4,466 research outputs found
Size-structured populations: immigration, (bi)stability and the net growth rate
We consider a class of physiologically structured population models, a first
order nonlinear partial differential equation equipped with a nonlocal boundary
condition, with a constant external inflow of individuals. We prove that the
linearised system is governed by a quasicontraction semigroup. We also
establish that linear stability of equilibrium solutions is governed by a
generalized net reproduction function. In a special case of the model
ingredients we discuss the nonlinear dynamics of the system when the spectral
bound of the linearised operator equals zero, i.e. when linearisation does not
decide stability. This allows us to demonstrate, through a concrete example,
how immigration might be beneficial to the population. In particular, we show
that from a nonlinearly unstable positive equilibrium a linearly stable and
unstable pair of equilibria bifurcates. In fact, the linearised system exhibits
bistability, for a certain range of values of the external inflow, induced
potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin
The Invariant Measures of some Infinite Interval Exchange Maps
We classify the locally finite ergodic invariant measures of certain infinite
interval exchange transformations (IETs). These transformations naturally arise
from return maps of the straight-line flow on certain translation surfaces, and
the study of the invariant measures for these IETs is equivalent to the study
of invariant measures for the straight-line flow in some direction on these
translation surfaces. For the surfaces and directions for which our methods
apply, we can characterize the locally finite ergodic invariant measures of the
straight-line flow in a set of directions of Hausdorff dimension larger than
1/2. We promote this characterization to a classification in some cases. For
instance, when the surfaces admit a cocompact action by a nilpotent group, we
prove each ergodic invariant measure for the straight-line flow is a Maharam
measure, and we describe precisely which Maharam measures arise. When the
surfaces under consideration are finite area, the straight-line flows in the
directions we understand are uniquely ergodic. Our methods apply to translation
surfaces admitting multi-twists in a pair of cylinder decompositions in
non-parallel directions.Comment: 107 pages, 11 figures. Minor improvement
Steady states in a structured epidemic model with Wentzell boundary condition
We introduce a nonlinear structured population model with diffusion in the
state space. Individuals are structured with respect to a continuous variable
which represents a pathogen load. The class of uninfected individuals
constitutes a special compartment that carries mass, hence the model is
equipped with generalized Wentzell (or dynamic) boundary conditions. Our model
is intended to describe the spread of infection of a vertically transmitted
disease, for example Wolbachia in a mosquito population. Therefore the
(infinite dimensional) nonlinearity arises in the recruitment term. First we
establish global existence of solutions and the Principle of Linearised
Stability for our model. Then, in our main result, we formulate simple
conditions, which guarantee the existence of non-trivial steady states of the
model. Our method utilizes an operator theoretic framework combined with a
fixed point approach. Finally, in the last section we establish a sufficient
condition for the local asymptotic stability of the positive steady state
Segregation of granular binary mixtures by a ratchet mechanism
We report on a segregation scheme for granular binary mixtures, where the
segregation is performed by a ratchet mechanism realized by a vertically shaken
asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied
this system by computer simulations and found that most binary mixtures can be
segregated using an appropriately chosen ratchet, even when the particles in
the two components have the same size, and differ only in their normal
restitution coefficient or friction coefficient. These results suggest that the
components of otherwise non-segregating granular mixtures may be separated
using our method.Comment: revtex, 4 pages, 4 figures, submitte
Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density ~g/cm, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate , the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that , the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Model systems in SDHx-related pheochromocytoma/paraganglioma
Pheochromocytoma (PHEO) and paraganglioma (PGL) (together PPGL) are tumors with poor outcomes that arise from neuroendocrine cells in the adrenal gland, and sympathetic and parasympathetic ganglia outside the adrenal gland, respectively. Many follow germline mutations in genes coding for subunits of succinate dehydrogenase (SDH), a tetrameric enzyme in the tricarboxylic acid (TCA) cycle that both converts succinate to fumarate and participates in electron transport. Germline SDH subunit B (SDHB) mutations have a high metastatic potential. Herein, we review the spectrum of model organisms that have contributed hugely to our understanding of SDH dysfunction. In Saccharomyces cerevisiae (yeast), succinate accumulation inhibits alpha-ketoglutarate-dependent dioxygenase enzymes leading to DNA demethylation. In the worm Caenorhabditis elegans, mutated SDH creates developmental abnormalities, metabolic rewiring, an energy deficit and oxygen hypersensitivity (the latter is also found in Drosophila melanogaster). In the zebrafish Danio rerio, sdhb mutants display a shorter lifespan with defective energy metabolism. Recently, SDHB-deficient pheochromocytoma has been cultivated in xenografts and has generated cell lines, which can be traced back to a heterozygous SDHB-deficient rat. We propose that a combination of such models can be efficiently and effectively used in both pathophysiological studies and drug-screening projects in order to find novel strategies in PPGL treatment
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