# Free energy of singular sticky-sphere clusters.

@article{Kallus2016FreeEO, title={Free energy of singular sticky-sphere clusters.}, author={Yoav Kallus and Miranda C. Holmes-Cerfon}, journal={Physical review. E}, year={2016}, volume={95 2-1}, pages={ 022130 } }

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a…

## 18 Citations

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This work uses numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials to compare clusters obtained by continuation with different potentials.

### Simulating sticky particles: A Monte Carlo method to sample a Stratification

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This work introduces a Monte Carlo method to handle the case when constraints can break and form, and samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher- dimensional manifolds.

### Gregory-Newton problem for kissing sticky spheres

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All possible non-isomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model, and subsequently projected by…

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In this work, we analyzed an isotropic colloidal model incorporating both shortrange sticky attractions and long-range electrostatic repulsions. We computed the zero-shear viscosity and second virial…

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The application of a hard-sphere colloidal model with SALR interactions toward predicting the viscosity of dilute to semi-dilute protein solutions is shown and it is shown that it is the coupling between attractions and repulsions that gives rise to the observed experimental trends in solution viscosities as a function of pH, concentration, and ionic strength.

### Calculating the Symmetry Number of Flexible Sphere Clusters

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A numerical algorithm is introduced to compute the sticky symmetry group and symmetry number of a flexible sphere cluster using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit.

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A genetic algorithm is developed to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies.

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### From sticky-hard-sphere to Lennard-Jones-type clusters.

- PhysicsPhysical review. E
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A more realistic extended Lennard- Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.

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