arXiv subjects

Patrick B. Warren

Publications and source records attributed to Patrick B. Warren.

At least 37 records · Page 2Linked to original sources

arXiv2018

Why clothes don't fall apart: tension transmission in staple yarns

The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons-Coulomb friction laws yield a linear programming (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded, We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state. We argue the mechanism is generic, and in practical terms corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.

cond-mat.soft↗

arXiv2017

Diffusiophoresis in non-adsorbing polymer solutions: the Asakura-Oosawa model and stratification in drying films

A colloidal particle placed in an inhomogeneous solution of smaller non-adsorbing polymers will move towards regions of lower polymer concentration, in order to reduce the free energy of the interface between the surface of the particle and the solution. This phenomenon is known as diffusiophoresis. Treating the polymer as penetrable hard spheres, as in the Asakura-Oosawa model, a simple analytic expression for the diffusiophoretic drift velocity can be obtained. In the context of drying films we show that diffusiophoresis by this mechanism can lead to stratification under easily accessible experimental conditions. By stratification we mean spontaneous formation of a layer of polymer on top of a layer of the colloid. Transposed to the case of binary colloidal mixtures, this offers an explanation for the stratification observed recently in these systems [A. Fortini et al, Phys. Rev. Lett. 116, 118301 (2016)]. Our results emphasise the importance of treating solvent dynamics explicitly in these problems, and caution against the neglect of hydrodynamic interactions or the use of implicit solvent models in which the absence of solvent backflow results in an unbalanced osmotic force which gives rise to large but unphysical effects.

cond-mat.soft↗

arXiv2017

Dissipative particle dynamics: systematic parametrization using water-octanol partition coefficients

We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e. hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values.

cond-mat.soft↗

arXiv2014

Screening properties of four mesoscale smoothed charge models, with application to dissipative particle dynamics

We extend our previous study [J. Chem. Phys. 138, 204907 (2013)] to quantify the screening properties of four mesoscale smoothed charge models used in dissipative particle dynamics. Using a combination of the hypernetted chain integral equation closure and the random phase approximation, we identify regions where the models exhibit a real-valued screening length, and the extent to which this agrees with the Debye length in the physical system. We find that the second moment of the smoothed charge distribution is a good predictor of this behaviour. We are thus able to recommend a consistent set of parameters for the models.

cond-mat.soft↗

arXiv2013

Malliavin weight sampling: a practical guide

Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system's dynamics. It applies to systems in or out of equilibrium, in steady state or time-dependent situations, and has applications in the calculation of response coefficients, parameter sensitivities and Jacobian matrices for gradient-based parameter optimisation algorithms. The implementation of MWS has been described in the specific contexts of kinetic Monte Carlo and Brownian dynamics simulation algorithms. Here, we present a general theoretical framework for deriving the appropriate MWS update rule for any stochastic simulation algorithm. We also provide pedagogical information on its practical implementation.

cond-mat.stat-mech↗

arXiv2013

No-go theorem in many body dissipative particle dynamics

Many body dissipative particle dynamics (MDPD) is a particle-based simulation method in which the interaction potential is a sum of self energies depending on locally-sampled density variables. This functional form gives rise to density-dependent pairwise forces, however not all such force laws are derivable from a potential and the integrability condition for this to be the case provides a strong constraint. A strategy to assess the implications of this constraint is illustrated here by the derivation of a useful no-go theorem for multicomponent MDPD.

cond-mat.stat-mech↗

arXiv2013

Revisiting Riccioli's free fall calculations

In 1651 Giovanni Riccioli reported the earliest accurate measurements the acceleration due to gravity, g, from pendulum-timed free fall experiments. The use of Huygens' pendulum formula (published 1673) allows one to deduce the pendulum length from this data, free from assumptions about the conversion to modern units, and independent of the actual value of g. When this length is compared to the reported pendulum length, a 15% systematic error is revealed. This could perhaps be attributed to the difficulty Riccioli faced in subdividing the contemporary unit of length (the Roman foot) to the requisite millimeter accuracy.

physics.hist-ph↗

arXiv2013

Screening properties of Gaussian electrolyte models, with application to dissipative particle dynamics

We investigate the screening properties of Gaussian charge models of electrolyte solutions by analysing the asymptotic behaviour of the pair distribution functions. We use a combination of Monte-Carlo simulations with the hyper-netted chain integral equation closure, and the random phase approximation, to establish the conditions under which a screening length is well defined and the extent to which it matches the expected Debye length. For practical applications, for example in dissipative particle dynamics, we are able to summarise our results in succinct rules-of-thumb which can be used for mesoscale modeling of electrolyte solutions. We thereby establish a solid foundation for future work, such as the systematic incorporation of specific ion effects.

