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The calcium transient characteristics induced by fluid shear stress affect the osteoblast proliferation

Highlights: • External Ca{sup 2+} determines FSS-induced osteoblast proliferation and differentiation. • The mechanism relies on the mitochondrial energetic metabolism. • MCU enhanced TCA cycle and subsequently affecting cell cycle proteins. • FSS-induced intracellular calcium transients was crucial to the cell proliferation. Ca{sup 2+} signaling is essential for bone metabolism. Fluid shear stress (FSS), which can induce a rapid release of calcium from endoplasmic reticulum (ER) to produce calcium transients, plays a significant role in osteoblast proliferation and differentiation. However, it is still unclear of how calcium transients induced by FSS activating a number of downstream signals which subsequently regulate cell functions. In this study, we performed a group of Ca{sup 2+} transients models, which were induced by FSS to investigate the effects of different magnitudes of Ca{sup 2+} transients in osteoblast proliferation. Further, we performed a global proteomic profile of MC3T3-E1 cells in different Ca{sup 2+} transients models stimulated by FSS. GO enrichment and KEGG pathway analysis revealed that the TCA cycle was activated in the proliferating process. The activation of TCA needed mitochondrial Ca{sup 2+} uptake which were influenced by the amplitude of Ca{sup 2+} transients induced by FSS. Our work elucidate that osteoblast proliferation induced by FSS was related to the magnitude of calcium transients, which further activated energetic metabolism signaling pathway. This work revealed further understanding the mechanism of osteoblast proliferation induced by mechanic loading and help us to design new methods for osteoporosis therapy.

60 APPLIED LIFE SCIENCES↗

Three-dimensional flow in radial turbomachinery and its impact on design

In the two papers on the 'Theory of Blade Design for Large Deflections' published in 1984, a new inverse design technique was presented for designing the shape of turbomachinery blades in three-dimensional flow. The technique involves the determination of the blade profile from the specification of a distribution of the product of the radius and the pitched averaged tangential velocity (i.e., r bar-V(sub theta), the mean swirl schedule) within the bladed region. This is in contrast to the conventional inverse design technique for turbomachinery blading in two dimensional flow in which the blade surface pressure or velocity distribution is specified and the blade profile determined as a result; this is feasible in two-dimensional flow because the streamlines along the blade surfaces are known a priori. However, in three-dimensional flow, the stream surface is free to deform within the blade passage so that the streamlines on the blade surfaces are not known a priori; thus it is difficult and not so useful to prescribe the blade surface pressure or velocity distribution and determine the resulting blade profile. It therefore seems logical to prescribe the swirl schedule within the bladed region for designing a turbomachinery blade profile in three-dimensional flow. Furthermore, specifying r bar-V(sub theta) has the following advantages: (1) it is related to the circulation around the blade (i.e., it is an aerodynamic quantity); (2) the work done or extracted is approximately proportional to the overall change in r bar-V(sub theta) across a given blade row (Euler turbine equation); and (3) the rate of change of r bar-V(sub theta) along the mean streamline at the blade is related to the pressure jump across the blade and therefore the blade loading. Since the publications of those two papers, the technique has been applied to the design of a low speed as well as a high speed radial inflow turbine (for turbocharger applications) both of which showed definite improvements in performance over that of wheels of conventional designs, the design study of a high pressure ratio radial inflow turbine with and without splitter blades.

