Sharp Gradients Research Articles

Morphometric Analysis of Karkala Micro Watershed, Karkala Taluk Udupi District, Karnataka India

An integrated assessment of morphometric parameters has been conducted in this study with an objective of to develop the watershed and manage the available water resources in a hard rock terrain area at Karkala Taluk, Karnataka. According to the analysis of the Karkala micro-watershed, which is classified as closed basin with third-order dendritic drainage pattern, the watershed has a dense canopy of vegetation, a low relief, minute runoff, and a high infiltration rate. Drainage patterns are not greatly affected by geological structures. The basin's elongated shape is supported by the form factor, circulation ratio, and elongation ratio numbers. The Karkala micro-watershed's longitudinal profile exhibits a sharp gradient in the initial stages that has been progressively flattening as the river has weakened. Hypsometric integral found for the Karkala micro watershed is 0.5, showing the maturity stage of the basin. Low values for drainage density and texture, stream frequency, and infiltration number suggest that permeable rocks are underling and this controls the runoff in study area. Therefore, the integrated results of the morphometric assessment at the micro watershed level would be helpful for developing and managing water resources as well as for water harvesting.

On the construction of general large-amplitude spherically polarised Alfvén waves

In a magnetised plasma on scales well above ion kinetic scales, any constant-magnitude magnetic field, accompanied by parallel Alfvénic flows, forms a nonlinear solution in an isobaric, constant-density background. These structures, which are also known as spherically polarised Alfvén waves, are observed ubiquitously in the solar wind, presumably created by the growth of small-amplitude fluctuations as they propagate outwards in the corona. Here, we present a computational method to construct such solutions of arbitrary amplitude with general multidimensional structure, and explore some of their properties. The difficulty lies in computing a zero-divergence, constant-magnitude magnetic field, which leaves a single, quasi-free function to define the solution, while requiring strong constraints on any individual component of the field. Motivated by the physical process of wave growth in the solar wind, our method circumvents this issue by starting from low-amplitude Alfvénic fluctuations dominated by a strong mean field, then ‘growing’ magnetic perturbations into the large-amplitude regime. We present example solutions with non-trivial structure in one, two and three dimensions, demonstrating a clear tendency to form very sharp gradients or discontinuities, unless the solution is one-dimensional. As well as being useful as an input for other calculations, particularly the study of parametric decay, our results provide a natural explanation for the extremely sharp field discontinuities observed across magnetic field switchbacks in the low solar wind.

Sculpting Electrochemically Growing or Grown Microarchitectures.

Microarchitectures with complex interior structures are important for many applications. However, engineering complex interior structures within microarchitectures are challenging. This article reports the introduction of electrochemical sculpting processes to carve the microarchitectures during or after their electrochemical growing process to design the interior structure of the microarchitectures. The electrochemical growing and sculpting process tangle together under the constant voltage electrodeposition mode with their strength depending on the ion concentration gradient and the voltage value. The unique thawing process of the frozen electrolyte is used to create the desired sharp ion concentration gradient, and has the potential to control the strength of the sculpting and the growing processes. How to completely decouple the growing and the sculpting process is further studied to gain more accurate control over the interior structures of the microarchitectures. It is revealed that the sculpting process can be exclusively applied onto the electrochemically grown microarchitectures simply by reversing the electric field without triggering any growing processes. Microarchitectures with complex interior structures, including micropyramids with a single cavity exclusively at the outward or every apex to multi-walled hollow pyramids with designable wall numbers and inter-wall distances are prepared as examples.

