Comparative Study on High Strain Rate Fracture Modelling Using the Application of Explosively Driven Cylinder Rings

The effect of different constitutive modelling choices is crucial under a high strain rate as encountered in ballistic applications. Natural fragmentation of explosively driven cylinder rings is chosen as a simplified example to describe the ability of numerical simulations to describe fractures. The main research interests are the importance of (i) material imperfections, (ii) the accuracy of fracture models vs. damage models, (iii) the plasticity algorithm (stress update), (iv) the introduction of a triaxiality cutoff criterion to the damage models, and (v) different constitutive models (plasticity and damage). Due to the complexity of the propagation and coalescense of multiple cracks in classical methods, smoothed-particle hydrodynamics (SPH) is used as a tailor-made method to discretise the model. An elasto-plasticity model, a damage model and an equation of state describe the material behaviour. The required material parameters are determined based on stress–strain curves from quasi-static and dynamic tests. The Johnson–Cook model, with and without a modification of the strain rate term, and the Rusinek–Klepaczko model are used to describe plasticity. These plasticity models are combined either with the Johnson–Cook, the Lemaitre, or the Dolinski–Rittel damage model and the Mie–Grüneisen equation of state. The numerical results show that (i) a random distribution of initial damage increases irregularity of cracks, and gives more realistic fragment shapes, (ii) a coupling of plasticity model and fracture criterion has only a small effect on the fracture behaviour, (iii) using an iterative plasticity solver has a positive effect on the fracture behaviour, although this effect is marginal, (iv) adding a triaxiality cutoff criterion to the damage models improves the predicted fragment masses in the numerical simulations significantly, and (v) good accordance between experiments and numerical simulations are found for the Dolinski–Rittel and Lemaitre damage model with both plasticity models.

Gravity-wave-perturbed wind shears derived from SABER temperature observations

Large wind shears around the mesopause region play an important role in atmospheric neutral dynamics and ionospheric electrodynamics. Based on previous observations using sounding rockets, lidars, radars, and model simulations, large shears are mainly attributed to gravity waves (GWs) and modulated by tides (Liu, 2017). Based on the dispersion and polarization relations of linear GWs and the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature data from 2002 to 2019, a method of deriving GW-perturbed wind shears is proposed. The zonal-mean GW-perturbed shears have peaks (13–17 ms−1 km−1) at around the mesopause region, i.e., at z = 90–100 km at most latitudes and at z = 80–90 km around the cold summer mesopause. This latitude–height pattern is robust over the 18 years and agrees with model simulations. The magnitudes of the GW-perturbed shears exhibit year-to-year variations and agree with the lidar and sounding rocket observations in a climatological sense but are 60 %–70 % of the model results in the zonal-mean sense. The GW-perturbed shears are hemispherically asymmetric and have strong annual oscillation (AO) at around 80 km (above 92 km) at the northern (southern) middle and high latitudes. At middle to high latitudes, the peaks of AO shift from winter to summer and then to winter again with increasing height. However, these GW-perturbed shears may be overestimated because the GW propagation direction cannot be resolved by the method and may be underestimated due to the observational filter, sampling distance, and cutoff criterion of the vertical wavelength of GWs.

Gravity Waves induced Wind Shears Derived from SABER Temperature Observations

Large wind shears around the mesopause region play important roles in atmospheric neutral dynamics and ionospheric electrodynamics. Based on previous observations using sounding rockets, lidars, radars and model simulations, large shears are mainly attributed to gravity waves (GWs) and modulated by tides (Liu, 2017). Based on the dispersion and polarization relations of linear GWs and the SABER temperature data from 2002 to 2019, a method of deriving GW-induced wind shears is proposed. The zonal mean GW-induced shears have peaks (13–17 ms−1 km−1) at around the mesopause region, i.e., at z = 90–100 km at most latitudes and at z = 80–90 km around the cold summer mesopause. This latitude-height pattern is robust over the 18 years and coincides with model simulations. The magnitudes of the GW-induced shears exhibit year-to-year variations and coincide with the lidar and sounding rocket observations on climatology sense but are 60–70 % of the model results in the zonal mean sense. The GW-induced shears are hemispheric asymmetric and have strong annual oscillation (AO) at around 80 km (above 92 km) at the northern (southern) middle and high latitudes. At middle to high latitudes, the peaks of AO shift from winter to summer and then to winter again with increasing height. However, these GW-induced shears may be overestimated because the GW propagation direction cannot be resolved by the method and may be underestimated due to the observational filter, sampling distance and cutoff criterion of the vertical wavelength of GWs.

Mathematical Model Application to the Kinetic Study of Tumor Markers

In order to overcome the inefficient cutoff criterion in the management of neoplastic patients after therapy, in follow-up, in recurrence and in monitoring treatment, we have analysed some mathematical models to evaluate serial determinations of tumor markers, with the aim to ascertain the radicality of surgery or the presence of recurrences. Since a tracer study of the biological system of tumor markers is impossible, some information, such as rate factor and half-life, is obtained by determination of the marker after radical treatment. In steady state with two or more samples in time it is possible with adequate statistical models to establish a significant increase in the marker. In recurrence, if it is true that the secretion rate of the marker by a tumor is proportional to tumor mass, then increasing concentrations of the tumor marker would be a phenotypic expression of tumor growth. Therefore some mathematical models are proposed to evaluate the kinetics of tumor growth.

Sensitivity and specificity of the hydrogen breath-analysis test for detecting malabsorption of physiological doses of lactose.

We examined the changes in sensitivity and specificity that would occur with alterations in the sample-collection schedule and (or) cutoff criterion for the increase in hydrogen concentration in breath after administration of doses of lactose in the dietary range. In a breath-analysis test to classify individuals as lactose-absorbers or lactose-malabsorbers, 41 subjects drank 360 mL of intact cow's milk, containing 18 g of lactose, and breath samples were collected and analyzed at 30-min intervals for 5 h. An increase in H2 concentration of greater than or equal to 20 microL/L above basal values at any of the 10 intervals was diagnostic of malabsorption. Increases of greater than or equal to 18 or greater than or equal to 15 microL/L were only 85% as specific in classifying the same individuals. Reduction in the number of samples tested per subject uniformly reduced the sensitivity. However, a simplified procedure suitable for field studies (in which four samples--at 0, 2, 3, and 4 h--are collected and analyzed with greater than or equal to 20 microL/L as the cutoff value) gives 80% sensitivity and 100% specificity, as compared with the 11-sample procedure.