Tan, Choon S.↗

Mesoporous Fe{sub 3}O{sub 4}/hydroxyapatite composite for targeted drug delivery

Highlights: • Mesoporous Fe{sub 3}O{sub 4}/hydroxyapatite composite was synthesized by a simple, efficient and environmental friendly method. • The prepared material had a large surface area, high pore volume, and good magnetic separability. • DOX-loaded Fe{sub 3}O{sub 4}/hydroxyapatite composite exhibited surprising slow drug release behavior and pH-dependent behavior. - Abstract: In this contribution, we introduced a simple, efficient, and green method of preparing a mesoporous Fe{sub 3}O{sub 4}/hydroxyapatite (HA) composite. The as-prepared material had a large surface area, high pore volume, and good magnetic separability, which made it suitable for targeted drug delivery systems. The chemotherapeutic agent doxorubicin (DOX) was used to investigate the drug release behavior of Fe{sub 3}O{sub 4}/HA composite. The drug release profiles displayed a little burst effect and pH-dependent behavior. The release rate of DOX at pH 5.8 was larger than that at pH 7.4, which could be attributed to DOX protonation in acid medium. In addition, the released DOX concentrations remained at 0.83 and 1.39 μg/ml at pH 7.4 and 5.8, respectively, which indicated slow, steady, and safe release rates. Therefore, the as-prepared Fe{sub 3}O{sub 4}/hydroxyapatite composite could be an efficient platform for targeted anticancer drug delivery.

36 MATERIALS SCIENCE↗

Transport and Retention of Concentrated Oil-in-Water Emulsions in Porous Media

Oil-in-water emulsions are routinely used in subsurface remediation. In these applications, high oil loadings present a challenge to remedial design as mechanistic insights into transport and retention of concentrated emulsions is limited. In this paper, column experiments were designed to examine emulsion transport and retention over a range of input concentrations (1.3–23% wt). Droplet breakthrough and retention data from low concentration experiments were successfully described by existing particle transport models. These models, however, failed to capture droplet transport in more concentrated systems. At high oil fraction, breakthrough curves exhibited an early fall at the end of the emulsion pulse and extending tailing. Irrespective of input concentration, all retention profiles displayed hyper-exponential behavior. Here, we extended existing model formulations to include the additional mixing processes occurring when at high oil concentrations—with focus on the influence of deposited mass and viscous instabilities. The resulting model was parametrized with low concentration data and can successfully predict concentrated emulsion transport and retention. Finally, the role of retained mass and viscous instabilities on mixing conditions can also be applied more broadly to systems with temporal or spatially variant water saturation or when viscosity contrasts exist between fluids.

54 ENVIRONMENTAL SCIENCES↗

Model Intercomparison of the Impacts of Varying Cloud Droplet–Nucleating Aerosols on the Life Cycle and Microphysics of Isolated Deep Convection

The microphysical impacts of aerosol particles on scattered isolated deep convective cells near Houston, Texas, on 19 June 2013, are examined using multiple cloud-resolving model (CRM) simulations initialized with vertical profiles of low and high concentrations of cloud droplet–nucleating aerosols. These simulations formed part of the Model Intercomparison Project (MIP) conducted by the Deep Convective Working Group of the Aerosol, Cloud, Precipitation and Climate (ACPC) initiative. Each CRM generated a field of convective cells representing those observed during the case study with varying degrees of accuracy. The Tracking and Object-Based Analysis of Clouds (tobac) cell-tracking algorithm was applied to each MIP CRM simulation to track relatively long-lived convective cells (20–60 min). Most of the CRMs produced similar aerosol loading impacts on the warm phase of tracked cell properties with reduced autoconversion and accretion growth of rain, increased cloud water, reduced rainfall, and reduced near-surface evaporation of rain. The sign of aerosol impacts on the warm-phase properties of the convective cells was also quite consistent over cell lifetimes with the greatest magnitude of influence in the first half of the life cycle in most CRMs. In contrast, the ice-phase response to aerosol loading was highly variable among CRMs and included increases or decreases in ice amounts at inconsistent stages of the cell life cycle and midlevel versus upper-level changes in ice. This intermodel variability in ice is indicative both of the complex indirect interactions between aerosols and ice-phase processes in deep convection and their associated parameterizations.

