Logarithmic Shape Research Articles

Experimental investigation and theoretical modeling of cutting mechanics using serrated tines in drilling lunar regolith simulant

Drilling is a widely used method for exploring extra-terrestrial bodies and seeking information on astrobiology, material composition, and evolution of the universe. The bit cutter of the drill tool is the main component that is in intense contact with the regolith and is of great importance for guaranteeing the cutting performance during drilling. The tine is a special type of cutter, and currently, there is no theoretical model describing its interaction with a lunar regolith simulant during cutting. To address this gap, semi-tine and full-tine cutting tests were performed at different cutting speeds, cutting depths, regolith densities, and tip angles. The experimental results showed that the regolith failure zone has an elliptical shape in the top view and a logarithmic spiral shape in the side view. Based on the failure pattern, a tine cutting mechanics model was built, and its results were compared with those of the experiments. The model exhibited good prediction accuracy for the cutting force, with a maximum error not exceeding 30.96% and an average error of 13.81%. To apply the model to extra-terrestrial drilling, a conical drill bit with multi-row serrated tines was designed. By analyzing the error between the theoretical and experimental values of the rotational torque, the model was further refined to provide a better match with the actual cutting results. The proposed cutting mechanics model describing the tine-regolith interaction mechanism can provide a reference for predicting drilling loads during planetary exploration.

Audio fade profile customizing by imposing the audio volume initial rate of change

By adopting a rational function of degree 1, with the playback position in the course of an audio fade transition as the function input, and the audio volume as the function output, we advance a technique of setting up the audio fade profile by bringing forward a shape parameter that is directly proportional to the initial rate of change of the audio volume. We provide the relationships that are essential for computing the coefficients of the adopted rational function having at hand the audio effect characteristics, i.e. the fade length, initial volume, final volume and the parameter used for shaping. The versatility of the proposed technique is revealed by the numerous curves illustrating fade in, fade up, fade out and fade down transitions. The shape parameter is of key significance here having in view that it decides the pattern to follow. More precisely, one can set the value of the shape parameter in order to get either a fade effect that acts similar to the exponential shape fade or a fade effect that follows the pattern of the logarithmic shape fade. With a view to real time experimentation, a practical application, developed via plain JavaScript, is provided in the paper.

Multiethnic growth standards for fetal body composition and organ volumes derived from 3D ultrasonography

BackgroundA major goal of contemporary obstetrical practice is to optimize fetal growth and development throughout pregnancy. To date, fetal growth during prenatal care is assessed by performing ultrasonographic measurement of two-dimensional fetal biometry to calculate an estimated fetal weight. Our group previously established two-dimensional fetal growth standards using sonographic data from a large cohort with multiple sonograms. A separate objective of that investigation involved the collection of fetal volumes from the same cohort. ObjectiveThe Fetal 3D Study was designed to establish standards for fetal soft tissue and organ volume measurements by three-dimensional ultrasonography and compare growth trajectories with conventional two-dimensional measures where applicable. Study DesignThe NICHD Fetal 3D Study included research-quality images of singletons collected in a prospective, racially and ethnically diverse, low-risk cohort of pregnant individuals at 12 U.S. sites, with up to five scans per fetus (N=1,730 fetuses). Abdominal subcutaneous tissue thickness was measured from two-dimensional images and fetal limb soft tissue parameters extracted from three-dimensional multiplanar views. Cerebellar, lung, liver and kidney volumes were measured using virtual organ computer aided analysis (VOCAL). Fractional arm and thigh total volumes, and fractional lean limb volumes were measured, with fractional limb fat volume calculated by subtracting lean from total. For each measure, weighted curves (5th, 50th, 95th percentiles) were derived from 15-41 weeks’ using linear mixed models for repeated measures with cubic splines. ResultsSubcutaneous thickness of the abdomen, arm, and thigh increased linearly, with slight acceleration around 27-29 weeks. Fractional volumes of the arm, thigh, and lean limb volumes increased along a quadratic curvature, with acceleration around 29-30 weeks. In contrast, growth patterns for two-dimensional humerus and femur lengths demonstrated a logarithmic shape, with fastest growth in the 2nd trimester. The mid-arm area curve was similar in shape to fractional arm volume, with an acceleration around 30 weeks, whereas the curve for the lean arm area was more gradual. The abdominal area curve was similar to the mid-arm area curve with an acceleration around 29 weeks. The mid-thigh and lean area curves differed from the arm areas by exhibiting a deceleration at 39 weeks. The growth curves for the mid arm and thigh circumferences were more linear with some decelerations. Cerebellar two-dimensional diameter increased linearly, whereas cerebellar three-dimensional volume growth gradually accelerated until 32 weeks and then decelerated. Lung, kidney, and liver volumes all demonstrated gradual early growth followed by a linear acceleration beginning at 25 weeks for lungs, 26-27 weeks for kidneys, and 29 weeks for liver. ConclusionGrowth patterns and timing of maximal growth for three-dimensional lean and fat measures, limb and organ volumes differed from patterns revealed by traditional two-dimensional growth measures, suggesting these parameters reflect unique facets of fetal growth. Growth in these three-dimensional measures may be altered by genetic, nutritional, metabolic or environmental influences and pregnancy complications, in ways not identifiable using corresponding two-dimensional measures. Further investigation into the relationships of these three-dimensional standards to abnormal fetal growth, adverse perinatal outcomes, and health status in postnatal life is warranted.