Evaluation of machine learning methodologies using simple physics based conceptual models for flow in porous media

Machine learning (ML) techniques have drawn much attention in the engineering community due to recent advances in computational techniques and an enabling environment. However, often they are treated as black-box tools, which should be examined for their robustness and range of validity/applicability. This research presents an evaluation of their application to flow/transport in porous media, where exact solutions (obtained from physics-based models) are used to train ML algorithms to establish when and how these ML algorithms fail to predict the first order flow-physics. Exact solutions are used so as not to introduce artifacts from the numerical solutions.To test, validate, and predict the physics of flow in porous media using ML algorithms, one needs a reliable set of data that may not be readily available and/or the data might not be in suitable form (i.e. incomplete/missing reporting, metadata, or other relevant peripheral information). To overcome this, we first generated structured datasets for flow in porous media using simple representative building blocks of flow physics such as Buckley-Leverett, convection-dispersion equations, and viscous fingering. Then, the outcomes from those equations are fed into ML algorithms to examine their robustness and predictive strength of the key features, such as breakthrough time, and saturation and component profiles. In this research, we show that a physics-informed ML algorithm can capture the physical behavior and effects of various physical parameters (even when shocks and sharp gradients are present) on the features of the flow. Furthermore the ML approach can be utilized to solve inverse problems to estimate various physical parameters. In this study, we have focused on capturing the dominant flow physics on selected processes constituting the outcome of the physics of flow in porous media using ML algorithms. We expect that capturing the physics per selected processes can help solving more complex problems by providing correlative physical proxies.

Depth dose measurements in water for 11C and 10C beams with therapy relevant energies

Owing to the favorable depth-dose distribution and the radiobiological properties of heavy ion radiation, ion beam therapy shows an improved success/toxicity ratio compared to conventional radiotherapy. The sharp dose gradients and very high doses in the Bragg peak region, which represent the larger physical advantage of ion beam therapy, make it also extremely sensitive to range uncertainties. The use of β+-radioactive ion beams would be ideal for simultaneous treatment and accurate online range monitoring through PET imaging. Since all the unfragmented primary ions are potentially contributing to the PET signal, these beams offer an improved image quality while preserving the physical and radiobiological advantages of the stable counterparts. The challenging production of radioactive ion beams and the difficulties in reaching high intensities, have discouraged their clinical application. In this context, the project Biomedical Applications of Radioactive ion Beams (BARB) started at GSI (Helmholtzzentrum für Schwerionenforschung GmbH) with the main goal to assess the technical feasibility and investigate possible advantages of radioactive ion beams on the pre-clinical level. During the first experimental campaign 11C and 10C beams were produced and isotopically separated with the FRagment Separator (FRS) at GSI. The β+-radioactive ion beams were produced with a beam purity of 99% for all the beam investigated (except one case where it was 94%) and intensities potentially sufficient to treat a small animal tumors within few minutes of irradiation time, ∼106 particle per spill for the 10C and ∼107 particle per spill for the 11C beam, respectively. The impact of different ion optical parameters on the depth dose distribution was studied with a precision water column system. In this work, the measured depth dose distributions are presented together with results from Monte Carlo simulations using the FLUKA software.

Shapes of the fastest fish and optimal underwater and floating hulls

A streamlined shape of the best swimmers removes the boundary-layer separation and ensures a laminar flow pattern. The fastest fish have a very sharp convex nose (rostrum), the purpose of which remains unclear. The bodies of revolution similar to their shapes are analyzed in steady underwater and floating motion. The sources and sinks were located on the axis of symmetry and above the water surface to estimate the pressure on the body and the vertical velocities on the water surface. It was shown that the flow patterns on a special shaped body with concave nose has no stagnation points and ensure small values of the water surface elevation. These fact allow diminishing the maximum pressure on the surface and wave drag. Special shapes with the sharp concave nose and negative pressure gradients on their surface could be parts of the low drag underwater and floating hulls.

The Rigidity and Stability of Gradient Estimates

In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with non-negative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat equations and the related estimates for Dirichlet Green’s functions on Riemannian manifolds with non-negative Ricci curvature. Moreover, we also obtain the corresponding stability results.

