Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- Instantaneous gelation in coagulation dynamicsPublication . Costa, Fernando Pestana da; Carr, J.The coagulation equations are a model for the dynamics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters. For a certain class of rate coefficients we prove that the density is not conserved on any time interval.
- Asymptotic behavior of solutions to the Coagulation-Fragmentation Equations. II. Weak FragmentationPublication . Costa, Fernando Pestana da; Carr, J.The discrete coagulation-fragmentation equations are a model for the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. The assumptions made on the fragmentation coefficients have the physical interpretation that surface effects are important. Our results on the asymptotic behavior of solutions generalize the corresponding results of Ball, Carr, and Penrose for the Becker-Doring equation.
- Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentationPublication . Costa, Fernando Pestana da
- On the positivity of solutions to the Smoluchowski equationsPublication . Costa, Fernando Pestana daThe dynamics of cluster growth can be modelled by the following infinite system of ordinary differential equations, first proposed by Smoluchowski, [8], where cj=cj(t) represents the physical concentration of j-clusters (aggregates of j identical particles), aj,k=aj,k≥0 are the time-independent coagulation coefficients, measuring the effectiveness of the coagulation process between a j-cluster and a k-cluster, and the first sum in the right-hand side of (1) is defined to be zero if j = 1.
- On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equationsPublication . Costa, Fernando Pestana daIn this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations $$\dot{c}_{j} = \sum_{k=1}^{j-1}c_{j-k}c_{k} - 2c_{j}\sum_{k=1}^{\infty}c_{k}, j = 1, 2, \ldots$$ with general exponentially decreasing initial data, with density $\rho,$ have the following asymptotic behaviour $$\lim_{j, t \rightarrow\infty, \xi = j/t fixed, j \in {\cal J}} t^{2}c_{j}(t) = \frac{q}{\rho}\, e^{-\xi/\rho},$$ where ${\cal J} = \{j: c_{j}(t)>0, t>0\}$ and $q =\gcd \{j: c_{j}(0)>0\}.$
- Asymptotic behaviour of low density solutionsPublication . Costa, Fernando Pestana daThe asymptotic behaviour of solutions to the generalized Becker-Döring equations is studied. It is proved that solutions converge strongly to a unique equilibrium if the initial density is sufficiently small.
- A finite-dimensional dynamical model for gelation in coagulation processPublication . Costa, Fernando Pestana daWe study a finite-dimensional system of ordinary differential equations derived from Smoluchowski’s coagulation equations and whose solutions mimic the behaviour of the nondensity-conserving (geling) solutions in those equations. The analytic and numerical studies of the finite-dimensional system reveals an interesting dynamic behaviour in several respects: Firstly, it suggests that some special geling solutions to Smoluchowski’s equations discovered by Leyvraz can have an important dynamic role in gelation studies, and, secondly, the dynamics is interesting in its own right with an attractor possessing an unexpected structure of equilibria and connecting orbits.
- An uniqueness result for a class of wiener-space valued stochastic differential equationsPublication . Oliveira, Maria JoãoWe prove a generalization of Bismut-Itô-Kunita formula to infinite dimensions and derive an uniqueness result for Wiener space valued processes which holds for a special class of Bernstein processes.
- A generalized clark-ocone formulaPublication . Faria, Margarida de; Oliveira, Maria João; Streit, LudwigWe extend the Clark-Ocone formula to a suitable class of generalized Brownian functionals. As an example we derive a representation of Donsker's delta function as (limit of) a stochastic integral.
- Structure theorems for o-minimal expansions of groupsPublication . Edmundo, Mário JorgeLet R be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) R is semi-bounded, (2) R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that Th(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R-definable sets and a symbol for each definable endomorphism of the group (R,0,+).