Traversable wormhole supported by non-exotic gravitational fluid in the Lyra manifold

In this work, we construct traversable wormholes using a logarithmic shape function in the general theory of relativity (GTR) and Lyra geometry (LG). We observe that the gravitational fluid violates the null energy condition (NEC) in GTR whereas all the energy conditions (ECs) are satisfied in LG. The violation of NEC indicates the requirement of exotic matter in GTR for the construction of traversable wormhole whereas LG supports non-exotic matter for the same purpose. We analyze the stability of the wormholes using the Causality and Herrera’s cracking method and found that the obtained wormhole solution in the LG is stable.

Insights into the thermodynamic efficiency of Homann-Agrawal hybrid nanofluid flow

In this study, we investigate the characteristics of axisymmetric Homann and Agrawal flows over a stretching and spiraling surface at the stagnation point flow. The effects of uniform rotation and linear radial stretching of the disk are considered, along with the utilization of hybrid nanofluids. Specifically, titanium oxide and multi-walled carbon nanotubes are dispersed in engine oil to form the nanofluid. The surface velocity adopts a spiral logarithmic shape due to the combined influence of uniform rotation and radial stretching, while a perpendicular magnetic field is applied to the flow. Furthermore, we analyze the entropy generation of the hybrid nanofluid flow. To solve the problem, we employ a similarity transformation technique to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and utilize the bvp4c technique available in MATLAB. Graphical representations are employed to illustrate the impact of relevant parameters. This analysis yields valuable insights into the thermodynamic efficiency of fluid flow systems, enabling optimization of their design and performance. Understanding the influence of nanoparticle concentration and flow parameters on system efficiency is of utmost importance in developing more effective and efficient fluid flow systems. The study offers crucial insights applicable to a wide range of engineering applications, including heat exchangers, cooling systems, and other fluid flow systems.

Recurrence relation for real-time audio fading

Starting from shaping the audio fade profile by an invertible rational function, with playback position as the input, we derive a recurrence relation that enables the audio volume updating as long as the time domain discretization is carried out with a constant step size. The resulted recurrence relation yields the audio volume current value as rational function of its previous value only, thus being suitable for efficiently implementing real-time adjustable fades whenever the adopted programming language (or software framework) allows the invocation of timing events. A JavaScript implementation, prepared for straightaway experimentation, and put forward in the paper, highlights the convenience of associating the derived recurrence relation with the "setInterval()" method in order to perform real-time audio fades, which can resemble either the logarithmic shape fade or the fade of exponential shape.

