Random close packing (RCP) of spheres is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing more grain to be added to the container. In other words, shaking increases the density of packed objects. But shaking cannot increase the density indefinitely, a limit is reached, and if this is reached without obvious packing into an ordered structure, such as a regular crystal lattice, this is the empirical random close-packed density for this particular procedure of packing. The random close packing is the highest possible volume fraction out of all possible packing procedures.
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| - Empaquetamiento aleatorio (es)
- Empilement aléatoire compact (fr)
- Impacchettamento casuale (it)
- ランダム最密充填 (ja)
- Random close pack (en)
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| - ランダム最密充填（ランダムさいみつじゅうてん、英：Random Close Packing、略：RCP）は、固体物体をランダムに詰めたときに得られる最大体積分率を特徴付けるために使用される経験的なパラメーターである。 (ja)
- El empaquetamiento aleatorio es un parámetro empírico utilizado para conseguir la fracción de volumen máxima de objetos sólidos obtenidos al "empaquetar" estos objetos de manera aleatoria después de resuelto. Por ejemplo, cuando un contenedor está lleno de granos, al sacudir el recipiente se reducirá el volumen considerado por los objetos de manera individual, lo que permite añadir más grano al contenedor. (es)
- Random close packing (RCP) of spheres is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing more grain to be added to the container. In other words, shaking increases the density of packed objects. But shaking cannot increase the density indefinitely, a limit is reached, and if this is reached without obvious packing into an ordered structure, such as a regular crystal lattice, this is the empirical random close-packed density for this particular procedure of packing. The random close packing is the highest possible volume fraction out of all possible packing procedures. (en)
- L'impacchettamento compatto casuale (RCP, Random close packing) o impacchettamento casuale è un parametro empirico usato per caratterizzare la frazione di volume massima di oggetti solidi ottenuta quando essi vengono impacchettati casualmente. Per esempio, quando un contenitore solido viene riempito con chicchi di grano, scuotendo il contenitore si ridurrà il volume da loro occupato, permettendo perciò di aggiungere altro grano al recipiente. In altre parole tramite lo scuotimento si aumenta la densità degli oggetti impacchettati. (it)
- Un empilement aléatoire compact (rcp, pour l'anglais random close packing) est un empilement obtenu par compaction d'un ensemble d'objets (ou de figures géométriques) dont les positions initiales sont aléatoires. Sa compacité est inférieure à celle de l'empilement le plus compact possible des mêmes objets ou figures. (fr)
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| - El empaquetamiento aleatorio es un parámetro empírico utilizado para conseguir la fracción de volumen máxima de objetos sólidos obtenidos al "empaquetar" estos objetos de manera aleatoria después de resuelto. Por ejemplo, cuando un contenedor está lleno de granos, al sacudir el recipiente se reducirá el volumen considerado por los objetos de manera individual, lo que permite añadir más grano al contenedor. La fracción de volumen ocupado por los objetos sólidos en empaquetamiento aleatorio es 0,64 para objetos esféricos (monodisperso). Esto es significativamente menor que la fracción máxima de llenado teórico de 0,74048 que resulta de un empaquetamiento hexagonal (HCP - también conocido como empaquetamiento). Esta discrepancia demuestra que la "aleatoriedad" de la RCP es vital para la definición. (es)
- Un empilement aléatoire compact (rcp, pour l'anglais random close packing) est un empilement obtenu par compaction d'un ensemble d'objets (ou de figures géométriques) dont les positions initiales sont aléatoires. Sa compacité est inférieure à celle de l'empilement le plus compact possible des mêmes objets ou figures. Contrairement à la compacité maximale (celle d'un empilement compact) qu'on peut déduire d'une démonstration mathématique, la compacité d'un empilement aléatoire compact est généralement obtenue par des expériences ou des simulations numériques. Elle dépend un peu des conditions initiales et du processus de compaction. (fr)
- Random close packing (RCP) of spheres is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing more grain to be added to the container. In other words, shaking increases the density of packed objects. But shaking cannot increase the density indefinitely, a limit is reached, and if this is reached without obvious packing into an ordered structure, such as a regular crystal lattice, this is the empirical random close-packed density for this particular procedure of packing. The random close packing is the highest possible volume fraction out of all possible packing procedures. Experiments and computer simulations have shown that the most compact way to pack hard perfect same-size spheres randomly gives a maximum volume fraction of about 64%, i.e., approximately 64% of the volume of a container is occupied by the spheres. The problem of predicting theoretically the random close pack of spheres is difficult mainly because of the absence of a unique definition of randomness or disorder. The random close packing value is significantly below the maximum possible close-packing of same-size hard spheres into a regular crystalline arrangements, which is 74.04%. Both the face-centred cubic (fcc) and hexagonal close packed (hcp) crystal lattices have maximum densities equal to this upper limit, which can occur through the process of granular crystallisation. The random close packing fraction of discs in the plane has also been considered a theoretically unsolved problem because of similar difficulties. An analytical, though not in closed form, solution to this problem was found in 2021 by R. Blumenfeld. The solution was found by limiting the probability of growth of ordered clusters to be exponentially small and relating it to the distribution of `cells', which are the smallest voids surrounded by connected discs. The derived maximum volume fraction is 85.3542%, if only hexagonal lattice clusters are disallowed, and 85.2514% if one disallows also deformed square lattice clusters. An analytical and closed-form solution for both 2D and 3D, mechanically stable, random packings of spheres has been found by A. Zaccone in 2022 using the assumption that the most random branch of jammed states (maximally random jammed packings, extending up to the fcc closest packing) undergo crowding in a way qualitatively similar to an equilibrium liquid. The reasons for the effectiveness of this solution are the object of ongoing debate. (en)
- L'impacchettamento compatto casuale (RCP, Random close packing) o impacchettamento casuale è un parametro empirico usato per caratterizzare la frazione di volume massima di oggetti solidi ottenuta quando essi vengono impacchettati casualmente. Per esempio, quando un contenitore solido viene riempito con chicchi di grano, scuotendo il contenitore si ridurrà il volume da loro occupato, permettendo perciò di aggiungere altro grano al recipiente. In altre parole tramite lo scuotimento si aumenta la densità degli oggetti impacchettati. Esperimenti hanno dimostrato che il modo più compatto di impacchettare sfere offre come risultato una densità massima di circa il 64%. La ricerca più recente prevede analiticamente che la frazione di volume riempita dagli oggetti solidi nell'impacchettamento compatto casuale non può eccedere una densità limite di 63,4% per oggetti sferici (monodispersi). Questo è significativamente più piccolo della frazione massima di riempimento teorico di 0,74048 che risulta dall'impacchettamento compatto esagonale (HCP, hexagonal close pack - noto anche come ). Questa discrepanza dimostra che la "casualità" di RCP è vitale per la definizione. (it)
- ランダム最密充填（ランダムさいみつじゅうてん、英：Random Close Packing、略：RCP）は、固体物体をランダムに詰めたときに得られる最大体積分率を特徴付けるために使用される経験的なパラメーターである。 (ja)
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