Scale Kinematics Research Articles

Variable flavor number scheme for final state jets in DIS

We discuss massive quark effects in the endpoint region $x \to 1$ of inclusive deep inelastic scattering, where the hadronic final state is collimated and thus represents a jet. In this regime heavy quark pairs are generated via secondary radiation, i.e. due to a gluon splitting in light quark initiated contributions starting at $\mathcal{O}(\alpha_s^2)$ in the fixed-order expansion. Based on the factorization framework for massless quarks in Soft Collinear Effective Theory (SCET), we construct a variable flavor number scheme that deals with arbitrary hierarchies between the mass scale and the kinematic scales exhibiting a continuous behavior between the massless limit for very light quarks and the decoupling limit for very heavy quarks. We show that the threshold matching corrections for all gauge invariant components at the mass scale are related to each other via consistency conditions. This is explicitly demonstrated by recalculating the known threshold correction for the parton distribution function at $\mathcal{O}(\alpha_s^2 C_F T_F)$ within SCET. The latter contains large rapidity logarithms $\sim \ln(1-x)$ that can be summed by exponentiation. Their coefficients are universal which can be used to obtain potentially relevant higher order results for generic threshold corrections at colliders from computations in deep inelastic scattering. In particular, we extract the $\mathcal{O}(\alpha_s^3)$ threshold correction multiplied by a single rapidity logarithm from results obtained earlier.

Examining early-type galaxy scaling relations using simple dynamical models

We use dynamical models that include bulk rotation, velocity dispersion anisotropy and both stars and dark matter to explore the conditions that give rise to the early-type galaxy scaling relations referred to as the Fundamental Plane (FP) and Manifold (FM). The modelled scaling relations generally match the observed relations and are remarkably robust to all changes allowed within these models. The empirical relationships can fail beyond the parameter ranges where they were calibrated and we discuss the nature of those failures. Because the location of individual models relative to the FP and FM is sensitive to the adopted physical scaling of the models, unconstrained rescaling produces a much larger scatter about the scaling relations than that observed. We conclude that only certain combinations of scaling values, which define the physical radial and kinematic scale of the model, produce low scatter versions of the FP and FM. These combinations further result in reproducing a condition observed previously for galaxies, $r_c \rho_0 = $ constant, where $r_c$ is the scaling radius and $\rho_0$ is the central density. As such, we conclude that this empirical finding and global galaxy scaling relations are not independent and that finding the physical cause of one should lead to the solution to the other. Although our models are strictly for pressure supported galaxies, these results may well hold generally because the central density constraint was first identified in dwarf spheroidals but later extended to rotating giant galaxies and the FM applies to galaxies of any morphological type and luminosity class.

Reproducing tornadoes in laboratory using proper scaling

Experimentally simulated tornado-like vortices are related to field tornadoes in order to: (i) establish proper kinematic and dynamic scaling and (ii) attempt to determine a relationship between laboratory parameters and the Enhanced Fujita Scale (EF-Scale). Data from recent in-situ Doppler radar campaigns are analyzed using the Ground-Based Velocity Track Display (GBVTD) method and a unique dataset of three-dimensional axisymmetric tornado flow fields is generated. In parallel, Particle Image Velocimetry (PIV) results of the most recent experimental simulations of tornado vortices performed in the model WindEEE Dome (MWD) are analyzed and then compared with the GBVTD-retrieved full-scale data. Based on these comparisons, the swirl ratio of the full-scale tornadoes, as well as the length and velocity scaling ratios of the simulated tornadoes are identified. It is concluded that the MWD apparatus can generate tornado-like vortices equivalent to EF0 to low-end EF3 rated tornadoes in nature.

Scaling the Feeding Mechanism of Captive Alligator mississippiensis from Hatchling to Juvenile.

Small changes in size can lead to potential performance consequences and may influence an organism’s ability to utilize resources in its environment. As the American alligator (Alligator mississippiensis) transitions between neonate, juvenile and adult habitats (ontogenetic niche shifts), there are inevitably dynamic changes in their feeding performance. This study sought to investigate the scaling of the feeding mechanism and its performance from hatchling to juvenile size classes in A. mississippiensis. Feeding events were recorded during March 2011 at Rockefeller Wildlife Refuge (Grand Chenier, Louisiana). Thirty-six captive individuals were randomly sampled, ranging from 30.5 cm to 91.5 cm total length, and feeding events were recorded using a high speed camera at a rate of 300 fps. Results indicated that many linear, angular and timing kinematic variables scale allometrically with cranium length; whereas maximum gape velocity and duration of feeding bout do not scale with cranium length and remain constant between these size classes. Although it has been shown that there is an isometric relationship between cranial elements and body size in A. mississippiensis, this relationship is not transferred to linear and timing variables of prey-capture events. These allometric relationships echo other investigations of scaling relationships such as bite-force production and terrestrial locomotion.