Aerosol-cloud interaction↗

Validation of Saharan Dust Layer Characteristics with Lidar Observations

Lidar backscattering profiles available from the LITE data set have been used to estimate the optical depths of the Saharan dust layer over West Africa and E. Atlantic regions, in the context of validating the 3-D conceptual model of the Saharan dust plume proposed by Karyampudi and Carlson. The aerosol extinction profiles and optical depths were retrieved from LITE using the Fernald et al. (1972) method. An extinction-to-backscattering ratio, S(sub a), of 25 was selected for optical depth calculations. The spatial analysis of total column and Saharan dust layer optical depths show higher optical depths over W. Africa that decrease westward over E. Atlantic. The higher optical depths over W. Africa, in general, are associated with heavy dust being raised from the surface in dust source regions. Rapid depletion of these heavy dust particles, perhaps due to sedimentation, appear to decrease the dust loading within the dust layer as the plume leaves the west African continent. Higher optical depths are generally confined to the southern edge of the dust layer, where the middle level jet appears to transport the heavy dust concentrations that tend to mix downward from vertical mixing associated with the strong vertical shears underneath the middle jet. Thus, LITE measurements although, in general, validate the Saharan dust plume conceptual model, show maximum values of optical depths near the southern edge of the dust plume over the E. Atlantic region instead of near the center of the dust plume as described in the conceptual model.

Karyampudi, V. Mohan↗

Analysis of limited-diffractive and limited-dispersive X-waves generated by finite radial waveguides

In this work, we analyze the spatial and temporal features of electromagnetic X-waves propagating in free space and generated by planar radiating apertures. The performance of ideal X-waves is discussed and compared to practical cases where the important effects related to the finiteness of the radiating aperture and the wavenumber dispersion are taken into account. In particular, a practical device consisting of a radial waveguide loaded with radiating slots aligned along a spiral path is considered for the practical case in the millimeter-wave range. A common mathematical framework is defined for a precise comparison of the spatiotemporal properties and focusing capabilities of the generated X-wave. It is clearly shown that the fractional bandwidth of the radiating aperture has a key role in the longitudinal confinement of an X-wave in both ideal and practical cases. In addition, the finiteness of the radiating aperture as well as the wavenumber dispersion clearly affect both the transverse and the longitudinal profiles of the generated radiation as it travels beyond the depth-of-field of the generated X-wave. Nevertheless, the spatiotemporal properties of the X-wave are preserved even in this “dispersive-finite” case within a defined region and duration related to the nondiffractive range and fractional bandwidth of the spectral components of the generated X-wave. The proposed analysis may open new perspectives for the efficient generation of X-waves over finite radiating apertures at millimeter waves where the dispersive behavior of realistic devices is no longer negligible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fast GPU-Based Generation of Large Graph Networks From Degree Distributions

Synthetically generated, large graph networks serve as useful proxies to real-world networks for many graph-based applications. The ability to generate such networks helps overcome several limitations of real-world networks regarding their number, availability, and access. Here, we present the design, implementation, and performance study of a novel network generator that can produce very large graph networks conforming to any desired degree distribution. The generator is designed and implemented for efficient execution on modern graphics processing units (GPUs). Given an array of desired vertex degrees and number of vertices for each desired degree, our algorithm generates the edges of a random graph that satisfies the input degree distribution. Multiple runtime variants are implemented and tested: 1) a uniform static work assignment using a fixed thread launch scheme, 2) a load-balanced static work assignment also with fixed thread launch but with cost-aware task-to-thread mapping, and 3) a dynamic scheme with multiple GPU kernels asynchronously launched from the CPU. The generation is tested on a range of popular networks such as Twitter and Facebook, representing different scales and skews in degree distributions. Results show that, using our algorithm on a single modern GPU (NVIDIA Volta V100), it is possible to generate large-scale graph networks at rates exceeding 50 billion edges per second for a 69 billion-edge network. GPU profiling confirms high utilization and low branching divergence of our implementation from small to large network sizes. For networks with scattered distributions, we provide a coarsening method that further increases the GPU-based generation speed by up to a factor of 4 on tested input networks with over 45 billion edges.

