Interface model for non-equilibrium evaporation

A microscopic interface condition for condensing/evaporating interfaces is developed by combining a velocity dependent condensation probability [T. Tsuruta, H. Tanaka, T. Masuoka, Int. J. Heat Mass Transfer 42 (1999) 4107] and Maxwell type interface conditions with accommodation. Using methods from kinetic theory, macroscopic interface conditions for mass and energy transport across the phase boundary are derived. This model only applies to simple substances, where diffusive effects in the bulk phases are not present. The results are compared to classical non-equilibrium thermodynamics. The interface conditions are considered for the limit of small deviation from equilibrium, and the corresponding Onsager coefficients are computed. These results are useful as boundary conditions for non-equilibrium evaporation and condensation problems, as done previously by our group [M. Bond, H. Struchtrup, Phys. Rev. E 70 (2004) 061605].     

Thermal slip boundary conditions in vibrational nonequilibrium flows

This paper deals with new thermal jump boundary conditions at the wall in polyatomic gas flows. The calculations and results especially concern vibrational nonequilibrium conditions when the dissociation effects may be neglected. First the usual conditions are briefly described. Then the boundary conditions proposed in the paper are justified on the basis of previous experimental results and by developing direct heat flux calculations at the wall. Analytical expressions and numerical values of the various fluxes are presented.     

Wavefront aberrations in the accommodated human eye based on individual eye model

In this research, we firstly construct individual eye models based on the wavefront and the measured cornea structure of the eyes. Then we analyze the influence of accommodation on the wavefront aberrations based on individual eye model. The individual eye model has the same wavefront aberration as that measured from Hartmann–Shack wavefront sensor. The optical design software ZEMAX is used to construct the individual eye models for 20 normal eyes. Accommodative conditions are from 0 to –4 diopter in steps of one diopter. The variations of the total, the spherical, the coma and the higher-order root-mean-square wavefront aberrations, as accommodations, are illustrated. Influence of accommodation on wavefront aberration varies from individual to individual, and the variation magnitude is independent of the magnitude of the wavefront aberration of the eye.     

Computational modelling of fluid structure interaction at nano-scale boundaries with modified Maxwellian velocity distribution

The soft collisions among fluid–fluid and fluid-wall molecules are modeled from first principles. In particular, the assumption of Maxwellian distribution of velocities for thermalized molecules, in both parallel and perpendicular directions to the wall, has been re-evaluated with supporting experimental and/or numerical evidence.It is proposed that the normal component of molecular velocity post collision is conserved for all fluid molecules. The slip effect at the wall boundary, introduced by the surface roughness, is accounted by an accommodation coefficient f. A moving least square method is used to calculate macroscopic velocity values. The influence of molecular interaction on the macroscopic velocity distribution is investigated at 40 MPa and 300 K for slit pore, inclined and stepped wall configurations. The accommodation coefficient values f = 0, 0.07, 0.257, 0.45, 0.681 and 1; and acceleration values ranging from zero to 1 × 10¹¹ m/s² and 250 × 10¹¹ m/s² are used for comparison.The distribution of macroscopic velocity parallel to the wall is studied to observe the effect of the slip behaviour. The detailed study of average of velocity values at various magnitudes of acceleration has shown an evidence of characteristic low and high speed of molecular flows that is considered as significant and a comparison is sought with an equivalent laminar and turbulent flow style behaviour. The two dimensional vector and contour plots of macroscopic velocity provide further insights in understanding Continuum velocity distributions resulting from molecular fluid-wall interaction at nanoscale. The research has highlighted the need to develop molecular dynamics simulation techniques for non-periodic boundary conditions.     

Predetermined accommodations with a standardized testing protocol: Examining two accommodation supports for developing fraction thinking in students with mathematical difficulties

This study examined the effects of two pre-determined accommodations that were provided in a standardized testing. The two accommodations were meant to help students with difficulties in mathematics (SDMs) engage in unit thinking, reasoning, and coordination and consequently improve their ability to process fraction tasks. 23 middle school SDMs took the following tests and were asked to explain their solutions: a baseline fraction test without any accommodation; an annotated test with bolded information and additional simplified explanations; and a warming- up test that involved whole-number multiplicative reasoning tasks followed by the baseline test. Results show that while SDMs were able to construct and coordinate fraction units to solve fraction problems when appropriate accommodations were provided, standardized assessment with a predetermined “one-size-fits -all” accommodation could not meet the specific needs of all students with mathematics learning difficulties.     

A wavefront aberrometer for dynamic high-order aberration measurement

This research studied the dynamic aberration of human eyes at near vision. A wavefront aberrometer was developed based on the Hartmann-Shack theory. This aberrometer can achieve dynamical aberration measurement of the human eye. The Aberrometer induces ocular accommodation by a moving target at near vision, and records the vision information of human eyes simultaneously during ocular accommodation process using a Hartmann-Shack sensor. Nineteen eyes of 10 volunteers are tested. Eighty-four percent eyes have induced accommodation amplitude between 3 diopter (D) and 8D. The highest induced accommodation amplitude is 8.6D. The aberrometer produces results with high precision and repeatability, i.e. an accuracy root-mean-square (RMS) of 1/50^λ and a repeatability RMS of 1/500^λ.