89,040 research outputs found
Renormalization in Quantum Mechanics
We implement the concept of Wilson renormalization in the context of simple
quantum mechanical systems. The attractive inverse square potential leads to a
\b function with a nontrivial ultraviolet stable fixed point and the Hulthen
potential exhibits the crossover phenomenon. We also discuss the implementation
of the Wilson scheme in the broader context of one dimensional potential
problems. The possibility of an analogue of Zamolodchikov's function in
these systems is also discussed.Comment: 16 pages, UR-1310, ER-40685-760. (Additional references included.
A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow
We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations
Effects of backing plates on the electron exposure of thin polymer films
The effects of backing plates on the radiation dose received by thin nylon films were calculated using recently developed multilayer electron transport codes. The film dose increased with increasing atomic number of the backing plate. The estimated dose could be off by a factor of 2 or more if the backing plate were ignored in the calculations
A thin rivulet or ridge subject to a uniform transverse\ud shear stress at its free surface due to an external airflow
We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations
The pumpistor: a linearized model of a flux-pumped SQUID for use as a negative-resistance parametric amplifier
We describe a circuit model for a flux-driven SQUID. This is useful for
developing insight into how these devices perform as active elements in
parametric amplifiers. The key concept is that frequency mixing in a
flux-pumped SQUID allows for the appearance of an effective negative
resistance. In the three-wave, degenerate case treated here, a negative
resistance appears only over a certain range of allowed input signal phase.
This model readily lends itself to testable predictions of more complicated
circuits.Comment: 4 pages, 3 figure
Renormalization of Tamm-Dancoff Integral Equations
During the last few years, interest has arisen in using light-front
Tamm-Dancoff field theory to describe relativistic bound states for theories
such as QCD. Unfortunately, difficult renormalization problems stand in the
way. We introduce a general, non-perturbative approach to renormalization that
is well suited for the ultraviolet and, presumably, the infrared divergences
found in these systems. We reexpress the renormalization problem in terms of a
set of coupled inhomogeneous integral equations, the ``counterterm equation.''
The solution of this equation provides a kernel for the Tamm-Dancoff integral
equations which generates states that are independent of any cutoffs. We also
introduce a Rayleigh-Ritz approach to numerical solution of the counterterm
equation. Using our approach to renormalization, we examine several ultraviolet
divergent models. Finally, we use the Rayleigh-Ritz approach to find the
counterterms in terms of allowed operators of a theory.Comment: 19 pages, OHSTPY-HEP-T-92-01
Homoeopathy
Homoeopathy is a system of treating patients
using very low dose preparations according
to the principle: "like should be cured with
like". This paper summarises the research evidence
presented in a recent issue of Effective Health
Care on the effectiveness of homoeopathy.
Increasing numbers of patients are seeking
information on complementary medicines from
NHS health professionals. Results of a 1998 survey
of use and expenditure on complementary
medicine in England suggested that 28% of
respondents had either visited a complementary
therapist or had purchased an over the counter
herbal or homoeopathic remedy in the past year.
From this survey it was estimated that there
could be over 470 000 recent users of homoeopathic
remedies in England
Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach
Recently we have studied the Bloch effective Hamiltonian approach to bound
states in 2+1 dimensional gauge theories. Numerical calculations were carried
out to investigate the vanishing energy denominator problem. In this work we
study similarity renormalization approach to the same problem. By performing
analytical calculations with a step function form for the similarity factor, we
show that in addition to curing the vanishing energy denominator problem,
similarity approach generates linear confining interaction for large transverse
separations. However, for large longitudinal separations, the generated
interaction grows only as the square root of the longitudinal separation and
hence produces violations of rotational symmetry in the spectrum. We carry out
numerical studies in the G{\l}azek-Wilson and Wegner formalisms and present low
lying eigenvalues and wavefunctions. We investigate the sensitivity of the
spectra to various parameterizations of the similarity factor and other
parameters of the effective Hamiltonian, especially the scale . Our
results illustrate the need for higher order calculations of the effective
Hamiltonian in the similarity renormalization scheme.Comment: 31 pages, 4 figures, to be published in Physical Review
Directional genetic differentiation and asymmetric migration
Understanding the population structure and patterns of gene flow within
species is of fundamental importance to the study of evolution. In the fields
of population and evolutionary genetics, measures of genetic differentiation
are commonly used to gather this information. One potential caveat is that
these measures assume gene flow to be symmetric. However, asymmetric gene flow
is common in nature, especially in systems driven by physical processes such as
wind or water currents. Since information about levels of asymmetric gene flow
among populations is essential for the correct interpretation of the
distribution of contemporary genetic diversity within species, this should not
be overlooked. To obtain information on asymmetric migration patterns from
genetic data, complex models based on maximum likelihood or Bayesian approaches
generally need to be employed, often at great computational cost. Here, a new
simpler and more efficient approach for understanding gene flow patterns is
presented. This approach allows the estimation of directional components of
genetic divergence between pairs of populations at low computational effort,
using any of the classical or modern measures of genetic differentiation. These
directional measures of genetic differentiation can further be used to
calculate directional relative migration and to detect asymmetries in gene flow
patterns. This can be done in a user-friendly web application called
divMigrate-online introduced in this paper. Using simulated data sets with
known gene flow regimes, we demonstrate that the method is capable of resolving
complex migration patterns under a range of study designs.Comment: 25 pages, 8 (+3) figures, 1 tabl
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