P11.25.B Adjuvant high precision hypofractionated radiotherapy for resected brain metastases: single-institutional experience

Abstract Background The proportion of patients with solid tumor who develop brain metastases may be as high as 35%. Whenever possible, resection should be the first treatment option. Unfortunately, resection alone has recurrence rates up to 50-60%. In order to improve local control, adjuvant radiation to the surgical cavity is highly recommended. Single dose stereotactic radiosurgery (SRS) as well as hypofractionated stereotactic radiotherapy (HFSRT) have shown one-year local control rates from 70 to 90% with low incidence of radiation-induced toxicity. High precision hypofractionated radiotherapy (HFRT) using Volumetric Modulated Arc Therapy (VMAT) combines sharp dose gradients of SRS with a fractionated scheme, allowing high radiation doses per fraction while minimizing adverse events. Therefore, it could be used as an alternative to SRS for target volumes larger than 3 cm or close to sensitive brain areas. This study aims to analyze control parameters and toxicity of High precision HFRT after brain metastasis resection. Material and Methods We retrospectively analyzed 38 patients diagnosed with brain metastases underwent complete or subtotal surgical resection followed by adjuvant High precision HFRT between January and December 2019 at Catalan Institute of Oncology, Badalona. Radiation was delivered using VMAT technique with 6 MV photon beams. Patient immobilization was achieved using commercial radiotherapy-thermoplastic-mask and daily image guide control with CBCT (cone beam computed tomography) was performed. Statistical analysis was performed with SPSS.PASW.Statistics.v18. Results We identified 38 patients (47.4% men, 52.6% women) with a median age at diagnosis of 61 years [37 - 83 years]. Most of the primary neoplasms were from lung (50%) and breast cancer (24%). The median size of cavities was 10,5cc [0.4 - 75.5cc]. Radiation scheme was selected depending on size and location of the surgical cavity, primary tumor histology and patient’s performance status. Forty-two percent of patients received 27 Gy/3 fractions, 39% received 24 Gy/3 fractions and 7% received 18Gy/3fractions. The remaining four patients received 35 Gy/5fr (3%), 15 Gy/3fr (3%), 16 Gy/2fr (3%) and 30Gy/10fr (3%) respectively. With a median follow-up of 9.9 months, brain recurrence was observed in 23 patients (60%), with only 7 patients (18.4%) showing local relapse at surgical cavity. One-year local control rate was 81% for all patients. Radiation necrosis was confirmed by Positron Emission Tomography in 3 patients (7.8%). Leptomeningeal disease was observed in 5 patients (13.2%). No significant differences were observed between radiation schemes nor primary tumor histology. Conclusion Surgery followed by High precision HFRT delivered with VMAT technique is an effective and safe treatment alternative to SRS for selected patients with brain metastases.

Hydraulic geometric optimization on stagnating flow at the inlet of main pipe of underground pumping station

The underground pumping station is widely used in many important fields. However, the stagnating flow caused by the sharp geometric gradient at the interface between the primary pump intake and the main pipeline not only causes the performance deteriorations of the whole pump station but also leads to safety and operational stability challenges. In this paper, the numerical model of the related hydraulic phenomena is presented, moreover, the effectiveness and accuracy of the numerical model are verified by comparing it with the experimental results. The simulation results indicate that the hydraulic geometry optimization scheme at the inlet of the main pipe with 0.10 D (inner diameter of the main pipe) local rounding contributes the best effect on the hydraulic efficiency and operation stability of underground pump stations. The results may give a reference for the design of underground pump stations and the optimization of hydraulic geometry in related fields.

Resonant transformation of sonic-Alfven modes in solar spicules

The photospheric 5 min oscillations of the Sun can convert to Alfven waves by some conditions such as considering of a region and of a damping mechanism. Actually, 5 min oscillations appear in the photosphere and it does not seem to be able to pierce into the solar upper atmosphere because of the acoustic cut off of stratified medium and the sharp temperature gradient in the transition region. By perturbing the equilibrium state of the magnetized plasma, we showed that the acoustic and Alfven waves can interact through the nonlinear terms of the ideal MHD equations. We found that Alfven waves with twice the period of acoustic waves can propagate into upper layers when the speeds of sound and Alfven waves are equal. This condition obtain when ϖ=1/2ϖ .

Sharp gradient stability for the Sobolev inequality

We prove a sharp quantitative version of the p-Sobolev inequality for any 1<p<n, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for p≤2, while it depends on p for p>2.

