Comment on "Earth and Moon impact flux increased at the end of the Paleozoic".

Mazrouei et al (Reports, 18 January 2019, p. 253) found a nonuniform distribution of crater ages on Earth and the Moon, concluding that the impact flux increased about 290 million years ago. We show that the apparent increase on Earth can be explained by erosion, whereas that on the Moon may be an artifact of their calibration method.

A New Equation Solver for Modeling Turbulent Flow in Coupled Matrix-Conduit Flow Models.

Karst aquifers represent dual flow systems consisting of a highly conductive conduit system embedded in a less permeable rock matrix. Hybrid models iteratively coupling both flow systems generally consume much time, especially because of the nonlinearity of turbulent conduit flow. To reduce calculation times compared to those of existing approaches, a new iterative equation solver for the conduit system is developed based on an approximated Newton-Raphson expression and a Gauß-Seidel or successive over-relaxation scheme with a single iteration step at the innermost level. It is implemented and tested in the research code CAVE but should be easily adaptable to similar models such as the Conduit Flow Process for MODFLOW-2005. It substantially reduces the computational effort as demonstrated by steady-state benchmark scenarios as well as by transient karst genesis simulations. Water balance errors are found to be acceptable in most of the test cases. However, the performance and accuracy may deteriorate under unfavorable conditions such as sudden, strong changes of the flow field at some stages of the karst genesis simulations.

Nonlinear Flow Process: A New Package to Compute Nonlinear Flow in MODFLOW.

A new MODFLOW package (Nonlinear Flow Process; NLFP) simulating nonlinear flow following the Forchheimer equation was developed and implemented in MODLFOW-2005. The method is based on an iterative modification of the conductance calculated and used by MODFLOW to obtain an effective Forchheimer conductance. The package is compatible with the different layer types, boundary conditions, and solvers as well as the wetting capability of MODFLOW. The correct implementation is demonstrated using four different benchmark scenarios for which analytical solutions are available. A scenario considering transient flow in a more realistic setting and a larger model domain with a higher number of cells demonstrates that NLFP performs well under more complex conditions, although it converges moderately slower than the standard MODFLOW depending on the nonlinearity of flow. Thus, this new tool opens a field of opportunities to groundwater flow simulation with MODFLOW, especially for core sample simulation or vuggy karstified aquifers as well as for nonlinear flow in the vicinity of pumping wells.

Branching with local probability as a paradigm of self-organized criticality.

A self-organized critical branching process based on a local interaction rule is presented. In accordance with the self-organized branching process model introduced by Zapperi, Lauritsen, and Stanley, its event-size distribution follows a power law with scaling exponent τ=3/2, but the new model does not require a global variable to self-organize to a critical point. The self-organized critical behavior of the model seems to be extremely robust. The model may be seen as a new paradigm for progressive mechanical failure (e.g., earthquakes or landslides) or other avalanching phenomena, and perhaps even for self-organized criticality in general.

Basic properties of a three-dimensional spring-block model with long-range stress transfer.

Spring-block models have been very useful for understanding slip complexity of earthquakes. So far, however, they have been restricted to one or two dimensions or simple nearest-neighbor stress transfer. Here, we set up a three-dimensional spring-block model with long-range stress transfer and, in a second step, implement several simplifications to realize a considerable gain in computational efficiency. Qualitatively, the two versions do not differ and we use the fast version to investigate basic properties of the model and to compare to the Olami Feder Christensen (OFC) model. The spatial distribution of hypocenters is found to be scale free. At the end of a simulation of events 10(7), it takes a value of D2 approximately = 1.8+/-0.1. At this point, however, the spatial slip organization is not stationary yet and the fractal dimension still grows slightly. This does not affect respective frequency size statistics, though, which exhibit a clear power law with a characteristic cutoff that depends on the grid size. The statistics appear smoother than in the OFC model and lack the kink between events of size 1 and 2. In addition, strong periodicities of large events as in the OFC model do not occur in our model. In stark contrast to the OFC model, results remain the same if periodic boundaries are used. Another significant difference is the stableness of results against imposed disorder. Contrary to the OFC model, results do not change if threshold values are randomly distributed in an interval of +/-10% around the mean value. Concluding, the model that we propose shares the main properties of the OFC model, but outreaches the latter in being stable in a larger set of configurations.

Can the Bonn Risk Index be replaced by a simple measurement of the urinary concentration of free calcium ions?

