67:(RSA) model. The simplest RSA model related to deposition of spherical particles considers irreversible adsorption of circular disks. One disk after another is placed randomly at a surface. Once a disk is placed, it sticks at the same spot, and cannot be removed. When an attempt to deposit a disk would result in an overlap with an already deposited disk, this attempt is rejected. Within this model, the surface is initially filled rapidly, but the more one approaches saturation the slower the surface is being filled. Within the RSA model, saturation is sometimes referred to as jamming. For circular disks, saturation occurs at a coverage of 0.547. When the depositing particles are polydisperse, much higher surface coverage can be reached, since the small particles will be able to deposit into the holes in between the larger deposited particles. On the other hand, rod like particles may lead to much smaller coverage, since a few misaligned rods may block a large portion of the surface.
564:
480:
54:
201:
216:. This conjecture led to a great deal of work arguing in favor of it, against it, and finally computer simulations in two and three dimensions showing that it was a good approximation but not exact. The accuracy of this conjecture in higher dimensions is not known.
244:
757:
1980:
47:. In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc.
3224:
Perino, E. J.; Matoz-Fernandez, D. A.; Pasinetti1, P. M.; Ramirez-Pastor, A. J. (2017). "Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice".
1023:
1414:
2734:
Tarasevich, Yuri Yu; Laptev, Valeri V.; Vygornitskii, Nikolai V.; Lebovka, Nikolai I. (2015). "Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices".
75:
475:{\displaystyle \theta _{k}=k\int _{0}^{\infty }\exp \left(-u-2\sum _{j=1}^{k-1}{\frac {1-e^{-ju}}{j}}\right)du=k\int _{0}^{1}\exp \left(-2\sum _{j=1}^{k-1}{\frac {1-v^{j}}{j}}\right)dv}
27:
are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb and remain fixed for the rest of the process. RSA can be carried out in
551:
660:
2979:
Lebovka, Nikolai I.; Karmazina, Natalia; Tarasevich, Yuri Yu; Laptev, Valeri V. (2011). "Random sequential adsorption of partially oriented linear k-mers on a square lattice".
4456:
Chen, Elizabeth R.; Miranda Holmes-Cerfon (2017). "Random
Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane".
671:
3101:
Bonnier, B.; Hontebeyrie, M.; Leroyer, Y.; Meyers, Valeri C.; Pommiers, E. (1994). "Random sequential adsorption of partially oriented linear k-mers on a square lattice".
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611:
958:
913:
887:
861:
835:
809:
783:
1699:
1060:
937:
3278:
50:
An important result is the maximum surface coverage, called the saturation coverage or the packing fraction. On this page we list that coverage for many systems.
502:
237:
1194:
1171:
4794:
Blaisdell, B. Edwin; Herbert
Solomon (1982). "Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palásti".
4644:
Tory, E. M.; W. S. Jodrey; D. K. Pikard (1983). "Simulation of Random
Sequential Adsorption: Efficient Methods and Resolution of Conflicting Results".
3832:
Viot, P.; G. Targus; S. M. Ricci; J. Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior".
3872:
Viot, P.; G. Tarjus; S. Ricci; J.Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior".
1907:
2866:
Slutskii, M. G.; Barash, L. Yu.; Tarasevich, Yu. Yu. (2018). "Percolation and jamming of random sequential adsorption samples of large linear
3968:
Ciesśla, Michałl; Grzegorz Pająk; Robert M. Ziff (2015). "Shapes for maximal coverage for two-dimensional random sequential adsorption".
968:
2585:
Araujo, N. A. M.; Cadilhe, A. (2006). "Gap-size distribution functions of a random sequential adsorption model of segments on a line".
31:, in a mathematical analysis, or in experiments. It was first studied by one-dimensional models: the attachment of pendant groups in a
3348:
Meakin, P.; Cardy, John L.; Loh, John L.; Scalapino, John L. (1987). "Extended series expansions for random sequential adsorption".
2535:
Ziff, Robert M.; R. Dennis Vigil (1990). "Kinetics and fractal properties of the random sequential adsorption of line segments".
196:{\displaystyle \theta _{1}=\int _{0}^{\infty }\exp \left(-2\int _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)dx=0.7475979202534\ldots }
1373:
4116:
Torquato, S.; O. U. Uche; F. H. Stillinger (2006). "Random sequential addition of hard spheres in high
Euclidean dimensions".
4044:
Zhang, G.; S. Torquato (2013). "Precise algorithm to generate random sequential addition of hard hyperspheres at saturation".
2646:
Wang, Jian-Sheng; Pandey, Ras B. (1996). "Kinetics and jamming coverage in a random sequential adsorption of polymer chains".
4923:
4738:
Bonnier, B.; M. Hontebeyrie; C. Meyers (1993). "On the random filling of R^d by non-overlapping d-dimensional cubes".
4582:
Blaisdell, B. Edwin; Herbert
Solomon (1970). "On random sequential packing in the plane and a conjecture of Palasti".
2397:
563:
3789:
Viot, P.; G. Targus (1990). "Random
Sequential Addition of Unoriented Squares: Breakdown of Swendsen's Conjecture".
4918:
2923:
Vandewalle, N.; Galam, S.; Kramer, M. (2000). "A new universality for random sequential deposition of needles".
3744:
Vigil, R. Dennis; Robert M. Ziff (1989). "Random sequential adsorption of unoriented rectangles onto a plane".
3683:
Zhang, G. (2018). "Precise algorithm to generate random sequential adsorption of hard polygons at saturation".
567:
RSA of needles (infinitely thin line segments). This shows a dense stage although here saturation never occurs.
4837:
Cooper, Douglas W. (1989). "Random sequential packing simulations in three dimensions for aligned cubes".
3154:
Manna, S. S.; Svrakic, N. M. (1991). "Random sequential adsorption: line segments on the square lattice".
2201:
0.5470735(28), 0.547067(3), 0.547070, 0.5470690(7), 0.54700(6), 0.54711(16), 0.5472(2), 0.547(2), 0.5479,
507:
623:
4509:
Hinrichsen, Einar L.; Jens Feder; Torstein Jøssang (1990). "Random packing of disks in two dimensions".
3272:
3045:
Wang, J. S. (2000). "Series expansion and computer simulation studies of random sequential adsorption".
2312:
557:
53:
4368:
Cieśla, Michał; Aleksandra Nowak (2016). "Managing numerical errors in random sequential adsorption".
752:{\displaystyle {\frac {3{\sqrt {\pi }}({\text{erfi}}(2)-{\text{erfi}}(1))}{2e^{4}}}\approx 0.82365296}
4757:
4653:
4618:
4556:
4518:
4475:
4422:
4377:
4334:
4273:
4227:
4189:
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3926:
3881:
3841:
3798:
3753:
3702:
3615:
3555:
3546:
Brosilow, B. J.; R. M. Ziff; R. D. Vigil (1991). "Random sequential adsorption of parallel squares".
3485:
3427:
3384:
3314:
3244:
3163:
2998:
2942:
2889:
2811:
2753:
2665:
2604:
2544:
2409:
2370:
212:, who proposed that the coverage of d-dimensional aligned squares, cubes and hypercubes is equal to θ
4880:
Nord, R. S. (1991). "Irreversible random sequential filling of lattices by Monte Carlo simulation".
2508:
Flory, P. J. (1939). "Intramolecular
Reaction between Neighboring Substituents of Vinyl Polymers".
2307:
70:
For the one-dimensional parking-car problem, Renyi has shown that the maximum coverage is equal to
28:
4913:
4862:
4854:
4819:
4811:
4773:
4747:
4491:
4465:
4438:
4412:
4350:
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4159:
4125:
4087:
4053:
4011:
3977:
3950:
3916:
3814:
3726:
3692:
3476:
Privman, V.; Wang, J. S.; Nielaba, P. (1991). "Continuum limit in random sequential adsorption".
