431 research outputs found

### Mesoscopic Model for Diffusion-Influenced Reaction Dynamics

A hybrid mesoscopic multi-particle collision model is used to study
diffusion-influenced reaction kinetics. The mesoscopic particle dynamics
conserves mass, momentum and energy so that hydrodynamic effects are fully
taken into account. Reactive and non-reactive interactions with catalytic
solute particles are described by full molecular dynamics. Results are
presented for large-scale, three-dimensional simulations to study the influence
of diffusion on the rate constants of the A+CB+C reaction. In the limit of
a dilute solution of catalytic C particles, the simulation results are compared
with diffusion equation approaches for both the irreversible and reversible
reaction cases. Simulation results for systems where the volume fraction of
catalytic spheres is high are also presented, and collective interactions among
reactions on catalytic spheres that introduce volume fraction dependence in the
rate constants are studied.Comment: 9 pages, 5 figure

### Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

The effects of cluster diffusion on the submonolayer island density and
island-size distribution are studied for the case of irreversible growth of
compact islands on a 2D substrate. In our model, we assume instantaneous
coalescence of circular islands, while the cluster mobility is assumed to
exhibit power-law decay as a function of island-size with exponent mu. Results
are presented for mu = 1/2, 1, and 3/2 corresponding to cluster diffusion via
Brownian motion, correlated evaporation-condensation, and edge-diffusion
respectively, as well as for higher values including mu = 2,3, and 6. We also
compare our results with those obtained in the limit of no cluster mobility
corresponding to mu = infinity. In agreement with theoretical predictions of
power-law behavior of the island-size distribution (ISD) for mu < 1, for mu =
1/2 we find Ns({\theta}) ~ s^{-\tau} (where Ns({\theta}) is the number of
islands of size s at coverage {\theta}) up to a cross-over island-size S_c.
However, the value of {\tau} obtained in our simulations is higher than the
mean-field (MF) prediction {\tau} = (3 - mu)/2. Similarly, the value of the
exponent {\zeta} corresponding to the dependence of S_c on the average
island-size S (e.g. S_c ~ S^{\zeta}) is also significantly higher than the MF
prediction {\zeta} = 2/(mu+1). A generalized scaling form for the ISD is also
proposed for mu < 1, and using this form excellent scaling is found for mu =
1/2. However, for finite mu >= 1 neither the generalized scaling form nor the
standard scaling form Ns({\theta}) = {\theta} /S^2 f(s/S) lead to scaling of
the entire ISD for finite values of the ratio R of the monomer diffusion rate
to deposition flux. Instead, the scaled ISD becomes more sharply peaked with
increasing R and coverage. This is in contrast to models of epitaxial growth
with limited cluster mobility for which good scaling occurs over a wide range
of coverages.Comment: 12 pages, submitted to Physical Review

### Quantum Collapse and the Second Law of Thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net
result of conversion of heat into work. Quantum effects such as superposition
of states can improve an engine's efficiency by breaking detailed balance, but
this improvement comes at a cost due to excess entropy generated from collapse
of superpositions on measurement. We quantify these competing facets for a
quantum ratchet comprised of an ensemble of pairs of interacting two-level
atoms. We suggest that the measurement postulate of quantum mechanics is
intricately connected to the second law of thermodynamics. More precisely, if
quantum collapse is not inherently random, then the second law of
thermodynamics can be violated. Our results challenge the conventional approach
of simply quantifying quantum correlations as a thermodynamic work deficit.Comment: 11 pages, 2 figure

### Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation,
fluctuations are of the order of average values. In systems in thermodynamical
equilibrium, the variance of these fluctuations can be related to the
dissipation constant in the system, exploiting the Fluctuation-Dissipation
Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT)
additionally describe symmetry properties of the probability density functions
(PDFs) of the fluctuations of injected and dissipated energies. We
experimentally probe a model system: an electrical dipole driven out of
equilibrium by a small constant current $I$, and show that FT are
experimentally accessible and valid. Furthermore, we stress that FT can be used
to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just
studying the PDFs symmetries.Comment: Juillet 200

### Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a
combination of diffusive growth, size fragmentation and fragment coagulation.
Initially, we consider processes where coagulation is absent. In this case we
solve the rate equation exactly leading to size distributions of Bessel type
which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide
explicit formulas for the expansion coefficients in terms of Airy functions.
Introducing the coagulation term, the full non-linear model is mapped exactly
onto a Riccati equation that enables us to derive various asymptotic solutions
for the distribution function. In particular, we find a standard exponential
decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel
function for intermediate values of $x$. These findings are checked by
numerical simulations and we find perfect agreement between the theoretical
predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

### Reaction Pathways Based on the Gradient of the Mean First-Passage Time

Finding representative reaction pathways is necessary for understanding
mechanisms of molecular processes, but is considered to be extremely
challenging. We propose a new method to construct reaction paths based on mean
first-passage times. This approach incorporates information of all possible
reaction events as well as the effect of temperature. The method is applied to
exemplary reactions in a continuous and in a discrete setting. The suggested
approach holds great promise for large reaction networks that are completely
characterized by the method through a pathway graph.Comment: v2; 4 pages including 5 figure

### DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects

We investigate diffusion-limited reactions between a diffusing particle and a
target site on a semiflexible polymer, a key factor determining the kinetics of
DNA-protein binding and polymerization of cytoskeletal filaments. Our theory
focuses on two competing effects: polymer shape fluctuations, which speed up
association, and the hydrodynamic coupling between the diffusing particle and
the chain, which slows down association. Polymer bending fluctuations are
described using a mean field dynamical theory, while the hydrodynamic coupling
between polymer and particle is incorporated through a simple heuristic
approximation. Both of these we validate through comparison with Brownian
dynamics simulations. Neither of the effects has been fully considered before
in the biophysical context, and we show they are necessary to form accurate
estimates of reaction processes. The association rate depends on the stiffness
of the polymer and the particle size, exhibiting a maximum for intermediate
persistence length and a minimum for intermediate particle radius. In the
parameter range relevant to DNA-protein binding, the rate increase is up to
100% compared to the Smoluchowski result for simple center-of-mass motion. The
quantitative predictions made by the theory can be tested experimentally.Comment: 21 pages, 11 figures, 1 tabl

### Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and
merging as a model system for cluster dynamics in nature and society displaying
scale invariant properties. The clusters merge and fragment with rates
proportional to their sizes, conserving the total mass. The total number of
clusters grows continuously but the full time-dependent distribution can be
rescaled over at least 15 decades onto a universal curve which we derive
analytically. This curve includes a scale free solution with a scaling exponent
of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

### Smoluchowski's equation for cluster exogenous growth

We introduce an extended Smoluchowski equation describing coagulation
processes for which clusters of mass s grow between collisions with
$ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and
its collision kernel K is derived. In the general case, the gelation criterion
is determined. Exact solutions are found and scaling solutions are
investigated. Finally we show how these results apply to nucleation of discs on
a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig

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