A quadratic viscous fluid law for ice deduced from Steinemann's uni-axial compression and torsion experiments

The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

Perceptions of Control Influence Feelings of Boredom

Conditions of low and high perceived control often lead to boredom, albeit for different reasons. Whereas, high perceived control may be experienced as boring because the situation lacks challenge, low perceived control may be experienced as boring because the situation precludes effective engagement. In two experiments we test this proposed quadratic relationship. In the first experiment we had participants play different versions of the children's game “rock-paper-scissors” in which they arbitrarily won (intended to maximize feelings of control) or lost (to induce feelings of low control). Despite having only dichotomous conditions, participants reported experiencing a broad range of levels of perceived control. Consistent with our predictions, boredom was highest at low and high levels of perceived control (i.e., a quadratic relation between perceived control and felt boredom). Experiment 2 tested the notion that the mere prospect of gaining control may mitigate boredom. Participants given to believe (erroneously) that they could gain control over the game of rock, paper, scissors were less bored than those who believed there was no possibility of winning at greater than chance levels. This suggests that beliefs concerning prospective control, rather than a given level of perceived control per se, may predict engagement and boredom.

Characteristics of Slamming Pressure and Force for Trimaran Hull

In this paper, the characteristics of the impact pressure and force of a trimaran section was studied by Computational Fluid Dynamics (CFD). The time domain features of the slamming pressure or force showed a strong correlation with the penetration depth regardless of the specific ways of water entry. The effects of velocity and acceleration on the impact pressure and force were analyzed. It was found that the initial impact of the main hull and the wet-deck slamming were predominantly affected by the entry velocities, whilst the acceleration had almost no effect for initial impact. The impact velocity presented a quadratic relation with slamming pressure/forces, and the relation between acceleration and wet-deck slamming pressure/force was linear. These were consistent with the patterns implied by analytical models such as the Wagner or MLM (Modified Logvinovich model) theories.

AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS

We show that the cohomology intersection number of a twisted Gauss–Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic relation associated to period integrals of a certain family of K3 surfaces.

Can the BMI-Based Dose Regimen be Used to Reduce Injection Activity and to Obtain a Constant Image Quality in Oncological Patients by 18F-FDG Total-Body PET/CT Imaging?

Purpose PET image quality is influenced by the patient size according to the current guideline. The purpose was to propose an optimized dose regimen to yield a constant image quality independent of patient size to meet the clinical needs.Methods A first patient cohort of 78 consecutives for oncological patients (59.7±13.7 years) who underwent a total-body PET/CT scan were retrospectively enrolled to develop the regimen. The patients were equally distributed in four BMI groups according to WHO criteria. The liver SNR (Signal noise ratio, SNRL) was obtained through manually drawing ROIs and normalized (SNRnorm) by the injected activity and acquisition time. And fits of SNRnorm against different patient-dependent parameters were performed to determine the best correlating parameter and fit method. A qualitative assessment on image quality was performed using a 5-point Likert scale to determine the acceptable threshold of SNRL. And thus, an optimized regimen was proposed and validated by a second patient cohort with prospectively enrolled 38 oncological patients. Results The linear fit showed SNRnorm was the strongest correlation (R2 = 0.69) with the BMI than other patient-dependent parameters. The qualitative assessment revealed a SNRL of 14.0 as a threshold to achieve a sufficient image quality. The optimized dose regimen was determined as a quadratic relation with BMI: Injected activity = 39.2 MBq/(-0.03*BMI+1.49)2. In the validation study, the SNRL no longer decreased with the increase of BMI. There was no significant difference of the image quality, the SNRL, between different BMI groups (p > 0.05). In addition, the injected activity was reduced by 75.6±2.9 %, 72.1±4.0 %, 67.1±4.4 % and 64.8±3.5 % compared to the first cohort for the four BMI groups, respectively.Conclusion The study recommended a quadratic relation between the 18F-FDG injected activity and the patient’s BMI and propose a regimen for total-body PET imaging. In the regimen, the image quality can maintain in a constant level independent of patient size and meet the clinical requirement even with a reduced injected activity.

Empirical bolometric correction coefficients for nearby main-sequence stars in the Gaia era

ABSTRACT Nearby detached double-lined eclipsing binaries with most accurate data were studied and 290 systems were found with at least one main-sequence component having a metallicity of 0.008 ≤ Z ≤ 0.040. Stellar parameters, light ratios, Gaia Data Release 2 trigonometric parallaxes, extinctions and/or reddening were investigated and only 206 systems were selected as eligible to calculate empirical bolometric corrections. NASA/IPAC Galactic dust maps were the main source of extinctions. Unreliable extinctions at low Galactic latitudes |b| ≤ 5° were replaced with individual determinations, if they exist in the literature, else associated systems were discarded. The main-sequence stars of te remaining systems were used to calculate the bolometric corrections (BCs) and to calibrate the BC–Teff relation, which is valid in the range 3100–36 000 K. De-reddened (B − V)0 colours, on the other hand, allowed us to calibrate two intrinsic colour–effective temperature relations; the linear one is valid for $T_{\rm eff}\gt 10\, 000$ K, while the quadratic relation is valid for $T_{\rm eff}\lt 10\, 000$ K; that is, both are valid in the same temperature range in which the BC–Teff relation is valid. New BCs computed from Teff and other astrophysical parameters are tabulated, as well.

The Influence of Exercise Intensity on the Association Between Kilojoules Spent and Various Training Loads in Professional Cycling

Purpose: A valid measure for training load (TL) is an important tool for cyclists, trainers, and sport scientists involved in professional cycling. The aim of this study was to explore the influence of exercise intensity on the association between kilojoules (kJ) spent and different measures of TL to arrive at valid measures of TL. Methods: Four years of field data were collected from 21 cyclists of a professional cycling team, including 11,716 training and race sessions. kJ spent was obtained from power output measurements, and others TLs were calculated based on the session rating of perceived exertion (sRPE), heart rate (Lucia training impulse [luTRIMP]), and power output (training stress score [TSS]). Exercise intensity was expressed by the intensity factor (IF). To study the effect of exercise intensity on the association between kJ spent and various other TLs (sRPE, luTRIMP, and TSS), data from low- and high-intensity sessions were subjected to regression analyses using generalized estimating equations. Results: This study shows that the IF is significantly different for training and race sessions (0.59 [0.03] vs 0.73 [0.03]). Significant regression coefficients show that kJ spent is a good predictor of sRPE, and luTRIMP, as well as TSS. However, IF does not influence the associations between kJ spent and sRPE and luTRIMP, while the association with TSS is different when sessions are done with low or high IF. Conclusion: It seems that the TSS reacts differently to exercise intensity than sRPE and luTRIMP. A possible explanation could be the quadratic relation between IF and TSS.

An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library

We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. ``to be orthogonal'', ``to be tangent'', etc.), as new objects in an extended M\"obius--Lie geometry. It was recently demonstrated in several related papers, that such ensembles of cycles naturally parameterize many other conformally-invariant families of objects, e.g. loxodromes or continued fractions. The paper describes a method, which reduces a collection of conformally in\-vari\-ant geometric relations to a system of linear equations, which may be accompanied by one fixed quadratic relation. To show its usefulness, the method is implemented as a {\CPP} library. It operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality and metrics with any signatures. Numeric calculations can be done in exact or approximate arithmetic. In the two- and three-dimensional cases illustrations and animations can be produced. An interactive {\Python} wrapper of the library is provided as well.