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Добірка наукової літератури з теми "Ntegral equation for the non"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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Статті в журналах з теми "Ntegral equation for the non"

F. Kadhem, Mohanad, and Ali H. Alfayadh. "Mixed Homotopy Integral Transform Method for Solving Non-Linear ntegro-Differential Equation." Al-Nahrain Journal of Science 25, no. 1 (March 1, 2022): 35–40. http://dx.doi.org/10.22401/anjs.25.1.06.

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In this paper, we have applied Sawi transform with homotopyperturbation method to obtain analytic approximation for non-linear integro-differential Equations. The proposed technique is compared with homotopy perturbation method and Abood transform homotopy perturbation method. The results show that Sawi transform homotopy perturbation is an efficient approach to solve non-linear integro-differential equations.

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Journal, Baghdad Science. "An approximate solution for solving linear system of integral equation with application on "Stiff" problems." Baghdad Science Journal 2, no. 1 (March 6, 2005): 148–54. http://dx.doi.org/10.21123/bsj.2.1.148-154.

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DERMOUNE, Azzouz. "Non-commutative Burgers equation." Hokkaido Mathematical Journal 25, no. 2 (February 1996): 315–32. http://dx.doi.org/10.14492/hokmj/1351516727.

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Kremp, D., M. Bonitz, W. D. Kraeft, and M. Schlanges. "Non-Markovian Boltzmann Equation." Annals of Physics 258, no. 2 (August 1997): 320–59. http://dx.doi.org/10.1006/aphy.1997.5703.

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Shushin, A. I., and V. P. Sakun. "Non-Markovian stochastic Liouville equation." Physica A: Statistical Mechanics and its Applications 340, no. 1-3 (September 2004): 283–91. http://dx.doi.org/10.1016/j.physa.2004.04.018.

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Munro, W. J., and C. W. Gardiner. "Non-rotating-wave master equation." Physical Review A 53, no. 4 (April 1, 1996): 2633–40. http://dx.doi.org/10.1103/physreva.53.2633.

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Das, Amal K. "A non‐Fickian diffusion equation." Journal of Applied Physics 70, no. 3 (August 1991): 1355–58. http://dx.doi.org/10.1063/1.349592.

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Gaspard, P., and M. Nagaoka. "Non-Markovian stochastic Schrödinger equation." Journal of Chemical Physics 111, no. 13 (October 1999): 5676–90. http://dx.doi.org/10.1063/1.479868.

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Alexanian, Moorad. "Classical non-Markovian Boltzmann equation." Journal of Mathematical Physics 55, no. 8 (August 2014): 083301. http://dx.doi.org/10.1063/1.4886475.

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Doliwa, Adam. "Non-commutativeq-Painlevé VI equation." Journal of Physics A: Mathematical and Theoretical 47, no. 3 (December 23, 2013): 035203. http://dx.doi.org/10.1088/1751-8113/47/3/035203.

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Дисертації з теми "Ntegral equation for the non"

Daviau, Claude. "Equation de dirac non lineaire." Nantes, 1993. http://www.theses.fr/1993NANT2006.

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Partant de l'equation de dirac, le terme d'impulsion-energie de l'electron est simplifie. On obtient ainsi une equation d'ondes non lineaire, qui est etudiee en utilisant le formalisme de l'algebre de clifford d'espace-temps. La resolution est effectuee pour les ondes planes monochromatiques, qui sont sans energies negatives tant que la masse propre reste positive. Puis sont etudiees les invariances de l'equation: invariance relativiste, symetries p, t, c, invariances de jauge. La resolution de l'equation, pour l'atome d'hydrogene, est effectuee par separation des variables. La non linearite ne modifie que la partie radiale des equations. L'angle d'yvon-takabayasi s'annule dans le plan d'equation z=0, il en resulte la quantification des niveaux d'energie, avec pratiquement les memes niveaux que dans la theorie lineaire, avec les memes nombres quantiques. L'etude du tenseur d'impulsion-energie met en evidence une symetrie avec un autre tenseur. Il est possible d'etendre la jauge chirale de l'equation, ce qui amene au groupe u(1)su(2) de la theorie electro-faible, tout en preservant la conservation du courant electrique

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Hatimy, Abdelhalim. "Comportement des solutions d'un oscillateur non autonome a non linearites quadratiques." Toulouse, INSA, 1986. http://www.theses.fr/1986ISAT0016.