PURPOSE: It has been shown that a strong hyperbolic relationship exists between the urinary concentration of free Ca ions ([Ca]) and the amount of ammonium oxalate (Ox) that must be titrated in a standardized procedure to a urine sample to induce CaOx crystallization. The ratio of [Ca] to (Ox) is termed the Bonn Risk Index (BRI). Most data plot around a hyperbola described by the formula, [Ca] x (Ox) = constant. Due to the high relationship between [Ca] and (Ox) one may argue that determining only 1 of the 2 BRI parameters, preferably [Ca], is sufficient to describe the urine crystallization risk. MATERIALS AND METHODS: Based on 195 urine samples taken from CaOx stone formers and healthy subjects we compared the sensitivity and specificity of BRI, and its corresponding [Ca] value by calculating ROC curves. Furthermore, ROC curves of the established risk indexes, namely the model value of urinary supersaturation and the model value of the urine activity product, are presented. RESULTS: Our results clearly demonstrate that 1) BRI has the highest sensitivity and specificity of the tested indexes, 2) (Ox) cannot be reliably predicted from [Ca] and 3) determining [Ca] alone revealed a meaningful first estimate of urine CaOx crystallization risk according to BRI. CONCLUSIONS: To avail ourselves of the high quality of BRI in patient treatment the additional determination of (Ox) is required.

Properties of foreshocks and aftershocks of the nonconservative self-organized critical Olami-Feder-Christensen model.

Following Phys. Rev. Lett. 88, 238501 (2002)] who discovered aftershocks and foreshocks in the Olami-Feder-Christensen (OFC) discrete block-spring earthquake model, we investigate to what degree the simple toppling mechanism of this model is sufficient to account for the clustering of real seismicity in time and space. We find that synthetic catalogs generated by the OFC model share many properties of real seismicity at a qualitative level: Omori's law (aftershocks) and inverse Omori's law (foreshocks), increase of the number of aftershocks and of the aftershock zone size with the mainshock magnitude. There are, however, significant quantitative differences. The number of aftershocks per mainshock in the OFC model is smaller than in real seismicity, especially for large mainshocks. We find that foreshocks in the OFC catalogs can be in large part described by a simple model of triggered seismicity, such as the epidemic-type aftershock sequence (ETAS) model. But the properties of foreshocks in the OFC model depend on the mainshock magnitude, in qualitative agreement with the critical earthquake model and in disagreement with real seismicity and with the ETAS model.

Determination of the calcium oxalate crystallization risk from urine samples: the BONN Risk Index in comparison to other risk formulas.

PURPOSE: Regular risk evaluation and risk monitoring during stone therapy are recommended measures to ensure reduction of recurrence of crystal formation. This strategy optimizes the patient treatment by a more individual approach and decreases expensive over treatment. We evaluated the BONN Risk Index (BRI) through data actualization and evaluation refinement. The BRI was compared with the most common methods of risk evaluation, namely calculation of relative urinary calcium oxalate (CaOx) supersaturation (RS) and of the urine activity product (AP)CaOx index to estimate the urine AP with respect to CaOx. MATERIALS AND METHODS: A total of 201, 12 and 24-hour urine samples were collected from 95 healthy volunteers and from 106 CaOx stone formers. Crystallization experiments following the BRI method were performed. RS and APCaOx were calculated from urinalysis. Data were indexed and individually grouped into 8 classes, and frequency distributions were plotted. A calculation scheme for the BRI based estimation of the statistical probability of a clinically healthy person being a (still nondetected) CaOx stone former is provided. RESULTS: Logarithmically arranged BRI groups from healthy subject and patient data showed Gaussian frequency distributions. Compared with RS and APCaOx BRI allowed optimum distinction between healthy subjects and stone formers. The healthy subject probability of already being a CaOx stone former strongly increased with increasing BRI. CONCLUSIONS: The BRI for evaluating CaOx crystallization risk allows reliable distinction between healthy subjects and CaOx stone formers. Although RS and APCaOx require much more analytical efforts for determination, their results do not show higher reliability.

The alteration of urine composition due to stone material present in the urinary tract.

OBJECTIVES: Based on a recently introduced mathematical model approach we show that uroliths located in the urinary tract (UT) can substantially deplete the urinary concentrations of lithogenic constituents by continuous growth. METHODS: To illustrate the influence of the urinary depletion effect on urinalysis, a "typical" calcium oxalate (CaOx) stone former, presently not stone-free, was investigated. Serum and urine samples were analyzed. Several metabolic tests were performed. Crystallization risk according to the BONN-Risk-Index (BRI) and the relative supersaturation in respect to CaOx (RS(CaOx)) were determined. X-ray films taken before and after a period of six months were evaluated in order to estimate stone size and average stone growth rate taken place within that period. RESULTS: Regarding CaOx urolithiasis the urine samples show a pathologically altered pH, a low 24h-citric acid excretion, and a low 24h-urine volume. Neither calcium nor oxalate excretion data reflect values indicating these substances as risk factors. However, BRI and RS(CaOx) reflect a high crystallization risk. The patient's intestinal oxalate absorption is high. Applying the depletion model, the patient's 24h-urine composition shifts from normooxaluric to hyperoxaluric. CONCLUSION: In the patient, a hitherto undetected hyperoxaluria is diagnosed when in-vivo stone growth is taken into account. This is a clear indication that the metabolic status can only be evaluated correctly in "stone-free" patients. Any stone material present in the UT must be considered in urinalysis interpretation as the stone-related urinary depletion effect is of high clinical relevance. A helpful nomogram is presented, allowing the estimation of the extent of urinary depletion caused by CaOx uroliths.

