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1
LeBrasseur, Nicole. "Catastrophe gradient drives anaphase B." Journal of Cell Biology 177, no. 6 (June 18, 2007): 944a. http://dx.doi.org/10.1083/jcb.1776iti5.
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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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Konopelchenko, B. G., and G. Ortenzi. "Gradient catastrophe and flutter in vortex filament dynamics." Journal of Physics A: Mathematical and Theoretical 44, no. 43 (October 7, 2011): 432001. http://dx.doi.org/10.1088/1751-8113/44/43/432001.
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Masoero, Davide, and Andrea Raimondo. "Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe." Letters in Mathematical Physics 103, no. 5 (January 24, 2013): 559–83. http://dx.doi.org/10.1007/s11005-013-0605-x.
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Radko, Timour. "Applicability and failure of the flux-gradient laws in double-diffusive convection." Journal of Fluid Mechanics 750 (May 30, 2014): 33–72. http://dx.doi.org/10.1017/jfm.2014.244.
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AbstractDouble-diffusive flux-gradient laws are commonly used to describe the development of large-scale structures driven by salt fingers – thermohaline staircases, collective instability waves and intrusions. The flux-gradient model assumes that the vertical transport is uniquely determined by the local background temperature and salinity gradients. While flux-gradient laws adequately capture mixing characteristics on scales that greatly exceed those of primary double-diffusive instabilities, their accuracy rapidly deteriorates when the scale separation between primary and secondary instabilities is reduced. This study examines conditions for the breakdown of the flux-gradient laws using a combination of analytical arguments and direct numerical simulations. The applicability (failure) of the flux-gradient laws at large (small) scales is illustrated through the example of layering instability, which results in the spontaneous formation of thermohaline staircases from uniform temperature and salinity gradients. Our inquiry is focused on the properties of the ‘point-of-failure’ scale ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H_{pof}$) at which the vertical transport becomes significantly affected by the non-uniformity of the background stratification. It is hypothesized that$H_{pof} $can control some key characteristics of secondary double-diffusive phenomena, such as the thickness of high-gradient interfaces in thermohaline staircases. A more general parametrization of the vertical transport – the flux-gradient-aberrancy law – is proposed, which includes the selective damping of relatively short wavelengths that are inadequately represented by the flux-gradient models. The new formulation is free from the unphysical behaviour of the flux-gradient laws at small scales (e.g. the ultraviolet catastrophe) and can be readily implemented in theoretical and large-scale numerical models of double-diffusive convection.
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Konopelchenko, B. G., and G. Ortenzi. "Quasi-Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter." Studies in Applied Mathematics 130, no. 2 (September 5, 2012): 167–99. http://dx.doi.org/10.1111/j.1467-9590.2012.00563.x.
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Zakharov, S. V. "Asymptotic solution of a Cauchy problem in a neighbourhood of a gradient catastrophe." Sbornik: Mathematics 197, no. 6 (June 30, 2006): 835–51. http://dx.doi.org/10.1070/sm2006v197n06abeh003780.
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Kolesnykov, A. V., S. V. Semenova, and О. О. Makovetska. "SIMULATION OF COMPOSITES STRUCTURE FORMATION PROCESSES USING THE METHODS OF THE CATASTROPHE THEORY." Modern construction and architecture, no. 6 (December 25, 2023): 90–98. http://dx.doi.org/10.31650/2786-6696-2023-6-90-98.
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The paper examines the possibility to model the structure formation processes in binder materials using some methods of catastrophe theory. Events at the level of coexistence and interaction of macroscopic and microscopic phenomena are analyzed. The dynamics of transformations at this level of material organization is considered using the method of structural potential, similar to the thermodynamic one, with the possibility of its empirical identification based on the processing of microscopic images. The transition to the potential functions of the theory of catastrophes is carried out by means of geometric parameterization ‒ selection of areas of the volume occupied by material phases and areas associated with interface boundaries. The model of structure formation is presented as a phenomenon in stochastic gradient systems caused by the emergence of features of the structural potential and their transformation upon changing the controlling physicochemical parameters. The possibility of adapting the apparatus of phase diagrams of three-component systems to the considered tasks and its affinity with catastrophe theory models is shown. The structural-phase diagram is constructed by analogy to the Gibbs-Roseboom method on a triangle, while the coordinates are parts of components with different geometric structures ‒ cavities, continuous material at a given scale and interfaces with the surrounding transformed material. From the potential functions of the theory of catastrophes, those that correspond to the analyzed system are reasonably selected - umbilical functions, and in the simplified version ‒ potentials of one variable. A scheme for the study of materials using methods of structural potentials has been developed, which is based on the determination of mesoscopic scales for the material being studied, on the transition to the frequency characteristics of the image, then to the structural potential, which determines the range of structures realized in the material and, in the future, to the transition from structural potentials to physical properties.
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Aksenov, A. V., and K. P. Druzhkov. "Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe." Известия Российской академии наук. Механика жидкости и газа, no. 1 (January 1, 2023): 135–43. http://dx.doi.org/10.31857/s0568528122600734.
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The system of equations that describes one-dimensional polytropic gas flows is considered. The invariants up to the second order of characteristics of the considered system of equations are classified. The method of reducing the Cauchy problems to systems of ordinary differential equations is proposed. Examples of the solutions without gradient catastrophe are constructed using invariants of characteristics supplementary to the Riemann invariants.
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Beisenbi, М. А., and Zh O. Basheyeva. "Solving output control problems using Lyapunov gradient-velocity vector function." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 4 (August 1, 2019): 2874. http://dx.doi.org/10.11591/ijece.v9i4.pp2874-2879.
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This paper describes a controller and observer parameter definition approach in one input-one output (closed-loop) control systems using Lyapunov gradient-velocity vector function. Construction of the vector function is based on the gradient nature of the control systems and the parity of the vector functions with the potential function from the theory of catastrophe. Investigation of the closed-loop control system’s stability and solution of the problem of controller (determining the coefficient of magnitude matrix) and observer (calculation of the matrix elements of the observing equipment) synthesis is based on the direct methods of Lyapunov. The approach allows to select parameters based on the requested characteristics of the system.
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Cheerambathur, Dhanya K., Gul Civelekoglu-Scholey, Ingrid Brust-Mascher, Patrizia Sommi, Alex Mogilner, and Jonathan M. Scholey. "Quantitative analysis of an anaphase B switch: predicted role for a microtubule catastrophe gradient." Journal of Cell Biology 177, no. 6 (June 18, 2007): 995–1004. http://dx.doi.org/10.1083/jcb.200611113.
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Anaphase B in Drosophila embryos is initiated by the inhibition of microtubule (MT) depolymerization at spindle poles, which allows outwardly sliding interpolar (ip) MTs to drive pole–pole separation. Using fluorescence recovery after photobleaching, we observed that MTs throughout the preanaphase B spindle are very dynamic and display complete recovery of fluorescence, but during anaphase B, MTs proximal to the poles stabilize and therefore display lower recovery than those elsewhere. Fluorescence microscopy of the MT tip tracker EB1 revealed that growing MT plus ends localize throughout the preanaphase B spindle but concentrate in the overlap region of interpolar MTs (ipMTs) at anaphase B onset. None of these changes occurred in the presence of nondegradable cyclin B. Modeling suggests that they depend on the establishment of a spatial gradient of MT plus-end catastrophe frequencies, decreasing toward the equator. The resulting redistribution of ipMT plus ends to the overlap zone, together with the suppression of minus-end depolymerization at the poles, could constitute a mechanical switch that initiates spindle elongation.
