Search results for: diffusive Johnson-Segalman model

Authors: D. Gueribiz, F. Jacquemin, S. Fréour

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During their service life, composite materials are submitted to humid environments. The moisture absorbed by their matrix polymer induced internal stresses which can lead to multi-scale damage and may reduce the lifetime of composite structures. The estimation of internal stresses is based at a first on realistic evaluation of the diffusive behavior of composite materials. Generally, the modeling and simulation of the diffusive behavior of composite materials are extensively investigated through decoupled models based on the assumption of Fickien behavior. For these approaches, the concentration and the deformation (or stresses), the two state variables of the problem considered are governed by independent equations which are solved separately. In this study, a model coupling diffusive behavior with stresses state for a polymer matrix composite reinforced with impermeable fibers is proposed, the investigation of diffusive behavior is based on a more general thermodynamic approach which introduces a dependence of diffusive behavior on internal stresses state. The coupled diffusive behavior modeling was established in first for homogeneous and isotropic matrix and it is, thereafter, extended to impermeable unidirectional composites.

Keywords: composites materials, moisture diffusion, effective moisture diffusivity, coupled moisture diffusion

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Authors: Sameena Tarannum, S. Pranesh

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The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: gravity modulation, Oldroyd-b liquid, triple diffusive convection, venezian approach

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Authors: Safia Akram

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In this article, the effects of peristaltic transport with double-diffusive convection in nanofluids through an asymmetric channel with different waveforms is presented. Mathematical modelling for two-dimensional and two directional flows of a Jeffrey fluid model along with double-diffusive convection in nanofluids are given. Exact solutions are obtained for nanoparticle fraction field, concentration field, temperature field, stream functions, pressure gradient and pressure rise in terms of axial and transverse coordinates under the restrictions of long wavelength and low Reynolds number. With the help of computational and graphical results the effects of Brownian motion, thermophoresis, Dufour, Soret, and Grashof numbers (thermal, concentration, nanoparticles) on peristaltic flow patterns with double-diffusive convection are discussed.

Keywords: nanofluid particles, peristaltic flow, Jeffrey fluid, magnetic field, asymmetric channel, different waveforms

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Authors: Sameena Tarannum, S. Pranesh

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A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.

Keywords: couple stress liquid, Ginzburg-Landau model, rotation, triple diffusive convection

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Ila Thakur, Atul Srivastava, Shyamprasad Karagadde

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The phenomenon of double-diffusive convection is driven by density gradients created by two different components (e.g., temperature and concentration) having different molecular diffusivities. The evolution of horizontal double-diffusive layers (DDLs) is one of the outcomes of double-diffusive convection occurring in a laterally/vertically cooled rectangular cavity having a pre-existing vertically stable composition field. The present work mainly focuses on different characteristics of the formation and merging of double-diffusive layers by imposing lateral/vertical thermal gradients in a vertically stable compositional field. A CFD-based twodimensional fluent model has been developed for the investigation of the aforesaid phenomena. The configuration containing vertical thermal gradients shows the evolution and merging of DDLs, where, elements from the same horizontal plane move vertically and mix with surroundings, creating a horizontal layer. In the configuration of lateral thermal gradients, a specially oriented convective roll was found inside each DDL and each roll was driven by the competing density change due to the already existing composition field and imposed thermal field. When the thermal boundary layer near the vertical wall penetrates the salinity interface, it can disrupt the compositional interface and can lead to layer merging. Different analytical scales were quantified and compared for both configurations. Various combinations of solutal and thermal Rayleigh numbers were investigated to get three different regimes, namely; stagnant regime, layered regime and unicellular regime. For a particular solutal Rayleigh number, a layered structure can originate only for a range of thermal Rayleigh numbers. Lower thermal Rayleigh numbers correspond to a diffusion-dominated stagnant regime. Very high thermal Rayleigh corresponds to a unicellular regime with high convective mixing. Different plots identifying these three regimes, number, thickness and time of existence of DDLs have been studied and plotted. For a given solutal Rayleigh number, an increase in thermal Rayleigh number increases the width but decreases both the number and time of existence of DDLs in the fluid domain. Sudden peaks in the velocity and heat transfer coefficient have also been observed and discussed at the time of merging. The present study is expected to be useful in correlating the double-diffusive convection in many large-scale applications including oceanography, metallurgy, geology, etc. The model has also been developed for three-dimensional geometry, but the results were quite similar to that of 2-D simulations.

