Статті в журналах: "Gradient discontinuity"

1

Zakharov, S. V., and A. M. Il'in. "From weak discontinuity to gradient catastrophe." Sbornik: Mathematics 192, no. 10 (October 31, 2001): 1417–33. http://dx.doi.org/10.1070/sm2001v192n10abeh000599.

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2

Carriero, M., A. Leaci, and F. Tomarelli. "Free gradient discontinuity and image inpainting." Journal of Mathematical Sciences 181, no. 6 (March 2012): 805–19. http://dx.doi.org/10.1007/s10958-012-0716-4.

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3

Liu, Yahong, Meize Li, Kun Song, Yuhao Jing, Jiale Guo, Qingyu Hai, and Xiaopeng Zhao. "Broadband gradient phase discontinuity all-dielectric metasurface." Modern Physics Letters B 34, no. 15 (March 30, 2020): 2050168. http://dx.doi.org/10.1142/s0217984920501687.

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In recent years, metasurfaces have widely been studied due to their ability to offer a spatially varying phase response, low losses, ultrathin size, and easy fabrication. In this paper, a gradient phase discontinuity all-dielectric metasurface consisting of arrays of silicon cube resonator is designed. By adjusting the dimension of the silicon cube resonator, a [Formula: see text] transmission phase covered from [Formula: see text] to [Formula: see text] with [Formula: see text] phase intervals is realized in a frequency from 9.7 GHz to 11.8 GHz. We demonstrate the all-dielectric metasurface can produce the anomalous refraction, vortex beams, and wave-focusing in the microwave and infrared band, respectively. It can be expected that the proposed metasurfaces can find wide applications in communication, designing integrated optical devices, and focusing lenses.

4

Brill, J. P. "Discontinuities in the Orkiszewski Correlation for Predicting Pressure Gradients in Wells." Journal of Energy Resources Technology 111, no. 1 (March 1, 1989): 34–36. http://dx.doi.org/10.1115/1.3231398.

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The Orkiszewski correlation is used extensively in the petroleum industry for predicting pressure gradients when gas and liquid flow simultaneously in wells. Unfortunately, the correlation contains a parameter called the liquid distribution coefficient, Γ, that can be discontinuous at a superficial mixture velocity of 10 ft/sec. The liquid distribution coefficient is used to predict both the elevation and friction components of the pressure gradient for slug flow. The accepted trial and error method for integrating the pressure gradient to obtain pressure loss in wells can fail to converge when pressure gradients are discontinuous. Examples of discontinuities in Γ for oil as the continuous phase are presented for several liquid viscosities ranging from 0.3 to 200 cp and for pipe diameters of 1.049, 2.441 and 6.049 in. It was found that a constraint recommended for Γ when mixture velocity <10 ft/sec was essentially useless. It was also found that a constraint for velocities >10 ft/sec could actually increase the magnitude of pressure gradient discontinuity. Convergence of pressure loss calculations when the discontinuity was encountered was possible only if the convergence tolerance was temporarily relaxed.

5

Gobbino, Massimo, and Maria Giovanna Mora. "Finite-difference approximation of free-discontinuity problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 3 (June 2001): 567–95. http://dx.doi.org/10.1017/s0308210500001001.

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We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.

6

Gobbino, Massimo, and Maria Giovanna Mora. "Finite-difference approximation of free-discontinuity problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 3 (June 2001): 567–95. http://dx.doi.org/10.1017/s0308210501000257.

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We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.

7

Aifantis,, K. E., and H. Askes,. "Gradient Elasticity with Interfaces as Surfaces of Discontinuity for the Strain Gradient." Journal of the Mechanical Behavior of Materials 18, no. 4 (August 2007): 283–306. http://dx.doi.org/10.1515/jmbm.2007.18.4.283.

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8

Liu, Yahong, Congcong Liu, Kun Song, Meize Li, and Xiaopeng Zhao. "A broadband high-transmission gradient phase discontinuity metasurface." Journal of Physics D: Applied Physics 51, no. 9 (February 12, 2018): 095103. http://dx.doi.org/10.1088/1361-6463/aaa92d.

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9

Saadon-Grosman, Noam, Zohar Tal, Eyal Itshayek, Amir Amedi, and Shahar Arzy. "Discontinuity of cortical gradients reflects sensory impairment." Proceedings of the National Academy of Sciences 112, no. 52 (December 11, 2015): 16024–29. http://dx.doi.org/10.1073/pnas.1506214112.

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Topographic maps and their continuity constitute a fundamental principle of brain organization. In the somatosensory system, whole-body sensory impairment may be reflected either in cortical signal reduction or disorganization of the somatotopic map, such as disturbed continuity. Here we investigated the role of continuity in pathological states. We studied whole-body cortical representations in response to continuous sensory stimulation under functional MRI (fMRI) in two unique patient populations—patients with cervical sensory Brown-Séquard syndrome (injury to one side of the spinal cord) and patients before and after surgical repair of cervical disk protrusion—enabling us to compare whole-body representations in the same study subjects. We quantified the spatial gradient of cortical activation and evaluated the divergence from a continuous pattern. Gradient continuity was found to be disturbed at the primary somatosensory cortex (S1) and the supplementary motor area (SMA), in both patient populations: contralateral to the disturbed body side in the Brown-Séquard group and before repair in the surgical group, which was further improved after intervention. Results corresponding to the nondisturbed body side and after surgical repair were comparable with control subjects. No difference was found in the fMRI signal power between the different conditions in the two groups, as well as with respect to control subjects. These results suggest that decreased sensation in our patients is related to gradient discontinuity rather than signal reduction. Gradient continuity may be crucial for somatotopic and other topographical organization, and its disruption may characterize pathological processing.

