Presence Of Curvature Research Articles

Investigating rheological characteristics of nonlinear fluid model in an asymmetric channel: A peristaltic pumping of blood with curvature and hydrodynamic impacts

Theoretical research is investigated for the steady rheology of incompressible blood from an asymmetric (penetrable) channel in the presence of curvature and non-linear hydrodynamic impacts. The motion takes place in an asymmetric channel due to a train of sinusoidal (complex nature) waves along the channel boundaries having different phases. In this study, the Casson fluid is used as blood. The governing equations are modeled in terms of Cartesian coordinates. The impacts of non-linear curvature become significant on the transportation of biological fluid in a complex domain such as the non-pregnant uterus at a higher Reynolds number. An approximate solution of flow models is obtained to the second order in the wavenumber (giving the curvature effect). A domain transformation is used to transform the variable cross-sectional of the flow regime into the uniform cross-section. This transformation helps to find the closed-form solution of transformed rheological equations in higher order. The physical impacts of the curvature parameter, Casson parameter, phase difference, flow rate, Reynolds number, and permeability parameter on the axial velocity, pressure gradient, stress tensor, trapping phenomena, and pressure rise are investigated. The velocity of blood is smaller as it is associated with the viscous fluid. The number of boluses was reduced by increasing the Casson parameter and Reynolds number in the trapping phenomenon. The stress tensor is an increasing function of the permeability parameter and the Reynolds number. The pressure gradient is affected by the permeability parameter. The comparison between viscous fluid and blood is also addressed in the current study. The outcomes of the current study arise in the medical domains, blood study, manufacturing of nano-blood pumps, bio-physical food processing, and chemical industry.

A unified approach to three themes in harmonic analysis (I & II): (I) The linear Hilbert transform and maximal operator along variable curves (II) Carleson type operators in the presence of curvature

This paper constitutes the first part of a study that addresses three rich historical themes in harmonic analysis that, in the non-zero curvature setting, investigate the boundedness properties along variable curves for(I) the linear Hilbert transform and analogous maximal operator,(II) the Carleson-type operators, and(III) the bilinear Hilbert transform and analogous maximal operator.Our Main Theorem in this paper states that, given a general variable curve γ(x,t) in the plane that is assumed only to be measurable in x and to satisfy suitable non-zero curvature in t and extra (mild) non-degeneracy conditions, the operators at (I) and (II) defined along the curve γ are Lp-bounded for 1<p<∞.Our result provides a new and unified treatment of the first two themes as well as a unitary approach within the x-variable setting for both the singular integral and the maximal operator versions of (I).At the heart of our approach is the LGC–methodology introduced here, which encompasses three key ingredients:(1)phase/space discretization that confines the phase of the multiplier to oscillate at the linear level,(2)adapted Gabor frame discretization of the input function(s), and(3)cancelation extraction via the analysis of the time-frequency correlation(s) capturing the non-zero curvature of γ.

On charged particle dynamics near flat solid surface

The motion of a non-relativistic charged particle near flat solid surface at small sliding angles is examined within the formalism of the effective potential composed by interaction of a particle with surface atoms and excited plasmons. As known, the presence of curvature in a solid surface can result in forming a set of discrete quantum states for a particle in the potential well of interaction with the surface.In this work we demonstrate that, at the glancing to flat-surface motion of fast charged particles, small channeling oscillations can be also observed for some special conditions. It is shown that the effective interaction potential represents a shallow well capable to hold a particle in a bound state. We succeeded to analytically determine the energy levels of a particle in such a potential well, as well as the critical angle for a particle to be trapped, in terms of known critical angle of channeling in crystals and a newly proposed function for simplification.

