Relevant bibliographies by topics / Weak maximum principle

Academic literature on the topic 'Weak maximum principle'

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Published: 9 March 2023

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Journal articles on the topic "Weak maximum principle"

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Hamada, Y., H. Kawai, and K. Kawana. "Weak scale from the maximum entropy principle." Progress of Theoretical and Experimental Physics 2015, no. 3 (March 19, 2015): 33B06–0. http://dx.doi.org/10.1093/ptep/ptv011.

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Hill, C. Denson, and Mauro Nacinovich. "Weak pseudoconcavity and the maximum modulus principle." Annali di Matematica Pura ed Applicata 182, no. 1 (April 2003): 103–12. http://dx.doi.org/10.1007/s10231-002-0059-8.

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Meyer, J. C., and D. J. Needham. "Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (July 8, 2014): 20140079. http://dx.doi.org/10.1098/rspa.2014.0079.

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In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.
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Šolín, Pavel, and Tomáš Vejchodský. "A weak discrete maximum principle for hp-FEM." Journal of Computational and Applied Mathematics 209, no. 1 (December 2007): 54–65. http://dx.doi.org/10.1016/j.cam.2006.10.028.

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Amendola, M. E., L. Rossi, and A. Vitolo. "Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains." Abstract and Applied Analysis 2008 (2008): 1–19. http://dx.doi.org/10.1155/2008/178534.

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We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.
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Stehlík, Petr, and Jonáš Volek. "Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/791304.

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We study reaction-diffusion equations with a general reaction functionfon one-dimensional lattices with continuous or discrete timeux′ (or Δtux)=k(ux-1-2ux+ux+1)+f(ux),x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time) exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
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Radice, Teresa, and Gabriella Zecca. "The Maximum principle of Alexandrov for very weak solutions." Journal of Differential Equations 256, no. 3 (February 2014): 1133–50. http://dx.doi.org/10.1016/j.jde.2013.10.010.

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de Pinho, Maria do Rosário, and Achim Ilchmann. "Weak maximum principle for optimal control problems with mixed constraints." Nonlinear Analysis: Theory, Methods & Applications 48, no. 8 (March 2002): 1179–96. http://dx.doi.org/10.1016/s0362-546x(01)00094-3.

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Zhuge, Jinping. "Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains." Journal of Functional Analysis 279, no. 12 (December 2020): 108786. http://dx.doi.org/10.1016/j.jfa.2020.108786.

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Huang, Xueping. "Stochastic incompleteness for graphs and weak Omori–Yau maximum principle." Journal of Mathematical Analysis and Applications 379, no. 2 (July 2011): 764–82. http://dx.doi.org/10.1016/j.jmaa.2011.02.009.

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Dissertations / Theses on the topic "Weak maximum principle"

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Daghighi, Abtin. "The Maximum Principle for Cauchy-Riemann Functions and Hypocomplexity." Licentiate thesis, Mittuniversitetet, Institutionen för tillämpad naturvetenskap och design, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-17701.

