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Статті в журналах з теми "Divergence form operators"
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Milakis, Emmanouil, and Tatiana Toro. "Divergence form operators in Reifenberg flat domains." Mathematische Zeitschrift 264, no. 1 (November 14, 2008): 15–41. http://dx.doi.org/10.1007/s00209-008-0450-2.
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Barlow, Martin T., and Richard F. Bass. "Divergence Form Operators on Fractal-like Domains." Journal of Functional Analysis 175, no. 1 (August 2000): 214–47. http://dx.doi.org/10.1006/jfan.2000.3597.
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Boccardo, L., and B. Dacorogna. "Monotonicity of certain differential operators in divergence form." Manuscripta Mathematica 64, no. 2 (June 1989): 253–60. http://dx.doi.org/10.1007/bf01160123.
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Barlow, Martin T. "On the Liouville Property for Divergence Form Operators." Canadian Journal of Mathematics 50, no. 3 (June 1, 1998): 487–96. http://dx.doi.org/10.4153/cjm-1998-026-9.
Повний текст джерелаАнотація:
AbstractIn this paper we construct a bounded strictly positive function σ such that the Liouville property fails for the divergence form operator L= ▽ (σ2▽). Since in addition Δσ/σ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schrödinger operators.
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Song, Liang, and Ming Xu. "VMO spaces associated with divergence form elliptic operators." Mathematische Zeitschrift 269, no. 3-4 (September 3, 2010): 927–43. http://dx.doi.org/10.1007/s00209-010-0774-6.
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Maekawa, Yasunori, and Hideyuki Miura. "On domain of Poisson operators and factorization for divergence form elliptic operators." manuscripta mathematica 152, no. 3-4 (June 13, 2016): 459–512. http://dx.doi.org/10.1007/s00229-016-0858-7.
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ter Elst, A. F. M., and Derek W. Robinson. "High order divergence-form elliptic operators on Lie groups." Bulletin of the Australian Mathematical Society 55, no. 2 (April 1997): 335–48. http://dx.doi.org/10.1017/s0004972700034006.
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Okazawa, Noboru. "Sectorialness of second order elliptic operators in divergence form." Proceedings of the American Mathematical Society 113, no. 3 (March 1, 1991): 701. http://dx.doi.org/10.1090/s0002-9939-1991-1072347-4.
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Rozkosz, Andrzej. "Weak convergence of diffusions corresponding to divergence form operators." Stochastics and Stochastic Reports 57, no. 1-2 (August 1996): 129–57. http://dx.doi.org/10.1080/17442509608834055.
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Miyazaki, Yoichi. "Schauder theory for Dirichlet elliptic operators in divergence form." Journal of Evolution Equations 13, no. 2 (March 27, 2013): 443–80. http://dx.doi.org/10.1007/s00028-013-0186-2.
Повний текст джерелаДисертації з теми "Divergence form operators"
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Zheng, Hao. "Obstacle problems with elliptic operators in divergence form." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18279.
Повний текст джерелаАнотація:
Doctor of PhilosophyDepartment of Mathematics
Ivan Blank
Under the guidance of Dr. Ivan Blank, I study the obstacle problem with an elliptic operator in divergence form. First, I give all of the nontrivial details needed to prove a mean value theorem, which was stated by Caffarelli in the Fermi lectures in 1998. In fact, in 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for elliptic operators in divergence form with bounded measurable coefficients. The formula stated by Caffarelli is much simpler, but he did not include the proof. Second, I study the obstacle problem with an elliptic operator in divergence form. I develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results allow us to begin the study of the regularity of the free boundary in the case where the coefficients are in the space of vanishing mean oscillation (VMO).
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Aryal, Ashok. "Geometry of mean value sets for general divergence form uniformly elliptic operators." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/36205.
Повний текст джерелаАнотація:
Doctor of PhilosophyDepartment of Mathematics
Ivan Blank
In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.
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Trey, Baptiste. "Existence et régularité des formes optimales pour des problèmes d'optimisation spectrale Free boundary regularity for a multiphase shape optimization problem. Communications in Partial Dfferential Equations Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form Existence and regularity of optimal shapes for elliptic operators with drift. Calculus of Variations and Partial Differential Equations." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM019.
Повний текст джерелаАнотація:
Dans cette thèse, on étudie l'existence et la régularité des formes optimales pour certains problèmes d'optimisation spectrale qui font intervenir un opérateur elliptique avec condition de Dirichlet.On s'intéresse d'abord au problème de la minimisation de la valeur propre principale d'un opérateur avec un terme de transport borné.Que le terme de transport soit fixé ou non, ce problème admet une solution parmi les quasi-ouverts, et si le terme de transport est en outre le gradient d'une fonction Lipschitzienne, alors les solutions sont des ouverts localement de classe C^{1,alpha} en dehors de points exceptionnels.On étudie ensuite en dimension deux la régularité des solutions à un problème d'optimisation à plusieurs phases pour la première valeur propre du Laplacien de Dirichlet.Enfin, on s'intéresse aux ensembles optimaux pour la somme des k premières valeurs propres d'un opérateur elliptique sous forme divergence. On montre que les k premières fonctions propres sur un ensemble optimal sont lipschitziennes de sorte que les ensembles optimaux sont ouverts, et on étudie ensuite la régularité de la frontière des ensembles optimauxIn this thesis, we study the existence and the regularity of optimal shapes for some spectral optimization problems involving an elliptic operator with Dirichlet boundary condition.First of all, we consider the problem of minimizing the principal eigenvalue of an operator with bounded drift under inclusion and volume constraints.Whether the drift is fixed or not, this problem admits solutions among the class of quasi-open sets, and if the drift is furthermore the gradient of a Lipschitz continuous function, then the solutions are open sets and C^{1,alpha}-regular except on a set of exceptional points.Next, we study in dimension two the regularity of the solutions to a multi-phase optimization problem for the first eigenvalue of the Dirichlet Laplacian.Finally, we focus on the optimal sets for the sum of the first k eigenvalues of an operator in divergence form. We prove that the first k eigenfunctions on an optimal set are Lipschitz continuous so that the optimal sets are open sets, and we then study the regularity of the boundary of the optimal sets
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Aleksanyan, Hayk. "Periodic homogenization of Dirichlet problem for divergence type elliptic operators." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15958.
