Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport

Microstructural and metabolic changes in the brains of concussed athletes

Les commotions cérébrales ont longtemps été considérées comme une blessure ne comportant que peu ou pas de conséquences. Cependant, la mise à la retraite forcée de plusieurs athlètes de haut niveau, liée au fait d'avoir subi des commotions cérébrales multiples, a porté cette question au premier plan de la culture scientifique et sportive. Malgré la sensibilisation croissante du public et la compréhension scientifique accrue des commotions cérébrales, il reste encore beaucoup d’inconnus au sujet de ces blessures. En effet, il est difficile de comprendre comment cette atteinte peut avoir des effets si profonds malgré le fait qu’elle n’entraîne apparemment pas de conséquences physiques apparentes lorsque les techniques traditionnelles d’imagerie cérébrale sont utilisées. Les techniques de neuroimagerie fonctionnelle ont cependant contribué à répondre aux nombreuses questions entourant les conséquences des commotions cérébrales ainsi qu'à accroître la compréhension générale de la physiopathologie de commotions cérébrales. Bien que les techniques de base telles que l'imagerie structurelle comme les scans TC et IRM soient incapables de détecter des changements structurels dans la grande majorité des cas (Ellemberg, Henry, Macciocchi, Guskiewicz, & Broglio, 2009; Johnston, Ptito, Chankowsky, & Chen, 2001), d'autres techniques plus précises et plus sensibles ont été en mesure de détecter avec succès des changements dans le cerveau commotionné. Des études d’IRM fonctionelle ont entre autres établi une solide relation entre les altérations fonctionnelles et les symptômes post-commotionels (Chen, Johnston, Collie, McCrory, & Ptito, 2007; Chen et al., 2004; Chen, Johnston, Petrides, & Ptito, 2008; Fazio, Lovell, Pardini, & Collins, 2007). Les mesures électrophysiologiques telles que les potentiels évoqués cognitifs (ERP) (Gaetz, Goodman, & Weinberg, 2000; Gaetz & Weinberg, 2000; Theriault, De Beaumont, Gosselin, Filipinni, & Lassonde, 2009; Theriault, De Beaumont, Tremblay, Lassonde, & Jolicoeur, 2010) et la stimulation magnétique transcrânienne ou SMT (De Beaumont, Brisson, Lassonde, & Jolicoeur, 2007; De Beaumont, Lassonde, Leclerc, & Theoret, 2007; De Beaumont et al., 2009) ont systématiquement démontré des altérations fonctionnelles chez les athlètes commotionnés. Cependant, très peu de recherches ont tenté d'explorer davantage certaines conséquences spécifiques des commotions cérébrales, entre autres sur les plans structural et métabolique. La première étude de cette thèse a évalué les changements structurels chez les athlètes commotionnés à l’aide de l'imagerie en tenseur de diffusion (DTI) qui mesure la diffusion de l'eau dans la matière blanche, permettant ainsi de visualiser des altérations des fibres nerveuses. Nous avons comparé les athlètes commotionnés à des athlètes de contrôle non-commotionnés quelques jours après la commotion et de nouveau six mois plus tard. Nos résultats indiquent un patron constant de diffusion accrue le long des voies cortico-spinales et dans la partie du corps calleux reliant les régions motrices. De plus, ces changements étaient encore présents six mois après la commotion, ce qui suggère que les effets de la commotion cérébrale persistent bien après la phase aiguë. Les deuxième et troisième études ont employé la spectroscopie par résonance magnétique afin d'étudier les changements neurométaboliques qui se produisent dans le cerveau commotionné. La première de ces études a évalué les changements neurométaboliques, les aspects neuropsychologiques, et la symptomatologie dans la phase aiguë post-commotion. Bien que les tests neuropsychologiques aient été incapables de démontrer des différences entre les athlètes commotionnés et non-commotionnés, des altérations neurométaboliques ont été notées dans le cortex préfrontal dorsolatéral ainsi que dans le cortex moteur primaire, lesquelles se sont avérées corréler avec les symptômes rapportés. La deuxième de ces études a comparé les changements neurométaboliques immédiatement après une commotion cérébrale et de nouveau six mois après l’atteinte. Les résultats ont démontré des altérations dans le cortex préfrontal dorsolatéral et moteur primaire dans la phase aiguë post-traumatique, mais seules les altérations du cortex moteur primaire ont persisté six mois après la commotion. Ces résultats indiquent que les commotions cérébrales peuvent affecter les propriétés physiques du cerveau, spécialement au niveau moteur. Il importe donc de mener davantage de recherches afin de mieux caractériser les effets moteurs des commotions cérébrales sur le plan fonctionnel.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

The Navier-Stokes Equations with Time Delay

In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Influence of vanadium on electrical and microstructural properties of CaCu3Ti4O12/CaTiO3

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal and sub-optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright (C) 2001 John Wiley & Sons, Ltd.

