arXiv subjects

Daan Frenkel

Publications and source records attributed to Daan Frenkel.

At least 73 records · Page 4Linked to original sources

arXiv2014

Superposition Enhanced Nested Sampling

The theoretical analysis of many problems in physics, astronomy and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal with these classes of problems, but such simulations suffer from a ubiquitous sampling problem: the probability of sampling a particular state is proportional to its entropic weight. Devising an algorithm capable of sampling efficiently the full phase space is a long-standing problem. Here we report a new hybrid method for the exploration of multimodal parameter spaces exhibiting broken ergodicity. Superposition enhanced nested sampling (SENS) combines the strengths of global optimization with the unbiased/athermal sampling of nested sampling, greatly enhancing its efficiency with no additional parameters. We report extensive tests of this new approach for atomic clusters that are known to have energy landscapes for which conventional sampling schemes suffer from broken ergodicity. We also introduce a novel parallelization algorithm for nested sampling.

cond-mat.stat-mech↗

arXiv2014

Numerical evidence for nucleated self-assembly of DNA brick structures

The observation by Ke et al. [Science 338, 1177 (2012)] that large numbers of short, pre-designed DNA strands can assemble into three-dimensional target structures came as a great surprise, as no colloidal self-assembling system has ever achieved the same degree of complexity. That failure seemed easy to rationalise: the larger the number of distinct building blocks, the higher the expected error rate for self-assembly. The experiments of Ke et al. have disproved this argument. Here, we report Monte Carlo simulations of the self-assembly of a DNA brick cube, comprising approximately 1000 types of DNA strand, using a simple model. We model the DNA strands as lattice tetrahedra with attractive patches, the interaction strengths of which are computed using a standard thermodynamic model. We find that, within a narrow temperature window, the target structure assembles with high probability. Our simulations suggest that mis-assembly is disfavoured because of a slow nucleation step. As our model incorporates no aspect of DNA other than its binding properties, these simulations suggest that, with proper design of the building blocks, other systems, such as colloids, may also assemble into truly complex structures.

cond-mat.soft↗

arXiv2014

Numerical calculation of granular entropy

We present numerical simulations that allow us to compute the number of ways in which $N$ particles can pack into a given volume $V$. Our technique modifies the method of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 poly-disperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor $1/N!$ to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as $S=-\sum_i p_i\ln p_i -\ln N!$, where $p_i$ denotes the probability to generate the $i$-th packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, whilst distinct from the one proposed by Edwards assumed (J. Phys.: Condens.Matter 2, SA63(1990)), does have all the properties Edwards assumed.

cond-mat.soft↗

arXiv2014

Accounting for adsorption and desorption in lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. Associated to the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g. in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic, but also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a Lattice-Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account on the time-dependent diffusion coefficient in a more complex porous medium.

physics.flu-dyn↗

arXiv2014

Designing stimulus-sensitive colloidal walkers

Colloidal particles with DNA `legs' that can bind reversibly to receptors on a surface can be made to `walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how controllable parameters, e.g. coating density and binding strength, affect the dynamics of such colloids. We find that competition between thermodynamic and kinetic trends imply that there is an optimal value for both, the binding strength and the number of `legs' for which transport is fastest. Using available thermodynamic data on DNA binding, we indicate how directionally reversible, temperature-controlled transport of colloidal walkers can be achieved. In particular, the present results should make it possible to design a chromatographic technique that can be used to separate colloids with different DNA functionalization.

cond-mat.soft↗

arXiv2013

Why Colloidal Systems can be described by Statistical Mechanics: Some not very original comments on the Gibbs paradox

Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical Mechanics predicts such behaviour if one accepts that the configurational integral of a system of N colloids must be divided by N!. In many textbooks it is argued that the factor N! corrects for the fact that identical particles (in the quantum mechanical sense) are indistinguishable. Clearly, this argument does not apply to colloids. This articles explains why, nevertheless, all is well. The point has been made before, but has not yet sunk in. I also discuss the effect of polydispersity.