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On considere un oscillateur domine par deux non linearites quadratiques, soumis a une force excitatrice periodique et decrit par une equation differentielle ordinaire d'ordre 2 (e). Une premiere etude est basee sur la recurrence associee (e) etablie selon la methode des sections de poincare. On identifie les singularites de (e) correspondant aux synchronisations principales et sous-harmoniques d'ordre 2 de (e). On etablit les domaines de synchronisation harmonique principale et sous-harmonique d'ordre 2 dans l'espace des parametres de (e). On decelle un regime stationnaire quasi-periodique non synchronise avec la force exterieure. Le domaine de synchronisation sous-harmonique d'ordre 2 s'avere le plus important. La co-existence de deux singularites attractives de dimensions differentes est notee. Une etude analytique permet de confirmer ces resultats

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Sili, Ali. "Deux problèmes d'évolution non linéaires." Paris 6, 1987. http://www.theses.fr/1987PA066113.

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On montre l'existence d'états stationnaires pour l'équation de Dirac non linéaire avec un potentiel radial. Dans la deuxième partie, on établit des estimations uniformes en temps pour les solutions d'équation de Klein Gordon non linéaires.

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Kedge, Christopher J. "A new non-cubic equation of state." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0017/MQ49698.pdf.

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Oswald, Luc. "Etude de problemes non lineaires avec singularites." Paris 6, 1987. http://www.theses.fr/1987PA066060.

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Cette these est composee de dix articles que nous avons regroupes en deux parties. La premiere partie est constituee par l'etude et la classification des singularites isolees, premierement, d'une equation elliptique avec diffusion, deuxiemement, de l'equation parabolique correspondante. Dans la seconde partie sont etablis des resultats d'existence pour des problemes elliptiques semi-lineaires. Ces problemes sont caracterises respectivement, par une non-linearite singuliere, une condition de neumann degeneree, une non-linearite sous lineaire et, enfin, des exposants de sobolev critiques

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Федчишина, Ірина Юріївна. "Уточнення апроксимації де Вілдера для оцінки ймовірності банкрутства у страховій моделі Крамера-Лундберга". Master's thesis, Київ, 2018. https://ela.kpi.ua/handle/123456789/23449.

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В магістерській дисертації запропонований новий підхід до наближеного знаходження ймовірності банкрутства страхової компанії на нескінченному часовому горизонті. Необхідність такого наближеного знаходження зумовлюється тим, що точне значення ймовірності банкрутства, будучи розв’язком складного інтегрального рівняння, часто не може бути виражене в явній аналітичній формі. Ідея розробленого методу полягає в заміні процесу страхового ризику на інший процес ризику зі страховими виплатами, розподіленими за законом, що є сумішшю двох експоненціальних розподілів. Для такого процесу ризику ймовірність банкрутства відома в аналітичній формі. Заміна реалізується шляхом прирівнювання перших п’яти кумулянтів початкового та нового процесів ризику.
In the master's thesis a new approach to the approximate finding of the ruin probability of an insurance company on an infinite time horizon is proposed. The need for such an approximate finding is due to the fact that the exact value of the ruin probability, being a solution to a complex integral equation, can often not be expressed in explicit analytical form. The idea of the developed method is to replace the process of risk with another risk process with insurance payments distributed according to the law, which is a mixture of two exponential distributions. For such a risk process, the ruin probability is known in analytical form. Replacement is realized by equating the first five cumulants of the initial and new risk processes.
В магистерской диссертации предложен новый поход к приближенному нахождению вероятности банкротства страховой компании на бесконечном временном горизонте. Необходимость такого приближенного нахождения обусловлено тем, что точное значение вероятности банкротства, будучи решением сложного интегрального уравнения, часто не может быть выражено в явной аналитической форме. Идея разработанного метода заключается в замене процесса страхового риска на другой процесс риска со страховыми выплатами, распределенными по закону, который является смесью двух экспоненциальных распределений. Для такого процесса риска вероятность банкротства известна в аналитической форме. Замена реализуется путем приравнивания первых пяти кумулянтов начального и нового процессов риска.