Crystal orientation mapping and microindentation reveal anisotropy in Porites skeletons

Structures made by scleractinian corals support diverse ocean ecosystems. Despite the importance of coral skeletons and their predicted vulnerability to climate change, few studies have examined the mechanical and crystallographic properties of coral skeletons at the micro- and nano-scales. Here, we investigated the interplay of crystallographic and microarchitectural organization with mechanical anisotropy within Porites skeletons by measuring Young’s modulus and hardness along surfaces transverse and longitudinal to the primary coral growth direction. We observed micro-scale anisotropy, where the transverse surface had greater Young’s modulus and hardness by ∼ 6 GPa and 0.2 GPa, respectively. Electron backscatter diffraction (EBSD) revealed that this surface also had a higher percentage of crystals oriented with the a-axis between ± 30–60∘, relative to the longitudinal surface, and a broader grain size distribution. Within a region containing a sharp microscale gradient in Young’s modulus, nanoscale indentation mapping, energy dispersive spectroscopy (EDS), EBSD, and Raman crystallography were performed. A correlative trend showed higher Young’s modulus and hardness in regions with individual crystal bases (c-axis) facing upward, and in crystal fibers relative to centers of calcification. These relationships highlight the difference in mechanical properties between scales (i.e. crystals, crystal bundles, grains). Observations of crystal orientation and mechanical properties suggest that anisotropy is driven by microscale organization and crystal packing rather than intrinsic crystal anisotropy. In comparison with previous observations of nanoscale isotropy in corals, our results illustrate the role of hierarchical architecture in coral skeletons and the influence of biotic and abiotic factors on mechanical properties at different scales. Statement of significanceCoral biomineralization and the ability of corals’ skeletal structure to withstand biotic and abiotic forces underpins the success of reef ecosystems. At the microscale, we show increased skeletal stiffness and hardness perpendicular to the coral growth direction. By comparing nano- and micro-scale indentation results, we also reveal an effect of hierarchical architecture on the mechanical properties of coral skeletons and hypothesize that crystal packing and orientation result in microscale anisotropy. In contrast to previous findings, we demonstrate that mechanical and crystallographic properties of coral skeletons can vary between surface planes, within surface planes, and at different analytical scales. These results improve our understanding of biomineralization and the effects of scale and direction on how biomineral structures respond to environmental stimuli.

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance is often attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results demonstrate in the context of mass conservation that this leads to significant, spurious variance loss in regions of mass convergence and gain in regions of mass divergence. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

Analysis of MONARC and ACTIVATE Airborne Aerosol Data for Aerosol-Cloud Interaction Investigations: Efficacy of Stairstepping Flight Legs for Airborne In Situ Sampling

A challenging aspect of conducting airborne in situ observations of the atmosphere is how to optimize flight plans for specific objectives and constraints associated with weather and flight restrictions. For aerosol-cloud interaction research, two recent campaigns utilized a “stairstepping” approach whereby an aircraft conducts level legs at various altitudes while moving forward with each subsequent leg: the 2019 MONterey Aerosol Research Campaign (MONARC) over the northeast Pacific and the 2020–2022 Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) over the northwest Atlantic. We examine the homogeneity of several atmospheric variables both vertically and horizontally in the marine boundary layer with a focus on the sub-cloud environment. In well-mixed boundary layers, there was generally good horizontal and vertical homogeneity in potential temperature, winds, water vapor mixing ratio, various trace gases, and many aerosol variables. Selected aerosol variables exhibited the most variability owing to sensitivity to humidity and near-cloud conditions (supermicrometer aerosol concentrations), coastal pollution gradients (e.g., organic aerosol mass), and small spatial scale phenomena such as new particle formation (aerosol number concentration for particles with diameter &gt;3 nm). Illustrative cases are described when stairstepping can pose issues requiring extra caution for data analysis: (i) poor vertical mixing and layers decoupled from those below; (ii) multiple cloud layers; (iii) fluctuating cloud base/top and boundary layer top heights; and (iv) horizontal variability across specific features leading to sharp gradients such as right near coastlines and over the Gulf Stream with strong sea surface temperature changes. Results from this study provide a guide both for future studies aiming to examine these mission datasets and for designing new airborne campaigns.

