276 research outputs found
Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems
We derive an effective Hamiltonian for a quantum system constrained to a
submanifold (the constraint manifold) of configuration space (the ambient
space) by an infinite restoring force. We pay special attention to how this
Hamiltonian depends on quantities which are external to the constraint
manifold, such as the external curvature of the constraint manifold, the
(Riemannian) curvature of the ambient space, and the constraining potential. In
particular, we find the remarkable fact that the twisting of the constraining
potential appears as a gauge potential in the constrained Hamiltonian. This
gauge potential is an example of geometric phase, closely related to that
originally discussed by Berry. The constrained Hamiltonian also contains an
effective potential depending on the external curvature of the constraint
manifold, the curvature of the ambient space, and the twisting of the
constraining potential. The general nature of our analysis allows applications
to a wide variety of problems, such as rigid molecules, the evolution of
molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.
Wetting problem for multi-component fluid mixtures
In this paper we propose an extension of the Cahn method to binary mixtures
and study the problem of wetting near a two-phase critical point without any
assumption on the form of intermolecular potentials. A comparison between
Cahn's method and later works by Sullivan, Evans et al is made. By using an
expression of the energy of interaction between solid surface and liquids
proposed recently by Gouin, we obtain the equations of density profiles and the
boundary conditions on a solid surface. In the case of a convex free energy, a
one-dimensional solution of a linear problem is proposed for the density
profiles between a bulk and on a solid wall. A non-linear model of binary
mixtures extending Cahn's results for simple fluids is also studied. For the
case of a purely attractive wall we have established a criterion of a first
order transition in terms of the structure of the level set of the homogeneous
part of the free energy. Additively, explicit expressions of density profiles
near the wall are proposed. They allow one to consider the adsorption of
mixture components by a solid wall.Comment: 20 pages and 4 figure
A new ultrafast and high-throughput mass spectrometric approach for the therapeutic drug monitoring of the multi-targeted anti-folate pemetrexed in plasma from lung cancer patients
An analytical assay has been developed and validated for ultrafast and high-throughput mass spectrometric determination of pemetrexed concentrations in plasma using matrix assisted laser desorption/ionization–triple quadrupole–tandem mass spectrometry. Patient plasma samples spiked with the internal standard methotrexate were measured by multiple reaction monitoring. The detection limit was 0.4 fmol/μL, lower limit of quantification was 0.9 fmol/μL, and upper limit of quantification was 60 fmol/μL, respectively. Overall observed pemetrexed concentrations in patient samples ranged between 8.7 (1.4) and 142.7 (20.3) pmol/μL (SD). The newly developed mass spectrometric assay is applicable for (routine) therapeutic drug monitoring of pemetrexed concentrations in plasma from non-small cell lung cancer patients
Stabilization of oscillations in a phase transition model
In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. In particular we investigate how the presence of stochastic perturbations affects this phenomenon in its asymptotic behavior. Two different sufficient conditions are provided in order to prevent the formation of microstructure: the first one for Stratonovich’s noise while the second for Itˆo’s noise. The main contribution of the paper is that these conditions are independent of the initial values unlike in the deterministic model. Thus, we can interpret our results as some kind of
stabilization produced by both types of noise.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí
Analytical approximations for spatial stochastic gene expression in single cells and tissues
Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
Agent-based stochastic models for finite populations have recently received
much attention in the game theory of evolutionary dynamics. Both the ultimate
fixation and the pre-fixation transient behavior are important to a full
understanding of the dynamics. In this paper, we study the transient dynamics
of the well-mixed Moran process through constructing a landscape function. It
is shown that the landscape playing a central theoretical "device" that
integrates several lines of inquiries: the stable behavior of the replicator
dynamics, the long-time fixation, and continuous diffusion approximation
associated with asymptotically large population. Several issues relating to the
transient dynamics are discussed: (i) multiple time scales phenomenon
associated with intra- and inter-attractoral dynamics; (ii) discontinuous
transition in stochastically stationary process akin to Maxwell construction in
equilibrium statistical physics; and (iii) the dilemma diffusion approximation
facing as a continuous approximation of the discrete evolutionary dynamics. It
is found that rare events with exponentially small probabilities, corresponding
to the uphill movements and barrier crossing in the landscape with multiple
wells that are made possible by strong nonlinear dynamics, plays an important
role in understanding the origin of the complexity in evolutionary, nonlinear
biological systems.Comment: 34 pages, 4 figure
Quantizing Constrained Systems: New Perspectives
We consider quantum mechanics on constrained surfaces which have
non-Euclidean metrics and variable Gaussian curvature. The old controversy
about the ambiguities involving terms in the Hamiltonian of order hbar^2
multiplying the Gaussian curvature is addressed. We set out to clarify the
matter by considering constraints to be the limits of large restoring forces as
the constraint coordinates deviate from their constrained values. We find
additional ambiguous terms of order hbar^2 involving freedom in the
constraining potentials, demonstrating that the classical constrained
Hamiltonian or Lagrangian cannot uniquely specify the quantization: the
ambiguity of directly quantizing a constrained system is inherently
unresolvable. However, there is never any problem with a physical quantum
system, which cannot have infinite constraint forces and always fluctuates
around the mean constraint values. The issue is addressed from the perspectives
of adiabatic approximations in quantum mechanics, Feynman path integrals, and
semiclassically in terms of adiabatic actions.Comment: 11 pages, 2 figure
An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints
In this work, we introduce an algorithm to compute the derivatives of
physical observables along the constrained subspace when flexible constraints
are imposed on the system (i.e., constraints in which the hard coordinates are
fixed to configuration-dependent values). The presented scheme is exact, it
does not contain any tunable parameter, and it only requires the calculation
and inversion of a sub-block of the Hessian matrix of second derivatives of the
function through which the constraints are defined. We also present a practical
application to the case in which the sought observables are the Euclidean
coordinates of complex molecular systems, and the function whose minimization
defines the constraints is the potential energy. Finally, and in order to
validate the method, which, as far as we are aware, is the first of its kind in
the literature, we compare it to the natural and straightforward
finite-differences approach in three molecules of biological relevance:
methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio
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