4,126 research outputs found
One Kind of Multiple Dimensional Markovian BSDEs with Stochastic Linear Growth Generators
In this article, we deal with a multiple dimensional coupled Markovian BSDEs
system with stochastic linear growth generators with respect to volatility
processes. An existence result is provided by using approximation techniques.Comment: arXiv admin note: text overlap with arXiv:1412.121
Theory of Side-Chain Liquid Crystal Polymers: Bulk Behavior and Chain Conformation
We study the thermodynamics and chain conformation of side-chain liquid crystal polymers (SCLCPs) in the bulk using the self-consistent-field approach and a new model to account for the coupling between the orientation of the side-chain liquid-crystal (LC) groups and that of the backbone segments. The new model accounts for both a global coupling between the polymer backbone and the nematic field and a local coupling between the polymer backbone and its attached LC group. Here, the terms global and local refer to the chemical (backbone) distance between the groups. A phenomenological parameter is introduced to represent the coupling strength and nature of the attachment, i.e., end-on vs side-on. The nematic field is shown to control the chain conformation through both the global and the local coupling effects. For the side-on SCLCPs, these two coupling effects act cooperatively so that the chain conformation is always prolate. For the end-on SCLCPs, these two effects act competitively. The chain conformation can be either oblate or prolate in this case, and depends on the relative strengths of these two couplings. On the other hand, the chain conformation also affects the nematic field, primarily through the global coupling. The prolate conformation enhances the nematic field and increases the phase transition temperature, whereas the oblate conformation frustrates the nematic field and decreases the transition temperature. The nematic order parameter is found to be determined mainly by the reduced temperature, and is not sensitive to the coupling effects. Furthermore, we show that the grafting density of the LC side groups has a significant effect on the chain conformation due to the orientational competition between the LC attached and unattached segments. For the end-on SCLCPs with lower graft density, the conformation of the chain backbone can be oblate at higher temperatures and prolate at lower temperatures, in agreement with the re-entrant nematic phase observed in experiments
Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures
We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions
On the theoretical description of weakly charged surfaces
It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid
description for charged surfaces in the so-called weak coupling limit. Here, we
show that the image charge repulsion creates a depletion boundary layer that
cannot be captured by a regular perturbation approach. The correct
weak-coupling theory must include the self-energy of the ion due to the image
charge interaction. The image force qualitatively alters the double layer
structure and properties, and gives rise to many non-PB effects, such as
nonmonotonic dependence of the surface energy on concentration and charge
inversion. In the presence of dielectric discontinuity, there is no limiting
condition for which the PB theory is valid
Inhomogeneous screening near a dielectric interface
Screening is one of the most important concepts in the study of charged
systems. Near a dielectric interface, the ion distribution in a salt solution
can be highly nonuniform. Here, we develop a theory that self-consistently
treats the inhomogeneous screening effects. At higher concentrations when the
bulk Debye screening length is comparable to the Bjerrum length, the double
layer structure and interfacial properties are significantly affected by the
inhomogeneous screening. In particular, the depletion zone is considerably
wider than that predicted by the bulk screening approximation or the WKB
approximation. For asymmetric salts, the inhomogeneous screening leads to
enhanced charge separation and surface potential.Comment: 5 figure
Branching ratios, asymmetries and polarizations of decays
We analyzed the nonleptonic decays with by employing the perturbative QCD (PQCD) factorization
approach. Here the branching ratios, the asymmetries and the complete set
of polarization observables are investigated systematically. Besides the
traditional contributions from the factorizable and nonfactorizable diagrams at
the leading order, the next-to-leading order (NLO) vertex corrections could
also provide considerable contributions. The PQCD predictions for the branching
ratios of the decays are consistent
with the measured values within errors. As for decays, the branching ratios can reach the order of and could
be measured in the LHCb and Belle-II experiments. The numerical results show
that the direct asymmetries of the considered decays are very small. Thus
the observation of any large direct asymmetry for these decays will be a
signal for new physics. The mixing induced asymmetries in the neutral
modes are very close to , which suggests that these channels
can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa
(CKM) angle and . We found that the longitudinal polarization
fractions are suppressed to due to the large nonfactorizable
contributions. The magnitudes and phases of the two transverse amplitudes
and are roughly equal, which
is an indication for the approximate light quark helicity conservation in these
decays. The overall polarization observables of and
channels are also in good agreement with the
experimental measurements as reported by LHCb and BaBar. Other results can also
be tested by the LHCb and Belle-II experiments.Comment: 14 pages, 1 figure, 6 table
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