Experimental and theoretical approach of the hydrolysis of pelleted magnesium alloys scraps

Industrial Mg alloys scraps containing 3% of Al and 3% of Zn (and about 20% of MgO and Mg(OH)2) were ball milled with the addition of 5 wt% C and 5 wt% of Ni, Cu, Co or SiO2. 3 h of ball milling were needed to obtain optimum hydrolysis performances of the mixtures (e.g. yields of almost 90% obtained within 1 min). Pellets of such obtained powder were prepared as it is easier for an application. The shape of the hydrolysis curves highlights first an incubation period depending on the compactness of the pellets and then a second part with a logarithmic shape. A new model is presented that allows to take into account both parts of the hydrolysis curve. The model is applied successfully to all the pellets having various compactness.

The Analysis of Patterns of Two COVID-19 Outbreak Clusters in China.

Since the emergence of COVID-19, there have been many local outbreaks with foci at shopping malls in China. We compared and analyzed the epidemiological and spatiotemporal characteristics of local COVID-19 outbreaks in two commercial locations, a department store building (DSB) in Baodi District, Tianjin, and the Xinfadi wholesale market (XFD) in Fengtai District, Beijing. The spread of the infection at different times was analyzed by the standard deviation elliptical method. The spatial transfer mode demonstrated that outbreaks started at the center of each commercial location and spread to the periphery. The number of cases and the distance from the central outbreak showed an inverse proportional logarithmic function shape. Most cases were distributed within a 10 km radius; infected individuals who lived far from the outbreak center were mainly infected by close-contact transmission at home or in the workplace. There was no efficient and rapid detection method at the time of the DSB outbreak; the main preventative measure was the timing of COVID-19 precautions. Emergency interventions (closing shopping malls and home isolation) were initiated five days before confirmation of the first case from the shopping center. In contrast, XFD closed after the first confirmed cases appeared, but those infected during this outbreak benefitted from efficient nucleic acid testing. Quick results and isolation of infected individuals were the main methods of epidemic control in this area. The difference in the COVID-19 epidemic patterns between the two shopping malls reflects the progress of Chinese technology in the prevention and control of COVID-19.

Where is the forest core area? Gradients of flora in the ecotone of urban forests in Warsaw

Urban forests are very important ecosystems, performing key cultural services and having crucial regulatory functions. However, naturally valuable areas in cities continue to decline or undergo irreversible transformations. It is necessary to determine the extent of human influence on forest ecosystems in highly urbanized environments. Our study examined the indicators of diversity, naturalness, lability, and stability of flora along transects from edge to center of six urban forests. Furthermore, the shape of gradients of changes and the threshold distance and straightness between forest edge and core for these indicators were measured. Finally, the impact of the number of inhabitants, the degree of protection, and the size and shape of the forests on each indicator separately and their aggregation in the form of the Flora Transformation Index were analyzed. The findings revealed that the gradients of changes were rarely linear and showed a logarithmic or polynomial shape. The most regular gradients were observed for lability and naturalness of flora. The regularity of the shape of the thresholds differed between the studied indicators. The threshold distance was relatively far (93–113 m) and depended heavily on human influence, but forest shape and area were also very important. Our results showed that legal protection, even as a reserve, has no effect in the case of solid human penetration of the forest. Our findings are expected to help determine suitable indicators for defining threshold values, i.e., the size of the edge and core zones of urban forests, which is crucial to the protection of the native plant species pool.

Effects of modulator shape at thresholds and supra-thresholds spectral modulation perception

Spectral modulation detection is common method to assess spectral envelope perception in research and clinical settings. Prior investigations into spectral modulation (SM) detection have used two different modulator shapes: a sinusoidal envelope on a logarithmic amplitude scale or a sinusoidal envelope on a linear amplitude scale. The former creates a sinusoidally shaped excitation pattern, while the latter creates an excitation pattern with broad peaks and sharp valleys. What impact, if any, modulator shape has on SM perception at detection threshold or at supra-threshold levels is unknown. To investigate potential perceptual differences between waveform shapes: (1) SM detection was measured for modulation frequencies ranging from 0.5 to 8.0 cycles/octave; (2) Spectral modulation masking was measured for SM frequencies of 0.5 and 2.0 cycles/octave. The SM phase of the masker was manipulated (0, 90, or 180 degrees) so that maskers had a peak, a midpoint, or a valley at 1147 Hz. Tone detection (1147 Hz) was measured for the logarithmic and linear sinusoidal SM envelope shapes for each of the three phases. Results revealed significant differences between the two spectral envelope shapes for both spectral modulation detection and for spectral modulation masking. [Work supported by NIH R01DC015051].