Influence of urinary stones on the composition of a 24-hour urine sample.

BACKGROUND: It can be assumed that stones in the urinary tract continuously increase in size by incorporating material from urine. Consequently, urine will exhibit depleted concentrations of lithogenic constituents when urinary stones are present in the patient's urinary tract. METHODS: To calculate the influence of the depletion effect, we considered two different models of stone growth. In the first model, the increase in stone size depends only on the urinary concentration of a lithogenic substance; the second model also considers the surface area of the growing stone. The case of only one kidney being affected by stone formation is considered separately. We discuss example calculations involving the formation of calcium oxalate. RESULTS: The calculated depletion effects are of a nonnegligible order of magnitude. Assuming both a measured oxalate concentration of, e.g., 0.37 mmol/L and a reasonable in vivo stone growing rate of 10 mm(3)/day, a relative underestimation of the real "in situ" oxalate concentration between approximately 21% (model 1) and approximately 42% (model 2) occurs. The depletion effect increases markedly with increasing stone growth rate. CONCLUSIONS: Metabolic status can be evaluated correctly only in patients who have been declared "stone-free", e.g., after stone removal. Because the expected stone-related depletion effect in most cases is of high clinical relevance, we recommend estimating the effect of the order of magnitude of the depletion on actual urinary composition.

Comparison of laser-probe and photometric determination of the urinary crystallization risk of calcium oxalate.

A variety of equipment is used for the observation of precipitation processes which occur in urinary samples. The Bonn-Risk-Index, a measure of the calcium oxalate crystallization risk of human urine, has been developed with the use of an in-line laser-probe gauge. For basic research or in clinical laboratories, however, this instrument, which fulfills industrial requirements for the evaluation of particle size distributions, is not widely available. The evaluation of an alternative method to determine the Bonn-Risk-Index based on a more commonly available apparatus would therefore be useful. In vitro crystallization experiments with 124 native urine samples from stone-forming and non-stone forming individuals were performed in order to determine their crystallization risk according to the Bonn-Risk-Index approach. The onset of an induced urinary crystallization was detected by simultaneous sample monitoring with an in-line laser-probe and a conventional dip-in photometer. A decrease of the sample's relative light transmissivity from initially 100% to 98% was assumed to be a reliable photometer-based criterion to indicate that crystallization actually began. The laser-probe signal was set as the reference measure. Linear regression analysis of the results of the laser-probe and the photometer-based Bonn-Risk-Index determinations reveals a significant and close correlation between the two measures. Method comparison by statistical evaluation shows i) that no significant deviation from linearity exists and ii) that both methods are statistically identical. The differences in the results are small enough to be confident that the photometer can be used in place of the laser-probe for clinical purposes. The photometer is a reliable, easy-to-use and cost-effective method for the determination of a triggered crystallization event in a urine sample. The assumed 98% criterion allows the determination of the Bonn-Risk-Index with adequate accuracy.

Foreshocks and aftershocks in the Olami-Feder-Christensen model.

With the help of numerical simulations we show that the established Olami-Feder-Christensen earthquake model exhibits sequences of foreshocks and aftershocks; this behavior has not been recognized in previous studies. Our results are consistent with Omori's empirical law, but the exponents predicted by the model are lower than observed in nature. The occurrence of foreshocks and aftershocks can be attributed to the nonconservative character of the Olami-Feder-Christensen model.

Determination of urinary calcium-oxalate formation risk with BONN-Risk-Index and EQUIL applied to a family.

Apart from environmental and acquired risk factors, a person's genetic predisposition may have a distinct influence on the probability of the onset of urolithiasis. To investigate the family related development of calcium oxalate, CaOx, crystallization risk, we studied urines from three generations of the same family. The paternal line has been suffering from CaOx-urolithiasis for at least two generations; no case of urolithiasis has been reported from the maternal line and the youngest generation.We applied the BONN-Risk-Index and the computer program EQUIL to determine the crystallization risk of each family member (n = 7). We clearly verified by probability calculations of the existence of the two risk groups within the family and showed that one of the siblings of the youngest generation may have inherited the stone-formation risk from its paternal relatives as this person clearly reflects a high risk pattern.