10

Acharya, Amit, Huang Tang, Sunil Saigal, and John L. Bassani. "On boundary conditions and plastic strain-gradient discontinuity in lower-order gradient plasticity." Journal of the Mechanics and Physics of Solids 52, no. 8 (August 2004): 1793–826. http://dx.doi.org/10.1016/j.jmps.2004.02.005.

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11

Piontek, Sebastian, and Thomas Schmidt. "Higher integrability for the gradient of Mumford-Shah almost-minimizers." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 6. http://dx.doi.org/10.1051/cocv/2019063.

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We extend a recent higher-integrability result for the gradient of minimizers of the Mumford-Shah functional to a suitable class of almost-minimizers. The extension crucially depends on an L∞ gradient estimate up to regular portions of the discontinuity set of an almost-minimizer.

12

BOUCHITTÉ, G., C. DUBS, and P. SEPPECHER. "REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS." Mathematical Models and Methods in Applied Sciences 10, no. 07 (October 2000): 1073–97. http://dx.doi.org/10.1142/s0218202500000549.

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We consider a class of smooth local nonconvex functionals defined on W2,2(Ω), depending on a small parameter ε and we prove that they converge, as ε tends to 0, to a functional F(u,Ω) with a bulk density depending on the gradient of u and a surface energy concentrated on the jump set of u. This provides a new alternative to the approximation of free discontinuity problems, which applies in particular to the Mumford–Shah model.

13

Emmanuel, I., K. D. Adedayo, B. Adeyemi, and O. S. Ojo. "Meteorological parameter anomalies and anomalous radio propagation over Nigeria." Nigeria Journal of Pure and Applied Physics 9, no. 1 (April 21, 2020): 34–50. http://dx.doi.org/10.4314/njpap.v9i1.7.

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Distribution and variation of anomalous radio propagation, temperature and relative humidity anomalies were obtained and analyzed using six years (2010-2015) Era interim data. Seasonal spatial distribution of refractivity gradient and its components were analyzed. The result showed that about 90% of wet component contributed to the variation of refractivity gradient. Highest range of refractivity gradients and its wet components were obtained during the wet season. The result of correlation between ducting occurrence and temperature showed strong negative correlation except in Lagos where positive correlation of 3% was observed. However, positive correlation which ranges between 39% and 70% exist between duct occurrence and relative humidity except in Lagos in Nigeria. Refractivity gradients, relative humidity anomaly and temperature experience a monthly variation. These variations can be attributed to the seasonal movement of inter-tropical discontinuity (ITD) across Nigeria. Keywords: anomalous, anomaly, correlation, ITD

14

Cortes, P. M. "Cortical Intracellular Electrical Potential in Roots of Unstressed and Stressed Sunflower Seedlings. II. Radial Profiles and Oscillations." Functional Plant Biology 24, no. 5 (1997): 651. http://dx.doi.org/10.1071/pp96037.

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Various models have been proposed to explain how plants can extract water from dry soil against a gradient in water potential. According to one model, it is hypothesised that water uptake from dry soil is associated with a radial gradient in the intracellular electrical potential (Ec) of root cortical cells such that the potential in the outer cells is relatively hyperpolarised. As a partial test of this model, a microelectrode was used to measure radial profiles of Ec in intact roots of sunflower (Helianthus annuus) seedlings. The seedlings were subjected to either a control (unstressed) or one of two stress treatments. Water stress was rapidly imposed and relieved by lowering and raising the level of nutrient solution in a tank which contained all the seedling roots except the lateral root in which Ec was measured. There was a gradient in Ec in roots of unstressed plants with the potential of the outer cortical cells being relatively depolarised. The imposition of stress shifted the gradient in accordance with the hypothesis. Increasing the magnitude of the osmotic potential of the solution perfusing the measured portion of a lateral root of a stressed seedling resulted in a discontinuity in the profile between the second and third cortical layers. The gradients in the profile of Ec indicate there is a limitation in intercellular electrical coupling and the appearance of a discontinuity may indicate a decrease in coupling. Three types of occasional, spontaneous oscillations in Ec are characterised. One type of oscillation may be additional evidence that the electrical coupling between the cortical cell layers is variable and depends on the transport and status of water in the roots.

15

Hanada, Mitsuhiko. "Effects of Peripheral Gradient of Color Saturation on the Feeling of Being Dazzled." Perception 48, no. 5 (April 13, 2019): 412–27. http://dx.doi.org/10.1177/0301006619842496.

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The feeling of being dazzled that is evoked by images consisting of an achromatic uniform center surrounded by regions with a luminance gradient was investigated. The effects of type of color saturation gradient in the peripheral region on the feeling of being dazzled were examined. Stimulus configuration was also varied. For the stimulus configuration of a disk-annulus, the feeling of being dazzled was lower for an increasing saturation gradient from the center to the periphery than for decreasing and no-saturation gradients when the center and the periphery maximum luminances were the same. This suggests that the presence of a chromaticity difference between the disk and the surrounding annulus strengthens the feeling of being dazzled. Similar results were obtained for the stimulus configuration of a star shape. For the stimulus configuration of a cross shape, quite different results were obtained; the chromaticity discontinuity had little or opposite effect. These results suggest that chromaticity border and stimulus configurations are factors in the feeling of being dazzled that is evoked by images with luminance gradient.

