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

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

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

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

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

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.

The Adult Respiratory Distress Syndrome: Clinical Features, Factors Influencing Prognosis and Principles of Management

This report redescribes the adult respiratory distress syndrome and discusses factors which influence prognosis and presents principles of management

Adaptive plasticity of killifish (Fundulus heteroclitus) embryos: dehydration-stimulated development and differential aquaporin-3 expression

13 pages, 7 figures, 3 tablesEmbryos of the marine killifish Fundulus heteroclitus are adapted to survive aerially. However, it is unknown if they are able to control development under dehydration conditions. Here, we show that air-exposed blastula embryos under saturated relative humidity were able to stimulate development, and hence the time of hatching was advanced with respect to embryos continuously immersed in seawater. Embryos exposed to air at later developmental stages did not hatch until water was added, while development was not arrested. Air-exposed embryos avoided dehydration probably because of their thickened egg envelope, although it suffered significant evaporative water loss. The potential role of aquaporins as part of the embryo response to dehydration was investigated by cloning the aquaporin-0 (FhAqp0), -1a (FhAqp1a), and -3 (FhAqp3) cDNAs. Functional expression in Xenopus laevis oocytes showed that FhaAqp1a was a water-selective channel, whereas FhAqp3 was permeable to water, glycerol, and urea. Expression of fhaqp0 and fhaqp1a was prominent during organogenesis, and their mRNA levels were similar between water- and air-incubated embryos. However, fhaqp3 transcripts were highly and transiently accumulated during gastrulation, and the protein product was localized in the basolateral membrane of the enveloping epithelial cell layer and in the membrane of ingressing and migrating blastomers. Interestingly, both fhaqp3 transcripts and FhAqp3 polypeptides were downregulated in air-exposed embryos. These data demonstrate that killifish embryos respond adaptively to environmental desiccation by accelerating development and that embryos are able to transduce dehydration conditions into molecular responses. The reduced synthesis of FhAqp3 may be one of these mechanisms to regulate water and/or solute transport in the embryo.This study was supported by the European Commission New and Emerging Science and Technologies (NEST) program (contract no. 012674-2 Sleeping Beauty) and by a grant from the Spanish Ministry of Education and Science (MEC; AGL2004-00316/ACU) to J. Cerda`. Participation of C. Zapater and F. Chauvigne´ was financed by a predoctoral fellowship from MEC (Spain) and by the European Commission [Marie Curie Research Training Network Aqua (glycero)porins, MRTN-CT-2006-035995], respectively.Peer reviewe