1,819 research outputs found
New representation of orbital motion with arbitrary angular momenta
A new formulation is presented for a variational calculation of -body
systems on a correlated Gaussian basis with arbitrary angular momenta. The
rotational motion of the system is described with a single spherical harmonic
of the total angular momentum , and thereby needs no explicit coupling of
partial waves between particles. A simple generating function for the
correlated Gaussian is exploited to derive the matrix elements. The formulation
is applied to various Coulomb three-body systems such as , and up to in order to show its usefulness and
versatility. A stochastic selection of the basis functions gives good results
for various angular momentum states.Comment: Revte
‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions
This paper discusses the breakup of capillary jets of dilute polymer solutions and the dynamics associated with the transition from dripping to jetting. High-speed digital video imaging reveals a new scenario of transition and breakup via periodic growth and detachment of large terminal drops. The underlying mechanism is discussed and a basic theory for the mechanism of breakup is also presented. The dynamics of the terminal drop growth and trajectory prove to be governed primarily by mass and momentum balances involving capillary, gravity and inertial forces, whilst the drop detachment event is controlled by the kinetics of the thinning process in the viscoelastic ligaments that connect the drops. This thinning process of the ligaments that are subjected to a constant axial force is driven by surface tension and resisted by the viscoelasticity of the dissolved polymeric molecules. Analysis of this transition provides a new experimental method to probe the rheological properties of solutions when minute concentrations of macromolecules have been added.Schlumberger FoundationMIT Class of 1951 Fellowship Fun
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
Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters
We report a first-principles theoretical study of hyperfine interactions,
zero-point effects and defect energetics of muonium and hydrogen impurities in
silicon and germanium. The spin-polarized density functional method is used,
with the crystalline orbitals expanded in all-electron Gaussian basis sets. The
behaviour of hydrogen and muonium impurities at both the tetrahedral and
bond-centred sites is investigated within a supercell approximation. To
describe the zero-point motion of the impurities, a double adiabatic
approximation is employed in which the electron, muon/proton and host lattice
degrees of freedom are decoupled. Within this approximation the relaxation of
the atoms of the host lattice may differ for the muon and proton, although in
practice the difference is found to be slight. With the inclusion of zero-point
motion the tetrahedral site is energetically preferred over the bond-centred
site in both silicon and germanium. The hyperfine and superhyperfine
parameters, calculated as averages over the motion of the muon, agree
reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
Precise variational solutions are given for problems involving diverse
fermionic and bosonic -body systems. The trial wave functions are chosen
to be combinations of correlated Gaussians, which are constructed from products
of the single-particle Gaussian wave packets through an integral
transformation, thereby facilitating fully analytical calculations of the
matrix elements. The nonlinear parameters of the trial function are chosen by a
stochastic technique. The method has proved very efficient, virtually exact,
and it seems feasible for any few-body bound-state problems emerging in nuclear
or atomic physics.Comment: 39 pages (revtex) + 3 figures (appended as compressed uuencoded .ps
files
Proposal of an extended t-J Hamiltonian for high-Tc cuprates from ab initio calculations on embedded clusters
A series of accurate ab initio calculations on Cu_pO-q finite clusters,
properly embedded on the Madelung potential of the infinite lattice, have been
performed in order to determine the local effective interactions in the CuO_2
planes of La_{2-x}Sr_xCuO_4 compounds. The values of the first-neighbor
interactions, magnetic coupling (J_{NN}=125 meV) and hopping integral
(t_{NN}=-555 meV), have been confirmed. Important additional effects are
evidenced, concerning essentially the second-neighbor hopping integral
t_{NNN}=+110meV, the displacement of a singlet toward an adjacent colinear
hole, h_{SD}^{abc}=-80 meV, a non-negligible hole-hole repulsion
V_{NN}-V_{NNN}=0.8 eV and a strong anisotropic effect of the presence of an
adjacent hole on the values of the first-neighbor interactions. The dependence
of J_{NN} and t_{NN} on the position of neighbor hole(s) has been rationalized
from the two-band model and checked from a series of additional ab initio
calculations. An extended t-J model Hamiltonian has been proposed on the basis
of these results. It is argued that the here-proposed three-body effects may
play a role in the charge/spin separation observed in these compounds, that is,
in the formation and dynamic of stripes.Comment: 24 pages, 4 figures, submitted to Phys. Rev.