16

Vogt, J., A. Albert, and O. Marghitu. "Analysis of three-spacecraft data using planar reciprocal vectors: methodological framework and spatial gradient estimation." Annales Geophysicae 27, no. 8 (August 19, 2009): 3249–73. http://dx.doi.org/10.5194/angeo-27-3249-2009.

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Abstract. In the context of ESA's Cluster mission, four-point array techniques are widely used to analyze space plasma phenomena such as shocks and discontinuities, waves and turbulence, and spatial gradients. Due to failures of single instruments on the Cluster spacecraft fleet, there is also need for array processing of three-point measurements. In this paper we identify planar reciprocal vectors as a generic tool for this purpose. The class of three-point techniques introduced here includes methods for discontinuity analysis, wave identification, and spatial gradient determination. Parameter vectors can be resolved fully in the spacecraft plane but further assumptions or physical constraints have to be specified to estimate the normal components. We focus on the gradient estimation problem where we check and illustrate our approach using Cluster measurements.

17

Angelillo, M., E. Babilio, and A. Fortunato. "Folding of Thin Walled Tubes as a Free Gradient Discontinuity Problem." Journal of Elasticity 82, no. 3 (March 2006): 243–71. http://dx.doi.org/10.1007/s10659-005-9033-1.

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18

Wang, Kang, Lei Zhang, and Shaoqiang Tang. "Discovery of PDEs driven by data with sharp gradient or discontinuity." Computers & Mathematics with Applications 140 (June 2023): 33–43. http://dx.doi.org/10.1016/j.camwa.2023.03.021.

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19

Small, Ernest, and Manal Fawzy. "Morphogeographic variation in the Medicago monantha complex." Canadian Journal of Botany 70, no. 6 (June 1, 1992): 1292–301. http://dx.doi.org/10.1139/b92-162.

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Morphogeographic variation in the Asian annual Medicago monantha has required clarification. The present numerical taxonomic study in relation to geographical distribution revealed an east–west gradient of the principal correlated characters. Although previous taxonomists had not perceived this gradient as such, in fact it is reflected in traditional taxonomic treatments, i.e., the four commonly recognized subspecies (which are often considered separate species) replace each other in an east–west direction in stepwise overlapping fashion with respect to morphology and geography. The most evident difference observed was with respect to the areas delimited on the surface of the fruit by the intersecting veins; the fruit areoles are more elongated in the western phase than in the east. Given the absence of evident discontinuity or even relative discontinuity in M. monantha, formal delimitation of the traditionally recognized infraspecific taxa seems unjustified. Key words: Medicago monantha, Trigonella, cline, taxonomy, classification, systematics.

20

Fjell, Anders M., Chi-Hua Chen, Donatas Sederevicius, Markus H. Sneve, Håkon Grydeland, Stine K. Krogsrud, Inge Amlien, et al. "Continuity and Discontinuity in Human Cortical Development and Change From Embryonic Stages to Old Age." Cerebral Cortex 29, no. 9 (October 24, 2018): 3879–90. http://dx.doi.org/10.1093/cercor/bhy266.

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AbstractThe human cerebral cortex is highly regionalized, and this feature emerges from morphometric gradients in the cerebral vesicles during embryonic development. We tested if this principle of regionalization could be traced from the embryonic development to the human life span. Data-driven fuzzy clustering was used to identify regions of coordinated longitudinal development of cortical surface area (SA) and thickness (CT) (n = 301, 4–12 years). The principal divide for the developmental SA clusters extended from the inferior–posterior to the superior–anterior cortex, corresponding to the major embryonic morphometric anterior–posterior (AP) gradient. Embryonic factors showing a clear AP gradient were identified, and we found significant differences in gene expression of these factors between the anterior and posterior clusters. Further, each identified developmental SA and CT clusters showed distinguishable life span trajectories in a larger longitudinal dataset (4–88 years, 1633 observations), and the SA and CT clusters showed differential relationships to cognitive functions. This means that regions that developed together in childhood also changed together throughout life, demonstrating continuity in regionalization of cortical changes. The AP divide in SA development also characterized genetic patterning obtained in an adult twin sample. In conclusion, the development of cortical regionalization is a continuous process from the embryonic stage throughout life.

21

MARCOU, ALICE. "REFLECTION OF DISCONTINUITIES FOR NONLINEAR WEAKLY STABLE BOUNDARY VALUE PROBLEMS." Journal of Hyperbolic Differential Equations 09, no. 01 (March 2012): 133–75. http://dx.doi.org/10.1142/s021989161250004x.

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This paper is concerned with the reflection of nonlinear discontinuous waves, for weakly well-posed hyperbolic boundary value problems, satisfying the (WR) condition, that is in a case where the IBVP is neither strongly stable, nor strongly unstable. We study how the singularities of a striated solution are reflected when the solution hits the boundary. We prove striated estimates and L∞ estimates and observe the loss of one derivative: we show that a discontinuity of the gradient of the solution across a hyperplane can be reflected in a discontinuity across a hyperplane of the solution itself.

22

Hamzah, Rostam Affendi, Haidi Ibrahim, and Anwar Hasni Abu Hassan. "STEREO MATCHING ALGORITHM BASED ON ILLUMINATION CONTROL TO IMPROVE THE ACCURACY." Image Analysis & Stereology 35, no. 1 (February 23, 2016): 39. http://dx.doi.org/10.5566/ias.1369.

