13,820 research outputs found
Bond Order via Light-Induced Synthetic Many-body Interactions of Ultracold Atoms in Optical Lattices
We show how bond order emerges due to light mediated synthetic interactions
in ultracold atoms in optical lattices in an optical cavity. This is a
consequence of the competition between both short- and long-range interactions
designed by choosing the optical geometry. Light induces effective many-body
interactions that modify the landscape of quantum phases supported by the
typical Bose-Hubbard model. Using exact diagonalization of small system sizes
in one dimension, we present the many-body quantum phases the system can
support via the interplay between the density and bond (or matter-wave
coherence) interactions. We find numerical evidence to support that dimer
phases due to bond order are analogous to valence bond states. Different
possibilities of light-induced atomic interactions are considered that go
beyond the typical atomic system with dipolar and other intrinsic interactions.
This will broaden the Hamiltonian toolbox available for quantum simulation of
condensed matter physics via atomic systems.Comment: Accepted in New Journal of Physic
Stability of a stochastically perturbed model of intracellular single-stranded RNA virus replication
Replication of single-stranded RNA virus can be complicated, compared to that
of double-stranded virus, as it require production of intermediate antigenomic
strands that then serve as template for the genomic-sense strands. Moreover,
for ssRNA viruses, there is a variability of the molecular mechanism by which
genomic strands can be replicated. A combination of such mechanisms can also
occur: a fraction of the produced progeny may result from a stamping-machine
type of replication that uses the parental genome as template, whereas others
may result from the replication of progeny genomes. F. Mart\'{\i}nez et al. and
J. Sardany\'{e}s at al. suggested a deterministic ssRNA virus intracellular
replication model that allows for the variability in the replication
mechanisms.
To explore how stochasticity can affect this model principal properties, in
this paper we consider the stability of a stochastically perturbed model of
ssRNA virus replication within a cell. Using the direct Lyapunov method, we
found sufficient conditions for the stability in probability of equilibrium
states for this model. This result confirms that this heterogeneous model of
single-stranded RNA virus replication is stable with respect to stochastic
perturbations of the environment
On a general implementation of - and -adaptive curl-conforming finite elements
Edge (or N\'ed\'elec) finite elements are theoretically sound and widely used
by the computational electromagnetics community. However, its implementation,
specially for high order methods, is not trivial, since it involves many
technicalities that are not properly described in the literature. To fill this
gap, we provide a comprehensive description of a general implementation of edge
elements of first kind within the scientific software project FEMPAR. We cover
into detail how to implement arbitrary order (i.e., -adaptive) elements on
hexahedral and tetrahedral meshes. First, we set the three classical
ingredients of the finite element definition by Ciarlet, both in the reference
and the physical space: cell topologies, polynomial spaces and moments. With
these ingredients, shape functions are automatically implemented by defining a
judiciously chosen polynomial pre-basis that spans the local finite element
space combined with a change of basis to automatically obtain a canonical basis
with respect to the moments at hand. Next, we discuss global finite element
spaces putting emphasis on the construction of global shape functions through
oriented meshes, appropriate geometrical mappings, and equivalence classes of
moments, in order to preserve the inter-element continuity of tangential
components of the magnetic field. Finally, we extend the proposed methodology
to generate global curl-conforming spaces on non-conforming hierarchically
refined (i.e., -adaptive) meshes with arbitrary order finite elements.
Numerical results include experimental convergence rates to test the proposed
implementation
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