Saturation phenomena of a nonlocal eigenvalue problem: the Riemannian case

ABSTRACT In this paper we investigate the Riemannian extensibility of saturation phenomena treated first in the Euclidean framework by Brandolini et al. [Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem. Adv Math (N Y). 2011;228(4):2352–2365.]. The saturation problem is formulated in terms of the first eigenvalue of the perturbation of the Laplace-Beltrami operator by the integral of the unknown function: the first eigenvalue increases with the weight affecting the integral up to a finite critical value and then remains constant, i.e. it saturates. Given a Riemannian manifold with certain curvature constraints, by using symmetrization arguments and sharp isoperimetric inequalities, we reduce the general problem to a variational one, formulated on either positively or negatively curved Riemannian model spaces; in addition, the possible scenarios for the optimal domains turn to be either geodesic balls or the union of two disjoint geodesic balls. We then explicitly compute the eigenvalues and eigenfunctions in terms of the radii, curvature and weight. A sufficient condition (incompatibility of a system of nonlinear equations involving special functions) is given that implies similar saturation phenomena to the Euclidean case. Due to its highly nonlinear character of the reduced problem (arising from the presence of curvature and special functions), we provide only partial answers to the original problem. However, both analytical computations and numerical tests suggest that the required incompatibility always persists. In addition, in the limit cases when the curvature tends to zero (for both positive an negative curvature), our results reduce to the Euclidean version.

Correction to Lagrangian for bouncing cosmologies in f(Q) gravity

Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann–Lemaître–Robertson–Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical or semianalytical solutions for symmetric bounce, super-bounce, oscillatory bounce, matter bounce, and exponential bouncing model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.

PD12-07 PENILE FRACTURE SURGERY: DOES IT IMPACT SEXUAL FUNCTION?

You have accessJournal of UrologyCME1 Apr 2023PD12-07 PENILE FRACTURE SURGERY: DOES IT IMPACT SEXUAL FUNCTION? Alberto Costa Silva, Vasco Rodrigues, Carlos Martins-Silva, and Afonso Morgado Alberto Costa SilvaAlberto Costa Silva More articles by this author , Vasco RodriguesVasco Rodrigues More articles by this author , Carlos Martins-SilvaCarlos Martins-Silva More articles by this author , and Afonso MorgadoAfonso Morgado More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003259.07AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Surgical exploration with closure of tunica albuginea is the proposed treatment for penile fracture. The recovery of sexual function is the main result desired by the Urologist and the patient. METHODS: Retrospective analysis of data from patients undergoing surgical correction penile fracture between 2007 and 2022 in a tertiary hospital. Trauma mechanism, extension, laterality and location of the lesion and the presence of urethral lesion were evaluated. The number of weeks until resumption of sexual activity was obtained. Erectile function was assessed with the International Index of Erectile Function 5 (IIEF5). The evolution of erectile function after the episode was classified as worsening, maintenance or improvement. The presence of glans hypoesthesia, penile curvature, penile nodule palpation were also evaluated. Self-satisfaction with the scar and self-perception of body image was rated from 0 to 10. RESULTS: A population of 69 patients with a mean age of 42.30±12.98 years (mean±standard deviation) was obtained. Sexual intercourse, self-inflicted injury and masturbation were the cause of 85.5%, 4.3% and 2.9% of fractures, respectively. The diagnosis was supported by ultrasound in 62.3%. The lesion affected the right cavernous in 43.5%, the left in 40.6% and both in 15.9%. The dorsal and ventral location of the lesion appeared in 26.1% and 73.9%, corresponding to 36.2%, 40.6% and 23.2% in the proximal, middle and distal thirds, respectively. Acquired penile curvature appeared in 14.5% and none required surgical correction. The median postoperative IIEF-5 was 24. Erectile function deteriorated to levels of dysfunction in 5.8% (n=4). Of these, two have an IIEF-5 of 18 and two of 15, with one of the latter taking avanafil 100 mg. Decreased erectile function was associated with the distal location of the lesion (p=0.028) and the presence of curvature (p=0.038). The glans hypoesthesia appeared in 2.9% and was associated with the distal location (p=0.033). The sensation of a penile nodule appeared in 4.3% and was more frequent in bilateral lesions (p=0.039). The resumption of sexual activity occurred in a median of 7 weeks, not being associated with any of the variables evaluated. Self-satisfaction with body image had a median of 9, with lower values associated with the presence of curvature (p=0.009), more extensive lesions (p=0.023) and concomitant urethral injury (p=0.025). A median of self-satisfaction with the scar of 8 was obtained, associated with the presence of curvature (p=0.004). CONCLUSIONS: In our study, fractures of the cavernous bodies with distal involvement are associated with degradation of erectile function and hypoesthesia of the glans, being more frequent in patients with later resumption of sexual activity. The cases of erectile dysfunction identified were mild and only one required pharmacological treatment. The curvature acquired after fracture did not require surgical correction, although it is associated with worsening erectile function, less self-satisfaction with the scar and with body image, the latter also being associated with more extensive injuries and concomitant urethral injury. Source of Funding: None © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e402 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Alberto Costa Silva More articles by this author Vasco Rodrigues More articles by this author Carlos Martins-Silva More articles by this author Afonso Morgado More articles by this author Expand All Advertisement PDF downloadLoading ...