3330:
3304:
3260:
3234:
3136:
3110:
3054:
3022:
2988:
2958:
2932:
2905:
2879:
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2689:
2655:
2628:
2594:
1714:
1625:
1437:
1118:
589:
4679:
Akeda, Yoshiaki; Motoo Hori (1976). "On random sequential packing in two and three dimensions".
943:
898:
872:
846:
820:
794:
768:
40:
4609:
Dickman, R.; J. S. Wang; I. Jensen (1991). "Random sequential adsorption of parallel squares".
3295:
Gan, C. K.; Wang, J.-S. (1998). "Extended series expansions for random sequential adsorption".
1678:
4289:
4243:
4151:
4079:
4003:
3942:
3718:
3571:
3501:
3443:
3128:
3014:
2769:
2681:
2620:
1045:
922:
504:
goes to infinity, this gives the Renyi result above. For k = 2, this gives the Flory result
4889:
4846:
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4765:
4720:
4688:
4661:
4626:
4591:
4564:
4526:
4483:
4430:
4385:
4342:
4315:
Cieśla, Michał; Ziff, Robert (2018). "Boundary conditions in random sequential adsorption".
4281:
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2612:
2560:
2552:
2517:
2451:
2417:
2378:
209:
3907:
Cieśla, Michał (2014). "Properties of random sequential adsorption of generalized dimers".
3641:
Sutton, Clifton (1989). "Asymptotic packing densities for two-dimensional lattice models".
3375:
Baram, Asher; Fixman, Marshall (1995). "Random sequential adsorption: Long time dynamics".
2435:
2274:
0.562009(4), 0.5623(4), 0.562(2), 0.5565(15), 0.5625(5), 0.5444(24), 0.5629(6), 0.562(2),
1674:
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2815:
2757:
2669:
2608:
2548:
2413:
2374:
4403:
Wang, Jian-Sheng (1994). "A fast algorithm for random sequential adsorption of discs".
3606:
Nakamura, Mitsunobu (1986). "Random sequential packing in square cellular structures".
487:
222:
44:
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3175:
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2556:
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4091:
4015:
3954:
3730:
3334:
3026:
2962:
2909:
2781:
2693:
4180:
Meakin, Paul (1992). "Random sequential adsorption of spheres of different sizes".
2632:
3219:
3217:
3215:
3213:
3211:
3209:
3207:
3205:
3140:
2339:
Rényi, A. (1958). "On a one-dimensional problem concerning random space filling".
556:
For percolation thresholds related to random sequentially adsorbed particles, see
239:-mers on a one-dimensional lattice, we have for the fraction of vertices covered,
4264:
Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cuboids".
3203:
3201:
3199:
3197:
3195:
3193:
3191:
3189:
3187:
3185:
3439:
3411:
2800:"Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices"
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2677:
4389:
4346:
4218:
Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cubes".
4147:
4075:
3938:
3714:
3256:
3010:
2901:
2765:
2616:
2421:
2361:
Widom, B. J. (1966). "Random
Sequential Addition of Hard Spheres to a Volume".
4893:
4724:
4692:
4595:
4487:
4434:
3654:
2302:
36:
4530:
3497:
1029:
Saturation coverage of segments of two lengths on a one dimensional continuum
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3124:
3096:
3094:
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3090:
3088:
3086:
3084:
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1975:{\displaystyle \theta _{k}\sim \theta _{\infty }+0.316/k+0.114/k^{2}\ldots }
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4247:
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4083:
4007:
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3722:
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3018:
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2624:
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3132:
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4130:
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3309:
3115:
3059:
2937:
2729:
2727:
2725:
2723:
2660:
2599:
2565:
1612:
Saturation coverage for particles with neighbors exclusion on 2d lattices
1150:
0.906820(2), 0.906, 0.9068, 0.9062, 0.906, 0.905(9), 0.906, 0.906823(2),
24:
2721:
2719:
2717:
2715:
2713:
2711:
2709:
2707:
2705:
2703:
2521:
4858:
4815:
3999:
57:
Saturation in the random sequential adsorption (RSA) of circular disks.
32:
4711:
Jodrey, W. S.; E. M. Tory (1980). "Random sequential packing in R^n".
4285:
4239:
2382:
4665:
4630:
3893:
3853:
3765:
3396:
3361:
3326:
2974:
2972:
2824:
4850:
4807:
4470:
4329:
3982:
3697:
3239:
2884:
4058:
3921:
2993:
2748:
1018:{\displaystyle \theta _{k}\sim \theta _{\infty }+0.2162/k+\ldots }
1904:
For k = ∞, see "2d aligned squares" below. Asymptotic behavior:
61:
The blocking process has been studied in detail in terms of the
2256:
Saturation coverages for aligned squares, cubes, and hypercubes
2861:
2859:
2857:
2855:
2853:
2851:
2849:
2847:
2845:
2843:
2841:
2839:
2837:
2835:
1033:
R = size ratio of segments. Assume equal rates of adsorption
4111:
4109:
4107:
4105:
4103:
4101:
2282:
0.4227(6), 0.42(1), 0.4262, 0.430(8), 0.422(8), 0.42243(5)
3867:
3865:
3863:
2485:
2483:
2481:
2479:
2477:
2475:
2473:
2471:
2469:
2183:
Saturation coverages for disks, spheres, and hyperspheres
1409:{\displaystyle \theta _{k}\sim \theta _{\infty }+\ldots }
4317:
Journal of
Statistical Mechanics: Theory and Experiment
3541:
3539:
3537:
3535:
3227:
Journal of
Statistical Mechanics: Theory and Experiment
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771:
674:
626:
592:
510:
490:
247:
225:
78:
4547:
Feder, Jens (1980). "Random sequential adsorption".
1986:
Saturation coverage for randomly oriented 2d systems
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4213:
4211:
4175:
4173:
4039:
4037:
4035:
4033:
4031:
4029:
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1974:
1730:
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1641:
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1408:
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1134:
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907:
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231:
195:
4882:Journal of Statistical Computation and Simulation
4713:Journal of Statistical Computation and Simulation
2580:
2578:
2576:
2454:(1960). "On some random space filling problems".
4706:
4704:
4702:
2793:
2791:
2490:Krapivsky, P.; S. Redner; E. Ben-Naim (2010).
2398:"Random and cooperative sequential adsorption"
3601:
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3585:
8:
3290:
3288:
2012:0.523-0.532, 0.530(1), 0.530(1), 0.52760(5)
3277:: CS1 maint: numeric names: authors list (
4542:
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205:the so-called Renyi car-parking constant.
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1627:
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273:
268:
252:
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152:
139:
133:
128:
101:
96:
83:
77:
3414:Kinetics of random sequential adsorption
2259:
2186:
2145:
2070:
1989:
1704:
1657:0.3641323(1), 0.36413(1), 0.3641330(5),
1615:
1427:
1108:
1035:
579:
562:
52:
2324:
3270:
2440:From MathWorld--A Wolfram Web Resource
2067:2d oblong shapes with maximal coverage
2492:A Kinetic View of Statistical Physics
2173:randomly oriented cuboids 0.75:1:1.3
43:. Other early works include those of
7:
2209:0.3841307(21), 0.38278(5), 0.384(1)
2160:0.3841307(21), 0.38278(5), 0.384(1)
1746:0.74793(1), 0.747943(37), 0.749(1),
1662:Honeycomb lattice with NN exclusion
546:{\displaystyle \theta _{1}=1-e^{-2}}
1762:0.64793(1), 0.647927(22) 0.646(1),
655:{\displaystyle 1-e^{-2}=0.86466472}
2798:Nord, R. S.; Evans, J. W. (1985).