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Nikitenkova, S., and E. Pelinovsky. "Strongly Nonlinear Transverse Perturbations in Phononic Crystals." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/348920.
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The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.
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JENSSEN, HELGE KRISTIAN, and ROBIN YOUNG. "GRADIENT DRIVEN AND SINGULAR FLUX BLOWUP OF SMOOTH SOLUTIONS TO HYPERBOLIC SYSTEMS OF CONSERVATION LAWS." Journal of Hyperbolic Differential Equations 01, no. 04 (December 2004): 627–41. http://dx.doi.org/10.1142/s021989160400024x.
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We consider two new classes of examples of sup-norm blowup in finite time for strictly hyperbolic systems of conservation laws. The explosive growth in amplitude is caused either by a gradient catastrophe or by a singularity in the flux function. The examples show that solutions of uniformly strictly hyperbolic systems can remain as smooth as the initial data until the time of blowup. Consequently, blowup in amplitude is not necessarily strictly preceded by shock formation.
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Sun, Xiao, Shu Zhong Wang, and You Lian Lu. "Study on the Rheology of Foam Fracturing Fluid with Mixture Model." Advanced Materials Research 512-515 (May 2012): 1747–52. http://dx.doi.org/10.4028/www.scientific.net/amr.512-515.1747.
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Numerical simulation study on the rheology or foam fluid was carried through by treating inner phase as granular fluid with mixture model. The simulation results show that the gas phase is well distributed on cross-section. Besides, the higher the foam quality, the higher the velocity gradient near the wall. For turbulent properties, the turbulent kinetic energy and viscosity increase as the foam quality increases. With the same foam quality, the bigger the bubble diameter, the higher the turbulent viscosity and turbulent kinetic energy. What’s more, the foam quality 63% is a catastrophe point at which the rheology of foam fracturing fluid changes sharply. The change trend of turbulent viscosity along radial direction is different between the regions where the foam quality is below and over catastrophe point, and in the latter the change trend is flatter. From the simulation results it can be seen that the mixture model is more applicable and effective to the region where foam quality is over 63%.
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Dogterom, M., M. A. Félix, C. C. Guet, and S. Leibler. "Influence of M-phase chromatin on the anisotropy of microtubule asters." Journal of Cell Biology 133, no. 1 (April 1, 1996): 125–40. http://dx.doi.org/10.1083/jcb.133.1.125.
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In many eukaryotic cells going through M-phase, a bipolar spindle is formed by microtubules nucleated from centrosomes. These microtubules, in addition to being "captured" by kinetochores, may be stabilized by chromatin in two different ways: short-range stabilization effects may affect microtubules in close contact with the chromatin, while long-range stabilization effects may "guide" microtubule growth towards the chromatin (e.g., by introducing a diffusive gradient of an enzymatic activity that affects microtubule assembly). Here, we use both meiotic and mitotic extracts from Xenopus laevis eggs to study microtubule aster formation and microtubule dynamics in the presence of chromatin. In "low-speed" meiotic extracts, in the presence of salmon sperm chromatin, we find that short-range stabilization effects lead to a strong anisotropy of the microtubule asters. Analysis of the dynamic parameters of microtubule growth show that this anisotropy arises from a decrease in the catastrophe frequency, an increase in the rescue frequency and a decrease in the growth velocity. In this system we also find evidence for long-range "guidance" effects, which lead to a weak anisotropy of the asters. Statistically relevant results on these long-range effects are obtained in "high-speed" mitotic extracts in the presence of artificially constructed chromatin stripes. We find that aster anisotropy is biased in the direction of the chromatin and that the catastrophe frequency is reduced in its vicinity. In this system we also find a surprising dependence of the catastrophe and the rescue frequencies on the length of microtubules nucleated from centrosomes: the catastrophe frequency increase and the rescue frequency decreases with microtubule length.
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Aksenov, A. V., and K. P. Druzhkov. "Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe." Fluid Dynamics 58, no. 1 (February 2023): 136–44. http://dx.doi.org/10.1134/s0015462822601899.
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Radko, Timour. "Thermohaline layering on the microscale." Journal of Fluid Mechanics 862 (January 14, 2019): 672–95. http://dx.doi.org/10.1017/jfm.2018.976.
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A theoretical model is developed which illustrates the dynamics of layering instability, frequently realized in ocean regions with active fingering convection. Thermohaline layering is driven by the interplay between large-scale stratification and primary double-diffusive instabilities operating at the microscale – temporal and spatial scales set by molecular dissipation. This interaction is described by a combination of direct numerical simulations and an asymptotic multiscale model. The multiscale theory is used to formulate explicit and dynamically consistent flux laws, which can be readily implemented in large-scale analytical and numerical models. Most previous theoretical investigations of thermohaline layering were based on the flux-gradient model, which assumes that the vertical transport of density components is uniquely determined by their local background gradients. The key deficiency of this approach is that layering instabilities predicted by the flux-gradient model have unbounded growth rates at high wavenumbers. The resulting ultraviolet catastrophe precludes the analysis of such basic properties of layering instability as its preferred wavelength or the maximal growth rate. The multiscale model, on the other hand, incorporates hyperdiffusion terms that stabilize short layering modes. Overall, the presented theory carries the triple advantage of (i) offering an explicit description of the interaction between microstructure and layering modes, (ii) taking into account the influence of non-uniform stratification on microstructure-driven mixing, and (iii) avoiding unphysical behaviour of the flux-gradient laws at small scales. While the multiscale approach to the parametrization of time-dependent small-scale processes is illustrated here on the example of fingering convection, we expect the proposed technique to be readily adaptable to a wide range of applications.
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Beysenbi, M. A., and A. A. Maimurynova. "Solution of the problem of synthesis of the main contour oftheadaptive controlsystem for unstableand deterministic chaotic processes with m-inputs and n-outputs in the «Hyperbolic umbilic» catastrophe class." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 85, no. 3 (September 15, 2022): 99–109. http://dx.doi.org/10.47533/2020.1606-146x.182.
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An urgent problem in the conditions of uncertainty of the parameters of the control object and external influences, for the control of unstable and deterministic chaotic processes, is the use of adaptation methods. In this case, the reference model with the desired dynamics and the main control loop of the adaptive system are constructed in the catastrophe class “hyperbolic umbilic”, and the aperiodic robust stability of the reference model with the desired dynamics and the main control loop of the self-organizing adaptive system with an increased potential for robust stability is studied by the gradient-velocity method of the vector function Lyapunov.
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Wang, Mingcan, and Xiangjun Wang. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations." Mathematics 12, no. 7 (April 3, 2024): 1081. http://dx.doi.org/10.3390/math12071081.