The influence of sintering process and atmosphere on the non-ohmic properties of SnO2 based varistor

The non-ohmic properties of the 98.95% SnO2 + 1.0 CoO + 0.05 Nb2O5 (all in mole%) system, as well as the influence of sintering temperature and atmosphere on these properties, were characterized in this study. The maximum non-linear coefficient (alpha = 32) was obtained for a sintering temperature of 1300 degrees C in an oxygen atmosphere and this maximum is associated with the presence of O in SnO2 grain boundaries, as interface defects. Experimental results also indicate thermionic-type conduction mechanisms, which are associated with the potential barrier of Schottky or Poole-Frenkel types.

MnO2 influence on the electrical properties of SnO2-based ceramic systems

Tin dioxide is an n-type semiconductor that when doped with other metallic oxides exhibits non-linear electric behavior with high non-linear coefficient values typical of a varistor. In this work, electrical properties of the SnO2.CoO.Ta2O5 and SnO2.CoO.MnO2.Ta2O5 ceramics systems were studied with the objective of analyzing the influence of MnO2 on sintering behavior and electrical properties of these systems. The compacts were prepared by powder mixture process and sintered at 1300°C for 1 hour, in air, using a constant heating rate of 10°C/min. The morphological and structural properties were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The densities of the sintered ceramics were measured using the Archimedes method. The SnO2.CoO.Ta2O5 and SnO2.CoO.MnO2.Ta2O5 systems presented breakdown fields (Eb) about 3100 V.cm-1 and 3800 V.cm-1, respectively, and non-linear coefficient (α) about 10 and 20, respectively.

Investigation of the relationship between load and loss factors for a Brazilian electric utility

With the considerable increase of the losses in electric utilities of developing countries, such as Brazil, there is an investigation for loss calculation methodologies, considering both technical (inherent of the system) and non-technical (usually associated to the electricity theft) losses. In general, all distribution networks know the load factor, obtained by measuring parameters directly from the network. However, the loss factor, important for the energy loss cost calculation, can only be obtained in a laborious way. Consequently, several formulas have been developed for obtaining the loss factor. Generally, it is used the expression that relates both factors, through the use of a coefficient k. Last reviews introduce a range of factor k within 0.04 - 0.30. In this work, an analysis with real life load curves is presented, determining new values for the coefficient k in a Brazilian electric utility. © 2006 IEEE.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Detecção de bordas em imagens digitais através de um processo de difusão anisotrópica não linear

The edges detection model by a non-linear anisotropic diffusion, consists in a mathematical model of smoothing based in Partial Differential Equation (PDE), alternative to the conventional low-pass filters. The smoothing model consists in a selective process, where homogeneous areas of the image are smoothed intensely in agreement with the temporal evolution applied to the model. The level of smoothing is related with the amount of undesired information contained in the image, i.e., the model is directly related with the optimal level of smoothing, eliminating the undesired information and keeping selectively the interest features for Cartography area. The model is primordial for cartographic applications, its function is to realize the image preprocessing without losing edges and other important details on the image, mainly airports tracks and paved roads. Experiments carried out with digital images showed that the methodology allows to obtain the features, e.g. airports tracks, with efficiency.

A statistical analysis of loss factor to determine the energy losses

Given that the total amount of losses in a distribution system is known, with a reliable methodology for the technical loss calculation, the non-technical losses can be obtained by subtraction. A usual method of calculation technical losses in the electric utilities uses two important factors: load factor and the loss factor. The load factor is usually obtained with energy and demand measurements, whereas, to compute the loss factor it is necessary the learning of demand and energy loss, which are not, in general, prone of direct measurements. In this work, a statistical analysis of this relationship using the curves of a sampling of consumers in a specific company is presented. These curves will be summarized in different bands of coefficient k. Then, it will be possible determine where each group of consumer has its major concentration of points. ©2008 IEEE.