Doubly nonlocal reaction-diffusion equation and the emergence of species

The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one describes reproduction with different phenotypes. Linear stability analysis of the homogeneous in space stationary solution is carried out. Existence of travelling waves is proved in the case of narrow kernels of the integrals. Periodic travelling waves are observed in numerical simulations. Existence of stationary solutions in the form of pulses is shown, and transition from periodic waves to pulses is studied. In the applications to the speciation theory, the results of this work signify that new species can emerge only if they do not have common offsprings. Thus, it is shown how Darwin's definition of species as groups of morphologically similar individuals is related to Mayr's definition as groups of individuals that can breed only among themselves.Comment: 15 pages, 4 figure

Re/making the 'Meeting Place' - Transforming Toronto's Public Spaces Through Creative Placemaking, Indigenous Story And Planning

The theme of Toronto as a middle ground has been often referenced by historians and archaeologists alike: "geographically a meeting point between Canada's vast natural resource wilderness, such Atlantic Ocean seaports as New York and Montreal, and the sprawling continental Midwest, and since prehistory, a place of meditation and exchange between different cultures and peoples" (Carruthers, 2008, p.7). The international community might know Toronto as one of the best cities in the world in liveability or quality of living (Mercer survey, 2016). Unfortunately, our city's important legacy as a middle ground or a "meeting point" has not been adequately celebrated both locally and internationally. The purpose of the research is to highlight the city's diverse culture and identity as a modern world city with a unique Indigenous heritage that goes back centuries, beyond the colonial era. Looking at history and its representation through the post-colonial lens, my research has the potential to not only build our unique sense of identity and pride as city's inhabitants, but to also serve as an important link in ongoing Canadian reconciliation efforts, in light of Truth and Reconciliation Commission (TRC) 2015 report and recommendations. I study how unearthing Toronto's forgotten/erased Indigenous historic narratives can remake our city a true "Meeting Place". I believe that by celebrating our pre-colonial history we have an opportunity to make Toronto more livable, more inclusive, more just city for all its Lefebvre's citadins. The research focuses on studying the city's Indigenous background, its current state of representation; on undertaking a comparative analysis of relative cases throughout the world; and on developing a local case study. Ideally, future steps will lead to establishing a centrally located art/history project and/or a network of small-scale public places where our Aboriginal history is showcased and celebrated. Toronto's story - our sense of place - will not be complete without acknowledging our Aboriginal roots. Beyond historical representation set in the past tense, it is imperative to talk in the present and even future language. Recognition of the continuous presence of Indigenous peoples on this territory is one of the building blocks in re-claiming the city by its Indigenous inhabitants. It is also an essential milestone in the process of Reconciliation

Computational Algorithm for Some Problems with Variable Geometrical Structure

International audienceThe work is devoted to the computational algorithm for a problem of plant growth. The plant is represented as a system of connected intervals corresponding to branches. We compute the concentration distributions inside the branches. The originality of the problem is that the geometry of the plant is not a priori given. It evolves in time depending on the concentrations of plant hormones found as a solution of the problem. New branches appear in the process of plant growth. The algorithm is adapted to an arbitrary plant structure and an arbitrary number of branches

Properness and Topological Degree for Nonlocal Reaction-Diffusion Operators

International audienceThe paper is devoted to integro-differential operators, which correspond to non-local reaction-diffusion equations considered on the whole axis. Their Fredholm property and properness will be proved. This will allow one to define the topological degree

Reaction-diffusion waves with nonlinear boundary conditions

International audienceA reaction-di usion equation with nonlinear boundary condition is considered in a two-dimensional in nite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method

Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order

We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding articl