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The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high-dimensional cases, has stagnated. The development of deep learning provides ideas for its high-dimensional solution. In this paper, our focus lies on the fully coupled forward–backward stochastic differential equation. We design a neural network structure tailored to the characteristics of the equation and develop a hybrid BiGRU model for solving it. We introduce the time dimension based on the sequence nature after discretizing the FBSDE. By considering the interactions between preceding and succeeding time steps, we construct the BiGRU hybrid model. This enables us to effectively capture both long- and short-term dependencies, thus mitigating issues such as gradient vanishing and explosion. Residual learning is introduced within the neural network at each time step; the structure of the loss function is adjusted according to the properties of the equation. The model established above can effectively solve fully coupled forward–backward stochastic differential equations, effectively avoiding the effects of dimensional catastrophe, gradient vanishing, and gradient explosion problems, with higher accuracy, stronger stability, and stronger model interpretability.
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Rozanova, Olga. "Criterium for the gradient catastrophe for the non-isentropic gas dynamics equations in the one dimensional case." PAMM 7, no. 1 (December 2007): 2040051–52. http://dx.doi.org/10.1002/pamm.200700695.
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Beisenbi, Мamyrbek, and Samal Kaliyeva. "Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions." Eastern-European Journal of Enterprise Technologies 1, no. 3 (121) (February 28, 2023): 6–14. http://dx.doi.org/10.15587/1729-4061.2023.274063.
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One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements
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Kay, Alan R., and Mordecai P. Blaustein. "Evolution of our understanding of cell volume regulation by the pump-leak mechanism." Journal of General Physiology 151, no. 4 (February 19, 2019): 407–16. http://dx.doi.org/10.1085/jgp.201812274.
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All animal cells are surrounded by a flexible plasma membrane that is permeable to water and to small ions. Cells thus face a fundamental problem: the considerable tension that their membranes would experience if the osmotic influx of water, driven by the presence of impermeant intracellular ions, was left unopposed. The pivotal study that described the cell’s remedy for this impending osmotic catastrophe—the “pump-leak mechanism” (PLM)—was published in the Journal of General Physiology by Tosteson and Hoffman in 1960. Their work revealed how the sodium pump stabilizes cell volume by eliminating the osmotic gradient. Here we describe the mechanistic basis of the PLM, trace the history of its discovery, and place it into the context of our current understanding.
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Jardón-Kojakhmetov, Hildeberto, Christian Kuehn, and Maximilian Steinert. "The hyperbolic umbilic singularity in fast-slow systems." Nonlinearity 37, no. 9 (August 14, 2024): 095036. http://dx.doi.org/10.1088/1361-6544/ad6bde.
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Abstract Fast-slow systems with three slow variables and gradient structure in the fast variables have, generically, hyperbolic umbilic, elliptic umbilic or swallowtail singularities. In this article we provide a detailed local analysis of a fast-slow system near a hyperbolic umbilic singularity. In particular, we show that under some appropriate non-degeneracy conditions on the slow flow, the attracting slow manifolds jump onto the fast regime and fan out as they cross the hyperbolic umbilic singularity. The analysis is based on the blow-up technique, in which the hyperbolic umbilic point is blown up to a 5-dimensional sphere. Moreover, the reduced slow flow is also blown up and embedded into the blown-up fast formulation. Further, we describe how our analysis is related to classical theories such as catastrophe theory and constrained differential equations.
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He, M. M., K. Q. Wu, and Z. Q. Zhang. "A new method for introducing plastic zone and tangential stress into tunnelling strain rockburst prediction." Géotechnique Letters 12, no. 3 (September 1, 2022): 1–34. http://dx.doi.org/10.1680/jgele.21.00129.
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This paper on a criterion for rockbursts is focused mainly on the stress concentration and gradient change of the tangential stress of the surrounding rock. Two parameters are introduced into tunnelling strain rockburst prediction: the radius of the plastic zone and the radial stress at the elastoplastic junction after excavating the surrounding rock. A new rockburst criterion is proposed based on the mechanism for throwing-type rockbursts and catastrophe theory. Meanwhile, a new multi-factor index for identifying rockburst classification is given based on rockbursts in actual engineering. The results show that there is a certain correlation between strain rockbursts and the plastic-zone radius and radial stress of the surrounding rock, which can be estimated using the mechanical parameters and stress distribution before excavation, whereupon strain rockbursts can be predicted. By dividing the rockburst interval through a large number of rockburst examples, the accuracy of the criterion reaches 80.36%, and the accuracy for moderate-to-strong rockbursts reaches 83.33%.
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Brust-Mascher, Ingrid, and Jonathan M. Scholey. "Mitotic motors and chromosome segregation: the mechanism of anaphase B." Biochemical Society Transactions 39, no. 5 (September 21, 2011): 1149–53. http://dx.doi.org/10.1042/bst0391149.
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Anaphase B spindle elongation plays an important role in chromosome segregation. In the present paper, we discuss our model for anaphase B in Drosophila syncytial embryos, in which spindle elongation depends on an ip (interpolar) MT (microtubule) sliding filament mechanism generated by homotetrameric kinesin-5 motors acting in concert with poleward ipMT flux, which acts as an ‘on/off’ switch. Specifically, the pre-anaphase B spindle is maintained at a steady-state length by the balance between ipMT sliding and ipMT depolymerization at spindle poles, producing poleward flux. Cyclin B degradation at anaphase B onset triggers: (i) an MT catastrophe gradient causing ipMT plus ends to invade the overlap zone where ipMT sliding forces are generated; and (ii) the inhibition of ipMT minus-end depolymerization so flux is turned ‘off’, tipping the balance of forces to allow outward ipMT sliding to push apart the spindle poles. We briefly comment on the relationship of this model to anaphase B in other systems.
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ALBEVERIO, SERGIO, and OLGA ROZANOVA. "THE NON-VISCOUS BURGERS EQUATION ASSOCIATED WITH RANDOM POSITION IN COORDINATE SPACE: A THRESHOLD FOR BLOW UP BEHAVIOUR." Mathematical Models and Methods in Applied Sciences 19, no. 05 (May 2009): 749–67. http://dx.doi.org/10.1142/s0218202509003607.
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It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We consider this equation assuming that the particle paths in the medium are governed by a random process with a variance which depends in a polynomial way on the velocity. Given an initial distribution of the particles which is uniform in space and with the initial velocity linearly depending on the position, we show both analytically and numerically that there exists a threshold effect: if the power in the above variance is less than 1, then the noise does not influence the solution behavior, in the following sense: the mean of the velocity when we keep the value of position fixed goes to infinity outside the origin. If, however, the power is larger or equal to 1, then this mean decays to zero as the time tends to a critical value.
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Gardner, Melissa K., Chad G. Pearson, Brian L. Sprague, Ted R. Zarzar, Kerry Bloom, E. D. Salmon, and David J. Odde. "Tension-dependent Regulation of Microtubule Dynamics at Kinetochores Can Explain Metaphase Congression in Yeast." Molecular Biology of the Cell 16, no. 8 (August 2005): 3764–75. http://dx.doi.org/10.1091/mbc.e05-04-0275.
