139,595 research outputs found
Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles
We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) for
inverting vertical profile information of atmospheric methane from ground based
Fourier transform infrared (FTIR) measurements at Sodankyl\"a, Northern
Finland. The measurements belong to the word wide TCCON network for greenhouse
gas measurements and, in addition to providing accurate greenhouse gas
measurements, they are important for validating satellite observations. LIS
allows construction of an efficient Markov chain Monte Carlo sampling algorithm
that explores only a reduced dimensional space but still produces a good
approximation of the original full dimensional Bayesian posterior distribution.
This in effect makes the statistical estimation problem independent of the
discretization of the inverse problem. In addition, we compare LIS to a
dimension reduction method based on prior covariance matrix truncation used
earlier (S. Tukiainen et al. 2016)
First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach
A coagulation-decoagulation model is introduced on a chain of length L with
open boundary. The model consists of one species of particles which diffuse,
coagulate and decoagulate preferentially in the leftward direction. They are
also injected and extracted from the left boundary with different rates. We
will show that on a specific plane in the space of parameters, the steady state
weights can be calculated exactly using a matrix product method. The model
exhibits a first-order phase transition between a low-density and a
high-density phase. The density profile of the particles in each phase is
obtained both analytically and using the Monte Carlo Simulation. The two-point
density-density correlation function in each phase has also been calculated. By
applying the Yang-Lee theory we can predict the same phase diagram for the
model. This model is further evidence for the applicability of the Yang-Lee
theory in the non-equilibrium statistical mechanics context.Comment: 10 Pages, 3 Figures, To appear in Journal of Physics A: Mathematical
and Genera
Entanglement reduction induced by geometrical confinement in polymer thin films
We report simulation results on melts of entangled linear polymers confined
in a free-standing thin film. We study how the geometric constraints imposed by
the confinement alter the entanglement state of the system compared to the
equivalent bulk system using various observables. We find that the confinement
compresses the chain conformation uniaxially, decreasing the volume pervaded by
the chain, which in turn reduces the number of the accessible inter-chain
contact that could lead to entanglements. This local and non-uniform effect
depends on the position of the chain within the film. We also test a recently
presented theory that predicts how the number of entanglements decreases with
geometrical confinement.Comment: 28 pages, 10 figure
Monte Carlo simulations of interfaces in polymer blends
We review recent simulation studies of interfaces between immiscible
homopolymer phases. Special emphasis is given to the presentation of efficient
simulation techniques and powerful methods of data analysis, such as the
analysis of capillary wave spectra. Possible reasons for polymer
incompatibility and ways to relate model dependent interaction parameters to an
effective Flory Huggins parameter are discussed. Various interfaces are then
considered and characterised with respect to their microscopic structure and
thermodynamic properties. In particular, interfaces between homopolymers of
equal or disparate stiffness are studied, interfaces containing diblock
copolymers, and interfaces confined in thin films. The results are related to
the phase behaviour of ternary homopolymer/copolymer systems, and to wetting
transitions in thin films.Comment: To appear in Annual Reviews of Computational Physics, edt. D.
Stauffe
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