Relevant bibliographies by topics / B-evolution Equations

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'B-evolution Equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "B-evolution Equations"

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Banasiak, J. "B-bounded semigroups and implicit evolution equations." Abstract and Applied Analysis 5, no. 1 (2000): 13–32. http://dx.doi.org/10.1155/s1085337500000087.

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The aim of this paper is to show an application of the recently introducedB-bounded semigroups in the theory of implicit and degenerate evolution equations. The most interesting feature of this approach is its applicability to problems with noncloseable operators.
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Dalsen, Marié Grobbelaar-Van. "Semilinear evolution equations and fractional powers of a closed pair of operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 105, no. 1 (1987): 101–15. http://dx.doi.org/10.1017/s0308210500021946.

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SynopsisThe nonlinear evolution problem [Bu(t)]′ = A(t, Bu)u + f(t, Bu) with B a constant linear operator and A = A(t, Bu) a time-dependent nonlinear operator from one Banach space to another, is studied. Existence and uniqueness results are obtained by making use of the theory of B-evolutions and the fractional powers of A and B. Two examples are presented in which the theory is applied to nonlinear equations with dynamic boundary conditions.
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Qiao, Zhijun, and Walter Strampp. "L–A–B representation for nonlinear evolution equations and its applications." Physica A: Statistical Mechanics and its Applications 293, no. 1-2 (April 2001): 143–56. http://dx.doi.org/10.1016/s0378-4371(00)00593-8.

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Ahmed, N. U., and S. Kerbal. "Stochastic systems governed by B-evolutions on Hilbert spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 5 (1997): 903–20. http://dx.doi.org/10.1017/s0308210500026792.

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SynopsisIn this paper, we consider the question of existence of solutions and their regularity properties for a large class of stochastic evolution equations governed by B-evolutions involving two different Hilbert spaces. This allows dynamic boundary conditions together with noisy boundary data. They cover also stochastic boundary value problems. Our results are illustrated by two practical examples.
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Gühring, Gabriele, and Frank Räbiger. "Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations." Abstract and Applied Analysis 4, no. 3 (1999): 169–94. http://dx.doi.org/10.1155/s1085337599000214.

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We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation(d/dt)u(t)=Au(t)+B(t)u(t)+f(t),t∈ℝ, where(A,D(A))is a Hille-Yosida operator on a Banach spaceX,B(t),t∈ℝ, is a family of operators inℒ(D(A)¯,X)satisfying certain boundedness and measurability conditions andf∈L loc 1(ℝ,X). The solutions of the corresponding homogeneous equations are represented by an evolution family(UB(t,s))t≥s. For various function spacesℱwe show conditions on(UB(t,s))t≥sandfwhich ensure the existence of a unique solution contained inℱ. In particular, if(UB(t,s))t≥sisp-periodic there exists a unique bounded solutionusubject to certain spectral assumptions onUB(p,0),fandu. We apply the results to nonautonomous semilinear retarded differential equations. For certainp-periodic retarded differential equations we derive a characteristic equation which is used to determine the spectrum of(UB(t,s))t≥s.
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Bertsch, M., R. Dal Passo, and R. Kersner. "The evolution of turbulent bursts: the b—ε model." European Journal of Applied Mathematics 5, no. 4 (December 1994): 537–57. http://dx.doi.org/10.1017/s0956792500001601.

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We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.
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Wang, Xiao Li, Jian Qin Mei, and Zhen Hua Wu. "Auto-Bäcklund Transformations Derived via the Implicit C-D Pair." Applied Mechanics and Materials 268-270 (December 2012): 1345–48. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.1345.

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By the implicit C-D pairs, a new approach to auto-B¨acklund transformations of nonlinear evolution equations is presented in this paper. The auto-B¨acklund transformations for combined KdV and MKdV equations are obtained by this approach.
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Mahmudov, N. I. "Existence and approximate controllability of Sobolev type fractional stochastic evolution equations." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 2 (June 1, 2014): 205–15. http://dx.doi.org/10.2478/bpasts-2014-0020.

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Abstract We study the existence of mild solutions and the approximate controllability concept for Sobolev type fractional semilinear stochastic evolution equations in Hilbert spaces. We prove existence of a mild solution and give sufficient conditions for the approximate controllability. In particular, we prove that the fractional linear stochastic system is approximately controllable in [0, b] if and only if the corresponding deterministic fractional linear system is approximately controllable in every [s, b], 0 ≤ s < b. An example is provided to illustrate the application of the obtained results.
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Arlotti, Luisa. "A new characterization ofB-bounded semigroups with application to implicit evolution equations." Abstract and Applied Analysis 5, no. 4 (2000): 227–44. http://dx.doi.org/10.1155/s1085337501000331.