MP18-11 DOES LEVEL OF TRAINEE INVOLVEMENT HAVE AN IMPACT ON HYPOSPADIAS TIP REPAIR OUTCOME?

You have accessJournal of UrologyCME1 Apr 2023MP18-11 DOES LEVEL OF TRAINEE INVOLVEMENT HAVE AN IMPACT ON HYPOSPADIAS TIP REPAIR OUTCOME? Vinaya Bhatia, Rocio Goodman, Maria Jabbour, and Walid Farhat Vinaya BhatiaVinaya Bhatia More articles by this author , Rocio GoodmanRocio Goodman More articles by this author , Maria JabbourMaria Jabbour More articles by this author , and Walid FarhatWalid Farhat More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003238.11AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Teaching hypospadias repair to trainees is a major component of pediatric urology fellowship training but is not a focus of training junior residents. Herein, we reviewed outcomes of distal hypospadias repairs performed by a single surgeon in the proficiency stage of practice in a residency program and compared these outcomes to those for the same surgeon in the same stage in a fellowship program. METHODS: We reviewed all distal tubularized incised plate repairs performed by a single surgeon from 2019-2021. Data included age, meatal location, presence of curvature, operative time, occurrence of complications, and follow-up duration. Of note, resident involvement comprised mainly assisting in penile degloving urethroplasty and included skin closure under direct supervision. Our outcomes were compared to previously published data using descriptive statistics and Fisher’s exact tests, in which a p<0.05 was designated as statistically significant. RESULTS: A total of 52 patients met our inclusion criteria. A total of 5 patients had a megameatus, 6 had a glanular hypospadias, and 34 had a distal shaft hypospadias. The median age at surgery was 0.72 months (IQR 0.75 months). All patients did have an indwelling stent post-operatively. One patient (3.3%) was found to have complications, which were fistulae and meatal stenosis (Table 1). The time to complication for this patient was 6 months. When comparing previous data to the current data, the overall complication rates were lower (p=0.03), with overall complication rates of 15% (29/187) versus 3% (1/52). CONCLUSIONS: This is the first study directly comparing hypospadias surgical outcomes for the same surgeon in a different practice setting, specifically fellowship and residency programs. Though the detailed role of fellows in hypospadias repair might not be well delineated, it did entail autonomy and delegation, while residents only assisted or performed skin closure under supervision. Our data suggest that fellowship training programs might need to determine key steps for hypospadias repair they teach or delegate. This process should be delivered in a gradual manner gauged to the level of trainees to ensure that outcomes are improved. Source of Funding: None © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e227 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Vinaya Bhatia More articles by this author Rocio Goodman More articles by this author Maria Jabbour More articles by this author Walid Farhat More articles by this author Expand All Advertisement PDF downloadLoading ...

Effects of radiation, curvature, and preferential diffusion on the extinction of laminar non-premixed flames

