Statistically interacting vacancy particles

Bakhti, Benaoumeur; Karbach, Michael; Maass, Philipp; Mokim, Mohammad; Müller, Gerhard

doi:10.1103/physreve.89.012137

Cited by 15 publications

(32 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The statistical mechanics of compact and nested particles at level 1 was worked out in great generality for a lattice-gas application [11]. The extension particles that we introduce in Secs.…”

Section: Particles At Two Levelsmentioning

confidence: 99%

Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles

Öz

Gundlach

et al. 2020

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds between monomers or of entire groups of monomers to tension is governed by the activation of statistically interacting particles representing quanta of extension or contraction. This method of analysis is capable of describing thermal unbending of the freely-jointed or worm-like chain kind, linear or nonlinear contour elasticity, and structural transformations including effects of cooperativity. The versatility of this approach is demonstrated in an application to double-stranded DNA undergoing torsionally unconstrained stretching across three regimes of mechanical response including an overstretching transition. The three-regime forceextension characteristic, derived from a single free-energy expression, accurately matches empirical evidence. (c) J τ J J (b) (d) (a) FIG. 1: (Color online) Schematic representations for a chain of N = 7 monomers of (a) the reference state, (b) a state under tension with extension particles activated, (c) a state under tension and torque with twist-contraction particles activated, and (d) a state under tension with extension particles and contact particles activated.

show abstract

Section: Particles At Two Levelsmentioning

confidence: 99%

Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles

Öz

Gundlach

et al. 2020

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…For such cases an exact DFT calculation of density profiles tends to be be impracticable and calculations based on recursion relation for partition functions [9,12] are cumbersome. For long-range firstneighbor interactions, the SIVP method [10] provides a user-friendly way to derive the EOS.…”

Section: Eos Methods and Sivp Approachmentioning

confidence: 99%

“…These profiles depend systematically on σ without producing any additional features. From [10] we know that the effects of attractive or repulsive contact interactions of finite strength fade away completely in the continuum limit.…”

Section: Contact Interaction Via Sivpmentioning

confidence: 99%

Monodisperse hard rods in external potentials

et al. 2015

Self Cite

View full text Add to dashboard Cite

We consider linear arrays of cells of volume V c populated by monodisperse rods of size σ V c , σ = 1,2, . . ., subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as V c → 0, σ → ∞ at nonzero and finite σ V c , connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.

show abstract

“…= U S /N p s V c is the gravitational self-energy relative to a reference state of choice.Ŝ is the ILG entropy density, e.g. from [33], integrated over the space available to the particles:Ŝ…”

Section: F Free Energymentioning

confidence: 99%

Density profiles of a self-gravitating lattice gas in one, two, and three dimensions

et al. 2018

Self Cite

View full text Add to dashboard Cite

We consider a lattice gas in spaces of dimensionality D=1,2,3. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in D=3, a logarithmic potential in D=2, and a distance-independent force in D=1. Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in D=1 and power-law decay in D=2 with temperature-dependent exponents in both cases. In D=2 the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in D=3 with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In D=3 a cluster of finite mass can be stabilized at T>0 via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profiles. For the free energy needed to identify the equilibrium state we introduce a construction of gravitational self-energy that works in all D for the lattice gas. The decay rate of the density profile of an open cluster is shown to transform via a stretched exponential for 1

show abstract

Statistically interacting vacancy particles

Cited by 15 publications

References 27 publications

Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles

Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles

Monodisperse hard rods in external potentials

Density profiles of a self-gravitating lattice gas in one, two, and three dimensions

Contact Info

Product

Resources

About