Keywords: double diffusive layers, natural convection, Rayleigh number, thermal gradients, compositional gradients

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Authors: Hichem Boulechfar, Mahfoud Djezzar

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Two-dimensional double diffusive natural convection in an annular elliptical space filled with fluid-saturated porous medium, is analyzed by solving numerically the mass balance, momentum, energy and concentration equations, using Darcy's law and Boussinesq approximation. Both walls delimiting the annular space are maintained at two uniform different temperatures and concentrations. The external parameter considered is the Lewis number. For the present work, the heat and mass transfer for natural convection is studied for the case of aiding buoyancies, where the flow is generated in a cooperative mode by both temperature and solutal gradients. The local Nusselt and Sherwood numbers are presented in term of the external parameter.

Keywords: double diffusive, natural convection, porous media, elliptical annulus

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Authors: Jatupon Em-Udom, Nirand Pisutha-Arnond

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The phase-field-crystal, PFC, approach is a density-functional-type material model with an atomic resolution on a diffusive timescale. Spatially, the model incorporates periodic nature of crystal lattices and can naturally exhibit elasticity, plasticity and crystal defects such as grain boundaries and dislocations. Temporally, the model operates on a diffusive timescale which bypasses the need to resolve prohibitively small atomic-vibration time steps. The PFC model has been used to study many material phenomena such as grain growth, elastic and plastic deformations and solid-solid phase transformations. In this study, the pressure-controlled dynamic equation for the PFC model was developed to simulate a single-component system under externally applied pressure; these coupled equations are important for studies of deformable systems such as those under constant pressure. The formulation is based on the non-equilibrium thermodynamics and the thermodynamics of crystalline solids. To obtain the equations, the entropy variation around the equilibrium point was derived. Then the resulting driving forces and flux around the equilibrium were obtained and rewritten as conventional thermodynamic quantities. These dynamics equations are different from the recently-proposed equations; the equations in this study should provide more rigorous descriptions of the system dynamics under externally applied pressure.

Keywords: driving forces and flux, evolution equation, non equilibrium thermodynamics, Onsager’s reciprocal relation, phase field crystal model, thermodynamics of single-component solid

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Authors: Norazam Arbin, Habibis Saleh, Ammar Alsabery, Ishak Hashim

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Double-diffusive natural convection in an open top cavity with partial vertical heating and salting sources is investigated numerically. Different temperatures and concentrations are applied at the source location on the right and left walls while the other remains adiabatic except at the open top surface. Various combinations of sources arrangements are imposed at the vertical walls in order to observe the significant impact to the convection. An iterative finite different method is used to solve the dimensionless governing equations. The effects of Marangoni number and sources arrangements on the contours of streamlines, isotherms, and concentrations are visualized as the outcome of the numerical solutions. The average Nusselt and Sherwood number are presented for various sources arrangements. It is clearly observed that the sources arrangements gave major impact on the heat and mass transfer rates. A horizontal-like pattern is found for sources arrangements that near the top-free surface.

Keywords: double-diffusive, Marangoni effect, partial heating, salting

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Authors: Débora P. Jaeschke, Eduardo A. Merlo, Rosane Rech, Giovana D. Mercali, Ligia D. F. Marczak