The combined effects of radiative heat loss, curvature, and preferential diffusion on laminar non-premixed flames (or flamelets) are investigated in this work by using asymptotic analysis. A general theoretical description of flame temperature and extinction is derived for curved flames with non-unity Lewis numbers and radiative heat loss. Special attention is paid to the effects of curvature and radiative heat loss on the flammability limits. The results show that (1) a curved flamelet always has two extinction limits: one is the kinetic extinction limit, and the other is the curvature-induced extinction limit for the adiabatic case or the radiative extinction limit for the radiative case; (2) the curvature exerts a different influence on the adiabatic and radiative flames. Specifically for the adiabatic flame, it is found that both flame temperature and flame position significantly decrease as the curvature increases and that a new extinction limit at a low stretch rate occurs due to the existence of curvature. Furthermore, a higher curvature coupled with the increase in the Lewis number results in a lower flammability limit and narrower flammable zone. Therefore, the presence of curvature has a negative impact on the adiabatic flame. On the contrary, for the radiative flame, the results show that the increase in curvature has a positive effect on the flammability limit and thereby increases the flammable zone. It is expected that curved flamelets hold smaller (larger) flammable zones than planar flamelets under the adiabatic (radiative) condition. All results show that the change in flame curvature has a stronger effect on the flame structure and extinction than the deviation of the Lewis number from unity.

Finite Element Systems for Vector Bundles: Elasticity and Curvature

We develop a theory of finite element systems, for the purpose of discretizing sections of vector bundles, in particular those arising in the theory of elasticity. In the presence of curvature, we prove a discrete Bianchi identity. In the flat case, we prove a de Rham theorem on cohomology groups. We check that some known mixed finite elements for the stress–displacement formulation of elasticity fit our framework. We also define, in dimension two, the first conforming finite element spaces of metrics with good linearized curvature, corresponding to strain tensors with Saint-Venant compatibility conditions. Cochains with coefficients in rigid motions are given a key role in relating continuous and discrete elasticity complexes.

Phenomenology of curvature-induced quantum-gravity effects

Several studies have been devoted to the possibility that quantum gravity might tangibly affect relativistic kinematics for particles propagating from distant astrophysical sources to our telescopes, but the relevant literature has so far focused exclusively on a subclass of scenarios such that the quantum-gravity effects are independent of (macroscopic) curvature. It was assumed that a phenomenology for quantum-gravity effects that are triggered by curvature might be a dead end because of a double suppression: by the smallness of the characteristic quantum-gravity length scale and by the smallness of curvature. This state of affairs is becoming increasingly unsatisfactory in light of some recent quantum-gravity studies providing evidence of the fact that the presence of curvature might be required in order to have the novel relativistic properties. We here analyze an explicit scenario for curvature-induced quantum-gravity effects, and show that the smallness of curvature does not pose a challenge for phenomenology since it is compensated by the large distances traveled by the particles considered in the relevant phenomenological studies. We also observe that the present data situation for particles propagating from distant astrophysical sources to our telescopes, while inconclusive, provides more encouragement for our curvature-induced effects than for the curvature-independent effects that were so far studied.

Analysis of the development of the flame brush in turbulent premixed spherical flames

The thickness of the turbulent flame brush is central to the modeling of premixed turbulent combustion and the theory of turbulent diffusion is often applied to explain the growth of the brush with varying success. However, numerous studies have shown that the brush evolves differently from the dispersion of material points on the account of flame propagation, density changes across the front, and hydrodynamic instabilities. Modifications to turbulent diffusion theory to incorporate these effects are challenging since the theory is Lagrangian. In this article, we present an alternate Eulerian framework based on the surface density formalism. We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data. We characterize quantitatively two mechanisms: one related to the mean velocity gradient induced by thermal expansion and the other due to flame propagation in the presence of curvature. We demonstrate that the net effect of these two processes is to hinder the growth of the turbulent flame brush in the present configuration. Our analysis supports the notion that the turbulent flame brush does not grow indefinitely, rather it attains a maximum thickness.

A general higher-order model for vibration analysis of axially moving doubly-curved panels/shells

In this research a general model to study the vibration behavior of axially moving two-dimensional continuums in the presence of curvature along the moving axis is developed. To this end, an axially moving doubly-curved panel of variable radius of curvature is considered. The integral boundary value problem is obtained based on a higher-order shear deformation with first-order thickness stretching theory. Due to its high accuracy and computational performance, spectral Chebyshev approach is used to numerically solve the boundary value problem. Considering the geometry capabilities of the developed model, dynamics of various axially moving structures such as flat, singly- and doubly-curved plates/shells in different engineering applications with different boundary conditions can be investigated. The numerical results confirmed that the calculated natural frequencies for axially moving flat plates and circular cylindrical shells are in excellent agreement to those found in the literature and obtained via finite element approach. Furthermore, the effects of the axial velocity, thickness stretching, curvature ratio, and boundary conditions on the natural frequencies and stability behavior of the doubly-curved panels are investigated.