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During metaphase in budding yeast mitosis, sister kinetochores are tethered to opposite poles and separated, stretching their intervening chromatin, by singly attached kinetochore microtubules (kMTs). Kinetochore movements are coupled to single microtubule plus-end polymerization/depolymerization at kinetochore attachment sites. Here, we use computer modeling to test possible mechanisms controlling chromosome alignment during yeast metaphase by simulating experiments that determine the 1) mean positions of kinetochore Cse4-GFP, 2) extent of oscillation of kinetochores during metaphase as measured by fluorescence recovery after photobleaching (FRAP) of kinetochore Cse4-GFP, 3) dynamics of kMTs as measured by FRAP of GFP-tubulin, and 4) mean positions of unreplicated chromosome kinetochores that lack pulling forces from a sister kinetochore. We rule out a number of possible models and find the best fit between theory and experiment when it is assumed that kinetochores sense both a spatial gradient that suppresses kMT catastrophe near the poles and attachment site tension that promotes kMT rescue at higher amounts of chromatin stretch.
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Guzina, Bojan B., and Fatemeh Pourahmadian. "Why the high-frequency inverse scattering by topological sensitivity may work." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2179 (July 2015): 20150187. http://dx.doi.org/10.1098/rspa.2015.0187.
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This study deciphers the topological sensitivity (TS) as a tool for the reconstruction and characterization of impenetrable anomalies in the high-frequency regime. It is assumed that the anomaly is simply connected and convex, and that the measurements of the scattered field are of the far-field type. In this setting, the formula for TS—which quantifies the perturbation of a cost functional due to a point-like impenetrable scatterer—is expressed as a pair of nested surface integrals: one taken over the boundary of a hidden obstacle, and the other over the measurement surface. Using multipole expansion, the latter integral is reduced to a set of antilinear forms featuring Green's function and its gradient. The remaining expression is distilled by evaluating the scattered field on the surface of an obstacle via Kirchhoff approximation, and pursuing an asymptotic expansion of the resulting Fourier integral. In this way, the TS is found to survive upon three asymptotic lynchpins, namely (i) the near-boundary approximation for sampling points close to the ‘exposed’ surface of an obstacle; (ii) uniform expansions synthesizing the diffraction catastrophes for sampling points near caustic surfaces, lines and points; and (iii) stationary phase approximation. Within the framework of catastrophe theory, it is shown that, in the case of the full source aperture, the TS is asymptotically dominated by the (explicit) near-boundary term—which explains the previously reported reconstruction capabilities of this class of indicator functionals. The analysis further shows that, when the (Dirichlet or Neumann) character of an anomaly is unknown beforehand, the latter can be effectively exposed by assuming point-like Dirichlet perturbation and considering the sign of the leading term inside the reconstruction.
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Bertola, Marco, and Alexander Tovbis. "Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I." Communications on Pure and Applied Mathematics 66, no. 5 (February 25, 2013): 678–752. http://dx.doi.org/10.1002/cpa.21445.
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Gudkov, I., I. Volkohon, V. Illienko, M. Lazarev, and A. Klepko. "Impact of radioactive contamination of soils on the diversity of micropopulation and the transformation of organic substances." Agricultural Science and Practice 9, no. 3 (April 20, 2023): 3–17. http://dx.doi.org/10.15407/agrisp9.03.003.
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Aim. To study the impact of different levels of radioactive contamination on the organic matter decomposition and the population development of microbial decomposers of organic matter in soil. Methods. Gamma-spectrometry for the determination of the relative activity of 137Cs and beta-spectrometry for the determination of the relative activity of 90Sr in order to choose the contamination range for the studies; Tea Bag Іndex (TBI), the standard glob- ally accepted method to determine the rate of organic matter decomposition; gas chromatography – to determine the impact of the investigated factors on the formation of the biomass of microorganisms by means of the СО2 production potential; classic microbiological methods, using elective media to estimate the population densities of culturable microbial decomposers. Results. The studies (from April to September 2021) comprised two soils with different radioactive contamination ranges: Range No. 1 in Narodychi district of Zhytomyr region (the village Khrystynivka, 3 sampling points) in the unconditional (obligatory) resettlement zone after the catastrophe in the Chornobyl nuclear power plant (ChNPP) (it has an absorbed dose rate gradient, evaluated for soil microorganisms, from 0.2 μGy/h (at sampling point Narodychi-1: 51,24076°N, 29,21497°E) to 1.57 μGy/h (at sampling point Naro- dychi-3: 51,23815°N, 29,22245°E)), located on the agricultural field, abandoned after the catastrophe and Range No. 2, located on the afforested area, directly bordering the territory of the so-called Red Forest in the ChNPP ex- clusion zone (4 sampling points – the first three points – natural ecosystems, and 4th – pyrogenically transformed territory after fires in 2020) with the absorbed dose rate gradient from 3.7 μGy/h (at sampling point ChEZ-1: 51,38595°N, 30,03035°E) to 84.0 μGy/h (at sampling point ChEZ-4: 51,38231°N, 30,03298°E). The dependence of the studied indicators on the gradient of soil contamination with radionuclides was demonstrated and these are the conditions that the difference is more than 400 times in the values of the ionizing radiation absorbed dose rates formed by radionuclides in soil. In Range No. 1 (on the fallow land), with the increase in the dose rate up from 0.2 to 1.57 μGy/h, there was statistically significant increase of mineralization coefficient and percentage of reduced weight of rooibos tea between the least and most contaminated sampling points), stimulation of the development of micromycetes (by 1.2–2.3 times), cellulose-decomposing bacteria (by 7.1–7.9 times), and ammonifying bacteria (by 1.8–6.3 times) due to a significant increasing the number of colony-forming units in points with higher radio- nuclide contamination and an increase of microbial biomass in soil more than twofold between the least and most contaminated sampling point of Range No. 1.In Range No. 2, in the ChNPP exclusion zone, characterized by low parameters of sod-podzolic soil fertility (humus content from 1.2 ± 0.2 to 0.9 ± 0.1 %, exchangeable acidity from 4.0 ± 0.1 to 5.0 ± 0.7), the number of micromycetes and ammonifying bacteria in soil was one-two orders below the indices of Range No. 1. Micromycetes dominated in the groups of cellulose-decomposing microorganisms. There was statistically significant increase of mineralization coefficient and percentage of reduced weight of rooibos tea with increasing of radionuclide contamination level for the first three plots: ChEZ-1, ChEZ-2 and ChEZ-3 of Range No. 2. Conclusions. In the fallow land of the unconditional (obligatory) resettlement zone, the increase of the radia- tion absorbed dose rate in soil by one order from 0.2 to 1.57 μGy/h does not inhibit the development of microorgan- isms in soil, rather it stimulates their activity and increases their numbers. On poor sod-podzolic soils in the exclu- sion zone of the Chernobyl nuclear power plant, the preponderance of development of micromycetes over bacterial cellulolytics is noticeable. The radioactive contamination affected the development of soil microorganisms and the biological processes in soils not only in the first years after the Chornobyl catastrophe, which has been described in the literature, but has had its influence for rather a long time (for over thirty years after the accident). Among the microorganisms of a saccharolytic mode of organic plant residuals decomposition, the micromycetes dominate.