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Rey, Olivier. "Équations elliptiques non linéaires avec l'exposant critique de Sobolev." Palaiseau, Ecole polytechnique, 1989. http://www.theses.fr/1989EPXX0009.

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On s'interesse a l'existence et au comportement de solutions positives, nulles au bord, d'equations elliptiques non-lineaires faisant intervenir l'exposant critique de sobolev, sur des domaines bores reguliers de dimension superieure ou egale a 33. On etudie les problemes variationnels associs, dont les fonctionnelles ne verifient pas la condition de palais-smale. On demontre differents resultats d'existence, de multiplicite, de concentration et de bifurcation des solutions en fonction de l'equation et des proprietes geometriques et topologiques du domaine. On analyse en particulier le role joue par la fonction de green dans ce type de problemes

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Bacha, Inès. "Traitement symbolique des systèmes d'équations différentielles non linéaires au voisinage des singularités." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10078.

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Cette these se rattache a l'etude locale des equations differentielles, elle est composee de trois parties dependantes. Dans la premiere partie, nous presentons differentes theories telles que les formes normales, les transformations quasi-monomiales ainsi que celle du polygone de newton afin de mettre en place un algorithme pour simplifier les systemes planaires d'equations differentielles au voisinage des singularites isolees. Cet algorithme se base essentiellement sur les travaux d'a. Bruno sur les solutions locales des systemes d'equations differentielles. Quelques exemples d'application sont donnes afin d'illustrer ce travail. Dans la deuxieme partie, les differentes theories precedentes ainsi que l'etude des courbes algebriques nous permettent d'etendre cet algorithme dans l'espace. Dans la partie finale, nous proposons une methode de reduction de l'ordre des systemes differentiels en dimension n.

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Mouzaoui, Lounès. "Régimes asymptotiques pour l'équation de Schrödinger non linéaire non locale." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20241/document.

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Cette thèse est consacrée à l'étude de quelques régimes asymptotiques de l'équation de Schrödinger semi-classique, en présence d'une non-linéarité non-locale de type Hartree. Elle comporte 3 parties, sous forme de 4 chapitres et une annexe. L'objet de la première partie, constituée du premier et deuxième chapitre, est l'étude du comportement asymptotique du modèle précédent pour un noyau singulier autour de l'origine, pour une condition initiale asymptotiquement de type WKB, en régime faiblement non-linéaire. Dans le premier chapitre nous montrons que sous certaines conditions de régularité sur la condition initiale, la solution est encore de type WKB à l'ordre principal, un résultat que nous obtenons dans le cadre fonctionnel de l'algèbre de Wiener. Nous donnons une preuve alternative au résultat précédent dans le cas particulier de l'équation de Schrödinger-Poisson dans le cadre fonctionnel d'espace de Sobolev rescalé, où la considération de correcteurs est nécessaire pour construire une solution approchée et pouvoir décrire la solution à l'ordre principal. La deuxième partie de cette thèse, objet du troisième chapitre, est consacrée à l'étude de la propagation de paquets d'onde pour un système couplé d'équations de Hartree en régime semi-classique, en présence de potentiels extérieurs sous-quadratiques. Nous décrivons analytiquement et numériquement le comportement asymptotique à l'ordre principal des fonctions d'onde solution du système, lorsqu'elles sont soumises à une condition initiale en forme de paquets d'onde, pour différentes tailles de non-linéarité. La dernière partie est constituée du quatrième chapitre et de l'annexe. Dans le quatrième chapitre nous considérons le problème de Cauchy de l'équation de Hartree avec noyau homogène ou dont la transformée de Fourier est dans un espace de Lebesgue, dans le cadre fonctionnel de l'algèbre de Wiener. Nous montrons quelques résultats sur le caractère bien posé du problème pour les noyaux considérés, dans des espaces faisant intervenir l'algèbre de Wiener. Nous concluons par une annexe dans laquelle nous considérons le problème de Cauchy de l'équation de Schrödinger-Poisson, en présence d'un potentiel extérieur indépendant du temps, dans les espaces de Sobolev pondérés. Nous étendons des résultats déjà obtenus sur l'existence de solutions globales dans les espaces de Sobolev sans poids lorsque le potentiel extérieur est nul, en montrant l'existence de solutions globales en temps dans les espaces de Sobolev pondérés pour toute régularité
This thesis is devoted to the study of some asymptotic regimes of the semi-classical Schrödinger equation, in the presence of a nonlocal nonlinearity of Hartree-type . The purpose of the first part, consisting of the first and second chapter is the study of the asymptotic behavior of the previous model with a singular kernel around the origin for an initial data asymptotically of WKB-type, in a weakly nonlinear regime. In the first chapter we show that under some regularity conditions on the initial data, the solution still is of WKB-type at leading order, a result that we get in the functional framework of the Wiener algebra . We give an alternative proof to the previous result in the particular case of the Schrödinger-Poisson equation in the functional framework of rescaled Sobolev space, where the consideration of correctors is necessary to construct an approximate solution to describe the solution at leading order.The second part of this thesis, the subject of the third chapter is devoted to the study the propagation of wave packets for a coupled system of Hartree equations in a semi-classical regime , in the presence of sub-quadratic external potentials. We describe analytically and numerically the asymptotic behavior of the leading order of the wave functions solution of the system, for an initial data in the form of wave packets for different sizes of nonlinearity.The final part consists of the fourth chapter and appendix.In the fourth chapter we consider the Cauchy problem of the Hartree equation with a homogeneous kernel or of Fourier transform in a Lebesgue space, in the functional framework of the Wiener algebra. We show some results on the well-posedness of the problem for the considered kernels, in spaces involving the Wiener algebra.We conclude with an appendix in which we consider the Cauchy problem for the Schrödinger-Poisson equation in the presence of a time independent external potential in the weighted Sobolev spaces. We extend the results already obtained on the existence of global solutions in Sobolev spaces without weight when the external potential is reduced to zero, by showing the existence of global solutions in time in the weighted Sobolev spaces for all regularity