cond-mat.soft↗

arXiv2013

Visualizing Basins of Attraction for Different Minimization Algorithms

We report a study of the basins of attraction for potential energy minima defined by different minimisation algorithms for an atomic system. We find that whereas some minimisation algorithms produce compact basins, others produce basins with complex boundaries or basins consisting of disconnected parts. Such basins deviate from the "correct" basin of attraction defined by steepest-descent pathways, and the differences can be controlled to some extent by adjustment of the maximum step size. The choice of the most convenient minimisation algorithm depends on the problem in hand. We show that while L-BFGS is the fastest minimiser, the FIRE algorithm is also quite fast, and can lead to less fragmented basins of attraction.

physics.comp-ph↗

arXiv2013

Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental data

We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying single-stranded DNA strands of length comparable to the colloids' size. We show that in this regime, the common theoretical approach of assuming pairwise additivity of the colloidal pair interactions leads to quantitatively and sometimes even qualitatively wrong predictions of the phase behaviour of DNA-grafted colloids. Comparing to experimental data, we find that our coarse-grained model correctly predicts the equilibrium structure and melting temperature of the formed solids. Due to limited experimental information on the persistence length of single-stranded DNA, some quantitative discrepancies are found in the prediction of spatial quantities. With the availability of better experimental data, the present approach provides a path for the rational design of DNA-functionalised building blocks that can self-assemble in complex, three-dimensional structures.

cond-mat.soft↗

arXiv2013

A simple analytical formula for the free-energy of ligand-receptor mediated interactions

Recently \1, we presented a general theory for calculat- ing the strength and properties of colloidal interactions mediated by ligand-receptor bonds (such as those that bind DNA-coated colloids). In this communication, we derive a surprisingly simple analytical form for the inter- action free energy, which was previously obtainable only via a costly numerical thermodynamic integration. As a result, the computational effort to obtain potentials of in- teraction is significantly reduced. Moreover, we can gain insight from this analytic expression for the free energy in limiting cases. In particular, the connection of our general theory to other previous specialised approaches is now made transparent. This important simplification will significantly broaden the scope of our theory.

cond-mat.soft↗

arXiv2012

Layering, freezing and re-entrant melting of hard spheres in soft confinement

Confinement can have a dramatic effect on the behavior of all sorts of particulate systems and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. Whilst we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g. in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles.

cond-mat.soft↗

arXiv2012

Simulations: the dark side

This paper discusses the Monte Carlo and Molecular Dynamics methods. Both methods are, in principle, simple. However, simple does not mean risk-free. In the literature, many of the pitfalls in the field are mentioned, but usually as a footnote - and these footnotes are scattered over many papers. The present paper focuses on the `dark side' of simulation: it is one big footnote. I should stress that `dark', in this context, has no negative moral implication. It just means: under-exposed.

cond-mat.stat-mech↗

arXiv2012

Probing ergodicity in granular matter

When a granular system is tapped, its volume changes. Here, using a well-defined macroscopic protocol, we prepare an ensemble of granular systems and track the statistics of volume changes as a function of the number of taps. This is in contrast to previous studies, which have focused on single trajectories and assumed ergodicity. We devise a new method to assess the convergence properties of a sequence of ensemble volume histograms and introduce a reasonable approximate version of an invariant histogram. We then compare these invariant histograms with histograms generated by sampling a long trajectory for one system and observe nonergodicity, which we quantify. Finally, we use the overlapping histogram method to assess potential compatibility with Edwards' canonical assumption. Our histograms are incompatible with this assumption.