Numerical simulation of a relativistic magnetron using a fluid electron model

An approach to numerically modeling relativistic magnetrons, in which the electrons are represented with a relativistic fluid, is described. A principal effect in the operation of a magnetron is space-charge-limited (SCL) emission of electrons from the cathode. We have developed an approximate SCL emission boundary condition for the fluid electron model. This boundary condition prescribes the flux of electrons as a function of the normal component of the electric field on the boundary. We show the results of a benchmarking activity that applies the fluid SCL boundary condition to the one-dimensional Child–Langmuir diode problem and a canonical two-dimensional diode problem. Simulation results for a two-dimensional A6 magnetron are then presented. Computed bunching of the electron cloud occurs and coincides with significant microwave power generation. Numerical convergence of the solution is considered. Sharp gradients in the solution quantities at the diocotron resonance, spanning an interval of three to four grid cells in the most well-resolved case, are present and likely affect convergence.

Energetic electron scattering by kinetic Alfvén waves at strong magnetic field gradients of dipolarization front

Energetic electron scattering and precipitation from the Earth's plasma sheet to the ionosphere is an important contributor to magnetosphere–ionosphere coupling. In this study, we investigate the role of one of the most intense wave emissions, kinetic Alfvén waves (KAWs), in energetic electron scattering. We have evaluated the effect of KAWs on energetic electrons within a curved magnetic field configuration exhibiting sharp cross field gradients. The magnetic field in Earth's magnetotail plasma sheet with an embedded dipolarization front is used as a working example. Taking into account electron bounce motion and perpendicular guiding-center drifts, we have shown that electrons with energies of tens to hundreds of keV can be scattered by KAWs in pitch angle and momentum through Doppler-shifted Landau resonance near the magnetic equator. The bounce-averaged pitch-angle diffusion coefficients for near-loss-cone (∼2°) electrons are on the order of 10–7–10–6 rad2/s for a characteristic KAW amplitude of 1 mV/m and approach the strong diffusion limit of ∼10–4 rad2/s for amplitudes of greater than 10 mV/m. These results suggest that under such ambient conditions, KAWs can pitch-angle scatter energetic electron population into the loss cone. In Earth's plasma sheet, this scattering is, thus, very likely to cause significant precipitation during active times. The diffusion coefficients of energetic electrons at large pitch angles (∼45°–∼80°) are more than two orders of magnitude larger than those of electrons near the loss cone, suggesting that KAWs contribute to isotropization of anisotropic electrons due to adiabatic heating should they drift into the vicinity of the magnetic field gradient.

Geochemical and microbiological profiles in hydrothermal extreme acidic environments (Pisciarelli Spring, Campi Flegrei, Italy).

Although terrestrial hydrothermal systems are considered among the most fascinating environments, how their unique and extreme conditions can affect microorganisms selection and the role in biogeochemical cycles has not yet been well elucidated. A combined geochemical and microbiological exploration in waters and sediments from 10 sampling points along a sharp temperature gradient (15-90°C) within an extremely acidic hydrothermal system (Pisciarelli Spring, Campi Flegrei area, southern Italy) displayed how hydrothermal fluids influence the microbial dynamics. This area was characterized by high levels of reduced gaseous species (e.g. H2S, H2, CH4, CO) and very low pH values (<2.3). Thermodynamic calculations revealed a high microbial catabolic potential in oxidation/reduction reactions of N-, S- and Fe-bearing species. Overall, an increase of the archaeal/bacterial abundance ratio was observed by decreasing temperature and pH values. In particular, Archaea and Bacteria were present in almost equal cell abundance (up to 1.1 × 109 and 9.3 × 108 cell/g, respectively) in the <70°C sampling points (average pH = 2.09); on the contrary, the highest temperature waters (85-90°C; average pH = 2.26) were characterized by a low abundance of archaeal cells. The high-throughput sequencing of the 16S rRNA genes indicated strong differences in archaeal and bacterial communities composition along the temperature gradient. However, the microbiome in this extreme environment was mainly constituted by chemoautotrophic microorganisms that were likely involved in N-, S- and Fe-bearing species transformations (e.g. Acidianus infernus, Ferroplasma acidarmanus, Acidithiobacillus,Sulfobacillus,Thaumarchaeota), in agreement with thermodynamic calculations.

