724 research outputs found
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
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
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
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
Ideal gas behavior of a strongly-coupled complex (dusty) plasma
In a laboratory, a two-dimensional complex (dusty) plasma consists of a
low-density ionized gas containing a confined suspension of Yukawa-coupled
plastic microspheres. For an initial crystal-like form, we report ideal gas
behavior in this strongly-coupled system during shock-wave experiments. This
evidence supports the use of the ideal gas law as the equation of state for
soft crystals such as those formed by dusty plasmas.Comment: 5 pages, 5 figures, 5 authors, published versio
Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method
Homogeneous nucleation and growth in a simplest two-dimensional phase field
model is numerically studied using the cell dynamics method. Whole process from
nucleation to growth is simulated and is shown to follow closely the
Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation.
Specifically the time evolution of the volume fraction of new stable phase is
found to follow closely the KJMA formula. By fitting the KJMA formula directly
to the simulation data, not only the Avrami exponent but the magnitude of
nucleation rate and, in particular, of incubation time are quantitatively
studied. The modified Avrami plot is also used to verify the derived KJMA
parameters. It is found that the Avrami exponent is close to the ideal
theoretical value m=3. The temperature dependence of nucleation rate follows
the activation-type behavior expected from the classical nucleation theory. On
the other hand, the temperature dependence of incubation time does not follow
the exponential activation-type behavior. Rather the incubation time is
inversely proportional to the temperature predicted from the theory of
Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to
restrict thermal noise in simulation to deduce correct Avrami exponent is also
discussed.Comment: 9 pages, 8 figures, Journal of Chemical Physics to be publishe
A diffusion-induced transition in the phase separation of binary fluid mixtures subjected to a temperature ramp
Demixing of binary fluids subjected to slow temperature ramps shows repeated
waves of nucleation which arise as a consequence of the competition between
generation of supersaturation by the temperature ramp and relaxation of
supersaturation by diffusive transport and flow. Here, we use an
advection-reaction-diffusion model to study the oscillations in the weak- and
strong-diffusion regime. There is a sharp transition between the two regimes,
which can only be understood based on the probability distribution function of
the composition rather than in terms of the average composition. We argue that
this transition might be responsible for some yet unclear features of
experiments, like the appearance of secondary oscillations and bimodal droplet
size distributions.Comment: 6 pages, 3 color figure
Quantized time correlation function approach to non-adiabatic decay rates in condensed phase: Application to solvated electrons in water and methanol
A new, alternative form of the golden rule formula defining the non-adiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the non-adiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via MD simulations. The formalism is applied to the problem of the non-adiabatic relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvent, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated non-adiabatic coupling
Event-Based Modeling with High-Dimensional Imaging Biomarkers for Estimating Spatial Progression of Dementia
Event-based models (EBM) are a class of disease progression models that can
be used to estimate temporal ordering of neuropathological changes from
cross-sectional data. Current EBMs only handle scalar biomarkers, such as
regional volumes, as inputs. However, regional aggregates are a crude summary
of the underlying high-resolution images, potentially limiting the accuracy of
EBM. Therefore, we propose a novel method that exploits high-dimensional
voxel-wise imaging biomarkers: n-dimensional discriminative EBM (nDEBM). nDEBM
is based on an insight that mixture modeling, which is a key element of
conventional EBMs, can be replaced by a more scalable semi-supervised support
vector machine (SVM) approach. This SVM is used to estimate the degree of
abnormality of each region which is then used to obtain subject-specific
disease progression patterns. These patterns are in turn used for estimating
the mean ordering by fitting a generalized Mallows model. In order to validate
the biomarker ordering obtained using nDEBM, we also present a framework for
Simulation of Imaging Biomarkers' Temporal Evolution (SImBioTE) that mimics
neurodegeneration in brain regions. SImBioTE trains variational auto-encoders
(VAE) in different brain regions independently to simulate images at varying
stages of disease progression. We also validate nDEBM clinically using data
from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In both
experiments, nDEBM using high-dimensional features gave better performance than
state-of-the-art EBM methods using regional volume biomarkers. This suggests
that nDEBM is a promising approach for disease progression modeling.Comment: IPMI 201
Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections
The extension of quantum trajectory theory to incorporate realistic
imperfections in the measurement of solid-state qubits is important for quantum
computation, particularly for the purposes of state preparation and
error-correction as well as for readout of computations. Previously this has
been achieved for low-frequency (dc) weak measurements. In this paper we extend
realistic quantum trajectory theory to include radio frequency (rf) weak
measurements where a low-transparency quantum point contact (QPC), coupled to a
charge qubit, is used to damp a classical oscillator circuit. The resulting
realistic quantum trajectory equation must be solved numerically. We present an
analytical result for the limit of large dissipation within the oscillator
(relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode
of operation is considered. Here the QPC is biased (dc) as well as subjected to
a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be
a low-efficiency charge-qubit detector, that may nevertheless be higher than
the dc-QPC (which is subject to 1/f noise).Comment: 12 pages, 2 colour figures. v3 is published version (minor changes
since v2
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