arXiv subjects

Aubrey Jaffer

Publications and source records attributed to Aubrey Jaffer.

4 recordsLinked to original sources

arXiv2023

Natural Convection Heat Transfer from an Isothermal Plate

Using boundary-layer theory, natural convection heat transfer formulas which are accurate over a wide range of Rayleigh numbers ($Ra$) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning $1<Ra<10^{12}$ has 5.4% root-mean-squared relative error (RMSRE) from the new upward-facing heat transfer formula. Applied to downward-facing plates, this novel approach outperforms the Schulenberg (1985) formula's 4.6% RMSRE with 3.8% on four peer-reviewed data-sets spanning $10^6<Ra<10^{12}$. The introduction of the harmonic mean as the characteristic-length metric for vertical and downward-facing plates extends those rectangular plate formulas to other convex shapes, achieving 3.8% RMSRE on vertical disk convection from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995).

physics.flu-dyn↗

arXiv2018

Oseen Flow in Paint Marbling

Paint marbling refers to techniques for creating intricate designs in colored paints floating on a liquid surface. If the marbling motions are executed slowly, then this layer of paints can be modeled as a two-dimensional incompressible Newtonian fluid. In this highly constrained model many marbling techniques can be exactly represented by closed form homeomorphisms. Homeomorphisms can be composed and compute the composite mapping at any resolution. Computing homeomorphisms directly is orders of magnitude faster than finite-element methods in solving paint marbling flows. Most marbling patterns involve drawing rakes from one side of the tank to the other; and these can be modeled by exact closed form homeomorphisms. But pictorial designs for flowers and animals use short strokes of a single stylus; presented is an exact velocity field for Oseen fluid flow and its application to creating short stroke marbling homeomorphisms.

physics.flu-dyn↗

arXiv2015

Recurrence for Pandimensional Space-Filling Functions

A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling curves, the finite approximations to space-filling functions, have found application in global optimization, database indexing, and dimension reduction among others. For these applications the desired transforms are mapping a scalar to multidimensional coordinates and mapping multidimensional coordinates to a scalar. Presented are recurrences which produce space-filling functions and curves of any rank $d\ge2$ based on serpentine Hamiltonian paths on $({\bf Z}\bmod s)^d$ where $s\ge2$. The recurrences for inverse space-filling functions are also presented. Both Peano and Hilbert curves and functions and their generalizations to higher dimensions are produced by these recurrences. The computations of these space-filling functions and their inverse functions are absolutely convergent geometric series. The space-filling functions are constructed as limits of integer recurrences and equivalently as non-terminating real recurrences. Scaling relations are given which enable the space-filling functions and curves and their inverses to extend beyond the unit area or volume and even to all of $d$-space. This unification of pandimensional space-filling curves facilitates quantitative comparison of curves generated from different Hamiltonian paths. The isotropy and performance in dimension reduction of a variety of space-filling curves are analyzed. For dimension reduction it is found that Hilbert curves perform somewhat better than Peano curves and their isotropic variants.

cs.CG↗

arXiv2013

Easy Accurate Reading and Writing of Floating-Point Numbers

Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than those previously published. The values are stable under repeated conversions between the formats. Unlike Java-1.8, the scientific representations generated use only the minimum number of mantissa digits needed to convert back to the original binary values.

math.NA↗