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This paper presents a new method of pixel based stereo matching algorithm using illumination control. The state of the art algorithm for absolute difference (AD) works fast, but only precise at low texture areas. Besides, it is sensitive to radiometric distortions (i.e., contrast or brightness) and discontinuity areas. To overcome the problem, this paper proposes an algorithm that utilizes an illumination control to enhance the image quality of absolute difference (AD) matching. Thus, pixel intensities at this step are more consistent, especially at the object boundaries. Then, the gradient difference value is added to empower the reduction of the radiometric errors. The gradient characteristics are known for its robustness with regard to the radiometric errors. The experimental results demonstrate that the proposed algorithm performs much better when using a standard benchmarking dataset from the Middlebury Stereo Vision dataset. The main contribution of this work is a reduction of discontinuity errors that leads to a significant enhancement on matching quality and accuracy of disparity maps.

23

Badar, Waqas, Husna Ali, Olivia N. Brooker, Elis Newham, Tim Snow, Nicholas J. Terrill, Gianluca Tozzi, Peter Fratzl, Martin M. Knight, and Himadri S. Gupta. "Collagen pre-strain discontinuity at the bone—Cartilage interface." PLOS ONE 17, no. 9 (September 15, 2022): e0273832. http://dx.doi.org/10.1371/journal.pone.0273832.

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The bone-cartilage unit (BCU) is a universal feature in diarthrodial joints, which is mechanically-graded and subjected to shear and compressive strains. Changes in the BCU have been linked to osteoarthritis (OA) progression. Here we report existence of a physiological internal strain gradient (pre-strain) across the BCU at the ultrastructural scale of the extracellular matrix (ECM) constituents, specifically the collagen fibril. We use X-ray scattering that probes changes in the axial periodicity of fibril-level D-stagger of tropocollagen molecules in the matrix fibrils, as a measure of microscopic pre-strain. We find that mineralized collagen nanofibrils in the calcified plate are in tensile pre-strain relative to the underlying trabecular bone. This behaviour contrasts with the previously accepted notion that fibrillar pre-strain (or D-stagger) in collagenous tissues always reduces with mineralization, via reduced hydration and associated swelling pressure. Within the calcified part of the BCU, a finer-scale gradient in pre-strain (0.6% increase over ~50μm) is observed. The increased fibrillar pre-strain is linked to prior research reporting large tissue-level residual strains under compression. The findings may have biomechanical adaptative significance: higher in-built molecular level resilience/damage resistance to physiological compression, and disruption of the molecular-level pre-strains during remodelling of the bone-cartilage interface may be potential factors in osteoarthritis-based degeneration.

24

Hayes, LM. "Reflection of Magnetoionic Waves from a Steep Density Gradient. I. Incident Extraordinary Mode." Australian Journal of Physics 38, no. 5 (1985): 687. http://dx.doi.org/10.1071/ph850687.

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Calculations ofthe relative magnitudes of the four secondary waves produced when a magneto ionic wave encounters an electron density discontinuity within an anisotropic plasma are presented. We identify the different conditions under which each of the secondary waves is the dominant mode, and determine some general properties of the reflection process.

25

Zhang, Debin, Xiaofang Cheng, and Peiqi Wang. "Theoretical research on the discontinuity of temperature gradient under interfacial heat transfer." Journal of Physics: Conference Series 2360, no. 1 (November 1, 2022): 012034. http://dx.doi.org/10.1088/1742-6596/2360/1/012034.

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The interfacial thermal conductivity has always been undetermined, and the discontinuity of temperature gradient at the interface will also cause problems in the study of the driving force of heat transfer. Based on Fourier’s law, the generalized Fourier’s law is proposed by assigning a subscript to the thermal conductivity, which can describe the unobstructed and blocked state of the heat transfer at the interface. By comparing the phenomena of the heat transfer and waterflow at the interface, it is deduced that the interfacial thermal conductivity always takes the smaller value among the thermal conductivities on both sides of the interface. Through adjusting the thermal conductivity, the temperature gradient is continuous at the interface, which guarantees the driving force of the interfacial heat transfer.

26

Akhavan-Tafti, M., J. Kasper, J. Huang, and S. Bale. "Discontinuity analysis of the leading switchback transition regions." Astronomy & Astrophysics 650 (June 2021): A4. http://dx.doi.org/10.1051/0004-6361/202039508.

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Context. Magnetic switchbacks are magnetic structures characterized as intervals of sudden reversal in the radial component of the pristine solar wind’s magnetic field. Switchbacks comprise of magnetic spikes that are preceded and succeeded by switchback transition regions within which the radial magnetic field reverses. Determining switchback generation and evolution mechanisms will further our understanding of the global circulation and transportation of the Sun’s open magnetic flux. Aims. The present study juxtaposes near-Sun switchback transition regions’ characteristics with similar magnetic discontinuities observed at greater radial distances with the goal of determining local mechanism(s) through which switchback transition regions may evolve. Methods. Measurements from fields and plasma suites aboard the Parker Solar Probe were utilized to characterize switchback transition regions. Minimum variance analysis (MVA) was applied on the magnetic signatures of the leading switchback transition regions. The leading switchback transition regions with robust MVA solutions were identified and categorized based on their magnetic discontinuity characteristics. Results. It is found that 78% of the leading switchback transition regions are rotational discontinuities (RD). Another 21% of the leading switchback transition regions are categorized as “either” discontinuity (ED), defined as small relative changes in both magnitude and the normal component of the magnetic field. The RD-to-ED event count ratio is found to reduce with increasing distance from the Sun. The proton radial temperature sharply increases (+ 29.31%) at the leading RD-type switchback transition regions, resulting in an enhanced thermal pressure gradient. Magnetic curvature at the leading RD-type switchback transition regions is often negligible. Magnetic curvature and the thermal pressure gradient are parallel (i.e., “bad” curvature) in 74% of the leading RD-type switchback transition regions. Conclusions. The leading switchback transition regions may evolve from RD-type into ED-type magnetic discontinuities while propagating away from the Sun. Local magnetic reconnection is likely not the main driver of this evolution. Other drivers, such as plasma instabilities, need to be investigated to explain the observed significant jump in proton temperature and the prevalence of bad curvature at the leading RD-type switchback transition regions.

