Effect of oscillatory shear on the mechanical properties and crystalline morphology of linear low density polyethylene

In this study,effects of oscillatory shear with different frequencies(0-2.5 Hz) and amplitudes(0-20 mm) on the mechanical properties and crystalline morphology of linear low density polyethylene(LLDPE) were investigated.It was found that the mechanical properties of LLDPE are improved because of the more perfect crystalline structure when LLDPE crystallizes under low-frequency and small-amplitude(0.2 Hz/4 mm) oscillatory shear.The mechanical properties can be further improved by increasing either the frequency or the amplitude of oscillatory shear.The Young's modulus and tensile strength of LLDPE are improved by 27% and 20%,respectively,when the frequency is increased to 2.5 Hz and the amplitude is maintained at 4 mm; while the Young's modulus and tensile strength are improved by 49% and 47%,respectively,when the amplitude is increased to 20 mm and the frequency is remained as 0.2 Hz.The crystallinity and microstructure of LLDPE under different oscillatory shear conditions were investigated by using differential scanning calorimetry,wide angle X-ray diffraction and scanning electron microscopy to shed light on the mechanism for the improvement of mechanical properties.     

Characterization of silicone oil emulsions stabilized by TiO2 suspensions pre-adsorbed SDS

To study the effects of pre-adsorbed emulsifier on Pickering emulsion stability, the preparation of silicone oil emulsions by TiO₂ suspensions pre-adsorbed sodium dodecyl sulfate (SDS) at the fixed TiO₂ concentration of 0.15 g was carried out below a fiftieth of critical micelle concentration (cmc) of SDS, where all added amounts of SDS are adsorbed on the TiO₂ particles. The stability of the Pickering emulsions incorporating TiO₂ suspensions pre-adsorbed SDS was investigated by measuring the volume fraction of emulsified silicone oil, adsorbed amounts of TiO₂ suspensions pre-adsorbed SDS, oil droplet size, and some rheological responses such as the stress-strain sweep curve and strain and frequency dependences of dynamic viscoelastic moduli. The silicone oil was almost emulsified by TiO₂ suspensions pre-adsorbed SDS above cmc/10³. Increasing in the adsorbed amount of SDS on the TiO₂ particles leads to an increase in the adsorbed amounts of TiO₂ suspensions pre-adsorbed SDS. Such silicone oil emulsions for the first time showed two yield stresses in the stress-strain sweep curve as well as the oscillatory stress-strain curve. The respective yield stresses also increase with an increase in the adsorbed amounts of TiO₂ suspensions pre-adsorbed SDS. From such characteristic rheological properties and a partial sedimentation of some TiO₂ particles remained in the dispersion medium, we proposed the formation of a three dimensional network of the flocculated TiO₂ particles pre-adsorbed SDS on the silicone oil droplets.     

Pattern recognition minimizes entropy production in a neural network of electrical oscillators

We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Hölzel and Krischer, 2011 [13]). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.     

Some properties of the vertical structure operators for hydrostatic atmospheric models

Hydrostatic atmospheric models in a generalized vertical coordinate are considered. The governing equations are linearized with respect to a general basic state including arbitrary vertical variation of the reference temperature profile. Vertical structure equations are derived and studied for both continuous and discretized models. Some properties of vertical normal modes are defined and a comparison between continuous and discrete cases is made.     

A rapid solution of a kind of 1D Fredholm oscillatory integral equation

How to solve oscillatory integral equations rapidly and accurately is an issue that attracts special attention in many engineering fields and theoretical studies. In this paper, a rapid solution method is put forward to solve a kind of special oscillatory integral equation whose unknown function is much less oscillatory than the kernel function. In the method, an improved-Levin quadrature method is adopted to solve the oscillatory integrals. On the one hand, the employment of this quadrature method makes the proposed method very accurate; on the other hand, only a small number of small-scaled systems of linear equations are required to be solved, so the computational complexity is also very small. Numerical examples confirm the advantages of the method.     

Influences of oscillatory structural forces on dewetting of nanoparticle-laden ultra-thin films

To understand the influences of nanoparticleson dewetting in ultra-thin films,both linear stability theory and numerical simulations are performed in the presentstudy,with the consideration of oscillatory structural(OS)forces.Long scale approximation is utilized to simplify thehydrodynamic and diffusion equations to a nonlinear systemfor film thickness and nanoparticle concentration.Resultsshow that the presence of nanoparticles generally suppressesthe dewetting process.Two physical mechanisms responsible for this phenomenon are addressed in the present study.When the oscillatory structural forces are relatively smaller,the essential feature of film evolution is similar to the case ofparticle-free flow.The reduction of the linear growth rate andthe postponement of film rupturing can be attributed to theincrement of the viscosity due to the presence of nanoparticles.On the other hand,when the intensity of the OS forcesbecomes stronger,the stepwise thinning of film can be observed which prevents the film from rupture.Numerical simulations indicate that this phenomenon is caused by the existence of a stable zone due to the oscillatory nature of thestructural forces.Another interesting finding is that the nonuniformity of the distribution of nanoparticle concentrationmight destabilize a spinodally stable film,and trigger the occurrence of film dewetting.     

Microgravity experiments of single droplet combustion in oscillatory flow at elevated pressure

An experimental study for 1-butanol single droplet flames in constant and oscillatory flow fields was conducted under microgravity conditions at elevated pressure. In the constant flow experiments, flow velocities from 0 to 40 cm/s were tested. Using obtained data of d², the burning rate constants were evaluated. The burning rate constant in the quiescent condition was also calculated successfully at high pressure by the extrapolation method based on the Frössling relation. In the oscillatory flow experiments, the flow velocities were varied from 0 to 40 cm/s at the frequencies of 2–40 Hz. Results showed that the burning rate constant during the droplet lifetime varied following the quasi-steady relation at 0.1 MPa; however, in the conditions with higher frequencies at 0.4 MPa, the average burning velocity became larger than that for the constant flow case with the velocity equivalent to the maximum velocity in the oscillatory flow. Under the condition where the burning rate constant increased, it was observed that the flame did not sufficiently move back upstream, leading to enhancement of the heat transfer from the flame to the droplet surface. Therefore, the instantaneous burning rate constant increased. To investigate the mechanism of such flame behavior, the ratio of two characteristic times, τ_f/τ_D (τ_f: flow oscillation characteristic time, τ_D: diffusion characteristic time), were compared. As the flow oscillatory frequency increased, τ_f/τ_D becomes smaller. τ_f/τ_D also became smaller at high pressure. If τ_f/τ_D is small due to the small mass diffusion rate, the droplet flame could not move back to the appropriate position for the minimum velocity in steady flow, leading to an increase of the burning rate constant, especially in the case of higher frequency at high pressure.     

A note on Marcinkiewicz integral operators

This paper is primarily concerned with proving the L^p boundedness of Marcinkiewicz integral operators with kernels belonging to certain block spaces. We also show the optimality of our condition on the kernel for the L² boundedness of the Marcinkiewicz integral.