Small Angle X-ray Scattering (SAXS) is an ideal characterization tool to explore nanoscale systems. In order to investigate nanostructural changes of materials under realistic sample environments, it is essential to equip SAXS with diverse in situ capabilities based on the corresponding requirements. In this paper, we highlight the representative experimental setups and corresponding applications of five widely used in situ capabilities: temperature, pressure, stretching, flow-through, and electric field. Additionally, we also briefly introduce other four in situ techniques including humidity, high-throughput, rheology, and magnetic field.
An electrode configuration with microhollow array dielectric and anode was developed to obtain parallel vacuum arc discharge. Compared with the conventional electrodes, more than 10 parallel microhollow discharges were ignited for the new configuration, which increased the discharge area significantly and made the cathode eroded more uniformly. The vacuum discharge channel number could be increased effectively by decreasing the distances between holes or increasing the arc current. Experimental results revealed that plasmas ejected from the adjacent hollow and the relatively high arc voltage were two key factors leading to the parallel discharge. The characteristics of plasmas in the microhollow were investigated as well. The spectral line intensity and electron density of plasmas in microhollow increased obviously with the decease of the microhollow diameter.
Ablation processes of ribbon-array loads, as well as wire-array loads for comparison, were investigated on Qiangguang-1 accelerator. The ultraviolet framing images indicate that the ribbon-array loads have stable passages of currents, which produce axially uniform ablated plasma. The end-on x-ray framing camera observed the azimuthally modulated distribution of the early ablated ribbon-array plasma and the shrink process of the x-ray radiation region. Magnetic probes measured the total and precursor currents of ribbon-array and wire-array loads, and there exists no evident difference between the precursor currents of the two types of loads. The proportion of the precursor current to the total current is 15% to 20%, and the start time of the precursor current is about 25 ns later than that of the total current. The melting time of the load material is about 16 ns, when the inward drift velocity of the ablated plasma is taken to be 1.5 × 107 cm/s.
Direct application of Bayes' theorem to generalized data yields a posterior probability distribution function (PDF) that is a product of a prior PDF of generalized data and a likelihood function, where generalized data consists of model parameters, measured data, and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero, leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since posterior expectation values of any function of generalized data are integrals of that function over all generalized data weighted by the posterior PDF, all elements of generalized data may be viewed as nuisance parameters marginalized by this integration. One simple form of posterior PDF is obtained when the prior PDF and the likelihood function are normal PDFs. For linear models without a defect this PDF becomes equivalent to constrained least squares (CLS) method, that is, the χ2 minimization method.
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