1,715 research outputs found
Semigroup analysis of structured parasite populations
Motivated by structured parasite populations in aquaculture we consider a
class of size-structured population models, where individuals may be recruited
into the population with distributed states at birth. The mathematical model
which describes the evolution of such a population is a first-order nonlinear
partial integro-differential equation of hyperbolic type. First, we use
positive perturbation arguments and utilise results from the spectral theory of
semigroups to establish conditions for the existence of a positive equilibrium
solution of our model. Then, we formulate conditions that guarantee that the
linearised system is governed by a positive quasicontraction semigroup on the
biologically relevant state space. We also show that the governing linear
semigroup is eventually compact, hence growth properties of the semigroup are
determined by the spectrum of its generator. In the case of a separable
fertility function, we deduce a characteristic equation, and investigate the
stability of equilibrium solutions in the general case using positive
perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen
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Problematic Internet Use and Problematic Online Gaming Are Not the Same: Findings from a Large Nationally Representative Adolescent Sample
There is an ongoing debate in the literature whether problematic internet use (PIU) and problematic online gaming (POG) are two distinct conceptual and nosological entities or whether they are the same. The present study contributes to this question by examining the interrelationship and the overlap between PIU and POG in terms of gender, school achievement, time spent using the internet and/or online gaming, psychological wellbeing, and preferred online activities. Questionnaires assessing these variables were administered to a nationally representative sample of adolescent gamers (N=2,073; mean age 16.4 years, SD=0.87, 68.4% male). Data showed that internet use was a common activity among adolescents while online gaming was engaged in by a considerably smaller group. Similarly, more adolescents met the criteria for PIU than for POG and a small group of adolescents showed symptoms of both problem behaviors. The most notable difference between the two problem behaviors was in terms of gender. POG was much more strongly associated with being male. Self-esteem had low effect sizes on both behaviors, while depressive symptoms were associated with both PIU and POG, affecting PIU slightly more. In terms of preferred online activities, PIU was positively associated with online gaming, online chatting, and social networking while POG was only associated with online gaming. Based on our findings POG appears to be a conceptually different behavior than PIU and therefore data support the notion that Internet Addiction Disorder and Internet Gaming Disorder are separate nosological entities
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
Coupling between static friction force and torque for a tripod
If a body is resting on a flat surface, the maximal static friction force
before motion sets in is reduced if an external torque is also applied. The
coupling between the static friction force and static friction torque is
nontrivial as our studies for a tripod lying on horizontal flat surface show.
In this article we report on a series of experiments we performed on a tripod
and compare these with analytical and numerical solutions. It turns out that
the coupling between force and torque reveals information about the microscopic
properties at the onset to sliding.Comment: 7 pages, 4 figures, revte
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
DNA uptake into nuclei: Numerical and analytical results
The dynamics of polymer translocation through a pore has been the subject of
recent theoretical and experimental works. We have considered theoretical
estimates and performed computer simulations to understand the mechanism of DNA
uptake into the cell nucleus, a phenomenon experimentally investigated by
attaching a small bead to the free end of the double helix and pulling this
bead with the help of an optical trap. The experiments show that the uptake is
monotonous and slows down when the remaining DNA segment becomes very short.
Numerical and analytical studies of the entropic repulsion between the DNA
filament and the membrane wall suggest a new interpretation of the experimental
observations. Our results indicate that the repulsion monotonically decreases
as the uptake progresses. Thus, the DNA is pulled in (i) either by a small
force of unknown origin, and then the slowing down can be interpreted only
statistically; (ii) or by a strong but slow ratchet mechanism, which would
naturally explain the observed monotonicity, but then the slowing down requires
additional explanations. Only further experiments can unambiguously distinguish
between these two mechanisms.Comment: 12 pages, 6 figures, submitted to J. Phys. Cond. Ma
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