1 % Year for live projects
7 @string{CC-BY-SA-3.0-US = "CC BY-SA 3.0 US"}
8 @string{CC-BY-NC-SA-3.0-US = "CC BY-NC-SA 3.0 US"}
12 @string{Drexel = "Drexel University"}
16 @string{AAPT = "American Association of Physics Teachers"}
17 @string{APS = "American Physical Society"}
18 @string{ASQ = "American Society for Quality"}
19 @string{Blackwell = "Blackwell Publishing Ltd."}
20 @string{DLA = "Digital Library and Archives, Virginia Polytechnic
21 Institute and State University"}
22 @string{PH = "Prentice Hall, Inc."}
23 @string{WSS = "Wiley Subscription Services, Inc., A Wiley Company"}
27 @string{Crowell-address = "2233 Loma Alta Dr., Fullerton, CA 92833"}
28 @string{UpperSaddleRiver = "Upper Saddle River, NJ 07458"}
32 @string{AJP = "American Journal of Physics"}
33 @string{ASQ:HEB = "ASQ Higher Education Brief"}
34 @string{IJBMM = "International Journal of Biological Macromolecules"}
35 @string{JEE = "Journal of Engineering Education"}
36 @string{JEB = "Journal of Experimental Biology"}
37 @string{JITE = "Journal of Industrial Teacher Education"}
38 @string{Nature = "Nature"}
39 @string{NDTL = "New Directions for Teaching and Learning"}
40 @string{PRL = "Physical Review Letters"}
41 @string{PR:E = "Physical Review E Statistical, Nonlinear and Soft-Matter Physics"}
42 @string{Science = "Science"}
46 @string{MBelloni = "Belloni, Mario"}
47 @string{RPBehringer = "Behringer, Robert P."}
48 @string{RBrent = "Brent, Rebecca"}
49 @string{WChristian = "Christian, Wolfgang"}
50 @string{SPChung = "Chung, Shih-Ping"}
51 @string{EICorwin = "Corwin, Eric I."}
52 @string{CHCrouch = "Crouch, Catherine H."}
53 @string{BCrowell = "Crowell, Benjamin"}
54 @string{LDeslauriers = "Deslauriers, Louis"}
55 @string{RLHDeits = "Deits, Robin L. H."}
56 @string{RMFelder = "Felder, Richard M."}
57 @string{MWGilmer = "Gilmer, Matthew W."}
58 @string{JGomberg = "Gomberg, Joan"}
59 @string{RRHake = "Hake, Richard R."}
60 @string{AEHosoi = "Hosoi, A. E."}
61 @string{HMJaeger = "Jaeger, Heinrich M."}
62 @string{PAJohnson = "Johnson, Paul A."}
63 @string{SDJohnson = "Johnson, Scott D."}
64 @string{MCJohnston = "Johnston, Mitchell C."}
65 @string{PKim = "Kim, Pilnam"}
66 @string{WKing = "King, W.~Trevor"}
67 @string{MKnuth = "Knuth, Matt"}
68 @string{CAKoh = "Koh, Carolyn A."}
69 @string{PGLafond = "Lafond, Patrick G."}
70 @string{JLochhead = "Lochhead, Jack"}
71 @string{TSMajmudar = "Majmudar, Trushant S."}
72 @string{CMarone = "Marone, Chris"}
73 @string{EMazur = "Mazur, Eric"}
74 @string{EMyftiu = "Myftiu, Eglind"}
75 @string{SRNagel = "Nagel, Sidney R."}
76 @string{MPrince = "Prince, Michael"}
77 @string{MRoche = "Roch\'e, Matthieu"}
78 @string{HSavage = "Savage, Heather"}
79 @string{ESchelew = "Schelew, Ellen"}
80 @string{EDSloan = "Sloan, E. Dendy"}
81 @string{HAStone = "Stone, Howard A."}
82 @string{MSu = "Su, Meihong"}
83 @string{AKSum = "Sum, Amadeu K."}
84 @string{AWhimbey = "Whimbey, Arthur"}
85 @string{CWieman = "Wieman, Carl"}
86 @string{AGWinter = "Winter, Amos G."}
87 @string{DTWu = "Wu, David T."}
88 @string{GYang = "Yang, Guoliang"}
92 title = {Open source single molecule force spectroscopy},
96 url = {http://blog.tremily.us/Thesis/},
97 eprint = {http://blog.tremily.us/Thesis/draft.pdf},
101 author = WKing #" and "# MSu #" and "# GYang,
102 title = "{M}onte {C}arlo simulation of mechanical unfolding of proteins
103 based on a simple two-state model",
107 address = "Department of Physics, Drexel University, 3141
108 Chestnut Street, Philadelphia, PA 19104, USA.",
114 alternative_issn = "1879-0003",
115 doi = "10.1016/j.ijbiomac.2009.12.001",
116 url = "http://www.sciencedirect.com/science/article/B6T7J-
117 4XWMND2-1/2/7ef768562b4157fc201d450553e5de5e",
119 keywords = "Atomic force microscopy;Mechanical unfolding;Monte Carlo
120 simulation;Worm-like chain;Single molecule methods",
121 abstract = "Single molecule methods are becoming routine biophysical
122 techniques for studying biological macromolecules. In mechanical
123 unfolding of proteins, an externally applied force is used to induce
124 the unfolding of individual protein molecules. Such experiments have
125 revealed novel information that has significantly enhanced our
126 understanding of the function and folding mechanisms of several types
