scholarly journals Annihilating random walks and perfect matchings of planar graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Massimiliano Mattera

International audience We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model.

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1097-1228 ◽  
Author(s):  
MASAHITO YAMAZAKI

This paper summarizes recent developments in the theory of Bogomol'nyi–Prasad–Sommerfield (BPS) state counting and the wall crossing phenomena, emphasizing in particular the role of the statistical mechanical model of crystal melting. This paper is divided into two parts, which are closely related to each other. In the first part, we discuss the statistical mechanical model of crystal melting counting BPS states. Each of the BPS states contributing to the BPS index is in one-to-one correspondence with a configuration of a molten crystal, and the statistical partition function of the melting crystal gives the BPS partition function. We also show that smooth geometry of the Calabi–Yau manifold emerges in the thermodynamic limit of the crystal. This suggests a remarkable interpretation that an atom in the crystal is a discretization of the classical geometry, giving an important clue as such to the geometry at the Planck scale. In the second part, we discuss the wall crossing phenomena. Wall crossing phenomena states that the BPS index depends on the value of the moduli of the Calabi–Yau manifold, and jumps along real codimension one subspaces in the moduli space. We show that by using type IIA/M-theory duality, we can provide a simple and an intuitive derivation of the wall crossing phenomena, furthermore clarifying the connection with the topological string theory. This derivation is consistent with another derivation from the wall crossing formula, motivated by multicentered BPS extremal black holes. We also explain the representation of the wall crossing phenomena in terms of crystal melting, and the generalization of the counting problem and the wall crossing to the open BPS invariants.


2003 ◽  
Vol 119 (8) ◽  
pp. 4582-4591 ◽  
Author(s):  
Melissa R. Feeney ◽  
Pablo G. Debenedetti ◽  
Frank H. Stillinger

2016 ◽  
Author(s):  
Masaki Sasai ◽  
George Chikenji ◽  
Tomoki P. Terada

AbstractA simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The ϕ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.


2020 ◽  
Author(s):  
Jonathan Carney ◽  
David Roundy ◽  
Cory M. Simon

Metal-organic frameworks (MOFs) are modular and tunable nano-porous materials with applications in gas storage, separations, and sensing. Flexible/dynamic components that respond to adsorbed gas can give MOFs unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, position of the wheel, and differential energy of adsorption depend on temperature, pressure, and the interactions of the gas/wheel with the stations. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature-sensitive and to release more or less heat upon adsorption. The model also uncovers a non-monotonic relationship between the temperature and the position of the wheel if gas out-competes the wheel for its preferable station.


2005 ◽  
Vol 19 (15n17) ◽  
pp. 2921-2926
Author(s):  
Lu CAI

A statistical mechanical model was used to calculate the curvature of the 5 chemically synthesized DNAs which contain repeats sequences ( CCTG )n · ( CAGG )n and ( ATTCT )n · ( AGAAT )n associated with human diseases. 8% polyacrylamide gel analyses were also performed for these 5 DNAs. The results indicate the curvature of the sequences CCTG/bend and ATTCT/bend are larger than that of the sequences CCTG/straight and ATTCT/straight. The curvature of straight/bend is larger than that of CCTG/straight and ATTCT/straight, and smaller than that of CCTG/bend and ATTCT/bend. There exists good consistent between theoretical prediction and experimental data.


2016 ◽  
Vol 111 (11) ◽  
pp. 2534-2545 ◽  
Author(s):  
Duyu Chen ◽  
Wen Yih Aw ◽  
Danelle Devenport ◽  
Salvatore Torquato

Author(s):  
Mikkel L. Bødker ◽  
Johan B. Pedersen ◽  
Francisco Muñoz ◽  
John C. Mauro ◽  
Morten M. Smedskjaer

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