Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model

In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. 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

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

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

Diagonal form factors and heavy-heavy-light three-point functions at weak coupling

In this paper we consider a special kind of three-point functions of HHL type at weak coupling in N = 4 SYM theory and analyze its volume dependence. At strong coupling this kind of three-point functions were studied recently by Bajnok, Janik and Wereszczynski. The authors considered some cases of HHL correlator in the su(2) sector and, relying on their explicit results, formulated a conjecture about the form of the volume dependence of the symmetric HHL structure constant to be valid at any coupling up to wrapping corrections. In order to test this hypothesis we considered the HHL correlator in su(2) sector at weak coupling and directly showed that, up to one loop, the finite volume dependence has exactly the form proposed in. Another side of the conjecture suggests that computation of the symmetric structure constant is equivalent to computing the corresponding set of infinite volume form factors, which can be extracted as the coefficients of finite volume expansion. In this sense, extracting appropriate coefficients from our result gives a prediction for the corresponding infinite volume form factors

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 Vibrations and Stochastic Resonance of Short Oligomeric Springs

There is growing interest in molecular structures that exhibit dynamics similar to bistable mechanical systems. These structures have the potential to be used as nanodevices with two distinct states. Particularly intriguing are structures that display spontaneous vibrations and stochastic resonance. Previously, through molecular dynamics simulations, it was discovered that short pyridine-furan springs, when subjected to force loading, exhibit the bistable dynamics of a Duffing oscillator. In this study, we extend these simulations to include short pyridine-pyrrole and pyridine-furan springs in a hydrophobic solvent. Our findings demonstrate that these systems also display the bistable dynamics of a Duffing oscillator, accompanied by spontaneous vibrations and stochastic resonance activated by thermal noise.Comment: arXiv admin note: substantial text overlap with arXiv:2110.0409

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