127 of proteins. To obtain information on the unfolding kinetics and the
128 free energy landscape of the protein molecule from mechanical unfolding
129 data, a Monte Carlo simulation based on a simple two-state kinetic
130 model is often used. In this paper, we provide a detailed description
131 of the procedure to perform such simulations and discuss the
132 approximations and assumptions involved. We show that the appearance of
133 the force versus extension curves from mechanical unfolding of proteins
134 is affected by a variety of experimental parameters, such as the length
135 of the protein polymer and the force constant of the cantilever. We
136 also analyze the errors associated with different methods of data
137 pooling and present a quantitative measure of how well the simulation
138 results fit experimental data. These findings will be helpful in
139 experimental design, artifact identification, and data analysis for
140 single molecule studies of various proteins using the mechanical
146 @unpublished{ 2013-05-thesis,
147 title= {Open source single molecule force spectroscopy},
152 note= {Thesis defense, Drexel University},
153 address = {Drexel University},
154 url = {http://blog.tremily.us/posts/Thesis/talk/},
157 @unpublished{ 2013-01-columbia,
158 title= {Collaborative version control with {G}it},
162 note= {Software Carpentry boot camp, Columbia University},
163 address = {Columbia University},
166 @unpublished{ 2009-10-life-cycles,
167 title= {Software life-cycles and alphabet soup},
171 note= {Drexel Physics Graduate Student Association},
172 address = {Drexel University}
175 @unpublished{ 2008-06-locks,
176 title= {Manipulating combination locks \& Ray tracing with polarization},
180 note= {Drexel Physics Graduate Student Association},
181 address = {Drexel University}
184 @unpublished{ 2006-05-quantum-computing,
185 title= {Quantum Computing},
188 note= {Rochester Solid State final},
189 address = {University of Rochester}
195 @unpublished{ 2013-04-swc,
196 title= {Teaching Software Carpentry: Better Science through Science},
200 note= {Drexel CoAS Research Day},
201 address = {Philadelphia, Pennsylvania},
204 @unpublished{ 2012-04-calibcant,
205 title= {Thermally calibrating {AFM} cantilever spring constants},
209 note= {Drexel CoAS Research Day},
210 address = {Philadelphia, Pennsylvania},
213 @unpublished{ 2011-04-saswsim,
214 title= {Flexible parallel simulations and packaging},
218 note= {Drexel CoAS Research Day},
219 address = {Philadelphia, Pennsylvania},
222 @unpublished{ 2010-04-open-source,
223 title= {Open source software in experimental protein unfolding},
227 note= {Drexel CoAS Research Day},
228 address = {Philadelphia, Pennsylvania},
231 @unpublished{ 2009-03-roughness,
232 title= {Experimental Estimation of the Free Energy Landscape
233 Roughness of Protein Molecules},
237 note= {Biophysical Society Annual Meeting},
238 address = {Philadelphia, Pennsylvania},
241 @unpublished{ 2008-04-sawsim,
242 title= {Simulated mechanical unfolding of single proteins},
246 note= {Drexel CoAS Research Day},
247 address = {Philadelphia, Pennsylvania},
250 @unpublished{ 2008-02-stiffness,
251 title= {Effects of Cantilever Stiffness on Unfolding Force in AFM
256 note= {Biophysical Society Annual Meeting},
257 address = {Long Beach, California},
262 @article{ lochhead87,
263 author = JLochhead #" and "# AWhimbey,
264 title = {Teaching analytical reasoning through thinking aloud pair
273 url = {http://dx.doi.org/10.1002/tl.37219873007},
274 doi = {10.1002/tl.37219873007},
275 abstract = {The TAPPS technique is a useful device for the
276 teaching of problem solving because it causes learners to pay
277 attention to basic reasoning skills.},
282 title = {Interactive-engagement versus traditional methods: A
283 six-thousand-student survey of mechanics test data for
284 introductory physics courses},
293 doi = {10.1119/1.18809},
294 url = {http://ajp.aapt.org/resource/1/ajpias/v66/i1/p64_s1},
295 keywords = {teaching, education, classical mechanics},
296 abstract = {A survey of pre/post-test data using the
297 Halloun--Hestenes Mechanics Diagnostic test or more recent Force
298 Concept Inventory is reported for 62 introductory physics
299 courses enrolling a total number of students $N=6542$. A
