134 research outputs found
Two-dimensional stability analysis in a HIV model with quadratic logistic growth term
We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth
term and continue the analysis of the previous article [6]. We now take the
viral diffusion in a two-dimensional environment. The model consists of two
ODEs for the concentrations of the target T cells, the infected cells, and a
parabolic PDE for the virus particles. We study the stability of the uninfected
and infected equilibria, the occurrence of Hopf bifurcation and the stability
of the periodic solutions.Comment: To appear on Commun. Pure Appl. Ana
Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem
In this paper we are interested in a rigorous derivation of the
Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm,
we consider a two-dimensional Stefan problem in a strip, a simplified version
of a solid-liquid interface model. Near the instability threshold, we introduce
a small parameter and define rescaled variables accordingly. At
fixed , our method is based on: definition of a suitable linear 1D
operator, projection with respect to the longitudinal coordinate only,
Lyapunov-Schmidt method. As a solvability condition, we derive a
self-consistent parabolic equation for the front. We prove that, starting from
the same configuration, the latter remains close to the solution of K--S on a
fixed time interval, uniformly in sufficiently small
Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors
In this work, a pricing model for a defaultable corporate bond with credit
rating migration risk is established. The model turns out to be a free boundary
problem with two free boundaries. The latter are the level sets of the solution
but of different kinds. One is from the discontinuous second order term, the
other from the obstacle. Existence, uniqueness, and regularity of the solution
are obtained. We also prove that two free boundaries are . The
asymptotic behavior of the solution is also considered: we show that it
converges to a traveling wave solution when time goes to infinity. Moreover,
numerical results are presented
Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface
In this paper we analyze the stability of the traveling wave solution for an
ignition-temperature, first-order reaction model of thermo-diffusive
combustion, in the case of high Lewis numbers (). The system of
two parabolic PDEs is characterized by a free interface at which ignition
temperature is reached. We turn the model to a fully nonlinear
problem in a fixed domain. When the Lewis number is large, we define a
bifurcation parameter and a perturbation parameter
. The main result is the existence of a critical value
close to at which Hopf bifurcation holds for
small enough. Proofs combine spectral analysis and non-standard
application of Hurwitz Theorem with asymptotics as
Working time dimensions and well-being : a cross-national study of Finnish and German health care employees
Health care professionals often face irregular working hours and high work pace. We studied associations of the five working time dimensions duration (weekly working hours), timing (shift work and weekend work), on-call work, working time autonomy, and work tempo (deadline and performance pressure) with well-being among health care employees in Finland and Germany. We used data on working time dimensions and indicators of well-being (work-life conflict, poor perceived health, sleep difficulties, and fatigue) from a cohort of 5050 hospital employees (Working Hours in the Finnish Public Sector Study 2015, WHFPS) and 1450 employees in the health care sector in Germany responding to the German BAuA-Working Time Survey in 2015 (BAuA-WTS). Findings from logistic regression analyses showed that high work tempo was associated with increased work-life conflict (WHFPS: odds ratio [OR] = 3.64, 95%CI 3.04-4.36 and BAuA-WTS: OR = 2.29, 95%CI 1.60-3.27), sleep difficulties (OR = 1.75, 95%CI 1.43-2.15 and OR = 1.33, 95%CI 1.03-1.71) and fatigue (OR = 2.13, 95%CI 1.77-2.57 and OR = 1.64, 95%CI 1.29-2.10) in both datasets. Weekend work was associated with increased work-life conflict (OR = 1.48, 95%CI 1.27-1.72 and OR = 1.61, 95%CI 1.12-2.32); and high working time autonomy with decreased work-life conflict (control over the timing of breaks: OR = 0.65, 95%CI 0.55-0.78 and OR = 0.52, 95%CI 0.33-0.81). The associations between other working time dimensions and well-being were less consistent. These results suggest that tight deadlines, performance pressure, weekend work and lack of working time autonomy are linked to impaired well-being among health care employees.Peer reviewe