cond-mat.stat-mech↗

arXiv2012

Collective sedimentation of colloids in grafted polymer layers

We present Monte Carlo simulations of colloidal particles pulled into grafted polymer layers by external fields. The insertion free energy of a single colloid into the polymer layer is qualitatively different for surfaces with an ordered and a disordered distribution of grafting points. Moreover, the tendency of colloidal particles to traverse the grafting layer is strongly size dependent. In dense colloidal suspensions, under the influence of sufficiently strong external force, a collective instability allows the colloids to penetrate and form internally ordered, columnar structures spanning the polymer layer. Depending on the conditions, these colloidal clusters may be isolated or laterally percolating. The morphology of the observed patterns can be controlled by the external fields, which opens up new routes for the design of thin structured films.

cond-mat.soft↗

arXiv2012

Running faster together: huge speed up of thermal ratchets due to hydrodynamic coupling

We present simulations that reveal a surprisingly large effect of hydrodynamic coupling on the speed of thermal ratchet motors. The model that we use considers particles performing thermal ratchet motion in a hydrodynamic solvent. Using particle-based, mesoscopic simulations that maintain local momentum conservation, we analyze quantitatively how the coupling to the surrounding fluid affects ratchet motion. We find that coupling can increase the mean velocity of the moving particles by almost two orders of magnitude, precisely because ratchet motion has both a diffusive and a deterministic component. The resulting coupling also leads to the formation of aggregates at longer times. The correlated motion that we describe increases the efficiency of motor-delivered cargo transport and we speculate that the mechanism that we have uncovered may play a key role in speeding up molecular motor-driven intracellular transport.

cond-mat.soft↗

arXiv2012

Emergence of Critical Phenomena in Full Configuration Interaction Quantum Monte Carlo

There has been recent literature discussion on the origin and severity of the `sign problem' in full configuration interaction quantum Monte Carlo (FCIQMC) and its `initiator' adaptation (i-FCIQMC), methods of interest and potential because they allow for exact (FCI) ground-state solutions to be obtained often at a much reduced computational cost. In this study we aim to use a simple order parameter, describing the `sign structure' of the stochastic wavefunction representation, to empirically characterise the fundamentally different collective behaviour of the walker population in both methods.

physics.chem-ph↗

arXiv2012

A general theory of DNA-mediated and other valence-limited interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC .

cond-mat.soft↗

arXiv2012

A parameter-free, solid-angle based, nearest-neighbor algorithm

We propose a parameter-free algorithm for the identification of nearest neighbors. The algorithm is very easy to use and has a number of advantages over existing algorithms to identify nearest- neighbors. This solid-angle based nearest-neighbor algorithm (SANN) attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4π. The algorithm can be used to analyze 3D images, both from experiments as well as theory, and as the algorithm has a low computational cost, it can also be used "on the fly" in simulations. In this paper, we describe the SANN algorithm, discuss its properties, and compare it to both a fixed-distance cutoff algorithm and to a Voronoi construction by analyzing its behavior in bulk phases of systems of carbon atoms, Lennard-Jones particles and hard spheres as well as in Lennard-Jones systems with liquid-crystal and liquid-vapor interfaces.

cond-mat.soft↗

arXiv2012

Quantitative prediction of the phase diagram of DNA-functionalized nano-colloids

We present a coarse-grained model of DNA-functionalized colloids that is computationally tractable. Importantly, the model parameters are solely based on experimental data. Using this highly simplified model, we can predict the phase behavior of DNA-functionalized nano-colloids without assuming pairwise additivity of the inter-colloidal interactions. Our simulations show that for nano-colloids, the assumption of pairwise additivity leads to substantial errors in the estimate of the free energy of the crystal phase. We compare our results with available experimental data and find that the simulations predict the correct structure of the solid phase and yield a very good estimate of the melting temperature. Current experimental estimates for the contour length and persistence length of single-stranded DNA sequences are subject to relatively large uncertainties. Using the best available estimates, we obtain predictions for the crystal lattice constants that are off by a few percent: this indicates that more accurate experimental data on ssDNA are needed to exploit the full power of our coarse-grained approach.

cond-mat.soft↗