2142:Saturation coverage for 3d systems
1929:
1395:
1284:0.6686, 0.668(9), 0.668 0.6682(6)
990:
926:
274:
102:
14:
2456:Publ. Math. Inst. Hung. Acad. Sci
2341:Publ. Math. Inst. Hung. Acad. Sci
1654:Square lattice with NN exclusion
39:, and the car-parking problem by
1424:-mers on a 2d triangular lattice
208:Then followed the conjecture of
4266:The Journal of Chemical Physics
4220:The Journal of Chemical Physics
4796:Journal of Applied Probability
1701:squares on a 2d square lattice
1665:0.37913944(1), 0.38(1), 0.379
722:
719:
713:
702:
696:
688:
1:
3069:10.1016/S0927-7757(99)00444-6
4770:10.1016/0378-4371(93)90180-C
4569:10.1016/0022-5193(80)90358-6
4202:10.1016/0378-4371(92)90006-C
2870:-mers on a square lattice".
1105:-mers on a 2d square lattice
64:random sequential adsorption
23:) refers to a process where
17:Random sequential adsorption
3628:10.1088/0305-4470/19/12/020
3440:10.1103/PhysRevLett.62.2642
3176:10.1088/0305-4470/24/12/003
2678:10.1103/PhysRevLett.77.1773
2557:10.1088/0305-4470/23/21/044
2436:"Rényi's Parking Constants"
2225:0.1707761(46), 0.16102(4),
2217:0.2600781(37), 0.25454(9),
1738:(fraction of sites filled)
1731:{\displaystyle \theta _{k}}
1649:(fraction of sites filled)
1642:{\displaystyle \theta _{k}}
1461:(fraction of sites filled)
1454:{\displaystyle \theta _{k}}
1142:(fraction of sites filled)
1135:{\displaystyle \theta _{k}}
613:(fraction of sites filled)
606:{\displaystyle \theta _{k}}
576:-mers on 1d lattice systems
4940:
4390:10.1016/j.susc.2016.04.014
4148:10.1103/PhysRevE.74.061308
4076:10.1103/PhysRevE.88.053312
3939:10.1103/PhysRevE.89.042404
3811:10.1209/0295-5075/13/4/002
3715:10.1103/PhysRevE.97.043311
3011:10.1103/PhysRevE.84.061603
2902:10.1103/PhysRevE.98.062130
2766:10.1103/PhysRevE.91.012109
2617:10.1103/PhysRevE.73.051602
2422:10.1103/RevModPhys.65.1281
2233:0.109302(19), 0.09394(5),
1062:(fraction of line filled)
953:{\displaystyle 0.74759792}
908:{\displaystyle 0.74760008}
882:{\displaystyle 0.74761954}
856:{\displaystyle 0.74781413}
830:{\displaystyle 0.74976335}
804:{\displaystyle 0.76957741}
778:{\displaystyle 0.80389348}
4894:10.1080/00949659108811358
4725:10.1080/00949658008810351
4596:10.1017/S0021900200110630
4488:10.1007/s00332-017-9385-2
4435:10.1142/S0129183194000817
3655:10.1080/15326348908807126
1694:{\displaystyle k\times k}
1268:0.6755, 0.678, 0.6765(6)
1252:0.6892, 0.689, 0.6893(4)
4531:10.1103/PhysRevA.41.4199
4347:10.1088/1742-5468/aab685
3498:10.1103/PhysRevB.43.3366
3257:10.1088/1742-5468/aa79ae
2494:. Cambridge Univ. Press.
2168:0.3686(15), 0.36306(60)
2165:randomly oriented cubes
1300:0.6628 0.665, 0.6637(6)
4693:10.1093/biomet/63.2.361
3568:10.1103/PhysRevA.43.631
3125:10.1103/PhysRevE.49.305
3047:Colloids and Surfaces A
1778:0.603355(55) 0.603(1),
1675:Saturation coverage of
1420:Saturation coverage of
1101:Saturation coverage of
1055:{\displaystyle \theta }
932:{\displaystyle \infty }
572:Saturation coverage of
3970:Phys. Chem. Chem. Phys
2287:4d aligned hypercubes
2001:equilateral triangles
1976:
1754:0.67961(1), 0.681(1),
1732:
1695:
1643:
1455:
1410:
1370:Asymptotic behavior:
1190:
1167:
1136:
1056:
1019:
965:Asymptotic behavior:
954:
933:
909:
883:
857:
831:
805:
779:
753:
656:
607:
568:
547:
498:
476:
435:
328:
233:
197:
58:
3608:J. Phys. A: Math. Gen
3410:Evans, J. W. (1989).
3156:J. Phys. A: Math. Gen
2955:10.1007/s100510051047
2537:J. Phys. A: Math. Gen
2396:Evans, J. W. (1993).
2313:Percolation threshold
1977:
1810:0.57807(5) 0.578(1),
1786:0.59476(4) 0.593(1),
1770:0.62968(1) 0.628(1),
1733:
1696:
1644:
1456:
1411:
1364:0.660(2), 0.583(10),
1191:
1168:
1137:
1057:
1020:
955:
934:
910:
884:
858:
832:
806:
780:
754:
657:
608:
566:
558:Percolation threshold
548:
499:
477:
409:
302:
234:
198:
56:
4405:Int. J. Mod. Phys. C
2434:Weisstein, Eric W.,
1908:
1715:
1679:
1626:
1438:
1374:
1184:
1161:
1119:
1046:
969:
944:
923:
899:
873:
847:
821:
795:
769:
672:
624:
590:
508:
488:
245:
223:
76:
4924:Colloidal chemistry
4762:1993PhyA..198....1B
4658:1991JChPh..94.8252D
4623:1991JChPh..94.8252D
4561:1980JThBi..87..237F
4523:1990PhRvA..41.4199H
4480:2017JNS....27.1743C
4427:1994IJMPC...5..707W
4382:2016SurSc.651..182C
4339:2018JSMTE..04.3302C
4278:2018JChPh.149s4704C
4232:2018JChPh.148b4501C
4194:1992PhyA..187..475M
4140:2006PhRvE..74f1308T
4068:2013PhRvE..88e3312Z
3992:2015PCCP...1724376C
3976:(37): 24376–24381.
3931:2014PhRvE..89d2404C
3886:1992JChPh..97.5212V
3846:1992JChPh..97.5212V
3803:1990EL.....13..295V
3758:1989JChPh..91.2599V
3707:2018PhRvE..97d3311Z
3620:1986JPhA...19.2345N
3560:1991PhRvA..43..631B
3490:1991PhRvB..43.3366P
3432:1989PhRvL..62.2642E
3389:1995JChPh.103.1929B
3319:1998JChPh.108.3010G
3249:2017JSMTE..07.3206P
3168:1991JPhA...24L.671M
3003:2011PhRvE..84f1603L
2947:2000EPJB...14..407V
2894:2018PhRvE..98f2130S
2816:1985JChPh..82.2795N
2758:2015PhRvE..91a2109T
2670:1996PhRvL..77.1773W
2609:2006PhRvE..73e1602A
2549:1990JPhA...23.5103Z
2522:10.1021/ja01875a053
2414:1993RvMP...65.1281E
2375:1966JChPh..44.3888W
2308:Particle deposition
2271:2d aligned squares
2266:Saturated coverage
2193:Saturated coverage
2152:Saturated coverage
2080:Saturated coverage
1996:Saturated coverage
1711:Saturated coverage
1622:Saturated coverage
1434:Saturated coverage
1115:Saturated coverage
1042:Saturated coverage
586:Saturated coverage
391:
278:
138:
106:
29:computer simulation
4000:10.1039/c5cp03873a
2049:regular enneagons
2033:regular heptagons
2017:regular pentagons
1972:
1728:
1691:
1639:
1451:
1406:
1316:0.6618, 0.6628(9)
1132:
1052:
1015:
950:
929:
905:
879:
853:
827:
801:
775:
749:
652:
603:
569:
543:
494:
472:
377:
264:
229:
193:
124:
92:
59:
4919:Materials science
4286:10.1063/1.5061695
4240:10.1063/1.5007319
3685:Physical Review E
3643:Stochastic Models
3614:(12): 2345–2351.