Scaling of olfactory antennae of the terrestrial hermit crabs Coenobita rugosus and Coenobita perlatus during ontogeny.

Although many lineages of terrestrial crustaceans have poor olfactory capabilities, crabs in the family Coenobitidae, including the terrestrial hermit crabs in the genus Coenobita, are able to locate food and water using olfactory antennae (antennules) to capture odors from the surrounding air. Terrestrial hermit crabs begin their lives as small marine larvae and must find a suitable place to undergo metamorphosis into a juvenile form, which initiates their transition to land. Juveniles increase in size by more than an order of magnitude to reach adult size. Since odor capture is a process heavily dependent on the size and speed of the antennules and physical properties of the fluid, both the transition from water to air and the large increase in size during ontogeny could impact odor capture. In this study, we examine two species of terrestrial hermit crabs, Coenobita perlatus H. Milne-Edwards and Coenobita rugosus H. Milne-Edwards, to determine how the antennule morphometrics and kinematics of flicking change in comparison to body size during ontogeny, and how this scaling relationship could impact odor capture by using a simple model of mass transport in flow. Many features of the antennules, including the chemosensory sensilla, scaled allometrically with carapace width and increased slower than expected by isometry, resulting in relatively larger antennules on juvenile animals. Flicking speed scaled as expected with isometry. Our mass-transport model showed that allometric scaling of antennule morphometrics and kinematics leads to thinner boundary layers of attached fluid around the antennule during flicking and higher odorant capture rates as compared to antennules which scaled isometrically. There were no significant differences in morphometric or kinematic measurements between the two species.

Full-Body Postural Control of a Humanoid Robot with Both Imitation Learning and Skill Innovation

In this paper, we present a novel methodology to obtain imitative and innovative postural movements in a humanoid based on human demonstrations in a different kinematic scale. We collected motion data from a group of human participants standing up from a chair. Modeling the human as an actuated 3-link kinematic chain, and by defining a multi-objective reward function of zero moment point and joint torques to represent the stability and effort, we computed reward profiles for each demonstration. Since individual reward profiles show variability across demonstrating trials, the underlying state transition probabilities were modeled using a Markov chain. Based on the argument that the reward profiles of the robot should show the same temporal structure of those of the human, we used differential evolution to compute a trajectory that fits all humanoid constraints and minimizes the difference between the robot reward profile and the predicted profile if the robot imitates the human. Therefore, robotic imitation involves developing a policy that results in a temporal reward structure, matching that of a group of human demonstrators across an array of demonstrations. Skill innovation was achieved by optimizing a signed reward error after imitation was achieved. Experimental results using the humanoid HOAP-3 are shown.

Nuclear structure functions at low- $$x$$ x in a holographic approach

Nuclear effects in deep inelastic scattering at low $$x$$ are phenomenologically described changing the typical dynamical and/or kinematical scales characterizing the free nucleon case. In a holographic approach, this rescaling is an analytical property of the computed structure function $$F_2(x,Q^2)$$ . This function is given by the sum of a conformal term and of a contribution due to quark confinement, depending on IR hard-wall parameter $$z_0$$ and on the mean square distances, related to a parameter $$Q^\prime $$ , among quarks and gluons in the target. The holographic structure function per nucleon in a nucleus $$A$$ is evaluated showing that a rescaling of the typical nucleon size, $$z_0$$ and $$Q^\prime $$ , due to nuclear binding, can be reabsorbed in a $$Q^2$$ -rescaling scheme. The difference between neutron and proton structure functions and the effects of the longitudinal structure functions can also be taken into account. The obtained theoretical results favorably compare with the experimental data.