27

Czapiewska, Natalia, Sonia Paź, Marcin K. Dyderski, and Andrzej M. Jagodziński. "Continuum of floristic composition between two plant communities – Carici elongatae-Alnetum and Fraxino-Alnetum." Forest Research Papers 78, no. 4 (December 1, 2017): 285–96. http://dx.doi.org/10.1515/frp-2017-0032.

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Abstract One of the crucial debates in vegetation ecology is whether plant communities are discontinuous, distinguishable units or whether they change continuously. Phytosociology assumes discontinuity and its methodology requires subjective sampling during vegetation inventories. For that reason, some researchers argue that phytosociology artificially creates discontinuity among plant communities. Our aim was to assess the continuity between ash-alder riparian forest (Fraxino-Alnetum), and alder swamp forest (Carici elongatae-Alnetum), and to check whether discontinuity observed between these two plant associations is an effect of subjective sample plot choice. We conducted 57 phytosociological relevés within a regular grid covering potential sites of both plant communities. All relevés were arranged in order of decreasing relative cover of the diagnostic species for each plant association resulting in a gentle gradient, indicating a continuous transition from Fraxino-Alnetum to Carici elongatae-Alnetum. Similar results were obtained by detrended correspondence analysis. The proportion of species from the Querco-Fagetea class, typical to Fraxino-Alnetum, was decreasing with increasing proportion of species from the Alnetea glutinosae class, typical to Carici elongatae-Alnetum. This shift followed a gradient of ecological light-moisture indicator values. Our results confirmed continuous transition between two plant communities and led us to the conclusion that discontinuity resulted from the standard sampling protocol used in classical phytosociology. This protocol, however, is useful in searching for typological patterns, required for classification of plant communities, which is the main aim of phytosociology. Nevertheless, it does not provide full insight into the variability of vegetation and introduces uncertainty when trying to understand ecosystem dynamics. This uncertainty should be taken into account when phytosociological data are used for nature conservation recommendations and to draw conclusion about vegetation dynamics.

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Lansdell, Benjamin James, and Konrad Paul Kording. "Neural spiking for causal inference and learning." PLOS Computational Biology 19, no. 4 (April 4, 2023): e1011005. http://dx.doi.org/10.1371/journal.pcbi.1011005.

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When a neuron is driven beyond its threshold, it spikes. The fact that it does not communicate its continuous membrane potential is usually seen as a computational liability. Here we show that this spiking mechanism allows neurons to produce an unbiased estimate of their causal influence, and a way of approximating gradient descent-based learning. Importantly, neither activity of upstream neurons, which act as confounders, nor downstream non-linearities bias the results. We show how spiking enables neurons to solve causal estimation problems and that local plasticity can approximate gradient descent using spike discontinuity learning.

29

Andreas Heuch, Peter. "Experimental Evidence for Aggregation of Salmon Louse Copepodids (Lepeophtheirus Salmonis) in Step Salinity Gradients." Journal of the Marine Biological Association of the United Kingdom 75, no. 4 (November 1995): 927–39. http://dx.doi.org/10.1017/s002531540003825x.

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The copepod Lepeophtheirus salmonis Krayer (Copepoda: Caligida), the salmon louse, is a parasite of salmonids. The vertical distribution of the infective stage, the copepodid, was studied in salinity gradients with one step increase of 15‰ (154%e> on top of 304‰), 5‰ (25–4‰ on top of 30–4‰) and 2%> (28–4‰ on top of 304‰) in 1-m perspex columns. Copepodid distribution in a linear gradient, where the salinity increased from 154‰ at 0 cm depth to 304‰ at 87–5 cm, was also recorded. Homogeneous 304‰ salinity columns served as the control. In these, the animals gathered in the top section of the water column in response to 1 h of light from above, and spread downwards in response to 4 h of darkness. In columns with a 15‰ step increase in salinity with depth, copepodids aggregated just underneath the discontinuity irrespective of light conditions. In step salinity gradients of 5‰ and 2‰ S, under both light regimes, animals were significantly more numerous in the step sections compared with the control. In the linear gradient, significant numbers of copepodids accumulated at approximately 20‰ salinity when subjected to 1 h of light. In the dark, there were no significant aggregations. Copepodids were found in 15–17–2‰ salinity in all linear gradient experiments.

30

Hager, Bradford H. "Properties of the Core-Mantle Boundary." Symposium - International Astronomical Union 129 (1988): 377. http://dx.doi.org/10.1017/s0074180900135065.