Effects of first-order chemical reaction and melting heat on hybrid nanoliquid flow over a nonlinear stretched curved surface with shape factors

The aim of the current study is to disclose the results of shape factor analysis of the flow of a hybrid nanofluid over a curved sheet. The flow is caused by a stretchable curved sheet. Mathematical modeling and analyses have been performed in the presence of curvature, melting heat and heterogeneous-homogeneous reactions. Autocatalysis and the coefficients of the reactant are dealt with in a similar manner. The physical properties of the fluid, including the fluid velocity, the heat and mass transfer properties, the skin friction and the Nusselt number have been acquired and analyzed under the influences of the dimensionless curvature, melting and heterogeneous–homogeneous reaction variables. Boundary layer approximations are used in the mathematical formulation. Suitable transformations have been used to transform differential equations into nonlinear ordinary differential equations. The resulting nonlinear system of equations has been analyzed via the matlab bvp4c solver. Comparisons of nanoliquids with the hybrid nanoliquid are presented through graphs and tables. The results of this analysis show that the skin friction and the heat transfer rate in the hybrid nanofluid are seen more prominently than those of the nanofluid for larger values of the curvature parameter [Formula: see text].

Determining track-induced lateral thermal expansion forces on a curved railway track

This research studies the development of lateral thermal expansion forces on a curved railway track. The geometric alignment of a railway right of way often requires railway tracks to be curved. This curvature which is usually defined by the radius of curvature or degree of curvature represents a higher level of complexity in the track’s analysis and design process. Particularly, presence of curvature on the track introduces multiple sources of force in the lateral (radial) direction, including, but not limited to, lateral thermal expansion, lateral wheel/rail forces due to centrifugal action, lateral components of vertical loads, bogie hunting and nosing effects of locomotives, and vehicle curving dynamics. Some of these forces are well understood such as centrifugal forces while some are not as well understood, such as lateral thermal expansion forces. To bridge this gap, this research studies the development of track-induced lateral thermal expansion forces on a curved railway track. In this research, the curved track is assumed to be an arbitrary arc section of a circular track and is modeled as an equivalent idealized circular ring for analysis. Owing to its importance, three analytical methods are used to include: 1) Timoshenko thermoelastic stress analysis in cylindrical coordinate system, 2) mechanics of thin wall cylinders and 3) adaptation of a variational calculus formulation method from a previous comparable study. A fourth analysis approach is also introduced using a commercially available finite element analysis package. The results of these analyses are compared through a wide range of parametric studies and are then validated by the finite element analysis. The results of this study showed that the several methods presented in this paper, could be used to approximate thermally induced expansion behavior (pre-buckling) on a curved railway track. While all three techniques are effective, the Timoshenko stress analysis method appears to be the most suitable as it is a direct method that examines the stress build up from the element level and takes into account additional material properties, such as the Poisson effect. The research resulted in a methodology for determining load transfer from thermally induced forces in curved railroad track to the fastener and supporting structure.

Alfvén Wave Parallel Electric Field in the Dipole Model of the Magnetosphere: Gyrokinetic Treatment

AbstractA mechanism for generation of the parallel electric field by Alfvén wave in the dipole model of the magnetosphere in full gyrokinetics is proposed. The parallel electric field of the Alfvén mode is caused by the coupling of the Alfvén and electrostatic modes due to the plasma inhomogeneity and field line curvature in presence of the trapped hot electrons. The parallel electric field is described by an inhomogeneous integral equation arising from the averaging of the bounce motion of hot electrons. It was found that the parallel electric field is localized near the ionosphere at the heights below 0.5 Earth's radius. For typical Alfvén wave amplitudes observed in space, the parallel electric field potential reaches the values of several kV, which can provide enough acceleration for the precipitating auroral electrons.