Fracture characterization from noisy displacement data using artificial neural networks

Mechanical characterization of fractures, i.e., identifying their characteristic parameters such as energy release rate, is crucial to assess the safety and stability of structural members. This is generally achieved using a combination of finite element analysis and optimization. Machine learning models are increasingly used to characterize engineering problems. While such models have shown impressive performance on smooth data, their performance diminishes significantly on data with discontinuities and sharp gradients. For fractures, this issue is more severe due to the singular solutions in the vicinity of the fracture tips. To resolve this difficulty, leveraging classical fracture mechanics, we construct custom functions, using neural networks, containing fundamental solutions of fracture mechanics. Through a series of examples, we demonstrate the proposed framework not only captures the singular solution and characteristic parameters accurately on both noise-free and noisy data, but also is highly efficient due to its simplicity and small number of parameters.

Nanoscale sharp bandgap gradient for efficiency improvement of Cu2ZnSn(S, Se)4 thin film solar cells

Due to the difficulty in controlling the post-selenization/sulfurization process accurately, single-graded structure with a lower bandgap on the surface is easy to form in the Cu 2 ZnSn(S, Se) 4 absorber. This will lower the built-in potential and lead to the formation of undesirable “cliff” type band alignment in the device, and hence a drastic V oc -deficit and lower efficiency are expected. Herein, an effective and versatile method to improve the V oc and efficiency of Cu 2 ZnSn(S, Se) 4 solar cells through bandgap engineering was presented in this work. A sharp surface bandgap gradient with larger surface bandgap was constructed simply by sputtering a nanoscale Cu 2 ZnSnS 4 layer on the surface of Cu 2 ZnSn(S, Se) 4 absorber. Under the coactions of surface sharp bandgap gradient and the single bandgap gradient existed in the Cu 2 ZnSn(S, Se) 4 absorber naturally, a quasi-U-shaped bandgap gradient was constructed inside the absorber. Benefited from the enlarged surface bandgap, favorable U-shaped bandgap gradient and appropriate band alignment at the absorber/buffer interface, a best efficiency of 9.9% with a V oc of 450 mV, a J sc of 35.26 mA/cm 2 and a fill factor (FF) of 62.73% was achieved. • Improving the V oc and efficiency of CZTSSe device by bandgap engineering. • Sharp surface bandgap gradient construction. • Formation of quasi-U-shaped bandgap gradient in the CZTSSe absorber. • Appropriate band alignment between CZTSSe/CdS heterointerface.

A moving finite element method for solving two-dimensional coupled Burgers’ equations at high Reynolds numbers

The coupled Burgers’ equations at high Reynolds numbers usually have sharp gradients or are discontinuous in the solution. Therefore, it is difficult to obtain analytical solutions. This paper aims to use the moving finite element method proposed by Li et al. (2001) to get stable and high-precision numerical solutions for the coupled Burgers’ equations at high Reynolds numbers. The method decouples the mesh equation and partial differential equation (PDE) into two unrelated parts, mesh reconstruction and PDE solver. The mesh reconstruction constructs the harmonic mapping between the physical and logical domains through an iterative method so that the mesh structure maintains harmonics after multiple numerical integrations. We compute three classic numerical examples. Numerical results show that the moving finite element method effectively solve the coupled Burgers’ equations at high Reynolds numbers, obtain stable numerical results, and achieve higher numerical accuracy. During the evolution of the solution, the mesh is always concentrated in the position where the solution has sharp gradients.