Froth-like Minimizers of a Non-Local Free Energy Functional with Competing Interactions

We investigate the ground and low energy states of a one dimensional non-local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are “froth-like”: if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective “sharp interface” one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.     

Temperature analysis of laser heated polymers on microsecond time scales

To investigate the temperature profiles on laser heated polymer films, we track the thermal radiation with 1 μs time and 1 μm spatial resolution. The resulting two-dimensional temperature graphs are compared to finite element simulations in order to understand the heat conversion and flow. The temperature measurement setup consists of a NIR laser and an optical detection system, which includes high performance optics and a microsecond gated camera, equipped with several interference filters. In this way the thermal radiation is detected in the visible range with spectral resolution. Fitting the spectrum with Planck’s law, two-dimensional micrographs of the temperature distribution are obtained. For polystyrene surfaces we were able to analyze the heating and the ablation behavior. Good agreement was found between experimental results and finite element simulations, when ablation is limited to a few tens of nanometers of the film thickness. Ablation of polystyrene starts at 150°C, 50 K above the glass transition temperature. We suggest a photomechanical ablation mechanism at that threshold fluence. For ablation at higher fluence and peak temperature, experiments indicate a thermal decomposition reaction. The temperature range of spinodal decomposition is not reached and can in our case be ruled out as ablation mechanism.     

Negative index photonic crystal lenses based on carbon nanotube arrays

We report a novel utilization of periodic arrays of carbon nanotubes in the realization of diffractive photonic crystal lenses. Carbon nanotube arrays with nanoscale dimensions (lattice constant 400 nm and tube radius 50 nm) displayed a negative refractive index in the optical regime where the wavelength is of the order of array spacing. A detailed computational analysis of band gaps and optical transmission through the nanotubes based planar, convex and concave shaped lenses was performed. Due to the negative-index these lenses behaved in an opposite fashion compared to their conventional counter parts. A plano-concave lens was established and numerically tested, displaying ultra-small focal length of 1.5 μm (～2.3 λ) and a near diffraction-limited spot size of 400 nm (～0.61 λ).     

Three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching sheet embedded into a porous medium

A three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching surface placed into a porous medium is examined. Similarity transformations are used to convert time-dependent partial differential equations into nonlinear ordinary differential equations. The transformed equations are then solved analytically by the homotopy analysis method and numerically by the shooting technique combined with the Runge–Kutta–Fehlberg method. The results obtained by both methods are compared with available reported data. The effects of the Casson fluid parameter, magnetic field parameter, and unsteadiness parameter on the velocity and local skin friction coefficients are discussed in detail.     

Computational modeling of an MHD flow of a non-Newtonian fluid over an unsteady stretching sheet with viscous dissipation effects

An investigation has been conducted on the MHD Casson fluid and heat transfer over an unsteady stretching sheet with viscous dissipation effects. With suitable dimensionless variables, partial differential equations are reduced to ordinary differential equations, which are then solved by the homotopy analysis method. Dependences of flow characteristics on various parameters involved into the equations are obtained.     

Physiological Transportation of Casson Fluid in a Plumb Duct

This paper is devoted to a study of the peristaltic motion of a Casson fluid of a non-Newtonian fluid accompanied in a horizontai tube.To characterize the non-Newtonian fluid behavior,we have considered the Casson fluid model.Suitable similarity transformations are utilized to transform the governing partial differential momentum into the non-linear ordinary differential equations.Exact analytical solutions of these equations are obtained and are the properties of velocity,pressure and profiles are then studied graphically.     

Complexity factor for charged spherical system

In this paper, we study the complexity factor for a charged anisotropic self-gravitating object. We formulate the Einstein–Maxwell field equations, Tolman–Opphenheimer–Volkoff equation, and the mass function. We form the structure scalars by the orthogonal splitting of the Riemann tensor and then find the complexity factor with the help of these scalars. Finally, we investigate some astrophysical objects for the vanishing of complexity condition. It is found that the presence of the electromagnetic field decreases the complexity of the system.     

