1,720,964 research outputs found
An Inverse Problem for a Nonlinear Diffusion-Convection Equation
No full textA method for constructing the Dirichlet-to-Neumann map for a nonlinear diffusion-convection equation is presented. The problem is reduced to the solution of a nonlinear integral equation in one independent variable. Existence and uniqueness of the solution may be proven for small times via a contraction mapping technique
Influence of drivers ability in a discrete vehicular traffic model
No full textA vehicular tra±c model is presented, based on the so-called Kinetic Theory of Active Particles.
Vehicles are characterized by a lattice of discrete speeds and by the driving ability of the drivers.
The evolution of the system is modeled through nonlinear interactions, whose output is
described by stochastic games. The results of numerical simulations are consistent with experimental
measurements of traffic flo
Learning dynamics towards modeling living systems. Reply to comments on "Collective learning modeling based on the kinetic theory of active particles"
No full textOur paper presents a review and critical analysis on a mathematical theory of learning in populations composed of many interacting individuals. Furthermore, it attempts to provide a foundational mathematical framework which may incorporate the main features of the learning process in view of applications to modeling complex systems, including crowds, swarms, and social systems.
The proposed approach is based on the kinetic theory of active particles which has been specifically developed to deal with living systems. The novelty of the contribution is the focus on collective, rather than individual, learning dynamics. This topic presents a certain analogy with evolutionary game theory, where populations take the place of individual players
On the Well Posedness of the Initial Value Problem in a Kinetic Traffic Flow Model
No full textA traffic flow model is discussed in the framework of the Kinetic Theory of Active Particles (KTAP). Each active particle is a vehicledriver pair characterized by a discrete velocity and by a driving ability. The systemevolves through non-linear interactions which are modeled by the so-called Tables of Games. An evolution equation is derived and a theorem of existence and uniqueness of the solution for a finite time is proved. The results of numerical simulations which are consistent with the results of experimental evidence, are also shown
On a Coupled System of Shallow Water Equations Admitting Travelling Wave Solutions
Full text linkWe consider three inviscid, incompressible, irrotational fluids that are contained between the rigid walls y = −h and y = h +H
and that are separated by two free interfaces. A generalized nonlocal spectral (NSP) formulation is developed, from which
asymptotic reductions of stratified fluids are obtained, including coupled nonlinear generalized Boussinesq equations and (1 + 1)-dimensional shallow water equations. A numerical investigation of the (1 + 1)-dimensional case shows the existence of solitary
wave solutions which have been investigated for different values of the characteristic parameters
Hydrogen-Bonding Effects on Infrared Spectra from Anharmonic Computations: Uracil–Water Complexes and Uracil Dimers
No full textHydrogen-bonding
interactions lead to significant changes in the
infrared (IR) spectrum, like frequency shifts of the order of magnitude
of hundreds of cm<sup>–1</sup> and increases of IR intensity
for bands related to vibrational modes of functional groups directly
involved in the hydrogen-bonded bridges. We are actively developing
a comprehensive and robust computational protocol aimed at the quantitative
reproduction of the spectra of bio-organic and hybrid organic/inorganic
molecular systems with a proper account of the variety of intra- and
intermolecular interactions. We have resorted to fully anharmonic
quantum mechanical computations within the generalized second-order
vibrational perturbation theory (GVPT2) approach, combined with the
B3LYP-D3 method, in conjunction with basis sets of double-ζ
plus polarization quality. Such an approach has been validated in
a previous work (Phys. Chem.
Chem. Phys. 2014, 16, 10112−10128) for simulating
the IR spectra of the monomers of nucleobases and some of their dimers.
In the present contribution we have extended our computational protocol
toward hybrid models, with the harmonic part computed at the B2PLYP
level, in conjunction with the maug-cc-pVTZ basis set, or by a cost-effective
ONIOM B2PLYP:B3LYP focused model, where only part of the molecular
system forming the hydrogen bonds is treated at the B2PLYP level of
theory. In this work experimental frequencies available for a set
of four uracil–water complexes have been considered as references
for the computational methodologies applied to the simulation of hydrogen-bonding
effects on the infrared spectrum, obtaining average uncertainties
of about 22 cm<sup>–1</sup> for B3LYP-D3/N07D and improved
description within 10 cm<sup>–1</sup> by hybrid B2PLYP/B3LYP-D3
approaches. The same computational schemes have been next applied
to simulate fully anharmonic IR spectra of six different hydrogen-bonded
uracil dimers, providing reliable support for future experimental
investigations on hydrogen-bonded systems
New trends on the systems approach to modeling SARS-CoV-2 pandemics in a globally connected planet
Full text linkThis paper presents a critical analysis of the literature and perspective research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It goes beyond deterministic population dynamics to consider several key complexity features of the system under consideration. In particular, the multiscale features of the dynamics from contagion to the subsequent dynamics of competition between the immune system and the proliferating virus. Other topics addressed in this work include the propagation of epidemics in a territory, taking into account local transportation networks, the heterogeneity of the population and the study of social and economic problems in populations involved in the spread of epidemics. The overall content aims to show how new mathematical tools can be developed to address the above topics and how mathematical models and simulations can contribute to the decision making of crisis managers
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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