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Carotenoids are high value added pigments that can be alternatively extracted from some microalgae species. However, the application of carotenoids synthetized by microalgae is still limited due to the utilization of organic toxic solvents. In this context, studies involving alternative extraction methods have been conducted with more sustainable solvents to replace and reduce the solvent volume and the extraction time. The aim of the present work was to evaluate the extraction time of carotenoids from the microalgae Heterochlorella luteoviridis using moderate electric field (MEF) as a pre-treatment to the extraction. The extraction methodology consisted of a pre-treatment in the presence of MEF (180 V) and ethanol (25 %, v/v) for 10 min, followed by a diffusive step performed for 50 min using a higher ethanol concentration (75 %, v/v). The extraction experiments were conducted at 30 °C and, to keep the temperature at this value, it was used an extraction cell with a water jacket that was connected to a water bath. Also, to enable the evaluation of MEF effect on the extraction, control experiments were performed using the same cell and conditions without voltage application. During the extraction experiments, samples were withdrawn at 1, 5 and 10 min of the pre-treatment and at 1, 5, 30, 40 and 50 min of the diffusive step. Samples were, then, centrifuged and carotenoids analyses were performed in the supernatant. Furthermore, an exhaustive extraction with ethyl acetate and methanol was performed, and the carotenoids content found for this analyses was considered as the total carotenoids content of the microalgae. The results showed that the application of MEF as a pre-treatment to the extraction influenced the extraction yield and the extraction time during the diffusive step; after the MEF pre-treatment and 50 min of the diffusive step, it was possible to extract up to 60 % of the total carotenoids content. Also, results found for carotenoids concentration of the extracts withdrawn at 5 and 30 min of the diffusive step did not presented statistical difference, meaning that carotenoids diffusion occurs mainly in the very beginning of the extraction. On the other hand, the results for control experiments showed that carotenoids diffusion occurs mostly during 30 min of the diffusive step, which evidenced MEF effect on the extraction time. Moreover, carotenoids concentration on samples withdrawn during the pre-treatment (1, 5 and 10 min) were below the quantification limit of the analyses, indicating that the extraction occurred in the diffusive step, when ethanol (75 %, v/v) was added to the medium. It is possible that MEF promoted cell membrane permeabilization and, when ethanol (75 %) was added, carotenoids interacted with the solvent and the diffusion occurred easily. Based on the results, it is possible to infer that MEF promoted the decrease of carotenoids extraction time due to the increasing of the permeability of the cell membrane which facilitates the diffusion from the cell to the medium.

Keywords: moderate electric field (MEF), pigments, microalgae, ethanol

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Authors: Christina Jery, R. K. Anjana, D. N. Arnepalli, R. Sobha

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Modern landfills employ a composite liner consisting of a geomembrane overlying a compacted clay liner (CCL) or a geosynthetic clay liner (GCL) as a barrier system. The primary function of a barrier system is to control the contaminant transport from the leachate (dissolved phase) and landfill gas (vapour phase) out of the landfill thereby minimizing the environmental impact. This study is undertaken to investigate the diffusive migration of VOCs through composite liners. VOCs are known hazardous air pollutants were often existing in both the vapour phase and dissolved phase. These compounds are known to diffuse readily through the polymeric geomembranes. The objective of the research is to develop a comprehensive data set of diffusive parameters involved in the diffusion of VOCs in the composite liner (1.5 mm HDPE geomembrane overlying a 30mm compacted clay layer). For this purpose, the study aims to develop a new experimental setup for determining the diffusion characteristics. The key parameters of diffusion (partitioning, diffusion and permeation coefficients) are examined. The diffusion tests are carried out both in aqueous and vapor phase. Finally, an attempt is also made to study the effect of low temperature on the diffusion characteristics.

Keywords: diffusion, sorption, organic compounds, composite liners, geomembrane

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Authors: Subhayan Maity

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Complete scenario of cosmic evolution from emergent phase to late time acceleration (i.e. non-singular ever expanding Universe) is a popular preference in the recent cosmology. Yet one can’t exclude the idea that other type of evolution pattern of the Universe may also be possible. Especially, the bouncing scenario is becoming a matter of interest now a days. The present work is an exhibition of such a different pattern of cosmic evolution where the evolution of Universe has been shown as a cyclic thermodynamic process. Under diffusion mechanism (non-equilibrium thermodynamic process), the cosmic evolution has been modelled as [ emergent - accelerated expansion - decelerated expansion - decelerated contraction - accelerated contraction - emergent] .