3162:(12): L671–L676.
2872:Physical Review E
2543:(21): 5103–5108.
2383:10.1063/1.1726548
2369:(10): 3888–3894.
2347:(109–127): 30–36.
2294:
2293:
2279:3d aligned cubes
2253:
2252:
2180:
2179:
2139:
2138:
2064:
2063:
2057:regular decagons
2041:regular octagons
2025:regular hexagons
1902:
1901:
1669:
1668:
1609:
1608:
1368:
1367:
1098:
1097:
963:
962:
741:
711:
694:
686:
497:{\displaystyle k}
459:
358:
232:{\displaystyle k}
165:
4931:
4898:
4897:
4877:
4871:
4870:
4834:
4828:
4827:
4791:
4782:
4781:
4755:
4753:cond-mat/9302023
4735:
4729:
4728:
4708:
4697:
4696:
4676:
4670:
4669:
4666:10.1063/1.460109
4641:
4635:
4634:
4631:10.1063/1.460109
4606:
4600:
4599:
4579:
4573:
4572:
4544:
4535:
4534:
4517:(8): 4199–4209.
4506:
4500:
4499:
4473:
4464:(6): 1743–1787.
4458:J. Nonlinear Sci
4453:
4447:
4446:
4420:
4418:cond-mat/9402066
4400:
4394:
4393:
4365:
4359:
4358:
4332:
4312:
4306:
4305:
4261:
4252:
4251:
4215:
4206:
4205:
4177:
4168:
4167:
4133:
4131:cond-mat/0608402
4113:
4096:
4095:
4061:
4041:
4020:
4019:
3985:
3965:
3959:
3958:
3924:
3904:
3898:
3897:
3894:10.1063/1.463820
3880:(7): 5212–5218.
3869:
3858:
3857:
3854:10.1063/1.463820
3829:
3823:
3822:
3786:
3780:
3779:
3777:
3766:10.1063/1.457021
3752:(4): 2599–2602.
3741:
3735:
3734:
3700:
3680:
3659:
3658:
3638:
3632:
3631:
3603:
3580:
3579:
3543:
3510:
3509:
3484:(4): 3366–3372.
3473:
3452:
3451:
3407:
3401:
3400:
3397:10.1063/1.469717
3383:(5): 1929–1933.
3372:
3366:
3365:
3362:10.1063/1.452085
3356:(4): 2380–2382.
3345:
3339:
3338:
3327:10.1063/1.475687
3312:
3310:cond-mat/9710340
3303:(7): 3010–3012.
3292:
3283:
3282:
3276:
3268:
3242:
3221:
3180:
3179:
3151:
3145:
3144:
3118:
3116:cond-mat/9307043
3098:
3073:
3072:
3062:
3060:cond-mat/9903139
3053:(1–3): 325–343.
3042:
3031:
3030:
2996:
2976:
2967:
2966:
2940:
2938:cond-mat/0004271
2920:
2914:
2913:
2887:
2863:
2830:
2829:
2827:
2825:10.1063/1.448279
2810:(6): 2795–2810.
2795:
2786:
2785:
2751:
2731:
2698:
2697:
2663:
2661:cond-mat/9605038
2654:(9): 1773–1776.
2643:
2637:
2636:
2602:
2600:cond-mat/0404422
2582:
2571:
2570:
2568:
2532:
2526:
2525:
2516:(6): 1518–1521.
2510:J. Am. Chem. Soc
2505:
2496:
2495:
2487:
2464:
2463:
2448:
2442:
2432:
2426:
2425:
2408:(4): 1281–1329.
2393:
2387:
2386:
2358:
2349:
2348:
2336:
2290:0.3129, 0.3341,
2260:
2246:8d hyperspheres
2238:7d hyperspheres
2230:6d hyperspheres
2222:5d hyperspheres
2214:4d hyperspheres
2187:
2146:
2071:
1990:
1981:
1979:
1978:
1973:
1968:
1967:
1958:
1944:
1933:
1932:
1920:
1919:
1737:
1735:
1734:
1729:
1727:
1726:
1705:
1700:
1698:
1697:
1692:
1648:
1646:
1645:
1640:
1638:
1637:
1616:
1460:
1458:
1457:
1452:
1450:
1449:
1428:
1415:
1413:
1412:
1407:
1399:
1398:
1386:
1385:
1195:
1193:
1192:
1189:{\displaystyle }
1187:
1172:
1170:
1169:
1166:{\displaystyle }
1164:
1141:
1139:
1138:
1133:
1131:
1130:
1109:
1061:
1059:
1058:
1053:
1036:
1024:
1022:
1021:
1016:
1005:
994:
993:
981:
980:
959:
957:
956:
951:
938:
936:
935:
930:
914:
912:
911:
906:
888:
886:
885:
880:
862:
860:
859:
854:
836:
834:
833:
828:
810:
808:
807:
802:
784:
782:
781:
776:
758:
756:
755:
750:
742:
740:
739:
738:
725:
712:
709:
695:
692:
687:
682:
676:
661:
659:
658:
653:
645:
644:
612:
610:
609:
604:
602:
601:
580:
552:
550:
549:
544:
542:
541:
520:
519:
503:
501:
500:
495:
481:
479:
478:
473:
465:
461:
460:
455:
454:
453:
437:
434:
423:
390:
385:
364:
360:
359:
354:
353:
352:
330:
327:
316:
277:
272:
257:
256:
238:
236:
235:
230:
202:
200:
199:
194:
177:
173:
166:
161:
160:
159:
140:
137:
132:
105:
100:
88:
87:
4939:
4938:
4934:
4933:
4932:
4930:
4929:
4928:
4904:
4903:
4902:
4901:
4879:
4878:
4874:
4851:10.2307/3214426
4839:J. Appl. Probab
4836:
4835:
4831:
4808:10.2307/3213489
4793:
4792:
4785:
4737:
4736:
4732:
4710:
4709:
4700:
4678:
4677:
4673:
4652:(12): 439–445.
4643:
4642:
4638:
4608:
4607:
4603:
4584:J. Appl. Probab
4581:
4580:
4576:
4546:
4545:
4538:
4508:
4507:
4503:
4455:
4454:
4450:
4402:
4401:
4397:
4370:Surface Science
4367:
4366:
4362:
4314:
4313:
4309:
4263:
4262:
4255:
4217:
4216:
4209:
4179:
4178:
4171:
4115:
4114:
4099:
4043:
4042:
4023:
3967:
3966:
3962:
3906:
3905:
3901:
3871:
3870:
3861:
3831:
3830:
3826:
3788:
3787:
3783:
3743:
3742:
3738:
3682:
3681:
3662:
3640:
3639:
3635:
3605:
3604:
3583:
3545:
3544:
3513:
3475:
3474:
3455:
3420:Phys. Rev. Lett
3409:
3408:
3404:
3374:
3373:
3369:
3347:
3346:
3342:
3294:
3293:
3286:
3269:
3223:
3222:
3183:
3153:
3152:
3148:
3100:
3099:
3076:
3044:
3043:
3034:
2978:
2977:
2970:
2925:Eur. Phys. J. B
2922:
2921:
2917:
2865:
2864:
2833:
2797:
2796:
2789:
2733:
2732:
2701:
2648:Phys. Rev. Lett
2645:
2644:
2640:
2584:
2583:
2574:
2534:
2533:
2529:
2507:
2506:
2499:
2489:
2488:
2467:
2450:
2449:
2445:
2433:
2429:
2395:
2394:
2390:
2360:
2359:
2352:
2338:
2337:
2326:
2321:
2299:
2258:
2185:
2144:
2129:smoothed dimer
2118:spherocylinder
2069:
1988:
1959:
1924:
1911:
1906:
1905:
1718:
1713:
1712:
1703:
1677:
1676:
1629:
1624:
1623:
1614:
1441:
1436:
1435:
1426:
1390:
1377:
1372:
1371:
1182:
1181:
1173:0.846, 0.8366
1159:
1158:
1122:
1117:
1116:
1107:
1094:0.7941038(58)
1086:0.7599829(63)
1078:0.7544753(62)
1044:
1043:
1031:
985:
972:
967:
966:
942:
941:
921:
920:
897:
896:
871:
870:
845:
844:
819:
818:
793:
792:
767:
766:
730:
726:
677:
670:
669:
633:
622:
621:
593:
588:
587:
578:
530:
511:
506:
505:
486:
485:
445:
438:
402:
398:
338:
331:
289:
285:
248:
243:
242:
221:
220:
215:
188:0.7475979202534
148:
141:
117:
113:
79:
74:
73:
12:
11:
5:
4937:
4935:
4927:
4926:
4921:
4916:
4906:
4905:
4900:
4899:
4888:(4): 231–240.