300 consistent analysis over diverse student populations in high
301 schools, colleges, and universities is obtained if a rough
302 measure of the average effectiveness of a course in promoting
303 conceptual understanding is taken to be the average normalized
304 gain $\langle g\rangle$. The latter is defined as the ratio of
305 the actual average gain
306 ($\%\langle\text{post}\rangle-\%\langle\text{pre}\rangle$) to
307 the maximum possible average gain
308 ($100-\%\langle\text{pre}\rangle$). Fourteen ``traditional'' (T)
309 courses ($N=2084$) which made little or no use of
310 interactive-engagement (IE) methods achieved an average gain
311 $\langle g\rangle_{\text{T} - \text{ave}} = 0.23\pm0.04$ (std dev).
312 In sharp contrast, 48 courses ($N=4458$) which made substantial
313 use of IE methods achieved an average gain
314 $\langle g\rangle_{\text{IE}-\text{ave}} = 0.48\pm0.14$ (std dev),
315 almost two standard deviations of
316 $\langle g\rangle_{\text{IE}-\text{ave}}$ above that of the
317 traditional courses. Results for 30 ($N=3259$) of the above 62
318 courses on the problem-solving Mechanics Baseline test of
319 Hestenes--Wells imply that IE strategies enhance problem-solving
320 ability. The conceptual and problem-solving test results
321 strongly suggest that the classroom use of IE methods can
322 increase mechanics-course effectiveness well beyond that
323 obtained in traditional practice.},
327 author = SDJohnson #" and "# SPChung,
328 title = {The Effect of Thinking Aloud Pair Problem Solving
329 ({TAPPS}) on the Troubleshooting Ability of Aviation Technician
338 issn-online = {1938-1603},
339 url = {http://scholar.lib.vt.edu/ejournals/JITE/v37n1/john.html},
340 license = CC-BY-NC-SA-3.0-US,
344 author = WChristian #" and "# MBelloni,
345 title = {Physlets: Teaching Physics with Interactive Curricular Material},
348 address = UpperSaddleRiver,
350 isbn = {0-13-029341-5},
351 isbn-13 = {978-0-1302-9341-1},
352 url = {http://webphysics.davidson.edu/physletprob/},
356 author = CHCrouch #" and "# EMazur,
357 title = {Peer Instruction: Ten years of experience and results},
366 doi = {10.1119/1.1374249},
367 url = {http://ajp.aapt.org/resource/1/ajpias/v69/i9/p970_s1},
368 keywords = {teaching, problem solving, educational courses},
369 abstract = {We report data from ten years of teaching with Peer
370 Instruction (PI) in the calculus- and algebra-based introductory
371 physics courses for nonmajors; our results indicate increased
372 student mastery of both conceptual reasoning and quantitative
373 problem solving upon implementing PI. We also discuss ways we
374 have improved our implementation of PI since introducing it in
375 1991. Most notably, we have replaced in-class reading quizzes
376 with pre-class written responses to the reading, introduced a
377 research-based mechanics textbook for portions of the course,
378 and incorporated cooperative learning into the discussion
379 sections as well as the lectures. These improvements are
380 intended to help students learn more from pre-class reading and
381 to increase student engagement in the discussion sections, and
382 are accompanied by further increases in student understanding.},
387 title = {Does Active Learning Work? {A} Review of the Research},
394 publisher = Blackwell,
396 doi = {10.1002/j.2168-9830.2004.tb00809.x},
397 url = {http://dx.doi.org/10.1002/j.2168-9830.2004.tb00809.x},
398 keywords = {active, collaborative, cooperative, problem-based learning},
399 abstract = {This study examines the evidence for the effectiveness
400 of active learning. It defines the common forms of active
401 learning most relevant for engineering faculty and critically
402 examines the core element of each method. It is found that there
403 is broad but uneven support for the core elements of active,
404 collaborative, cooperative and problem-based learning.},
408 author = RMFelder #" and "# RBrent,
409 title = {Active learning: An introduction},
416 url = {http://asq.org/edu/2009/08/best-practices/active-learning-an-introduction.%20felder.html?shl=093530},
417 eprint = {http://www4.ncsu.edu/unity/lockers/users/f/felder/public/Papers/ALpaper(ASQ).pdf},
418 abstract = {Richard M. Felder and Rebecca Brent describe active