Keywords: non-equilibrium thermodynamics, non singular evolution of universe, cyclic evolution, diffusive fluid

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Authors: Rangoli Goyal, Rama Bhargava

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The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, diffusiophoresis, Brownian motion

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Authors: Kaewpradap Amornrat, Endo Takahiro, Kadowaki Satoshi

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The combustion of hydrogen-oxygen (H2-O2) mixtures was investigated to consider the reduction of carbon dioxide (CO2) and nitrogen oxide (NOx) as the greenhouse emission. Normally, the flame speed of combustion H2-O2 mixtures are very fast thus it is necessary to control the limit of mixtures with CO2 addition as H2-O2-CO2 combustion. The limit of hydrogen was set and replaced by CO2 with O2:CO2 ratio as 1:3.76, 1:4 and 1:5 for this study. In this study, the combustion of H2-O2 -CO2 on flat burner at equivalence ratio =0.5 was investigated for 10, 15 and 20 L/min of flow rate mixtures. When the ratio of CO2 increases, the power spectral density is lower, the size of attractor and cellular flame become larger because the decrease of hydrogen replaced by CO2 affects the diffusive-thermal instability. Moreover, the flow rate mixtures increases, the power spectral density increases, the size of reconstructed attractor and cell size become smaller due to decreasing of instability. The results show that the variation of CO2 and mixture flow rate affects the instability of cellular premixed flames on flat burner.

Keywords: instability, H2-O2-CO2 combustion, flat burner, diffusive-thermal instability

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Authors: T. Chinyoka

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We present the Johnson-Segalman constitutive model to capture certain fluid flow phenomena that has been experimentally observed in the flow of complex polymeric fluids. In particular, experimentally observed phenomena such as shear banding, spurt and slip are explored and/or explained in terms of the non-monotonic shear-stress versus shear-rate relationships. We also explore the effects of the inclusion of physical flow aspects such as wall porosity on shear banding. We similarly also explore the effects of the inclusion of mathematical modelling aspects such as stress diffusion into the stress constitutive models in order to predict shear-stress (or shear-rate) paths. We employ semi-implicit finite difference methods for all the computational solution procedures.

Keywords: Johnson-Segalman model, diffusive Johnson-Segalman model, shear banding, finite difference methods, complex fluid flow

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Authors: H. Namazi, H. T. N. Kuan

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Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick’s first law doesn’t consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick’s first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick’s first law, Fick’s first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results.

Keywords: Fick's first law, flux, diffusion, time delay, modified Fick’s first law

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Authors: Arnab Mondal, Sanjeev Kumar Sharma, Ranjit Kumar Upadhyay

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We study the spatiotemporal dynamics of a neuronal cable. The processes of one- dimensional (1D) and 2D diffusion are considered for a single variable, which is the membrane voltage, i.e., membrane voltage diffusively interacts for spatiotemporal pattern formalism. The recovery and other variables interact through the membrane voltage. A 3D Leech-Heart (LH) model is introduced to investigate the nonlinear responses of an excitable neuronal cable. The deterministic LH model shows different types of firing properties. We explore the parameter space of the uncoupled LH model and based on the bifurcation diagram, considering v_k2_ashift as a bifurcation parameter, we analyze the 1D diffusion dynamics in three regimes: bursting, regular spiking, and a quiescent state. Depending on parameters, it is shown that the diffusive system may generate regular and irregular bursting or spiking behavior. Further, it is explored a 2D diffusion acting on the membrane voltage, where different types of patterns can be observed. The results show that the LH neurons with different firing characteristics depending on the control parameters participate in a collective behavior of an information processing system that depends on the overall network.

Keywords: bifurcation, pattern formation, spatio-temporal dynamics, stability analysis

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Authors: A. Ja, J. Belabid, A. Cheddadi

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This paper reports the numerical simulation of double diffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: natural convection, double-diffusion, porous medium, annular geometry, finite differences

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Authors: Soroush Hooshyar, Mohamadali Masoudian, Natalie Germann