4872:
4845:(3): 664–670.
4829:
4802:(2): 382–390.
4783:
4730:
4698:
4687:(2): 361–366.
4671:
4646:J. Theor. Biol
4636:
4601:
4590:(3): 667–698.
4574:
4555:(2): 237–254.
4549:J. Theor. Biol
4536:
4501:
4448:
4411:(4): 707–715.
4395:
4360:
4307:
4272:(19): 194704.
4253:
4207:
4188:(3): 475–488.
4169:
4097:
4021:
3960:
3899:
3859:
3824:
3797:(4): 295–300.
3781:
3736:
3660:
3649:(4): 601–615.
3633:
3581:
3554:(2): 631–638.
3511:
3453:
3402:
3367:
3340:
3284:
3181:
3146:
3109:(1): 305–312.
3074:
3032:
2968:
2931:(3): 407–410.
2915:
2831:
2787:
2699:
2638:
2572:
2527:
2497:
2465:
2443:
2427:
2402:Rev. Mod. Phys
2388:
2350:
2323:
2322:
2320:
2317:
2316:
2315:
2310:
2305:
2298:
2295:
2292:
2291:
2288:
2284:
2283:
2280:
2276:
2275:
2272:
2268:
2267:
2264:
2257:
2254:
2251:
2250:
2247:
2243:
2242:
2241:0.068404(16),
2239:
2235:
2234:
2231:
2227:
2226:
2223:
2219:
2218:
2215:
2211:
2210:
2207:
2203:
2202:
2199:
2195:
2194:
2191:
2184:
2181:
2178:
2177:
2174:
2170:
2169:
2166:
2162:
2161:
2158:
2154:
2153:
2150:
2143:
2140:
2137:
2136:
2133:
2130:
2126:
2125:
2122:
2119:
2115:
2114:
2111:
2108:
2104:
2103:
2100:
2097:
2093:
2092:
2089:
2086:
2082:
2081:
2078:
2075:
2068:
2065:
2062:
2061:
2058:
2054:
2053:
2050:
2046:
2045:
2042:
2038:
2037:
2034:
2030:
2029:
2026:
2022:
2021:
2018:
2014:
2013:
2010:
2006:
2005:
2002:
1998:
1997:
1994:
1987:
1984:
1971:
1966:
1962:
1957:
1953:
1950:
1947:
1943:
1939:
1936:
1931:
1927:
1923:
1918:
1914:
1900:
1899:
1896:
1892:
1891:
1888:
1884:
1883:
1880:
1876:
1875:
1872:
1868:
1867:
1864:
1860:
1859:
1856:
1852:
1851:
1848:
1844:
1843:
1840:
1836:
1835:
1832:
1828:
1827:
1824:
1820:
1819:
1816:
1812:
1811:
1808:
1804:
1803:
1800:
1796:
1795:
1792:
1788:
1787:
1784:
1780:
1779:
1776:
1772:
1771:
1768:
1764:
1763:
1760:
1756:
1755:
1752:
1748:
1747:
1744:
1740:
1739:
1725:
1721:
1709:
1702:
1690:
1687:
1684:
1673:
1667:
1666:
1663:
1659:
1658:
1655:
1651:
1650:
1636:
1632:
1620:
1613:
1610:
1607:
1606:
1603:
1599:
1598:
1595:
1591:
1590:
1587:
1583:
1582:
1579:
1575:
1574:
1571:
1567:
1566:
1563:
1559:
1558:
1555:
1551:
1550:
1547:
1543:
1542:
1539:
1535:
1534:
1531:
1527:
1526:
1523:
1519:
1518:
1515:
1511:
1510:
1507:
1503:
1502:
1499:
1495:
1494:
1491:
1487:
1486:
1483:
1479:
1478:
1475:
1471:
1470:
1467:
1463:
1462:
1448:
1444:
1432:
1425:
1418:
1405:
1402:
1397:
1393:
1389:
1384:
1380:
1366:
1365:
1362:
1358:
1357:
1354:
1350:
1349:
1346:
1342:
1341:
1338:
1334:
1333:
1330:
1326:
1325:
1322:
1318:
1317:
1314:
1310:
1309:
1306:
1302:
1301:
1298:
1294:
1293:
1290:
1286:
1285:
1282:
1278:
1277:
1274:
1270:
1269:
1266:
1262:
1261:
1258:
1254:
1253:
1250:
1246:
1245:
1242:
1238:
1237:
1234:
1230:
1229:
1228:0.7479, 0.747
1226:
1222:
1221:
1218:
1214:
1213:
1210:
1206:
1205:
1202:
1198:
1197:
1179:
1175:
1174:
1156:
1155:trimers k = 3
1152:
1151:
1148:
1144:
1143:
1129:
1125:
1113:
1106:
1099:
1096:
1095:
1092:
1088:
1087:
1084:
1080:
1079:
1076:
1072:
1071:
1068:
1064:
1063:
1051:
1040:
1030:
1027:
1014:
1011:
1008:
1004:
1000:
997:
992:
988:
984:
979:
975:
961:
960:
949:
939:
928:
916:
915:
904:
894:
890:
889:
878:
868:
864:
863:
852:
842:
838:
837:
826:
816:
812:
811:
800:
790:
786:
785:
774:
764:
760:
759:
748:
745:
737:
733:
729:
724:
721:
718:
715:
707:
704:
701:
698:
690:
685:
680:
667:
663:
662:
651:
648:
643:
640:
636:
632:
629:
619:
615:
614:
600:
596:
584:
577:
570:
540:
537:
533:
529:
526:
523:
518:
514:
493:
471:
468:
464:
458:
452:
448:
444:
441:
433:
430:
427:
422:
419:
416:
412:
408:
405:
401:
397:
394:
389:
384:
380:
376:
373:
370:
367:
363:
357:
351:
348:
345:
341:
337:
334:
326:
323:
320:
315:
312:
309:
305:
301:
298:
295:
292:
288:
284:
281:
276:
271:
267:
263:
260:
255:
251:
228:
213:
192:
189:
186:
183:
180:
176:
172:
169:
164:
158:
155:
151:
147:
144:
136:
131:
127:
123:
120:
116:
112:
109:
104:
99:
95:
91:
86:
82:
45:Benjamin Widom
13:
10:
9:
6:
4:
3:
2:
4936:
4925:
4922:
4920:
4917:
4915:
4912:
4911:
4909:
4895:
4891:
4887:
4883:
4876:
4873:
4868:
4864:
4860:
4856:
4852:
4848:
4844:
4840:
4833:
4830:
4825:
4821:
4817:
4813:
4809:
4805:
4801:
4797:
4790:
4788:
4784:
4779:
4775:
4771:
4767:
4763:
4759:
4754:
4749:
4745:
4741:
4734:
4731:
4726:
4722:
4718:
4714:
4707:
4705:
4703:
4699:
4694:
4690:
4686:
4682:
4675:
4672:
4667:
4663:
4659:
4655:
4651:
4647:
4640:
4637:
4632:
4628:
4624:
4620:
4616:
4612:
4611:J. Chem. Phys
4605:
4602:
4597:
4593:
4589:
4585:
4578:
4575:
4570:
4566:
4562:
4558:
4554:
4550:
4543:
4541:
4537:
4532:
4528:
4524:
4520:
4516:
4512:
4505:
4502:
4497:
4493:
4489:
4485:
4481:
4477:
4472:
4467:
4463:
4459:
4452:
4449:
4444:
4440:
4436:
4432:
4428:
4424:
4419:
4414:
4410:
4406:
4399:
4396:
4391:
4387:
4383:
4379:
4375:
4371:
4364:
4361:
4356:
4352:
4348:
4344:
4340:
4336:
4331:
4326:
4323:(4): 043302.
