Analysis of Convective Transport of Temperature-Dependent Viscosity forNon-Newtonian Erying Powell Fluid: A Numerical Approach

Non-Newtonian is a type of fluid that does not comply with the viscosity under the Law of Newton and is being widely used in industrial applications.These include those related to chemical industries,cosmetics manufacturing,pharmaceutical field,food processing,as well as oil and gas activities.The inability of the conventional equations of Navier–Stokes to accurately depict rheological behavior for certain fluids led to an emergence study for non-Newtonian fluids’models.In line with this,a mathematical model of forced convective flow on non-Newtonian Eyring Powell fluid under temperature-dependent viscosity(TDV)circumstance is formulated.The fluid model is embedded with the Newtonian heating(NH)boundary condition as a heating circumstance and is assumed to move over a stretching sheet acting vertically.Using appropriate similarity variables,the respective model was converted into ordinary differential equations(ODE),which was later solved utilizing the Keller box approach.The present model is validated by comparing the existing output in literature at certain special limiting cases,where the validation results display a firm agreement.The current outputs for the proposed model are shown in tabular and graphical form for variation of skin friction plus Nusselt number,velocity and temperature distribution,respectively.

EXISTENCE OF CLOSED ORBITS FOR A DIFFERENTIAL EQUATION MODEL CONCERNING MULTI-MOLECULE REACTIONS

The existence of closed orbits for the biochemical reaction model was discussed. It was also pointed out that the equation has no closed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition.

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

Neonatal Death Rates: Lack of Equal Access to Hospital Obstetric Service and Intensive Therapy

Aim: To identify the association between access to obstetric and neonatal hospital service and neonatal death rates. Method: Quantitative and retrospective research retrieved from Declaration of Live Newly-born Children;Declaration of Death;Investigation Chart on Municipal Child Mortality, between 2000 and 2009, at the Nucleus of Information on Mortality Rates. The population studied comprised 537 neonatal deaths and mothers with residence in the municipality, and investigated by the work team of the Committee for the Investigation of Mother-Child Deaths. Data were analyzed in Epi Info 2002? computer program and the Statistical Package for the Social Sciences? was used. Chi-square Test and Fischer’s Exact Test were applied at p < 0.05. Results: 63.7% of 537 neonates were born in hospitals with maternities and neonatal intensive therapy unit;60.7% weighed ≤1.500 grams;76.7% had a pregnancy age of ≤36 weeks;73% died of asphyxia in the 1st minute and 73.5% died during the perinatal period. Throughout the ten years of analysis, access to hospital obstetric service without NITU reduced death rate from 25% in 2000 to 6.8% in 2009. There was a significant statistical association between place of delivery and maternal socio-demographic variables (maternal age bracket p = 0.028;schooling p = 0.000;family income p = 0.000);occupation p = 0.000) and neonatal variables (race/skin color p = 0.007;type of delivery p = 0.000;weight at birth p = 0.000;pregnancy age p = 0.000 and Apgar Score 1st minute p = 0.000 and Apgar Score 5th minute p = 0.007). Conclusion: Although the municipal government provides obstetric services and specialized neonatal care, this right is not extensive to all;gaps at different levels in mother-child care should be identified to reduce neonatal deaths.

Mixed Convection of Non-Newtonian Erying Powell Fluid with Temperature-Dependent Viscosity over a Vertically Stretched Surface

The viscosity of a substance or material is intensely influenced by the temperature,especially in the field of lubricant engineering where the changeable temperature is well executed.In this paper,the problem of temperature-dependent viscosity on mixed convection flow of Eyring Powell fluid was studied together with Newtonian heating thermal boundary condition.The flow was assumed to move over a vertical stretching sheet.The model of the problem,which is in partial differential equations,was first transformed to ordinary differential equations using appropriate transformations.This approach was considered to reduce the complexity of the equations.Then,the transformed equations were solved using the Keller box method under the finite difference scheme approach.The validation process of the results was performed,and it was found to be in an excellent agreement.The results on the present computation are shown in tabular form and also graphical illustration.The major finding was observed where the skin friction and Nusselt number were boosted in the strong viscosity.

Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution

Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry,all states except W class(and their linear combination)lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits,we indicate that all N-qubit states(N>5)obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.

The core-merging giant impact in Earth's accretion history and its implications

The Earth’s accretion process is accompanied by a large number of collisions.It is widely accepted that collisions dominate the Earth’s late accretion stage.Among all these collisions,there is a special type of collision called Core-merging giant impact(CMGI),in which much or most the impactor’s core merges directly with the protoEarth’s core.This core-merging scenario plays an important role in the Earth’s accretion process and deeply affects the formation of the Earth’s core and mantle.However,because CMGI is a small probability event,it has not been fully studied.Here we use the SPH method to comprehensively study all possible CMGIs in the Earth’s accretion history.We find that CMGI only occurs in the initial conditions with small impact angle,small impact velocity and big impactor.We further discuss the implications of CMGI.We are confident that CMGI inevitably causes the chemical disequilibrium of the Earth’s core and mantle.The CMGI process also brings many light elements into the Earth’s core.In particular,if the Moon-forming giant impact is a CMGI,then CMGI can also explain the abnormal content of HSEs in the Earth’s current mantle.