UNIFIED METHOD FOR CALCULATION OF VERTICAL PULLING CAPACITY OF HORIZONTAL STRIP ANCHOR PLATE IN SAND

Currently, the research on bearing mechanism and capacity calculation of horizontal anchor plate has the problem of artificially distinguishing shallow and deep bury conditions without consistent standard. In this article, a logarithmic spiral shape function was proposed to describe the continuous evolution of the sliding surface of the soil around the anchor plate, and the unified mechanical model of ultimate bearing capacity was established with no need to consider the bury condition. According to the relationship among the buried depth of anchor plate, the distance from the sliding surface intersection to the anchor plate and the distance from the tangent point of vertical line of the sliding surface to the anchor plate, the limit equilibrium analysis method was used in three different situations to deduce the unified theoretical solution of vertical pullout ultimate bearing capacity of horizontal strip anchor plate. The results show that, the new mechanical model can well reflect the continuous variation of the sliding surface with the buried depth ratio, and no need to artificially distinguish the bury condition. In the comparative calculation and analysis of five test cases in loose and dense sand, the unified theoretical solution ranks the second among nine methods, and has good adaptability.

Influence of Roller-End Axial Profiling Type on Lubrication Performance in Thermal Elastohydrodynamic Finite Line Contacts

Abstract This study presents a finite-element-based numerical investigation of the influence of roller-end axial profiling type on the lubrication performance of thermal elastohydrodynamic finite line contacts. Performance is evaluated with respect to the reference case of straight rollers. The two most commonly used profiling types (i.e., dub-off and logarithmic) are compared under similar profiling length and height. It is found that a logarithmic profile outperforms a dub-off one by all accounts (i.e., frictional dissipation, lubricant film thickness, pressure buildup, and temperature rise), unless an extremely steep logarithmic shape is adopted. In the latter case, lubricant film thickness and pressure buildup may end up being negatively affected.

Structural recirculation and refractory hypoxemia under femoro-jugular veno-venous extracorporeal membrane oxygenation.

The performance of each veno-venous extracorporeal membrane oxygenation (vv-ECMO) configuration is determined by the anatomic context and cannula position. A mathematical model was built considering bicaval specificities to simulate femoro-jugular configuration. The main parameters to define were cardiac output (QC ), blood flow in the superior vena cava (QSVC ), extracorporeal pump flow (QEC ), and pulmonary shunt (kS-PULM ). The obtained variables were extracorporeal flow ratio in the superior vena cava (EFRSVC =QEC /[QEC +QSVC ]), recirculation coefficient (R), effective extracorporeal pump flow (Qeff-EC =[1-R]×QEC ), Qeff-EC /QC ratio, and arterial blood oxygen saturation (SaO2 ). EFRSVC increased logarithmically when QEC increased. High QC or high QSVC /QC decreased EFRSVC (range, 68%-85% for QEC of 5L/min). R also increased following a logarithmic shape when QEC increased. The R rise was earlier and higher for low QC and high QSVC /QC (range, 12%-49% for QEC of 5L/min). The Qeff-EC /QC ratio (between 0 and 1) was equal to EFRSVC for moderate and high QEC . The Qeff-EC /QC ratio presented the same logarithmic profile when QEC increased, reaching a plateau (range, 0.67-0.91 for QEC /QC =1; range, 0.75-0.94 for QEC /QC =1.5). The Qeff-EC /QC ratio was linearly associated with SaO2 for a given pulmonary shunt. SaO2 <90% was observed when the pulmonary shunt was high (Qeff-EC /QC ≤0.7 with kS-PULM =0.7 or Qeff-EC /QC ≤0.8 with kS-PULM =0.8). Femoro-jugular vv-ECMO generates a systematic structural recirculation that gradually increases with QEC . EFRSVC determines the Qeff-EC /QC ratio, and thereby oxygen delivery and the superior cava shunt. EFRSVC cannot exceed a limit value, explaining refractory hypoxemia in extreme situations.

