107 research outputs found
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented
Probability distribution of the sizes of largest erased-loops in loop-erased random walks
We have studied the probability distribution of the perimeter and the area of
the k-th largest erased-loop in loop-erased random walks in two-dimensions for
k = 1 to 3. For a random walk of N steps, for large N, the average value of the
k-th largest perimeter and area scales as N^{5/8} and N respectively. The
behavior of the scaled distribution functions is determined for very large and
very small arguments. We have used exact enumeration for N <= 20 to determine
the probability that no loop of size greater than l (ell) is erased. We show
that correlations between loops have to be taken into account to describe the
average size of the k-th largest erased-loops. We propose a one-dimensional
Levy walk model which takes care of these correlations. The simulations of this
simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte
Generalized Relativistic Meson Wave Function
We study the most general, relativistic, constituent meson
wave function within a new covariant framework. We find that by including a
tensor wave function component, a pure valence quark model is now capable of
reproducing not only all static pion data (, )
but also the distribution amplitude, form factor , and structure
functions. Further, our generalized spin wave function provides a much better
detailed description of meson properties than models using a simple
relativistic extension of the nonrelativistic wave function.Comment: 17 pages, REXTeX 3.0 file, (uuencoded postscript files of 8 figures
appended
Virus shapes and buckling transitions in spherical shells
We show that the icosahedral packings of protein capsomeres proposed by
Caspar and Klug for spherical viruses become unstable to faceting for
sufficiently large virus size, in analogy with the buckling instability of
disclinations in two-dimensional crystals. Our model, based on the nonlinear
physics of thin elastic shells, produces excellent one parameter fits in real
space to the full three-dimensional shape of large spherical viruses. The
faceted shape depends only on the dimensionless Foppl-von Karman number
\gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the
protein shell, \kappa is its bending rigidity and R is the mean virus radius.
The shape can be parameterized more quantitatively in terms of a spherical
harmonic expansion. We also investigate elastic shell theory for extremely
large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral
shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure
On the equilibria of finely discretized curves and surfaces
Our goal is to identify the type and number of static equilibrium points of
solids arising from fine, equidistant -discretrizations of smooth, convex
surfaces. We assume uniform gravity and a frictionless, horizontal, planar
support. We show that as approaches infinity these numbers fluctuate around
specific values which we call the imaginary equilibrium indices associated with
the approximated smooth surface. We derive simple formulae for these numbers in
terms of the principal curvatures and the radial distances of the equilibrium
points of the solid from its center of gravity. Our results are illustrated on
a discretized ellipsoid and match well the observations on natural pebble
surfaces.Comment: 21 pages, 2 figure
Nuclear effects in the Drell-Yan process at very high energies
We study Drell-Yan (DY) dilepton production in proton(deuterium)-nucleus and
in nucleus-nucleus collisions within the light-cone color dipole formalism.
This approach is especially suitable for predicting nuclear effects in the DY
cross section for heavy ion collisions, as it provides the impact parameter
dependence of nuclear shadowing and transverse momentum broadening, quantities
that are not available from the standard parton model. For p(D)+A collisions we
calculate nuclear shadowing and investigate nuclear modification of the DY
transverse momentum distribution at RHIC and LHC for kinematics corresponding
to coherence length much longer than the nuclear size. Calculations are
performed separately for transversely and longitudinally polarized DY photons,
and predictions are presented for the dilepton angular distribution.
Furthermore, we calculate nuclear broadening of the mean transverse momentum
squared of DY dileptons as function of the nuclear mass number and energy. We
also predict nuclear effects for the cross section of the DY process in heavy
ion collisions. We found a substantial nuclear shadowing for valence quarks,
stronger than for the sea.Comment: 46 pages, 18 figures, title changed and some discussion added,
accepted for publication in PR
The PHENIX Experiment at RHIC
The physics emphases of the PHENIX collaboration and the design and current
status of the PHENIX detector are discussed. The plan of the collaboration for
making the most effective use of the available luminosity in the first years of
RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program
available at http://www.rhic.bnl.gov/phenix
The parent?infant dyad and the construction of the subjective self
Developmental psychology and psychopathology has in the past been more concerned with the quality of self-representation than with the development of the subjective agency which underpins our experience of feeling, thought and action, a key function of mentalisation. This review begins by contrasting a Cartesian view of pre-wired introspective subjectivity with a constructionist model based on the assumption of an innate contingency detector which orients the infant towards aspects of the social world that react congruently and in a specifically cued informative manner that expresses and facilitates the assimilation of cultural knowledge. Research on the neural mechanisms associated with mentalisation and social influences on its development are reviewed. It is suggested that the infant focuses on the attachment figure as a source of reliable information about the world. The construction of the sense of a subjective self is then an aspect of acquiring knowledge about the world through the caregiver's pedagogical communicative displays which in this context focuses on the child's thoughts and feelings. We argue that a number of possible mechanisms, including complementary activation of attachment and mentalisation, the disruptive effect of maltreatment on parent-child communication, the biobehavioural overlap of cues for learning and cues for attachment, may have a role in ensuring that the quality of relationship with the caregiver influences the development of the child's experience of thoughts and feelings
Evaluation of sesamum gum as an excipient in matrix tablets
In developing countries modern medicines are often beyond the affordability of the majority of the population. This is due to the reliance on expensive imported raw materials despite the abundance of natural resources which could provide an equivalent or even an improved function. The aim of this study was to investigate the potential of sesamum gum (SG) extracted from the leaves of Sesamum radiatum (readily cultivated in sub-Saharan Africa) as a matrix former. Directly compressed matrix tablets were prepared from the extract and compared with similar matrices of HPMC (K4M) using theophylline as a model water soluble drug. The compaction, swelling, erosion and drug release from the matrices were studied in deionized water, 0.1 N HCl (pH 1.2) and phosphate buffer (pH 6.8) using USP apparatus II. The data from the swelling, erosion and drug release studies were also fitted into the respective mathematical models. Results showed that the matrices underwent a combination of swelling and erosion, with the swelling action being controlled by the rate of hydration in the medium. SG also controlled the release of theophylline similar to the HPMC and therefore may have use as an alternative excipient in regions where Sesamum radiatum can be easily cultivated
Electrode surface treatment and electrochemical impedance spectroscopy study on carbon/carbon supercapacitors
Power improvement in supercapacitors is mainly
related to lowering the internal impedance. The real part of
the impedance at a given frequency is called ESR (equivalent
series resistance). Several contributions are included in the ESR: the electrolyte resistance (including the separator), the active material resistance (with both ionic and electronic parts) and the active material/current collector interface resistance. The first two contributions have been intensively described and studied by many authors. The first part of this paper is focused on the use of surface treatments as a way to decrease the active
material/current collector impedance. Al current collector
foils have been treated following a two-step procedure: electrochemical etching and sol-gel coating by a highly-covering, conducting carbonaceous material. It aims to increase the Al foil/active material surface contact leading to lower resistance. In a second part, carbon-carbon supercapacitor impedance is discussed in term of complex capacitance and complex power from electrochemical impedance spectroscopy data. This representation permits extraction of a relaxation time constant that provides important information on supercapacitor behaviour. The influence of carbon nanotubes addition on electrochemical performance of carbon/carbon supercapacitors has also been studied by electrochemical impedance spectroscopy
- …