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Temporal excitation patterns on the cerebral cortex as a result of migraine modeling
(Springer Proceedings in Physics, 20160629)The complex, highly individual, geometry of the cerebral cortex in humans presents a major challenge in studying the spreading of spontaneous neuronal activity. Recent computational advances [1] allow to simulate the ... 
The airfoil equation on near disjoint intervals: Approximate models and polynomial solutions
(Journal of Computational and Applied Mathematics, 20160101)The airfoil equation is considered over two disjoint intervals. Assuming the distance between the intervals is small an approximate solution is found and relationships between this approximation and the solution of the ... 
The asymptotic behaviour of the heat equation in a twisted DirichletNeumann waveguide
(Journal of Differential Equations, 20111231)We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay ... 
The behavior of domain decomposition methods when the overlapping length is large
(Central European Journal of Mathematics, 20141231)In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm ... 
The dynamics of vortex filaments with corners
(Communications on Pure and Applied Analysis (CPAA), 20150701)This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the socalled binormal flow. The case of a regular polygon ... 
The economics of the cloud: Price competition and congestion
(Performance Evaluation Review, 20141231)[No abstract available] 
The emergence of selforganization in complex systemsPreface
(Chaos, Solitons and Fractals, 20151231)[No abstract available] 
The Hardy inequality and the heat equation in twisted tubes
(Journal des Mathematiques Pures et Appliquees, 20101231)We show that a twist of a threedimensional tube of uniform crosssection yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for ... 
The initial value problem for the binormal flow with rough data
(Annales Scientifiques de l'Ecole Normale Superieure, 20151231)In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ... 
The L∞null controllability of parabolic equation with equivalued surface boundary conditions
(Asymptotic Analysis, 20131231)In this paper, we obtain the L∞null controllability of the parabolic equation with equivalued surface boundary conditions in Ω×[0,T]. The control is supported in the product of an open subset of Ω and a subset of [0,T] ... 
The MWright function as a generalization of the Gaussian density for fractional diffusion processes
(Fractional Calculus and Applied Analysis, 20131231)The leading role of a special function of the Wrighttype, referred to as MWright or Mainardi function, within a parametric class of selfsimilar stochastic processes with stationary increments, is surveyed. This class ... 
The maximum angle condition is not necessary for convergence of the finite element method
(Numerische Mathematik, 20121231)We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition ... 
The Modellers' Halting Foray into Ecological Theory: Or, What is This Thing Called 'Growth Rate'?
(Acta Biotheoretica, 20151231)This discussion paper describes the attempt of an imagined group of nonecologists ("Modellers" ) to determine the population growth rate from field data. The Modellers wrestle with the multiple definitions of the growth ... 
The nearextreme density of intraday logreturns
(Physica A: Statistical Mechanics and its Applications, 20121231)The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by nonstationarity and dependence between ... 
The price of forgetting in parallel and nonobservable queues
(Performance Evaluation, 20111231)We consider a brokerbased network of nonobservable parallel queues and analyze the minimum expected response time and the optimal routing policy when the broker has the memory of its previous routing decisions. We provide ... 
The subelliptic ∞Laplace system on CarnotCarathéodory spaces
(Advances in Nonlinear Analysis, 20131231)Given a CarnotCarathéodory space Ω ⊆ ℝn with associated frame of vector fields X = {X<inf>1</inf>,⋯, X<inf>m</inf>}, we derive the subelliptic ∞Laplace system for mappings u: Ω → ℝN, which reads δX∞u:=(Xu ⊗ Xu + 
The turnpike property infinitedimensional nonlinear optimal control
(Journal of Differential Equations, 20141231)Turnpike properties have been established long time ago in finitedimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given ... 
The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks
(Nonlinear Analysis: Real World Applications, 20131231)In this article we study, by the vanishing viscosity method, the sensitivity analysis of an optimal control problem for 1D scalar conservation laws in the presence of shocks. It is reduced to investigate the vanishing ... 
The Vortex Filament Equation as a Pseudorandom Generator
(Acta Applicandae Mathematicae, 20150801)In this paper, we consider the evolution of the socalled vortex filament equation (VFE), $$ X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ... 
The wave equation: Control and numerics
(Lecture Notes in Mathematics, 20121231)In these Notes we make a selfcontained presentation of the theory that has been developed recently for the numerical analysis of the controllability properties of wave propagation phenomena and, in particular, for the ...