Well-posedness for a class of nonlinear degenerate parabolic equations

In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces

Covert Ephemeral Communication in Named Data Networking

In the last decade, there has been a growing realization that the current Internet Protocol is reaching the limits of its senescence. This has prompted several research efforts that aim to design potential next-generation Internet architectures. Named Data Networking (NDN), an instantiation of the content-centric approach to networking, is one such effort. In contrast with IP, NDN routers maintain a significant amount of user-driven state. In this paper we investigate how to use this state for covert ephemeral communication (CEC). CEC allows two or more parties to covertly exchange ephemeral messages, i.e., messages that become unavailable after a certain amount of time. Our techniques rely only on network-layer, rather than application-layer, services. This makes our protocols robust, and communication difficult to uncover. We show that users can build high-bandwidth CECs exploiting features unique to NDN: in-network caches, routers' forwarding state and name matching rules. We assess feasibility and performance of proposed cover channels using a local setup and the official NDN testbed

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Modeling characterization of the vertical and temporal variability of environmental DNA in the mesopelagic ocean

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Allan, E. A., DiBenedetto, M. H., Lavery, A. C., Govindarajan, A. F., & Zhang, W. G. Modeling characterization of the vertical and temporal variability of environmental DNA in the mesopelagic ocean. Scientific Reports, 11(1), (2021): 21273, https://doi.org/10.1038/s41598-021-00288-5.Increasingly, researchers are using innovative methods to census marine life, including identification of environmental DNA (eDNA) left behind by organisms in the water column. However, little is understood about how eDNA is distributed in the ocean, given that organisms are mobile and that physical and biological processes can transport eDNA after release from a host. Particularly in the vast mesopelagic ocean where many species vertically migrate hundreds of meters diurnally, it is important to link the location at which eDNA was shed by a host organism to the location at which eDNA was collected in a water sample. Here, we present a one-dimensional mechanistic model to simulate the eDNA vertical distribution after its release and to compare the impact of key biological and physical parameters on the eDNA vertical and temporal distribution. The modeled vertical eDNA profiles allow us to quantify spatial and temporal variability in eDNA concentration and to identify the most important parameters to consider when interpreting eDNA signals. We find that the vertical displacement by advection, dispersion, and settling has limited influence on the eDNA distribution, and the depth at which eDNA is found is generally within tens of meters of the depth at which the eDNA was originally shed from the organism. Thus, using information about representative vertical migration patterns, eDNA concentration variability can be used to answer ecological questions about migrating organisms such as what depths species can be found in the daytime and nighttime and what percentage of individuals within a species diurnally migrate. These findings are critical both to advance the understanding of the vertical distribution of eDNA in the water column and to link eDNA detection to organism presence in the mesopelagic ocean as well as other aquatic environments.This research is part of the Woods Hole Oceanographic Institution’s Ocean Twilight Zone project, funded as part of The Audacious Project housed at TED

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis

In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function

Coexistence and optimal control problems for a degenerate predator-prey model

In this paper we present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered. \ua9 2010 Elsevier Inc

Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption

International audienceThe behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption ∂_t u − ∆_p u + |∇u|^{p−1} = 0 in (0, ∞) × R^N , and fast diffusion 2N/(N + 1) < p < 2. Given a non-negative and radially symmetric initial condition with a non-increasing profile which decays sufficiently fast as |x| → ∞, it is shown that the corresponding solution u to the above equation approaches a uniquely determined separate variable solution of the form U (t, x) = (T_e − t)^{1/(2−p)} f_* (|x|), (t, x) ∈ (0, T_e) × R^N , as t → T_e , where T_e denotes the finite extinction time of u. A cornerstone of the convergence proof is an underlying variational structure of the equation. Also, the selected profile f_* is the unique non-negative solution to a second order ordinary differential equation which decays exponentially at infinity. A complete classification of solutions to this equation is provided, thereby describing all separate variable solutions of the original equation. One important difficulty in the uniqueness proof is that no monotonicity argument seems to be available and it is overcome by the construction of an appropriate Pohozaev functional

Numerical and experimental investigation of a lightweight bonnet for pedestrian safety

A topic of great consideration in current vehicle development in Europe is pedestrian protection. The enforcement of a new regulation trying to decrease the injuries to head, pelvis, and leg of pedestrian impacted by cars, is imposing great changes in vehicles' front design. In the present work a design solution for the bonnet, which is the main body part interacting with the human head during a car to pedestrian collision, is proposed. This solution meets the stiffness and safety targets, takes into account the manufacturing and recyclability requirements and gives a relevant contribution to vehicle lightweight. Thus this proposed solution puts in evidence that safety and lightweight are not incompatible targets. The amount of potential injury to the pedestrian head is evaluated, as prescribed by the standard test procedures, by means of a headform launched on the bonnet. However, the standard approach based on the head injury criterion (HIC) value only is reported to be largely unsatisfactory: therefore, a new experimental methodology for the measurement of the translational and the rotational accelerations has been developed, and the experimental results are reported. This would be a starting point for the evolution of currently adopted injury criteria to increase the safety of the vulnerable road user