Повний текст джерелаАнотація:
The thesis studies homogenization of Dirichlet boundary value problems for divergence type elliptic operators, and the associated boundary layer issues. This type of problems for operators with periodically oscillating coeffcients, and fixed boundary data are by now a classical topic largely due to the celebrated work by Avellaneda and Lin from late 80's. The case when the operator and the Dirichlet boundary data exhibit periodic oscillations simultaneously was a longstanding open problem, and a progress in this direction has been achieved only very recently, in 2012, by Gerard-Varet and Masmoudi who proved a homogenization result for the simultaneously oscillating case with an algebraic rate of convergence in L2. Aimed at understanding the homogenization process of oscillating boundary data, in the first part of the thesis we introduce and develop Fourier-analytic ideas into the study of homogenization of Dirichlet boundary value problems for elliptic operators in divergence form. In smooth and bounded domains, for fixed operator and periodically oscillating boundary data we prove pointwise, as well as Lp convergence results the homogenization problem. We then investigate the optimality (sharpness) of our Lp upper bounds. Next, for the above mentioned simultaneously oscillating problem studied by Gerard-Varet and Masmoudi, we establish optimal Lp bounds for homogenization in some class of operators. For domains with non smooth boundary, we study similar boundary value homogenization problems for scalar equations set in convex polygonal domains. In the vein of smooth boundaries, here as well for problems with fixed operator and oscillating Dirichlet data we prove pointwise, and Lp convergence results, and study the optimality of our Lp bounds. Although the statements are somewhat similar with the smooth setting, challenges for this case are completely different due to a radical change in the geometry of the domain. The second part of the work is concerned with the analysis of boundary layers arising in periodic homogenization. A key difficulty toward the homogenization of Dirichlet problem for elliptic systems in divergence form with periodically oscillating coefficients and boundary condition lies in identification of the limiting Dirichlet data corresponding to the effective problem. This question has been addressed in the aforementioned work by Gerard-Varet and Masmoudi on the way of proving their main homogenization result. Despite the progress in this direction, some very basic questions remain unanswered, for instance the regularity of this effective data on the boundary. This issue is directly linked with the up to the boundary regularity of homogenized solutions, but perhaps more importantly has a potential to cast light on the homogenization process. We initiate the study of this regularity problem, and prove certain Lipschitz continuity result. The work also comprises a study on asymptotic behaviour of solutions to boundary layer systems set in halfspaces. By a new construction we show that depending on the normal direction of the hyperplane, convergence of the solutions toward their tails far away from the boundaries can be arbitrarily slow. This last result, combined with the previous studies gives an almost complete picture of the situation.
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Martinez, Miguel. "INTERPRETATIONS PROBABILISTES D'OPERATEURS SOUS FORME DIVERGENCE ET ANALYSE DE METHODES NUMERIQUES ASSOCIEES." Phd thesis, Université de Provence - Aix-Marseille I, 2004. http://tel.archives-ouvertes.fr/tel-00006472.
Повний текст джерелаАнотація:
L'analyse et l'approximation de solutions des Equations Differentielles Stochastiques (E.D.S.) possédant des coefficients discontinus est un sujet qui n'a pas ete traité de facon pleinement satisfaisante. Ce problème devient particulierement motivant lorsque l'on cherche à approcher, par des méthodes de Monte-Carlo, les solutions de certaines Equations aux Derivées Partielles (E.D.P) qui font également intervenir des coefficients discontinus. C'est par exemple le cas, bien connu en Physique, des E.D.P.s avec opérateur sous forme divergence (O.F.D.) dont les coefficients sont discontinus et que nous étudions dans ce mémoire : les discontinuités traduisent alors les irrégularités du milieu dans lequel évolue le système étudié. Cette thèse propose de nouveaux résultats pour l'analyse et l'approximation de solutions des E.D.S. qui sont reliées à un O.F.D. dont les coefficients sont discontinus. Les aspects statistiques des modèles en jeu sont également étudiés.
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Perrin, Nicolas. "Méthodes stochastiques en dynamique moléculaire." Thesis, Nice, 2013. http://www.theses.fr/2013NICE4011/document.
Повний текст джерелаАнотація:
Cette thèse présente deux sujets de recherche indépendants concernant l'application de méthodes stochastiques à des problèmes issus de la dynamique moléculaire. Dans la première partie, nous présentons des travaux liés à l'interprétation probabiliste de l'équation de Poisson-Boltzmann qui intervient dans la description du potentiel électrostatique d'un système moléculaire. Après avoir introduit l'équation de Poisson-Boltzmann et les principaux outils mathématiques utilisés, nous nous intéressons à l'équation linéaire parabolique de Poisson-Boltzmann. Avant d’énoncer le résultat principal de la thèse, nous étendons des résultats d'existence et unicité des équations différentielles stochastiques rétrogrades. Nous donnons ensuite une interprétation probabiliste de l'équation non-linéaire de Poisson-Boltzmann sous la forme de la solution d'une équation différentielle stochastique rétrograde. Enfin, dans une seconde partie prospective, nous commençons l'étude d'une méthode proposée par Paul Malliavin de détection des variables lentes et rapides d'une dynamique moléculaireThis thesis presents two independent research topics. Both are related to the application of stochastic problems to molecular dynamics. In the first part, we present a work related to the probabilistic interpretation of the Poisson-Boltzmann equation. This equation describes the electrostatic potential of a molecular system. After an introduction to the Poisson-Boltzmann equation, we focus on the parabolic and linear equation. After extending an existence and uniqueness result for backward stochastic differential equations, we establish a probabilistic interpretation of the nonlinear Poisson-Boltzmann equation with backward stochastic differential equations. Finally, in a more prospective second part, we initiate a study of a slow and fast variables detection method due to Paul Malliavin
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Battaglia, Erika. "Famiglie Normali per Operatori Sub-ellittici e i Teoremi di Montel e Koebe." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5712/.
