Lecture notes on probability, statistics, and experimental errors; an elementary summary for students of experimental science.

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An experimental verification of newton's second law

We describe an experimental procedure to probe the validity of Newton's second law. The experimental arrangement allows us to accelerate a glider on an air track by means of forces that are both steady and known. We also show how to determine acceleration from average speeds calculated for successive time intervals of the motion measured by using several electronic counters connected to a single-crystal oscillator circuit. Within experimental errors, the experiments clearly show the proportionality between acceleration and force for a fixed mass and between acceleration and inverse of mass for a fixed force. © by the Sociedade Brasileira de Física.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Electrical conductivity and dielectric relaxation studies on microwave synthesized Na2SO4 center dot NaPO3 center dot MoO3 glasses

Electrical conductivity and dielectric relaxation studies on SO4 (2-) doped modified molybdo-phosphate glasses have been carried out over a wide range of composition, temperature and frequency. The d.c. conductivities which have been measured by both digital electrometer (four-probe method) and impedance analyser are comparable. The relaxation phenomenon has been rationalized using electrical modulus formalism. The use of modulus representation in dielectric relaxation studies has inherent advantages viz., experimental errors arising from the contributions of electrode-electrolyte interface capacitances are minimized. The relaxation observed in the present study is non-Debye type. The activation energies for relaxation were determined using imaginary parts of electrical modulus peaks which were close to those of the d.c. conductivity implying the involvement of similar energy barriers in both the processes. The enhanced conductivity in these glasses can be attributed to the migration of Na+, in expanded structures due to the introduction of SO4 (2-) ions.

低密度台阶形闪耀光栅的制作

介绍了制作低密度闪耀光栅的过程,在制作时,对传统的制作过程进行了改进,有效提高了制作质量。以40μm闪耀光栅为例介绍了制作的过程,得到了良好的光栅表面形貌,并且闪耀级次的衍射效率达到了70%以上。相比传统的制作方法,效率提高了5%～10%。对比了理论上的衍射效率,分析了实验误差,发现把存在对准误差的光栅进行处理将会有效地提高其衍射效率,为进一步提高闪耀光栅的衍射效率提供了依据。

Absolute oscillator strengths for iron, copper, cadmium and gold measured by the atomic beam method

Absolute f-values for 7 transitions in the first spectra of 4 elements have been measured using the atomic beam absorption technique. The equivalent widths of the absorption lines are measured with a photoelectric scanner and the atomic beam density is determined by continuously weighing a part of it with a sensitive automatic microbalance. The complete theory is presented and corrections are calculated to cope with gas absorption by the deposit on the microbalance pan and atoms which do not stick to the pan. An additional correction for the failure of the assumption of effusive flow in the formation of the atomic beam at large densities has been measured experimentally.

The following f-values were measured:

Fe: f_λ3720 = 0.0430 ± 8%

Cu: f_λ3247 = 0.427 ± 4.5%, f_λ3274 = 0.206 ± 4.7%, f_λ2492 = 0.0037 ± 9%

Cd: f_λ3261 = 0.00190 ± 7%, f_λ2288 = 1.38 ± 12%

Au: f_λ2428 = 0.283 ± 5.3%

Comparison with other accurately measured f-values, where they exist, shows agreement within experimental errors.

Bayesian parameter identification for vibro-acoustic models with nonparametric uncertainty

Vibration and acoustic analysis at higher frequencies faces two challenges: computing the response without using an excessive number of degrees of freedom, and quantifying its uncertainty due to small spatial variations in geometry, material properties and boundary conditions. Efficient models make use of the observation that when the response of a decoupled vibro-acoustic subsystem is sufficiently sensitive to uncertainty in such spatial variations, the local statistics of its natural frequencies and mode shapes saturate to universal probability distributions. This holds irrespective of the causes that underly these spatial variations and thus leads to a nonparametric description of uncertainty. This work deals with the identification of uncertain parameters in such models by using experimental data. One of the difficulties is that both experimental errors and modeling errors, due to the nonparametric uncertainty that is inherent to the model type, are present. This is tackled by employing a Bayesian inference strategy. The prior probability distribution of the uncertain parameters is constructed using the maximum entropy principle. The likelihood function that is subsequently computed takes the experimental information, the experimental errors and the modeling errors into account. The posterior probability distribution, which is computed with the Markov Chain Monte Carlo method, provides a full uncertainty quantification of the identified parameters, and indicates how well their uncertainty is reduced, with respect to the prior information, by the experimental data. © 2013 Taylor & Francis Group, London.

