878 research outputs found
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
Meristem identity gene expression during curd proliferation and flower initiation in Brassica oleracea
The regulation of reproductive development in cauliflower (Brassica oleracea var. botrytis DC) and broccoli (B. oleracea L. var. italica Plenck) is unusual in that most enlargement occurs while development is arrested at a distinct stage. Cauliflower and broccoli curds are composed of inflorescence meristems and flower buds, respectively. To determine whether this arrest is maintained by altered expression of the genes that specify these steps in Arabidopsis, the expression of each copy of their homologues (MADS-box genes BoAP1-a, BoAP1-c, BoCAL, BoFUL-a, BoFUL-b, BoFUL-c, and BoFUL-d; and non-MADS-box genes BoLFY, AP2, UFO, and BoTFL1) and the cauliflower curd-specific genes CCE1 and BoREM1 were measured simultaneously in heads that were arrested at different developmental stages by varying temperature, but had a common genotype. Transcript abundance of BoFUL paralogues and BoLFY was highest at the cauliflower stage of arrest, consistent with these genes initiating inflorescence meristems. The expression of other genes was the same regardless of the developmental stage of arrest. The expected models can therefore be excluded, wherein maintenance of arrest at the inflorescence meristem is a consequence of suppression of BoCAL, BoAP1-a, or BoLFY, or failure to suppress BoTFL1. Floral primordia and floral buds were normal in boap1-a boap1-c bocal triple mutants; therefore, other meristem identity genes can specify floral initiation (A-function) in B. oleracea. BoTFL1, a strong repressor of flowering in Arabidopsis, did not suppress the formation of the floral primordium in B. oleracea. Initiation of floral primordia and enlargement of floral buds in broccoli and cauliflower is not controlled solely by homologues of the genes that do so in Arabidopsi
Weakly regular Floquet Hamiltonians with pure point spectrum
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on
the parameter omega. We assume that the spectrum of H is discrete, {h_m (m =
1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian
operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose
that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m -
h_n)^(-sigma) < infinity where mu_{mn} = sqrt(min{M_m,M_n)) M_m M_n. We show
that in that case there exist a suitable norm to measure the regularity of V,
denoted epsilon, and positive constants, epsilon_* & delta_*, such that: if
epsilon
|Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure point
spectrum for all omega in Omega_infinity.Comment: 35 pages, Latex with AmsAr
Tissue fusion over non-adhering surfaces
Tissue fusion eliminates physical voids in a tissue to form a continuous
structure and is central to many processes in development and repair. Fusion
events in vivo, particularly in embryonic development, often involve the
purse-string contraction of a pluricellular actomyosin cable at the free edge.
However in vitro, adhesion of the cells to their substrate favors a closure
mechanism mediated by lamellipodial protrusions, which has prevented a
systematic study of the purse-string mechanism. Here, we show that monolayers
can cover well-controlled mesoscopic non-adherent areas much larger than a cell
size by purse-string closure and that active epithelial fluctuations are
required for this process. We have formulated a simple stochastic model that
includes purse-string contractility, tissue fluctuations and effective friction
to qualitatively and quantitatively account for the dynamics of closure. Our
data suggest that, in vivo, tissue fusion adapts to the local environment by
coordinating lamellipodial protrusions and purse-string contractions
Bound states in straight quantum waveguides with combined boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional straight strip. We impose the combined
Dirichlet and Neumann boundary conditions on different parts of the boundary.
Several statements on the existence or the absence of the discrete spectrum are
proven for two models with combined boundary conditions. Examples of
eigenfunctions and eigenvalues are computed numerically.Comment: 24 pages, LaTeX 2e with 4 eps figure
Pulse-driven quantum dynamics beyond the impulsive regime
We review various unitary time-dependent perturbation theories and compare
them formally and numerically. We show that the Kolmogorov-Arnold-Moser
technique performs better owing to both the superexponential character of
correction terms and the possibility to optimize the accuracy of a given level
of approximation which is explored in details here. As an illustration, we
consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure
On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum
of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha,
with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay
as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously
differentiable in the strong sense and such that the matrix entries with
respect to the spectral decomposition of H obey the estimate
|V(t)_{m,n}|0,
p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be
arbitrarily small provided p is sufficiently large and \epsilon is small
enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the
diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where
\sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the
Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was
discussed earlier in the literature by Howland
On the stability of periodically time-dependent quantum systems
The main motivation of this article is to derive sufficient conditions for
dynamical stability of periodically driven quantum systems described by a
Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} |
(psi(t),H(t) psi(t)) |<\infty where psi(t) denotes a trajectory at time t of
the quantum system under consideration. We start from an analysis of the domain
of the quasi-energy operator. Next we show, under certain assumptions, that if
the spectrum of the monodromy operator U(T,0) is pure point then there exists a
dense subspace of initial conditions for which the mean value of energy is
uniformly bounded in the course of time. Further we show that if the propagator
admits a differentiable Floquet decomposition then || H(t) psi(t) || is bounded
in time for any initial condition psi(0), and one employs the quantum KAM
algorithm to prove the existence of this type of decomposition for a fairly
large class of H(t). In addition, we derive bounds uniform in time on
transition probabilities between different energy levels, and we also propose
an extension of this approach to the case of a higher order of
differentiability of the Floquet decomposition. The procedure is demonstrated
on a solvable example of the periodically time-dependent harmonic oscillator.Comment: 39 page
Soybean, 1962-1966
Cover title."University of Missouri Agricultural Experiment Station in cooperation with Agricultural Research Service, U.S. Dept. Agriculture.
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