5,412 research outputs found
Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
Viscous fingering experiments in Hele-Shaw cells lead to striking pattern
formations which have been the subject of intense focus among the physics and
applied mathematics community for many years. In recent times, much attention
has been devoted to devising strategies for controlling such patterns and
reducing the growth of the interfacial fingers. We continue this research by
reporting on numerical simulations, based on the level set method, of a
generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is
altered. First, we investigate how imposing constant and time-dependent
injection rates in a Hele-Shaw cell that is either standard, tapered or
rotating can be used to reduce the development of viscous fingering when an
inviscid fluid is injected into a viscous fluid over a finite time period. We
perform a series of numerical experiments comparing the effectiveness of each
strategy to determine how these non-standard Hele-Shaw configurations influence
the morphological features of the inviscid-viscous fluid interface. Tapering
plates in either converging or diverging directions leads to reduced metrics of
viscous fingering at the final time when compared to the standard parallel
configuration, especially with carefully chosen injection rates; for the
rotating plate case, the effect is even more dramatic, with sufficiently large
rotation rates completely stabilising the interface. Next, we illustrate how
the number of non-splitting fingers can be controlled by injecting the inviscid
fluid at a time-dependent rate while increasing the gap between the plates.
Simulations compare well with previous experimental results for various
injection rates and geometric configurations. Further, we demonstrate how the
fully nonlinear dynamics of the problem affect the number of fingers that
emerge and how well this number agrees with predictions from linear stability
analysis
On the Existence of Bertrand-Nash Equilibrium Prices Under Logit Demand
This article presents a proof of the existence of Bertrand-Nash equilibrium
prices with multi-product firms and under the Logit model of demand that does
not rely on restrictive assumptions on product characteristics, firm
homogeneity or symmetry, product costs, or linearity of the utility function.
The proof is based on conditions for the indirect utility function, fixed-point
equations derived from the first-order conditions, and a direct analysis of the
second-order conditions resulting in the uniqueness of profit-maximizing
prices. Several subsequent results also demonstrate that price equilibrium
under the Logit model of demand cannot adequately describe multi-product
pricing.Comment: 39 Page
Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed Logit Demand: A Technical Framework for Analysis and Efficient Computational Methods
This article presents a detailed technical framework for modeling with
Bertrand-Nash equilibrium prices under Mixed Logit demand. Two coercive
fixed-point equations provide more stable computational methods than those
obtained from the literal first-order conditions. Assumptions to justify
derivation and use of these equations are provided. A brief discussion of a
GMRES-Newton method with hookstep globalization strategy originally due to
Viswanath is also given. This article can be considered a supplement to an
article by the authors forthcoming in the journal {\em Operations Research}.Comment: 57 page
An analytical approach to solution of two- point boundary condition problems in optimal guidance Summary report, May 1965 - Apr. 1966
Analytical approaches to path-adaptive guidance functions, circular orbit trajectories, and use of Fortran-compiled program
Scenarios for optimizing potato productivity in a lunar CELSS
The use of controlled ecological life support system (CELSS) in the development and growth of large-scale bases on the Moon will reduce the expense of supplying life support materials from Earth. Such systems would use plants to produce food and oxygen, remove carbon dioxide, and recycle water and minerals. In a lunar CELSS, several factors are likely to be limiting to plant productivity, including the availability of growing area, electrical power, and lamp/ballast weight for lighting systems. Several management scenarios are outlined in this discussion for the production of potatoes based on their response to irradiance, photoperiod, and carbon dioxide concentration. Management scenarios that use 12-hr photoperiods, high carbon dioxide concentrations, and movable lamp banks to alternately irradiate halves of the growing area appear to be the most efficient in terms of growing area, electrical power, and lamp weights. However, the optimal scenario will be dependent upon the relative 'costs' of each factor
Population response of triploid grass carp to declining levels of hydrilla in the Santee Cooper Reservoirs, South Carolina
Approximately 768,500 triploid grass carp (
Ctenopharyngodon
idella
Valenciennes) were stocked into the Santee Cooper
reservoirs, South Carolina between 1989 and 1996 to
control hydrilla (
Hydrilla verticillata
(L.f.) Royle). Hydrilla
coverage was reduced from a high of 17,272 ha during 1994
to a few ha by 1998. During 1997, 1998 and 1999, at least 98
triploid grass carp were collected yearly for population monitoring.
Estimates of age, growth, and mortality, as well as
population models, were used in the study to monitor triploid
grass carp and predict population trends. Condition declined
from that measured during a previous study in 1994.
The annual mortality rate was estimated at 28% in 1997, 32%
in 1998 and 39% in 1999; however, only the 1999 mortality
rate was significantly different. Few (2 out of 98) of the triploid
grass carp collected during 1999 were older than age 9.
We expect increased mortality due to an aging population
and sparse hydrilla coverage. During 1999, we estimated about
63,000 triploid grass carp system wide and project less than
3,000 fish by 2004, assuming no future stocking.
management, population size
Ctenopharyngodon idella, Hydrill
Two-interface and thin filament approximation in Hele--Shaw channel flow
For a viscous fluid trapped in a Hele--Shaw channel, and pushed by a pressure
difference, the fluid interface is unstable due to the Saffman--Taylor
instability. We consider the evolution of a fluid region of finite extent,
bounded between two interfaces, in the limit the interfaces are close, that is,
when the fluid region is a thin liquid filament separating two gases of
different pressure. In this limit, we derive a geometric flow rule that
describes the normal velocity of the filament centreline, and evolution of the
filament thickness, as functions of the thickness and centreline curvature. We
show that transverse flow along the filament is necessary to regularise the
instability. Numerical simulation of the thin filament flow rule is shown to
closely match level-set computations of the complete two-interface model, and
solutions ultimately evolve to form a bubble of increasing radius and
decreasing thickness
Light emitting diodes as a plant lighting source
Electroluminescence in solid materials is defined as the generation of light by the passage of an electric current through a body of solid material under an applied electric field. A specific type of electroluminescence, first noted in 1923, involves the generation of photons when electrons are passed through a p-n junction of certain solid materials (junction of a n-type semiconductor, an electron donor, and a p-type semiconductor, an electron acceptor). The development of this light emitting semiconductor technology dates back less than 30 years. During this period of time, the LED has evolved from a rare and expensive light generating device to one of the most widely used electronic components. A number of LED characteristics are of considerable importance in selecting a light source for plant lighting in a controlled environment facility. Of particular importance is the characteristic that light is generated by an LED at a rate far greater than the corresponding thermal radiation predicted by the bulk temperature of the device as defined by Plank's radiation law. This is in sharp contrast to other light sources, such as an incandescent or high intensity discharge lamp. A plant lighting system for controlled environments must provide plants with an adequate flux of photosynthetically active radiation, plus providing photons in the spectral regions that are involved in the photomorphogenic and phototropic responses that result in normal plant growth and development. Use of light sources that emit photons over a broad spectral range generally meet these two lighting requirements. Since the LED's emit over specific spectral regions, they must be carefully selected so that the levels of photsynthetically active and photomorphogenic and phototropic radiation meet these plant requirements
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