Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al_2O_3-Cu/H_2O hybrid nanofluid

The characteristics of heat transfer in the three-dimensional stagnationpoint flow past a stretching/shrinking surface of the Al_2O_3-Cu/H_2O hybrid nanofluid with anisotropic slip are investigated. The partial differential equations are converted into a system of ordinary differential equations by valid similarity transformations. The simplified mathematical model is solved computationally by the bvp4c approach in the MATLAB operating system. This solving method is capable of generating more than one solutions when suitable initial guesses are proposed. The results are proven to have dual solutions, which consequently lead to the application of a stability analysis that verifies the achievability of the first solution. The findings reveal infinite values of the dual solutions at several measured parameters causing the non-appearance of the turning points and the critical values. The skin friction increases with the addition of nanoparticles, while the escalation of the anisotropic slip effect causes a reduction in the heat transfer rate.     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite(PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes(CNTs) and nanoclay(NC) simultaneously. The governing equations are derived based on the first shear deformation theory(FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams,as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.     

Mechanical response of fabric sheets to three-dimensional bending,twisting, and stretching

A model for the mechanics of woven fabrics is developed in the framework of two-dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of appropriate constitutive equations. The model accounts for the strain of the fabric and additional effects associated with the normal bending, geodesic bending, and twisting of the constituent fibers.     

A modern approach to the solution and analysis of the Simha-Somcynsky model for the description of pressure-volume-temperature properties of polymer fluids

We revisit the Simha-Somcynsky model of polymer fluids with the purpose of developing novel theoretical and computational approaches to simplify and speed up its solution as well as the fitting of experimental data, and decrease its level of mathematical complexity. We report a novel method that allows us to solve one of the two equations of the model exactly, thus putting the level of mathematical difficulty on a par with the one of other models for polymer fluids. Moreover, we describe a computational algorithm capable of fitting all five parameters of the model in an unbiased way. The results obtained reproduce literature results and fit experimental pressure-volume-temperature and solubility parameter data for three polymers very accurately. Moreover, the new techniques allow for the investigation of the model at very low temperatures. Unexpectedly, the model predicts behaviors that could be interpreted as a glass transition, as routinely observed in dilatometry and differential scanning calorimetry, and a glass phase. We compared the predicted and experimental T g’s for cis poly(1,4-butadiene) and found an excellent quantitative agreement.     

Inversion of electrical mobility measurements using bipolar or unipolar chargers for the arbitrary distribution of channels

The inversion of the particle size distribution from electrical mobility measurements is analyzed.Three different methods are adapted for a dot-matrix approach to the problem,especially for non-square or singular matrices,and applied to electrical mobility measurements from fixed or scanning voltages.Multiply charged particles,diffusion losses,arbitrary voltage steps and noise were considered,which results in non-adjoining and overlapping transfer functions.The individual contribution of the transfer functions in each size interval was geometrically estimated,which requires only its characteristic mobilities.The methodology is applied to mobility measurements from particles charged with unipolar and bipolar chargers.However,the method can be extrapolated to any charging method with a defined charge distribution,and retrieval of the singly charged particle distribution and mean charge from a tandem differential mobility analysis configuration was successfully demonstrated.