859 research outputs found
Interaction of paraffin wax gels with ethylene/vinyl acetate copolymers
The commercial grades of ethylene/vinyl acetate (EVA) co-polymers have found application as pour point" depressants in refined fuels. This study focuses on their behavior as additives to crude oils, where the intent is to reduce the yield stress of the gels that can form when the oil exits the reservoir. The model crude oils consisted of 4 wt % wax in decane. At EVA dosage levels of similar to200 ppm, the reduction in yield stress is 3 orders of magnitude for the C-36 wax, whereas the reduction is 1 order of magnitude for C-32 and only 3-fold for the C-28 wax. This decrease in efficiency with decreasing wax carbon number indicates that the EVA materials would not provide an adequate reduction in yield stress to ensure against gelation in pipeline transport. Neutron scattering studies, as a function of temperature, of the self-assembly of the EVA co-polymers show dramatically different aggregated structures in decane. The EVA with the lowest ethylene content shows scattering that increases with a power-law exponent of similar to1.6. This scattering behavior is typical for weakly aggregating polymer gels. In contrast, the EVA with the higher ethylene content shows a transition from surface scattering (found for strongly segregated objects) to a plateau whose height is dependent on temperature. Micrographs of the wax crystal morphology indicate that the ethylene-poor EVA alters the wax crystal habit at higher concentrations more effectively than does its higher-ethylene-content counterpart, whereas the latter EVA grade seems to form more wax crystals at low concentrations
Interaction of paraffin wax gels with random crystalline/amorphous hydrocarbon copolymers
The control mechanisms involved in the modification of wax crystal dimensions in crude oils and refined fuels are of joint scientific and practical interest. An understanding of these mechanisms allows strategies to be developed that lead to decreases in crude oil pour points or (for refined fuels) cold filter plugging points. The attainment of these goals involves the control and modification of wax crystals that spontaneously form in mixed hydrocarbon systems upon decreasing temperature. This work reports on the influence of random crystalline-amorphous block copolymers (ethylene-butene) upon the rheology of model oils. In a parallel fashion small-angle neutron scattering was exploited to gain microscopic insight as to how added poly(ethylene-butene) copolymers modify the wax crystal structures. The copolymers with different contents of polyethylene are highly selective with respect to wax crystal modification. Thus, the copolymer with the highest crystalline tendency is more efficient for the larger wax molecules while the less crystalline one is more efficient for the lower waxes
An Isoperimetric Inequality for Fundamental Tones of Free Plates
We establish an isoperimetric inequality for the fundamental tone (first
nonzero eigenvalue) of the free plate of a given area, proving the ball is
maximal. Given , the free plate eigenvalues and eigenfunctions
are determined by the equation
together with certain natural boundary conditions. The boundary conditions are
complicated but arise naturally from the plate Rayleigh quotient, which
contains a Hessian squared term . We adapt Weinberger's method from
the corresponding free membrane problem, taking the fundamental modes of the
unit ball as trial functions. These solutions are a linear combination of
Bessel and modified Bessel functions.Comment: PhD thesis. Papers are in preparatio
Segue Between Favorable and Unfavorable Solvation
Solvation of small and large clusters are studied by simulation, considering
a range of solvent-solute attractive energy strengths. Over a wide range of
conditions, both for solvation in the Lennard-Jones liquid and in the SPC model
of water, it is shown that the mean solvent density varies linearly with
changes in solvent-solute adhesion or attractive energy strength. This behavior
is understood from the perspective of Weeks' theory of solvation [Ann. Rev.
Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.Comment: 8 pages, 7 figure
Coulomb plus power-law potentials in quantum mechanics
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the
Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q >
-2 and q \ne 0. We show by envelope theory that the discrete eigenvalues
E_{n\ell} of H may be approximated by the semiclassical expression
E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.
Values of mu and nu are prescribed which yield upper and lower bounds.
Accurate upper bounds are also obtained by use of a trial function of the form,
psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for
V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with
comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure
Resting and reactive frontal brain electrical activity (EEG) among a non-clinical sample of socially anxious adults: does concurrent depressive mood matter?
A number of studies have noted that the pattern of resting frontal brain electrical activity (EEG) is related to individual differences in affective style in healthy infants, children, and adults and some clinical populations when symptoms are reduced or in remission. We measured self-reported trait shyness and sociability, concurrent depressive mood, and frontal brain electrical activity (EEG) at rest and in anticipation of a speech task in a non-clinical sample of healthy young adults selected for high and low social anxiety. Although the patterns of resting and reactive frontal EEG asymmetry did not distinguish among individual differences in social anxiety, the pattern of resting frontal EEG asymmetry was related to trait shyness after controlling for concurrent depressive mood. Individuals who reported a higher degree of shyness were likely to exhibit greater relative right frontal EEG activity at rest. However, trait shyness was not related to frontal EEG asymmetry measured during the speech-preparation task, even after controlling for concurrent depressive mood. These findings replicate and extend prior work on resting frontal EEG asymmetry and individual differences in affective style in adults. Findings also highlight the importance of considering concurrent emotional states of participants when examining psychophysiological correlates of personality
Semiclassical energy formulas for power-law and log potentials in quantum mechanics
We study a single particle which obeys non-relativistic quantum mechanics in
R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2,
then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may
be represented exactly by the semiclassical expression E_{n\ell}(q) =
min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) =
ln(r). By writing one power as a smooth transformation of another, and using
envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are
monotone increasing. Recent refinements to the comparison theorem of QM in
which comparison potentials can cross over, allow us to prove for n = 1 that
Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q}
is monotone decreasing. Thus P(q) cannot increase too slowly. This result
yields some sharper estimates for power-potential eigenvlaues at the bottom of
each angular-momentum subspace.Comment: 20 pages, 5 figure
Self Consistent Molecular Field Theory for Packing in Classical Liquids
Building on a quasi-chemical formulation of solution theory, this paper
proposes a self consistent molecular field theory for packing problems in
classical liquids, and tests the theoretical predictions for the excess
chemical potential of the hard sphere fluid. Results are given for the self
consistent molecular fields obtained, and for the probabilities of occupancy of
a molecular observation volume. For this system, the excess chemical potential
predicted is as accurate as the most accurate prior theories, particularly the
scaled particle (Percus-Yevick compressibility) theory. It is argued that the
present approach is particularly simple, and should provide a basis for a
molecular-scale description of more complex solutions.Comment: 6 pages and 5 figure
Fluctuations of water near extended hydrophobic and hydrophilic surfaces
We use molecular dynamics simulations of the SPC-E model of liquid water to
derive probability distributions for water density fluctuations in probe
volumes of different shapes and sizes, both in the bulk as well as near
hydrophobic and hydrophilic surfaces. To obtain our results, we introduce a
biased sampling of coarse-grained densities, which in turn biases the actual
solvent density. The technique is easily combined with molecular dynamics
integration algorithms. Our principal result is that the probability for
density fluctuations of water near a hydrophobic surface, with or without
surface-water attractions, is akin to density fluctuations at the water-vapor
interface. Specifically, the probability of density depletion near the surface
is significantly larger than that in bulk. In contrast, we find that the
statistics of water density fluctuations near a model hydrophilic surface are
similar to that in the bulk
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