5,414 research outputs found
Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields
The S-matrix theory formulation of closed-orbit theory recently proposed by
Granger and Greene is extended to atoms in crossed electric and magnetic
fields. We then present a semiclassical quantization of the hydrogen atom in
crossed fields, which succeeds in resolving individual lines in the spectrum,
but is restricted to the strongest lines of each n-manifold. By means of a
detailed semiclassical analysis of the quantum spectrum, we demonstrate that it
is the abundance of bifurcations of closed orbits that precludes the resolution
of finer details. They necessitate the inclusion of uniform semiclassical
approximations into the quantization process. Uniform approximations for the
generic types of closed-orbit bifurcation are derived, and a general method for
including them in a high-resolution semiclassical quantization is devised
Higher order glass-transition singularities in colloidal systems with attractive interactions
The transition from a liquid to a glass in colloidal suspensions of particles
interacting through a hard core plus an attractive square-well potential is
studied within the mode-coupling-theory framework. When the width of the
attractive potential is much shorter than the hard-core diameter, a reentrant
behavior of the liquid-glass line, and a glass-glass-transition line are found
in the temperature-density plane of the model. For small well-width values, the
glass-glass-transition line terminates in a third order bifurcation point, i.e.
in a A_3 (cusp) singularity. On increasing the square-well width, the
glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail)
singularity at a critical well width. Close to the A_3 and A_4 singularities
the decay of the density correlators shows stretching of huge dynamical
windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin
Comparative simulation study of colloidal gels and glasses
Using computer simulations, we identify the mechanisms causing aggregation
and structural arrest of colloidal suspensions interacting with a short-ranged
attraction at moderate and high densities. Two different non-ergodicity
transitions are observed. As the density is increased, a glass transition takes
place, driven by excluded volume effects. In contrast, at moderate densities,
gelation is approached as the strength of the attraction increases. At high
density and interaction strength, both transitions merge, and a logarithmic
decay in the correlation function is observed. All of these features are
correctly predicted by mode coupling theory
Evidence for Unusual Dynamical Arrest Scenario in Short Ranged Colloidal Systems
Extensive molecular dynamics simulation studies of particles interacting via
a short ranged attractive square-well (SW) potential are reported. The
calculated loci of constant diffusion coefficient in the
temperature-packing fraction plane show a re-entrant behavior, i.e. an increase
of diffusivity on cooling, confirming an important part of the high
volume-fraction dynamical-arrest scenario earlier predicted by theory for
particles with short ranged potentials. The more efficient localization
mechanism induced by the short range bonding provides, on average, additional
free volume as compared to the hard-sphere case and results in faster dynamics.Comment: 4 pages, 3 figure
Molecular dynamics simulation of the fragile glass former ortho-terphenyl: a flexible molecule model
We present a realistic model of the fragile glass former orthoterphenyl and
the results of extensive molecular dynamics simulations in which we
investigated its basic static and dynamic properties. In this model the
internal molecular interactions between the three rigid phenyl rings are
described by a set of force constants, including harmonic and anharmonic terms;
the interactions among different molecules are described by Lennard-Jones
site-site potentials. Self-diffusion properties are discussed in detail
together with the temperature and momentum dependencies of the
self-intermediate scattering function. The simulation data are compared with
existing experimental results and with the main predictions of the Mode
Coupling Theory.Comment: 20 pages and 28 postscript figure
Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study
Previous theoretical, along with early simulation and experimental, studies
have indicated that particles with a short-ranged attraction exhibit a range of
new dynamical arrest phenomena. These include very pronounced reentrance in the
dynamical arrest curve, a logarithmic singularity in the density correlation
functions, and the existence of `attractive' and `repulsive' glasses. Here we
carry out extensive molecular dynamics calculations on dense systems
interacting via a square-well potential. This is one of the simplest systems
with the required properties, and may be regarded as canonical for interpreting
the phase diagram, and now also the dynamical arrest. We confirm the
theoretical predictions for re-entrance, logarithmic singularity, and give the
first direct evidence of the coexistence, independent of theory, of the two
coexisting glasses. We now regard the previous predictions of these phenomena
as having been established.Comment: 15 pages,15 figures; submitted to Phys. Rev.
Dynamics in a supercooled molecular liquid: Theory and Simulations
We report extensive simulations of liquid supercooled states for a simple
three-sites molecular model, introduced by Lewis and Wahnstr"om [L. J. Lewis
and G. Wahnstr"om, Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of
ortho-terphenyl. The large system size and the long simulation length allow to
calculate very precisely --- in a large q-vector range --- self and collective
correlation functions, providing a clean and simple reference model for
theoretical descriptions of molecular liquids in supercooled states. The time
and wavevector dependence of the site-site correlation functions are compared
with detailed predictions based on ideal mode-coupling theory, neglecting the
molecular constraints. Except for the wavevector region where the dynamics is
controlled by the center of mass (around 9 nm-1), the theoretical predictions
compare very well with the simulation data.
Metastable Dynamics of the Hard-Sphere System
The reformulation of the mode-coupling theory (MCT) of the liquid-glass
transition which incorporates the element of metastability is applied to the
hard-sphere system. It is shown that the glass transition in this system is not
a sharp one at the special value of the density or the packing fraction, which
is in contrast to the prediction by the conventional MCT. Instead we find that
the slowing down of the dynamics occurs over a range of values of the packing
fraction. Consequently, the exponents governing the sequence of time
relaxations in the intermediate time regime are given as functions of packing
fraction with one additional parameter which describes the overall scale of the
metastable potential energy for defects in the hard-sphere system. Implications
of the present model on the recent experiments on colloidal systems are also
discussed.Comment: 21 pages, 5 figures (available upon request), RevTEX3.0, JFI
Preprint
Conversational correlates of children's acquisition of mental verbs and a theory of mind
The purpose of this study was to conduct a detailed examination of the ways mothers use mental verbs in conversations with three- and four-year-old children, and to link these usages to the children's developing understanding of mental verbs and a theory of mind. Sixty three- and four-year-olds, either attending preschool (PS) or not (NPS) were given tasks assessing mental verb distinctions and false belief. Their mothers' mental verb use was coded for (a) frequency, (b) type of utterance, (c) type of subordinate clause, (d) the person of the subject of the verb, and (e) the certainty of think. Within the three-year-olds, the NPS children performed significantly better on the mental verb comprehension task; moreover, compared to the PS mothers, the NPS mothers were found to use: (1) less statements and more questions, (2) less first person utterances and more second person utterances, and (3) think in its `very certain' form less often. In regression analyses, children's mental verb and false belief performance were positively predicted by maternal mental verb 1) questions, and 2) single clause utterances; the children's performance was negatively predicted by statements. These findings indicate how maternal input has the potential to promote or hinder children's understanding of the mind.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline
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