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Many soft materials such as polymer solutions can develop localized bands with different shear rates, which are known as shear bands. Using the generalized bracket approach of nonequilibrium thermodynamics, we recently developed a new two-fluid model to study shear banding for semi-dilute polymer solutions. The two-fluid approach is an appropriate means for describing diffusion processes such as Fickian diffusion and stress-induced migration. In this approach, it is assumed that the local gradients in concentration and, if accounted for, also stress generate a nontrivial velocity difference between the components. Since the differential velocity is treated as a state variable in our model, the implementation of the boundary conditions arising from the derivative diffusive terms is straightforward. Our model is a good candidate for benchmark simulations because of its simplicity. We analyzed its behavior in cylindrical Couette flow, a rectilinear channel flow, and a 4:1 planar contraction flow. The latter problem was solved using the OpenFOAM finite volume package and the impact of shear banding on the lip and salient vortices was investigated. For the other smooth geometries, we employed a standard Chebyshev pseudospectral collocation method. The results showed that the steady-state solution is unique with respect to initial conditions, deformation history, and the value of the diffusivity constant. However, smaller the value of the diffusivity constant is, the more time it takes to reach the steady state.

Keywords: nonequilibrium thermodynamics, planar contraction, polymer solutions, shear banding, two-fluid approach

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Authors: Seema Dhariwal, Kiran Maan, Ruchi Baghel, Apoorva Sharma, Poonam Rana

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Introduction: Traumatic brain injury (TBI) is defined as the temporary or permanent alteration in brain function and pathology caused by an external mechanical force. It represents the leading cause of mortality and morbidity among children and youth individuals. Various models of TBI in rodents have been developed in the laboratory to mimic the scenario of injury. Blast overpressure injury is common among civilians and military personnel, followed by accidents or explosive devices. In addition to this, the lateral Controlled cortical impact (CCI) model mimics the blunt, penetrating injury. Method: In the present study, we have developed two different mild TBI models using blast and CCI injury. In the blast model, helium gas was used to create an overpressure of 130 kPa (±5) via a shock tube, and CCI injury was induced with an impact depth of 1.5mm to create diffusive and focal injury, respectively. C57BL/6J male mice (10-12 weeks) were divided into three groups: (1) control, (2) Blast treated, (3) CCI treated, and were exposed to different injury models. Serum was collected on Day1 and day7, followed by biphasic extraction using MTBE/Methanol/Water. Prepared samples were separated on Charged Surface Hybrid (CSH) C18 column and acquired on UHPLC-Q-TOF-MS using ESI probe with inhouse optimized parameters and method. MS peak list was generated using Markerview TM. Data were normalized, Pareto-scaled, and log-transformed, followed by multivariate and univariate analysis in metaboanalyst. Result and discussion: Untargeted profiling of lipids generated extensive data features, which were annotated through LIPID MAPS® based on their m/z and were further confirmed based on their fragment pattern by LipidBlast. There is the final annotation of 269 features in the positive and 182 features in the negative mode of ionization. PCA and PLS-DA score plots showed clear segregation of injury groups to controls. Among various lipids in mild blast and CCI, five lipids (Glycerophospholipids {PC 30:2, PE O-33:3, PG 28:3;O3 and PS 36:1 } and fatty acyl { FA 21:3;O2}) were significantly altered in both injury groups at Day 1 and Day 7, and also had VIP score >1. Pathway analysis by Biopan has also shown hampered synthesis of Glycerolipids and Glycerophospholipiods, which coincides with earlier reports. It could be a direct result of alteration in the Acetylcholine signaling pathway in response to TBI. Understanding the role of a specific class of lipid metabolism, regulation and transport could be beneficial to TBI research since it could provide new targets and determine the best therapeutic intervention. This study demonstrates the potential lipid biomarkers which can be used for injury severity diagnosis and identification irrespective of injury type (diffusive or focal).

Keywords: LipidBlast, lipidomic biomarker, LIPID MAPS®, TBI

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Authors: P. M. Kundu, L. R. Singo, J. O. Odiyo