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This licentiate thesis contains results on the maximum principle forCauchy–Riemann functions (CR functions) on weakly 1-concave CRmanifolds and hypocomplexity of locally integrable structures. Themaximum principle does not hold true in general for smooth CR functions,and basic counterexamples can be constructed in the presenceof strictly pseudoconvex points. We prove a maximum principle forcontinuous CR functions on smooth weakly 1-concave CR submanifolds.Because weak 1-concavity is also necessary for the maximumprinciple, a consequence is that a smooth generic CR submanifold ofCn obeys the maximum principle for continuous CR functions if andonly if it is weakly 1-concave. The proof is then generalized to embeddedweakly p-concave CR submanifolds of p-complete complexmanifolds. The second part concerns hypocomplexity and hypoanalyticstructures. We give a generalization of a known result regardingautomatic smoothness of solutions to the homogeneous problemfor the tangential CR vector fields given local holomorphic extension.This generalization ensures that a given locally integrable structureis hypocomplex at the origin if and only if it does not allow solutionsnear the origin which cannot be represented by a smooth function nearthe origin.
Uppsatsen innehåller resultat om maximumprincipen för kontinuerligaCauchy–Riemann funktioner (CR-funktioner) på svagt 1-konkava CRmångfalder,samt hypokomplexitet för lokalt integrerbara strukturer.Maximumprincipen gäller inte generellt för släta CR funktioner ochmotexempel kan konstrueras givet strängt pseudokonvexa punkter.Vi bevisar en maximumprincip för kontinuerliga CR-funktioner påsläta inbäddade svagt 1-konkava CR-mångfalder. Eftersom svagt 1-konkavitet också är nödvändigt får vi som konsekvens att för slätageneriska inbäddade CR-mångfalder i Cn gäller att maximum-principenför kontinuerliga CR-funktioner håller om och endast om CR-mångfaldenär svagt 1-konkav. Vi generaliserar satsen till svagt p-konkava CRmångfalderi p-kompletta mångfalder. Den andra delen behandlarhypokomplexitet och hypoanalytiska strukturer. Vi generaliserar enkänd sats om automatisk släthet för lösningar till de tangentiella CRekvationerna,givet existensen av lokal holomorf utvidgning. Generaliseringenger att en lokalt integrerbar struktur är hypokomplex iorigo om och endast om den inte tillåter lösningar nära origo som inteär släta nära origo.

Forskning finansierad av Forskarskolan i Matematik och Beräkningsvetenskap (FMB), baserad i Uppsala.

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JÃnior, Elzon CÃzar Bezerra. "Um estudo sobre regularidade de soluÃÃes de equaÃÃes diferenciais parciais elÃpticas." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17187.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
O objetivo principal deste trabalho à o estudo da regularidade de soluÃÃes de equaÃÃes diferenciais parciais elÃpticas de segunda ordem, serÃo usadas tÃcnicas tais como o princÃpio do mÃximo, estimativas a priori e a desigualdade de Harnack. Por fim generalizamos o conceito de soluÃÃo buscando soluÃÃes no espaÃo de Sobolev W2,p(Ω).
The main objective of this work is to study the regularity of solutions of elliptic partial differential equations of second order, will be used techniques such as the principle of maximum estimates a priori and the unequal Harnack. Finally generalize the solution concept seeking solutions in the Sobolev space W2,p((Ω).
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Evans, Lawrence C. 1949. "A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/59784.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 125-126).
This thesis consists of two results. The first result is a strong maximum principle for certain parabolic systems of equations, which, for illustrative purposes, I consider as reaction-diffusion systems. Using the theory of viscosity solutions, I give a proof which extends the previous theorem to no longer require any regularity assumptions on the boundary of the convex set in which the system takes its values. The second result is an approximation scheme for reflected stochastic differential equations (SDE) of the Stratonovich type. This is a joint result with Professor Daniel W. Stroock. We show that the distribution of the solution to such a reflected SDE is the weak limit of the distribution of the solutions of the reflected SDEs one gets by replacing the driving Brownian motion by its N-dyadic linear interpolation. In particular, we can infer geometric properties of the solutions to a Stratonovich reflected SDE from those of the solutions to the approximating reflected SDE.
Ph.D.
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Daghighi, Abtin. "Regularity and uniqueness-related properties of solutions with respect to locally integrable structures." Doctoral thesis, Mittuniversitetet, Avdelningen för ämnesdidaktik och matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-21641.

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We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. We give a generalization of a known result regarding automatic smoothness of solutions to the homogeneous problem for the tangential CR vector fields given local holomorphic extension. This generalization ensures that a given locally integrable structure is hypocomplex at the origin if and only if it does not allow solutions near the origin which cannot be represented by a smooth function near the origin. We give a sufficient condition under which it holds true that if a smooth CR function f on a smooth generic embedded CR submanifold, M, of C^n, vanishes to infinite order along a C^infty-smooth curve  \gamma in M, then f vanishes on an M-neighborhood of \gamma. We prove a local maximum principle for certain locally integrable structures.