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The core-mantle boundary (CMB), separating the molten metallic core from the overlying solid silicate mantle, marks the largest discontinuity in mechanical properties within the Earth. The ∼ 200 km thick region just above the CMB, named D″ by Bullen (1950), is characterized by an anomalous gradient in seismic velocity versus depth. D″ was originally interpreted as a region with a strong compositional gradient due to the accumulation of dense material at the base of the mantle. Subsequently, the anomalous gradient was interpreted as the result of a strong temperature gradient in a hot thermal boundary layer at the base of the mantle, an interpretation motivated by the requiremnet that heat involved in generating the geodynamo must be transported out of the core and through the mantle by convection.

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Ellis, Lucy Eunsun, and Nicholas Edward Jones. "Longitudinal trends in regulated rivers: a review and synthesis within the context of the serial discontinuity concept." Environmental Reviews 21, no. 3 (September 2013): 136–48. http://dx.doi.org/10.1139/er-2012-0064.

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Dams alter the geomorphology, water quality, temperature regime, and flow regime of lotic systems influencing the resources and habitat of fish, benthic invertebrates, and lower trophic levels. Since the inception of the river continuum concept and the serial discontinuity concept (SDC), biotic and abiotic impacts below impoundments have been the focus of many lotic studies. However, recovery gradients below dams are rarely examined in sufficient detail and no current synthesis of longitudinal impacts in regulated rivers exists. This understanding is needed to build ecological relationships in regulated rivers to inform environmental flows science and management. In this review, we provide evidence for SDC predictions on physical, chemical, and biological recovery in regulated rivers. Additionally, we determine how these changes are reflected in the benthic community. Our review suggests that two recovery gradients exist in regulated rivers: (1) a longer, thermal gradient taking up to hundreds of kilometres downstream; and (2) a shorter, resource subsidy gradient recovering within 1–4 km downstream of an impoundment. Total benthic invertebrate abundance varies considerably, with both increases and reductions observed at near-dam sites and varying in recovery downstream. Much of this variability stems from the degree of flow alteration and resource subsidies from the upstream reservoir. In contrast, benthic diversity is often reduced below dams irrespective of dam location and operation with little recovery observed downstream. The community at near-dam sites is largely composed of filter-feeding invertebrates which are quickly replaced downstream, while stoneflies are reduced below impoundments with limited downstream recovery. Despite a lack of formal testing, studies support SDC predictions. The SDC still provides a useful theoretical framework for hypothesis testing, and future studies should further expand the SDC to include empirical estimation within the context of the landscape.

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DUBE, RK. "Upper Mantle Structure in and around the Indian sub-continent." MAUSAM 20, no. 1 (April 30, 2022): 47–52. http://dx.doi.org/10.54302/mausam.v20i1.5428.

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The structure of the Upper Mantle has been studied from the P-wave travel times, using the computation of Dowling and Nuttli. Results indicate the presence of a low velocity layer 140 km below the M-discontinuity and its thickness is estimated as about 50 km. A steep velocity gradient below the low velocity layer explains the observed results.

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Dal Maso, Gianni, Gianluca Orlando, and Rodica Toader. "Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation." Advances in Calculus of Variations 10, no. 2 (April 1, 2017): 183–207. http://dx.doi.org/10.1515/acv-2015-0036.

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AbstractWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to ${L^{1}}$ convergence.

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Hayes, LM. "Reflection of Magnetoionic Waves from a Steep Density Gradient. II. Incident Ordinary Mode." Australian Journal of Physics 38, no. 5 (1985): 705. http://dx.doi.org/10.1071/ph850705.

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We consider the case of an ordinary mode wave incident on a density discontinuity in an anisotropic plasma. The relative magnitudes of the two transmitted and two reflected modes produced by the incident 0 mode are calculated, and the dominant secondary mode is determined for different incident wave parameters and plasma parameters. An application of this work to the interpretation of the polarization of certain solar radio bursts is considered.

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PERCIVALE, DANILO, and FRANCO TOMARELLI. "A VARIATIONAL PRINCIPLE FOR PLASTIC HINGES IN A BEAM." Mathematical Models and Methods in Applied Sciences 19, no. 12 (December 2009): 2263–97. http://dx.doi.org/10.1142/s021820250900411x.

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We focus on a variational model of an elastic–plastic beam which is clamped at both endpoints and subject to a transverse L∞ load: the mathematical formulation is a 1D free discontinuity problem with second-order energy dependent on gradient-jump integrals but not on the cardinality of gradient-discontinuity set. The related energy is not lower semicontinuous in BH; moreover the relaxed energy is finite also when second derivatives have Cantor part. Nevertheless we show that if a safe load condition is fulfilled, then minimizers exist and they actually belong to SBH, say their second derivative has no Cantor part. If in addition a stronger condition on load is fulfilled, then minimizer is unique and belongs to H2. Moreover, we can always select one minimizer whose number of plastic hinges does not exceed 2 and is the limit of minimizers of penalized problems. When the load stays in the gap between safe load and regularity condition, then minimizers with hinges are allowed; if in addition the load is symmetric and strictly positive, then there is uniqueness of minimizer, the hinges of such minimizer are exactly two and they are located at the endpoints.

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Chessa, J., and T. Belytschko. "An Extended Finite Element Method for Two-Phase Fluids." Journal of Applied Mechanics 70, no. 1 (January 1, 2003): 10–17. http://dx.doi.org/10.1115/1.1526599.