4322:
4318:
4311:
4308:
4303:
4299:
4295:
4291:
4287:
4283:
4279:
4275:
4271:
4267:
4260:
4258:
4254:
4249:
4245:
4241:
4237:
4233:
4229:
4226:(2): 024501.
4225:
4221:
4214:
4212:
4208:
4203:
4199:
4195:
4191:
4187:
4183:
4176:
4174:
4170:
4165:
4161:
4157:
4153:
4149:
4145:
4141:
4137:
4132:
4127:
4124:(6): 061308.
4123:
4119:
4112:
4110:
4108:
4106:
4104:
4102:
4098:
4093:
4089:
4085:
4081:
4077:
4073:
4069:
4065:
4060:
4055:
4052:(5): 053312.
4051:
4047:
4040:
4038:
4036:
4034:
4032:
4030:
4028:
4026:
4022:
4017:
4013:
4009:
4005:
4001:
3997:
3993:
3989:
3984:
3979:
3975:
3971:
3964:
3961:
3956:
3952:
3948:
3944:
3940:
3936:
3932:
3928:
3923:
3918:
3915:(4): 042404.
3914:
3910:
3903:
3900:
3895:
3891:
3887:
3883:
3879:
3875:
3874:J. Chem. Phys
3868:
3866:
3864:
3860:
3855:
3851:
3847:
3843:
3839:
3835:
3834:J. Chem. Phys
3828:
3825:
3820:
3816:
3812:
3808:
3804:
3800:
3796:
3792:
3785:
3782:
3776:
3775:2027.42/70834
3771:
3767:
3763:
3759:
3755:
3751:
3747:
3746:J. Chem. Phys
3740:
3737:
3732:
3728:
3724:
3720:
3716:
3712:
3708:
3704:
3699:
3694:
3691:(4): 043311.
3690:
3686:
3679:
3677:
3675:
3673:
3671:
3669:
3667:
3665:
3661:
3656:
3652:
3648:
3644:
3637:
3634:
3629:
3625:
3621:
3617:
3613:
3609:
3602:
3600:
3598:
3596:
3594:
3592:
3590:
3588:
3586:
3582:
3577:
3573:
3569:
3565:
3561:
3557:
3553:
3549:
3542:
3540:
3538:
3536:
3534:
3532:
3530:
3528:
3526:
3524:
3522:
3520:
3518:
3516:
3512:
3507:
3503:
3499:
3495:
3491:
3487:
3483:
3479:
3472:
3470:
3468:
3466:
3464:
3462:
3460:
3458:
3454:
3449:
3445:
3441:
3437:
3433:
3429:
3425:
3421:
3417:
3415:
3406:
3403:
3398:
3394:
3390:
3386:
3382:
3378:
3377:J. Chem. Phys
3371:
3368:
3363:
3359:
3355:
3351:
3350:J. Chem. Phys
3344:
3341:
3336:
3332:
3328:
3324:
3320:
3316:
3311:
3306:
3302:
3298:
3297:J. Chem. Phys
3291:
3289:
3285:
3280:
3274:
3266:
3262:
3258:
3254:
3250:
3246:
3241:
3236:
3233:(7): 073206.
3232:
3228:
3220:
3218:
3216:
3214:
3212:
3210:
3208:
3206:
3204:
3202:
3200:
3198:
3196:
3194:
3192:
3190:
3188:
3186:
3182:
3177:
3173:
3169:
3165:
3161:
3157:
3150:
3147:
3142:
3138:
3134:
3130:
3126:
3122:
3117:
3112:
3108:
3104:
3097:
3095:
3093:
3091:
3089:
3087:
3085:
3083:
3081:
3079:
3075:
3070:
3066:
3061:
3056:
3052:
3048:
3041:
3039:
3037:
3033:
3028:
3024:
3020:
3016:
3012:
3008:
3004:
3000:
2995:
2990:
2987:(6): 029902.
2986:
2982:
2975:
2973:
2969:
2964:
2960:
2956:
2952:
2948:
2944:
2939:
2934:
2930:
2926:
2919:
2916:
2911:
2907:
2903:
2899:
2895:
2891:
2886:
2881:
2878:(6): 062130.
2877:
2873:
2869:
2862:
2860:
2858:
2856:
2854:
2852:
2850:
2848:
2846:
2844:
2842:
2840:
2838:
2836:
2832:
2826:
2821:
2817:
2813:
2809:
2805:
2804:J. Chem. Phys
2801:
2794:
2792:
2788:
2783:
2779:
2775:
2771:
2767:
2763:
2759:
2755:
2750:
2745:
2742:(1): 012109.
2741:
2737:
2730:
2728:
2726:
2724:
2722:
2720:
2718:
2716:
2714:
2712:
2710:
2708:
2706:
2704:
2700:
2695:
2691:
2687:
2683:
2679:
2675:
2671:
2667:
2662:
2657:
2653:
2649:
2642:
2639:
2634:
2630:
2626:
2622:
2618:
2614:
2610:
2606:
2601:
2596:
2593:(5): 051602.