Funding  by FMB, based at Uppsala University.

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ANSELLI, ANDREA. "PHI-CURVATURES, HARMONIC-EINSTEIN MANIFOLDS AND EINSTEIN-TYPE STRUCTURES." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/703786.

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The aim of this thesis is to study the geometry of a Riemannian manifold M, with a special structure, called Einstein-type structure, depending on 3 real parameters, a smooth map phi into a target Riemannian manifold N, and a smooth function, called potential function, on M itself. We will occasionally let some of the parameters be smooth functions. The setting generalizes various previously studied situations:, Ricci solitons, almost Ricci-solitons, Ricci-harmonic solitons, quasi-Einstein manifolds and so on. By taking a constant potential function those structures reduces to harmonic-Einstein manifolds, that are a generalization of Einstein manifolds. The main ingredient of our analysis is the study of certain modified curvature tensors on M related to the map phi, called phi-curvatures, obtaining, for instance, their transformation laws under a conformal change of metric, and to develop a series of results for harmonic-Einstein manifolds that parallel those obtained for Einstein manifolds some times ago and also in the very recent literature. Einstein-type structures may be obtained, for some special values of the parameters involved, by a conformal deformation of a harmonic-Einstein manifold or even as the base of a warped product harmonic-Einstein manifold. The latter fact applies not only in the Riemannian but also in the Lorentzian setting and thus some Einstein-type structures are connected with solutions of the Einstein field equations, which are of particular interest in General Relativity. The main result of the thesis is the locally characterization, via a couple of integrability conditions and mild assumptions on the potential function, of Einstein-type structures with vanishing phi-Bach curvature (in the direction of the potential) as a warped product with harmonic-Einstein base and with an open real interval as fibre, extending in a very non trivial way a recent result for Bach flat Ricci solitons. Moreover the map phi depends only on the base of the warped product and not on the fibre . We also consider rigidity, triviality and non-existence results, both in the compact and non-compact cases. This is done via integral formulas and, in the non-compact case, via analytical tools, like the weak maximum principle and the classical results of Obata, Tashiro, Kanai.
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Books on the topic "Weak maximum principle"

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Edmunds, D. E., and W. D. Evans. Generalized Dirichlet and Neumann Boundary-Value Problems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0006.

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In this chapter, the generalized or weak interpretation of the Dirichlet and Neumann problems for general elliptic expressions is motivated and then the Lax–Milgram Theorem is used to set the problems in the framework of eigenvalue problems for operators acting in Hilbert space. Results on variational inequalities in Chapter IV are applied to establish Stampacchia’s weak maximum principle, and this leads to the notion of capacity.
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Book chapters on the topic "Weak maximum principle"

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Andrews, Ben, and Christopher Hopper. "The Weak Maximum Principle." In Lecture Notes in Mathematics, 115–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16286-2_7.

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Bianchini, Bruno, Luciano Mari, Patrizia Pucci, and Marco Rigoli. "Weak Maximum Principle and Liouville’s Property." In Geometric Analysis of Quasilinear Inequalities on Complete Manifolds, 131–63. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-62704-1_7.

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Capuzzo Dolcetta, Italo. "On the Weak Maximum Principle for Degenerate Elliptic Operators." In Trends in Control Theory and Partial Differential Equations, 89–104. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17949-6_5.

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Alías, Luis J., Paolo Mastrolia, and Marco Rigoli. "Sufficient Conditions for the Validity of the Weak Maximum Principle." In Springer Monographs in Mathematics, 203–70. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24337-5_4.

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Bonnard, Bernard, Monique Chyba, and Jérémy Rouot. "Weak Maximum Principle and Application to Swimming at Low Reynolds Number." In Geometric and Numerical Optimal Control, 11–62. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94791-4_2.

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Paneah, B. "Degenerated Elliptic Boundary Value Problems for Weak Coupled Systems. Solvability and Maximum Principle." In New Results in Operator Theory and Its Applications, 208–15. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8910-0_15.