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Lowman, Nicholas K., and M. A. Hoefer. "Dispersive shock waves in viscously deformable media." Journal of Fluid Mechanics 718 (February 8, 2013): 524–57. http://dx.doi.org/10.1017/jfm.2012.628.
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AbstractThe viscously dominated, low-Reynolds-number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behaviour when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low-density fluid through a viscously deformable conduit. These flows are modelled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or cross-sectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed-form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviours are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small- to moderate-amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.
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F. Abd El-Aal, Mohamed. "Economic Crisis Treatment Based on Artificial Intelligence." Jurnal Institutions and Economies 16, no. 3 (July 1, 2024): 97–116. http://dx.doi.org/10.22452/ijie.vol16no3.5.
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Abstract: There are many possible causes of an economic crisis—a financial downturn, a banking meltdown, political strife (e.g., the Russia-Ukraine war), or a health-related catastrophe (e.g., Covid-19). Some of these crises are expected, while others are “bolts from the sky.” However, what is certain is that all these crises, whatever their cause, have a negative impact on global gross domestic product (GDP). If we can identify the components of output that have the most impact in an economic crisis, we might be able to mitigate its effects. Therefore, this paper uses machine learning algorithms to determine how the components of expenditure and sectoral value-added approach impact global GDP. The gradient boosting algorithm is the most accurate model for predicting and determining the impact of independent variables on a dependent variable. The results indicate that government spending has the largest effect on global GDP, accounting for 68.3% of the impact. The economic sector with the most impact on global GDP is the service sector, which affects global output by 42.3%, followed by the agricultural sector at 30.2%. Thus, stimulating government spending and the service sector may reduce the negative effects of an economic crisis.
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Zakharov, Sergey V. "EVOLUTION OF A MULTISCALE SINGULARITY OF THE SOLUTION OF THE BURGERS EQUATION IN THE 4-DIMENSIONAL SPACE–TIME." Ural Mathematical Journal 8, no. 1 (July 29, 2022): 136. http://dx.doi.org/10.15826/umj.2022.1.012.
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The solution of the Cauchy problem for the vector Burgers equation with a small parameter of dissipation \(\varepsilon\) in the \(4\)-dimensional space-time is studied: $$ \mathbf{u}_t + (\mathbf{u}\nabla) \mathbf{u} = \varepsilon \triangle \mathbf{u}, \quad u_{\nu} (\mathbf{x}, -1, \varepsilon) = - x_{\nu} + 4^{-\nu}(\nu + 1) x_{\nu}^{2\nu + 1}, $$ With the help of the Cole–Hopf transform \(\mathbf{u} = - 2 \varepsilon \nabla \ln H,\) the exact solution and its leading asymptotic approximation, depending on six space-time scales, near a singular point are found. A formula for the growth of partial derivatives of the components of the vector field \(\mathbf{u}\) on the time interval from the initial moment to the singular point, called the formula of the gradient catastrophe, is established: $$ \frac{\partial u_{\nu} (0, t, \varepsilon)}{\partial x_{\nu}} = \frac{1}{t} \left[ 1 + O \left( \varepsilon |t|^{- 1 - 1/\nu} \right) \right]\!, \quad \frac{t}{\varepsilon^{\nu /(\nu + 1)} } \to -\infty, \quad t \to -0.$$The asymptotics of the solution far from the singular point, involving a multistep reconstruction of the space-time scales, is also obtained: $$ u_{\nu} (\mathbf{x}, t, \varepsilon) \approx - 2 \left( \frac{t}{\nu + 1} \right)^{1/2\nu} \tanh \left[ \frac{x_{\nu}}{\varepsilon} \left( \frac{t}{\nu + 1} \right)^{1/2\nu} \right]\!, \quad \frac{t}{\varepsilon^{\nu /(\nu + 1)} } \to +\infty. $$
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Anjani, Suputri Devi D., D. Manjusha, P. Pujith, Ch G. V. Satyanarayana, V. Sailusha, and Reddy G. Vivekananda. "Comparative analysis for survival prediction from titanic disaster using machine learning." i-manager’s Journal on Software Engineering 18, no. 1 (2023): 36. http://dx.doi.org/10.26634/jse.18.1.20137.
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Among the most notorious shipwrecks in history is the Titanic. Out of the 2,224 passengers and crew, 1,502 perished when the Titanic sank on April 15, 1912, during her maiden voyage, following an iceberg collision. Ship safety laws have improved as a result of this dramatic disaster that stunned the world. Scientists and investigators are beginning to understand what could have caused some passengers to survive while others perished in the Titanic catastrophe. A contributing factor in the high death toll from the shipwreck was the insufficient number of lifeboats available for both passengers and the crew. An intriguing finding from the sinking is that certain individuals, such as women and children, had a higher chance of surviving than others. Since the accident, new regulations were drafted mandating that the number of lifeboats match the number of passenger seats. Numerous machine learning techniques were used to forecast the passengers' survival rate. Preprocessing and data cleaning are essential measures to reduce bias. In this paper, decision trees and random forests, two machine learning techniques, are used to determine the probability of passenger survival. The primary goal of this work is to distinguish between the two distinct machine learning algorithms to analyze traveler survival rates based on accuracy. Machine learning technologies are utilized to forecast which passengers would survive the accident. The highest accuracy achieved is 81.10% for Gradient Boost Trees.
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Tang, Jinyu, Mohammed N. Ansari, and William R. Rossen. "Quantitative Modeling of the Effect of Oil on Foam for Enhanced Oil Recovery." SPE Journal 24, no. 03 (January 28, 2019): 1057–75. http://dx.doi.org/10.2118/194020-pa.
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Summary The effectiveness of foam for mobility control in the presence of oil is key to foam enhanced oil recovery (EOR). A fundamental property of foam EOR is the existence of two steady-state flow regimes: the high-quality regime and the low-quality regime. Experimental studies have sought to understand the effect of oil on foam through its effect on these two regimes. Here, we explore the effect of oil on the two flow regimes for one widely used foam model. The STARS (CMG 2015) foam model includes two algorithms for the effect of oil on foam: In the “wet-foam” model, oil changes the mobility of full-strength foam in the low-quality regime, and in the “dry-out” model, oil alters the limiting water saturation around which foam collapses. We examine their effects as represented in each model on the two flow regimes using a Corey relative permeability function for oil. Specifically, we plot the pressure-gradient contours that define the two flow regimes as a function of superficial velocities of water, gas, and oil, and show how oil shifts behavior in the regimes. The wet-foam model shifts behavior in the low-quality regime with no direct effect on the high-quality regime. The dry-out model shifts behavior in the high-quality regime but not the low-quality regime. At fixed superficial velocities, both models predict multiple steady states at some injection conditions. We perform a stability analysis of these states using a simple 1D simulator with and without incorporating capillary diffusion. The steady state attained after injection depends on the initial state. In some cases, it appears that the steady state at the intermediate pressure gradient is inherently unstable, as represented in the model. In some cases, the introduction of capillary diffusion is required to attain a uniform steady state in the medium. The existence of multiple steady states, with the intermediate one being unstable, is reminiscent of catastrophe theory and of studies of foam generation without oil.