2592:
2588:
2581:
2579:
2577:
2573:
2567:
2566:2027.42/48820
2562:
2558:
2554:
2550:
2546:
2542:
2538:
2531:
2528:
2523:
2519:
2515:
2511:
2504:
2502:
2498:
2493:
2486:
2484:
2482:
2480:
2478:
2476:
2474:
2472:
2470:
2466:
2461:
2457:
2453:
2447:
2444:
2441:
2437:
2431:
2428:
2423:
2419:
2415:
2411:
2407:
2403:
2399:
2392:
2389:
2384:
2380:
2376:
2372:
2368:
2364:
2363:J. Chem. Phys
2357:
2355:
2351:
2346:
2342:
2335:
2333:
2331:
2329:
2325:
2318:
2314:
2311:
2309:
2306:
2304:
2301:
2300:
2296:
2289:
2286:
2285:
2281:
2278:
2277:
2273:
2270:
2269:
2265:
2262:
2261:
2255:
2249:0.04230(21),
2248:
2245:
2244:
2240:
2237:
2236:
2232:
2229:
2228:
2224:
2221:
2220:
2216:
2213:
2212:
2208:
2205:
2204:
2200:
2197:
2196:
2192:
2189:
2188:
2182:
2176:0.40187(97),
2175:
2172:
2171:
2167:
2164:
2163:
2159:
2156:
2155:
2151:
2148:
2147:
2141:
2134:
2131:
2128:
2127:
2123:
2120:
2117:
2116:
2112:
2109:
2106:
2105:
2101:
2098:
2095:
2094:
2090:
2087:
2084:
2083:
2079:
2077:aspect ratio
2076:
2073:
2072:
2066:
2059:
2056:
2055:
2051:
2048:
2047:
2043:
2040:
2039:
2035:
2032:
2031:
2027:
2024:
2023:
2019:
2016:
2015:
2011:
2008:
2007:
2003:
2000:
1999:
1995:
1992:
1991:
1985:
1983:
1969:
1964:
1960:
1955:
1951:
1948:
1945:
1941:
1937:
1934:
1925:
1921:
1916:
1912:
1898:0.562038(33)
1897:
1894:
1893:
1890:0.562127(33)
1889:
1886:
1885:
1882:0.562346(33)
1881:
1878:
1877:
1874:0.562647(31)
1873:
1870:
1869:
1866:0.563074(52)
1865:
1862:
1861:
1858:0.564405(51)
1857:
1854:
1853:
1849:
1846:
1845:
1842:0.567077(40)
1841:
1838:
1837:
1833:
1830:
1829:
1826:0.571916(27)
1825:
1822:
1821:
1817:
1814:
1813:
1809:
1806:
1805:
1802:0.582233(39)
1801:
1798:
1797:
1793:
1790:
1789:
1785:
1782:
1781:
1777:
1774:
1773:
1769:
1766:
1765:
1761:
1758:
1757:
1753:
1750:
1749:
1745:
1742:
1741:
1723:
1719:
1710:
1707:
1706:
1688:
1685:
1682:
1672:
1664:
1661:
1660:
1656:
1653:
1652:
1634:
1630:
1621:
1618:
1617:
1611:
1604:
1601:
1600:
1596:
1593:
1592:
1588:
1585:
1584:
1580:
1577:
1576:
1572:
1569:
1568:
1564:
1561:
1560:
1556:
1553:
1552:
1548:
1545:
1544:
1540:
1537:
1536:
1532:
1529:
1528:
1524:
1521:
1520:
1516:
1513:
1512:
1508:
1505:
1504:
1500:
1497:
1496:
1492:
1489:
1488:
1484:
1481:
1480:
1476:
1473:
1472:
1468:
1466:dimers k = 2
1465:
1464:
1446:
1442:
1433:
1430:
1429:
1423:
1419:
1417:
1403:
1400:
1391:
1387:
1382:
1378:
1363:
1360:
1359:
1355:
1352:
1351:
1347:
1344:
1343:
1339:
1336:
1335:
1331:
1328:
1327:
1323:
1320:
1319:
1315:
1312:
1311:
1307:
1304:
1303:
1299:
1296:
1295:
1291:
1288:
1287:
1283:
1280:
1279:
1275:
1272:
1271:
1267:
1264:
1263:
1259:
1256:
1255:
1251:
1248:
1247:
1244:0.7103, 0.71
1243:
1240:
1239:
1235:
1232:
1231:
1227:
1224:
1223:
1219:
1216:
1215:
1211:
1208:
1207:
1203:
1200:
1199:
1196:0.8094 0.81
1180:
1177:
1176:
1157:
1154:
1153:
1149:
1147:dimers k = 2
1146:
1145:
1127:
1123:
1114:
1111:
1110:
1104:
1100:
1093:
1090:
1089:
1085:
1082:
1081:
1077:
1074:
1073:
1069:
1066:
1065:
1049:
1041:
1038:
1037:
1034:
1028:
1026:
1012:
1009:
1006:
1002:
998:
995:
986:
982:
977:
973:
947:
940:
918:
917:
902:
895:
892:
891:
876:
869:
866:
865:
850:
843:
840:
839:
824:
817:
814:
813:
798:
791:
788:
787:
772:
765:
762:
761:
746:
743:
735:
731:
727:
716:
705:
699:
683:
678:
668:
665:
664:
649:
646:
641:
638:
634:
630:
627:
620:
617:
616:
598:
594:
585:
582:
581:
575:
571:
565:
561:
559:
554:
538:
535:
531:
527:
524:
521:
516:
512:
491:
482:
469:
466:
462:
456:
450:
446:
442:
439:
431:
428:
425:
420:
417:
414:
410:
406:
403:
399:
395:
392:
387:
382:
378:
374:
371:
368:
365:
361:
355:
349:
346:
343:
339:
335:
332:
324:
321:
318:
313:
310:
307:
303:
299:
296:
293:
290:
286:
282:
279:
269:
265:
261:
258:
253:
249:
240:
226:
217:
211:
210:Ilona Palásti
206:
203:
190:
187:
184:
181:
178:
174:
170:
167:
162:
156:
153:
149:
145:
142:
134:
129:
125:
121:
118:
114:
110:
107:
97:
93:
89:
84:
80:
71:
68:
66:
65:
55:
51:
48:
46:
42:
38:
34:
30:
26:
22:
18:
4885:
4881:
4875:
4842:
4838:
4832:
4799:
4795:
4743:
4739:
4733:
4719:(2): 87–93.
4716:
4712:
4684:
4680:
4674:
4649:
4645:
4639:
4617:(12): 8252.
4614:
4610:
4604:
4587:
4583:
4577:
4552:
4548:
4514:
4511:Phys. Rev. A
4510:
4504:
4461:
4457:
4451:
4408:
4404:
4398:
4373:
4369:
4363:
4320:
4316:
4310:
4269:
4265:
4223:
4219:
4185:
4181:
4121:
4118:Phys. Rev. E
4117:
4049:
4046:Phys. Rev. E
4045:
3973:
3969:
3963:
3912:
3909:Phys. Rev. E
3908:
3902:
3877:
3873:
3837:
3833:
3827:
3794:
3790:
3784:
3749:
3745:
3739:
3688:
3684:
3646:
3642:
3636:
3611:
3607:
3551:
3548:Phys. Rev. A
3547:
3481:
3478:Phys. Rev. B
3477:
3426:(22): 2642.
3423:
3419:
3413:
3412:"Comment on
3405:
3380:
3376:
3370:
3353:
3349:
3343:
3300:
3296:
3273:cite journal
3230:
3226:
3159:
3155:
3149:
3106:
3103:Phys. Rev. E
3102:
3050:
3046:
2984:
2981:Phys. Rev. E
2980:
2928:
2924:
2918:
2875:
2871:
2867:
2807:
2803:
2739:
2736:Phys. Rev. E
2735:
2651:
2647:
2641:
2590:
2587:Phys. Rev. E
2586:
2540:
2536:
2530:
2513:
2509:
2491:
2459:
2455:
2446:
2439:
2430:
2405:
2401:
2391:
2366:
2362:
2344:
2340:
1982:. See also
1903:
1850:0.56516(10)
1834:0.56841(10)
1670:
1605:0.6060(13),
1469:0.9142(12),
1421:
1369:
1102:
1032:
964:
573:
555:
483:
241:
218:
207:
204:
72:
69:
63:
62:
60:
49:
41:Alfréd Rényi
20:
16:
15:
4746:(1): 1–10.
4376:: 182–186.
3840:(7): 5212.
2452:Palasti, I.
2206:3d spheres
2060:0.54421(6)
2052:0.54405(5)
2044:0.54238(5)
2036:0.54210(6)
2028:0.53913(5)
2020:0.54130(5)
2004:0.52590(4)
1597:0.6090(8),
1589:0.6108(7),
1581:0.6129(7),
1573:0.6153(6),
1565:0.6183(6),
1557:0.6220(7),
1549:0.6276(6),
1541:0.6362(6),
1533:0.6515(6),
1525:0.6786(6),
1517:0.6912(6),
1509:0.7091(6),
1501:0.7371(7),
1493:0.7584(6),
1485:0.7892(5),
1477:0.8364(6),
1260:0.6809(5),
1070:0.74759792
893:k = 100000
4908:Categories
4681:Biometrika
4471:1709.05029
4330:1712.09663
3983:1506.08164
3698:1803.08348
3240:1703.07680
2885:1810.06800
2462:: 353–359.