Restudy on the wave functions of Gamma(nS) states in the light-front quark model and the radiative decays of Gamma(nS) -> eta(b) + gamma

The light-front quark model has been applied to calculate the transition matrix elements of heavy hadron decays. However, it is noted that using the traditional wave functions of the light-front quark model given in the literature, the theoretically determined decay constants of the Gamma(nS) obviously contradict the data. This implies that the wave functions must be modified. Keeping the orthogonality among the nS states and fitting their decay constants, we obtain a series of the wave functions for Gamma(nS). Based on these wave functions and by analogy with the hydrogen atom, we suggest a modified analytical form for the Gamma(nS) wave functions. Using the modified wave functions, the obtained decay constants are close to the experimental data. Then we calculate the rates of radiative decays of Gamma(nS) -> eta(b) + gamma. Our predictions are consistent with the experimental data on decays Gamma(3S) -> eta(b) + gamma within the theoretical and experimental errors.

THE DETERMINATION OF STANDARD ELECTROMOTIVE FORCE OF CELL Cu vertical bar CuSO4 vertical bar Hg2SO4-Hg AT DIFFERENT TEMPERATURES

The emfs of Cu|CuSO_4|Hg_2SO_4-Hg were determined at 5 temperature points from 278.15K to 313.15K. Based on the Pitzer' s Equation a polynomial approximation for the determination of standard emf, E_m, was proposed. The values of E_m obtained by author's method agree with values of E_m obtained by the extended Debye-Huckel equation within experimental errors. Compared with the extrapolation result of extended Debye-Huckel equation, the uncertainty by the selecting of parameter of ion size was avoided.By the...

Irradiation of oxygen and water ices at by 4 keV singly and doubly charged ions; sputtering and molecular synthesis

The icy surfaces of dust grains in the Interstellar Medium and those of comets, satellites and Kuiper Belt Objects are continuously exposed tophoton and charged particle irradiation. These energetic particles maysputter and induce chemical changes in the ices and the underlyingsurfaces.In the present work 258 nm thick O2 and H2O ices were deposited at 10 K with the thickness measured by a laser interferometer method. Asimple model fit to the reflected laser intensity as measured by aphotodiode detector enabled the refractive index of the ices to bedetermined. The ices were then irradiated with various singly and doublycharged ions such as He+, 13C+, N+, O+ , Ar+, 13C2+, N2+ and O2+ at 4keV. The decrease in ice thickness as a function of ion dose wasmonitored by a laser interferometer and the model used to determine thesputtering yield as shown in Figure 1.In the case of O2 ice thesputtering yields increased with increasing ion mass in good agreementwith a model calculation [Fama, J, Shi, R.A Baragiola, Surface Sci.,602, 156 (2007)]. In the case of O2 ice, O2+ has a significant lowersputtering yield when compared to O+. The sputtering yields for O2 icewere found to be at least 9 times larger compared to those for H2O ice.For H2O ice the sputter yields for C, N and O ions were found todecrease with increasing mass. Doubly charged C, N and O ions which werefound to have the same sputtering yield as the singly charged ionswithin the experimental errors. A preliminary TPD study was carried outusing a QMS to detect the desorbed species from water ice afterirradiation by 6 × 10^15 ions of 13C+ and 13C2+. The formation of13CO and 13CO2 was observed with the yield of 13CO almost of a factor of100 larger than of 13CO2. This is in contrast to our earlier work whereonly CO¬2 was observed.

Elastic constants of Ni-Mn-Ga magnetic shape memory alloys

We have measured the adiabatic second order elastic constants of two Ni-Mn-Ga magnetic shape memory crystals with different martensitic transition temperatures, using ultrasonic methods. The temperature dependence of the elastic constants has been followed across the ferromagnetic transition and down to the martensitic transition temperature. Within experimental errors no noticeable change in any of the elastic constants has been observed at the Curie point. The temperature dependence of the shear elastic constant C' has been found to be very different for the two alloys. Such a different behavior is in agreement with recent theoretical predictions for systems undergoing multi-stage structural transitions.

Robust performance testing for digital forensic tools

In previous work, the authors presented a theoretical lower bound on the required number of testing runs for performance testing of digital forensic tools. However, experimental errors are inevitable in laboratory settings, occurring as measurement errors or as random errors and can result in practical situations where the number of testing runs is far from the theoretical bound. This paper adapts our former work to tolerate such errors in the testing results. The contribution of our new methodology enables the tester to achieve performance testing results of high quality from a manageable number of observations and in a dynamic but controllable way. This is of particular interest to forensic testers who do not have access to sophisticated equipment and who can allocate only a small amount of time to testing.

