2,744 research outputs found
Discrete Symmetries of Complete Intersection Calabi-Yau Manifolds
In this paper, we classify non-freely acting discrete symmetries of complete
intersection Calabi- Yau manifolds and their quotients by freely-acting
symmetries. These non-freely acting symmetries can appear as symmetries of
low-energy theories resulting from string compactifications on these Calabi-Yau
manifolds, particularly in the context of the heterotic string. Hence, our
results are relevant for four-dimensional model building with discrete
symmetries and they give an indication which symmetries of this kind can be
expected from string theory. For the 1695 known quotients of complete
intersection manifolds by freely-acting discrete symmetries, non-freely-acting,
generic symmetries arise in 381 cases and are, therefore, a relatively common
feature of these manifolds. We find that 9 different discrete groups appear,
ranging in group order from 2 to 18, and that both regular symmetries and
R-symmetries are possible.Comment: 23 pages; minor changes: updated a reference, removed unclear
sentenc
Highly Symmetric Quintic Quotients
The quintic family must be the most studied family of Calabi-Yau threefolds.
Particularly symmetric members of this family are known to admit quotients by
freely acting symmetries isomorphic to . The
corresponding quotient manifolds may themselves be symmetric. That is, they may
admit symmetries that descend from the symmetries that the manifold enjoys
before the quotient is taken. The formalism for identifying these symmetries
was given a long time ago by Witten and instances of these symmetric quotients
were given also, for the family , by Goodman and
Witten. We rework this calculation here, with the benefit of computer
assistance, and provide a complete classification. Our motivation is largely to
develop methods that apply also to the analysis of quotients of other CICY
manifolds, whose symmetries have been classified recently. For the
quotients of the quintic family, our list
contains families of smooth manifolds with symmetry ,
and , families of singular manifolds with four
conifold points, with symmetry and , and rigid
manifolds, each with at least a curve of singularities, and symmetry
. We intend to return to the computation of the symmetries of
the quotients of other CICYs elsewhere.Comment: 18 pages, 8 table
Synchronisation of stochastic oscillators in biochemical systems
A formalism is developed which describes the extent to which stochastic
oscillations in biochemical models are synchronised. It is based on the
calculation of the complex coherence function within the linear noise
approximation. The method is illustrated on a simple example and then applied
to study the synchronisation of chemical concentrations in social amoeba. The
degree to which variation of rate constants in different cells and the volume
of the cells affects synchronisation of the oscillations is explored, and the
phase lag calculated. In all cases the analytical results are shown to be in
good agreement with those obtained through numerical simulations
A Semester on the Road to Santiago: The Long-term Impacts of Walking the Camino de Santiago with a Family-like Study Abroad Group
In this paper, research findings are presented from a small, longitudinal study using qualitative data on the long-term impacts of a unique, semester-long, study abroad program at Franklin Pierce University. In this programme, students study the history and contemporary renaissance of the Camino de Santiago pilgrimage and then walk the entire route in northern Spain as pilgrims. Alumni who participated in one of four trips conducted in the fall of 2011, 2013, 2015 and 2017 were asked in 2022 to respond to five open-ended questions about how their semester abroad impacted their lives, to what degree they thought their study-abroad group functioned as a ‘family’ and how that impacted their experience. Twenty-one alumni responded to the questionnaire; all indicating to varying degrees that the program had life-changing impacts that had influenced and were continuing to shape their lives. Their responses are organised into seven themes that describe the long-term impacts of the program. The researcher’s interpretations also draw on his memories and extensive field notes on experiences that occurred on the four trips, as well as the reflective essays students wrote based on their personal journals immediately upon their return from their semester abroad. The results are situated in the context of research on short and long-term impacts of study abroad and within the liberal education mission of U.S. institutions of higher education
Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos
We develop a formalism to describe the discrete-time dynamics of systems
containing an arbitrary number of interacting species. The individual-based
model, which forms our starting point, is described by a Markov chain, which in
the limit of large system sizes is shown to be very well-approximated by a
Fokker-Planck-like equation, or equivalently by a set of stochastic difference
equations. This formalism is applied to the specific case of two species: one
predator species and its prey species. Quasi-cycles --- stochastic cycles
sustained and amplified by the demographic noise --- previously found in
continuous-time predator-prey models are shown to exist, and their behavior
predicted from a linear noise analysis is shown to be in very good agreement
with simulations. The effects of the noise on other attractors in the
corresponding deterministic map, such as periodic cycles, quasiperiodicity and
chaos, are also investigated.Comment: 21 pages, 12 figure
Suppressing escape events in maps of the unit interval with demographic noise
We explore the properties of discrete-time stochastic processes with a
bounded state space, whose deterministic limit is given by a map of the unit
interval. We find that, in the mesoscopic description of the system, the large
jumps between successive iterates of the process can result in probability
leaking out of the unit interval, despite the fact that the noise is
multiplicative and vanishes at the boundaries. By including higher-order terms
in the mesoscopic expansion, we are able to capture the non-Gaussian nature of
the noise distribution near the boundaries, but this does not preclude the
possibility of a trajectory leaving the interval. We propose a number of
prescriptions for treating these escape events, and we compare the results with
those obtained for the metastable behavior of the microscopic model, where
escape events are not possible. We find that, rather than truncating the noise
distribution, censoring this distribution to prevent escape events leads to
results which are more consistent with the microscopic model. The addition of
higher moments to the noise distribution does not increase the accuracy of the
final results, and it can be replaced by the simpler Gaussian noise.Comment: 14 pages, 13 figure
INVESTIGATION OF HIGH PERFORMANCE CHELATION ION CHROMATOGRAPHY FOR TRACE METAL DETERMINATIONS
ICI Chemicals & Polymers,
The Heath,
Runcorn,
Cheshire.
WA7 4QD.
U.K
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