Повний текст джерелаАнотація:
Scopo della tesi è di estendere un celebre teorema di Montel, sulle famiglie normali di funzioni olomorfe, all'ambiente sub-ellittico delle famiglie di soluzioni u dell'equazione Lu=0, dove L appartiene ad un'ampia classe di operatori differenziali alle derivate parziali reali del secondo ordine in forma di divergenza, comprendente i sub-Laplaciani sui gruppi di Carnot, i Laplaciani sub-ellittici su arbitrari gruppi di Lie, oltre all'operatore di Laplace-Beltrami su varietà di Riemann. A questo scopo, forniremo una versione sub-ellittica di un altro notevole risultato, dovuto a Koebe, che caratterizza le funzioni armoniche come punti fissi di opportuni operatori integrali di media con nuclei non banali. Sarà fornito anche un adeguato sostituto della formula integrale di Cauchy.
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QAFSAOUI, MAHMOUD. "Operateurs elliptiques d'ordre superieur sous forme divergence a coefficients peu reguliers, estimations gaussiennes de leurs noyaux de la chaleur et applications." Amiens, 1999. http://www.theses.fr/1999AMIE0102.
Повний текст джерелаАнотація:
L'objet de cette these est l'etude d'une classe d'operateurs elliptiques homogenes d'ordre superieur sous forme divergence, sur r n, a coefficients complexes, independants du temps et peu reguliers. Nous nous interessons tout particulierement a la taille et a la regularite du noyau du semi-groupe engendre par un tel operateur. Ces operateurs sont de la forme l 0 = $$ | | = m , | | = m (1) md (a d ), ou a , l (r n,c) independants du temps. On suppose en outre que ces operateurs sont elliptiques au sens de l'inegalite de garding forte : il existe une constante 0 > 0 telle que pour tout u , h m(r n), re $$. Davies a montre que le noyau k t(x,y) du semi-groupe e - t l o a toujours une estimation gaussienne superieure lorsque n < 2m. Auscher et tchamitchian ont etendu ce resultat au cas de l'egalite (i. E. N = 2m). Pour le cas restant, davies a donne des contre-exemples mettant en defaut la borne gaussienne. Le resultat principal de cette these est l'equivalence, lorsque n > 2m, entre les deux proprietes suivantes : (i) il existe une constante c 0 > 0 telle que pour tout r > 0, x 0,r n et pour toute solution faible v de l 0v = 0 sur b r(x 0), on ait pour tout 0 < r r, $$. (ii) il existe l , 0, 1,, m 1,v , 0,1 et des constantes c et a > 0 telles que, pour tout t > 0 et x,y,h , r n, on ait $$. La preuve de ((i) (ii)) repose en grande partie sur la methode de morrey-campanato. Celle-ci permet l'amelioration de la regularite elliptique dans les espaces qui portent le meme nom. Pour la partie ((ii) (i)), l'outil est une inegalite de type caccioppoli sous une condition d'ellipticite mois forte, a savoir l'ellipticite au sens de garding : pour tout $$, ou c est une constante dependant uniquement de $$ et de l'ellipticite. Une autre partie de la these est consacree aux exemples et aux applications de cette equivalence. Le point essentiel est qu'il est facile en general de verifier la condition (i), ce qui implique les estimations gaussiennes. Nous avons etudie en particulier le cas des coefficients uniformement continus ou dans vmo. Une generalisation des operateurs du type (a), ou a est une fonction non reguliere, a ete traitee. Nous avons etudie egalement des problemes lies a la theorie de la perturbation, notamment le probleme des perturbations multiplicatives et de la perturbation par des termes d'ordre inferieur.
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Alharbi, Abdulrahman. "On the Lp-Integrability of Green’s function for Elliptic Operators." Thesis, 2019. http://hdl.handle.net/10754/655516.
Повний текст джерелаАнотація:
In this thesis, we discuss some of the results that were proven by Fabes and Stroock in 1984. Our main purpose is to give a self-contained presentation of the proof of this results. The first result is on the existence of a “reverse H ̈older inequality” for the Green’s function. We utilize the work of Muckenhoupt on the reverse Ho ̈lder inequality and its connection to the A∞ class to establish a comparability property for the Green’s functions. Additionally, we discuss some of the underlying preliminaries. In that, we prove the Alexandrov-Bakelman-Pucci estimate, give a treatment to the Ap and A∞ classes of Muckenhoupt, and establish two intrinsic lemmas on the behavior of Green’s function.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.
Повний текст джерелаАнотація:
The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth.
A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded.
This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ.
Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
Книги з теми "Divergence form operators"
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Ryan, Jennifer D. Diversity and Divergence in the Improvisational Evolution of Literary Genres. Edited by Benjamin Piekut and George E. Lewis. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199892921.013.010.
Повний текст джерелаАнотація:
This chapter examines the evolution of three types of improvisation: a mode of literary composition, a method through which to advocate social change, and a theoretical practice. The theory that attempts to account for such improvisational strategies both simulates the material activity of improvisation and identifies the presence of improvisation itself as indicative of the first stage in an emerging literary genre. The chapter demonstrates the interrelated operations of these strategies through applied analyses of two texts, Mark Z. Danielewski’s experimental haunted-house novel House of Leaves (2000) and Edward P. Jones’s neo-slave narrative The Known World (2003). The argument locates improvisatory techniques in these two novels; examines the ways in which they diverge from preexisting theoretical trends in the fields of improvisation studies, postmodernist fiction, and the neo-slave narrative; and identifies these new improvisatory modes as signs of hitherto uncategorized literary forms.