Maximally-localized generalized Wannier functions for composite energy bands
We discuss a method for determining the optimally-localized set of
generalized Wannier functions associated with a set of Bloch bands in a
crystalline solid. By ``generalized Wannier functions'' we mean a set of
localized orthonormal orbitals spanning the same space as the specified set of
Bloch bands. Although we minimize a functional that represents the total spread
sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method
proceeds directly from the Bloch functions as represented on a mesh of
k-points, and carries out the minimization in a space of unitary matrices
U_mn^k describing the rotation among the Bloch bands at each k-point. The
method is thus suitable for use in connection with conventional
electronic-structure codes. The procedure also returns the total electric
polarization as well as the location of each Wannier center. Sample results for
Si, GaAs, molecular C2H4, and LiCl will be presented.Comment: 22 pages, two-column style with 4 postscript figures embedded. Uses
REVTEX and epsf macros. Also available at
http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_wan
Evolutionary relationships between Rhynchosporium lolii sp. nov. and other Rhynchosporium species on grass.
Copyright: 2013 King et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedThe fungal genus Rhynchosporium (causative agent of leaf blotch) contains several host-specialised species, including R. commune (colonising barley and brome-grass), R. agropyri (couch-grass), R. secalis (rye and triticale) and the more distantly related R. orthosporum (cocksfoot). This study used molecular fingerprinting, multilocus DNA sequence data, conidial morphology, host range tests and scanning electron microscopy to investigate the relationship between Rhynchosporium species on ryegrasses, both economically important forage grasses and common wild grasses in many cereal growing areas, and other plant species. Two different types of Rhynchosporium were found on ryegrasses in the UK. Firstly, there were isolates of R. commune that were pathogenic to both barley and Italian ryegrass. Secondly, there were isolates of a new species, here named R. lolii, that were pathogenic only to ryegrass species. R. lolii was most closely related to R. orthosporum, but exhibited clear molecular, morphological and host range differences. The species was estimated to have diverged from R. orthosporum ca. 5735 years before the present. The colonisation strategy of all of the different Rhynchosporium species involved extensive hyphal growth in the sub-cuticular regions of the leaves. Finally, new species-specific PCR diagnostic tests were developed that could distinguish between these five closely related Rhynchosporium species.Peer reviewedFinal Published versio
Experimental and theoretical investigation of ligand effects on the synthesis of ZnO nanoparticles
ZnO nanoparticles with highly controllable particle sizes(less than 10 nm) were synthesized using organic capping ligands in Zn(Ac)2 ethanolic solution. The molecular structure of the ligands was found to have significant influence on the particle size. The multi-functional molecule tris(hydroxymethyl)-aminomethane (THMA) favoured smaller particle distributions compared with ligands possessing long hydrocarbon chains that are more frequently employed. The adsorption of capping ligands on ZnnOn crystal nuclei (where n = 4 or 18 molecular clusters of(0001) ZnO surfaces) was modelled by ab initio methods at the density functional theory (DFT) level. For the molecules examined, chemisorption proceeded via the formation of Zn...O, Zn...N, or Zn...S chemical bonds between the ligands and active Zn2+ sites on ZnO surfaces. The DFT results indicated that THMA binds more strongly to the ZnO surface than other ligands, suggesting that this molecule is very effective at stabilizing ZnO nanoparticle surfaces. This study, therefore, provides new insight into the correlation between the molecular structure of capping ligands and the morphology of metal oxide nanostructures formed in their presence
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