97 MATHEMATICS AND COMPUTING↗

Recoveries of Oil and Hydrolyzed Sugars from Corn Germ Meal by Hydrothermal Pretreatment: A Model Feedstock for Lipid-Producing Energy Crops

Vegetable oil is extracted from oil rich seeds, such as soybeans. Genetic engineering of green plants to accumulate oil in vegetative tissue is a future source of oil that promises increased land productivity and the use of marginal lands. However, the low concentration of lipids in current engineered plant biomass samples makes the oil extraction process challenging and expensive. In this study, liquid hot water (LHW) pretreatment was investigated to enhance oil recovery from the solids and increase enzymatic hydrolysis efficiency of such feedstocks. Corn germ meal was chosen as a model feedstock representing lipid-producing energy crops. Germ meal was pretreated at 160 and 180 °C for 10 and 15 min at 20% w/w solids loading. Enzymatic hydrolysis on the pretreated solid was performed. After pretreatment, the oil concentration increased by 2.2 to 4.2 fold. The most severe pretreatment condition of LHW, at 180 °C for 15 min, gave the maximum oil concentration (9.7%, w/w), the highest triacylglycerol (TAG) content of the extracted oil (71.6%), and the highest conversions of glucose and xylose (99.0% and 32.8%, respectively). This study demonstrates that the optimal pretreatment condition for corn germ meal is 180 °C LHW for 15 min. Pretreatment improves lipids recovery from oil bearing biomass with little or no effect on the lipid profile.

09 BIOMASS FUELS↗

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE↗

Development of solid-lubricated ball-screws for use in space

Ball-screws lubricated by solid lubricant films containing molybdenum disulphide are developed. The ball-screws (shaft diameter: phi 25 mm, length: 667 mm) were operated under a load of 40 to 120 N at a speed of 1.5 to 200 rpm at 10(exp -5) Pa. First, ball-screws made of stainless steel SUS 440C were studied using test equipment originally designed for this study. To reduce weight, the next step taken was to develop a ball-screw made of 6Al-4V-titanium. Long wear-life of more than 1 x 10(exp 7) revolutions was achieved with solid lubricated ball-screws made of SUS 440C and 6Al-4V-titanium in a hard vacuum. According to the surface profile of the shaft measured after 1 x 10(exp 7) revolutions, more solid lubricant remained on the surface of 6Al-4V-titanium than that of stainless steel. Auger and EPMA analysis confirmed lubrication was maintained by solid lubricant on nuts and screws after the lubricant films on the balls were worn off.

Chiba, Masatoshi↗

Probabilistic Assessment of a CMC Turbine Vane

In order to demonstrate the advanced CMC technology under development within the Ultra Efficient Engine Technology (UEET) program, it has been planned to fabricate, test and analyze an all CMC turbine vane made of a SiC/SiC composite material. The objective was to utilize a 5-II Satin Weave SiC/CVI SiC/ and MI SiC matrix material that was developed in-house under the Enabling Propulsion Materials (EPM) program, to design and fabricate a stator vane that can endure successfully 1000 hours of engine service conditions operation. The design requirements for the vane are to be able to withstand a maximum of 2400 F within the substrate and the hot surface temperature of 2700 F with the aid of an in-house developed Environmental/Thermal Barrier Coating (EBC/TBC) system. The vane will be tested in a High Pressure Burner Rig at NASA Glenn Research Center facility. This rig is capable of simulating the engine service environment. The present paper focuses on a probabilistic assessment of the vane. The material stress/strain relationship shows a bilinear behavior with a distinct knee corresponding to what is often termed as first matrix cracking strength. This is a critical life limiting consideration for these materials. The vane is therefore designed such that the maximum stresses are within this limit so that the structure is never subjected to loads beyond the first matrix cracking strength. Any violation of this design requirement is considered as failure. Probabilistic analysis is performed in order to determine the probability of failure based on this assumption. In the analysis, material properties, strength, and pressures are considered random variables. The variations in properties and strength are based on the actual experimental data generated in house. The mean values for the pressures on the upper surface and the lower surface are known but their distributions are unknown. In the present analysis the pressures are considered normally distributed with a nominal variation. Temperature profile on the vane is obtained by performing a CFD analysis and is assumed to be deterministic.