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Chow, Bennett, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni. "Weak maximum principles for scalars, tensors, and systems." In Mathematical Surveys and Monographs, 1–65. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/144/01.

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Chow, Bennett, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni. "Weak and strong maximum principles on noncompact manifolds." In Mathematical Surveys and Monographs, 139–95. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/144/03.

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Mincsovics, Miklós E., and Tamás L. Horváth. "On the Differences of the Discrete Weak and Strong Maximum Principles for Elliptic Operators." In Large-Scale Scientific Computing, 614–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29843-1_70.

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Jacob, Maria, Cláudia Neves, and Danica Vukadinović Greetham. "Extreme Value Statistics." In Forecasting and Assessing Risk of Individual Electricity Peaks, 61–84. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28669-9_4.

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Abstract When studying peaks in electricity demand, we may be interested in understanding the risk of a certain large level for demand being exceeded. For example, there is potential interest in finding the probability that the electricity demand of a business or household exceeds the contractual limit. An alternative, yet in principle equivalent way, involves assessment of maximal needs for electricity over a certain period of time, like a day, a week or a season within a year. This would stem from the potential interested in quantifying the largest electricity consumption for a substation, household or business.
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Conference papers on the topic "Weak maximum principle"

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Suski, Damian, and Radoslaw Pytlak. "The weak maximum principle for hybrid systems." In 2016 24th Mediterranean Conference on Control and Automation (MED). IEEE, 2016. http://dx.doi.org/10.1109/med.2016.7535943.

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do Rosario de Pinho, Maria, M. Margarida A. Ferreira, and Fernando A. C. C. Fontes. "A weak maximum principle for control problems with state constraints." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7075917.

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Mohammad Saberali, S., and Hamidreza Amindavar. "Weak BPSK signal detection in the presence of cochannel interference with time varying characteristics using maximum entropy principle." In ICASSP 2008 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2008. http://dx.doi.org/10.1109/icassp.2008.4518329.

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Natalini, Gianni, and Enrico Sciubba. "Choice of the Pseudo-Optimal Configuration of a Cooled Gas-Turbine Blade Based on a Constrained Minimization of the Global Entropy Production Rate." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-509.

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The problem of determining the optimal configuration of a cooled gas-turbine blade is approached by an entropy minimization technique proposed in previous works by the same authors. The present paper describes the application of the same line of thought to a more complex (and realistic) pseudo-optimization procedure, in which the objective function is again the global entropy generation rate, but two integral constraints are added to the original formulation: the maximum blade temperature (weak constraint) and the overall enthalpy drop of the working fluid in the blade passage (strong constraint). The discontinuous optimization procedure is presented here in an application which resembles a trial-and-error technique, but can be rigorously and formally described and implemented [12]. As a “zero configuration”, a realistic 2-D geometry is considered, and the thermo-fluiddynamic field around it is computed via a standard finite-element code. Then, the entropy generation rates in the blade/fluid system are calculated, and the value of the overall enthalpy drop of the gas as well as the value and location of the maximum blade temperature are recorded. Keeping all other parameters fixed (in particular, maintaining the same cooling air flowrate), the geometry of the blade is slightly “perturbed”, by introducing arbitrary modifications in the blade profile, the number and location of cooling holes, etc. Again, the velocity and temperature fields are computed, and inlet conditions are tuned so that the overall enthalpy drop remains approximately constant and the blade maximum temperature does not exceed a certain assigned value. An “optimal” configuration is found, which is affected by the minimal entropy generation rate, while abiding to the imposed constraints. The procedure is demonstrated on a realistic blade profile, and is shown to produce a better performing cascade, at least in this 2-D simulation. The extension to 3-D problems is — in principle — straightforward (but see Section 3 for further comments).
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Ajimosun, Isaac, Emmanuel Okoro, and Olafuyi Olalekan. "Modeling the Critical Pressure Below which Sand Production will Occur based on Extended Mogi-Coulomb Failure Criterion." In SPE Nigeria Annual International Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/211953-ms.