Magneto-optics of massive Dirac fermions in bulk Bi2Se3
We report on magneto-optical studies of Bi2Se3, a representative member of
the 3D topological insulator family. Its electronic states in bulk are shown to
be well described by a simple Dirac-type Hamiltonian for massive particles with
only two parameters: the fundamental bandgap and the band velocity. In a
magnetic field, this model implies a unique property - spin splitting equal to
twice the cyclotron energy: Es = 2Ec. This explains the extensive
magneto-transport studies concluding a fortuitous degeneracy of the spin and
orbital split Landau levels in this material. The Es = 2Ec match differentiates
the massive Dirac electrons in bulk Bi2Se3 from those in quantum
electrodynamics, for which Es = Ec always holds.Comment: 5 pages, 3 figures and Supplementary materials, to be published in
Physical Review Letter
Childhood craniopharyngioma: greater hypothalamic involvement before surgery is associated with higher homeostasis model insulin resistance index
<p>Abstract</p> <p>Background</p> <p>Obesity seems to be linked to the hypothalamic involvement in craniopharyngioma. We evaluated the pre-surgery relationship between the degree of this involvement on magnetic resonance imaging and insulin resistance, as evaluated by the homeostasis model insulin resistance index (HOMA). As insulin-like growth factor 1, leptin, soluble leptin receptor (sOB-R) and ghrelin may also be involved, we compared their plasma concentrations and their link to weight change.</p> <p>Methods</p> <p>27 children with craniopharyngioma were classified as either grade 0 (n = 7, no hypothalamic involvement), grade 1 (n = 8, compression without involvement), or grade 2 (n = 12, severe involvement).</p> <p>Results</p> <p>Despite having similar body mass indexes (BMI), the grade 2 patients had higher glucose, insulin and HOMA before surgery than the grade 0 (P = 0.02, <0.05 and 0.02 respectively) and 1 patients (P < 0.02 and <0.03 for both insulin and HOMA). The grade 0 (5.8 ± 4.9) and 1 (7.2 ± 5.3) patients gained significantly less weight (kg) during the year after surgery than did the grade 2 (16.3 ± 7.4) patients. The pre-surgery HOMA was positively correlated with these weight changes (P < 0.03).</p> <p>The data for the whole population before and 6–18 months after surgery showed increases in BMI (P < 0.0001), insulin (P < 0.005), and leptin (P = 0.0005), and decreases in sOB-R (P < 0.04) and ghrelin (P < 0.03).</p> <p>Conclusion</p> <p>The hypothalamic involvement by the craniopharyngioma before surgery seems to determine the degree of insulin resistance, regardless of the BMI. The pre-surgery HOMA values were correlated with the post-surgery weight gain. This suggests that obesity should be prevented by reducing inn secretion in those cases with hypothalamic involvement.</p
Abe homotopy classification of topological excitations under the topological influence of vortices
Topological excitations are usually classified by the th homotopy group
. However, for topological excitations that coexist with vortices, there
are case in which an element of cannot properly describe the charge of
a topological excitation due to the influence of the vortices. This is because
an element of corresponding to the charge of a topological excitation
may change when the topological excitation circumnavigates a vortex. This
phenomenon is referred to as the action of on . In this paper,
we show that topological excitations coexisting with vortices are classified by
the Abe homotopy group . The th Abe homotopy group is
defined as a semi-direct product of and . In this framework, the
action of on is understood as originating from noncommutativity
between and . We show that a physical charge of a topological
excitation can be described in terms of the conjugacy class of the Abe homotopy
group. Moreover, the Abe homotopy group naturally describes vortex-pair
creation and annihilation processes, which also influence topological
excitations. We calculate the influence of vortices on topological excitations
for the case in which the order parameter manifold is , where is
an -dimensional sphere and is a discrete subgroup of . We show
that the influence of vortices on a topological excitation exists only if
is even and includes a nontrivial element of .Comment: 36 pages, 12 figure
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