Hyperbolic predators vs parabolic preys

We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for preys. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of predators can be directed towards region with high prey density. Moreover, Lotka-Volterra type right hand sides describe the feeding. A theorem ensuring existence, uniqueness, continuous dependence of weak solutions and various stability estimates is proved, in any space dimension. Numerical integrations show a few qualitative features of the solutions.Comment: 35 pages, 7 figure

NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technolog

For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam. Using realistic parameters, solutions to this model obtained through numerical integrations meet qualitative properties of real cuts. Moreover, the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt

Isentropic Fluid Dynamics in a Curved Pipe

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1]

Stability and Optimization in Structured Population Models on Graphs

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.Comment: 22 pages, 7 figure

On the Stability Functional for Conservation Laws

This note is devoted to the explicit construction of a functional defined on all pairs of \L1 functions with small total variation, which is equivalent to the \L1 distance and non increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional by Bressan, Liu and Yang.Comment: 26 page

Satellite To Satellite Doppler Tracking (SSDT) for mapping of the Earth's gravity field

Two SSDT schemes were evaluated: a standard, low-low, SSDT configuration, which both satellites are in basically the same low altitude nearly circular orbit and the pair is characterized by small angular separation; and a more general configuration in which the two satellites are in arbitrary orbits, so that different configurations can be comparatively analyed. The standard low-low SSDT configuration is capable of recovering 1 deg X 1 deg surface anomalies with a strength as low as 1 milligal, located on the projected satellite path, when observing from a height as large as 300 km. The Colombo scheme provides an important complement of SSDT observations, inasmuch as it is sensitive to radial velocity components, while keeping at the same performance level both measuring sensitivity and measurement resolution

The Compressible to Incompressible Limit of 1D Euler Equations: the Non Smooth Case

We prove a rigorous convergence result for the compressible to incompressible limit of weak entropy solutions to the isothermal 1D Euler equations.Comment: 16 page

Differential Equations Modeling Crowd Interactions

Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting non locally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians, and also with other "agents".Comment: 26 pages, 5 figure

THE ROLE OF THE STRUCTURAL CHARACTERISTIC LENGTH IN FRC STRUCTURES

In the framework of the CEN Committee involved in the writing of the fiber reinforced concrete structure standards, a strong debate has been focused on the possibility to use a stress-strain rather than a stress- crack opening constitutive relationship, even if only the second one is physically meaningful after the cracking of the matrix. The use of a stress-strain model, even if it can be regarded as an effective simplification in many cases as it is in R/C structures, can be justified by the rough choice of a unique crack spacing in the range of 125 mm. In the paper, the modeling of different FRC cross sections and in particular of a thin-walled open cross-section profile longitudinally reinforced with steel bars like a FRC box-culvert (U-channel) highlights as only the use of a correct structural characteristic length when a simplified Navier-Bernoulli plane section model is adopted prevents the overestimation of the bearing capacity in bending. A comparison with F.E. model and previous experimental tests on full-scale structures are also proposed