Exact partition functions for some one-dimensional models via the isobaric ensemble

Bishop, Marvin; Boonstra, Martin A.

doi:10.1119/1.13204

Cited by 17 publications

(61 citation statements)

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“…As it is well known, the thermodynamics of models like ours can be solved exactly (see e.g. [26]). In particular, the partition function and the equation of state in the P − T ensemble is…”

Section: The Hard-point Chain Modelmentioning

confidence: 93%

Energy diffusion in hard-point systems

Delfini

Denisov

Lepri

et al. 2007

Eur. Phys. J. Spec. Top.

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Abstract. We investigate the diffusive properties of energy fluctuations in a onedimensional diatomic chain of hard-point particles interacting through a squarewell potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent γ = 3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the "stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenario.

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Section: The Hard-point Chain Modelmentioning

confidence: 93%

Energy diffusion in hard-point systems

Delfini

Denisov

Lepri

et al. 2007

Eur. Phys. J. Spec. Top.

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“…21 Since (z) is short ranged, we may assume that each guest molecule interact with its nearest neighbors alone, which is the only prerequisite for the calculation. Then the isobaric partition function, i.e., the Laplace transform of Eq.…”

Section: B Approximate Evaluation Of the Occupancymentioning

confidence: 99%

Formation of ice nanotube with hydrophobic guests inside carbon nanotube

Tanaka

Koga

2005

The Journal of Chemical Physics

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ABSTRACT]A composite ice nanotube inside a carbon nanotube has been explored by molecular dynamics and grandcanonical Monte Carlo simulations. It is made from an octagonal ice nanotube whose hollow space contains hydrophobic guest molecules such as neon, argon, and methane. It is shown that the attractive interaction of the guest molecules stabilizes the ice nanotube. The guest occupancy of the hollow s p a c e is calculated by the same method as applied to clathrate hydrates.2

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“…2.1.2. We focus on the equation of state (i.e., the relationship between pressure, density, and temperature), the isothermal [1 (11) 2 (11) ] a n * =0.7 MC n * =0.7 [1 (11) 2 (11) ] a n * =0.1 MC n * =0.1 susceptibility, and the excess internal energy per particle. Given the approximate character of our proposals, the results will in general depend on the route followed to obtain those thermodynamic quantities.…”

Section: Thermodynamic Propertiesmentioning

confidence: 99%

“…(2.4), (2.5), and (2.8). In particular, for the SW potential (4.1) one has (11) 2 (11) 3 (11) ] a (-), [1 (11) 2 (11) 3 (11) ] b (--), and [1 (11) 2 (11) 3 (11) ] c (---).…”

Section: Thermodynamic Propertiesmentioning

confidence: 99%

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

Fantoni

Santos

2017

J Stat Phys

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As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, p 1 (r), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearestneighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of p 1 (r) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

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Exact partition functions for some one-dimensional models via the isobaric ensemble

Abstract: The isobaric ensemble is employed to obtain the exact partition functions of a number of one-dimensional models: rigid rod, square well, and triangle well. The equations of state are also determined.

Cited by 17 publications

References 0 publications

Energy diffusion in hard-point systems

Energy diffusion in hard-point systems

Formation of ice nanotube with hydrophobic guests inside carbon nanotube

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

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