606 research outputs found
Notes on aerodynamic forces on airship hulls
For a first approximation the air flow around the airship hull is assumed to obey the laws of perfect (i.e. free from viscosity) incompressible fluid. The flow is further assumed to be free from vortices (or rotational motion of the fluid). These assumptions lead to very great simplifications of the formulae used but necessarily imply an imperfect picture of the actual conditions. The value of the results depends therefore upon the magnitude of the forces produced by the disturbances in the flow caused by viscosity with the consequent production of vortices in the fluid. If these are small in comparison with the forces due to the assumed irrotational perfect fluid flow the results will give a good picture of the actual conditions of an airship in flight
Inertia Factors of Ellipsoids for Use in Airship Design
This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author
Classical-path integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling
Simulations that couple different classical molecular models in an adaptive
way by changing the number of degrees of freedom on the fly, are available
within reasonably consistent theoretical frameworks. The same does not occur
when it comes to classical-quantum adaptivity. The main reason for this is the
difficulty in describing a continuous transition between the two different kind
of physical principles: probabilistic for the quantum and deterministic for the
classical. Here we report the basic principles of an algorithm that allows for
a continuous and smooth transition by employing the path integral description
of atoms.Comment: 8 pages 4 figure
The Pack Method for Compressive Tests of Thin Specimens of Materials Used in Thin-Wall Structures
The strength of modern lightweight thin-wall structures is generally limited by the strength of the compression members. An adequate design of these members requires a knowledge of the compressive stress-strain graph of the thin-wall material. The "pack" method was developed at the National Bureau of Standards with the support of the National Advisory Committee for Aeronautics to make possible a determination of compressive stress-strain graphs for such material. In the pack test an odd number of specimens are assembled into a relatively stable pack, like a "pack of cards." Additional lateral stability is obtained from lateral supports between the external sheet faces of the pack and outside reactions. The tests seems adequate for many problems in structural research
On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess
We propose two techniques aimed at improving the convergence rate of steady
state and eigenvalue solvers preconditioned by the inverse Stokes operator and
realized via time-stepping. First, we suggest a generalization of the Stokes
operator so that the resulting preconditioner operator depends on several
parameters and whose action preserves zero divergence and boundary conditions.
The parameters can be tuned for each problem to speed up the convergence of a
Krylov-subspace-based linear algebra solver. This operator can be inverted by
the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose
to generate an initial guess of steady flow, leading eigenvalue and eigenvector
using orthogonal projection on a divergence-free basis satisfying all boundary
conditions. The approach, including the two proposed techniques, is illustrated
on the solution of the linear stability problem for laterally heated square and
cubic cavities
Colored-noise thermostats \`a la carte
Recently, we have shown how a colored-noise Langevin equation can be used in
the context of molecular dynamics as a tool to obtain dynamical trajectories
whose properties are tailored to display desired sampling features. In the
present paper, after having reviewed some analytical results for the stochastic
differential equations forming the basis of our approach, we describe in detail
the implementation of the generalized Langevin equation thermostat and the
fitting procedure used to obtain optimal parameters. We discuss in detail the
simulation of nuclear quantum effects, and demonstrate that, by carefully
choosing parameters, one can successfully model strongly anharmonic solids such
as neon. For the reader's convenience, a library of thermostat parameters and
some demonstrative code can be downloaded from an on-line repository
Binary pattern tile set synthesis is NP-hard
In the field of algorithmic self-assembly, a long-standing unproven
conjecture has been that of the NP-hardness of binary pattern tile set
synthesis (2-PATS). The -PATS problem is that of designing a tile assembly
system with the smallest number of tile types which will self-assemble an input
pattern of colors. Of both theoretical and practical significance, -PATS
has been studied in a series of papers which have shown -PATS to be NP-hard
for , , and then . In this paper, we close the
fundamental conjecture that 2-PATS is NP-hard, concluding this line of study.
While most of our proof relies on standard mathematical proof techniques, one
crucial lemma makes use of a computer-assisted proof, which is a relatively
novel but increasingly utilized paradigm for deriving proofs for complex
mathematical problems. This tool is especially powerful for attacking
combinatorial problems, as exemplified by the proof of the four color theorem
by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and
Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by
Konev and Lisitsa using computer programs. We utilize a massively parallel
algorithm and thus turn an otherwise intractable portion of our proof into a
program which requires approximately a year of computation time, bringing the
use of computer-assisted proofs to a new scale. We fully detail the algorithm
employed by our code, and make the code freely available online
Elastic Constants of Quantum Solids by Path Integral Simulations
Two methods are proposed to evaluate the second-order elastic constants of
quantum mechanically treated solids. One method is based on path-integral
simulations in the (NVT) ensemble using an estimator for elastic constants. The
other method is based on simulations in the (NpT) ensemble exploiting the
relationship between strain fluctuations and elastic constants. The strengths
and weaknesses of the methods are discussed thoroughly. We show how one can
reduce statistical and systematic errors associated with so-called primitive
estimators. The methods are then applied to solid argon at atmospheric
pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good
agreement with available experimental data on elastic constants is found for
helium 3. Predictions are made for the thermal expectation value of the kinetic
energy of solid helium 3.Comment: 9 pages doublecolumn, 6 figures, submitted to PR
Dynamics of ions in the selectivity filter of the KcsA channel
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications
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