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Abstract Sand production is of great concern in the Oil and Gas industry because of the economical, operational and technical problems that come with the phenomenon. Several sand prediction models are available in the literatures, but little or no consideration has been given to non-linearity of failure criterion used to develop the sand prediction models. Hence, a non-linear form of Mogi-Coulomb failure criterion was adopted in this research to develop a sand prediction model and simple sand prediction software. The most used rock failure criteria developed over the years for analyzing brittle failure of rocks is Mohr-Coulomb failure criterion. Published literatures have shown deficient in some field scenarios. Reason for these deficiencies was largely associated with the implicit assumption made in Mohr-Coulomb criterion that, the intermediate principal stress (σ2) has no influence on rock strength. So, this criterion is only based on the maximum and minimum principal stresses (σ1 and σ3) and only applicable to rock failure under conventional triaxial stress states (σ1 > σ2 = σ3). However, for a polyaxial stress state σ1 > σ2 > σ3), studies have proved that the intermediate principal stress (σ2) has a pronounced effect on rock strength and should not be neglected. Hence, Mohr–Coulomb criterion is relatively conservative in predicting sanding onset and therefore not very accurate for sand prediction models. As a result, this research presents a simple 3D sand prediction model based on Extended Mogi-Coulomb criterion that considered the non-linear relationships between most of field parameters when considering rock failure. The extended Mogi-Coulomb criterion is a nonlinear or parabolic form of Mogi-Coulomb criterion which accounts for the influence of the intermediate principal stress on rock strength and also very suitable for weak rocks. A fourth order polynomial equation was derived from first principle by combining both constitutive stress laws and the parabolic Mogi-Coulomb failure criterion. Then, Matlab software was used to develop a script and solution to the equation. And finally, the model solution was used to build simple graphic user interface software called ‘A.I Sand Predicton’ using Java programming language. Model verification was carried out by simulating several data available in the literatures and the solution was observed consistent with field observations. The solution of the critical wellbore pressure calculated using the "A.I Sand Predicton Software" was also found consistent with solution from Matlab and Mathematica softwares, respectively, which makes the software validated and reliable. Also, the case study shows that the critical wellbore pressure reduces as the strength parameters a, b, and c of the Extended Mogi-Coulomb criterion increases. Hence, the analytical model developed in this research using the extended Mogi-Coulomb criterion can reliably and accurately predict onset sand production.
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Xiang, Xu, Erik Svangstu, Øyvind Nedrebø, Bernt Jakobsen, Mathias Egeland Eidem, Per Norum Larsen, and Bernt Sørby. "Viscous Damping Modelling of Floating Bridge Pontoons With Heaving Skirt and its Impact on Bridge Girder Bending Moments." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61041.

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The current floating bridge concepts of Norwegian Public Roads Administration (Statens vegvesen, NPRA) use a flange shape part at the bottom part of the pontoons. The flange is in principle similar to the damping plates used in the offshore industry for SPAR type of structures. The project group initiated the flange part based on the requirement of extra added mass for tuning the bridge system Eigen-modes. Thus, the important modes can be shifted out of the main wave energy zone. The current study will focus on the damping effects of such structure. The damping effects on weak axis bending moment prediction is studied. The modelling of such damping is first proposed according to relevant literature based on both numerical and experimental studies. Since the reference studies were mainly focused on cylindrical structures, it is difficult to obtain an accurate estimation of the damping coefficient for the current bridge pontoon design, which contains a rectangular part between two half-cylindrical parts. In addition, the estimation of pontoon motions needs the input of damping coefficient, which means that the evaluation of damping coefficient is an iteration process. In order to include the uncertainties, a conservative value was adopted to represent the damping effect. The comparison of accounting for the damping effects or not has been given for all the bridge pontoons. The results show that the damping effects are important at the peaks of the responses; in addition, the reduction of the predicted maximum bending moments can be expected around 10–15 percent along different positions of the bridge. However, a further investigation also shows that viscous excitation would increase the bending moments slightly. The comparison also indicates the value of further investigating the effects by CFD or model test methods.
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Jeong, David Y., Yim H. Tang, and A. Benjamin Perlman. "Semi-Analytical Approach to Estimate Railroad Tank Car Shell Puncture." In 2011 Joint Rail Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/jrc2011-56028.

