Length Uncertainty Research Articles

Stochastic Finite Element Analysis of Buckling of Frame Structure with Uncertain Initial Stresses

When members having uncertainty in length are assembled into a frame structure, uncertain initial stresses are generated in it. This may influence the buckling load which is related with structural safety and reliability. Stochastic finite element method on the basis of the second order perturbation technique is developed in this class of problem and the formation for two dimensional frame structure is presented. The rates of change of eigenvalue for plural random variables are efficiently computed based on the single solution of the governing equation. It is demonstrated in numerical examples that the expectation and variance of buckling load are successfully evaluated for given moments of random variables.

Opticohydrodynamic properties of high‐molecular‐weight DNA. III. The effects of NaCl concentration

AbstractExcluded volume and persistence length of high‐molecular‐weight DNA from T2 bacteriophage have been evaluated over a range of NaCl concentrations from 0.005 to 2.0M using low‐shear flow‐birefringence and intrinsic‐viscosity data. Uncertainty in persistence length due to ambiguity in the assignment of intrinsic birefringence has been avoided by calibrating the data at 0.2M NaCl using a recently reported persistence‐length value based upon photon correlation spectroscopy [Jolly, D. & Eisenberg, H. (1976) Biopolymers 15, 61]. Results at high salt concertrations are in satisfactory agreement with other estimates of excluded volume and chain flexibility in the literature, but at very low salt concentrations they reflect greater chain expansion than has heretofore been reported. The extinction‐angle data imply a transition from a nondraining chain with excluded volume at 0.1M NaCl to an almost freely draining chain at 0.005M NaCl. Over this same salt range, the experimental persistencelength data agree very well with Flory's thermodynamic chain‐expansion theory [Flory, P. J. (1953) J. Chem. Phys. 21, 162], but are in generally poor agreement with other theoretical treatments. A detailed comparison of the results with other data in the literature suggests that the combined flow‐birefringence‐intrinsic‐viscosity technique employed here may be more sensitive to the distribution of chain stiffness and excluded volume in polyelectroytechain expansion of DNA than are othe rhydrodynamic methods such as sedimentation or intrinsic viscosity alone.

A gas-thermostated large liquid hydrogen target for experiments with μ-meson beam

A liquid hydrogen target, containing 250 l of liquid hydrogen, with a ratio between the working space and the reservoir of 1.5:1, is described. A radiation shield cooled by evaporating gas is used to insulate the target. The diameter of the beam windows is 30 cm. Mean quantity of hydrogen along the beam is 14.35 g cm −2, the amount of other matter along the beam is 0.75 g cm 2, and across the beam is 2.75 g cm 2. Uncertainty in target length is not more than 1.5%, liquid hydrogen evaporation is 5 litres per day, and operating time with refills is 20 days.

Quenching of the2S01Metastable State of Helium by an Electric Field

A time-of-flight technique has been used to measure the quenching of the $2^{1}S_{0}$ metastable state of helium by a static electric field. Neutral ground-state helium atoms effusing from a cooled source slit are immediately excited to the $2^{1}S_{0}$ and $2^{3}S_{1}$ metastable states by a pulse of antiparallel magnetically focused electrons. The metastable beam is collimated before passing through a uniform electric field region 0.5 m long and is then preferentially detected at the end of the time-of-flight region, 1.825 m from the electron gun. The time-of-flight distribution for the $2^{1}S_{0}$ state is separated from that of the $2^{3}S_{1}$ state by illuminating the beam before the electric field region with an rf-discharge helium lamp. The $2^{1}S_{0}$ state is quenched by resonant absorption of a 20 581-\AA{} photon, raising the atom to the $2^{1}P_{1}$ state, which then decays to the $^{1}S_{0}$ ground state; the $2^{3}S_{1}$ state remains unaffected because it is the ground state for the triplet system. The $2^{1}S_{0}$ time-of-flight distribution is therefore obtained from the difference between the full beam and the quenched beam. The number of $2^{1}S_{0}$ atoms arriving at the detector in specific velocity intervals with the electric field off is compared to the number with the field on to determine the quenching rate ($=k{E}^{2}$). The result for the quenching constant $k$ for both ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ with $E$ in kV/cm is $k=0.933\ifmmode\pm\else\textpm\fi{}0.005$; this value is in good agreement with theory and with an earlier less accurate experiment. The error in the present experiment arises from a 0.5% uncertainty in the effective length of the electric field region.

Interaction Lengths of Energetic Pions and Protons in Iron

The interaction lengths of pions and protons in iron have been measured using an ionization spectrometer composed of alternating layers of iron and plastic scintillator. These measurements cover an energy range from 9.3 to 18 GeV. The interaction lengths were determined by accurate statistical analyses of the experimental data using the maximum-likelihood method. The dependence of the interaction length on the parameters used to define an interaction was studied, and the results reported employ parameters chosen to minimize the percentage uncertainty in the interaction length. The mean interaction length of pions was found to be approximately 20% greater than that of protons. No significant dependence on the energy of the incident primary was found in the range measured. Consistency was found with the great variety of accelerator measurements made to date, all of which report greater interaction lengths than those reported by the cosmic-ray measurements.

A treatment of experimental resolution

A method is described for imposing conditions of experimental resolution broadening on a theoretical model to be compared with data obtained in time-of-light experiments. The method is illustrated by an example based on a neutron inelastic scattering experiment. Functions describing the actual time and velocity distributions in the incident beam are determined empirically. These functions are convolved with cross sections derived from a theoretical model for scattering by the use of Monte Carlo techniques. The Monte Carlo procedure also takes into account the contribution to the resolution function of path length uncertainties and finite analyzer time channel widths.