2319:References
2303:Adsorption
2135:0.5833(5)
2102:0.5793(1)
2085:rectangle
1895:k = 16384
1818:0.574(1),
1794:0.583(1),
1353:k = 16384
1308:0.6634(6)
1292:0.6655(7)
1276:0.6714(5)
948:0.74759792
903:0.74760008
877:0.74761954
867:k = 10000
851:0.74781413
825:0.74976335
799:0.76957741
773:0.80389348
747:0.82365296
650:0.86466472
37:Paul Flory
4914:Chemistry
4867:124311298
4824:118248194
4740:Physica A
4443:119032105
4355:118969644
4182:Physica A
4059:1402.4883
3922:1403.3200
3819:250852782
3265:119374271
2994:1109.3271
2749:1412.7267
2198:2d disks
2124:0.583(1)
2113:0.583(1)
2091:0.553(1)
1970:…
1930:∞
1926:θ
1922:∼
1913:θ
1887:k = 4096
1879:k = 1024
1720:θ
1686:×
1631:θ
1443:θ
1404:…
1396:∞
1392:θ
1388:∼
1379:θ
1345:k = 8192
1337:k = 4096
1329:k = 2048
1321:k = 1024
1124:θ
1075:R = 1.05
1050:θ
1013:…
991:∞
987:θ
983:∼
974:θ
927:∞
841:k = 1000
744:≈
706:−
684:π
639:−
631:−
595:θ
536:−
528:−
513:θ
443:−
429:−
411:∑
404:−
396:
379:∫
344:−
336:−
322:−
304:∑
297:−
291:−
283:
275:∞
266:∫
250:θ
191:…
154:−
146:−
126:∫
119:−
111:
103:∞
94:∫
81:θ
35:chain by
25:particles
4778:11802063
4496:26861078
4302:53727841
4294:30466287
4248:29331110
4164:15604775
4156:17280063
4092:14810845
4084:24329384
4016:14368653
4008:26330194
3955:12961099
3947:24827257
3731:46892756
3723:29758708
3448:10040048
3335:97703000
3027:25377751
3019:22304098
2963:11142384
2910:53709717
2782:35537612
2774:25679572
2694:36659964
2686:10063168
2625:16802941
2297:See also
2157:spheres
2107:ellipse
2009:squares
1871:k = 512
1863:k = 256
1855:k = 128
1847:k = 100
1602:k = 128
1594:k = 100
1356:0.6561
1348:0.6571
1332:0.6596
1324:0.6592
1313:k = 512
1305:k = 384
1297:k = 256
1289:k = 192
1281:k = 128
1220:0.7579
1212:0.7703
1204:0.7868
1083:R = 1.1
815:k = 100
666:trimers
4859:3214426
4816:3213489
4758:Bibcode
4654:Bibcode
4619:Bibcode
4557:Bibcode
4519:Bibcode
4476:Bibcode
4423:Bibcode
4378:Bibcode
4335:Bibcode
4274:Bibcode
4228:Bibcode
4190:Bibcode
4136:Bibcode
4064:Bibcode
3988:Bibcode
3927:Bibcode
3882:Bibcode
3842:Bibcode
3799:Bibcode
3754:Bibcode
3703:Bibcode
3616:Bibcode
3576:9905079
3556:Bibcode
3506:9997649
3486:Bibcode
3428:Bibcode
3385:Bibcode
3315:Bibcode
3245:Bibcode
3164:Bibcode
3133:9961218
2999:Bibcode
2943:Bibcode
2890:Bibcode
2812:Bibcode
2754:Bibcode
2666:Bibcode
2633:8046084
2605:Bibcode
2545:Bibcode
2410:Bibcode
2371:Bibcode
2263:system
2190:system
2149:system
2132:1.6347
2099:1.5098
2074:system
1993:system
1839:k = 64
1831:k = 50
1823:k = 32
1815:k = 30
1807:k = 20
1799:k = 16
1791:k = 15
1783:k = 10
1708:system
1619:system
1586:k = 90
1578:k = 80
1570:k = 70
1562:k = 60
1554:k = 50
1546:k = 40
1538:k = 30
1530:k = 20
1522:k = 12
1514:k = 10
1431:system
1340:0.6575
1273:k = 96
1265:k = 64
1257:k = 48
1249:k = 32
1241:k = 16
1236:0.7405
1112:system
1039:system
789:k = 10
618:dimers
583:system
33:polymer
4865:
4857:
4822:
4814:
4776:
4494:
4441:
4353:
4300:
4292:
4246:
4162:
4154:
4090:
4082:
4014:
4006:
3953:
3945:
3817:
3729:
3721:
3574:
3504:
3446:
3333:
3263:
3141:131089
3139:
3131:
3025:
3017:
2961:
2908:
2780:
2772:
2692:
2684:
2631:
2623:
2096:dimer
2088:1.618
1775:k = 8
1767:k = 5
1759:k = 4
1751:k = 3
1743:k = 2
1506:k = 8
1498:k = 6
1490:k = 5
1482:k = 4
1474:k = 3
1361:k = ∞
1233:k = 9
1225:k = 8
1217:k = 7
1209:k = 6
1201:k = 5
1178:k = 4
1091:R = 2
1067:R = 1
999:0.2162
763:k = 4
4863:S2CID
4855:JSTOR
4820:S2CID
4812:JSTOR
4774:S2CID
4748:arXiv
4492:S2CID
4466:arXiv
4439:S2CID
4413:arXiv
4351:S2CID
4325:arXiv
4298:S2CID
4160:S2CID
4126:arXiv
4088:S2CID
4054:arXiv
4012:S2CID
3978:arXiv
3951:S2CID
3917:arXiv
3815:S2CID
3727:S2CID
3693:arXiv
3331:S2CID
3305:arXiv
3261:S2CID
3235:arXiv
3137:S2CID
3111:arXiv
3055:arXiv
3023:S2CID
2989:arXiv
2959:S2CID
2933:arXiv
2906:S2CID
2880:arXiv
2778:S2CID
2744:arXiv
2690:S2CID
2656:arXiv
2629:S2CID
2595:arXiv
2121:1.75
1952:0.114
1938:0.316
484:When
4321:2018
4290:PMID
4244:PMID
4152:PMID
4080:PMID
4004:PMID
3943:PMID
3719:PMID
3572:PMID
3502:PMID
3444:PMID
3279:link
3231:2017
3129:PMID
3015:PMID
2770:PMID
2682:PMID
2621:PMID
2110:2.0
919:k =
710:erfi
693:erfi
219:For
4890:doi
4847:doi
4804:doi
4766:doi
4744:198
4721:doi
4689:doi
4662:doi
4650:102
4627:doi
4592:doi
4565:doi
4527:doi
4484:doi
4431:doi
4386:doi
4374:651
4343:doi
4282:doi
4270:149
4236:doi
4224:148
4198:doi
4186:187
4144:doi
4072:doi
3996:doi
3935:doi
3890:doi
3850:doi
3807:doi
3791:EPL
3770:hdl
3762:doi
3711:doi
3651:doi
3624:doi
3564:doi
3494:doi
3436:doi
3393:doi
3381:103
3358:doi
3323:doi
3301:108
3253:doi
3172:doi
3121:doi
3065:doi
3051:165
3007:doi
2951:doi
2898:doi
2820:doi
2762:doi
2674:doi
2613:doi
2561:hdl
2553:doi
2518:doi
2418:doi
2379:doi
393:exp
280:exp
108:exp
21:RSA
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