Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Reaction-diffusion wave fronts: Multigeneration biological species under climate change

A generalization of reaction-diffusion models to multigeneration biological species is presented. It is based on more complex random walks than those in previous approaches. The new model is developed analytically up to infinite order. Our predictions for the speed agree to experimental data for several butterfly species better than existing models. The predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Tree-based message diffusion for managing replicated data in unreliable and resource-constrained peer-to-peer environment

Abstract This thesis proposes a set of adaptive broadcast solutions and an adaptive data replication solution to support the deployment of P2P applications. P2P applications are an emerging type of distributed applications that are running on top of P2P networks. Typical P2P applications are video streaming, file sharing, etc. While interesting because they are fully distributed, P2P applications suffer from several deployment problems, due to the nature of the environment on which they perform. Indeed, defining an application on top of a P2P network often means defining an application where peers contribute resources in exchange for their ability to use the P2P application. For example, in P2P file sharing application, while the user is downloading some file, the P2P application is in parallel serving that file to other users. Such peers could have limited hardware resources, e.g., CPU, bandwidth and memory or the end-user could decide to limit the resources it dedicates to the P2P application a priori. In addition, a P2P network is typically emerged into an unreliable environment, where communication links and processes are subject to message losses and crashes, respectively. To support P2P applications, this thesis proposes a set of services that address some underlying constraints related to the nature of P2P networks. The proposed services include a set of adaptive broadcast solutions and an adaptive data replication solution that can be used as the basis of several P2P applications. Our data replication solution permits to increase availability and to reduce the communication overhead. The broadcast solutions aim, at providing a communication substrate encapsulating one of the key communication paradigms used by P2P applications: broadcast. Our broadcast solutions typically aim at offering reliability and scalability to some upper layer, be it an end-to-end P2P application or another system-level layer, such as a data replication layer. Our contributions are organized in a protocol stack made of three layers. In each layer, we propose a set of adaptive protocols that address specific constraints imposed by the environment. Each protocol is evaluated through a set of simulations. The adaptiveness aspect of our solutions relies on the fact that they take into account the constraints of the underlying system in a proactive manner. To model these constraints, we define an environment approximation algorithm allowing us to obtain an approximated view about the system or part of it. This approximated view includes the topology and the components reliability expressed in probabilistic terms. To adapt to the underlying system constraints, the proposed broadcast solutions route messages through tree overlays permitting to maximize the broadcast reliability. Here, the broadcast reliability is expressed as a function of the selected paths reliability and of the use of available resources. These resources are modeled in terms of quotas of messages translating the receiving and sending capacities at each node. To allow a deployment in a large-scale system, we take into account the available memory at processes by limiting the view they have to maintain about the system. Using this partial view, we propose three scalable broadcast algorithms, which are based on a propagation overlay that tends to the global tree overlay and adapts to some constraints of the underlying system. At a higher level, this thesis also proposes a data replication solution that is adaptive both in terms of replica placement and in terms of request routing. At the routing level, this solution takes the unreliability of the environment into account, in order to maximize reliable delivery of requests. At the replica placement level, the dynamically changing origin and frequency of read/write requests are analyzed, in order to define a set of replica that minimizes communication cost.

Altered structural connectivity in patients with medial temporal lobe epilepsy: A Diffusion Spectrum Imaging and Graph Analysis study

In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Estimates of electronic coupling for excess electron transfer in DNA

Electronic coupling Vda is one of the key parameters that determine the rate of charge transfer through DNA. While there have been several computational studies of Vda for hole transfer, estimates of electronic couplings for excess electron transfer (ET) in DNA remain unavailable. In the paper, an efficient strategy is established for calculating the ET matrix elements between base pairs in a π stack. Two approaches are considered. First, we employ the diabatic-state (DS) method in which donor and acceptor are represented with radical anions of the canonical base pairs adenine-thymine (AT) and guanine-cytosine (GC). In this approach, similar values of Vda are obtained with the standard 6-31 G* and extended 6-31++ G* basis sets. Second, the electronic couplings are derived from lowest unoccupied molecular orbitals (LUMOs) of neutral systems by using the generalized Mulliken-Hush or fragment charge methods. Because the radical-anion states of AT and GC are well reproduced by LUMOs of the neutral base pairs calculated without diffuse functions, the estimated values of Vda are in good agreement with the couplings obtained for radical-anion states using the DS method. However, when the calculation of a neutral stack is carried out with diffuse functions, LUMOs of the system exhibit the dipole-bound character and cannot be used for estimating electronic couplings. Our calculations suggest that the ET matrix elements Vda for models containing intrastrand thymine and cytosine bases are essentially larger than the couplings in complexes with interstrand pyrimidine bases. The matrix elements for excess electron transfer are found to be considerably smaller than the corresponding values for hole transfer and to be very responsive to structural changes in a DNA stack