Exact density functionals in one dimension

Buschle, Joachim; Maass, Philipp; Dieterich, W.

doi:10.1088/0305-4470/33/4/101

Cited by 25 publications

(43 citation statements)

References 22 publications

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“…It is interesting to note that equating the expressions for the local pressure in Eqs. (14) and (23) [or Eq. (24)] yields an integral equation connecting the pair distribution with the density.…”

Section: Eos Methods and Sivp Approachmentioning

confidence: 99%

“…The analysis carried out in [21] is based on former work [12,14,[18][19][20] and expresses the grand potential as a density functional, i.e. a functional of the mean occupation numbers of rodsñ i .…”

Section: B Exact Density Functionalsmentioning

confidence: 99%

“…To tackle this question analytically, exact results for inhomogeneous systems are required. For hard rods with first-neighbor interactions in one dimension, exact treatments are possible via recursion relations for partition functions [9,12] or density functional theory (DFT) [13][14][15]. These methods allow for the exact derivation of density profiles as well as many-body distribution functions.…”

Section: Introductionmentioning

confidence: 99%

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Monodisperse hard rods in external potentials

et al. 2015

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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.

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Section: Eos Methods and Sivp Approachmentioning

confidence: 99%

Section: B Exact Density Functionalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monodisperse hard rods in external potentials

et al. 2015

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“…Finally we can use J N = α (1 − τ 1 N ) to write the above formula in a more compact notation, as We compute here an estimate of the density of isolated particles of size in the bulk ( τ i , 1 i N − l). To do so, we use an approximation from Lakatos and Chou [2], assuming that the number of states of n particles of length l, confined to a length of N ≥ n lattice sites, is given by the partition function [61] Z(n, N ) = N − ( − 1)n n .…”

Section: J Application To Ribosome Profiling Data and Comparison Witmentioning

confidence: 99%

Theoretical analysis of the distribution of isolated particles in the TASEP: Application to mRNA translation rate estimation

Duc

Saleem

Song

2017

Preprint

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The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the mRNA during translation. Applying this model to quantify translation dynamics from ribosome profiling data is not straightforward, however, and it requires characterizing the extent of interference, since the experimental protocol may be biased against nearby ribosomes. To evaluate and correct for this potential bias, we provide here a theoretical analysis of the distribution of isolated particles in the TASEP. In the classical form of the model in which each particle occupies only a single site, we obtain exact analytic solutions using the Matrix Ansatz. We then employ a refined mean field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from S. cerevisiae suggests a potential bias against the detection of nearby ribosomes with gap distance less than ∼ 3 codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate can be robustly estimated, and show that approximately 1% of the translating ribosomes get obstructed. Lastly, we find that, on average, the termination rate is near optimal in that it is close to the minimum value needed to not limit the ribosome flux.

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“…This can be achieved by using exact free energy functionals, which are available for certain onedimensional systems [18,19,20].…”

Section: One Dimension: Exact Functionalsmentioning

confidence: 99%

Kinetics in one-dimensional lattice gas and Ising models from time-dependent density-functional theory

Kessler

Dieterich

et al. 2002

Phys. Rev. E

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Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of non-equilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is useful also for treating more complex problems.

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Exact density functionals in one dimension

Cited by 25 publications

References 22 publications

Monodisperse hard rods in external potentials

Monodisperse hard rods in external potentials

Theoretical analysis of the distribution of isolated particles in the TASEP: Application to mRNA translation rate estimation

Kinetics in one-dimensional lattice gas and Ising models from time-dependent density-functional theory

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