Murthy, Pappu L. N.↗

A Simplified Approach for the Rapid Generation of Transient Heat-Shield Environments

A simplified approach has been developed whereby transient entry heating environments are reliably predicted based upon a limited set of benchmark radiative and convective solutions. Heating, pressure and shear-stress levels, non-dimensionalized by an appropriate parameter at each benchmark condition are applied throughout the entry profile. This approach was shown to be valid based on the observation that the fully catalytic, laminar distributions examined were relatively insensitive to altitude as well as velocity throughout the regime of significant heating. In order to establish a best prediction by which to judge the results that can be obtained using a very limited benchmark set, predictions based on a series of benchmark cases along a trajectory are used. Solutions which rely only on the limited benchmark set, ideally in the neighborhood of peak heating, are compared against the resultant transient heating rates and total heat loads from the best prediction. Predictions based on using two or fewer benchmark cases at or near the trajectory peak heating condition, yielded results to within 5-10 percent of the best predictions. Thus, the method provides transient heating environments over the heat-shield face with sufficient resolution and accuracy for thermal protection system design and also offers a significant capability to perform rapid trade studies such as the effect of different trajectories, atmospheres, or trim angle of attack, on convective and radiative heating rates and loads, pressure, and shear-stress levels.

Wurster, Kathryn E.↗

Implementing Reliability Centered Maintenance (RCM) with State of the Art PT&I Technologies

Building on the work that was started two decades ago, Jacobs Space Operations Group has utilized state of the art PTI technologies to assess the current condition of the assets they manage under the Test and Operations Support Contract (TOSC). Specifically, the Asset Management department leveraged the benefits of ultrasound technology to quantify a motor issue in the Liquid Oxygen Storage Area, and troubleshoot the sources prior to loading the tank to perform Verification and Validation (VV) activities. This technology was efficient, easy to implement, and provided system engineers with data on a possible source of the problem. In situations where legacy motors are exhibiting unexpected noises, it may seem easier to remove and refurbish the motor and replace the bearings because that solution resolves most of the common causes of the noise. However, that solution would have involved additional spending and may not have solved issues stemming from the foundation, if those existed. By utilizing the ultrasound equipment provided by UE Systems, the sound profiles allowed Jacobs TOSC team to determine that the issue resembled a faulty bearing. After replacing the bearing, the unexpected noise ceased.

Reliability Centered Maintenance↗

An extreme metallicity, large-scale outflow from a star-forming galaxy at z ∼ 0.4

We present a detailed analysis of a large-scale galactic outflow in the circumgalactic medium of a massive (M{sub h}∼10{sup 12.5} M{sub ⊙}), star-forming (∼6.9 M{sub ⊙} yr{sup −1}), sub-L{sub *} (∼0.5L{sub B}{sup ∗}) galaxy at z = 0.39853 that exhibits a wealth of metal-line absorption in the spectra of the background quasar Q 0122−003 at an impact parameter of 163 kpc. The galaxy inclination angle (i=63{sup ∘}) and the azimuthal angle (Φ=73{sup ∘}) imply that the QSO sightline is passing through the projected minor-axis of the galaxy. The absorption system shows a multiphase, multicomponent structure with ultra-strong, wide velocity spread O VI (logN=15.16±0.04, Δv{sub 90} = 419 km s{sup −1}) and N V (logN=14.69±0.07, Δv{sub 90} = 285 km s{sup −1}) lines that are extremely rare in the literature. The highly ionized absorption components are well explained as arising in a low density (∼10{sup −4.2} cm{sup −3}), diffuse (∼10 kpc), cool (∼10{sup 4} K) photoionized gas with a super-solar metallicity ([X/H]≳0.3). From the observed narrowness of the Lyβ profile, the non-detection of S IV absorption, and the presence of strong C IV absorption in the low-resolution FOS spectrum, we rule out equilibrium/non-equilibrium collisional ionization models. The low-ionization photoionized gas with a density of ∼10{sup −2.5} cm{sup −3} and a metallicity of [X/H]≳−1.4 is possibly tracing recycled halo gas. We estimate an outflow mass of ∼2×10{sup 10} M{sub ⊙}, a mass-flow rate of ∼54 M{sub ⊙} yr{sup −1}, a kinetic luminosity of ∼9×10{sup 41} erg s{sup −1}, and a mass loading factor of ∼8 for the outflowing high-ionization gas. These are consistent with the properties of “down-the-barrel” outflows from infrared-luminous starbursts as studied by Rupke et al. Such powerful, large-scale, metal-rich outflows are the primary means of sufficient mechanical and chemical feedback as invoked in theoretical models of galaxy formation and evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

