81 research outputs found
Fluctuation-dissipation relation and stationary distribution for an exactly solvable many-particle model far from equilibrium
An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution as well as the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution, which is possible because the model derives from a particle Hamiltonian. The difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e. deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation
theorem, can be expressed in terms of a single non-equilibrium parameter \alpha that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates, the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energyconsuming protein motors. The comparison is excellent and allows to extract the non-equilibrium parameter \alpha from experimental spectral response and fluctuation data
Polyelectrolytes Adsorption: Chemical and Electrostatic Interactions
Mean-field theory is used to model polyelectrolyte adsorption and the
possibility of overcompensation of charged surfaces. For charged surfaces that
are also chemically attractive, the overcharging is large in high salt
conditions, amounting to 20-40% of the bare surface charge. However, full
charge inversion is not obtained in thermodynamical equilibrium for physical
values of the parameters. The overcharging increases with addition of salt, but
does not have a simple scaling form with the bare surface charge. Our results
indicate that more evolved explanation is needed in order to understand
polyelectrolyte multilayer built-up. For strong polymer-repulsive surfaces, we
derive simple scaling laws for the polyelectrolyte adsorption and overcharging.
We show that the overcharging scales linearly with the bare surface charge, but
its magnitude is very small in comparison to the surface charge. In contrast
with the attractive surface, here the overcharging is found to decrease
substantially with addition of salt. In the intermediate range of weak
repulsive surfaces, the behavior with addition of salt crosses over from
increasing overcharging (at low ionic strength) to decreasing one (at high
ionic strength). Our results for all types of surfaces are supported by full
numerical solutions of the mean-field equations.Comment: 17 pages, 7 figures, final version. to be published in PR
Multiple surface wave solutions on linear viscoelastic media
We study the generic dispersion relation of surface waves on a semi-infinite viscoelastic medium bounded by a 2D viscoelastic interface, including the effects of gravitation, surface tension and bending rigidity. The classical Rayleigh, capillary-gravity and Lucassen wave solutions result as limiting cases. We identify an additional solution that differs from all previously described waves in that gravitation, surface tension and bulk shear viscosity must simultaneously be nonzero, and which exists on a pure air-water interface. For a surfactant monolayer on water, the number of coexisting wave solutions switches between one and three, depending on interfacial compressibility and frequency
Unfolding and Folding Internal Friction of β‑Hairpins Is Smaller than That of α‑Helices
By the forced unfolding of polyglutamine and polyalanine
homopeptides in competing α-helix and β-hairpin secondary structures, we disentangle equilibrium free energetics from nonequilibrium dissipative effects. We find that α-helices are characterized by larger friction or dissipation upon
unfolding, regardless of whether they are free energetically preferred over β-hairpins or not. Our analysis, based on MD simulations for atomistic peptide
models with explicit water, suggests that this difference is related to the internal friction and mostly caused by the different number of intrapeptide hydrogen bonds in the α-helix and β-hairpin states
Cyclization dynamics of finite-length collapsed self-avoiding polymers
We study the end-point cyclization of ideal and interacting polymers as a function of chain length N. For the cyclization time �cyc of ideal chains we recover the known scaling �cyc � N2 for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling �cyc � N5=3. By extracting the memory kernel
that governs the non-Markovian end-point kinetics, we demonstrate that the dynamics of a finite-length collapsed chain is dominated by the crossover between swollen and collapsed behavior
Nonlinear fractional waves at elastic interfaces
We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface
Butane dihedral angle dynamics in water is dominated by internal friction
The dihedral dynamics of butane in water is known to be rather insensitive
to the water viscosity, possible explanations for this involve
inertial effects or Kramers’ turnover, the finite memory time of friction,
and the presence of so-called internal friction. In order to disentangle
these factors, we introduce a method to directly extract the
friction memory function from simulations in the presence of an arbitrary
free-energy landscape. By analysis of the dihedral friction in butane
for varying water viscosity, we demonstrate the existence of an
internal friction contribution. At normal water viscosity the internal
friction turns out to be eight times larger than the solvent friction and
thus completely dominates the effective friction. By comparison with
simulations of a constrained butane molecule that has the dihedral
as the only degree of freedom, we show that internal friction comes
from the six additional degrees of freedom in unconstrained butane
that are orthogonal to the dihedral angle reaction coordinate. While
the insensitivity of butane’s dihedral dynamics to water viscosity is
solely due to the presence of internal friction, inertial effects nevertheless
crucially influence the resultant transition rates. In contrast,
non-Markovian effects due to the finite memory time are present but
do not significantly influence the dihedral barrier crossing rate of
butane. These results not only settle the character of dihedral dynamics
in small molecular systems such as butane, they also have
important implications for the folding of polymers and protein
Markov state modeling reveals competing collective hydrogen bond rearrangements in liquid water
We construct a Markov state model for the dynamic rearrangement of the local hydrogen bond network in liquid water. The model is based on trajectories from classical molecular dynamics simulations and accounts for the dynamics of relative angular and separation coordinates of water molecules. We analyze first the conformational subspace of three water molecules and find five well separated dynamic modes with reaction times in the 2 - 5 ps range, which correspond to different interchanges of hydrogen bond donor and acceptors, followed by an entire continuum spectrum of modes. We then analyze the switching of one hydrogen bond between two water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along different intermediate states that involve alternative hydrogen bonds or unbound states
Surface states in nearly modulated systems
A Landau model is used to study the phase behavior of the surface layer for
magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz
point marking the boundary between modulated and homogeneous bulk phases. The
model incorporates surface and bulk fields and includes a term in the free
energy proportional to the square of the second derivative of the order
parameter in addition to the usual term involving the square of the first
derivative. In the limit of vanishing bulk field, three distinct types of
surface ordering are possible: a wetting layer, a non-wet layer having a small
deviation from bulk order, and a different non-wet layer with a large deviation
from bulk order which decays non-monotonically as distance from the wall
increases. In particular the large deviation non-wet layer is a feature of
systems at the Lifshitz point and also those having only homogeneous bulk
phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.
- …