442 research outputs found
Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model
In this paper, we investigated a density-dependent reaction-diffusion
equation, . This equation is known as the
extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is
widely used in the population dynamics, combustion theory and plasma physics.
By employing the suitable transformation, this equation was mapped to the
anomalous diffusion equation where the nonlinear reaction term was eliminated.
Due to its simpler form, some exact self-similar solutions with the compact
support have been obtained. The solutions, evolving from an initial state,
converge to the usual traveling wave at a certain transition time. Hence, it is
quite clear the connection between the self-similar solution and the traveling
wave solution from these results. Moreover, the solutions were found in the
manner that either propagates to the right or propagates to the left.
Furthermore, the two solutions form a symmetric solution, expanding in both
directions. The application on the spatiotemporal pattern formation in
biological population has been mainly focused.Comment: 5 pages, 2 figures, accepted by Phys. Rev.
Velocity fluctuations of population fronts propagating into metastable states
The position of propagating population fronts fluctuates because of the
discreteness of the individuals and stochastic character of processes of birth,
death and migration. Here we consider a Markov model of a population front
propagating into a metastable state, and focus on the weak noise limit. For
typical, small fluctuations the front motion is diffusive, and we calculate the
front diffusion coefficient. We also determine the probability distribution of
rare, large fluctuations of the front position and, for a given average front
velocity, find the most likely population density profile of the front.
Implications of the theory for population extinction risk are briefly
considered.Comment: 8 pages, 3 figure
Bose-Einstein condensation in an optical lattice: A perturbation approach
We derive closed analytical expressions for the order parameter
and for the chemical potential of a Bose-Einstein Condensate loaded into
a harmonically confined, one dimensional optical lattice, for sufficiently
weak, repulsive or attractive interaction, and not too strong laser
intensities. Our results are compared with exact numerical calculations in
order to map out the range of validity of the perturbative analytical approach.
We identify parameter values where the optical lattice compensates the
interaction-induced nonlinearity, such that the condensate ground state
coincides with a simple, single particle harmonic oscillator wave function
Coronavirus: Scientific insights and societal aspects
In December 2019, the first case of infection with a new virus COVID-19 (SARS-CoV-2), named coronavirus, was reported in the city of Wuhan, China. At that time, almost nobody paid any attention to it. The new pathogen, however, fast proved to be extremely infectious and dangerous, resulting in about 3–5% mortality. Over the few months that followed, coronavirus has spread over entire world. At the end of March, the total number of infections is fast approaching the psychological threshold of one million, resulting so far in tens of thousands of deaths. Due to the high number of lives already lost and the virus high potential for further spread, and due to its huge overall impact on the economies and societies, it is widely admitted that coronavirus poses the biggest challenge to the humanity after the second World war. The COVID-19 epidemic is provoking numerous questions at all levels. It also shows that modern society is extremely vulnerable and unprepared to such events. A wide scientific and public discussion becomes urgent. Some possible directions of this discussion are suggested in this article
Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks
Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation
The null energy condition and instability
We extend previous work showing that violation of the null energy condition
implies instability in a broad class of models, including gauge theories with
scalar and fermionic matter as well as any perfect fluid. Simple examples are
given to illustrate these results. The role of causality in our results is
discussed. Finally, we extend the fluid results to more general systems in
thermal equilibrium. When applied to the dark energy, our results imply that w
is unlikely to be less than -1.Comment: 11 pages, 5 figures, Revte
Synchronized dynamics of Tipula paludosa metapopulation in a southwestern Scotland agroecosystem: Linking pattern to process
Synchronization of population fluctuations at disjoint habitats has been observed in many studies, but its mechanisms often remain obscure. Synchronization may appear as a result of either interhabitat dispersal or regionally correlated environmental stochastic factors, the latter being known as the Moran effect. In this article, we consider the population dynamics of a common agricultural pest insect, Tipula paludosa, on a fragmented habitat by analyzing data derived from a multiannual survey of its abundance in 38 agricultural fields in southwestern Scotland. We use cross-correlation coefficients and show that there is a considerable synchronization between different populations across the whole area. The correlation strength exhibits an intermittent behavior, such that close populations can be virtually uncorrelated, but populations separated by distances up to approximately 150 km can have a cross-correlation coefficient close to one. To distinguish between the effects of stochasticity and dispersal, we then calculate a time-lagged cross-correlation coefficient and show that it possesses considerably different properties to the nonlagged one. In particular, the time-lagged correlation coefficient shows a clear directional dependence. The distribution of the time-lagged correlations with respect to the bearing between the populations has a striking similarity to the distribution of wind velocities, which we regard as evidence of long-distance wind-assisted dispersal
Spontaneous synchronization of two bistable pyridine-furan nanosprings connected by an oligomeric bridge
The intensive development of nanodevices acting as two-state systems has
motivated the search for nanoscale molecular structures whose long-term
conformational dynamics are similar to the dynamics of bistable mechanical
systems such as Euler arches and Duffing oscillators. Collective synchrony in
bistable dynamics of molecular-sized systems has attracted immense attention as
a potential pathway to amplify the output signals of molecular nanodevices.
Recently, pyridin-furan oligomers of helical shape that are a few nanometers in
size and exhibit bistable dynamics similar to a Duffing oscillator have been
identified through molecular dynamics simulations. In this article, we present
the case of dynamical synchronization of these bistable systems. We show that
two pyridine-furan springs connected by a rigid oligomeric bridge spontaneously
synchronize vibrations and stochastic resonance enhances the synchronization
effect
Using a multi-lens framework for landscape decisions
1. Landscape decisions are multi-faceted. Framing landscape decision-making as a governance process that requires a collective approach can encourage key stakeholders to come together to co-inform a discussion about their priorities and what constitutes good governance, leading to more holistic landscape decisions.
2. In this paper, we recognise that a suite of complementary and multi-dimensional approaches are in practice used to inform and evaluate land use decisions. We have called these approaches ‘lenses’ because they each provide a different perspective on the same problem. The four lenses are: i) Power and Market Gain, ii) Ecosystem Services, iii), Place-based Identity and iv) Ecocentric. Each brings a different set of evidence and viewpoints (narrative, qualitative and experiential, as well as quantitative metrics such as monetary) to the decision-making process and can potentially reveal problems and solutions that others do not.
3. Considering all lenses together allows dialogue to take place which can reveal the true complexities of landscape decision-making and can facilitate more effective and more holistic decisions. Employing the lenses requires governance structures that give equal weight to all lenses, enable dialogue and coexistence between top down and bottom-up approaches, and permit adaptation to local and granular place-specifics rather than developing “one-size-fits-all” solutions.
4. We propose that formalising the process of balancing all the lenses requires public participation, and that a lens approach should be used to support landscape decisions alongside a checklist that facilitates transparency in the conversation, showing how all evidence has been considered and critically assessed
- …