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Prah Ruger, Jennifer. Divergent Perspectives in Global Health Governance. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199694631.003.0005.
Повний текст джерелаАнотація:
The global health governance (GHG) literature frames health variously as a matter of security and foreign policy, human rights, or global public good. Divergence among these perspectives has forestalled the development of a consensus vision for global health. Global health policy will differ according to the frame applied. Fundamentally, GHG today operates on a rational actor model, encompassing a continuum from the purely self-interest-maximizing position at one extreme to a more nuanced approach that takes others’ interests into account when making one’s own calculations. Even where humanitarian concerns are clearly and admirably at play, however, the problem of motivations remains. Often narrow self-interest is also at work, and actors obfuscate this behind altruistic motives.
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Isett, Philip. Transport-Elliptic Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0027.
Повний текст джерелаАнотація:
This chapter solves the underdetermined, elliptic equation ∂ⱼQsuperscript jl = Usuperscript l and Qsuperscript jl = Qsuperscript lj (Equation 1069) in order to eliminate the error term in the parametrix. For the proof of the Main Lemma, estimates for Q and the material derivative as well as its spatial derivatives are derived. The chapter finds a solution to Equation (1069) with good transport properties by solving it via a Transport equation obtained by commuting the divergence operator with the material derivative. It concludes by showing the solutions, spatial derivative estimates, and material derivative estimates for the Transport-Elliptic equation, as well as cutting off the solution to the Transport-Elliptic equation.
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Mann, Peter. Legendre Transforms. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0033.
Повний текст джерелаАнотація:
This chapter introduces vector calculus to the reader from the very basics to a level appropriate for studying classical mechanics. However, it provides only the necessary vector calculus required to understand some of the operations perform in the text and perhaps support self-learning in more advanced topics, so the analysis is not be definitive. The chapter begins by examining the axioms of vector algebra, vector multiplication and vector differentiation, and then tackles the gradient, divergence and curl and other elements of vector integration. Topics discussed include contour integrals, the continuity equation, the Kronecker delta and the Levi-Civita symbol. Particular care is taken to explain every mathematical relation used in the main text, leaving no stone unturned!
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Sabino, Cassese. 3 The Administrative State in Europe. Oxford University Press, 2017. http://dx.doi.org/10.1093/law/9780198726401.003.0003.
Повний текст джерелаАнотація:
This chapter examines the ‘administrative state’ and its particular expressions in Europe. Coined in 1948 by the American political scientist Dwight Waldo, the administrative state stands for the exclusive link established between the state and administration. Administrative systems and administrative law were shaped according to the needs of the various different state models; as each nation-state developed along divergent lines, administrative systems diverged too. Therefore, public administrations and their systems of administrative law were seen as final enclaves of nationalism. Each system is said to be unique to the history and traditions of a specific society, and designed expressly for the society within which it operates. As such, the chapter makes a comparison between certain divergent models of state, before delving into other trends of statehood, and finally, it examines the impact of globalisation and the European Union on the administrative state.
Частини книг з теми "Divergence form operators"
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Stroock, Daniel W. "Diffusion semigroups corresponding to uniformly elliptic divergence form operators." In Lecture Notes in Mathematics, 316–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0084145.
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Ghergu, Marius, and Vicenţiu D. Rǎdulescu. "Liouville Type Theorems for Elliptic Operators in Divergence Form." In Springer Monographs in Mathematics, 19–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22664-9_2.
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Hieber, Matthias. "H∞-Calculus for Second Order Elliptic Operators in Divergence Form." In Partial Differential Operators and Mathematical Physics, 185–89. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9092-2_20.
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Saloff-Coste, L. "Parabolic Harnack inequality for divergence form second order differential operators." In Potential Theory and Degenerate Partial Differential Operators, 429–67. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0085-4_9.
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McOwen, Robert. "On Elliptic Operators in Nondivergence and in Double Divergence Form." In Analysis, Partial Differential Equations and Applications, 159–69. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9898-9_13.
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Talay, Denis. "On Probabilistic Analytical and Numerical Approaches for Divergence Form Operators with Discontinuous Coefficients." In Advances in Numerical Simulation in Physics and Engineering, 267–96. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02839-2_7.
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Chorwadwala, Anisa M. H., and Souvik Roy. "Placement of an Obstacle for Optimizing the Fundamental Eigenvalue of Divergence Form Elliptic Operators." In Advances in Mechanics and Mathematics, 157–83. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-90051-9_6.
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Kaliyeva, Kulyash. "Energy Conservation Law for the Turbulent Motion in the Free Atmosphere." In Advances in Systems Analysis, Software Engineering, and High Performance Computing, 105–38. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-8823-0.ch003.
Повний текст джерелаАнотація:
This chapter presents convergent-divergent flow in the free atmosphere which is governed by the three dimensional Navier-Stokes equations and deals with the fundamental problem of fluid dynamics. Considering air movement under influence divergence and rotation were found the true dependencies between the velocity vector and the pressure distribution. Following the classical procedure by using rotor operator and a well-known formula of vector analysis were obtained the second kind nonlinear Volterra-Fredholm integral equations in a matrix form which contained only three components of the velocity vector. According to the theory of the matrix operators were defined the velocity components by the successive approximation method. According to the obtained balance equation for the pressure distribution were defined significant properties of the transient convergent-divergent flow which provide a description of the constitutive relationships between three physical quantities: the velocity vector, the external and internal forces, the pressure distribution.
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Steane, Andrew M. "Further useful ideas." In Relativity Made Relatively Easy Volume 2, 133–43. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0011.
Повний текст джерелаАнотація:
The chapter discusses several further aspects of the physics and mathematics that prove very useful in practice. First we define 4-velocity, 4-momentum and 4-acceleration. Then we introduce the tetrad and show how it can be used to relate a given 4-momentum to the energy and momentum observed in a LIF (local inertial frame). Then we define covariant version of the vector operators div, grad, curl, and obtain simplified expressions for the divergence of a vector and an antisymmetric tensor. The generalized Gauss divergence theorem is then presented.
