Trajectories of directed lattice paths

Rensburg, E J Janse van

doi:10.1088/1402-4896/acbb3d

Cited by 3 publications

(10 citation statements)

References 25 publications

(45 reference statements)

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“…At sufficiently low temperatures, a test particle will likely localize in such a low density region until it diffuses away from the network due to thermal vibrations, or until the network degrades and releases it. The results here show that there is little scope for an adsorbed polymer chain to contain a test particle, as its density decreases with distance from the wall, as already seen in the model in reference [15]. However, a second (desorbed) polymer, grafted to the wall or to the first, may cause the formation of lower density regions, as seen in figures 9 and 11.…”

supporting

confidence: 67%

“…The plot shows low densities adjacent to the hard wall which increases with δ before it drops of farther from the wall. Since the lower path is adsorbed on the hard wall, this density of the top path is the same as the density for a single Dyck path determined in reference [15].…”

Section: The Probability Density Of Both Pathsmentioning

confidence: 97%

“…Figure 8 shows a low density region next to the hard wall. The most likely trajectory of the top path here is δ M = (1− ) [15], while its mean trajectory is δ = (2/ √ π) (1− ).…”

Section: The Probability Density Pmentioning

confidence: 99%

“…In this case ρE is the probability that the top path passes through the set E along its trajectory from (0, 0) to (1, 0), irrespective of the trajectory of the bottom path. ( , δ) is also the probability density of a single (desorbed) Dyck path in the scaling limit (see reference [15]). This is not unexpected, since the bottom path is adsorbed onto the hard wall, and the top path is screened from the wall, and does not interact with it.…”

Section: The Probability Density Pmentioning

confidence: 99%

“…In reference [15] a directed path model of a grafted linear polymer in a polymer coating was examined. It was shown there that the entropic repulsion between the hard wall and the directed path creates a low density region next to the wall, providing a metastable location for absorbed particles next to the wall.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagrams of confined square lattice linked polygons

Rensburg

Orlandini

2021

Phys. Rev. E

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The phase diagrams of two models of two confined and dense two dimensional ring polymers are examined numerically. The ring polymers are placed in a cavity, and are either linked or unlinked in the plane. The phase diagrams are found to be a function of the linking of the polymers, and include multicritical points where first order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.

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supporting

confidence: 67%

Section: The Probability Density Of Both Pathsmentioning

confidence: 97%

“…Figure 8 shows a low density region next to the hard wall. The most likely trajectory of the top path here is δ M = (1− ) [15], while its mean trajectory is δ = (2/ √ π) (1− ).…”

Section: The Probability Density Pmentioning

confidence: 99%

Section: The Probability Density Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase diagrams of confined square lattice linked polygons

Rensburg

Orlandini

2021

Phys. Rev. E

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Trajectories of square lattice staircase polygons

Janse van Rensburg

2023

Phys. Scr.

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The distribution of monomers in a coating of grafted and adsorbing polymers is modelled using a grafted staircase polygon in the square lattice. The adsorbing staircase polygon consists of a bottom and a top lattice path (branches) and the asymptotic probability density that vertices in the lattice are occupied by these paths is determined. This is a model consisting of two linear polymers grafted to a hard wall in a coating. The probability that either the bottom path, or the top path, of a staircase polygon passes through a lattice site with coordinates ( ⌊ ϵ n ⌋ , ⌊ δ n ⌋ ) , for 0 < ϵ < 1 and δ ≥ 0, is determined asymptotically as n → ∞ . This gives the probability density of vertices in the staircase polygon in the scaling limit (as n → ∞ ): P r f , ( both ) ( ϵ , δ ) = δ 2 ( 15 ϵ 2 1 − ϵ 2 − 12 δ 2 ϵ ( 1 − ϵ ) + 4 δ 4 ) 3 π ϵ 7 1 − ϵ 7 e − δ 2 / ϵ ( 1 − ϵ ) . The densities of other cases, grafted and adsorbed, and at the adsorption critical point (or special point), are also determined. In these cases the most likely and mean trajectories of the paths are determined. The results show that low density regions in the distribution induce entropic forces on test particles which confine them next to the hard wall, or between branches of the staircase polygon. These results give qualitative mechanisms for the stabilisation of a drug particle confined to a polymer coating in a drug delivery system such as a drug-eluding stent covered by a grafted polymer.

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Finanças Públicas Do Estado Do Rio De Janeiro: Notas Históricas E Comparativas

Aranha¹

2022

Economia Do Estado Do Rio De Janeiro: Crise, Desafios E Perspectivas

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Os autores desta obra: 1. Atestam não possuir qualquer interesse comercial que constitua um conflito de interesses em relação ao artigo científico publicado; 2.Declaram que participaram ativamente da construção dos respectivos manuscritos, preferencialmente na: a) Concepção do estudo, e/ou aquisição de dados, e/ou análise e interpretação de dados; b) Elaboração do artigo ou revisão com vistas a tornar o material intelectualmente relevante; c) Aprovação final do manuscrito para submissão.; 3. Certificam que os artigos científicos publicados estão completamente isentos de dados e/ou resultados fraudulentos; 4. Confirmam a citação e a referência correta de todos os dados e de interpretações de dados de outras pesquisas; 5.Reconhecem terem informado todas as fontes de financiamento recebidas para a consecução da pesquisa; 6. Autorizam a edição da obra, que incluem os registros de ficha catalográfica, ISBN, DOI e demais indexadores, projeto visual e criação de capa, diagramação de miolo, assim como lançamento e divulgação da mesma conforme critérios da Atena Editora. DECLARAÇÃO DA EDITORA A Atena Editora declara, para os devidos fins de direito, que: 1. A presente publicação constitui apenas transferência temporária dos direitos autorais, direito sobre a publicação, inclusive não constitui responsabilidade solidária na criação dos manuscritos publicados, nos termos previstos na Lei sobre direitos autorais (Lei 9610/98), no art. 184 do Código Penal e no art. 927 do Código Civil; 2. Autoriza e incentiva os autores a assinarem contratos com repositórios institucionais, com fins exclusivos de divulgação da obra, desde que com o devido reconhecimento de autoria e edição e sem qualquer finalidade comercial; 3. Todos os e-book são open access, desta forma não os comercializa em seu site, sites parceiros, plataformas de ecommerce, ou qualquer outro meio virtual ou físico, portanto, está isenta de repasses de direitos autorais aos autores; 4. Todos os membros do conselho editorial são doutores e vinculados a instituições de ensino superior públicas, conforme recomendação da CAPES para obtenção do Qualis livro; 5. Não cede, comercializa ou autoriza a utilização dos nomes e e-mails dos autores, bem como nenhum outro dado dos mesmos, para qualquer finalidade que não o escopo da divulgação desta obra. AGRADECIMENTOSÀ Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), pelo apoio financeiro concedido por meio do edital FAPERJ Nº 16/2019, viabilizando a publicação desta obra.

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Trajectories of directed lattice paths

Cited by 3 publications

References 25 publications

Phase diagrams of confined square lattice linked polygons

Phase diagrams of confined square lattice linked polygons

Trajectories of square lattice staircase polygons

Finanças Públicas Do Estado Do Rio De Janeiro: Notas Históricas E Comparativas

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