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Mehraban, Arash. "Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1736.

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In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the infinitesimal generator and the invariant surface condition for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear ordinary differential equation that could be explored numerically or perhaps solved in closed form.

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Книги з теми "Ntegral equation for the non"

Stiller, Wolfgang. Arrhenius Equation and Non-Equilibrium Kinectics: 100 Years Arrhenius Equation. Leipzig: B.G.Teubner Verlagsgesellschaft, 1989.

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Wolfgang, Stiller. Arrhenius equation and non-equilibrium kinetics: 100 years Arrhenius equation. Leipzig: BSB B.G. Teubner, 1989.

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Abarbanel, Saul. Non-reflecting boundary conditions for the compressible Navier-Stokes equations. Hampton, Va: Langley Research Center, 1986.

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Michelassi, V. Solution of the steady state incompressible Navier-Stokes equations in curvilinear non orthogonal coordinates. Rhode Saint Genese, Belgium: von Karman Institute for Fluid Dynamics, 1986.

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A non-equilibrium statistical mechanics: Without the assumption of molecular chaos. River Edge, N.J: World Scientific, 2003.

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Chen, Tian-Quan. A non-equilibrium statistical mechanics: Without the assumption of molecular chaos. Singapore: World Scientific, 2004.

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Shuen, Jian-Shun. A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds. Washington, D. C: American Institute of Aeronautics and Astronautics, 1992.

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Jonsson, Fan Yang. Non-linear structural equation models: Simulation studies of the Kenny-Judd model. Uppsala, Sweden: Uppsala University, 1997.

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Gutlyanskii, Vladimir. The Beltrami Equation: A Geometric Approach. New York, NY: Springer New York, 2012.

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Osher, Stanley J. High order essentially non-oscillatory schemes for Hamilton-Jacobi equations. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1990.

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Частини книг з теми "Ntegral equation for the non"

Mauri, Roberto. "Langevin Equation." In Non-Equilibrium Thermodynamics in Multiphase Flows, 25–33. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5461-4_3.

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Mauri, Roberto. "Fokker-Planck Equation." In Non-Equilibrium Thermodynamics in Multiphase Flows, 35–48. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5461-4_4.

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Fraga, Serafín, José Manuel García de la Vega, and Eric S. Fraga. "The Non-Linear Schrödinger Equation." In Lecture Notes in Chemistry, 106–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-51458-6_7.