Relative Economic Merits of Storage and Combustion Turbines for Meeting Peak Capacity Requirements under Increased Penetration of Solar Photovoltaics

Batteries with several hours of capacity provide an alternative to combustion turbines for meeting peak capacity requirements. Even when compared to state-of-the-art highly flexible combustion turbines, batteries can provide a greater operational value, which is reflected in a lower system-wide production cost. By shifting load and providing operating reserves, batteries can reduce the cost of operating the power system to a traditional electric utility. This added value means that, depending on battery life, batteries can have a higher cost than a combustion turbine of equal capacity and still produce a system with equal or lower overall life-cycle cost. For a utility considering investing in new capacity, the cost premium for batteries is highly sensitive to a variety of factors, including lifetime, natural gas costs, PV penetration, and grid generation mix. In addition, as PV penetration increases, the net electricity demand profile changes, which may reduce the amount of battery energy capacity needed to reliably meet peak demand.

14 SOLAR ENERGY↗

FY17 CSSE L2 Milestone Report: Analyzing Power Usage Characteristics of Workloads Running on Trinity.

This report summarizes the work performed as part of a FY17 CSSE L2 milestone to in- vestigate the power usage behavior of ASC workloads running on the ATS-1 Trinity plat- form. Techniques were developed to instrument application code regions of interest using the Power API together with the Kokkos profiling interface and Caliper annotation library. Experiments were performed to understand the power usage behavior of mini-applications and the SNL/ATDM SPARC application running on ATS-1 Trinity Haswell and Knights Landing compute nodes. A taxonomy of power measurement approaches was identified and presented, providing a guide for application developers to follow. Controlled scaling study experiments were performed on up to 2048 nodes of Trinity along with smaller scale ex- periments on Trinity testbed systems. Additionally, power and energy system monitoring information from Trinity was collected and archived for post analysis of "in-the-wild" work- loads. Results were analyzed to assess the sensitivity of the workloads to ATS-1 compute node type (Haswell vs. Knights Landing), CPU frequency control, node-level power capping control, OpenMP configuration, Knights Landing on-package memory configuration, and algorithm/solver configuration. Overall, this milestone lays groundwork for addressing the long-term goal of determining how to best use and operate future ASC platforms to achieve the greatest benefit subject to a constrained power budget.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Polar cap models of gamma-ray pulsars: Emision from single poles of nearly aligned rotators

We compare a new Monte Carlo simulation of polar cap models for gamma-ray pulsars with observations of sources detected above 10 MeV by the Compton Observatory (CGRO). We find that for models in which the inclination of the magnetic axis is comparable to the angular radius of the polar cap, the radiation from a single cap may exhibit a pusle with either a single broad peak as in PSR 1706-44 and PSR 1055-52, or a doubly peaked profile comparable to those observed from the Crab, Vela and Geminga pulsars. In general, double pulses are seen by observers whose line of sight penetrates into the cap interior and are due to enhanced emission near the rim. For cascades induced by culvature radiation, increased rim emission occurs even when electrons are accelerated over the entire cap, since electrons from the interior escape along magnetic field lines with less curvature and hence emit less radiation. However, we obtain better fits to the duty cycles of observed profiles if we make the empirical assumption that acceleration occurs only near the rim. In either case, the model energy spectra are consistent with most of the observed sources. The beaming factors expected from nearly aligned rotators, based on standard estimates for the cap radius, imply that their luminosities need not be as large as in the case of orthogonal rotators. However, small beam angles are also a difficutly with this model because they imply low detection probablities. In either case the polar cap radius is a critical factor, and in this context we point out that plasma loading of the field lines should make the caps larger than the usual estimates based on pure dipole fields.

Daugherty, Joseph K.↗

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