1,055 research outputs found
Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis
A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined
Spatial three-dimensional secondary instability compressible boundary-layer flows
Three-dimensional linear secondary instability theory is extended for compressible and high Mach number boundary layer flows. The small but finite amplitude compressible Tollmien-Schlichting wave effect on the growth of 3-D perturbations is investigated. The focus is on principal parametric resonance responsible for the strong growth of subharmonic in low disturbance environment. The effect of increasing Mach number on the onset, growth, the shape of eigenfunctions of the subharmonic is assessed, and the resulting vortical structure is examined
Secondary three-dimensional instability in compressible boundary layers
Three dimensional linear secondary instability theory is extended for compressible boundary layers on a flat plate in the presence of finite amplitude Tollmien-Schlichting waves. The focus is on principal parametric resonance responsible for strong growth of subharmonics in low disturbance environment
Effect of Suction on Controlling the Secondary Instability of Boundary Layers
The effect of suction on controlling the 3-D secondary instability is investigated for a boundary layer with pressure gradient in the presence of small but finite amplitude Tollmien-Schlichting wave. The focus is on principal parametric resonance responsible for strong growth of subharmonics in low disturbance environment. Calculations are presented for the effect of suction on the onset and amplification of the secondary instability in Blasius and Falkner-Skan flows, as well as its effect on controlling the production of the vortical structure
Foraging as an evidence accumulation process
A canonical foraging task is the patch-leaving problem, in which a forager
must decide to leave a current resource in search for another. Theoretical work
has derived optimal strategies for when to leave a patch, and experiments have
tested for conditions where animals do or do not follow an optimal strategy.
Nevertheless, models of patch-leaving decisions do not consider the imperfect
and noisy sampling process through which an animal gathers information, and how
this process is constrained by neurobiological mechanisms. In this theoretical
study, we formulate an evidence accumulation model of patch-leaving decisions
where the animal averages over noisy measurements to estimate the state of the
current patch and the overall environment. Evidence accumulation models belong
to the class of drift diffusion processes and have been used to model decision
making in different contexts. We solve the model for conditions where foraging
decisions are optimal and equivalent to the marginal value theorem, and perform
simulations to analyze deviations from optimal when these conditions are not
met. By adjusting the drift rate and decision threshold, the model can
represent different strategies, for example an increment-decrement or counting
strategy. These strategies yield identical decisions in the limiting case but
differ in how patch residence times adapt when the foraging environment is
uncertain. To account for sub-optimal decisions, we introduce an
energy-dependent utility function that predicts longer than optimal patch
residence times when food is plentiful. Our model provides a quantitative
connection between ecological models of foraging behavior and evidence
accumulation models of decision making. Moreover, it provides a theoretical
framework for potential experiments which seek to identify neural circuits
underlying patch leaving decisions
Mechanical Surface Waves Accompany Action Potential Propagation
Many studies have shown that a mechanical displacement of the axonal membrane
accompanies the electrical pulse defining the Action Potential (AP). Despite a
large and diverse body of experimental evidence, there is no theoretical
consensus either for the physical basis of this mechanical wave nor its
interdependence with the electrical signal. In this manuscript we present a
model for these mechanical displacements as arising from the driving of surface
wave modes in which potential energy is stored in elastic properties of the
neuronal membrane and cytoskeleton while kinetic energy is carried by the
axoplasmic fluid. In our model these surface waves are driven by the traveling
wave of electrical depolarization that characterizes the AP, altering the
compressive electrostatic forces across the membrane as it passes. This driving
leads to co-propagating mechanical displacements, which we term Action Waves
(AWs). Our model for these AWs allows us to predict, in terms of elastic
constants, axon radius and axoplasmic density and viscosity, the shape of the
AW that should accompany any traveling wave of voltage, including the AP
predicted by the Hodgkin and Huxley (HH) equations. We show that our model
makes predictions that are in agreement with results in experimental systems
including the garfish olfactory nerve and the squid giant axon. We expect our
model to serve as a framework for understanding the physical origins and
possible functional roles of these AWs in neurobiology.Comment: 6 pages 3 figures + 2 page supplemen
Goertler instability in compressible boundary layers along curved surfaces with suction and cooling
The Goertler instability of the laminar compressible boundary layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating streamwise vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear coordinate. The basic approximation of the disturbance equations, that includes the effect of the growth of the boundary layer, is considered and solved numerically. The effect of compressibility on critical stability limits, growth rates, and amplitude ratios of the vortices is evaluated for a range of Mach numbers for 0 to 5. The effect of wall cooling and suction of the boundary layer on the development of Goertler vortices is investigated for different Mach numbers
Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows
An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used
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