3,255 research outputs found
PT-symmetric operators and metastable states of the 1D relativistic oscillators
We consider the one-dimensional Dirac equation for the harmonic oscillator
and the associated second order separated operators giving the resonances of
the problem by complex dilation. The same operators have unique extensions as
closed PT-symmetric operators defining infinite positive energy levels
converging to the Schroedinger ones as c tends to infinity. Such energy levels
and their eigenfunctions give directly a definite choice of metastable states
of the problem. Precise numerical computations shows that these levels coincide
with the positions of the resonances up to the order of the width. Similar
results are found for the Klein-Gordon oscillators, and in this case there is
an infinite number of dynamics and the eigenvalues and eigenvectors of the
PT-symmetric operators give metastable states for each dynamics.Comment: 13 pages, 2 figure
Twist versus Nonlinear Stacking in Short DNA Molecules
The denaturation of the double helix is a template for fundamental biological
functions such as replication and transcription involving the formation of
local fluctuational openings. The denaturation transition is studied for
heterogeneous short sequences of DNA, i.e. base pairs, in the
framework of a mesoscopic Hamiltonian model which accounts for the helicoidal
geometry of the molecule. The theoretical background for the application of the
path integral formalism to predictive analysis of the molecule thermodynamical
properties is discussed. The base pair displacements with respect to the ground
state are treated as paths whose temperature dependent amplitudes are governed
by the thermal wavelength. The ensemble of base pairs paths is selected, at any
temperature, consistently with both the model potential and the second law of
thermodynamics. The partition function incorporates the effects of the base
pair thermal fluctuations which become stronger close to the denaturation. The
transition appears as a gradual phenomenon starting from the molecule segments
rich in adenine-thymine base pairs. Computing the equilibrium thermodynamics,
we focus on the interplay between twisting of the complementary strands around
the molecule axis and nonlinear stacking potential: it is shown that the latter
affects the melting profiles only if the rotational degrees of freedom are
included in the Hamiltonian. The use of ladder Hamiltonian models for the DNA
complementary strands in the pre-melting regime is questioned.Comment: Journal of Theoretical Biology (2014
Efficient construction of free energy profiles of breathing metal–organic frameworks using advanced molecular dynamics simulations
In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials
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