419 learning as anything course-related that all students in a class
420 session are called upon to do other than watching, listening and
421 taking notes. They provide suggestions as to what teachers and
422 professors can do to engage students in active learning and the
423 formats to use for those activities.},
426 @article{ deslauriers11,
427 author = LDeslauriers #" and "# ESchelew #" and "# CWieman,
428 title = {Improved Learning in a Large-Enrollment Physics Class},
436 doi = {10.1126/science.1201783},
437 url = {http://www.sciencemag.org/content/332/6031/862.abstract},
438 eprint = {http://www.sciencemag.org/content/332/6031/862.full.pdf},
439 abstract ={We compared the amounts of learning achieved using two
440 different instructional approaches under controlled
441 conditions. We measured the learning of a specific set of topics
442 and objectives when taught by 3 hours of traditional lecture
443 given by an experienced highly rated instructor and 3 hours of
444 instruction given by a trained but inexperienced instructor
445 using instruction based on research in cognitive psychology and
446 physics education. The comparison was made between two large
447 sections (N = 267 and N = 271) of an introductory undergraduate
448 physics course. We found increased student attendance, higher
449 engagement, and more than twice the learning in the section
450 taught using research-based instruction.},
453 @book{ crowell-light-and-matter,
455 title = {Light and Matter},
457 url = {http://www.lightandmatter.com/lm/},
458 eprint = {http://www.lightandmatter.com/lm.pdf},
459 source = {git://lightandmatter.com/physics},
460 license = CC-BY-SA-3.0-US,
463 @book{ crowell-simple-nature,
465 title = {Simple Nature},
467 url = {http://www.lightandmatter.com/area1sn.html},
468 eprint = {http://www.lightandmatter.com/simple.pdf},
469 source = {git://lightandmatter.com/physics},
470 license = CC-BY-SA-3.0-US,
473 @book{ crowell-mechanics,
477 url = {http://www.lightandmatter.com/mechanics/},
478 eprint = {http://www.lightandmatter.com/me.pdf},
479 source = {git://lightandmatter.com/physics},
480 license = CC-BY-SA-3.0-US,
483 @book{ crowell-conceptual-physics,
485 title = {Conceptual Physics},
487 url = {http://www.lightandmatter.com/cp/},
488 eprint = {http://www.lightandmatter.com/cp.pdf},
489 source = {git://lightandmatter.com/physics},
490 license = CC-BY-SA-3.0-US,
493 @book{ crowell-calculus,
497 url = {http://www.lightandmatter.com/calc/},
498 eprint = {http://www.lightandmatter.com/calc/calc.pdf},
499 source = {git://lightandmatter.com/physics},
500 license = CC-BY-SA-3.0-US,
503 @book{ crowell-general-relativity,
505 title = {General Relativity},
507 url = {http://www.lightandmatter.com/genrel},
508 eprint = {http://www.lightandmatter.com/genrel/genrel.pdf},
509 source = {git://lightandmatter.com/physics},
510 license = CC-BY-SA-3.0-US,
513 % Granular media and suspensions
516 author = EICorwin #" and "# HMJaeger #" and "# SRNagel,
517 title = {Structural signature of jamming in granular media},
521 address = {James Franck Institute, Department of Physics, The
522 University of Chicago, Chicago, Illinois 60637, USA.},
526 pages = {1075--1078},
528 doi = {10.1038/nature03698},
529 url = {http://www.ncbi.nlm.nih.gov/pubmed/15973404},
531 abstract = {Glasses are rigid, but flow when the temperature is
532 increased. Similarly, granular materials are rigid, but become
533 unjammed and flow if sufficient shear stress is applied. The rigid
534 and flowing phases are strikingly different, yet measurements
535 reveal that the structures of glass and liquid are virtually
536 indistinguishable. It is therefore natural to ask whether there is
537 a structural signature of the jammed granular state that
538 distinguishes it from its flowing counterpart. Here we find
539 evidence for such a signature, by measuring the contact-force
540 distribution between particles during shearing. Because the forces
541 are sensitive to minute variations in particle position, the
542 distribution of forces can serve as a microscope with which to
543 observe correlations in the positions of nearest neighbours. We
544 find a qualitative change in the force distribution at the onset
545 of jamming. If, as has been proposed, the jamming and glass
