14,333 research outputs found
Analyticity and criticality results for the eigenvalues of the biharmonic operator
We consider the eigenvalues of the biharmonic operator subject to several
homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show
that simple eigenvalues and elementary symmetric functions of multiple
eigenvalues are real analytic, and provide Hadamard-type formulas for the
corresponding shape derivatives. After recalling the known results in shape
optimization, we prove that balls are always critical domains under volume
constraint.Comment: To appear on the proceedings of the conference "Geometric Properties
for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in
Palinuro (Italy), May 25-29, 201
Boolean versus continuous dynamics on simple two-gene modules
We investigate the dynamical behavior of simple modules composed of two genes
with two or three regulating connections. Continuous dynamics for mRNA and
protein concentrations is compared to a Boolean model for gene activity. Using
a generalized method, we study within a single framework different continuous
models and different types of regulatory functions, and establish conditions
under which the system can display stable oscillations. These conditions
concern the time scales, the degree of cooperativity of the regulating
interactions, and the signs of the interactions. Not all models that show
oscillations under Boolean dynamics can have oscillations under continuous
dynamics, and vice versa.Comment: 8 pages, 10 figure
A dynamical systems approach to actin-based motility in Listeria monocytogenes
A simple kinematic model for the trajectories of Listeria monocytogenes is
generalized to a dynamical system rich enough to exhibit the resonant Hopf
bifurcation structure of excitable media and simple enough to be studied
geometrically. It is shown how L. monocytogenes trajectories and meandering
spiral waves are organized by the same type of attracting set.Comment: 6 pages, 2 figure
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