U-Pb zircon in situ dating with LA-MC-ICP-MS using a mixed detector configuration

The LA-MC-ICP-MS method applied to U-Pb in situ dating is still rapidly evolving due to improvements in both lasers and ICP-MS. To test the validity and reproducibility of the method, 5 different zircon samples, including the standard Temora-2, ranging in age between 2.2 Ga and 246 Ma, were dated using both LA-MC-ICP-MS and SHRIMP. The selected zircons were dated by SHRIMP and, after gentle polishing, the laser spot was driven to the same site or on the same zircon phase with a 213 nm laser microprobe coupled to a multi-collector mixed system. The data were collected with a routine spot size of 25 μm and, in some cases, of 15 and 40 μm. A careful cross-calibration using a diluted U-Th-Pb solution to calculate the Faraday reading to counting rate conversion factors and the highly suitable GJ-1 standard zircon for external calibrations were of paramount importance for obtaining reliable results. All age results were concordant within the experimental errors. The assigned age errors using the LA-MC-ICP-MS technique were, in most cases, higher than those obtained by SHRIMP, but if we are not faced with a high resolution stratigraphy, the laser technique has certain advantages.

Contributo sperimentale alla ridefinizione della diffusione in parete della camera di prova della galleria del vento Dallara

Joseph Nicolas Cugnot built the first primitive car in 1769 and approximately one hundred year later the first automotive race took place. Thanks to this, for the first time the aerodynamics principles began to be applied to cars. The aerodynamic study of a car is important to improve the performance on the road, or on the track. It purposely enhances the stability in the turns and increases the maximum velocity. However, it is also useful, decrease the fuel consumption, in order to reduce the pollution. Given that cars are a very complex body, the aerodynamic study cannot be conducted following an analytical method, but it is possible, in general, to choose between two different approaches: the numerical or the experimental one. The results of numerical studies depend on the computers’ potential and on the method use to implement the mathematical model. Today, the best way to perform an aerodynamic study is still experimental, which means that in the first phase of the design process the study is performed in a wind tunnel and in later phases directly on track. The automotive wind tunnels are singular mainly due to the test chamber, which typically contains a ground simulation system. The test chamber can have different types of walls: open walls, closed walls, adaptive walls or slotted walls. The best solution is to use the slotted walls because they minimize the interference between the walls and the streamlines, the interaction between the flow and the environment, and also to contain the overall costs. Furthermore, is necessary minimize the boundary layer at the walls, without accelerating the flow, in order to provide the maximum section of homogeneous flow. This thesis aims at redefining the divergent angle of the Dallara Automobili S.P.A. wind tunnel’s walls, in order to improve the overall homogeneity. To perform this study it was necessary to acquire the pressure data of the boundary layer, than it was created the profile of the boundary layer velocity and, to minimize the experimental errors, it was calculated the displacement thickness. The results obtained shows, even if the instrument used to the experiment was not the best one, that the boundary layer thickness could be minor in case of a low diffusion angle. So it is convenient to perform another experiment with a most sensitive instrument to verified what is the better wall configuration.

Revision of a Liquid Fuel Airblast Atomizer and Installation of a Laser Extinction System for Measurement of Soot Produced During Liquid Fuel Combustion

Studying liquid fuel combustion is necessary to better design combustion systems. Through more efficient combustors and alternative fuels, it is possible to reduce greenhouse gases and harmful emissions. In particular, coal-derived and Fischer-Tropsch liquid fuels are of interest because, in addition to producing fewer emissions, they have the potential to drastically reduce the United States' dependence on foreign oil. Major academic research institutions like the Pennsylvania State University perform cutting-edge research in many areas of combustion. The Combustion Research Laboratory (CRL) at Bucknell University is striving to develop the necessary equipment to be capable of both independent and collaborative research efforts with Penn State and in the process, advance the CRL to the forefront of combustion studies. The focus of this thesis is to advance the capabilities of the Combustion Research Lab at Bucknell. Specifically, this was accomplished through a revision to a previously designed liquid fuel injector, and through the design and installation of a laser extinction system for the measurement of soot produced during combustion. The previous liquid fuel injector with a 0.005" hole did not behave as expected. Through spray testing the 0.005" injector with water, it was determined that experimental errors were made in the original pressure testing of the injector. Using data from the spray testing experiment, new theoretical hole sizes of the injector were calculated. New injectors with 0.007" and 0.0085" orifices were fabricated and subsequently tested to qualitatively validate their behavior. The injectors were installed in the combustion rig in the CRL and hot-fire tested with liquid heptane. The 0.0085" injector yielded a manageable fuel pressure and produced a broad flame. A laser extinction system was designed and installed in the CRL. This involved the fabrication of a number of custom-designed parts and the specification of laser extinction equipment for purchase. A standard operating procedure for the laser extinction system was developed to provide a consistent, safe method for measuring soot formation during combustion.