32,110 research outputs found
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Bose-Einstein Condensates in Superlattices
We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns
Medical operations and life sciences activities on space station
Space station health maintenance facilities, habitability, personnel, and research in the medical sciences and in biology are discussed. It is assumed that the space station structure will consist of several modules, each being consistent with Orbiter payload bay limits in size, weight, and center of gravity
Space Station medical sciences concepts
Current life sciences concepts relating to Space Station are presented including the following: research, extravehicular activity, biobehavioral considerations, medical care, maintenance of dental health, maintaining health through physical conditioning and countermeasures, protection from radiation, atmospheric contamination control, atmospheric composition, noise pollution, food supply and service, clothing and furnishings, and educational program possibilities. Information on the current status of Soviet Space Stations is contained
Shell-model interpretation of high-spin states in 134-I
New experimental information has been recently obtained on the odd-odd
nucleus 134-I. We interpret the five observed excited states up to the energy
of ~3 MeV on the basis of a realistic shell-model calculation, and make
spin-parity assignments accordingly. A very good agreement is found between the
experimental and calculated energies.Comment: 3 pages, 1 figur
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates
We investigate the dynamics of an effectively one-dimensional Bose-Einstein
condensate (BEC) with scattering length subjected to a spatially periodic
modulation, . This "collisionally inhomogeneous" BEC is
described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is
a periodic function of . We transform this equation into a GP equation with
constant coefficient and an additional effective potential and study a
class of extended wave solutions of the transformed equation. For weak
underlying inhomogeneity, the effective potential takes a form resembling a
superlattice, and the amplitude dynamics of the solutions of the
constant-coefficient GP equation obey a nonlinear generalization of the Ince
equation. In the small-amplitude limit, we use averaging to construct
analytical solutions for modulated amplitude waves (MAWs), whose stability we
subsequently examine using both numerical simulations of the original GP
equation and fixed-point computations with the MAWs as numerically exact
solutions. We show that "on-site" solutions, whose maxima correspond to maxima
of , are significantly more stable than their "off-site" counterparts.Comment: 25 pages, 10 figures (many with several parts), to appear in Physica
D; higher resolution versions of some figures are available at
http://www.its.caltech.edu/~mason/paper
Nonlinearity Management in Optics: Experiment, Theory, and Simulation
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the (2+1)-dimensional focusing cubic nonlinear Schrödinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method
The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field
Let k be a global field and let k_v be the completion of k with respect to v,
a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected
algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let
G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma)
be its congruence kernel. Lubotzky has shown that C is infinite, confirming an
earlier conjecture of Serre. Here we provide complete solution of the
congruence subgroup problem for \Gamm$ by determining the structure of C. It is
shown that C is a free profinite product, one of whose factors is
\hat{F}_{\omega}, the free profinite group on countably many generators. The
most surprising conclusion from our results is that the structure of C depends
only on the characteristic of k. The structure of C is already known for a
number of special cases. Perhaps the most important of these is the
(non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the
ring of S-integers in k, with S=\{v\}, which plays a central role in the theory
of Drinfeld modules. The proof makes use of a decomposition theorem of
Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated
with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat
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