Domain Suppression in the Negative Differential Conductivity Region of Carbon Nanotubes by Applied AC Electric Field

We study theoretically the electron transport properties in achiral carbon nanotubes under the influence of an external electric field E(t) using Boltzmann’s transport equation to derive the current-density. A negative differential conductivity (NDC) is predicted in quasi-static approximation i.e., ωτ 0 is equal to the amplitude of the AC electric field E1. The peak of the NDC intensity occurs at very weaker fields than that of superlattice under the same conditions. The peak intensity decreases and shifts to right with the increase in the amplitude of the ac field. This mechanism suppresses the domain formation and therefore could be used in terahertz frequency generation.

A Criterion for Dependency of Algebraic Equations With Applications to Automated Theorem Proving

In this paper,a characteristic-set-based criterion is given to verify whether a polynomial is vanishing over an algebraic variety.The algorithm is feasible in practice,and does not depend on the decomposition of the variety.

Asymptotic solvers for ordinary differential equations with multiple frequencies

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.

QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.

MHD(SWCNTS+MWCNTS)/H_(2)O-Based Williamson Hybrid Nanofluids Flow Past Exponential Shrinking Sheet in Porous Medium

The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential equations which governed the model are first reduced to a set of ordinary differential equations by using the similarity transformation.Next,the BVP4C solver is applied to solve the equations by considering the pertinent fluid parameters such as the permeability parameter,the magnetic parameter,the Williamson parameter,the nanoparticle volume fractions and the wall mass transfer parameter.The single(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)nanoparticles are taken as the hybrid nanoparticles.It is found that the increase in magnetic parameter in SWCNT+MCWNT hybrid nanofluid results in an increase of 72.2%on skin friction compared to SWCNT nanofluid while maintaining reducing a small number of Nusselt number.This shows the potential of the Williamson hybrid nanofluid for friction application purposes especially in transportation like braking system,flushing fluid and mechanical engineering.

Millimeter gap contrast as a probe for turbulence level in protoplanetary disks

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks.Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data,and an exquisite determination of the temperature.In this work,taking the well-known HD 163296 disk as an example,we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence.With self-consistent radiative transfer models,we simultaneously analyzed the radial brightness profiles along the disk major and minor axes,and the azimuthal brightness profiles of the B67 and B100 rings.By fitting all the gap contrasts measured from these profiles,we constrained the gas-to-dust scale height ratioΛto be 3.0^(+0.3)_(−0.8),1.2^(+0.1)_(−0.1),and≥6.5 for the D48,B67,and B100 regions,respectively.The varying gas-to-dust scale height ratios indicate that the degree of dust settling changes with radius.The inferred values forΛtranslate into a turbulence level of α_(turb)<3×10^(−3) in the D48 and B100 regions,which is consistent with previous upper limits set by gas line observations.However,turbulent motions in the B67 ring are strong with α_(turb)∼1.2×10^(−2).Due to the degeneracy betweenΛand the depth of dust surface density drops,the turbulence strength in the D86 gap region is not constrained.

Thermal optimization of MHD nanofluid over a wedge by using response surface methodology:Sensitivity analysis

It is well documented that heat transfer is enhanced with addition of nanosized particles in fluid.But,in a mechanical system there are variety of factors influences the heat transfer.Some factors are significant while others are not.In this paper,authors will discuss sensitivity of different input parameters such as Le,Nt and Nb on output responses𝑁Nu_(x)and Sh_(x).To achieve this goal,the problem is modeled using basic conservation laws.The formulated model is a set of PDEs,which are converted to set of non-linear ODEs by using similarity transformation.Then these ODEs are solved numerically by using MATLAB built in package bvp4c and compared the numerical results with existing work and found good results.Sensitivity analysis is performed by employing RSM to determine the relationship between the input parameters such that 0.1≤Le≤1,0.1≤Nt≤1 and 0.1≤Nb≤1 and the output responses(Nu_(x)and Sh_(x)).ANOVA tables are generated by using RSM.By using the ANOVA tables the correlations between input parameters and output response are developed.To check the validity of correlated equations,the residuals are plotted graphically and show best correlations between input parameters and output responses.The high values of R^(2)=98.65 and AdjR^(2)=97.43 for Nu_(x)and R^(2)=97.83 and AdjR^(2)=95.88 for Sh_(x)demonstrates the high validity of ANOVA results to perform sensitivity analysis.Finally,we have conducted a sensitivity analysis of the responses and came to the important results that Nt and Nb is most sensitive to Nusselt number and Sherwood number respectively.

