Repositรณrio Colecรงรฃo:http://hdl.handle.net/10198/24982015-10-13T13:47:55Z2015-10-13T13:47:55ZDetermination of (0,2)-regular sets in graphsPacheco, Maria F.Cardoso, Domingos MoreiraLuz, Carlos J.http://hdl.handle.net/10198/108152014-10-15T01:00:46Z2013-01-01T00:00:00ZTรญtulo: Determination of (0,2)-regular sets in graphs
Autor: Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
Resumo: An eigenvalue of a graph is main iff its associated eigenspace is not orthogonal to the all-one vector j. The main characteristic polynomial of a graph G with p main distinct eigenvalues is ๐_๐บ (ฮป)=ฮป^๐โ๐_0 ฮป^(๐โ1)โ๐_1 ฮป^(๐โ2)-โฆ-๐_(๐โ2) ฮปโ๐_(๐โ1) and it has integer coefficients. If G has n vertices, the nxk walk matrix of G is ๐พ_๐=(j,๐จ_๐ฎj,๐จ_๐ฎ^"2" "j",โฆ,๐จ_๐ฎ^(๐โ๐) j) and W, the walk matrix of G, is ๐พ_๐ for which rank(๐พ_๐)=k. The number k coincides with the number of distinct main eigenvalues of G. In [2] it was proved that the coefficients of the main characteristic polynomial of G are the solutions of ๐พ๐ฟ=๐จ_๐ฎ^๐j. A (๏ซ,๏ด)- regular set [3] is a subset of the vertices of a graph inducing a ๏ซ-regular subgraph such that every vertex not in the subset has ๏ด neighbors in it. In [1], a strategy for the determination of (0,1)-regular sets is described and we generalize it in order to solve the problem of the determination of (0,2)-regular sets in arbitrary graphs. An algorithm for deciding whether or not a given graph has a (0,2)-regular set is described. Its complexity depends on the multiplicity of โ2 as an eigenvalue of the adjacency matrix of the graph. When such multiplicity is low, the generalization of the results in [1] assure that the algorithm is polynomial. An example of application of the algorithm to a graph for which this multiplicity is low is also presented.2013-01-01T00:00:00ZDetermination of (0,2)-regular sets in graphsPacheco, Maria F.Cardoso, Domingos MoreiraLuz, Carlos J.http://hdl.handle.net/10198/106602014-10-02T01:01:25Z2013-01-01T00:00:00ZTรญtulo: Determination of (0,2)-regular sets in graphs
Autor: Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
Resumo: An eigenvalue of a graph is main iff its associated eigenspace is not orthogonal to the all-one vector j. The main characteristic polynomial of a graph G with p main distinct eigenvalues is ๐_๐บ (ฮป)=ฮป^๐โ๐_0 ฮป^(๐โ1)โ๐_1 ฮป^(๐โ2)-โฆ-๐_(๐โ2) ฮปโ๐_(๐โ1) and it has integer coefficients. If G has n vertices, the nxk walk matrix of G is ๐พ_๐=(j,๐จ_๐ฎj,๐จ_๐ฎ^"2" "j",โฆ,๐จ_๐ฎ^(๐โ๐) j) and W, the walk matrix of G, is ๐พ_๐ for which rank(๐พ_๐)=k. The number k coincides with the number of distinct main eigenvalues of G. In [2] it was proved that the coefficients of the main characteristic polynomial of G are the solutions of ๐พ๐ฟ=๐จ_๐ฎ^๐j. A (๏ซ,๏ด)- regular set [3] is a subset of the vertices of a graph inducing a ๏ซ-regular subgraph such that every vertex not in the subset has ๏ด neighbors in it. In [1], a strategy for the determination of (0,1)-regular sets is described and we generalize it in order to solve the problem of the determination of (0,2)-regular sets in arbitrary graphs. An algorithm for deciding whether or not a given graph has a (0,2)-regular set is described. Its complexity depends on the multiplicity of โ2 as an eigenvalue of the adjacency matrix of the graph. When such multiplicity is low, the generalization of the results in [1] assure that the algorithm is polynomial. An example of application of the algorithm to a graph for which this multiplicity is low is also presented.2013-01-01T00:00:00ZFlow of red blood cells in microchannel networks: in vitro studiesCidre, DianaRodrigues, Raquel OliveiraFaustino, V.Pinto, ElmanoPinho, DianaBento, DavidFernandes, Carla S.Dias, Ricardo P.Lima, R.http://hdl.handle.net/10198/100392015-08-06T08:43:22Z2013-01-01T00:00:00ZTรญtulo: Flow of red blood cells in microchannel networks: in vitro studies
Autor: Cidre, Diana; Rodrigues, Raquel Oliveira; Faustino, V.; Pinto, Elmano; Pinho, Diana; Bento, David; Fernandes, Carla S.; Dias, Ricardo P.; Lima, R.