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An extended finite element method with arbitrary interior discontinuous gradients is applied to two-phase immiscible flow problems. The discontinuity in the derivative of the velocity field is introduced by an enrichment with an extended basis whose gradient is discontinuous across the interface. Therefore, the finite element approximation can capture the discontinuities at the interface without requiring the mesh to conform to the interface, eliminating the need for remeshing. The equations for incompressible flow are solved by a fractional step method where the advection terms are stabilized by a characteristic Galerkin method. The phase interfaces are tracked by level set functions which are discretized by the same finite element mesh and are updated via a stabilized conservation law. The method is demonstrated in several examples.

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Stąpór, Paweł. "An Improved XFEM for the Poisson Equation with Discontinuous Coefficients." Archive of Mechanical Engineering 64, no. 1 (March 1, 2017): 123–44. http://dx.doi.org/10.1515/meceng-2017-0008.

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Abstract Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

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Bach, Annika. "Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals". ESAIM: Control, Optimisation and Calculus of Variations 24, № 3 (2018): 1107–39. http://dx.doi.org/10.1051/cocv/2017027.

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We provide an approximation result for free-discontinuity functionals of the form 𝓕(u) = ∫Ωf(x, u, ∇u)dx + ∫Su∩Ωθ(x, νu)d𝓗n−1, u ∈ SBV2(Ω), where f is quadratic in the gradient-variable and θ is an arbitrary smooth Finsler metric. The approximating functionals are of Ambrosio-Tortorelli type and depend on the Hessian of the edge variable through a suitable nonhomogeneous metric ϕ.

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Степанов, Дмитрий, Dmitriy Stepanov, Иван Полянский, Ivan Polyanskiy, Михаил Фролов, and Mikhail Frolov. "Hybrid genetic method with gradient learning and predictionfor solving global optimization of multiextremal functions." Bulletin of Bryansk state technical university 2014, no. 3 (September 30, 2014): 138–46. http://dx.doi.org/10.12737/23144.

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In the article in order to determine the most effective global optimum multiextremal multivariate functions in the general case containing the points of discontinuity of the first and second kind, proposed modification of the genetic method. Numerical evaluation of the effectiveness of finding the global optimum of the proposed modification of the genetic method in comparison with a standard genetic algorithm and its known modifications made to a select group multiextremal test functions.

40

Li, Lulu, Haiyan Su, and Xinlong Feng. "Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods." Entropy 24, no. 2 (February 9, 2022): 255. http://dx.doi.org/10.3390/e24020255.

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In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.

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Beausir, Benoît, László S. Tóth, and Olivier Bouaziz. "Simulation of Texture Development of Plane Carbon Steel in Multipass Rolling Using Analytical Flow Function." Materials Science Forum 495-497 (September 2005): 1603–8. http://dx.doi.org/10.4028/www.scientific.net/msf.495-497.1603.

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Using a simple analytical flow function, an analysis of the deformation field in symmetrical rolling has been carried out. The so-obtained varying velocity gradient is incorporated into the Taylor polycrystal plasticity model to simulate the development of the deformation texture. The initial discontinuity in the deformation field of the entering material element on the flow lines is also taken into account. Multiple passes of the material is simulated. A strong texture gradient is obtained in good agreement with experiments carried out for rolling of plane carbon steel. It is shown that the shear component of the texture is strongly related to the nature of multiple passes of the rolling operation.

42

Li, wei, peng Wang, and junzheng Yue. "Research on plastic structural wave behavior and crashworthiness of continuous gradient mesoscopic foam structures under high speed impact." Journal of Physics: Conference Series 2478, no. 7 (June 1, 2023): 072008. http://dx.doi.org/10.1088/1742-6596/2478/7/072008.

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Abstract Under high speed impact, the macro and mesoscopic mechanical behavior, the stress wave propagation mechanism, and the relationship between density gradient and crashworthiness of continuous density gradient foam are the key issues to improve and optimize the protection capability of support structures. The numerical simulation of various density gradient foams is carried out, and the meso-discontinuity of foams is overcome by using the local gradient tensor method of least square error, and the plastic structure wavefronts with clear interfaces are obtained. The plastic structure wave propagation mechanism of foam with different density configurations was analyzed and the relationship between density gradient and crashworthiness was further revealed. The results show that inertia effect is the dominant factor of collapse in the early stage of impact. In the middle and late stage of impact, the dominant factor of collapse changes to the microscopic density of foam. The distribution of continuous density gradient significantly affects the impact resistance. Compared with low-high density configuration foam (LH), high-low density configuration gradient foam (HL) has a 140% increase in impact end force, a 24% decrease in support end force, a 3% decrease in maximum compression, and a 41% longer response time.

43

Shen, Yinong, and W. J. Drugan. "Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 569–76. http://dx.doi.org/10.1115/1.2897060.

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For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity (across which components of stress, strain, or material velocity jump) within a small-displacement-gradient formulation. For each case, an explicit proof of the impossibility of such a propagating surface (except at an elastic wave speed) is achieved for isotropic materials satisfying a Huber-Mises yield condition and associated flow rule, and we show that our method of proof can be generalized to a large class of anisotropic materials. Nevertheless, we demonstrate that moving surfaces of strong discontinuity cannot be ruled out for all stable (i.e., satisfying the maximum plastic work inequality) materials, as in the case of a material whose yield surface contains a linear portion. A clear knowledge of the conditions under which dynamically propagating strong discontinuity surfaces can and cannot exist is crucial to the attainment of correct and complete solutions to such practical elastic-plastic problems as dynamic crack propagation, impact and rapidly moving load problems, high-speed forming, cutting, and other manufacturing processes.