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Trèvese, D., G. Cirimele, and M. de Simone. "Matter Distribution in the Galaxy Clusters A 539 and A 2319." Symposium - International Astronomical Union 188 (1998): 329. http://dx.doi.org/10.1017/s0074180900115396.
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We performed a combined X-ray and optical analysis of the two clusters A539 and A2319, based on ROSAT PSPC 0.4-2.4 keV images of the public archive and F band photometry from microdensitometric scans of Palomar 48 inch plates (Trèvese et al. 1992, A&AS, 94, 327). Assuming spherical symmetry and following the methods adopted in Cirimele, Nesci, and Trèvese (1997, ApJ, 475, 11 (CNT97)) we derived the radial distribution of gas and galaxy densities ρgas and ρgal and we have computed the morphological parameter βxo ≡ d ln ρgas(r)/d ln ρgal(r), introduced in CNT97. This allows to check the validity of the hydrostatic equilibrium condition, which reads, for an isotropic and uniform velocity distribution of r.m.s. dispersion σr. In the case of A539, adopting σr=629 km s−1 from Fadda et al. (1996, ApJ, 473, 670) and T=1.57 keV David et al. (1996, ApJ, 473, 692), we obtained marginally consistent values of βspec= 1.54±0.50 and βxo=1.08±0.11. In the case of A2319 we took into account the presence of the secondary component A2319B (Oegerle et al. 1995, AJ, 110, 32) and the temperature gradient (Markevitch M. 1996, ApJ, 465, L1). The resulting radial increase of βspec is consistent with that of (βxo(r) + d ln T(r)/d ln ρgal), suggesting that the hydrostatic equilibrium holds also in the presence of a temperature gradient. The radial distribution of the total binding mass, the mass in galaxies and intergalactic gas show that in both clusters the gas mass profile is steeper than galaxies and total masses consistently with our previous results (CNT97). Adopting a constant gas temperature, the relevant baryon fractions are larger than 20 %, adding new evidence to the “baryon catastrophe”. Taking into account the radial decrease of gas temperature, the baryon fraction is further increased. This implies that either Ωo < 0.25, or that large halos of dark matter surround galaxy clusters, as suggested by White & Fabian (1995, MNRAS, 273, 72).
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Alekseeva, E. S., and A. E. Rassadin. "THE MODIFIED WHITHAM MODULATION THEORY FOR THE NONLINEAR KLEIN-GORDON-FOCK EQUATION WITH THE SIMPLEST RATIONAL FUNCTION AS ITS POTENTIAL." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 12–14. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).2.
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It is well-known that one can construct approximate solution of the nonlinear KleinGordon-Fock equation (NKGF) by means of the Whitham modulation theory (Whitham, 1977). In this work in the framework of the modified Whitham modulation theory presented at (Alekseeva, Rassadin, 2018) and (Kostromina et al., 2017) for NKGF with potential U(x) = (x–1/x)2 its asymptotic solution v(x, t) has been found. Due to isochronism of onedimensional movement of classical particle with unit mass in this potential amplitude a(x, t) of asymptotical solution obeys the linear transfer equation ∂a/∂t + V∂a/∂x = 0 with velocity V belonging to the interval –1<V<1. Peculiarity of the constructed solution is absence of gradient catastrophe therefore it is convenient for investigation of the next terms of asymptotic expansion of the NKGF solution with considered potential (Maslov, Omel’yanov, 1981). Product of Whitham-analogs of group and phase velocities of wave from constructed asymptotic solution of NKGF is equal to unit. This is the same value as for the linear Klein-Gordon-Fock equation. The mean square <v2(x, t)> of asymptotic solution of NKGF has been calculated under assumption that its initial phase shift is random value with stable distribution of probabilities. The obtained asymptotic solution due to its simplicity and informativity can be used by lecturers to illustrate abilities of the Whitham modulation theory.
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Suleimenova, S. T., Zh O. Musiripsha, N. P. Kabulov, and E. A. Ospanov. "Investigation of the stability of the control system of a self-balanced two-wheeled robot." Bulletin of Shakarim University. Technical Sciences, no. 2(10) (June 30, 2023): 38–45. http://dx.doi.org/10.53360/2788-7995-2023-2(10)-5.
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The main characteristics of the control system are the stability and quality of regulation. A stable system always returns to the equilibrium position after the external perturbation ceases to act. An unstable system goes into overdrive after the slightest push.A self-balancing robot has many different sensors. To maintain balance, a rotational motion sensor and an angular velocity sensor will be used. The speed of the motors can be controlled by changing the duty cycle of the pulse-width modulation. The robot model takes a voltage value as input and outputs the state of the system. At the output of the function, the value from the encoders and the gyroscope is given. The robot will stand only if a controller is developed that makes the whole system stable. The controller must ensure the stability of the robot. Since the position of the robot is unstable, in order to maintain balance, the movement of the robot must be in the same direction as the angle of the body. In modern control theory, there are many methods for stabilizing an unstable system.This paper presents a universal approach to constructing the Lyapunov vector function, based on the geometric interpretation of the theorem on the asymptotic stability of the direct Lyapunov method and the concepts of stability. This approach allows us to represent the Lyapunov function as a potential function, and the control system as gradient systems from catastrophe theory.
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Domínguez-Olmedo, Juan L., Álvaro Gragera-Martínez, Jacinto Mata, and Victoria Pachón Álvarez. "Machine Learning Applied to Clinical Laboratory Data in Spain for COVID-19 Outcome Prediction: Model Development and Validation." Journal of Medical Internet Research 23, no. 4 (April 14, 2021): e26211. http://dx.doi.org/10.2196/26211.
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Background The COVID-19 pandemic is probably the greatest health catastrophe of the modern era. Spain’s health care system has been exposed to uncontrollable numbers of patients over a short period, causing the system to collapse. Given that diagnosis is not immediate, and there is no effective treatment for COVID-19, other tools have had to be developed to identify patients at the risk of severe disease complications and thus optimize material and human resources in health care. There are no tools to identify patients who have a worse prognosis than others. Objective This study aimed to process a sample of electronic health records of patients with COVID-19 in order to develop a machine learning model to predict the severity of infection and mortality from among clinical laboratory parameters. Early patient classification can help optimize material and human resources, and analysis of the most important features of the model could provide more detailed insights into the disease. Methods After an initial performance evaluation based on a comparison with several other well-known methods, the extreme gradient boosting algorithm was selected as the predictive method for this study. In addition, Shapley Additive Explanations was used to analyze the importance of the features of the resulting model. Results After data preprocessing, 1823 confirmed patients with COVID-19 and 32 predictor features were selected. On bootstrap validation, the extreme gradient boosting classifier yielded a value of 0.97 (95% CI 0.96-0.98) for the area under the receiver operator characteristic curve, 0.86 (95% CI 0.80-0.91) for the area under the precision-recall curve, 0.94 (95% CI 0.92-0.95) for accuracy, 0.77 (95% CI 0.72-0.83) for the F-score, 0.93 (95% CI 0.89-0.98) for sensitivity, and 0.91 (95% CI 0.86-0.96) for specificity. The 4 most relevant features for model prediction were lactate dehydrogenase activity, C-reactive protein levels, neutrophil counts, and urea levels. Conclusions Our predictive model yielded excellent results in the differentiating among patients who died of COVID-19, primarily from among laboratory parameter values. Analysis of the resulting model identified a set of features with the most significant impact on the prediction, thus relating them to a higher risk of mortality.
