5,903 research outputs found
Exponential stabilization without geometric control
We present examples of exponential stabilization for the damped wave equation
on a compact manifold in situations where the geometric control condition is
not satisfied. This follows from a dynamical argument involving a topological
pressure on a suitable uncontrolled set
Geometric control of myogenic cell fate.
This work combines expertise in stem cell biology and bioengineering to define the system for geometric control of proliferation and differentiation of myogenic progenitor cells. We have created an artificial niche of myogenic progenitor cells, namely, modified extracellular matrix (ECM) substrates with spatially embedded growth or differentiation factors (GF, DF) that predictably direct muscle cell fate in a geometric pattern. Embedded GF and DF signal progenitor cells from specifically defined areas on the ECM successfully competed against culture media for myogenic cell fate determination at a clearly defined boundary. Differentiation of myoblasts into myotubes is induced in growth-promoting medium, myotube formation is delayed in differentiation-promoting medium, and myogenic cells, at different stages of proliferation and differentiation, can be induced to coexist adjacently in identical culture media. This method can be used to identify molecular interactions between cells in different stages of myogenic differentiation, which are likely to be important determinants of tissue repair. The designed ECM niches can be further developed into a vehicle for transplantation of myogenic progenitor cells maintaining their regenerative potential. Additionally, this work may also serve as a general model to engineer synthetic cellular niches to harness the regenerative potential of organ stem cells
Geometric control of bacterial surface accumulation
Controlling and suppressing bacterial accumulation at solid surfaces is
essential for preventing biofilm formation and biofouling. Whereas various
chemical surface treatments are known to reduce cell accumulation and
attachment, the role of complex surface geometries remains less well
understood. Here, we report experiments and simulations that explore the
effects of locally varying boundary curvature on the scattering and
accumulation dynamics of swimming Escherichia coli bacteria in
quasi-two-dimensional microfluidic channels. Our experimental and numerical
results show that a concave periodic boundary geometry can decrease the average
cell concentration at the boundary by more than 50% relative to a flat surface.Comment: 10 pages, 5 figure
Realizations of Real Low-Dimensional Lie Algebras
Using a new powerful technique based on the notion of megaideal, we construct
a complete set of inequivalent realizations of real Lie algebras of dimension
no greater than four in vector fields on a space of an arbitrary (finite)
number of variables. Our classification amends and essentially generalizes
earlier works on the subject.
Known results on classification of low-dimensional real Lie algebras, their
automorphisms, differentiations, ideals, subalgebras and realizations are
reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in
Appendix are correcte
The weak Pleijel theorem with geometric control
Let , be a bounded open set, and denote
by , the eigenvalues of the Dirichlet Laplacian
arranged in nondecreasing order, with multiplicities. The weak form of
Pleijel's theorem states that the number of eigenvalues ,
for which there exists an associated eigenfunction with precisely nodal
domains (Courant-sharp eigenvalues), is finite. The purpose of this note is to
determine an upper bound for Courant-sharp eigenvalues, expressed in terms of
simple geometric invariants of . We will see that this is connected
with one of the favorite problems considered by Y. Safarov.Comment: Revised Oct. 12, 2016. To appear in Journal of Spectral Theory 6
(2016
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