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Luvuvhu River catchment in South Africa experiences floods resulting from heavy rainfall of intensities exceeding 15 mm per hour associated with the Inter-tropical Convergence Zone (ITCZ). The generation of runoff is triggered by the rainfall intensity and soil moisture status. In this study, remote sensing and GIS techniques were used to analyze the hydrologic response to land cover changes. Runoff was calculated as a product of the net precipitation and a curve number coefficient. It was then routed using the Muskingum-Cunge method using a diffusive wave transfer model that enabled the calculation of response functions between start and end point. Flood frequency analysis was determined using theoretical probability distributions. Spatial data on land cover was obtained from multi-temporal Landsat images while data on rainfall, soil type, runoff and stream discharges was obtained by direct measurements in the field and from the Department of Water. A digital elevation model was generated from contour maps available at http://www.ngi.gov.za. The results showed that land cover changes had impacted negatively to the hydrology of the catchment. Peak discharges in the whole catchment were noted to have increased by at least 17% over the period while flood volumes were noted to have increased by at least 11% over the same period. The flood time to peak indicated a decreasing trend, in the range of 0.5 to 1 hour within the years. The synergism between remotely sensed digital data and GIS for land surface analysis and modeling was realized, and it was therefore concluded that hydrologic modeling has potential for determining the influence of changes in land cover on the hydrologic response of the catchment.

Keywords: catchment, digital elevation model, hydrological model, routing, runoff

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Entisar A. Elgmati

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Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

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Authors: Fateme Nokhodchi Bonab

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Studies related to magnetic resonance imaging (MRI) and drug delivery are reviewed in this study to demonstrate the role of transport theory in porous media in facilitating advances in biomedical applications. Diffusion processes are believed to be important in many therapeutic modalities such as: B. Delivery of drugs to the brain. We analyse the progress in the development of diffusion equations using the local volume average method and the evaluation of applications related to diffusion equations. Torsion and porosity have significant effects on diffusive transport. In this study, various relevant models of torsion are presented and mathematical modeling of drug release from biodegradable delivery systems is analysed. In this study, a new model of drug release kinetics from porous biodegradable polymeric microspheres under bulk and surface erosion of the polymer matrix is presented. Solute drug diffusion, drug dissolution from the solid phase, and polymer matrix erosion have been found to play a central role in controlling the overall drug release process. This work paves the way for MRI and drug delivery researchers to develop comprehensive models based on porous media theory that use fewer assumptions compared to other approaches.

Keywords: MRI, porous media, drug delivery, biomedical applications

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

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In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, heteroclinic orbits, steady state, traveling wave

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Authors: Suresh Sahu, Abhijeet M. Vaidya, Naresh K. Maheshwari

Abstract:

The efforts to understand the heat transfer behavior of supercritical water in supercritical water cooled reactor (SCWR) are ongoing worldwide to fulfill the future energy demand. The higher thermal efficiency of these reactors compared to a conventional nuclear reactor is one of the driving forces for attracting the attention of nuclear scientists. In this work, a solution procedure has been described for solving supercritical fluid flow problems in complex geometries. The solution procedure is based on non-staggered grid. All governing equations are discretized by finite volume method (FVM) in curvilinear coordinate system. Convective terms are discretized by first-order upwind scheme and central difference approximation has been used to discretize the diffusive parts. k-ε turbulence model with standard wall function has been employed. SIMPLE solution procedure has been implemented for the curvilinear coordinate system. Based on this solution method, 3-D Computational Fluid Dynamics (CFD) code has been developed. In order to demonstrate the capability of this CFD code in supercritical fluid flows, heat transfer to supercritical water in circular tubes has been considered as a test problem. Results obtained by code have been compared with experimental results reported in literature.

Keywords: curvilinear coordinate, body-fitted mesh, momentum interpolation, non-staggered grid, supercritical fluids

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Authors: Matthew Stephenson

Abstract:

We study the electrical conductivity of strongly disordered, strongly coupled quantum field theories, holographically dual to non-perturbatively disordered uncharged black holes. The computation reduces to solving a diffusive hydrostatic equation for an emergent horizon fluid. We demonstrate that a large class of theories in two spatial dimensions have a universal conductivity independent of disorder strength, and rigorously rule out disorder-driven conductor-insulator transitions in many theories. We present a (fine-tuned) axion-dilaton bulk theory which realizes the conductor-insulator transition, interpreted as a classical percolation transition in the horizon fluid. We address aspects of strongly disordered holography that can and cannot be addressed via mean-field modeling, such as massive gravity.

Keywords: theoretical physics, black holes, holography, high energy

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Authors: Mechlouch Ridha Fethi

Abstract:

This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

Procedia PDF Downloads 324