546 transitions are related, our observation of a structural signature
547 associated with jamming hints at the existence of a similar
548 structural difference at the glass transition--presumably too
549 subtle for conventional scattering techniques to uncover. Our
550 measurements also provide a determination of a granular
551 temperature that is the counterpart in granular systems to the
552 glass-transition temperature in liquids.},
555 @article{ majmudar05,
556 author = TSMajmudar #" and "# RPBehringer,
557 title = {Contact force measurements and stress-induced anisotropy
558 in granular materials},
565 doi = {10.1038/nature03805},
566 url = {http://www.nature.com/nature/journal/v435/n7045/full/nature03805.html},
567 eprint = {http://www.nature.com/nature/journal/v435/n7045/pdf/nature03805.pdf},
568 abstract ={Interparticle forces in granular media form an
569 inhomogeneous distribution of filamentary force
570 chains. Understanding such forces and their spatial
571 correlations, specifically in response to forces at the system
572 boundaries, represents a fundamental goal of granular
573 mechanics. The problem is of relevance to civil engineering,
574 geophysics and physics, being important for the understanding of
575 jamming, shear-induced yielding and mechanical response. Here we
576 report measurements of the normal and tangential grain-scale
577 forces inside a two-dimensional system of photoelastic disks
578 that are subject to pure shear and isotropic
579 compression. Various statistical measures show the underlying
580 differences between these two stress states. These differences
581 appear in the distributions of normal forces (which are more
582 rounded for compression than shear), although not in the
583 distributions of tangential forces (which are exponential in
584 both cases). Sheared systems show anisotropy in the
585 distributions of both the contact network and the contact
586 forces. Anisotropy also occurs in the spatial correlations of
587 forces, which provide a quantitative replacement for the idea of
588 force chains. Sheared systems have long-range correlations in
589 the direction of force chains, whereas isotropically compressed
590 systems have short-range correlations regardless of the
595 author = PAJohnson #" and "# HSavage #" and "# MKnuth #" and "#
596 JGomberg #" and "# CMarone,
597 title = {Effects of acoustic waves on stick--slip in granular
598 media and implications for earthquakes},
605 doi = {10.1038/nature06440},
606 url = {http://www.nature.com/nature/journal/v451/n7174/abs/nature06440.html},
607 eprint = {http://www.nature.com/nature/journal/v451/n7174/pdf/nature06440.pdf},
608 abstract ={It remains unknown how the small strains induced by
609 seismic waves can trigger earthquakes at large distances, in
610 some cases thousands of kilometres from the triggering
611 earthquake, with failure often occurring long after the waves
612 have passed. Earthquake nucleation is usually observed to take
613 place at depths of 10--20 km, and so static overburden should be
614 large enough to inhibit triggering by seismic-wave stress
615 perturbations. To understand the physics of dynamic triggering
616 better, as well as the influence of dynamic stressing on
617 earthquake recurrence, we have conducted laboratory studies of
618 stick--slip in granular media with and without applied acoustic
619 vibration. Glass beads were used to simulate granular fault zone
620 material, sheared under constant normal stress, and subject to
621 transient or continuous perturbation by acoustic waves. Here we
622 show that small-magnitude failure events, corresponding to
623 triggered aftershocks, occur when applied sound-wave amplitudes
624 exceed several microstrain. These events are frequently delayed
625 or occur as part of a cascade of small events. Vibrations also
626 cause large slip events to be disrupted in time relative to
627 those without wave perturbation. The effects are observed for
628 many large-event cycles after vibrations cease, indicating a
629 strain memory in the granular material. Dynamic stressing of
630 tectonic faults may play a similar role in determining the
631 complexity of earthquake recurrence.},