Modeling of traversable wormholes in exponential f(R, T) gravity

In the present communication, we have studied the existence of wormholes described by a logarithmic shape function, in the exponential f(R, T) gravity given by f(R, T) = R + 2ξeζt where ξ and ζ are arbitrary constants, under three different sets of physical constraints. The logarithmic shape function is well behaved, satisfying all the necessary constraints for traversable and asymptotically flat wormholes. The obtained wormhole solutions are analyzed from the energy conditions for different values of involved physical constants. It has been observed that our proposed shape function for the exponential form of f(R, T) gravity represents the existence of exotic matter with a standard violation of the NEC. Moreover, for the trace T = 0, for the general relativity case with R being replaced by R + 2, the wormhole geometry has been analyzed to prove the existence of exotic matter. Further, the behaviour of physical parameters, such as the energy density ρ, the trace T, and anisotropy parameter Δ, describing the geometry of the universe has been presented with the help of graphs.

Traversable wormholes with logarithmic shape function in f(R,T) gravity

In this work, a new form of the logarithmic shape function is proposed for the linear [Formula: see text] gravity, [Formula: see text] where [Formula: see text] is an arbitrary coupling constant, in wormhole geometry. The desired logarithmic shape function accomplishes all necessary conditions for a traversable and asymptotically flat wormhole. The obtained wormhole solutions are analyzed from the energy conditions for different values of [Formula: see text]. It has been observed that our proposed shape function for the linear form of [Formula: see text] gravity, represents the existence of exotic matter and non-exotic matter. Moreover, for [Formula: see text] i.e. for the general relativity case, the existence of exotic matter for the wormhole geometry has been confirmed. Further, the behavior of the radial state parameter [Formula: see text], the tangential state parameter [Formula: see text], and the anisotropy parameter △ describing the geometry of the universe, has been presented for different values of [Formula: see text] chosen in [Formula: see text].

Entanglement entropy at critical points of classical evolution in oscillatory and exotic singularity multiverse models

Using the 3rd quantization formalism we study the quantum entanglement of universes created in pairs within the framework of standard homogeneous and isotropic cosmology. In particular, we investigate entanglement quantities (entropy, temperature) around maxima, minima and inflection points of the classical evolution. The novelty from previous works is that we show how the entanglement changes in an extended minisuperspace parameterised by the scale factor and additionally, by the massless scalar field. We study the entanglement quantities for the universes which classically exhibit Big-Bang and other than Big-Bang (exotic) singularities such as Big-Brake, Big-Freeze, Big-Separation, and Little-Rip. While taking into account the scalar field, we find that the entanglement entropy is finite at the Big-Bang singularity and diverges at maxima or minima of expansion. As for the exotic singularity models we find that the entanglement entropy or the temperature in all the critical points and singularities is either finite or infinite, but it never vanishes. This shows that each of the universes of a pair is entangled to a degree parametrized by the entanglement quantities which measure the quantumness of the system. Apart from the von Neumann entanglement entropy, we also check the behaviour of the the Tsallis and the Renyi entanglement entropies, and find that they behave similarly as the meters of the quantumness. Finally, we find that the best-fit relation between the entanglement entropy and the Hubble parameter (which classically marks special points of the universe evolution) is of the logarithmic shape, and not polynomial, as one could initially expect.

Infarct growth patterns may vary in acute stroke due to large vessel occlusion and recanalization with endovascular therapy.

