797 research outputs found
Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations
We study in detail the application of renormalisation theory to models of
cluster aggregation and fragmentation of relevance to nucleation and growth
processes. In particular, we investigate the Becker-Doring (BD) equations,
originally formulated to describe and analyse non-equilibrium phase
transitions, but more recently generalised to describe a wide range of
physicochemical problems. We consider here rate coefficients which depend on
the cluster size in a power-law fashion, but now perturbed by small amplitude
random noise. Power-law rate coefficients arise naturally in the theory of
surface-controlled nucleation and growth processes. The noisy perturbations on
these rates reflect the effect of microscopic variations in such mean-field
coefficients, thermal fluctuations and/or experimental uncertainties. In the
present paper we generalise our earlier work that identified the nine classes
into which all dynamical behaviour must fall by investigating how random
perturbations of the rate coefficients influence the steady-state and kinetic
behaviour of the coarse-grained, renormalised system. We are hence able to
confirm the existence of a set of up to nine universality classes for such BD
systems.Comment: 30 pages, to appear in J Phys A Math Ge
Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients
We study in detail the application of renormalisation theory to models of
cluster aggregation and fragmentation of relevance to nucleation and growth
processes. We investigate the Becker-Dorging equations, originally formulated
to describe and analyse non-equilibrium phase transitions, and more recently
generalised to describe a wide range of physicochemical problems. In the
present paper we analyse how the systematic coarse-graining renormalisation of
the \BD system of equations affects the aggregation and fragmentation rate
coefficients. We consider the case of power-law size-dependent cluster rate
coefficients which we show lead to only three classes of system that require
analysis: coagulation-dominated systems, fragmentation-dominated systems and
those where coagulation and fragmentation are exactly balanced. We analyse the
late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge
The influence of base pair tautomerism on single point mutations in aqueous DNA
The relationship between base pair hydrogen bond proton transfer and the rate of spontaneous single point mutations at ambient temperatures and pressures in aqueous DNA is investigated. By using an ensemble-based multiscale computational modelling method, statistically robust rates of proton transfer for the A:T and G:C base pairs within a solvated DNA dodecamer are calculated. Several different proton transfer pathways are observed within the same base pair. It is shown that, in G:C, the double proton transfer tautomer is preferred, while the single proton transfer process is favoured in A:T. The reported range of rate coefficients for double proton transfer is consistent with recent experimental data. Notwithstanding the approximately 1000 times more common presence of single proton transfer products from A:T, observationally there is bias towards G:C to A:T mutations in a wide range of living organisms. We infer that the double proton transfer reactions between G:C base pairs have a negligible contribution towards this bias for the following reasons: (i) the maximum half-life of the G*:C* tautomer is in the range of picoseconds, which is significantly smaller than the milliseconds it takes for DNA to unwind during replication, (ii) statistically, the majority of G*:C* tautomers revert back to their canonical forms through a barrierless process, and (iii) the thermodynamic instability of the tautomers with respect to the canonical base pairs. Through similar reasoning, we also deduce that proton transfer in the A:T base pair does not contribute to single point mutations in DNA
Multiscale modelling and simulation: a position paper
We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by ‘multiscale modelling’, formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines
Dissipative Particle Dynamics with energy conservation
Dissipative particle dynamics (DPD) does not conserve energy and this
precludes its use in the study of thermal processes in complex fluids. We
present here a generalization of DPD that incorporates an internal energy and a
temperature variable for each particle. The dissipation induced by the
dissipative forces between particles is invested in raising the internal energy
of the particles. Thermal conduction occurs by means of (inverse) temperature
differences. The model can be viewed as a simplified solver of the fluctuating
hydrodynamic equations and opens up the possibility of studying thermal
processes in complex fluids with a mesoscopic simulation technique.Comment: 5 page
Foundations of Dissipative Particle Dynamics
We derive a mesoscopic modeling and simulation technique that is very close
to the technique known as dissipative particle dynamics. The model is derived
from molecular dynamics by means of a systematic coarse-graining procedure.
Thus the rules governing our new form of dissipative particle dynamics reflect
the underlying molecular dynamics; in particular all the underlying
conservation laws carry over from the microscopic to the mesoscopic
descriptions. Whereas previously the dissipative particles were spheres of
fixed size and mass, now they are defined as cells on a Voronoi lattice with
variable masses and sizes. This Voronoi lattice arises naturally from the
coarse-graining procedure which may be applied iteratively and thus represents
a form of renormalisation-group mapping. It enables us to select any desired
local scale for the mesoscopic description of a given problem. Indeed, the
method may be used to deal with situations in which several different length
scales are simultaneously present. Simulations carried out with the present
scheme show good agreement with theoretical predictions for the equilibrium
behavior.Comment: 18 pages, 7 figure
The influence of external electric fields on proton transfer tautomerism in the guanine-cytosine base pair
The Watson-Crick base pair proton transfer tautomers would be widely considered as a source of spontaneous mutations in DNA replication if not for their short lifetimes and thermodynamic instability. This work investigates the effects external electric fields have on the stability of the guanine-cytosine proton transfer tautomers within a realistic strand of aqueous DNA using a combination of ensemble-based classical molecular dynamics (MD) coupled to quantum mechanics/molecular mechanics (QM/MM). Performing an ensemble of calculations accounts for the stochastic aspects of the simulations while allowing for easier identification of systematic errors. The methodology applied in this work has previously been shown to estimate base pair proton transfer rate coefficients that are in good agreement with recent experimental data. A range of electric fields in the order of 104 to 109 V m-1 is investigated based on their real-life medicinal applications which include gene therapy and cancer treatments. The MD trajectories confirm that electric fields up to 1.00 × 109 V m-1 have a negligible influence on the structure of the base pairs within DNA. The QM/MM results show that the application of large external electric fields (1.00 × 109 V m-1) parallel to the hydrogen bonds increases the thermodynamic population of the tautomers by up to one order of magnitude; moreover, the lifetimes of the tautomers remain insignificant when compared to the timescale of DNA replication
Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media
The behaviour of two dimensional binary and ternary amphiphilic fluids under
flow conditions is investigated using a hydrodynamic lattice gas model. After
the validation of the model in simple cases (Poiseuille flow, Darcy's law for
single component fluids), attention is focussed on the properties of binary
immiscible fluids in porous media. An extension of Darcy's law which explicitly
admits a viscous coupling between the fluids is verified, and evidence of
capillary effects are described. The influence of a third component, namely
surfactant, is studied in the same context. Invasion simulations have also been
performed. The effect of the applied force on the invasion process is reported.
As the forcing level increases, the invasion process becomes faster and the
residual oil saturation decreases. The introduction of surfactant in the
invading phase during imbibition produces new phenomena, including
emulsification and micellisation. At very low fluid forcing levels, this leads
to the production of a low-resistance gel, which then slows down the progress
of the invading fluid. At long times (beyond the water percolation threshold),
the concentration of remaining oil within the porous medium is lowered by the
action of surfactant, thus enhancing oil recovery. On the other hand, the
introduction of surfactant in the invading phase during drainage simulations
slows down the invasion process -- the invading fluid takes a more tortuous
path to invade the porous medium -- and reduces the oil recovery (the residual
oil saturation increases).Comment: 48 pages, 26 figures. Phys. Rev. E (in press
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