The scaling of tongue projection in the veiled chameleon, Chamaeleo calyptratus

Within a year of hatching, chameleons can grow by up to two orders of magnitude in body mass. Rapid growth of the feeding mechanism means that bones, muscles, and movements change as chameleons grow while needing to maintain function. A previous morphological study showed that the musculoskeletal components of the feeding apparatus grow with negative allometry relative to snout–vent length (SVL) in chameleons. Here, we investigate the scaling of prey capture kinematics and muscle physiological cross-sectional area in the veiled chameleon, Chamaeleo calyptratus. The chameleons used in this study varied in size from approximately 3 to 18cm SVL (1–200g). Feeding sequences of 12 chameleons of different sizes were filmed and the timing of movements and the displacements and velocities of the jaws, tongue, and the hyolingual apparatus were quantified. Our results show that most muscle cross-sectional areas as well as tongue and hyoid mass scaled with isometry relative to mandible length, yet with negative allometry relative to SVL. Durations of movement also scaled with negative allometry relative to SVL and mandible length. Distances and angles generally scaled as predicted under geometric similarity (slopes of 1 and 0, respectively), while velocities generally scaled with slopes greater than 0 relative to SVL and mandible length. These data indicate that the velocity of jaw and tongue movements is generally greater in adults compared to juveniles. The discrepancy between the scaling of cross-sectional areas versus movements suggests changes in the energy storage and release mechanisms implicated in tongue projection.

Scale model for the confluent area of debris flow and main river: a case study of the Wenjia Gully

Abstract. When debris flow discharges into the main river, the deposition of debris raises the river bed, occupies the path of water conveyance and damages or even destroys buildings, resulting in considerable economic loss and possibly fatalities. Mathematical models are normally employed to compute debris flow. However, most of these models employ empirical formulae and coefficients and their results are seldom reliable. On the other hand, scale model tests associated with debris flow have seldom been conducted due to the lack of corresponding similarity laws and the difficulty of achieving the grain diameter scale. Focusing on pseudo-one-phase flow, this paper discusses the laws of similarity for the confluence of debris flow and main river and conducts a case study of the debris flow that occurred on 13 August 2010, in the Wenjia Gully, China. After satisfying the roughness scale, the kinematic viscosity coefficient scale, and the momentum ratio scale, it was found that the deposition terrain in the model test is consistent with the one in the prototype.

Asymmetric Hurricane Boundary Layer Structure from Dropsonde Composites in Relation to the Environmental Vertical Wind Shear

Abstract This study investigates the asymmetric structure of the hurricane boundary layer in relation to the environmental vertical wind shear in the inner core region. Data from 1878 GPS dropsondes deployed by research aircraft in 19 hurricanes are analyzed in a composite framework. Kinematic structure analyses based on Doppler radar data from 75 flights are compared with the dropsonde composites. Shear-relative quadrant-mean composite analyses show that both the kinematic and thermodynamic boundary layer height scales tend to decrease with decreasing radius, consistent with previous axisymmetric analyses. There is still a clear separation between the kinematic and thermodynamic boundary layer heights. Both the thermodynamic mixed layer and height of maximum tangential wind speed are within the inflow layer. The inflow layer depth is found to be deeper in quadrants downshear, with the downshear right (DR) quadrant being the deepest. The mixed layer depth and height of maximum tangential wind speed are alike at the eyewall, but are deeper outside in quadrants left of the shear. The results also suggest that air parcels acquire equivalent potential temperature θe from surface fluxes as they rotate through the upshear right (UR) quadrant from the upshear left (UL) quadrant. Convection is triggered in the DR quadrant in the presence of asymmetric mesoscale lifting coincident with a maximum in θe. Energy is then released by latent heating in the downshear left (DL) quadrant. Convective downdrafts bring down cool and dry air to the surface and lower θe again in the DL and UL quadrants. This cycling process may be directly tied to shear-induced asymmetry of convection in hurricanes.

The Dawes Review 1: Kinematic Studies of Star-Forming Galaxies Across Cosmic Time

AbstractThe last seven years have seen an explosion in the number of Integral Field galaxy surveys, obtaining resolved 2D spectroscopy, especially at high-redshift. These have taken advantage of the mature capabilities of 8–10 m class telescopes and the development of associated technology such as AO. Surveys have leveraged both high spectroscopic resolution enabling internal velocity measurements and high spatial resolution from AO techniques and sites with excellent natural seeing. For the first time, we have been able to glimpse the kinematic state of matter in young, assembling star-forming galaxies and learn detailed astrophysical information about the physical processes and compare their kinematic scaling relations with those in the local Universe. Observers have measured disc galaxy rotation, merger signatures, and turbulence-enhanced velocity dispersions of gas-rich discs. Theorists have interpreted kinematic signatures of galaxies in a variety of ways (rotation, merging, outflows, and feedback) and attempted to discuss evolution vs. theoretical models and relate it to the evolution in galaxy morphology. A key point that has emerged from this activity is that substantial fractions of high-redshift galaxies have regular kinematic morphologies despite irregular photometric morphologies and this is likely due to the presence of a large number of highly gas-rich discs. There has not yet been a review of this burgeoning topic. In this first Dawes review, I will discuss the extensive kinematic surveys that have been done and the physical models that have arisen for young galaxies at high-redshift.