44

Briane, Marc. "Reconstruction of isotropic conductivities from non smooth electric fields." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 1173–93. http://dx.doi.org/10.1051/m2an/2018013.

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In this paper we study the isotropic realizability of a given non smooth gradient field ∇u defined in ℝd, namely when one can reconstruct an isotropic conductivity σ > 0 such that σ∇u is divergence free in ℝd. On the one hand, in the case where ∇u is non-vanishing, uniformly continuous in ℝd and Δu is a bounded function in ℝd, we prove the isotropic realizability of ∇u using the associated gradient flow combined with the DiPerna, Lions approach for solving ordinary differential equations in suitable Sobolev spaces. On the other hand, in the case where ∇u is piecewise regular, we prove roughly speaking that the isotropic realizability holds if and only if the normal derivatives of u on each side of the gradient discontinuity interfaces have the same sign. Some examples of conductivity reconstruction are given.

45

Robinson, J. L., and P. S. Rand. "Discontinuity in fish assemblages across an elevation gradient in a southern Appalachian watershed, USA." Ecology of Freshwater Fish 14, no. 1 (March 2005): 14–23. http://dx.doi.org/10.1111/j.1600-0633.2005.00063.x.

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46

Carmona-Espíndola, Javier, José L. Gázquez, Alberto Vela, and S. B. Trickey. "Negative Electron Affinities and Derivative Discontinuity Contribution from a Generalized Gradient Approximation Exchange Functional." Journal of Physical Chemistry A 124, no. 7 (January 24, 2020): 1334–42. http://dx.doi.org/10.1021/acs.jpca.9b10956.

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47

Qiu, Xiang, HuiFei Wang, JianPing Luo, and Yulu Liu. "Characteristics of velocity gradient jumping discontinuity in steady Poiseuille flow of Johnson–Segalman fluid." International Journal of Non-Linear Mechanics 71 (May 2015): 72–82. http://dx.doi.org/10.1016/j.ijnonlinmec.2015.02.001.

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48

Buchbinder, Goetz G. R. "P-wave deflection or off-azimuth arrivals in the Charlevoix Seismic Zone." Bulletin of the Seismological Society of America 77, no. 6 (December 1, 1987): 2152–62. http://dx.doi.org/10.1785/bssa0770062152.

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Abstract During the months of August 1984 and October 1985, experiments were undertaken in the Charlevoix Seismic Zone to record high-frequency body waves from earthquakes. The seismograms were recorded by digital three-component seismographs. The experiments were conducted on the north shore of the St. Lawrence River only and covered nine sites. All but the two most northeasterly recording sites exhibited P-wave arrivals that arrived from azimuths that differed from the theoretical azimuth based on the computed hypocenter-station relationship. These differences amounted to several tens of degrees. Neither the errors in hypocenter location nor in the orientation of the horizontal seismometers are believed to be the cause of this difference. Theoretical computations based on a two-dimensional model with strong lateral velocity gradients or a discontinuity in velocity produce deviations of the direction of arrival of the P wave in a horizontal plane normal to the anomaly that can amount to several tens of degrees. Both the lateral gradient and discontinuity models satisfy the observed deviation of azimuth versus azimuth deflection. However, only the discontinuity satisfies the deflection versus hypocentral distance distribution, at least for distances to 20 km. Comparing the observed data with the theoretical values suggests that the anomaly in velocity occurs in a near-vertical plane striking parallel to the St. Lawrence River. This is also the direction of ancient extension faults in the region. Other structures were introduced 350 m.y. ago when the Charlevoix impact structure was formed. A number of anorthosite bodies with very high seismic velocities also outcrop in the region. Because of the high frequencies involved, the scale of the anomaly may well be only a few hundred meters, and the anomaly may most likely be located very close to, even directly beneath, the station.

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Churchman, C. M., A. Sackfield, and D. A. Hills. "Asymptotic Solutions for Contact Problems: The Effect of an Internal Discontinuity in Surface Profile." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 4 (April 1, 2006): 387–91. http://dx.doi.org/10.1243/09544062jmes179.

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The contact pressure adjacent to the apex of a tilted punch is studied and used to form a refined, two-term asymptote for the contact pressure at a point of discontinuous gradient interior to a half-plane contact problem. The asymptote is compared with the full solution for an example problem, the wheel with a flat.

50

Voitcu, Gabriel, and Marius Echim. "Crescent-shaped electron velocity distribution functions formed at the edges of plasma jets interacting with a tangential discontinuity." Annales Geophysicae 36, no. 6 (November 14, 2018): 1521–35. http://dx.doi.org/10.5194/angeo-36-1521-2018.

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Abstract. In this paper we discuss numerical simulations that illustrate a physical mechanism leading to the formation of crescent-shaped electron velocity distribution functions at the edges of a high-speed plasma jet impacting on a thin, steep and impenetrable tangential discontinuity with no magnetic shear. We use three-dimensional particle-in-cell simulations to compute the velocity distribution function of electrons in different areas of the plasma jet and at different phases of the interaction with the discontinuity. The simulation set-up corresponds to an idealized, yet relevant, magnetic configuration likely to be observed at the frontside magnetopause under the northward interplanetary magnetic field. The combined effect of the gradient-B drift and the remote sensing of large Larmor radius electrons leads to the formation of crescent-shaped electron velocity distribution functions. We provide examples of such distributions measured by a virtual satellite launched into the simulation domain.

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