572 research outputs found
A Finite-Size Scaling Study of a Model of Globular Proteins
Grand canonical Monte Carlo simulations are used to explore the metastable
fluid-fluid coexistence curve of the modified Lennard-Jones model of globular
proteins of ten Wolde and Frenkel (Science, v277, 1975 (1997)). Using both
mixed-field finite-size scaling and histogram reweighting methods, the joint
distribution of density and energy fluctuations is analyzed at coexistence to
accurately determine the critical-point parameters. The subcritical coexistence
region is explored using the recently developed hyper-parallel tempering Monte
Carlo simulation method along with histogram reweighting to obtain the density
distributions. The phase diagram for the metastable fluid-fluid coexistence
curve is calculated in close proximity to the critical point, a region
previously unattained by simulation.Comment: 17 pages, 10 figures, 2 Table
Anharmonic quantum contribution to vibrational dephasing
Based on a quantum Langevin equation and its corresponding Hamiltonian within
a c-number formalism we calculate the vibrational dephasing rate of a cubic
oscillator. It is shown that leading order quantum correction due to
anharmonicity of the potential makes a significant contribution to the rate and
the frequency shift. We compare our theoretical estimates with those obtained
from experiments for small diatomics , and .Comment: 21 pages, 1 figure and 1 tabl
Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins
Without invoking the Markov approximation, we derive formulas for vibrational
energy relaxation (VER) and dephasing for an anharmonic system oscillator using
a time-dependent perturbation theory. The system-bath Hamiltonian contains more
than the third order coupling terms since we take a normal mode picture as a
zeroth order approximation. When we invoke the Markov approximation, our theory
reduces to the Maradudin-Fein formula which is used to describe VER properties
of glass and proteins. When the system anharmonicity and the renormalization
effect due to the environment vanishes, our formulas reduce to those derived by
Mikami and Okazaki invoking the path-integral influence functional method [J.
Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode
of a small amino-acide like molecule, N-methylacetamide, in heavy water.Comment: 16 pages, 5 figures, 5 tables, submitted to J. Chem. Phy
Minimum free-energy path of homogenous nucleation from the phase-field equation
The minimum free-energy path (MFEP) is the most probable route of the
nucleation process on the multidimensional free-energy surface. In this study,
the phase-field equation is used as a mathematical tool to deduce the minimum
free-energy path (MFEP) of homogeneous nucleation. We use a simple
square-gradient free-energy functional with a quartic local free-energy
function as an example and study the time evolution of a single nucleus placed
within a metastable environment. The time integration of the phase-field
equation is performed using the numerically efficient cell-dynamics method. By
monitoring the evolution of the size of the nucleus and the free energy of the
system simultaneously, we can easily deduce the free-energy barrier as a
function of the size of the sub- and the super-critical nucleus along the MFEP.Comment: 8 pages, 5 figures, Journal of Chemical Physics accepted for
publicatio
Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy
The square-gradient density-functional model with triple-parabolic free
energy is used to study homogeneous bubble nucleation in a stretched liquid to
check the scaling rule for the work of formation of the critical bubble as a
function of scaled undersaturation , the
difference in chemical potential between the bulk undersaturated
and saturated liquid divided by between the liquid
spinodal and saturated liquid. In contrast to our study, a similar
density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J.
Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation
but other various quantities related to the critical bubble show the scaling
rule, however, we found virtually no scaling relationships in our model near
the coexistence. Although some quantities show almost perfect scaling relations
near the spinodal, the work of formation divided by the value deduced from the
classical nucleation theory shows no scaling in this model even though it
correctly vanishes at the spinodal. Furthermore, the critical bubble does not
show any anomaly near the spinodal as predicted many years ago. In particular,
our model does not show diverging interfacial width at the spinodal, which is
due to the fact that compressibility remains finite until the spinodal is
reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for
publicatio
Simulation and theory of vibrational phase relaxation in the critical and supercritical nitrogen: Origin of observed anomalies
We present results of extensive computer simulations and theoretical analysis
of vibrational phase relaxation of a nitrogen molecule along the critical
isochore and also along the gas-liquid coexistence. The simulation includes all
the different contributions [atom-atom (AA), vibration-rotation (VR) and
resonant transfer] and their cross-correlations. Following Everitt and Skinner,
we have included the vibrational coordinate () dependence of the interatomic
potential. It is found that the latter makes an important contribution. The
principal important results are: (a) a crossover from a Lorentzian-type to a
Gaussian line shape is observed as the critical point is approached along the
isochore (from above), (b) the root mean square frequency fluctuation shows
nonmonotonic dependence on the temperature along critical isochore, (c) along
the coexistence line and the critical isochore the temperature dependent
linewidth shows a divergence-like -shape behavior, and (d) the value
of the critical exponents along the coexistence and along the isochore are
obtained by fitting. The origin of the anomalous temperature dependence of
linewidth can be traced to simultaneous occurrence of several factors, (i) the
enhancement of negative cross-correlations between AA and VR contributions and
(ii) the large density fluctuations as the critical point (CP) is approached.
