On travelling-wave solutions to systems of conservation laws with singular viscosity

Abstract. The method of vanishing artificial viscosity is used to obtain smooth, largedata travelling-wave solutions to a class of conservation laws with semidefinite viscosity. The one-dimensional Navier-Stokes equations serve as an illustrating example.     

Glutaraldehyde crosslinking of arabinoxylan produced from corn ethanol residuals

This study investigated the possibility of substituting petroleum-based polymers with biopolymers for films and paper coatings. Arabinoxylan (AX) was extracted from distillers’ grains, a low-value corn ethanol byproduct, and modified through crosslinking with glutaraldehyde (GA) which was made into films and paper coatings. The effects of degree of substitution (DS) on film and coating properties of GA cross-linked AX, referred to as GAX, were investigated. The GAX films had markedly higher tensile strength, approximately 3 times higher than the unmodified AX films at low DS, with higher DS causing a negative effect on the film tensile strength. Compared to unmodified AX coating, paper coated with GAX also had significantly higher tensile index, presumably due to high adhesion between the coating and paper interface. When used as a coating binder with calcium carbonate pigments, GAX showed comparable performance to polyvinyl alcohol, a common industrial binder, demonstrating the potential to be substituted for the petroleum-based paper coating binder.     

Bistability in a hyperchaotic system with a line equilibrium

A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.     

Chaotic flows with a single nonquadratic term

This paper addresses a previously unexplored regime of three-dimensional dissipative chaotic flows in which all but one of the nonlinearities are quadratic. The simplest such systems are determined, and their equilibria and stability are described. These systems often have one or more infinite lines of equilibrium points and sometimes have stable equilibria that coexist with the strange attractors, which are sometimes hidden. Furthermore, the coefficient of the single nonquadratic term provides a simple means for scaling the amplitude and frequency of the system.     

Displacement front behavior of near miscible CO2 flooding in decane saturated synthetic sandstone cores revealed by magnetic resonance imaging

It is of great importance to study the CO₂-oil two-phase flow characteristic and displacement front behavior in porous media, for understanding the mechanisms of CO₂ enhanced oil recovery. In this work, we carried out near miscible CO₂ flooding experiments in decane saturated synthetic sandstone cores to investigate the displacement front characteristic by using magnetic resonance imaging technique. Experiments were done in three consolidated sandstone cores with the permeabilities ranging from 80 to 450 mD. The oil saturation maps and the overall oil saturation during CO₂ injections were obtained from the intensity of magnetic resonance imaging. Finally the parameters of the piston-like displacement fronts, including the front velocity and the front geometry factor (the length to width ratio) were analyzed. Experimental results showed that the near miscible vertical upward displacement is instable above the minimum miscible pressure in the synthetic sandstone cores. However, low permeability can restrain the instability to some extent.     

Stencil lithography of gold-black IR absorption coatings

Gold black coatings are deposited through a stencil shadow mask to produce infrared-absorbing patterns with sub-mm lateral dimensions. Such dimensions match the characteristic pitch of Long Wave Infrared (LWIR) array bolometers. Infrared spectral imaging with sub-micron spatial resolution reveals the spatial distribution of absorption across the pattern.     

Optimization of a tracer-based PLIF diagnostic for simultaneous imaging of EGR and temperature in IC engines

A tracer-based planar laser-induced fluorescence (TB-PLIF) imaging diagnostic using 3-pentanone has been optimized for use in IC engines. The diagnostic utilizes dual-wavelength excitation of 3-pentanone in the ultraviolet to make simultaneous measurements of exhaust gas residual mole fraction and temperature. A merit function based optimization of the diagnostic precision was performed which allowed for selection of optimal excitation wavelengths for the conditions of interest. Optimized system performance was validated in a motored optical engine over a wide range of in-cylinder temperatures and pressures. In-cylinder results verify the utility of the uncertainty estimates. Differences in magnitude between the estimated and measured precision were determined to be due to errors in parameter values used in the calculations. The observed 2.1% temperature precision at a temperature of 600 K was compared with previous TB-PLIF temperature measurements and shown to be approximately a factor of 2 better than previous results.