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Kellerbauer, Manuel. "Chapter 3 Approximation of Laws." In The EU Treaties and the Charter of Fundamental Rights. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198759393.003.211.
Повний текст джерелаАнотація:
Divergences between MS’ rules can create regulatory requirements that hinder the free movement of goods, persons, services, and capital and create unequal competitive conditions for economic operators in the internal market. Removing such hindrances and imbalances is the rationale of the Treaty provisions on the ‘Approximation of Laws’ laid down in Chapter 3 of Title VII TFEU. The provisions are thus meant to contribute to the aim of establishing an internal market set out in the first sentence of Article 3(3) TEU.
Тези доповідей конференцій з теми "Divergence form operators"
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Singh, Kriti, Fahd Siddiqui, Daniel Braga, Mohammadreza Kamyab, Curtis Cheatham, and Brian Harclerode. "ROP Optimization using a Hybrid Machine Learning and Physics-Based Multivariate Objective Function with Real-Time Vibration and Stick-Slip Filters." In IADC/SPE International Drilling Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/208751-ms.
Повний текст джерелаАнотація:
Abstract This paper presents a multi-dimensional optimization engine for optimizing real-time drilling operations by increasing Rate of Penetration (ROP) while reducing Non-Productive Time (NPT) events such as vibration, stick slip, and directional divergence. A key breakthrough here is the development of the vibration health monitoring tool that tracks and filters out recent drilling parameters responsible for high vibration and monitors the overall BHA health. Measurement While Drilling (MWD) or Rotary Steerable (RSS) providers often provide vibration data but are rarely used in real-time decision making by operators due to the lack of a standardized workflow and technology. A vibration monitoring tool is developed that consumes real-time data from downhole MWD/RSS providers for each axis - axial, lateral, and torsional. A database is created for common MWD/RSS tools containing information about moderate and severe thresholds for shock (G) and average (GRMS) values. The algorithm categorizes vibration data into "low", "medium" or "high". The overall tool health is computed by tracking the cumulative count of the shock values and time corresponding to the moderate and severe categories and comparing against the downhole provider’s specifications. A multivariate objective function is used to find the optimal Differential Pressure (DPRES) and Top Drive RPM (TDRPM) values from a parameter sweep within user-specified limits or default tool limits. The objective function consists of three components - ROP, downhole MSE, and rotational tendency. A machine-learning model is used to predict ROP as a function of DPRES and TDRPM values, whereas standard drilling equations are used for calculating MSE and rotational tendency. After eliminating the parameters correlated with high vibration or stick-slip instances in the previous 1,000 ft, the optimization engine recommends DPRES and TDRPM values that correspond to the minimum value of the objective function. The recommendations from the multivariate objective function are presented in the form of a drilling advisory system. The advisory system was tested live on a drilling rig in collaboration with an operator. The results from the field test are presented in the paper.
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Zhang, Jun, Emmanuelle Merced, Nelson Sepúlveda, and Xiaobo Tan. "Optimal Compression of a Generalized Prandtl-Ishlinskii Operator in Hysteresis Modeling." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3969.
Повний текст джерелаАнотація:
The Prandtl-Ishlinskii (PI) model is a popular hysteresis model that has been widely applied in smart materials-based systems. Recently, a generalized PI model is formulated that is capable of characterizing asymmetric, saturated hysteresis. The fidelity of the model hinges on accurate representation of envelope functions, play operator radii, and corresponding weights. For a given number of play operators, existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes based on entropy and relative entropy (Kullback-Leibler divergence) for optimal compression of a generalized PI model are proposed to best represent the original hysteresis model subject to a given complexity constraint, i.e., the number of play operators. The overall compression performance is expressed as a cost function, and is optimized using dynamic programming. The proposed compression schemes are applied to the modeling of the asymmetric hysteresis between resistance and temperature of a vanadium dioxide (VO2) film, and the effectiveness is further demonstrated in a model verification experiment. In particular, under the same complexity constraint, an entropy-based compression scheme and a Kullback-Leibler divergence-based compression scheme result in modeling errors around 37% and 48%, respectively, of that under a uniform compression scheme.
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Hiremath, Nandeesh, Dhwanil Shukla, Emily Hale, Taylor Sparacello, and Narayanan Komerath. "Slung Load Amplification Detector." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70252.
Повний текст джерелаАнотація:
Externally slung loads and their mission applications are becoming more common on human and autonomously piloted air vehicles. Flight speed is often limited not by the performance envelope but by the danger of divergent load oscillations. Certifying this limiting speed for every load-vehicle combination, is a huge barrier to operations. The conservatism dictated by this uncertainty may itself be life-threatening in critical applications. Computing the dynamics of slung loads for a specific load/vehicle combination has been hindered by lack of knowledge on bluffbody aeromechanics. The prevailing top-down approach is to incorporate slung load aeromechanics calculations into large comprehensive aeromechanics codes for rotorcraft. We argue for a bottom-up approach. This allows on-the-fly system identification and dynamics simulation. The Slung Load Amplification Detector (SLAD) concept provides an on-board safety system to predict, detect, avoid and alleviate divergent oscillations. SLAD is based on a knowledge base derived from wind tunnel data and simulation results including canonical geometries, as well as practical shapes. Validation of simulation results against two practical test cases lends confidence. SLAD allows reliable distinction between pseudo and absolute divergence, permitting an increase of as much as 50% speed in safe flight speed, and guidance on active alleviation of oscillations.
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Kuhlman, Luke Ray, Travis Gideon Thomas, John Carlton Pursell, Noah Anderson Buck, and Kayla Renee Scherer. "Optimizing Drillouts Using Live TFA." In SPE/ICoTA Well Intervention Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/208999-ms.