Resumo: Blood exhibits unique flow characteristics on micro-scale level, due to the complex biochemical structure of Red Blood Cells (RBCs) and their response to both shear and extensional flow, which influence the rheological properties and flow behavior of blood [1,2]. In the past years, several in
vitro studies where made and have revealed some physiologically significant phenomena, such as Fahraeus and Fahraeus-Lindqvist effect, that played a key role in recent developments of lab-onchip devices for blood sampling, analysis and cell culturing. However, the blood flow in microvascular networks phenomena it remains incompletely understood. Thus, it is important to
investigate in detail the behavior of RBCs flow occurring at a microchannel network, such as with divergent and convergent bifurcations. Previews in vitro studies in microchannels with a simple divergent and convergent bifurcation, have shown a pronounced cell depleted zone immediately
downstream of the apex of the convergent bifurcation. In the present work, by using a highspeed video microscopy system, we investigated the cell depleted zone in a microchannel network.
The working fluid used in this study was dextran 40 (Dx40) containing about 10% of haematocrit level (10 Hct) of ovine red blood cells. The high-speed video microscopy system used in our experiments consists of an inverted microscope (IX71, Olympus, Japan) combined with a highspeed
camera (i-SPEED LT, Olympus). A syringe pump Apparatus (PHD ULTRATM) with 1 ml
syringe (Terumo) was used to push the working fluids through the microchannel network.
Additionally, we investigated the effect of the flow rate on the formation of the cell free layer.2013-01-01T00:00:00ZBlood flow in a bifurcation and confluence microchannel: the effectof the cell-free layer in the velocity profilesPinho, DianaBento, DavidRodrigues, Raquel OliveiraFernandes, Carla S.Garcia, ValdemarLima, R.http://hdl.handle.net/10198/100142015-08-06T14:50:16Z2014-01-01T00:00:00ZTรญtulo: Blood flow in a bifurcation and confluence microchannel: the effectof the cell-free layer in the velocity profiles
Autor: Pinho, Diana; Bento, David; Rodrigues, Raquel Oliveira; Fernandes, Carla S.; Garcia, Valdemar; Lima, R.
Resumo: A few detailed studies have been performed in complex in vitro microvascular networks composed by bifurcations and confluences. The main purpose of the present work is to numerically simulate the flow of two distinct fluids through bifurcation
and confluence geometries, i. e red blood cells (RBCs) suspended in Dextran40 with about 14% of heamatocrit and pure water.
The simulations of pure water and RBCs flows were performed resorting to the commercial finite volume software package
FLUENT.
A well known hemodynamic phenomenon, known as Fahraeus-Lindqvist effect [1, 2], observed in both in vivo and in vitro
studies, results in the formation of a marginal cell-free layer (CFL) at regions adjacent to the wall [3]. Recently, studies have shown that the formation of the CFL is affected by the geometry of the microchannel and for the case of the confluences a CFL
tend to appear in the middle of the microchannel after the apex of the confluence [4, 5]. By using the CFL experimental data, the main objective of this work is to implement a CFL in the numerical simulations in order to obtain a better understanding of the effect of this layer on the velocity profiles.2014-01-01T00:00:00Z