76,597 research outputs found
Twisted and Nontwisted Bifurcations Induced by Diffusion
We discuss a diffusively perturbed predator-prey system. Freedman and
Wolkowicz showed that the corresponding ODE can have a periodic solution that
bifurcates from a homoclinic loop. When the diffusion coefficients are large,
this solution represents a stable, spatially homogeneous time-periodic solution
of the PDE. We show that when the diffusion coefficients become small, the
spatially homogeneous periodic solution becomes unstable and bifurcates into
spatially nonhomogeneous periodic solutions.
The nature of the bifurcation is determined by the twistedness of an
equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients
decrease. In the nontwisted case two spatially nonhomogeneous simple periodic
solutions of equal period are generated, while in the twisted case a unique
spatially nonhomogeneous double periodic solution is generated through
period-doubling.
Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic
bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex
files. Hard copy of figures available on request from
[email protected]
Tracking intracavernously injected adipose-derived stem cells to bone marrow.
The intracavernous (i.c.) injection of stem cells (SCs) has been shown to improve erectile function in various erectile dysfunction (ED) animal models. However, the tissue distribution of the injected cells remains unknown. In this study we tracked i.c.-injected adipose-derived stem cells (ADSCs) in various tissues. Rat paratesticular fat was processed for ADSC isolation and culture. The animals were then subject to cavernous nerve (CN) crush injury or sham operation, followed by i.c. injection of 1 million autologous or allogeneic ADSCs that were labeled with 5-ethynyl-2-deoxyuridine (EdU). Another group of rats received i.c. injection of EdU-labeled allogeneic penile smooth muscle cells (PSMCs). At 2 and 7 days post injection, penises and femoral bone marrow were processed for histological analyses. Whole femoral bone marrows were also analyzed for EdU-positive cells by flow cytometry. The results show that ADSCs exited the penis within days of i.c. injection and migrated preferentially to bone marrow. Allogenicity did not affect the bone marrow appearance of ADSCs at either 2 or 7 days, whereas CN injury reduced the number of ADSCs in bone marrow significantly at 7 but not 2 days. The significance of these results in relation to SC therapy for ED is discussed
Phase dynamics of inductively coupled intrinsic Josephson junctions and terahertz electromagnetic radiation
The Josephson effects associated with quantum tunneling of Cooper pairs
manifest as nonlinear relations between the superconductivity phase difference
and the bias current and voltage. Many novel phenomena appear, such as Shapiro
steps in dc cuurent-voltage (IV) characteristics of a Josephson junction under
microwave shining, which can be used as a voltage standard. Inversely, the
Josephson effects provide a unique way to generate high-frequency
electromagnetic (EM) radiation by dc bias voltage. The discovery of cuprate
high-Tc superconductors accelerated the effort to develop novel source of EM
waves based on a stack of atomically dense-packed intrinsic Josephson junctions
(IJJs), since the large superconductivity gap covers the whole terahertz
frequency band. Very recently, strong and coherent terahertz radiations have
been successfully generated from a mesa structure of
single crystal which works both as the source
of energy gain and as the cavity for resonance. It is then found theoretically
that, due to huge inductive coupling of IJJs produced by the nanometer junction
separation and the large London penetration depth of order of of
the material, a novel dynamic state is stabilized in the coupled sine-Gordon
system, in which kinks in phase differences are developed responding
to the standing wave of Josephson plasma and are stacked alternatively in the
c-axis. This novel solution of the inductively coupled sine-Gordon equations
captures the important features of experimental observations. The theory
predicts an optimal radiation power larger than the one available to date by
orders of magnitude, and thus suggests the technological relevance of the
phenomena.Comment: review article (69 pages, 30 figures
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