A generic property of globally smooth iterative roots

A generic property that there is no differentiable iterative root on the dosed interval I = [0, 1] for a kind of strictly increasing C’-smooth functions with two hyperbolic fixed points 0 and 1 is given. This is an interesting result because for the same kind of functions, the existence and uniqueness of continuous root on I, diflerentiable at one of the fixed points, is well known.

Characteristics of dry-wet abrupt alternation events in the middle and lower reaches of the Yangtze River Basin and the relationship with ENSO

During recent decades, more frequent flood-drought alternations have been seen in China as a result of global climate change and intensive human activities, which have sig- nificant implications on water and food security. To better identify the characteristics of flood-drought alternations, we proposed a modified dry-wet abrupt alternation index （DWAAI） and applied the new method in the middle and lower reaches of the Yangtze River Basin （YRB-ML） to analyze the long-term spatio-temporal characteristics of dry-wet abrupt alterna- tion （DWAA） events based on the daily precipitation observations at 75 rainfall stations in summer from 1960 to 2015. We found that the DWAA events have been spreading in the study area with higher frequency and intensity since 1960. In particular, the DWAA events mainly occurred in May and June in the northwest of the YRB-ML, including Hanjiang River Basin, the middle reaches of the YRB, north of Dongting Lake and northwest of Poyang Lake. In addition, we also analyzed the impact of El Nifio Southern Oscillation （ENSO） on DWAA events in the YRB-ML. The results showed that around 41.04% of DWAA events occurred during the declining stages of La Nifia or within the subsequent 8 months after La Nina, which implies that La Nina events could be predictive signals of DWAA events. Besides, significant negative correlations have been found between the modified DWAAI values of all the rainfall stations and the sea surface temperature anomalies in the Nino3.4 region within the 6 months prior to the DWAA events, particularly for the Poyang Lake watershed and the middle reaches of the YRB. This study has significant implications on the flood and drought control and water resources management in the YRB-ML under the challenge of future climate change.

Measuring vacuum polarization with high-power lasers

When exposed to intense electromagnetic fields, the quantum vacuum is expected to exhibit properties of a polarizable medium akin to a weakly nonlinear dielectric material. Various schemes have been proposed to measure such vacuum polarization effects using a combination of high- power lasers. Motivated by several planned experiments, we provide an overview of experimental signatures that have been suggested to confirm this prediction of quantum electrodynamics of real photon–photon scattering.

Energy convergence effect and jet phenomenon of shock-heavy spherical bubble interaction

We present computational results on the evolution of the shock-accelerated heavy bubbles surrounded by nitrogen with the Atwood number At = 0.497–0.677 and the emphasis is on the jet phenomenon caused by the shock focusing. The multi-fluid Eulerian equation is solved by a finite volume method based on MUSCL-Hancock approach. Based on the numerical schlieren and the distributions of density and pressure, it is found that there are three typical jet structures(outward jet, no jet, inward jet) for different combinations of gas mixture inside the bubble which determine the position of shock focusing relative to the downstream pole of the heavy bubble(upstream of the pole, at the pole, downstream the pole). Compared with the inward jet, the velocity of outward jet is obviously larger. As At increases, the moment of jet formation is postponed, and the maximal values and magnifications of pressure and density increase distinctly. Therefore, the energy convergence effects are heavily enhanced with the increase of bubble gas density.

GRID-INDEPENDENT CONSTRUCTION OF MULTISTEP METHODS

A new polynomial formulation of variable step size linear multistep methods is pre- sented, where each k-step method is characterized by a fixed set of k - 1 or k parameters. This construction includes all methods of maximal order （p = k for stiff, and p = k ＋ 1 for nonstiff problems）. Supporting time step adaptivity by construction, the new formulation is not based on extending classical fixed step size methods; instead classical methods are obtained as fixed step size restrictions within a unified framework. The methods are imple- mented in MATLAB, with local error estimation and a wide range of step size controllers. This provides a platform for investigating and comparing different multistep method in realistic operational conditions. Computational experiments show that the new multi- step method construction and implementation compares favorably to existing software, although variable order has not yet been included.

Observational constraints on running vacuum model

We investigate the power spectra of the CMB temperature and matter density in the running vacuum model(RVM) with the time-dependent cosmological constant of A=3 vH^2+ Λ_0, where H is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter v as well as the cosmological observables. Explicitly, we obtain v ≤1.54× 10^(-4)(68% confidence level) in the RVM with the best-fit χ_(RVM)~2 =13968.8, which is slightly smaller thanχ_(ΛCDM)~2= 13969.8 in the ΛCDM model of v = 0.