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This paper describes the development of engineering-based equations to estimate the puncture resistance of railroad tank cars under a generalized shell or side impact scenario. Resistance to puncture is considered in terms of puncture velocity, which is defined as the impact velocity at which puncture is expected to occur. In this context, puncture velocity represents a theoretical threshold limit. A given object striking the side of a tank car at an impact speed below the threshold velocity is not expected to penetrate the commodity-carrying tank. This definition for puncture velocity is similar to that for ballistic limit velocity, which is used to measure a target’s ability to withstand projectile impact in military applications [1]. The term “semi-analytical” is used to characterize the current approach in developing equations for shell puncture in order to distinguish the present work from the semi-empirical approach used previously to develop equations corresponding to head puncture. While several tests have been conducted to study tank car head puncture, only a limited number of tests have been performed to study tank car shell puncture. The semi-analytical approach employs a combination of three tactics to deal with the paucity of test data. The first tactic applies collision dynamics to derive an idealized relationship between impact speed and maximum force for a generalized tank car shell impact scenario. Specifically, the principle of conservation of energy is applied. The second tactic applies computational methods to simulate tank car shell impacts in greater detail. Specifically, finite element analysis is used to examine the force-deformation behavior of different tank car configurations under different loading conditions. Regression analyses are performed on the results of the detailed finite element results to develop best-fit curves to account for the effects of various factors such as shell thickness, tank diameter, internal pressure and indenter size. The third tactic is empirical, in which various factors are related to puncture force using empirical formulas that have been developed in research to examine impact resistance in pipeline applications. Results from applying the semi-analytical method to estimate shell puncture velocity are presented. Similarities and differences between the current method for shell puncture and the semi-empirical method for head puncture are discussed. In addition, results from sensitivity studies are presented to show the relative effect of different factors on estimated puncture velocity. These studies indicate that indenter size and internal pressure have the most significant effect on shell puncture velocity. Conversely, these studies indicate that tank diameter and ram car weight have a relatively weak effect on shell puncture velocity.
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Szwedowicz, J., Th Secall-Wimmel, P. Du¨nck-Kerst, A. Sonnenschein, D. Regnery, and M. Westfahl. "Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment — Part I." In ASME Turbo Expo 2007: Power for Land, Sea, and Air. ASMEDC, 2007. http://dx.doi.org/10.1115/gt2007-27502.