First-principles calculations of nitrogen-doped antimony triselenide: A prospective material for solar cells and infrared optoelectronic devices

This study is focused on calculation of the electronic structure and optical properties of non-metal doped Sb2Se3 using the first-principles method. One and two N atoms are introduced to Sb and Se sites in a Sb₂Se₃ crystal. When one and two N atoms are introduced into the Sb₂Se₃ lattice at Sb sites, the electronic structure shows that the doping significantly modifies the bandgap of Sb₂Se₃ from 1.11 eV to 0.787 and 0.685 eV, respectively. When N atoms are introduced to Se sites, the material shows a metallic behavior. The static dielectric constants ε1(0) for Sb₁₆Se₂₄, Sb₁₅N₁Se₂₄, Sb₁₄N₂Se₂₄, Sb₁₆Se₂₃N₁, and Sb₁₆Se₂₂N₂ are 14.84, 15.54, 15.02, 18.9, and 39.29, respectively. The calculated values of the refractive index n(0) for Sb₁₆Se₂₄, Sb₁₅N₁Se₂₄, Sb₁₄N₂Se₂₄, Sb₁₆Se₂₃N₁, and Sb₁₆Se₂₂N₂ are 3.83, 3.92, 3.86, 4.33, and 6.21, respectively. The optical absorbance and optical conductivity curves of the crystal for N-doping at Sb sites show a significant redshift towards the short-wave infrared spectral region as compared to N-doping at Se sites. The modulation of the static refractive index and static dielectric constant is mainly dependent on the doping level. The optical properties and bandgap narrowing effect suggest that the N-doped Sb₂Se₃is a promising new semiconductor and can be a replacement for GaSb due to its very similar bandgap and low cost.     

An Integrated Fuzzy Analytic Hierarchy Process (AHP) Model for Studying Significant Factors Associated with Frequent Lane Changing

Frequent lane changes cause serious traffic safety concerns, which involve fatalities and serious injuries. This phenomenon is affected by several significant factors related to road safety. The detection and classification of significant factors affecting lane changing could help reduce frequent lane changing risk. The principal objective of this research is to estimate and prioritize the nominated crucial criteria and sub-criteria based on participants’ answers on a designated questionnaire survey. In doing so, this paper constructs a hierarchical lane-change model based on the concept of the analytic hierarchy process (AHP) with two levels of the most concerning attributes. Accordingly, the fuzzy analytic hierarchy process (FAHP) procedure was applied utilizing fuzzy scale to evaluate precisely the most influential factors affecting lane changing, which will decrease uncertainty in the evaluation process. Based on the final measured weights for level 1, FAHP model estimation results revealed that the most influential variable affecting lane-changing is ‘traffic characteristics’. In contrast, compared to other specified factors, ‘light conditions’ was found to be the least critical factor related to driver lane-change maneuvers. For level 2, the FAHP model results showed ‘traffic volume’ as the most critical factor influencing the lane changes operations, followed by ‘speed’. The objectivity of the model was supported by sensitivity analyses that examined a range for weights’ values and those corresponding to alternative values. Based on the evaluated results, stakeholders can determine strategic policy by considering and placing more emphasis on the highlighted risk factors associated with lane changing to improve road safety. In conclusion, the finding provides the usefulness of the fuzzy analytic hierarchy process to review lane-changing risks for road safety.     

Low-temperature anomalies in the plastic response of crystalline materials

The non-uniform, wavy, temperature-dependence of the yield-stress and of the rate of logarithmic creep frequently observed in metals, alloys and non-metallic crystalline solids at low temperature, is shown to be largely a consequence of the progressive inhibition of dynamic recovery processes as T → 0 K. Plastic deformation becomes increasingly localised, resulting in high stress-concentrations. On allowing for this increase in the usual equations of the deformation kineties, the anomalies are very well accounted for.