MINLO: multi-scale improved NLO

Abstract In the present work we consider the assignment of the factorization and renormalization scales in hadron collider processes with associated jet production, at next-to-leading order (NLO) in perturbation theory. We propose a simple, definite prescription to this end, including Sudakov form factors to consistently account for the distinct kinematic scales occuring in such collisions. The scheme yields results that are accurate at NLO and, for a large class of observables, it resums to all orders the large logarithms that arise from kinematic configurations involving disparate scales. In practical terms the method is most simply understood as an NLO extension of the matrix element reweighting procedure employed in tree level matrix element-parton shower merging algorithms. By way of a proof-of-concept, we apply the method to Higgs and Z boson production in association with up to two jets.

The degeneracy between star formation parameters in dwarf galaxy simulations and the Mstar-Mhalo relation

We present results based on a set of N-Body/SPH simulations of isolated dwarf galaxies. The simulations take into account star formation, stellar feedback, radiative cooling and metal enrichment. The dark matter halo initially has a cusped profile, but, at least in these simulations, starting from idealised, spherically symmetric initial conditions, a natural conversion to a core is observed due to gas dynamics and stellar feedback. A degeneracy between the efficiency with which the interstellar medium absorbs energy feedback from supernovae and stellar winds on the one hand, and the density threshold for star formation on the other, is found. We performed a parameter survey to determine, with the aid of the observed kinematic and photometric scaling relations, which combinations of these two parameters produce simulated galaxies that are in agreement with the observations. With the implemented physics we are unable to reproduce the relation between the stellar mass and the halo mass as determined by Guo et al. (2010), however we do reproduce the slope of this relation.

It's tough to be small: dependence of burrowing kinematics on body size

Burrowing marine infauna are morphologically diverse and range in size over several orders of magnitude. Whilst effects of ontogenetic and morphological differences on running, flying and swimming are relatively well understood, similar analyses of burrowing mechanics and kinematics are lacking. The polychaete Nereis virens Sars extends its burrow by fracture, using an eversible pharynx to exert force on the walls of the burrow. The resulting stress is amplified at the anterior tip of the burrow, which extends when the stress exceeds the fracture toughness of the material. Here we show that the polychaete Cirriformia moorei extends its burrow by a similar mechanism, but by using its hydrostatic skeleton rather than an eversible pharynx. Based on the dimensionless wedge number, which relates work of fracture to work to maintain body shape against the elasticity of sediment, we predicted that smaller worms would exhibit behaviors characteristic of tougher sediments and that scaling of kinematics would reflect decreasing difficulty in fracturing sediment with increasing body size. We found that smaller worms were relatively blunter and thicker, and had a greater variation of thickness than larger worms as they burrowed. Although these kinematic differences increase the stress amplification at the crack tip, smaller worms still generate lower stress intensity factors. The greater relative body thickness and shape changes of smaller worms are consistent with ontogenetic changes in forces exerted by earthworms, and are likely driven by the challenge of exerting enough stress to extend a crack with a small body size.

Hadronic final states in deep-inelastic scattering with Sherpa

We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, defined by jets or individual hadrons, in deep-inelastic scattering are analysed and the corresponding results are compared to HERA data. The various sources of theoretical uncertainties of the approach are discussed and quantified. The extension to deeply inelastic processes provides the opportunity to validate the merging of matrix elements and parton showers in multi-scale kinematics inaccessible in other collider environments. It also allows to use HERA data on hadronic final states in the tuning of hadronisation models.

Small scale experimental testing to verify the effectiveness of the base isolation and tuned mass dampers combined control strategy

This paper presents the most significant results obtained within a broad-ranging experimental program aiming to evaluate both the effectiveness and the robustness of a Base Isolation (BIS) and a Tuned Mass Damper (TMD) combined control strategy (BI & TMD). Following a brief description of the experimental model set-up and the adopted kinematic scaling technique, this paper describes the identification procedures carried out to characterize the system''s model. The dynamic response of a small-scale model to recorded earthquake excitations, which has been scaled by using the Buckingham pi-theorem, are later presented and discussed. Finally, the effectiveness and robustness of the combined control strategy is evaluated by comparing the model's dynamic response. In particular, reduction in relative displacements and absolute accelerations due to the application of different mass damping systems is investigated.

