18,789 research outputs found
Absence of reflection as a function of the coupling constant
We consider solutions of the one-dimensional equation where is locally integrable, is integrable with supp, and
is a coupling constant. Given a family of solutions
which satisfy for all , we prove that the zeros of , the Wronskian of and , form a discrete set
unless . Setting , one sees that a particular
consequence of this result may be stated as: if the fixed energy scattering
experiment gives rise to a reflection coefficient
which vanishes on a set of couplings with an accumulation point, then .Comment: To appear in Journal of Mathematical Physic
The Order of Phase Transitions in Barrier Crossing
A spatially extended classical system with metastable states subject to weak
spatiotemporal noise can exhibit a transition in its activation behavior when
one or more external parameters are varied. Depending on the potential, the
transition can be first or second-order, but there exists no systematic theory
of the relation between the order of the transition and the shape of the
potential barrier. In this paper, we address that question in detail for a
general class of systems whose order parameter is describable by a classical
field that can vary both in space and time, and whose zero-noise dynamics are
governed by a smooth polynomial potential. We show that a quartic potential
barrier can only have second-order transitions, confirming an earlier
conjecture [1]. We then derive, through a combination of analytical and
numerical arguments, both necessary conditions and sufficient conditions to
have a first-order vs. a second-order transition in noise-induced activation
behavior, for a large class of systems with smooth polynomial potentials of
arbitrary order. We find in particular that the order of the transition is
especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version
accepted for publication by Phys. Rev.
Chaotic exploration and learning of locomotion behaviours
We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage
Development of control systems for space shuttle vehicles, volume 1
Control of winged two-stage space shuttle vehicles was investigated. Control requirements were determined and systems capable of meeting these requirements were synthesized. Control requirements unique to shuttles were identified. It is shown that these requirements can be satisfied by conventional control logics. Linear gain schedule controllers predominate. Actuator saturations require nonlinear compensation in some of the control systems
Detection and partial sequence analysis of gastrin mRNA by using an oligodeoxynucleotide probe.
Asymptotics and numerics of a family of two-dimensional generalized surface quasi-geostrophic equations
We study the generalised 2D surface quasi-geostrophic (SQG) equation, where the active scalar is given by a fractional power α of Laplacian applied to the stream function. This includes the 2D SQG and Euler equations as special cases. Using PoincarĂ©âs successive approximation to higher α-derivatives of the active scalar, we derive a variational equation for describing perturbations in the generalized SQG equation. In particular, in the limit α â 0, an asymptotic equation is derived on a stretched time variable Ï = αt, which unifies equations in the family near α = 0. The successive approximation is also discussed at the other extreme of the 2D Euler limit α = 2â0. Numerical experiments are presented for both limits. We consider whether the solution behaves in a more singular fashion, with more effective nonlinearity, when α is increased. Two competing effects are identified: the regularizing effect of a fractional inverse Laplacian (control by conservation) and cancellation by symmetry (nonlinearity depletion). Near α = 0 (complete depletion), the solution behaves in a more singular fashion as α increases. Near α = 2 (maximal control by conservation), the solution behave in a more singular fashion, as α decreases, suggesting that there may be some α in [0, 2] at which the solution behaves in the most singular manner. We also present some numerical results of the family for α = 0.5, 1, and 1.5. On the original time t, the H 1 norm of Ξ generally grows more rapidly with increasing α. However, on the new time Ï, this order is reversed. On the other hand, contour patterns for different α appear to be similar at fixed Ï, even though the norms are markedly different in magnitude. Finally, point-vortex systems for the generalized SQG family are discussed to shed light on the above problems of time scale
From SCHIP Benefit Design to Individual Coverage Decisions
The majority of states have implemented separate SCHIP (S-SCHIP) programs that significantly depart from Medicaid and resemble less comprehensive commercial products. This difference in program design may result in S-SCHIP potentially being less responsive to children with special needs (CSHCNs). This study explores how responsive insurers are to these higher than average needs. We found that, with one exception, insurers did not agree on the coverage of any specific service, but overall they provided coverage beyond state limits and exclusions. Second, the less acute the childhood condition, the more frequently insurers imposed exclusions. Finally, in the majority of states, some insurers excluded services that arguably should have been covered according to the plan/contract language. We conclude that SCHIP coverage at current levels may not be sufficient to care for CSHCNs, making external reviews of insurers\u27 coverage decisions and coordination with other sources of care important components of SCHIP program design
Gate-Controlled Electron Spin Resonance in a GaAs/AlGaAs Heterostructure
The electron spin resonance (ESR) of two-dimensional electrons is
investigated in a gated GaAs/AlGaAs heterostructure. We found that the ESR
resonance frequency can be turned by means of a gate voltage. The front and
back gates of the heterostructure produce opposite g-factor shift, suggesting
that electron g-factor is being electrostatically controlled by shifting the
equilibrium position of the electron wave function from one epitaxial layer to
another with different g-factors
Scattering of positrons and electrons by alkali atoms
Absolute total scattering cross sections (Q sub T's) were measured for positrons and electrons colliding with sodium, potassium, and rubidium in the 1 to 102 eV range, using the same apparatus and experimental approach (a beam transmission technique) for both projectiles. The present results for positron-sodium and -rubidium collisions represent the first Q sub T measurements reported for these collision systems. Features which distinguish the present comparisons between positron- and electron-alkali atom Q sub T's from those for other atoms and molecules (room-temperature gases) which have been used as targets for positrons and electrons are the proximity of the corresponding positron- and electron-alkali atom Q sub T's over the entire energy range of overlap, with an indication of a merging or near-merging of the corresponding positron and electron Q sub T's near (and above) the relatively low energy of about 40 eV, and a general tendency for the positron-alkali atom Q sub T's to be higher than the corresponding electron values as the projectile energy is decreased below about 40 eV
Inhomogeneous scalar field solutions and inflation
We present new exact cosmological inhomogeneous solutions for gravity coupled
to a scalar field in a general framework specified by the parameter .
The equations of motion (and consequently the solutions) in this framework
correspond either to low-energy string theory or Weyl integrable spacetime
according to the sign of . We show that different inflationary
behaviours are possible, as suggested by the study of the violation of the
strong energy condition. Finally, by the analysis of certain curvature scalars
we found that some of the solutions may be nonsingular.Comment: LaTex file, 14 page
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