cond-mat.soft↗

arXiv2013

Phase behaviour and the random phase approximation for ultrasoft restricted primitive models

Phase separation of the ultrasoft restricted primitive model (URPM) with Gaussian charges is re-investigated in the random phase approximation (RPA)---the 'Level A' approximation discussed by Nikoubashman, Hansen and Kahl [J. Chem. Phys. 137, 094905 (2012)]. We find that the RPA predicts a region of low temperature vapour-liquid coexistence, with a critical density much lower than that observed in either simulations or more refined approximations (we also remark that the RPA critical point for a related model with Bessel charges can be solved analytically). This observation suggests that the hierarchy of approximations introduced by Nikoubashman et al. should be analogous to those introduced by Fisher and Levin for the restricted primitive model [Phys. Rev. Lett. 71, 3826 (1993)], which makes the inability of these approximations to capture the observed URPM phase behaviour even more worthy of investigation.

cond-mat.stat-mech↗

arXiv2012

Self-consistent field theory for the interactions between keratin intermediate filaments

We have developed a model for the interactions between keratin intermediate filaments based on self-consistent field theory. The intermediate filaments are represented by charged surfaces, and the disordered terminal domains of the keratins are represented by charged heteropolymers grafted to these surfaces. We estimate the system is close to a charge compensation point where the heteropolymer grafting density is matched to the surface charge density. Using a protein model with amino acid resolution for the terminal domains, we find that the terminal chains can mediate a weak attraction between the keratin surfaces. The origin of the attraction is a combination of bridging and electrostatics. The attraction disappears when the system moves away from the charge compensation point, or when excess small ions and/or NMF-representing free amino acids are added. These results are in concordance with experimental observations, and support the idea that the interaction between keratin filaments, and ultimately in part the elastic properties of the keratin-containing tissue, is controlled by a combination of the physico-chemical properties of the disordered terminal domains and the composition of the medium in the inter-filament region.

cond-mat.soft↗

arXiv2012

Computing sensitivity coefficients in Brownian dynamics simulations by Malliavin weight sampling

We present a method for computing parameter sensitivities and response coefficients in Brownian dynamics simulations. The method involves tracking auxiliary variables (Malliavin weights) in addition to the usual particle positions, in an unperturbed simulation. The Malliavin weights sample the derivatives of the probability density with respect to the parameters of interest and are also interesting dynamical objects in themselves. Malliavin weight sampling is simple to implement, applies to equilibrium or nonequilibrium, steady state or time-dependent systems, and scales more efficiently than standard finite difference methods

cond-mat.stat-mech↗

arXiv2012

The shape of a ponytail and the statistical physics of hair fiber bundles

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an 'equation of state'. From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

cond-mat.stat-mech↗

arXiv2012

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting

Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for perturbed values of the parameters. Here, we use trajectory reweighting to derive a method for computing sensitivity coefficients in stochastic simulations without explicitly perturbing the parameter values, avoiding the need for repeated simulations. The method allows the simultaneous computation of multiple sensitivity coefficients. Our approach recovers results originally obtained by application of the Girsanov measure transform in the general theory of stochastic processes [A. Plyasunov and A. P. Arkin, J. Comp. Phys. 221, 724 (2007)]. We build on these results to show how the method can be used to compute steady-state sensitivity coefficients from a single simulation run, and we present various efficiency improvements. For models of biochemical signaling networks the method has a particularly simple implementation. We demonstrate its application to a signaling network showing stochastic focussing and to a bistable genetic switch, and present exact results for models with linear propensity functions.

physics.comp-ph↗

arXiv2009

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.

q-bio.MN↗

arXiv2009

Cells, cancer, and rare events: homeostatic metastability in stochastic non-linear dynamics models of skin cell proliferation

A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a paradigm for the onset of cancer. A novel way in which this can arise is if the homeostatic fixed point becomes metastable, so that the cell populations can escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multi-stage model of carcinogenesis. This offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.

q-bio.CB↗

arXiv2008

Scaling theory for diffusion limited cluster aggregation in a porous medium

A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are predicted, connected by smooth crossovers. The first regime is at low primary particle concentrations where the primary particles stick individually to the walls. The second regime is at intermediate concentrations where clusters grow to a certain size, smaller than the pore size, then stick individually to the walls. The third regime is at high concentrations where the final state is a pore-space-filling network.

cond-mat.soft↗

arXiv2007

The wall shear rate distribution for flow in random sphere packings

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As phi --> 0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.

cond-mat.soft↗

arXiv2007

Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimise free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional non-equilibrium thermodynamics, although it does satisfy a minimum entropy production principle. It can be used to motivate extensions of constraint-based modelling, for example to microbial ecosystems.

q-bio.SC↗