The shroud optimization resulted in an increase in efficiency, total pressure loss and entropy were reduced. The combination of hub and shroud did not show overwhelming results which were achieved for the individual cases of the hub and the shroud. This may be caused by fact that there were too many control variables. The fourth case of optimization showed the best result because optimized hub was used as an initial geometry to optimize the shroud. The efficiency was increased more than the individual cases of optimization with a mass flow rate equal to the baseline design of the turbine. The results of artificial neural network and conjugate gradient method were compared.

Keywords: artificial neural network, axial turbine, conjugate gradient method, non-axisymmetric endwall, optimization

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Authors: Vittorio Astarita, Giuseppe Guido, Vincenzo Pasquale Giofre, Alessandro Vitale

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Traffic microsimulation has been used extensively to evaluate consequences of different traffic planning and control policies in terms of travel time delays, queues, pollutant emissions, and every other common measured performance while at the same time traffic safety has not been considered in common traffic microsimulation packages as a measure of performance for different traffic scenarios. Vehicle conflict techniques that were introduced at intersections in the early traffic researches carried out at the General Motor laboratory in the USA and in the Swedish traffic conflict manual have been applied to vehicles trajectories simulated in microscopic traffic simulators. The concept is that microsimulation can be used as a base for calculating the number of conflicts that will define the safety level of a traffic scenario. This allows engineers to identify unsafe road traffic maneuvers and helps in finding the right countermeasures that can improve safety. Unfortunately, most commonly used indicators do not consider conflicts between single vehicles and roadside obstacles and barriers. A great number of vehicle crashes take place with roadside objects or obstacles. Only some recent proposed indicators have been trying to address this issue. This paper introduces a new procedure based on the simulation of potential crash events for the evaluation of safety levels in microsimulation traffic scenarios, which takes into account also potential crashes with roadside objects and barriers. The procedure can be used to define new conflict indicators. The proposed simulation procedure generates with the random perturbation of vehicle trajectories a set of potential crashes which can be evaluated accurately in terms of DeltaV, the energy of the impact, and/or expected number of injuries or casualties. The procedure can also be applied to real trajectories giving birth to new surrogate safety performance indicators, which can be considered as “simulation-based”. The methodology and a specific safety performance indicator are described and applied to a simulated test traffic scenario. Results indicate that the procedure is able to evaluate safety levels both at the intersection level and in the presence of roadside obstacles. The procedure produces results that are expressed in the same unity of measure for both vehicle to vehicle and vehicle to roadside object conflicts. The total energy for a square meter of all generated crash can be used and is shown on the map, for the test network, after the application of a threshold to evidence the most dangerous points. Without any detailed calibration of the microsimulation model and without any calibration of the parameters of the procedure (standard values have been used), it is possible to identify dangerous points. A preliminary sensitivity analysis has shown that results are not dependent on the different energy thresholds and different parameters of the procedure. This paper introduces a specific new procedure and the implementation in the form of a software package that is able to assess road safety, also considering potential conflicts with roadside objects. Some of the principles that are at the base of this specific model are discussed. The procedure can be applied on common microsimulation packages once vehicle trajectories and the positions of roadside barriers and obstacles are known. The procedure has many calibration parameters and research efforts will have to be devoted to make confrontations with real crash data in order to obtain the best parameters that have the potential of giving an accurate evaluation of the risk of any traffic scenario.

Keywords: road safety, traffic, traffic safety, traffic simulation

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Authors: B. S. Premalatha, Kausalya Sahani

