%0 Book Section %1 statphys23_0558 %A Araújo, N.A.M. %A Cadilhe, A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K adsorption distribution fits gap-size jamming processes snug statphys23 stochastic topic-3 %T Competitive deposition of two size segments on a line %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=558 %X The Random Sequential Adsorption model (RSA) has been used to study the irreversible deposition of particles on a line where, in the experimental time scale, particles do not significantly diffuse. This model has been applied not only to the physical chemistry field but also to less traditional areas like biology, ecology, and sociology. Recently, the interested has shifted towards the study of binary mixtures, which can occur by either competitive adsorption or preadsorption. In the latter case adsorption of each particle size takes place separately, whilst in the competitive case, both particle sizes kinetically compete with each other for adsorption. We focus our study on the competitive case, and consider the irreversible deposition of a binary mixture of segments adsorbing on a line at equal fluxes. Since the deposition process is irreversible, the kinetics is characterized by a jamming state, where no further particles can be adsorbed. The dependence of jamming state on the size ratio of the two segment-types was studied, through Monte Carlo simulations, ranging the size ratio from one to 20. Of course, in the limit of size ratio equal to one, we obtain the classical, car-parking problem result. To study the morphology of the jamming state, we compute the gap-size distribution functions of the four gap types (AA, AB, BB, and BA) and their respective cumulants up to the fourth order. As the third and fourth cumulants are respectively related to the skewness and kurtosis, we use these quantities to analyze the gap-size distribution. We were able to grasp the non-trivial features appearing in the skewness and kurtosis by resorting to an heuristic argument to use a truncated exponential distribution function of the gaps. We used the first two cumulants, namely, the mean and second moment to parametrize the truncated exponential distribution of the gaps. We found qualitative agreement with the computational results and that, for AB-gap type, for small values of size ratio (lower than 1.55) the truncated exponential function does not follow the behavior of the gap-size distribution function, due to a type of events we classify as snug fits. Reference:\\ 1) N. A. M. Araújo and A. Cadilhe, Gap-size distribution of a random sequential adsorption model of segments on a line. Phys. Rev. E 73, 051602 (2006).

@incollection{statphys23_0558, abstract = {The Random Sequential Adsorption model (RSA) has been used to study the irreversible deposition of particles on a line where, in the experimental time scale, particles do not significantly diffuse. This model has been applied not only to the physical chemistry field but also to less traditional areas like biology, ecology, and sociology. Recently, the interested has shifted towards the study of binary mixtures, which can occur by either competitive adsorption or preadsorption. In the latter case adsorption of each particle size takes place separately, whilst in the competitive case, both particle sizes kinetically compete with each other for adsorption. We focus our study on the competitive case, and consider the irreversible deposition of a binary mixture of segments adsorbing on a line at equal fluxes. Since the deposition process is irreversible, the kinetics is characterized by a jamming state, where no further particles can be adsorbed. The dependence of jamming state on the size ratio of the two segment-types was studied, through Monte Carlo simulations, ranging the size ratio from one to 20. Of course, in the limit of size ratio equal to one, we obtain the classical, car-parking problem result. To study the morphology of the jamming state, we compute the gap-size distribution functions of the four gap types (AA, AB, BB, and BA) and their respective cumulants up to the fourth order. As the third and fourth cumulants are respectively related to the skewness and kurtosis, we use these quantities to analyze the gap-size distribution. We were able to grasp the non-trivial features appearing in the skewness and kurtosis by resorting to an heuristic argument to use a truncated exponential distribution function of the gaps. We used the first two cumulants, namely, the mean and second moment to parametrize the truncated exponential distribution of the gaps. We found qualitative agreement with the computational results and that, for AB-gap type, for small values of size ratio (lower than 1.55) the truncated exponential function does not follow the behavior of the gap-size distribution function, due to a type of events we classify as {\it snug fits}. Reference:\\ 1) N. A. M. Ara\'ujo and A. Cadilhe, {\it Gap-size distribution of a random sequential adsorption model of segments on a line}. Phys. Rev. E \textbf{73}, 051602 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ara\'ujo, N.A.M. and Cadilhe, A.}, biburl = {https://www.bibsonomy.org/bibtex/2246f22c2aeafacdb79456924dcce78f9/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {8a181fbe9782d01bd111b1b44cc374d7}, intrahash = {246f22c2aeafacdb79456924dcce78f9}, keywords = {adsorption distribution fits gap-size jamming processes snug statphys23 stochastic topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:23.000+0200}, title = {Competitive deposition of two size segments on a line}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=558}, year = 2007 }