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Sherwin, Keith, and Michael Horsley. "The non-flow energy equation." In Thermofluids, 123–36. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-4433-7_8.

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Sherwin, Keith, and Michael Horsley. "The non-flow energy equation." In Thermofluids, 25–27. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-6870-8_8.

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Kutz, Jose Nathan, and Edward Farnum. "Solitons and Ultra-Short Optical Waves: The Short-Pulse Equation Versus the Nonlinear Schrödinger Equation." In Non-Diffracting Waves, 451–71. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2013. http://dx.doi.org/10.1002/9783527671519.ch22.

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Kulish, P. P. "Reflection Equation Algebras and Quantum Groups." In Quantum and Non-Commutative Analysis, 207–20. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-2823-2_16.

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Kirchner, J., W. Meyer, and B. Hensel. "Non-stationary Langevin Equation in Cardiology." In IFMBE Proceedings, 318–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03882-2_84.

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Carvalho, Alexandre N., José A. Langa, and James C. Robinson. "A non-autonomous Chafee–Infante equation." In Applied Mathematical Sciences, 317–38. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4581-4_13.

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Carvalho, Alexandre N., José A. Langa, and James C. Robinson. "A non-autonomous damped wave equation." In Applied Mathematical Sciences, 361–76. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4581-4_15.

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Тези доповідей конференцій з теми "Ntegral equation for the non"

Wang, Qi, Jingsong Wei, Jianfeng Sun, and Jian Gao. "Non-scanning imaging laser Lidar equation." In 2012 International Conference on Optoelectronics and Microelectronics (ICOM). IEEE, 2012. http://dx.doi.org/10.1109/icoom.2012.6316256.

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Levin, B. M. "Integral Equation for Non-Directional Radiators." In 2018 XXIIIrd International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED). IEEE, 2018. http://dx.doi.org/10.1109/diped.2018.8543267.

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Smirnov, Fedor. "Dual Baxter's equation and quantum algebraic geometry." In Non-perturbative Quantum Effects 2000. Trieste, Italy: Sissa Medialab, 2000. http://dx.doi.org/10.22323/1.006.0033.

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Sklyar, Grigory M., and Grzegorz Szkibiel. "Optimal control of non-homogeneous wave equation." In Robotics (MMAR). IEEE, 2011. http://dx.doi.org/10.1109/mmar.2011.6031379.

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Bereziat, D., and I. Herlin. "Non-linear observation equation for motion estimation." In 2012 19th IEEE International Conference on Image Processing (ICIP 2012). IEEE, 2012. http://dx.doi.org/10.1109/icip.2012.6467161.

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Van Lil, Emmanuel H., and Pieter J. Luypaert. "Non-separable solutions of Helmholtz' equation revisited." In 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS). IEEE, 2017. http://dx.doi.org/10.23919/ursigass.2017.8105252.

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Ding, Dian-kun, and Xu-ping Zhang. "Method for solving logic equation set consist of zero-one non-zero and non-one type logic equation." In 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2010. http://dx.doi.org/10.1109/fskd.2010.5569693.

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Nghiem, Long X., and Peter H. Sammon. "A Non-Equilibrium Equation-of-State Compositional Simulator." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 1997. http://dx.doi.org/10.2118/37980-ms.

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GILES, MICHAEL. "Non-reflecting boundary conditions for Euler equation calculations." In 9th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-1942.

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Medina, L., and C. Wykes. "Array design based on non-linear equation constraints." In 1999 IEEE Ultrasonics Symposium. Proceedings. International Symposium. IEEE, 1999. http://dx.doi.org/10.1109/ultsym.1999.849491.

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Звіти організацій з теми "Ntegral equation for the non"

Kollosh, R. The Non-BPS Black Hole Attractor Equation. Office of Scientific and Technical Information (OSTI), February 2006. http://dx.doi.org/10.2172/876040.

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Burby, Joshua William, Nikos Kallinikos, and Robert MacKay. Grad-Shafranov equation for non-axisymmetric MHD equilibria. Office of Scientific and Technical Information (OSTI), June 2020. http://dx.doi.org/10.2172/1637686.