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For industrial condensing steam turbines operating at variable speed, Siemens has developed a last stage SK-blade family in the early 80s. The principle goal was to design a robust blade profile for the highest reliability and a good performance, which allow the operation in resonances under high steam mass flow and excessive condensing pressures. To suppress resonance stresses through friction dissipation, loosely fitted conical bolts are applied to the upper part of adjacent airfoils. In the early 80s, these capabilities were experimentally investigated and validated for the smallest SK-blade at a set-up of the real turbine unit. The tapered and twisted geometry of the smallest SK-blade has been scaled under consideration of the similar mechanical and aerodynamic characteristics. The entire scaled-up SK-blade family has proved its reliability in more than 500 industrial turbine units arranged for different power and speeds. In the last years there could be seen a trend to very large compression units, like GTL (Gas to Liquids), PTA (Acid Terephtalic) or Methanol plants. Therefore, the SK-blade family has been extended to larger airfoils using the well established scale concept based on the smallest SK-unit. In this paper, the mechanical capabilities of the smallest and large SK-blades coupled by the bolts are verified by using the Finite Element (FE) Method. The static analyses with friction sliding on the bolts and the linear dynamic behaviour of tuned disc assemblies are considered. The FE mesh quality and the proper restraint conditions at the radial root are accomplished by getting good agreements between the computed and measured resonance frequencies of the large freestanding blade at standstill. The validated mesh refinement and root boundary conditions are used further in all numerical FE analyses. For the large SK-disc assembly under spin pit conditions, the obtained FE results are in very good agreement with the experimental Campbell diagram. The determined positions of the gauges allow for identifying either stick-slip or sticking contact conditions at the bolts. The experimental spin pit results show mainly sticking contact conditions at the bolts because of too weak air jet excitation. Only in very narrow frequency ranges around resonance peaks, micro-slips on the friction bolts occur due to the resonance amplification of blade vibrations. This is proved indirectly by the evaluated damping values for spin pit conditions, which are bigger than the damping magnitudes of the disc assembly at standstill, which was measured with hammer tests. This empirical statement is approved by the FE steady-state dynamic results for the analytically determined amplitudes of the air jet excitation. The obtained results show that the proposed linear dynamic concept can be successfully applied to the design process of the scaled turbine discs of different dimensions with loosely assembled friction bolts for assessment of maximum static stresses and free vibration behaviour. The scaling design criteria of the blades with friction bolts are confirmed fully for natural frequencies and excitation conditions, but their real responses depending on the excitation amplitudes need to be obtained from the non-linear dynamic simulation which is considered in paper GT2007-27506 (Szwedowicz et al., 2007).
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9

Cai, Shaobiao, and Bharat Bhushan. "Contact Analysis of Multilayered Elastic/Plastic Solids With Rough Surfaces for Decreasing Friction and Wear." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-63942.

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A numerical three-dimensional contact model is presented to investigate the contact behavior of multilayered elastic-perfectly plastic solids with rough surfaces. The surface displacement and contact pressure distributions are obtained based on the variational principle with fast Fourier transform (FFT)-based scheme. Von Mises yield criterion is used to determine the onset of yield. The effective hardness is modeled and plays role when the local displacement meet the maximum displacement criterion. Simulations are performed to obtain the contact pressures, fractional total contact area, fractional plastic contact area, and surface/subsurface stresses. These contact statistics are analyzed to study the effects of the layer-to-substrate ratios of stiffness and hardness, surface roughness, and layers thickness of rough, two-layered elastic/plastic solids. The results yield insight into the effects of stiffness and hardness of layers and substrates, surface roughness, and applied load on the contact performance. The layer parameters leading to low friction, stiction, and wear are investigated and identified.
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10

Zhu, Xiaoxiang, Wenhu Wang, Ruisong Jiang, Yifeng Xiong, and Xiaofen Liu. "Modeling of Thrust Force in Ultrasonic Assisted Drilling of DD6 Superalloy." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-72966.

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Abstract Nickel-based superalloy DD6 is characterized by high strength, high temperature resistance, which makes it an ideal material for manufacturing aircraft engines. Ultrasonic assisted drilling is an advanced machining method, which greatly improves the machining performance of difficult-to-machine materials. The drilling thrust force has an important effect on the hole surface quality, burr height and bit wear. Therefore, it is necessary to predict the thrust force of ultrasonic assisted drilling. However, there are few reports about the thrust force modeling of ultrasonic assisted micro hole drilling. A thrust force prediction model for ultrasonic assisted micro-drilling is presented in this paper. Based on the basic cutting principle, the dynamic cutting thickness, dynamic cutting speed and acoustic softening effect caused by ultrasonic vibration are considered in this model. The model was verified by the ultrasonic assisted drilling experiments with different spindle speeds, feed rates, amplitudes and frequencies. The maximum error and minimum error of the average thrust force are 10.5% and 2.3%, respectively.
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Reports on the topic "Weak maximum principle"

1

Henson, V., G. Sanders, and J. Trask. Extremal eigenpairs of adjacency matrices wear their sleeves near their hearts: Maximum principles and decay rates for resolving community structure. Office of Scientific and Technical Information (OSTI), February 2013. http://dx.doi.org/10.2172/1084717.

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