Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

Dynamical Demixing of a Binary Mixture Under Sedimentation

We investigate the sedimentation dynamics of a binary mixture,the species of which differ by their Stokes coefficients but are identical otherwise.We analyze the sedimentation dynamics and the morphology of the final deposits using Brownian dynamics simulations for mixtures with a range of sedimentation velocities of both species.In addition,we use the lattice Boltzmann method to study hydrodynamic effects.We found a threshold in the difference of the sedimentation velocities above which the species in the final deposit are segregated.The degree of segregation increases with the difference in the Stokes coefficients or the sedimentation velocities above the threshold.We propose a simple analytical model that captures the main features of the simulated deposits.

Topological rearrangements and flow simulation of dry ordered foams

Flow through a narrow bent channel may induce topological rearrangements in a twodimensional monodispersed dry liquid foam.We use the Cellular Potts Model to simulate a foam under a variable driving force in order to investigate the strain-rate response from these rearrangements.We observe a set of foams’behaviors ranging from elastic,viscoelastic to fluid regime.Bubble’s topological rearrangements are localized and their cumulative rearrangements change linearly with time,thus nonavalanches critical behavior is found.The strain-rate affects the rate of topological rearrangements,its dependence on the drag force is nonlinear,obeying a Herschel–Bulkley-like relationship below the foam’s flow point.

Interface networks in models of competing species

We study a subclass of the May–Leonard stochastic model with an arbitrary,even number of species,leading to the rise of two competing partnerships where individuals are indistinguishable.By carrying out a series of accurate numerical stochastic simulations,we show that alliances compete each other forming spatial domains bounded by interfaces of empty sites.We solve numerically the mean field equations associated with the stochastic model in one and two spatial dimensions.We demonstrate that the stationary interface profile presents topological properties which are related to the asymptotic spatial distribution of species of enemy alliances far away from the interface core.Finally,we introduce a theoretical approach to model the formation of stable interfaces using spontaneous breaking of a discrete symmetry.We show that all the results provided by the soliton topological model,presented here for the very first time,are in agreement with the stochastic simulations and may be used as a tool for understanding the complex biodiversity in nature.

Retrieval of Elastic Green’s Tensor near a Cylindrical Inhomogeneity from Vector Correlations

Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and S waves. Insuch diffusive regime the P to S energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the Green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic Greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand S waves uniform but such that the energy ratio ES/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact Green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.

Potts Model with q States on Directed Barab´asi-Albert Networks

On directed Barab´asi-Albert networks with two and seven neighbours selected by each added site,the Ising model with spin S=1/2 was seen not to show a spontaneous magnetisation.Instead,the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms,but for Wolff cluster flipping the magnetisation decayed exponentially with time.However,on these networks the Ising model spin S=1 was seen to show a spontaneous magnetisation.In this case,a first-order phase transition for values of connectivity z=2 and z=7 is well defined.On these same networks the Potts model with q=3 and 8 states is now studied through Monte Carlo simulations.We also obtained for q=3 and 8 states a first-order phase transition for values of connectivity z=2 and z=7 for the directed Barab´asi-Albert network.Theses results are different from the results obtained for the same model on two-dimensional lattices,where for q=3 the phase transition is of second order,while for q=8 the phase transition is of first-order.

Majority-Vote on Undirected Barab´asi-Albert Networks

On Barab´asi-Albert networks with z neighbours selected by each added site,the Ising model was seen to show a spontaneous magnetisation.This spontaneous magnetisation was found below a critical temperature which increases logarithmically with system size.On these networks the majority-vote model with noise is now studied through Monte Carlo simulations.However,in this model,the order-disorder phase transition of the order parameter is well defined in this system and this was not found to increase logarithmically with system size.We calculate the value of the critical noise parameter qc for several values of connectivity z of the undirected Barab´asiAlbert network.The critical exponentesβ/ν,γ/νand 1/νwere also calculated for several values of z.