Envelope analysis applied to non-Hertzian contact simulations in damaged roller bearings

In the latest years many researcher focused on the possibility to foresee the failure of a mechanical system in the early stages in order to allow quick response times. Monitoring and diagnostics are at the base of those methodologies of predictive maintenance, which represents the standard for companies. Data acquired by monitoring systems are sometimes not sufficient to perform an effective diagnosis and to detect failures. In the present work the possibility of a defining a relation between the response of a system and the dimension of a defect causing the vibration is explored. Through a non-Hertzian contact model a roller bearing is studied and a correlation is sought between the size of the defect and the frequency content of the contact pressure time history. Resorting to a non-Hertzian approach enables the determination with good accuracy of the overpressures due to edge effects caused by the sudden change in curvature in presence of a defect. The estimation of the pressure variation can be used to estimate the amplitude of the harmonic content exciting the bearing during operation. Using algorithms for the signal analysis already assessed in the literature, in particular the envelope method, an in-depth analysis of the harmonic content of the signal to consider is possible. The possibility of building a correlation between the load and the size of the defect which might help to identify the dimension of a damage from the estimated frequency content. It is then possible to identify the presence and nature of the defect, allowing an early diagnosis of the failure.

Probing early universe with a generalized action

Possibly, the most general action in the background of isotropic and homogeneous space–time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective Hamiltonian operator in the presence of curvature squared terms suggests unitary time evolution of the quantum states, assuring conservation of probability. The oscillatory behaviour of the semi-classical wavefunction around a de-Sitter solution signals that the theory is classically allowed, and the universe enters an inflationary regime just after Planck’s era. In view of a hierarchy of Hubble flow parameters, and using a redefined effective potential, the complicated classical field equations in the presence of several coupling parameters, reduce to standard general-relativistic equations with a single scalar field. As a result, inflation has been studied without considering any additional flow parameters. Inflationary parameters lie very much within the presently available Planck’s data, and the model admits graceful exit from inflation.

Segmentation Effect on the Transferability of International Safety Performance Functions for Rural Roads in Egypt

This paper examines the transferability of the Safety Performance Function (SPF) of the Highway Safety Manual (HSM) and other 10 international SPFs for total crashes on rural multi-lane divided roads in Egypt. Four segmentation approaches are assessed in the transferability of the international SPFs, namely: (1) one-kilometer segments (S1); (2) homogenous sections (S2); (3) variable segments with respect to the presence of curvatures (S3); and (4) variable segments with respect to the presence of both curvatures and U-turns (S4). The Mean Absolute Deviation (MAD), Mean Prediction Bias (MPB), Mean Absolute Percentage Error (MAPE), Pearson χ2 statistic, and Z-score parameters are used to evaluate the performance of the transferred models. The overdispersion parameter (k) for each transferred model and each segmentation approach is recalibrated using the local data by the maximum likelihood method. Before estimating the transferability calibration factor (Cr), three methods were used to adjust the local crash prediction of the transferred models, namely: (1) the HSM default crash modification factors (CMFs); (2) local CMFs; and (3) recalibrating the constant term of the transferred model. The latter method is found to outperform the first two methods. Besides, the results show that the segmentation method would affect the performance of the transferability process. Moreover, the Italian SPFs based on the S1 segmentation method outperforms the HSM and all of the investigated international SPFs for transferring their models to the Egyptian rural roads.

A numerical approach for fluid deformable surfaces

Abstract

Harvesting correlations in Schwarzschild and collapsing shell spacetimes

We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spacetime and Schwarzschild spacetimes, and the detectors couple to the proper time derivative of the field. First we find that, with respect to the harvesting protocol, the Unruh vacuum agrees very well with the Vaidya vacuum near the horizon even for finite-time interactions. Second, all four vacua have different capacities for creating correlations between the detectors, with the Vaidya vacuum interpolating between the Unruh vacuum near the horizon and the Boulware vacuum far from the horizon. Third, we show that the black hole horizon inhibits any correlations, not just entanglement. Finally, we show that the efficiency of the harvesting protocol depend strongly on the signalling ability of the detectors, which is highly non-trivial in presence of curvature. We provide an asymptotic analysis of the Vaidya vacuum to clarify the relationship between the Boulware/Unruh interpolation and the near/far from horizon and early/late-time limits. We demonstrate a straightforward implementation of numerical contour integration to perform all the calculations.