Повний текст джерелаАнотація:
Abstract This paper examines how real-time force monitoring keeps operations on path by decreasing operational failures (such as stuck or parted pipe), reducing non-productive time (NPT), and increasing drillout efficiency (hour/plug). Utilizing interactive tubing force analysis (TFA) models with real-time data overlays provides coiled tubing operators with the data needed to reduce stuck pipe events, increase drillout efficiencies, and decrease mechanical failures (both on the surface and downhole). The key to optimizing efficiencies is maintaining consistent data that can be analyzed with the TFA. One current challenge is that analyzed data can only affect future operations if engineering controls are executed in the field. By using the interactive TFA and real-time operational data synchronously, users can positively impact their current and future operations by using data-driven decisions instead of predetermined processes. By implementing a cloud-based application in conjunction with software that acquires and stores field data, one field-based end user recognized real-time divergence from the modeled parameters. This is a key indicator of potential failures. The application allows for on-the-fly procedural corrections (such as stop and circulate) to alleviate operational risk for stuck pipe instances. In one case, the application indicated forewarned risk while running in hole that would have saved the service company and Exploration and Production (E&P) company more than 48 hours in NPT. Having cloud-connected software with pre-defined warnings provides the field, management, and engineering staff with real-time access to the same data, allowing quick and inclusive decisions to be made prior to potential failures. Without this implementation, only post-job analysis would have revealed the divergence of the field data from the predictive data. The live feed of operational data provided by the application prevented stuck pipe scenarios when well conditions changed. Personnel could not have made this prediction if the coiled tubing (CT) operator was relying solely on the pre-defined job scope and pre-job planning procedures. This paper expands on previous documentation where the TFA and real-time data were manually overlaid to significantly reduce an E&P's risk. This novel refinement of technology coalesces essential information to create a holistic view of operations thereby preventing issues rather than analyzing them after the fact.
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Falabretti, D., M. Delfanti, M. Merlo, J. M. Zaldivar, and F. Strozzi. "Divergence operator for the stability assessment of a microgrid weakly connected to the power system." In 2010 14th International Conference on Harmonics and Quality of Power (ICHQP). IEEE, 2010. http://dx.doi.org/10.1109/ichqp.2010.5625449.
Повний текст джерела
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Pradeep, A. M., Bhaskar Roy, V. Vaibhav, and D. Srinuvasu. "Study of Gas Turbine Exhaust Diffuser Performance and Its Enhancement by Shape Modifications." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22088.
Повний текст джерелаАнотація:
In this paper, results of studies on typical gas turbine exhaust diffuser geometry have been reported. This diffuser consists of an annular diffuser followed by a conical diffuser. The annular diffuser has 5 radial, backward swept struts. The studies were carried out at a Reynolds number of 7.7 × 105 based on the diffuser inlet diameter (hydraulic). Two inflow boundary conditions corresponding to (i) full load (low swirl) and (ii) part load (high swirl) operations of a typical gas turbine exit were separately simulated. The performance of the diffuser was assessed in terms of total pressure loss and static pressure recovery coefficient along the diffuser. It was observed that the baseline diffuser geometry had substantial losses owing to separation of the boundary layer, beginning as early as in the annular diffuser and continuing all the way up to the exit of the conical diffuser. The performance was found to worsen with higher inlet swirl. It was observed that the divergence angle in the annular part of the diffuser plays an important role in the initiation of flow separation. Interaction of inlet flow swirl with the struts also initiates considerable asymmetry in the flow pattern within the conical diffuser. Based on observations from the baseline geometry, several new annular diffuser geometries with different divergence angles and shapes were numerically studied. The shroud shapes were manipulated at specific locations like the plane of the strut leading edge, maximum airfoil thickness and the trailing edge of the struts. Significant performance improvements were observed in these simulated diffuser configurations. Two such annular diffuser geometries have been discussed in detail in this paper.
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Sou, Akira, Kosuke Hayashi, and Tsuyoshi Nakajima. "Evaluation of Volume Tracking Algorithms for Gas-Liquid Two-Phase Flows." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45164.
Повний текст джерелаАнотація:
Qualitative and quantitative evaluations of volume tracking algorithms such as DA, FLAIR, MARS, CIP and VTEMC were conducted. Wide variety of two-dimensional test problems including (1) a circle transported in simple translation and rotational field, (2) a bubble rising in 45° slanted gravity field, (3) zigzag motion of a bubble in a vertical channel, and (4) a bubble rising in a stagnant liquid in axissymmetric cylindrical coordinate were chosen in the present study. As a result of these tests, the superiority of the cell-centered piecewise linear algorithm with the divergence treatment in operator split and especially with embedded micro cells was confirmed. Applicability of these algorithms to three-dimensional problems has to be examined in the future works.
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Debnath, Pinku, and K. M. Pandey. "Performance Investigation on Single Phase Pulse Detonation Engine Using Computational Fluid Dynamics." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-66274.
Повний текст джерелаАнотація:
Pulse detonation engines (PDEs) are new concept propulsion technologies and unsteady propulsion system that operates cyclically and typically consists of four stages, filling of fuel/air mixture, combustion, blow down and purging. Out of these four processes, combustion is the most crucial one since it produces reliable and repeatable detonation wave. Detonation is a supersonic combustion process which is essentially a shock front driven by the energy release from the reaction zone in the flow right behind it. It is based on supersonic mode of combustion and causes rapid burning of a fuel-air mixture, typically tens of thousands of times faster than in a flame, that utilize repetitive detonations to produce thrust or power. PDE offers the potential to provide increased performance while simultaneously reducing engine weight, cost, and complexity relative to conventional propulsion systems currently in service. It has the potential to drastically reduce the cost of orbit transfer vehicle system as well as space vehicle attitude control system and can be used for wide range of military, civil and commercial applications. Due to its obvious advantages, worldwide attention has been paid to the scientific and technical issues concerning PDE. The present study deals with the convergence and divergence nozzle effects on specific thrust and pressure of Pulse Detonation Engine (PDE) using computational fluid dynamics (CFD). Pulse Detonation Engine having 88.3cm length and 9.5cm diameter combustion chamber, convergence nozzle, detonation tube and divergence nozzle were design in Gambit 2.3.16. FLUENT 6.3 predict the flow physics of pressure and specific thrust (Fs), increase in divergence nozzle compared to convergence nozzle and specific thrust of detonation tube was changed with the change of flight Mach number. A three dimension computational unstructured grid was developed which gives the best meshing accuracy as well as computational results. RNG k-ε turbulence model was used for the mass flow rate, pressure and velocity contours analysis with standard wall function.