This study aimed to investigate infarct growth patterns in stroke patients with large vessel occlusion (LVO) and successful recanalization by endovascular therapy (EVT). A total of 135 patients with LVO of the internal carotid artery or proximal segment of the middle cerebral artery admitted within 12h after onset, having baseline National Institute of Health Stroke Scale score ≥ 5 points, and successfully recanalized by EVT were enrolled. Infarct growth pattern models were developed based on infarct volumes on diffusion-weighted imaging before and after reperfusion. Single pattern models of linear, logarithmic, and exponential shapes were initially tested. Their appropriateness was predetermined. If none of these patterns was suitable, the best pattern model, which was the most suitable pattern among the three shapes selected for each individual, was tested. Clinical correlates were explored. Each single pattern model was tested for their suitability. However, none of the single pattern models successfully represented infarct growth curves: Of all subjects, only 63.7%, 62.2%, and 54.1% of patients were explained by the logarithmic, linear, and exponential model, respectively. Compared with the single pattern models, the best pattern model explained 80.7% of the subjects. The linear shape fit best in 40 patients, the logarithmic in 51, and the exponential in 44. Those fit best for the logarithmic pattern showed more favorable outcomes at discharge (31.4%) than did the others (linear, 10.0%; exponential, 9.1%; p = 0.01). Infarct growth patterns may vary among individual patients with acute stroke due to LVO and successful treatment with EVT. • Infarct growth during the acute stage of stroke is highly dynamic and the exact shape remains unknown. • Infarct growth pattern models were developed based on infarct volumes on diffusion-weighted imaging before and after reperfusion. • Infarct growth patterns may not be singular, rather various among individual patients with acute stroke due to LVO and successful treatment with EVT.

Wormhole modeling in R2 gravity with linear trace term

Morris and Thorne1 proposed traversable wormholes, hypothetical connecting tools, using the concept of Einstein’s general theory of relativity. In this paper, the modification of general relativity (in particular [Formula: see text] theory of gravity defined by Harko et al.2) is considered, to study the traversable wormhole solutions. The function [Formula: see text] is considered as [Formula: see text], where [Formula: see text] and [Formula: see text] are controlling parameters. The shape and redshift functions appearing in the metric of wormhole structure have significant contribution in the development of wormhole solutions. We have considered both variable and constant redshift functions with a logarithmic shape function. The energy conditions are examined, geometric configuration is analyzed and the radius of the throat is determined in order to have wormhole solutions in absence of exotic matter.

The variational multiscale formulation for the fully-implicit log-morphology equation as a tensor-based blood damage model.

We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical, negative eigenvalues. The resulting VMS stabilization terms for this so-called log-morph equation are presented together with their special numerical treatment. Results for a 2D rotating stirrer test case obtained from log-morph simulations with both SUPG and VMS stabilization show significantly improved numerical behavior if compared with Galerkin/least squares (GLS) stabilized untransformed morphology simulation results. The newly proposed method is also successfully applied to a state-of-the-art centrifugal ventricular assist device (VAD), and clear advantages of the VMS stabilization compared with the SUPG-stabilized formulation are presented.

Kondo physics of magnetic adatoms on metallic surfaces when the onset of the surface conduction density of states crosses the Fermi level

We study the role of the onset of Shockley states, $D_s$, belonging to (111) surfaces of Cu, Ag and Au in the Kondo effect when a magnetic impurity is deposited on them. When $D_s$ approaches to the Fermi level, $E_F$, thing that can be done by compressing (stretching) the metallic sample, we found that most of the thermodynamic and dynamic properties of the impurity are affected in a non trivial way. We model the system by a generic Anderson impurity model and solve it by using the numerical renormalization group, NRG, technique. In particular, the impurity contribution to magnetic susceptibility and entropy as a function of temperature exhibit negative values and goes to zero slowly in a logarithmic shape. Furthermore, we found a suppression of the spectral density weight at the Fermi level when $D_s\sim E_F$ even in the Kondo regime. As a consequence, the conductance through the impurity is strongly reduced by near $25\%$ of the unitary value $2e^2/h$. Finally, we analyze these features in realistic systems like Co on Ag(111) reported in the literature.