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Oerlemans, J. "A quasi-analytical ice-sheet model for climate studies." Nonlinear Processes in Geophysics 10, no. 4/5 (October 31, 2003): 441–52. http://dx.doi.org/10.5194/npg-10-441-2003.
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Abstract. A simple quasi-analytical model is developed to study the response of ice-sheets to climate change. The model is axisymmetrical and rests on a bed with a constant slope. The mechanics are highly parameterised. The climatic conditions are represented by the altitude of the runoff line. Above the runoff line the accumulation rate is constant (but may depend on, for instance, the ice-sheet size), below the runoff line the balance gradient is constant. The ice-sheet may extend into the sea and can respond to changes in sea level. At the grounding line the ice velocity is assumed to be proportional to the water depth. For this set-up an explicit expression for the total mass budget of the ice-sheet is derived. To illustrate the properties and possibilities of the model, equilibrium states are analysed and the response to periodic forcing is studied as well. The coupling of mass balance and surface elevation of the ice-sheet leads to nonlinear behaviour and branching of the equilibrium solutions. The qualitative behaviour of the system is that of the cusp catastrophe. Nonlinear effects are more pronounced when the slope of the bed is smaller. A case is discussed in which two ice-sheets are coupled by making the altitude of the runoff line dependent on the total area of the two ice-sheets. On two continents, having a slightly different glaciation threshold, periodic forcing of the altitude of the runoff line is imposed. It is shown that in such a situation variations on a long time scale (two to three times the period of the forcing) are introduced. Finally the model is forced by the GISP d18O record for the last 120 000 years. For an appropriate choice of parameters the model simulates well the waxing and waning of the Laurentide, Fennoscandian and Barentsz ice-sheets.
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Malaguti, S., A. Corli, and S. Trillo. "Control of gradient catastrophes developing from dark beams." Optics Letters 35, no. 24 (December 15, 2010): 4217. http://dx.doi.org/10.1364/ol.35.004217.
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Zhang, Yu Cheng, Guang Hua Yang, Hai Ying Hu, and Peng Liu. "Method to Identify the Critical Slip Surface of Side Slope via the Deformation Field and Stress Field Calculated through Deformation Modulus Elastoplasticity Strength Reduction Method." Applied Mechanics and Materials 90-93 (September 2011): 3–11. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.3.
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When strength reduction method is used for side slope analysis, only the intensive parameters are reduced and deformation parameters are not. The ideal elastoplastic model is adopted, and the safety factor is basically in agreement with that of the traditional limit equilibrium method. Main result is the safety factor of side slope, but non-linearity of soil is not considered actually during calculation, so it's hard to arrive at a real deformation field. Based on the deformation modulus elastoplasticity strength reduction method, research of this paper can achieve a more truthful deformation field. Considering the deficiencies in the current slip surface search techniques, this paper mainly studies how to determine the slip surface directly through the slope deformation field and stress field based on the analysis to their characteristics and the formation mechanism and characteristics of slip surface. Three methods to determine the slip surface are worked out: One is to use displacement gradient to identify the most disadvantageous slip surface; The second one is to determine the slip surface using the characteristics of FLAC calculation method and the characteristic that nodal velocity at non-slip area is near to zero and nodal velocity at slip area is very great; The last one is to use the deviation survey method in slope monitoring to track the nodal displacement in numerical analysis, and take the points with displacement catastrophe as those on the slip surface, and link those points to form a curve and finally get the critical slip surface. Analysis is made to the slip surface of clay slope with weak layer. Position of slip surface determined through these three methods is basically the same. Compared with traditional critical equilibrium method, these three methods can not only be applied to homogeneous side slope, but also be used to determine the slip surface of heterogeneous side slope. This paper makes a research on expansion of the application field of deformation modulus elastoplasticity strength reduction method.
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Silalahi, Meschac T., Darharta Dahrin, Dadi Abdurrahman, and Adrin Tohari. "Identification Of Liquefaction-Potential Zones Using The Gravity Method In Lolu Village, Central Sulawesi." Jurnal Penelitian Pendidikan IPA 9, no. 8 (August 25, 2023): 6206–12. http://dx.doi.org/10.29303/jppipa.v9i8.4830.
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A seismic event of magnitude 7.5 struck the Palu region in Central Sulawesi on September 28, 2018, precipitating a subsequent calamity in the form of a tsunami measuring 4-7 meters in height. This catastrophe was further compounded by the occurrence of liquefaction, leading to extensive devastation and a significant loss of life. In order to identify areas susceptible to liquefaction, it is anticipated that the employment of the gravity method, renowned for its capacity to discern density fluctuations associated with the mass of voluminous materials over a considerable detection range, will prove instrumental. The investigation of parameters and the characterization of liquefaction phenomena in regions previously afflicted by liquefaction disasters can be instrumental in devising strategies for mapping zones that are predisposed to such occurrences. The present study seeks to employ geophysical methods, specifically the gravity method, to delineate zones with the potential for liquefaction within the Lolu Village at Palu City, Central Sulawesi. Through the application of techniques designed to isolate regional and residual anomalies, it is envisaged that a clearer understanding of anomalies situated in shallower regions can be attained, with a specific focus on residential areas. Notably, due to liquefaction, approximately half of the residential areas have shifted a considerable distance of around 132 meters from their original positions. To facilitate the interpretation of subsurface layers, two-dimensional cross-sections are modeled to intersect the displaced and stationary areas. The residual map reveals discernible variations in anomaly values, with lower values observed in the areas that experienced liquefaction-induced movement. Subsurface modeling further demonstrates the presence of three distinct rock layers, namely a sandy layer, a gravel layer, and a rock layer. Additionally, the modeling depicts the formation of canals composed of hard rock, exhibiting varying thicknesses within the surface layer as a consequence of the liquefaction event in 2018. The existence of these canals serves as an indicator that when the sandy layer becomes saturated with water, it will flow along the topographical gradient, following the path of the subterranean canals that have formed.
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Hoffmann, C., E. G. Charalampidis, D. J. Frantzeskakis, and P. G. Kevrekidis. "Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems." Physics Letters A 382, no. 42-43 (October 2018): 3064–70. http://dx.doi.org/10.1016/j.physleta.2018.08.014.