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Choquette, Jeremie J., Sylvain Cornu, Mohamed ElSeify, and Raymond Karé. "Understanding Pipeline Strain Conditions: Case Studies Between ILI Axial and ILI Bending Measurement Techniques." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78577.
Повний текст джерелаАнотація:
In-Line inspection (ILI) tools consisting of combined sensor technologies provide a unique opportunity for operators to understand the conditions of pipelines. There is also an additional opportunity to contrast and validate individual sensing techniques against each other when their functionalities and purposes overlap. By using multi-technologies ILI measurements for strain, a pipeline operator can gain further insight into the pipeline strain behavior at any point along the length of the inspection. This paper establishes the relationship between ILI axial strain measurement tool data and conventional geometric strain data obtained from inertial measurement unit (IMU) based on data collected during in-service inspection of a 12″ liquid pipeline. Within any pipeline section, the tool configuration with circumferentially spaced strain sensors allows the use of appropriate analysis techniques to decompose the longitudinal strain into its primary components (axial, bending and out of roundness). The axial strain measurement tool sensing system provides an indirect measurement of bending strain that can be compared to the geometric measurement of bending strain determined from the pipeline trajectory as determined from the IMU analysis. Flexural bending strain resulting from horizontal directional drilling (HDD) is investigated in this paper. Convergences and divergences between the measurement techniques are presented. Data available from different strain technologies mounted on ILI tools offers an opportunity to conduct a comparative study and to provide a better understanding of a pipeline’s strain condition. This paper will present the framework for understanding the different strain measurement technologies and an investigation into the pipeline prior strain history (effects from fabrication, hydrostatic testing and external loads) and their corresponding impact on the material state at the time of inspection.
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Chanchlani, Kuldeep, Ranjit Gogoi, Sukumar Awasthi, Deepak Gunwant, and Nikhil Khanduja. "Divergence of Dynamometer Card Analysis from Actual Field Results at Light and Heavy Oil Fields of Mehsana." In ADIPEC. SPE, 2022. http://dx.doi.org/10.2118/211547-ms.
Повний текст джерелаАнотація:
Abstract The performance of rod pumped wells are analyzed based on routine monitoring methods of echo meter and dynamometer analysis. There are 1080 sucker rod pumps installed in various fields of Mehsana. Rod pumps fail due to rod-tubing wear and aggressive fluid-reservoir conditions. Diagnostic studies are carried out promptly to predict the cause of rod pump failure. Circulation and crane troubleshooting jobs are taken post-diagnostic jobs to confirm the failure mechanism. This paper will discuss prominent mechanisms of rod pump failure, the use of dynamometer cards to track failure, and troubleshooting jobs to prevent failure. In heavy oil fields, when the pump ceases to flow, the acquired dynamometer card showed a standing valve or traveling valve or both choked up. During troubleshooting by crane, polished rod load depicted sucker rod unscrewing or parting. The reasons for the divergence of dynamometer cards from troubleshooting jobs are the variation of fluid load due to fluid characteristics. The accessed dynamometer card indicates gas interference or gas lock despite low casing head pressure in light oil fields. During circulation job execution, the initial pumping pressure of the surface pump is quite high, which indicated obstruction across the subsurface pump. The obstruction causes no freefall of polished rod, requiring servicing by workover rig. During the pullout of the subsurface pump by workover rig, observations included downhole screen choked, gravel pack failure, wax deposition on sucker rods subsurface pump, and tailpipes choked with fine sand. Solids incursion in light oil fields and rod unscrew in heavy oil fields are difficult to differentiate on basis of dynamometer cards. This paper will be fruitful to operators in identifying the cases, where the dynamometer card interpretation and analysis deviate from field practices.
Звіти організацій з теми "Divergence form operators"
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Kira, Beatriz, Rutendo Tavengerwei, and Valary Mumbo. Points à examiner à l'approche des négociations de Phase II de la ZLECAf: enjeux de la politique commerciale numérique dans quatre pays d'Afrique subsaharienne. Digital Pathways at Oxford, March 2022. http://dx.doi.org/10.35489/bsg-dp-wp_2022/01.
