22/06/2001, 11:30 — 12:30 — Sala P3.10, Pavilhão de Matemática
Anne Robertson, University of Pittsburgh
A constitutive modeling of viscoelastic fluids with applications to flow in curved pipes
There are many real fluids such as water, which the Newtonianconstitutive equation describes extremely well in almost all flowsituations. Small amounts of polymer additive can have a dramaticeffect on the behavior of these liquids. For example, B. A. Tomsstudied flows in straight pipes and discovered that in theturbulent regime small amounts of polymer additive couldsignificantly reduce the pressure drop necessary to attain a givenflow rate. These changes in behavior are attributed to theviscoelastic nature of the polymeric solution and numerousconstitutive equations have been developed to model these fluids.In contrast, in curved pipes polymer additives were foundexperimentally both to alter the relationship between pressure dropand flow rate in the laminar regime and to alter the criticalReynolds number for transition to turbulence. In this talk, we willdiscuss results for steady, fully developed flows of viscoelasticfluids in curved pipes and contrast this behavior with flows ofNewtonian fluids. Following the approach of W. R. Dean and otherauthors, we have used regular perturbation methods to study flowsof viscoelastic fluids in curved pipes. We have obtained explicitsolutions to the perturbation equations at first order for secondorder fluids and a modified Oldroyd-B fluid. In the absence ofinertial effects, flows of Newtonian fluids in curved pipes do notdisplay a secondary flow, rather a uniaxial flow exists whichdiffers only slightly from the straight pipe solution. In contrast,even in the absence of inertial effects, the class of viscoelasticfluids studied display a secondary motion (see, e.g. Thomas 1963,Bowen et al. 1991, Robertson and Muller 1996). Significantly, for acountable number of combinations of material parameters andReynolds numbers, there is a loss of uniqueness of the solution tothe perturbation equations. For other values of material parametersand Reynolds number, a solution does not even exist. There is aregion in parameter space which is free of such singularities. Thislack of existence to the perturbation equations regardless of themagnitude of the curvature ratio, implies a lack of existence of asolution which is a steady, fully developed perturbation of thestraight pipe solution. The implications of this result are underinvestigation.
18/06/2001, 11:30 — 12:30 — Sala P3.10, Pavilhão de Matemática
Anne Robertson, University of Pittsburgh
A nonlinear, inelastic constitutive model for
cerebral arterial tissue, with applications to
intracranial aneurysms
08/06/2001, 11:30 — 12:30 — Sala P3.10, Pavilhão de Matemática
C. S. Chen, University of Nevada, Las Vegas
Meshless methods for the numerical solution of partial differential equations
11/05/2001, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
J. N. Lyness, Argonne National Laboratory
Remarks on cubature over triangles
08/05/2001, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
J. N. Lyness, Argonne National Laboratory
Some recent work in extrapolation quadrature
24/04/2001, 12:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Stig-Olof Londen, Helsinky University of Technology
On some fractional evolution equations
In this talk, we review some recent results on fractionalevolution equations of type $D^\alpha_t u+ Au = f$, $t\geq 0$,where $\alpha\in (0,2)$, $\alpha\neq 1$.
First, as a typical example, we consider the fractional Burgersequation. Next, we formulate a general result with $A$$m$-accretive. Some comments on maximal regularity follow; finallywe present an unsolved problem concerning fractional nonlinearhyperbolic equations.
20/04/2001, 15:15 — 16:15 — Sala P3.10, Pavilhão de Matemática
Jacques Baranger, Laboratoire MCS, Université de Lyon I
Sur la méthode des charactéristiques en élents finis discontinus
06/04/2001, 15:00 — 16:00 — Sala P4.35, Pavilhão de Matemática
Luís Nunes Vicente, Universidade de Coimbra
Métodos numéricos para optimização não linear. Aplicações edesafios
Os problemas de optimização não linear aparecem frequentementeassociados ao controlo em simulação, ao projecto em engenharia e àidentificação de parâmetros e ao ajuste de dados em experimentação.A função objectivo e as restrições apresentam, com regularidade,uma estrutura e um escalonamento próprios, associados àdiscretização de equações diferenciais.
Métodos numéricos modernos em optimização não linear, como sãopor exemplo os casos dos métodos SQP e dos métodos de regiões deconfiança, podem e devem ser adaptados para tirar partido dascaracterísticas da aplicação. Outras situações, como adegenerescência das restrições, por um lado, e a dificuldadecomputacional ou experimental em obter o valor das funções e dassuas derivadas, por outro, colocam sérios desafios aooptimizador.
08/03/2001, 12:00 — 13:00 — Sala P3.10, Pavilhão de Matemática
V. Starovoitov, Lavrentiev Institute of Hydrodynamics, Novosibirsk
On the motion of rigid bodies in a viscous non-homogeneous fluid
23/02/2001, 15:00 — 16:00 — Sala P3.31, Pavilhão de Matemática
Nadezhda Konyukhova, Computing Center of RAS, Moscow
On some singular BVP's for autonomous systems of nonlinear ODE's arising from hydrodynamics
16/02/2001, 15:00 — 16:00 — Sala P3.31, Pavilhão de Matemática
Nadezhda Konyukhova, Computing Center of RAS, Moscow
Multiple self similar solutions of theNonlinear Wave Equation in theinflationary cosmology
11/12/2000, 11:30 — 12:30 — Sala P5, Pavilhão de Matemática
Neville Ford, University of Liverpool
The approximate solution of fractional Differential Equations
06/12/2000, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Hervé Maillot, École Polytechnique, Palaiseau
Optimal Bounds and H-measures
We compute bound on effective properties of homogenizedmaterials in conduction and linear elasticity. We use $H$-measures,following the original ideas and exposition of Luc Tartar. After having recovered classical Hashin-Shtrikman simple bounds wepropose to deal with coupled bounds in conduction.
23/11/2000, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática
Hedia Chaker, LAMSIN, École Nationale d'Ingénieurs de Tunis
The high field asymptotics for degenerate semiconductors
22/11/2000, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática
Amel Ben Abda, LAMSIN, École Nationale d'Ingénieurs de Tunis
A non iterative process for cracks identification
10/11/2000, 15:30 — 16:30 — Sala P3.31, Pavilhão de Matemática
António Oliveira, Universidade Nova de Lisboa
Resolução numérica de problemas de valores de fronteira singulares para equações de Emden-Fowler
08/11/2000, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática
Jalel Ben Abdallah, LAMSIN, École Nationale d'Ingénieurs de Tunis
A non destructive approach for the identification of elastic contact stresses
08/10/2000, 15:30 — 16:30 — Sala P3.31, Pavilhão de Matemática
António Oliveira, Universidade Nova de Lisboa
Resolução numérica de problemas de valores de fronteira singulares para equações de Emden-Fowler
28/09/2000, 12:00 — 13:00 — Sala P3.10, Pavilhão de Matemática
Jindrich Necas, Matematický ústav Univerzity Karlovy, Praha and Northern Illinois University, DeKalb
A remark on the removable singularities for the solution of the Navier-Stokes equation
13/09/2000, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Adérito Araújo, Universidade de Coimbra
Propagação do erro na integração numérica de ondas solitárias
Iremos estudar a propagação do erro temporal na integração numérica de ondas solitárias que são solução da equação $u_t+u_x+(1/2)u_x^2-u_{xxt}=0$, usando uma interpretação geométrica dessas ondas como equilíbrios relativos. Mostraremos que o crescimento do erro é linear para métodos que preservam quantidades invariantes do problema e quadrático para métodos não conservativos. Serão apresentados alguns resultados numéricos.