Parametric Design of Parallel Force/Velocity Actuators: Force Distribution Analysis

Abstract In this paper we present the force distribution analysis for a dual input actuator called parallel force/velocity actuator (PFVA). We present five physical quantities that are relevant to the design and operation of PFVA-based systems. For each of them we (i) follow a first principles approach to develop a model, (ii) define dimensionless parameters and criteria that indicate the relative distribution of the quantity between the two inputs of the PFVA, (iii) express the basic model in terms of these dimensionless parameters, (iv) provide numerical examples using five candidate designs with commercial off-the-shelf components, (v) investigate the limiting case as the two inputs become more and more kinematically distinct, and (vi) suggest design guidelines based on our analysis. We studied four aspects of PFVA design: (i) mixing of position uncertainties of the two inputs, i.e., force actuator (FA) and velocity actuator (VA), (ii) distribution of static and inertia torques between the inputs for a given output loading condition, (iii) acceleration responsiveness, and lastly, (iv) effective stiffness of the PFVA system with respect to some basic design parameters of the PFVA. As an example result, we observed that the PFVA's effective stiffness will be at least 40% greater than that of the VA if the FA is 85% as efficient as the VA, the FA is 17% less stiff than the VA, and the kinematic scaling between the two inputs (FA and VA) is approximately 11.5. The results we obtained are organized into five design guidelines for the PFVA. To demonstrate the utility of this analysis and the guidelines, we present a design case study that describes a PFVA prototype. The results of this paper assist in better designing PFVA-based systems with a focus on the coupling between the two inputs.

Kinematic Robot-Based Evaluation Scales and Clinical Counterparts to Measure Upper Limb Motor Performance in Patients With Chronic Stroke

Background. Human-administered clinical scales are the accepted standard for quantifying motor performance of stroke subjects. Although they are widely accepted, these measurement tools are limited by interrater and intrarater reliability and are time-consuming to apply. In contrast, robot-based measures are highly repeatable, have high resolution, and could potentially reduce assessment time. Although robotic and other objective metrics have proliferated in the literature, they are not as well established as clinical scales and their relationship to clinical scales is mostly unknown. Objective. To test the performance of linear regression models to estimate clinical scores for the upper extremity from systematic robot-based metrics. Methods. Twenty kinematic and kinetic metrics were derived from movement data recorded with the shoulder-and-elbow InMotion2 robot (Interactive Motion Technologies, Inc), a commercial version of the MIT-Manus. Kinematic metrics were aggregated into macro-metrics and micro-metrics and collected from 111 chronic stroke subjects. Multiple linear regression models were developed to calculate Fugl-Meyer Assessment, Motor Status Score, Motor Power, and Modified Ashworth Scale from these robot-based metrics. Results. Best performance—complexity trade-off was achieved by the Motor Status Score model with 8 kinematic macro-metrics (R = .71 for training; R = .72 for validation). Models including kinematic micro-metrics did not achieve significantly higher performance. Performances of the Modified Ashworth Scale models were consistently low (R = .35-.42 for training; R = .08-.17 for validation). Conclusions. The authors identified a set of kinetic and kinematic macro-metrics that may be used for fast outcome evaluations. These metrics represent a first step toward the development of unified, automated measures of therapy outcome.

Scaling Relations for Intermediate-Energy Proton-Nucleus Reactions with Small Energy Losses

A kinematic scaling system, based on successes found for inclusive electron-nucleus continuum spectra, is developed and applied to (p, px) and (p, nx) data at beam energies from 346 to 1600 MeV. The emphasis is on ejectiles with the highest energies at small angles since these are the particles able to induce further reactions in thick samples of interest for current and future accelerator-driven neutron sources. The limits of the method are explored, and successes are used to identify gaps in the difficult data sets available. Scaling successes are able to allow interpolations and extrapolations needed for applications. Details of the method are presented in appendixes.

A kinematic subgrid scale model for large-eddy simulation of turbulence-generated sound

In the hybrid approach of large-eddy simulation (LES) and Lighthill's acoustic analogy for turbulence-generated sound, the turbulence source fields are obtained using an LES and the turbulence-generated sound at far fields is calculated from Lighthill's acoustic analogy. As only the velocity fields at resolved scales are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill's acoustic equation, has to be evaluated from the resolved velocity fields. As a result, the contribution from the unresolved velocity fields is missing in the conventional LES. The sound of missing scales is shown to be important and hence needs to be modeled. The present study proposes a kinematic subgrid-scale (SGS) model which recasts the unresolved velocity fields into Lighthill's stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with the imposed temporal statistics, which is consistent with the random sweeping hypothesis. The kinematic SGS model is used to calculate sound power spectra from isotropic turbulence and yields an improved result: the missing portion of the sound power spectra is approximately recovered in the LES.