Повний текст джерелаАнотація:
Realities such as the COVID-19 pandemic have expedited the move to online operations, highlighting the undeniable fact that the world is continuing to go digital. This emphasises the need for policymakers to regulate in a manner that allows them to harness digital trade benefits while also avoiding associated risk. However, given that digital trade remains unco-ordinated globally, with countries adopting different approaches to policy issues, national regulatory divergence on the matter continues, placing limits on the benefits that countries can obtain from digital trade. Given these disparities, ahead of the African Continental Free Trade Area (AfCFTA) Phase II Negotiations, African countries have been considering the best way to harmonise regulations on issues related to digital trade. To do this effectively, AfCFTA members need to identify where divergencies exist in their domestic regulatory systems. This will allow AfCFTA members to determine where harmonisation is possible, as well as what is needed to achieve such harmonisation. This report analyses the domestic regulations and policies of four focus countries – South Africa, Nigeria, Kenya and Senegal – comparing their regulatory approaches to five policy issues: i) regulation of online transactions; ii) cross-border data flows, data localisation, and personal data protection; iii) access to source code and technology transfer; iv) intermediary liability; and v) customs duties on electronic transmissions. The study highlights where divergencies exist in adopted approaches, indicating the need for the four countries – and AfCFTA members in general – to carefully consider the implications of the divergences, and determine where it is possible and beneficial to harmonise approaches. This was intended to encourage AfCFTA member states to take ownership of these issues and reflect on the reforms needed. As seen in Table 1 below, the study shows that the four countries diverge on most of the five policy issues. There are differences in how all four countries regulate online transactions – that is, e-signatures and online consumer protection. Nigeria was the only country out of the four to recognise all types of e-signatures as legally equivalent. Kenya and Senegal only recognise specific e-signatures, which are either issued or validated by a recognised institution, while South Africa adopts a mixed approach, where it recognises all e-signatures as legally valid, but provides higher evidentiary weight to certain types of e-signatures. Only South Africa and Senegal have specific regulations relating to online consumer protection, while Nigeria and Kenya do not have any clear rules. With regards to cross border data flows, data localisation, and personal data protection, the study shows that all four focus countries have regulations that consist of elements borrowed from the European Union (EU) General Data Protection Regulation (GDPR). In particular, this was regarding the need for the data subject's consent, and also the adequacy requirement. Interestingly, the study also shows that South Africa, Kenya and Nigeria also adopt data localisation measures, although at different levels of strictness. South Africa’s data localisation laws are mostly imposed on data that is considered critical – which is then required to be processed within South African borders – while Nigeria requires all data to be processed and stored locally, using local servers. Kenya imposes data localisation measures that are mostly linked to its priority for data privacy. Out of the four focus countries, Senegal is the only country that does not impose any data localisation laws. Although the study shows that all four countries share a position on customs duties on electronic transmissions, it is also interesting to note that none of the four countries currently have domestic regulations or policies on the subject. The report concludes by highlighting that, as the AfCFTA Phase II Negotiations aim to arrive at harmonisation and to improve intra-African trade and international trade, AfCFTA members should reflect on their national policies and domestic regulations to determine where harmonisation is needed, and whether AfCFTA is the right platform for achieving this efficiently.
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Lewis, Dustin. Three Pathways to Secure Greater Respect for International Law concerning War Algorithms. Harvard Law School Program on International Law and Armed Conflict, 2020. http://dx.doi.org/10.54813/wwxn5790.
Повний текст джерелаАнотація:
Existing and emerging applications of artificial intelligence in armed conflicts and other systems reliant upon war algorithms and data span diverse areas. Natural persons may increasingly depend upon these technologies in decisions and activities related to killing combatants, destroying enemy installations, detaining adversaries, protecting civilians, undertaking missions at sea, conferring legal advice, and configuring logistics. In intergovernmental debates on autonomous weapons, a normative impasse appears to have emerged. Some countries assert that existing law suffices, while several others call for new rules. Meanwhile, the vast majority of efforts by States to address relevant systems focus by and large on weapons, means, and methods of warfare. Partly as a result, the broad spectrum of other far-reaching applications is rarely brought into view. One normatively grounded way to help identify and address relevant issues is to elaborate pathways that States, international organizations, non-state parties to armed conflict, and others may pursue to help secure greater respect for international law. In this commentary, I elaborate on three such pathways: forming and publicly expressing positions on key legal issues, taking measures relative to their own conduct, and taking steps relative to the behavior of others. None of these pathways is sufficient in itself, and there are no doubt many others that ought to be pursued. But each of the identified tracks is arguably necessary to ensure that international law is — or becomes — fit for purpose. By forming and publicly expressing positions on relevant legal issues, international actors may help clarify existing legal parameters, pinpoint salient enduring and emerging issues, and detect areas of convergence and divergence. Elaborating legal views may also help foster greater trust among current and potential adversaries. To be sure, in recent years, States have already fashioned hundreds of statements on autonomous weapons. Yet positions on other application areas are much more difficult to find. Further, forming and publicly expressing views on legal issues that span thematic and functional areas arguably may help States and others overcome the current normative stalemate on autonomous weapons. Doing so may also help identify — and allocate due attention and resources to — additional salient thematic and functional areas. Therefore, I raise a handful of cross-domain issues for consideration. These issues touch on things like exercising human agency, reposing legally mandated evaluative decisions in natural persons, and committing to engage only in scrutable conduct. International actors may also take measures relative to their own conduct. To help illustrate this pathway, I outline several such existing measures. In doing so, I invite readers to inventory and peruse these types of steps in order to assess whether the nature or character of increasingly complex socio-technical systems reliant upon war algorithms and data may warrant revitalized commitments or adjustments to existing measures — or, perhaps, development of new ones. I outline things like enacting legislation necessary to prosecute alleged perpetrators of grave breaches, making legal advisers available to the armed forces, and taking steps to prevent abuses of the emblem. Finally, international actors may take measures relative to the conduct of others. To help illustrate this pathway, I outline some of the existing steps that other States, international organizations, and non-state parties may take to help secure respect for the law by those undertaking the conduct. These measures may include things like addressing matters of legal compliance by exerting diplomatic pressure, resorting to penal sanctions to repress violations, conditioning or refusing arms transfers, and monitoring the fate of transferred detainees. Concerning military partnerships in particular, I highlight steps such as conditioning joint operations on a partner’s compliance with the law, planning operations jointly in order to prevent violations, and opting out of specific operations if there is an expectation that the operations would violate applicable law. Some themes and commitments cut across these three pathways. Arguably, respect for the law turns in no small part on whether natural persons can and will foresee, understand, administer, and trace the components, behaviors, and effects of relevant systems. It may be advisable, moreover, to institute ongoing cross-disciplinary education and training as well as the provision of sufficient technical facilities for all relevant actors, from commanders to legal advisers to prosecutors to judges. Further, it may be prudent to establish ongoing monitoring of others’ technical capabilities. Finally, it may be warranted for relevant international actors to pledge to engage, and to call upon others to engage, only in armed-conflict-related conduct that is sufficiently attributable, discernable, and scrutable.