635 author = AGWinter #" and "# RLHDeits #" and "# AEHosoi,
636 title = {Localized fluidization burrowing mechanics of \emph{Ensis
641 address = {Department of Mechanical Engineering, Massachusetts
642 Institute of Technology, 77 Massachusetts Avenue,
643 Cambridge, MA 02139, USA. awinter@mit.edu},
647 pages = {2072--2080},
649 doi = {10.1242/jeb.058172},
650 url = {http://jeb.biologists.org/content/215/12/2072},
651 eprint = {http://jeb.biologists.org/content/215/12/2072.full.pdf},
653 keywords = {animals, biomechanics, bivalvia, movement, particle size,
655 abstract = {Muscle measurements of Ensis directus, the Atlantic
656 razor clam, indicate that the organism only has sufficient
657 strength to burrow a few centimeters into the soil, yet razor
658 clams burrow to over 70 cm. In this paper, we show that the
659 animal uses the motions of its valves to locally fluidize the
660 surrounding soil and reduce burrowing drag. Substrate
661 deformations were measured using particle image velocimetry
662 (PIV) in a novel visualization system that enabled us to see
663 through the soil and watch E. directus burrow in situ. PIV
664 data, supported by soil and fluid mechanics theory, show that
665 contraction of the valves of E. directus locally fluidizes the
666 surrounding soil. Particle and fluid mixtures can be modeled as
667 a Newtonian fluid with an effective viscosity based on the local
668 void fraction. Using these models, we demonstrate that E.
669 directus is strong enough to reach full burrow depth in
670 fluidized soil, but not in static soil. Furthermore, we show
671 that the method of localized fluidization reduces the amount of
672 energy required to reach burrow depth by an order of magnitude
673 compared with penetrating static soil, and leads to a burrowing
674 energy that scales linearly with depth rather than with depth
679 author = MRoche #" and "# EMyftiu #" and "# MCJohnston #" and "#
680 PKim #" and "# HAStone,
681 title = {Dynamic Fracture of Nonglassy Suspensions},
690 doi = {10.1103/PhysRevLett.110.148304},
691 url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.148304},
693 abstract = {We study the dynamic fracture of thin layers of
694 suspensions of non-Brownian rigid particles. The impact of a
695 projectile triggers a liquid-to-solid transition and a hole
696 opens in the layer. We show that the occurrence of fracture and
697 the spatial and dynamic features of the cracks depend mostly on
698 the thickness of the layer and the particle volume fraction. In
699 contrast, the properties of the fractured material seem
700 independent of volume fraction. Finally, we measure the velocity
701 of the crack tip, from which we estimate an effective value of
702 the shear modulus of the fractured material.},
706 author = PGLafond #" and "# MWGilmer #" and "# CAKoh #" and "#
707 EDSloan #" and "# DTWu #" and "# AKSum,
708 title = {Orifice jamming of fluid-driven granular flow},
717 doi = {10.1103/PhysRevE.87.042204},
718 url = {http://link.aps.org/doi/10.1103/PhysRevE.87.042204},
720 abstract = {The three-dimensional jamming of neutrally buoyant
721 monodisperse, bidisperse, and tridisperse mixtures of particles
722 flowing through a restriction under fluid flow has been
723 studied. During the transient initial accumulation of particles
724 at the restriction, a low probability of a jamming event is
725 observed, followed by a transition to a steady-state flowing
726 backlog of particles, where the jamming probability per particle
727 reaches a constant. Analogous to the steady-state flow in
728 gravity-driven jams, this results in a geometric distribution
729 describing the number of particles that discharge prior to a
730 jamming event. We develop new models to describe the transition
731 from an accumulation to a steady-state flow, and the jamming
732 probability after the transition has occurred. Predictions of
733 the behavior of the geometric distribution see the
734 log-probability of a jam occurring proportionally to
735 ($R_2^2-1$), where $R_2$ is the ratio of opening diameter to the
736 second moment number average particle diameter. This behavior is
737 demonstrated to apply to more general restriction shapes, and
738 collapses for all mixture compositions for the restriction sizes