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Sacks, R., B. Shore, M. Hermann, and S. Dixit. Liouville equation in the presence of non-colinear light beams. Office of Scientific and Technical Information (OSTI), February 1990. http://dx.doi.org/10.2172/7185663.

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Sirley Marques-Bonham. A new way to interpret the Dirac equation in a non-Riemannian manifold. Office of Scientific and Technical Information (OSTI), June 1989. http://dx.doi.org/10.2172/6026405.

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Waisman, E. M. Equation of State and Two-Body Correlations for Fluids of Non-Spherical Molecules. Fort Belvoir, VA: Defense Technical Information Center, January 1985. http://dx.doi.org/10.21236/ada151969.

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Pearson, Eric, Joel Kulesza, and Brian Kiedrowski. Derivation of the Future Time Equation for Analog, Non-Multiplying Monte Carlo Simulation. Office of Scientific and Technical Information (OSTI), May 2021. http://dx.doi.org/10.2172/1785476.

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Klibanov, Michael V., and Sergey E. Pamyatnykh. Global Uniqueness for a Coefficient Inverse Problem for the Non-Stationary Transport Equation via Carleman Estimate. Fort Belvoir, VA: Defense Technical Information Center, January 2006. http://dx.doi.org/10.21236/ada448486.

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Russo, David, and William A. Jury. Characterization of Preferential Flow in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, October 2001. http://dx.doi.org/10.32747/2001.7580681.bard.

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Preferential flow appears to be the rule rather than the exception in field soils and should be considered in the quantitative description of solute transport in the unsaturated zone of heterogeneous formations on the field scale. This study focused on both experimental monitoring and computer simulations to identify important features of preferential flow in the natural environment. The specific objectives of this research were: (1) To conduct dye tracing and multiple tracer experiments on undisturbed field plots to reveal information about the flow velocity, spatial prevalence, and time evolution of a preferential flow event; (2) To conduct numerical experiments to determine (i) whether preferential flow observations are consistent with the Richards flow equation; and (ii) whether volume averaging over a domain experiencing preferential flow is possible; (3) To develop a stochastic or a transfer function model that incorporates preferential flow. Regarding our field work, we succeeded to develop a new method for detecting flow patterns faithfully representing the movement of water flow paths in structured and non-structured soils. The method which is based on application of ammonium carbonate was tested in a laboratory study. Its use to detect preferential flow was also illustrated in a field experiment. It was shown that ammonium carbonate is a more conservative tracer of the water front than the popular Brilliant Blue. In our detailed field experiments we also succeeded to document the occurrence of preferential flow during soil water redistribution following the cessation of precipitation in several structureless field soils. Symptoms of the unstable flow observed included vertical fingers 20 - 60 cm wide, isolated patches, and highly concentrated areas of the tracers in the transmission zone. Soil moisture and tracer measurements revealed that the redistribution flow became fingered following a reversal of matric potential gradient within the wetted area. Regarding our simulation work, we succeeded to develop, implement and test a finite- difference, numerical scheme for solving the equations governing flow and transport in three-dimensional, heterogeneous, bimodal, flow domains with highly contrasting soil materials. Results of our simulations demonstrated that under steady-state flow conditions, the embedded clay lenses (with very low conductivity) in bimodal formations may induce preferential flow, and, consequently, may enhance considerably both the solute spreading and the skewing of the solute breakthrough curves. On the other hand, under transient flow conditions associated with substantial redistribution periods with diminishing water saturation, the effect of the embedded clay lenses on the flow and the transport might diminish substantially. Regarding our stochastic modeling effort, we succeeded to develop a theoretical framework for flow and transport in bimodal, heterogeneous, unsaturated formations, based on a stochastic continuum presentation of the flow and a general Lagrangian description of the transport. Results of our analysis show that, generally, a bimodal distribution of the formation properties, characterized by a relatively complex spatial correlation structure, contributes to the variability in water velocity and, consequently, may considerably enhance solute spreading. This applies especially in formations in which: (i) the correlation length scales and the variances of the soil properties associated with the embedded soil are much larger than those of the background soil; (ii) the contrast between mean properties of the two subdomains is large; (iii) mean water saturation is relatively small; and (iv) the volume fraction of the flow domain occupied by the embedded soil is relatively large.

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.

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