6,495 research outputs found
Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow
The problem considered here is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process yields, by analogy with the classical Euler differential equation, a pair of coupled nonlinear singular integral equations. Although analytical and numerical attempts to solve these equations prove to be unsuccessful, it is shown that the optimal plate shapes must have blunt noses. This problem is next formulated by a method using finite Fourier series expansions, and optimal shapes are obtained for various ratios of plate arc-length to plate width
Unsteady, Free Surface Flows; Solutions Employing the Lagrangian Description of the Motion
Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed
Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
We add simple tunnelling effects and ray-splitting into the recent
trajectory-based semiclassical theory of quantum chaotic transport. We use this
to derive the weak-localization correction to conductance and the shot-noise
for a quantum chaotic cavity (billiard) coupled to leads via
tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary
(positive) Ehrenfest time, . For all Ehrenfest times, we show
that the shot-noise is enhanced by the tunnelling, while the weak-localization
is suppressed. In the opaque barrier limit (small tunnelling rates with large
lead widths, such that Drude conductance remains finite), the weak-localization
goes to zero linearly with the tunnelling rate, while the Fano factor of the
shot-noise remains finite but becomes independent of the Ehrenfest time. The
crossover from RMT behaviour () to classical behaviour
() goes exponentially with the ratio of the Ehrenfest time
to the paired-paths survival time. The paired-paths survival time varies
between the dwell time (in the transparent barrier limit) and half the dwell
time (in the opaque barrier limit). Finally our method enables us to see the
physical origin of the suppression of weak-localization; it is due to the fact
that tunnel-barriers ``smear'' the coherent-backscattering peak over reflection
and transmission modes.Comment: 20 pages (version3: fixed error in sect. VC - results unchanged) -
Contents: Tunnelling in semiclassics (3pages), Weak-localization (5pages),
Shot-noise (5pages
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include
average treatment effects, policy effects, average derivatives, regression
decompositions, economic average equivalent variation, and parameters of
economic structural models. The regressions may be high dimensional. Plugging
machine learners into identifying equations can lead to poor inference due to
bias and/or model selection. This paper gives automatic debiasing for
estimating equations and valid asymptotic inference for the estimators of
effects of interest. The debiasing is automatic in that its construction uses
the identifying equations without the full form of the bias correction and is
performed by machine learning. Novel results include convergence rates for
Lasso and Dantzig learners of the bias correction, primitive conditions for
asymptotic inference for important examples, and general conditions for GMM. A
variety of regression learners and identifying equations are covered. Automatic
debiased machine learning (Auto-DML) is applied to estimating the average
treatment effect on the treated for the NSW job training data and to estimating
demand elasticities from Nielsen scanner data while allowing preferences to be
correlated with prices and income
Shot noise in semiclassical chaotic cavities
We construct a trajectory-based semiclassical theory of shot noise in clean
chaotic cavities. In the universal regime of vanishing Ehrenfest time \tE, we
reproduce the random matrix theory result, and show that the Fano factor is
exponentially suppressed as \tE increases. We demonstrate how our theory
preserves the unitarity of the scattering matrix even in the regime of finite
\tE. We discuss the range of validity of our semiclassical approach and point
out subtleties relevant to the recent semiclassical treatment of shot noise in
the universal regime by Braun et al. [cond-mat/0511292].Comment: Final version, to appear in Physical Review Letter
Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface
This paper attempts to determine the optimum profile of a two-dimensional plate that produces the maximum hydrodynamic lift while planing on a water surface, under the condition of no spray formation and no gravitational effect, the latter assumption serving as a good approximation for operations at large Froude numbers. The lift of the sprayless planing surface is maximized under the isoperimetric constraints of fixed chord length and fixed wetted arc-length of the plate. Consideration of the extremization yields, as the Euler equation, a pair of coupled nonlinear singular integral equations of the Cauchy type. These equations are subsequently linearized to facilitate further analysis. The analytical solution of the linearized problem has a branch-type singularity, in both pressure and flow angle, at the two ends of plate. In a special limit, this singularity changes its type, emerging into a logarithmic one, which is the weakest type possible. Guided by this analytic solution of the linearized problem, approximate solutions have been calculated for the nonlinear problem using the Rayleigh-Ritz method and the numerical results compared with the linearized theory
Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.
Inference in Linear Regression Models with Many Covariates and Heteroskedasticity
The linear regression model is widely used in empirical work in Economics,
Statistics, and many other disciplines. Researchers often include many
covariates in their linear model specification in an attempt to control for
confounders. We give inference methods that allow for many covariates and
heteroskedasticity. Our results are obtained using high-dimensional
approximations, where the number of included covariates are allowed to grow as
fast as the sample size. We find that all of the usual versions of Eicker-White
heteroskedasticity consistent standard error estimators for linear models are
inconsistent under this asymptotics. We then propose a new heteroskedasticity
consistent standard error formula that is fully automatic and robust to both
(conditional)\ heteroskedasticity of unknown form and the inclusion of possibly
many covariates. We apply our findings to three settings: parametric linear
models with many covariates, linear panel models with many fixed effects, and
semiparametric semi-linear models with many technical regressors. Simulation
evidence consistent with our theoretical results is also provided. The proposed
methods are also illustrated with an empirical application
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