The former makes the decay faster so that local density fluctuations are probed
on a femtosecond time scale. A mode coupling theory (MCT) analysis shows the
slow decay of the enhanced density fluctuations near critical point. The MCT
analysis demonstrates that the large enhancement of VR coupling near CP arises
from the non-Gaussian behavior of density fluctuation and this enters through a
nonzero value of the triplet direct correlation function.Comment: 35 pages, 15 figures, revtex4 (preprint form
Stability of critical bubble in stretched fluid of square-gradient density-functional model with triple-parabolic free energy
The square-gradient density-functional model with triple-parabolic free
energy, that was used previously to study the homogeneous bubble nucleation [J.
Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical
bubble nucleated within the bulk under-saturated stretched fluid. The stability
of the bubble is studied by solving the Schr\"odinger equation for the
fluctuation. The negative eigenvalue corresponds to the unstable growing mode
of the fluctuation. Our results show that there is only one negative eigenvalue
whose eigenfunction represents the fluctuation that corresponds to the
isotropically growing or shrinking nucleus. In particular, this negative
eigenvalue survives up to the spinodal point. Therefore the critical bubble is
not fractal or ramified near the spinodal.Comment: 9 pages, 8 figures, Journal of Chemical Physics accepted for
publicatio
Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids
Notwithstanding the long and distinguished history of studies of vibrational
energy relaxation, exactly how it is that high frequency vibrations manage to
relax in a liquid remains somewhat of a mystery. Both experimental and
theoretical approaches seem to say that there is a natural frequency range
associated with intermolecular motions in liquids, typically spanning no more
than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent
can absorb any vibrational energy within this "band", but how is it that
molecules can rid themselves of superfluous vibrational energies significantly
in excess of these values? We develop a theory for such processes based on the
idea that the crucial liquid motions are those that most rapidly modulate the
force on the vibrating coordinate -- and that by far the most important of
these motions are those involving what we have called the mutual nearest
neighbors of the vibrating solute. Specifically, we suggest that whenever there
is a single solvent molecule sufficiently close to the solute that the solvent
and solute are each other's nearest neighbors, then the instantaneous
scattering dynamics of the solute-solvent pair alone suffices to explain the
high frequency relaxation. The many-body features of the liquid only appear in
the guise of a purely equilibrium problem, that of finding the likelihood of
particularly effective solvent arrangements around the solute. These results
are tested numerically on model diatomic solutes dissolved in atomic fluids
(including the experimentally and theoretically interesting case of I_2 in Xe).
The instantaneous pair theory leads to results in quantitative agreement with
those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199
Quantum‐mechanical derivation of the Bloch equations: Beyond the weak‐coupling limit
This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/94/6/10.1063/1.460626Two nondegenerate quantum levels coupled off‐diagonally and linearly to a bath of quantum‐mechanical harmonic oscillators are considered. In the weak‐coupling limit one finds that the equations of motion for the reduced density‐matrix elements separate naturally into two uncoupled pairs of linear equations for the diagonal and off‐diagonal elements, which are known as the Bloch equations. The equations for the populations form the simplest two‐component master equation, and the rate constant for the relaxation of nonequilibrium population distributions is 1/T 1, defined as the sum of the ‘‘up’’ and ‘‘down’’ rate constants in the master equation. Detailed balance is satisfied for this master equation in that the ratio of these rate constants is equal to the ratio of the equilibrium populations. The relaxation rate constant for the off‐diagonal density‐matrix elements is known as 1/T 2. One finds that this satisfies the well‐known relation 1/T 2=1/2T 1. In this paper the weak‐coupling limit is transcended by deriving the Bloch equations to fourth order in the coupling. The equations have the same form as in the weak‐coupling limit, but the rate constants are calculated to fourth order. For the population‐relaxation rate constants this results in an extension to fourth order of Fermi’s golden rule. We find that these higher‐order rate constants do indeed satisfy detailed balance. Comparing the dephasing and population‐relaxation rate constants, we find that in fourth order 1/T 2≠1/2T 1
Degenerative Adversarial NeuroImage Nets: Generating Images that Mimic Disease Progression
Simulating images representative of neurodegenerative diseases is important for predicting patient outcomes and for validation of computational models of disease progression. This capability is valuable for secondary prevention clinical trials where outcomes and screening criteria involve neuroimaging. Traditional computational methods are limited by imposing a parametric model for atrophy and are extremely resource-demanding. Recent advances in deep learning have yielded data-driven models for longitudinal studies (e.g., face ageing) that are capable of generating synthetic images in real-time. Similar solutions can be used to model trajectories of atrophy in the brain, although new challenges need to be addressed to ensure accurate disease progression modelling. Here we propose Degenerative Adversarial NeuroImage Net (DaniNet)—a new deep learning approach that learns to emulate the effect of neurodegeneration on MRI by simulating atrophy as a function of ages, and disease progression. DaniNet uses an underlying set of Support Vector Regressors (SVRs) trained to capture the patterns of regional intensity changes that accompany disease progression. DaniNet produces whole output images, consisting of 2D-MRI slices that are constrained to match regional predictions from the SVRs. DaniNet is also able to maintain the unique brain morphology of individuals. Adversarial training ensures realistic brain images and smooth temporal progression. We train our model using 9652 T1-weighted (longitudinal) MRI extracted from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. We perform quantitative and qualitative evaluations on a separate test set of 1283 images (also from ADNI) demonstrating the ability of DaniNet to produce accurate and convincing synthetic images that emulate disease progression
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