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Background: Glomus jugulare tumors arise within the jugular foramen and are commonly seen in females particularly on the left side. Surgical excision of the tumor may cause lower cranial nerve deficits. Cranial nerve involvement produces hoarseness of voice, slurred speech, and dysphagia along with other physical symptoms, thereby affecting the quality of life of individuals. Though oncological clearance is mainly emphasized on while treating these individuals, little importance is given to their communication, voice and swallowing problems, which play a crucial part in daily functioning. Objective: To examine the functions of voice, speech and swallowing outcomes of the subjects, following excision of glomus jugulare tumor. Methods: Two female subjects aged 56 and 62 years had come with a complaint of change in voice, inability to swallow and reduced clarity of speech following surgery for left glomus jugulare tumor were participants of the study. Their surgical information revealed multiple cranial nerve palsies involving the left facial, left superior and recurrent branches of the vagus nerve, left pharyngeal, left soft palate, left hypoglossal and vestibular nerves. Functional outcomes of voice, speech and swallowing were evaluated by perceptual and objective assessment procedures. Assessment included the examination of oral structures and functions, dysarthria by Frenchey dysarthria assessment, cranial nerve functions and swallowing functions. MDVP and Dr. Speech software were used to evaluate acoustic parameters of voice and quality of voice respectively. Results: The study revealed that both the subjects, subsequent to excision of glomus jugulare tumor, showed a varied picture of affected oral structure and functions, articulation, voice and swallowing functions. The cranial nerve assessment showed impairment of the vagus, hypoglossal, facial and glossopharyngeal nerves. Voice examination indicated vocal cord paralysis associated with breathy quality of voice, weak voluntary cough, reduced pitch and loudness range, and poor respiratory support. Perturbation parameters as jitter, shimmer were affected along with s/z ratio indicative of voice fold pathology. Reduced MPD(Maximum Phonation Duration) of vowels indicated that disturbed coordination between respiratory and laryngeal systems. Hypernasality was found to be a prominent feature which reduced speech intelligibility. Imprecise articulation was seen in both the subjects as the hypoglossal nerve was affected following surgery. Injury to vagus, hypoglossal, gloss pharyngeal and facial nerves disturbed the function of swallowing. All the phases of swallow were affected. Aspiration was observed before and during the swallow, confirming the oropharyngeal dysphagia. All the subsystems were affected as per Frenchey Dysarthria Assessment signifying the diagnosis of flaccid dysarthria. Conclusion: There is an observable communication and swallowing difficulty seen following excision of glomus jugulare tumor. Even with complete resection, extensive rehabilitation may be necessary due to significant lower cranial nerve dysfunction. The finding of the present study stresses the need for involvement of as speech and swallowing therapist for pre-operative counseling and assessment of functional outcomes.

Keywords: functional outcome, glomus jugulare tumor excision, multiple cranial nerve impairment, speech and swallowing

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Authors: Angshuman Raha, Abesh Kumar Sanyal, Uttaran Bandyopadhyay, Kaushik Mallick, Kamalika Bhattacharyya, Subrata Gayen, Gaurab Nandi Das, Mohd. Ali, Kailash Chandra

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Indian Himalayan Region (IHR), due to its sheer latitudinal and altitudinal expanse, acts as a mixing ground for different zoogeographic faunal elements. The innumerable unique and distributional restricted rare species of IHR are constantly being threatened with extinction by the ongoing climate change scenario. Many of which might have faced extinction without even being noticed or discovered. Monitoring the community dynamics of a suitable taxon is indispensable to assess the effect of this global perturbation at micro-habitat level. Lepidoptera, particularly moths are suitable for this purpose due to their huge diversity and strict herbivorous nature. The present study aimed to collate scattered historical records of moths from IHR and spatially disseminate the same in Geographic Information System (GIS) domain. The study also intended to identify moth species with significant altitudinal shifts which could be prioritised for monitoring programme to assess the effect of climate change on biodiversity. A robust database on moths recorded from IHR was prepared from voluminous secondary literature and museum collections. Historical sampling points were transformed into richness grids which were spatially overlaid on altitude, annual precipitation and vegetation layers separately to show moth richness patterns along major environmental gradients. Primary samplings were done by setting standard light traps at 11 Protected Areas representing five Indian Himalayan biogeographic provinces. To identify significant altitudinal shifts, past and present altitudinal records of the identified species from primary samplings were compared. A consolidated list of 4107 species belonging to 1726 genera of 62 families of moths was prepared from a total of 10,685 historical records from IHR. Family-wise assemblage revealed Erebidae to be the most speciose family with 913 species under 348 genera, followed by Geometridae with 879 species under 309 genera and Noctuidae with 525 species under 207 genera. Among biogeographic provinces, Central Himalaya represented maximum records with 2248 species, followed by Western and North-western Himalaya with 1799 and 877 species, respectively. Spatial analysis revealed species richness was more or less uniform (up to 150 species record per cell) across IHR. Throughout IHR, the middle elevation zones between 1000-2000m encompassed high species richness. Temperate coniferous forest associated with 1500-2000mm rainfall zone showed maximum species richness. Total 752 species of moths were identified representing 23 families from the present sampling. 13 genera were identified which were restricted to specialized habitats of alpine meadows over 3500m. Five historical localities with high richness of >150 species were selected which could be considered for repeat sampling to assess climate change influence on moth assemblage. Of the 7 species exhibiting significant altitudinal ascend of >2000m, Trachea auriplena, Diphtherocome fasciata (Noctuidae) and Actias winbrechlini (Saturniidae) showed maximum range shift of >2500m, indicating intensive monitoring of these species. Great Himalayan National Park harbours most diverse assemblage of high-altitude restricted species and should be a priority site for habitat conservation. Among the 13 range restricted genera, Arichanna, Opisthograptis, Photoscotosia (Geometridae), Phlogophora, Anaplectoides and Paraxestia (Noctuidae) were dominant and require rigorous monitoring, as they are most susceptible to climatic perturbations.

Keywords: altitudinal shifts, climate change, historical records, Indian Himalayan region, Lepidoptera

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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