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Konopelchenko, B. G., and G. Ortenzi. "Homogeneous Euler equation: blow-ups, gradient catastrophes and singularity of mappings." Journal of Physics A: Mathematical and Theoretical 55, no. 3 (December 29, 2021): 035203. http://dx.doi.org/10.1088/1751-8121/ac42aa.
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Abstract The paper is devoted to the analysis of the blow-ups of derivatives, gradient catastrophes (GCs) and dynamics of mappings of R n → R n associated with the n-dimensional homogeneous Euler equation. Several characteristic features of the multi-dimensional case (n > 1) are described. Existence or nonexistence of blow-ups in different dimensions, boundness of certain linear combinations of blow-up derivatives and the first occurrence of the GC are among of them. It is shown that the potential solutions of the Euler equations exhibit blow-up derivatives in any dimension n. Several concrete examples in two- and three-dimensional cases are analysed. Properties of R u ̲ n → R x ̲ n mappings defined by the hodograph equations are studied, including appearance and disappearance of their singularities.
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Kannan, Kasi Rajesh, Ramalingam Vaira Vignesh, Kota Pavan Kalyan, and Myilsamy Govindaraju. "Development and tribological characterization of fly ash reinforced iron based functionally gradient friction materials." Engineering review 41, no. 3 (2021): 20–28. http://dx.doi.org/10.30765/er.1501.
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The tribological and thermal properties enable iron based sintered materials with hard phase ceramic reinforcements as promising friction material for heavy-duty wind turbines. In wind turbines, the braking system consists of aerodynamic and mechanical braking systems. During application of mechanical brakes, the friction materials are pressed against the rotating low-speed shaft. The desired braking efficiency is achieved by utilizing a number of friction materials, which in turn are joined in a steel backing plate. Though this arrangement increases the braking efficiency, the hard phase ceramic reinforcement particles reduces the bonding strength between the friction material and steel backing plate. The joint failure leads to catastrophic failure of wind turbine. Therefore, the need of the hour is to develop friction materials with functional gradients that have high wear resistance (contact area) and high bond strength (interface). In this study, an attempt is made to fabricate and characterize a friction material with gradient profile of composition along the cross section to provide functional gradient property. The functional gradient friction material is synthesized by gradient deposition of Fe, Cu, Cg, SiC and fly ash powders which is then compacted and sintered. The prepared functional gradient friction material was characterized in terms of microstructure and microhardness. The tribological performance (wear rate and coefficient of friction) of the developed functionally gradient friction material was investigated at various loads using pin-on disc apparatus. The results show that as the load increases, the wear rate decreases and at the same time the COF tends to increase at higher loads. The predominant wear mechanism was deduced from the morphology of the worn surface.
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Kim, Hoki, Woojin Lee, and Jaewook Lee. "Understanding Catastrophic Overfitting in Single-step Adversarial Training." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 8119–27. http://dx.doi.org/10.1609/aaai.v35i9.16989.
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Although fast adversarial training has demonstrated both robustness and efficiency, the problem of "catastrophic overfitting" has been observed. This is a phenomenon in which, during single-step adversarial training, the robust accuracy against projected gradient descent (PGD) suddenly decreases to 0% after a few epochs, whereas the robust accuracy against fast gradient sign method (FGSM) increases to 100%. In this paper, we demonstrate that catastrophic overfitting is very closely related to the characteristic of single-step adversarial training which uses only adversarial examples with the maximum perturbation, and not all adversarial examples in the adversarial direction, which leads to decision boundary distortion and a highly curved loss surface. Based on this observation, we propose a simple method that not only prevents catastrophic overfitting, but also overrides the belief that it is difficult to prevent multi-step adversarial attacks with single-step adversarial training.
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Lara, Mark J., Yaping Chen, and Benjamin M. Jones. "Recent warming reverses forty-year decline in catastrophic lake drainage and hastens gradual lake drainage across northern Alaska." Environmental Research Letters 16, no. 12 (November 19, 2021): 124019. http://dx.doi.org/10.1088/1748-9326/ac3602.
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Abstract Lakes represent as much as ∼25% of the total land surface area in lowland permafrost regions. Though decreasing lake area has become a widespread phenomenon in permafrost regions, our ability to forecast future patterns of lake drainage spanning gradients of space and time remain limited. Here, we modeled the drivers of gradual (steady declining lake area) and catastrophic (temporally abrupt decrease in lake area) lake drainage using 45 years of Landsat observations (i.e. 1975–2019) across 32 690 lakes spanning climate and environmental gradients across northern Alaska. We mapped lake area using supervised support vector machine classifiers and object based image analyses using five-year Landsat image composites spanning 388 968 km2. Drivers of lake drainage were determined with boosted regression tree models, using both static (e.g. lake morphology, proximity to drainage gradient) and dynamic predictor variables (e.g. temperature, precipitation, wildfire). Over the past 45 years, gradual drainage decreased lake area between 10% and 16%, but rates varied over time as the 1990s recorded the highest rates of gradual lake area losses associated with warm periods. Interestingly, the number of catastrophically drained lakes progressively decreased at a rate of ∼37% decade−1 from 1975–1979 (102–273 lakes draining year−1) to 2010–2014 (3–8 lakes draining year−1). However this 40 year negative trend was reversed during the most recent time-period (2015–2019), with observations of catastrophic drainage among the highest on record (i.e. 100–250 lakes draining year−1), the majority of which occurred in northwestern Alaska. Gradual drainage processes were driven by lake morphology, summer air and lake temperature, snow cover, active layer depth, and the thermokarst lake settlement index (R 2 adj = 0.42, CV = 0.35, p < 0.0001), whereas, catastrophic drainage was driven by the thawing season length, total precipitation, permafrost thickness, and lake temperature (R 2 adj = 0.75, CV = 0.67, p < 0.0001). Models forecast a continued decline in lake area across northern Alaska by 15%–21% by 2050. However these estimates are conservative, as the anticipated amplitude of future climate change were well-beyond historical variability and thus insufficient to forecast abrupt ‘catastrophic’ drainage processes. Results highlight the urgency to understand the potential ecological responses and feedbacks linked with ongoing Arctic landscape reorganization.
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Kshevetskii, S. P. "Analytical and numerical investigation of nonlinear internal gravity waves." Nonlinear Processes in Geophysics 8, no. 1/2 (April 30, 2001): 37–53. http://dx.doi.org/10.5194/npg-8-37-2001.
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Abstract. The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration), we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory coincidence of simulation outcomes with analytical ones is revealed and some examples of numerical simulations illustrating wave disintegration into solitons are given. The phenomenon of internal wave mixing is considered and is explained from the point of view of the results obtained. The numerical methods for internal wave simulation are examined. In particular, the influence of difference interval finiteness on a numerical solution is investigated. It is revealed that a numerical viscosity and numerical dispersion can play the role of regularizators to a nonlinear quasistatic problem. To avoid this effect, the grid steps should be taken less than some threshold values found theoretically.
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Samokhin, Alexey. "Gradient catastrophes and sawtooth solutions for a generalized Burgers equation on an interval." Journal of Geometry and Physics 85 (November 2014): 177–84. http://dx.doi.org/10.1016/j.geomphys.2014.05.007.
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