arXiv subjects

Mark A. Miller

Publications and source records attributed to Mark A. Miller.

32 records · Page 2Linked to original sources

arXiv2008

Structural trends in clusters of quadrupolar spheres

The influence of quadrupolar interactions on the structure of small clusters is investigated by adding a point quadrupole of variable strength to the Lennard-Jones potential. Competition arises between sheet-like arrangements of the particles, favoured by the quadrupoles, and compact structures, favoured by the isotropic Lennard-Jones attraction. Putative global potential energy minima are obtained for clusters of up to 25 particles using the basin-hopping algorithm. A number of structural motifs and growth sequences emerge, including star-like structures, tubes, shells and sheets. The results are discussed in the context of colloidal self-assembly.

cond-mat.soft↗

arXiv2007

Importance of Metastable States in the Free Energy Landscapes of Polypeptide Chains

We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding of a tube-like representation of a polypeptide chain gives rise to free energy landscapes that exhibit a small number of metastable minima corresponding to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the mid-point of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.

cond-mat.soft↗

arXiv2007

Patchy sticky hard spheres: analytical study and Monte Carlo simulations

We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a ``sticky'' Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a class of closures Cn hinging on a density expansion of the direct correlation function. We find that the locations of the two lines depend sensitively on both the total adhesive coverage and its distribution. The treatment is almost fully analytical within the chosen approximate theory. We test our findings by means of specialized Monte Carlo (MC) simulations and find the main qualitative features of the critical behaviour to be well captured in spite of the low density perturbative nature of the closure. The introduction of anisotropic attractions into a model suspension of spherical particles is a first step towards a more realistic description of globular proteins in solution.

cond-mat.stat-mech↗

arXiv2007

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold, and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.

cond-mat.soft↗

arXiv2007

Reversible gelation and dynamical arrest of dipolar colloids

We use molecular dynamics simulations of a simple model to show that dispersions of slightly elongated colloidal particles with long-range dipolar interactions, like ferrofluids, can form a physical (reversible) gel at low volume fractions. On cooling, the particles first self-assemble into a transient percolating network of cross-linked chains, which, at much lower temperatures, then undergoes a kinetic transition to a dynamically arrested state with broken ergodicity. This transition from a transient to a frozen gel is characterised by dynamical signatures reminiscent of jamming in much denser dispersions.

cond-mat.soft↗

arXiv2006

Depletion-induced percolation in networks of nanorods

Above a certain density threshold, suspensions of rod-like colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods.

cond-mat.soft↗

arXiv2005

Novel Structural Motifs in Clusters of Dipolar Spheres: Knots, Links and Coils

We present the structures of putative global potential energy minima for clusters bound by the Stockmayer (Lennard-Jones plus point dipole) potential. A rich variety of structures is revealed as the cluster size and dipole strength are varied. Most remarkable are groups of closed-loop structures with the topology of knots and links. Despite the large number of possibilities, energetically optimal structures exhibit only a few such topologies.

cond-mat.soft↗

arXiv2004

Modelling colloids with Baxter's adhesive hard sphere model

The structure of the Baxter adhesive hard sphere fluid is examined using computer simulation. The radial distribution function (which exhibits unusual discontinuities due to the particle adhesion) and static structure factor are calculated with high accuracy over a range of conditions and compared with the predictions of Percus--Yevick theory. We comment on rigidity in percolating clusters and discuss the role of the model in the context of experiments on colloidal systems with short-range attractive forces.

cond-mat.soft↗

arXiv2003

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid--vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are $τ_c=0.1133\pm0.0005$ and $ρ_c=0.508\pm0.01$. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class.

cond-mat.stat-mech↗

arXiv2002

3D Hydrodynamic Simulations of Relativistic Extragalactic Jets

We describe a new numerical 3D relativistic hydrodynamical code, the results of validation tests, and a comparison with earlier, 2D studies. The 3D code has been used to study the deflection and precession of relativistic flows. We find that even quite fast jets (gamma~10) can be significantly influenced by impinging on an oblique density gradient, exhibiting a rotation of the Mach disk in the jet's head. The flow is bent via a potentially strong, oblique internal shock that arises due to asymmetric perturbation of the flow by its cocoon. In extreme cases this cocoon can form a marginally relativistic flow orthogonal to the jet, leading to large scale dynamics quite unlike that normally associated with astrophysical jets. Exploration of a gamma=5 flow subject to a large amplitude precession (semi-angle 11.25dg) shows that it retains its integrity, with modest reduction in Lorentz factor and momentum flux, for almost 50 jet-radii, but thereafter, the collimated flow is disrupted. The flow is approximately ballistic, with velocity vectors not aligned with the local jet `wall'. We consider simple estimators of the flow emissivity in each case and conclude that a) while the oblique internal shocks which mediate a small change in the direction of the deflected flows have little impact on the global dynamics, significantly enhanced flow emission (by a factor of 2-3) may be associated with such regions; and b) the convolution of rest frame emissivity and Doppler boost in the case of the precessed jet invariably leads to a core-jet-like structure, but that intensity fluctuations in the jet cannot be uniquely associated with either change in internal conditions or Doppler boost alone, but in general are a combination of both factors.

astro-ph↗

arXiv1999

Structural relaxation in atomic clusters: Master equation dynamics

The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation towards the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analysed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.

cond-mat.stat-mech↗

arXiv1999

Energy Landscape of a Model Protein

The potential energy surface of an off-lattice model protein is characterized in detail by constructing a disconnectivity graph and by examining the organisation of pathways on the surface. The results clearly reveal the frustration exhibited by this system and explain why it does not fold efficiently to the global potential energy minimum. In contrast, when the frustration is removed by constructing a `Go-type' model, the resulting graph exhibits the characteristics expected for a folding funnel.

cond-mat↗

arXiv1998

Structural relaxation in Morse clusters: Energy landscapes

We perform a comprehensive survey of the potential energy landscapes of 13-atom Morse clusters, and describe how they can be characterized and visualized. Our aim is to detail how the global features of the funnel-like surface change with the range of the potential, and to relate these changes to the dynamics of structural relaxation. We find that the landscape becomes rougher and less steep as the range of the potential decreases, and that relaxation paths to the global minimum become more complicated.

cond-mat.stat-mech↗

arXiv1995

Regge Calculus as a Fourth Order Method in Numerical Relativity

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show that these averages actually converge to zero as the fourth power of the lattice spacing.

gr-qc↗