Interdisciplinary Applied Mathematics

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quality, 5


quality factor, 5, 107


R-TIRFM technique, 27 radial distribution function, 366 rarefaction, 31 rarefaction coefficient, 153 rarefied channel flow, 602 rarefied pipe flow, 605 Rayleigh-Ritz method, 675 reduced models


low-dimensional models, 56 residence time, 247 residence times, 344 Reynolds equation, 198, 199 derivation, 199 finite dimension effects, 209 generalized form, 203 multidimensional, 209 slip flow, 201 transition flow, 202 Reynolds number, 61 Reynolds-Vinogradova theory, 399 Riemann invariants, 517 Robin boundary conditions, 519 Roe-averaged velocity, 516


Rothe nozzle, 248 roughness, 25, 65


coordinate transformation, 136 effects, 136 random, 65


S expansion, 597, 598 sample injection, 298 scattering kernel, 586 Schwarz algorithm, 571, 649 second-order slip, 69 limitations, 65 sedimentation potential, 254 self-assembly, 27 dynamic, 28 static, 28 SEM, 25, 65, 196 separated flows, 73 external, 221 internal, 214


viscous normal stresses, 223 serpentine channel, 299 SFA, surface force apparatus, 387 shear-driven flow, 79 shock wave, 54 short channels


DSMC modeling, 234 effect of channel length, 236 effects of accommodation coefficients, 238


flowrate comparisons, 237 short-range potentials, 630 silicon micromachining, 1 simulation approaches, 37 SISO system, 694 slider bearing, 18, 197, 204 slip, 57


slip boundary condition, 459, 460 implementation, 519 slip condition liquids, 385 slip flow, 16, 20 slip flow regime, 57 slip length, 11 slip models


coefficients, 74 comparison, 74, 144 limitations and remarks, 76 remarks, 136


validations, 131 slip velocity, 69, 487 Sllod algorithm, 640 Sone’s theory, 592 species


flux, 261


specific impulse, 588


spectral element method, 506, 507,


545


specular reflection, 62 SPICE, 39, 41 spinodal wetting, 318 square-cube law, 2 square-well potential, 625 squeeze number, 209, 744 squeezed film, 197, 210


damping in complex geometries, 213


squeezing flow, 542 Stern layer, 256 STM, 65


Stokes drag, 224, 301 Stokes flow, 291 Stokes number, 91 Stokes second problem, 94, 198 Stokes’s equations, 55 Stokes’s hypothesis, 52 Stokes’s second problem, 275 Stokes-Einstein formula, 474 Stokes/DSMC coupling, 575 Stokesian dynamics, 539 streaming potential, 254 stress tensor, 52 stresslet, 546

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