3,582 research outputs found
Determination of climbing ability
The vertical distribution of the pressure, temperature, and density of the atmosphere varies from day to day. Thus, rates of climb on different days cannot be compared directly, but must be corrected with reference to a standard rate of diminution of air density with increasing altitude. The following problem, therefore, has to be solved. An airplane has climbed on a certain day under prevailing atmospheric conditions as shown by the barograph. How would the same airplane climb in a standard atmosphere? This problem has already been dealt with by Everling, using the monthly and yearly mean of the vertical temperature distribution. Von Mises solved the problem by arithmetical methods. Here, conditions are examined which shorten or lengthen the climbing time. In establishing the corrected barogram, computation seems more practical than graphical treatment. The basis of the answer to the question answered here is summed up in the remark that lift, drag, propeller thrust, and torque and engine power depend only on the density of the air and do not change with the pressure and temperature, provided that the density remains constant
Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder
The Kuramoto phase diffusion equation is a nonlinear partial differential
equation which describes the spatio-temporal evolution of a phase variable in
an oscillatory reaction diffusion system. Synchronization manifests itself in a
stationary phase gradient where all phases throughout a system evolve with the
same velocity, the synchronization frequency. The formation of concentric waves
can be explained by local impurities of higher frequency which can entrain
their surroundings. Concentric waves in synchronization also occur in
heterogeneous systems, where the local frequencies are distributed randomly. We
present a perturbation analysis of the synchronization frequency where the
perturbation is given by the heterogeneity of natural frequencies in the
system. The nonlinearity in form of dispersion, leads to an overall
acceleration of the oscillation for which the expected value can be calculated
from the second order perturbation terms. We apply the theory to simple
topologies, like a line or the sphere, and deduce the dependence of the
synchronization frequency on the size and the dimension of the oscillatory
medium. We show that our theory can be extended to include rotating waves in a
medium with periodic boundary conditions. By changing a system parameter the
synchronized state may become quasi degenerate. We demonstrate how perturbation
theory fails at such a critical point.Comment: 22 pages, 5 figure
Planetary geological studies
A global data base was assembled for the study of Mars crater ejecta morphology. The craters were classified as to morhology using individual photographic prints of Viking orbiter frames. Positional and scale information were derived by fitting digitized mosaic coordinates to lattitude-longitude coordinates of surface features from the Mars geodetic control net and feature coordinates from the U.S.G.S. series of 1:5,00,000 scale shaded relief maps. Crater morphology characteristics recorded are of two classes - attributes of each ejecta deposit and other crater charactersitics. Preliminary efforts to check the data base with findings of other workers are described
Population growth and persistence in a heterogeneous environment: the role of diffusion and advection
The spatio-temporal dynamics of a population present one of the most
fascinating aspects and challenges for ecological modelling. In this article we
review some simple mathematical models, based on one dimensional
reaction-diffusion-advection equations, for the growth of a population on a
heterogeneous habitat. Considering a number of models of increasing complexity
we investigate the often contrary roles of advection and diffusion for the
persistence of the population. When it is possible we demonstrate basic
mathematical techniques and give the critical conditions providing the survival
of a population, in simple systems and in more complex resource-consumer models
which describe the dynamics of phytoplankton in a water column.Comment: Introductory review of simple conceptual models. 45 pages, 15 figures
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Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer
The vertical distribution of phytoplankton is of fundamental importance for
the dynamics and structure of aquatic communities. Here, using an
advection-reaction-diffusion model, we investigate the distribution and
competition of phytoplankton species in a water column, in which inverse
resource gradients of light and a nutrient can limit growth of the biomass.
This problem poses a challenge for ecologists, as the location of a production
layer is not fixed, but rather depends on many internal parameters and
environmental factors. In particular, we study the influence of an upper mixed
layer (UML) in this system and show that it leads to a variety of dynamic
effects: (i) Our model predicts alternative density profiles with a maximum of
biomass either within or below the UML, thereby the system may be bistable or
the relaxation from an unstable state may require a long-lasting transition.
(ii) Reduced mixing in the deep layer can induce oscillations of the biomass;
we show that a UML can sustain these oscillations even if the diffusivity is
less than the critical mixing for a sinking phytoplankton population. (iii) A
UML can strongly modify the outcome of competition between different
phytoplankton species, yielding bistability both in the spatial distribution
and in the species composition. (iv) A light limited species can obtain a
competitive advantage if the diffusivity in the deep layers is reduced below a
critical value. This yields a subtle competitive exclusion effect, where the
oscillatory states in the deep layers are displaced by steady solutions in the
UML. Finally, we present a novel graphical approach for deducing the
competition outcome and for the analysis of the role of a UML in aquatic
systems.Comment: 20 pages, 8 figure
Optical read out and feedback cooling of a nanostring optomechanical cavity
Optical measurement of the motion of a 940 kHz mechanical resonance of a
silicon nitride nanostring resonator is demonstrated with a read out noise
imprecision reaching 37 dB below that of the resonator's zero-point
fluctuations. Via intensity modulation of the optical probe laser, radiation
pressure feedback is used to cool and damp the mechanical mode from an initial
room temperature occupancy of (K)
down to a phonon occupation of , representing a
mode temperature of mK. The five decades of cooling is enabled
by the system's large single-photon cooperativity and high
quantum efficiency of optical motion detection ().Comment: 13 pages, 13 figure
Consequences of fluctuating group size for the evolution of cooperation
Studies of cooperation have traditionally focused on discrete games such as
the well-known prisoner's dilemma, in which players choose between two pure
strategies: cooperation and defection. Increasingly, however, cooperation is
being studied in continuous games that feature a continuum of strategies
determining the level of cooperative investment. For the continuous snowdrift
game, it has been shown that a gradually evolving monomorphic population may
undergo evolutionary branching, resulting in the emergence of a defector
strategy that coexists with a cooperator strategy. This phenomenon has been
dubbed the 'tragedy of the commune'. Here we study the effects of fluctuating
group size on the tragedy of the commune and derive analytical conditions for
evolutionary branching. Our results show that the effects of fluctuating group
size on evolutionary dynamics critically depend on the structure of payoff
functions. For games with additively separable benefits and costs, fluctuations
in group size make evolutionary branching less likely, and sufficiently large
fluctuations in group size can always turn an evolutionary branching point into
a locally evolutionarily stable strategy. For games with multiplicatively
separable benefits and costs, fluctuations in group size can either prevent or
induce the tragedy of the commune. For games with general interactions between
benefits and costs, we derive a general classification scheme based on second
derivatives of the payoff function, to elucidate when fluctuations in group
size help or hinder cooperation.Comment: 22 pages, 5 figure
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