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We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and calledB-bounded semigroups. We first determine all the properties possessed by a couple(A,B)of operators if they generate aB-bounded semigroup(Y(t))t≥0. Then we determine the simplest further property of the couple(A,B)which can assure the existence of aC0-semigroup(T(t))t≥0such that for allt≥0,f∈D(B)we can writeY(t)f=T(t)Bf. Furthermore, we compare our result with the previous ones and finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations.
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CONTE, R. "ANALYTIC PATTERNS FOR CHAOTIC EQUATIONS." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 3918–24. http://dx.doi.org/10.1142/s0217979207044962.

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Chaotic evolution equations sometimes display regular patterns (fronts, kinks, holes), which often correspond to closed form analytic solutions. In the dissipative-dispersive Kuramoto and Sivashinsky travelling wave reduction u(x − ct), νu‴ + bu″ + μu′ + u2/2 + A = 0, ν ≠ 0, with (ν,b,μ,A) constants, such analytic solutions are known for heteroclinic solutions, but one has also observed (Toh, 1987) homoclinic solutions without corresponding analytic solutions yet. We review the search for the most general analytic solution admissible by this chaotic differential equation. Several investigations, both analytic by the Painlevé test (Thual and Frisch, 1986) and numerical by Padé approximants (Yee, Conte, Musette, 2003) indicate its quite probable single valuedness for any (ν,b,μ,A). Moreover, Nevanlinna theory on the growth of solutions near infinity rules out (Eremenko, 2005) the possibility for the singularities of this unknown closed form single valued expression to be only poles. We propose a qualitative closed form involving a deformed elliptic function.
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Dissertations / Theses on the topic "B-evolution Equations"

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Singh, Virath Sewnath. "A new approach to ill-posed evolution equations : C-regularized and B- bounded semigroups." Thesis, 2001. http://hdl.handle.net/10413/3638.

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The theory of semigroups of linear operators forms an integral part of Functional Analysis with substantial applications to many fields of the natural sciences. In this study we are concerned with the application to equations of mathematical physics. The theory of semigroups of bounded linear operators is closely related to the solvability of evolution equations in Banach spaces that model time dependent processes in nature. Well-posed evolution problems give rise to a semigroup of bounded linear operators. However, in many important and interesting cases the problem is ill-posed making it inaccessible to the classical semigroup theory. One way of dealing with this problem is to generalize the theory of semigroups. In this thesis we give an outline of the theory of two such generalizations, namely, C-regularized semigroups and B-bounded semigroups, with the inter-relations between them and show a number of applications to ill-posed problems.
Thesis (Ph.D.)-University of Natal, Durban, 2001.
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Lee, Wha-Suck. "An algebraic - analytic framework for the study of intertwined families of evolution operators." Thesis, 2015. http://hdl.handle.net/2263/43532.

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We introduce a new framework of generalized operators to handle vector valued distributions, intertwined evolution operators of B-evolution equations and Fokker Planck type evolution equations. Generalized operators capture these operators. The framework is a marriage between vector valued distribution theory and abstract harmonic analysis: a new convolution algebra is the offspring. The new algebra shows that convolution is more fundamental than operator composition. The framework is complete with a Hille-Yosida theorem for implicit evolution equations for generalized operators. Feller semigroups and processes fit perfectly into the framework of generalized operators. Feller semigroups are intertwined by the Chapman Kolmogorov equation. Our framework handles more complex intertwinements which naturally arise from a dynamic boundary approach to an absorbing barrier of a fly trap model: we construct an entwined pseudo Poisson process which is a pair of stochastic processes entwined by the extended Chapman Kolmogorov equation. Similarly, we introduce the idea of an entwined Brownian motion. We show that the diffusion equation of an entwined Brownian motion involves an implicit evolution equation on a suitable scalar test space. We end off by constructing a new convolution of operator valued measures which generalizes the convolution of Feller convolution semigroups.
Thesis (PhD)--University of Pretoria, 2015.
Mathematics and Applied Mathematics
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Kreye, Manuel. "A Unitary Perturbation Theory Approach to Real-Time Evolution in the Hubbard Model." Doctoral thesis, 2019. http://hdl.handle.net/21.11130/00-1735-0000-0005-128A-B.

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Books on the topic "B-evolution Equations"

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Oscillating patterns in image processing and nonlinear evolution equations: The fifteenth Dean Jacqueline B. Lewis memorial lectures. Providence, R.I: American Mathematical Society, 2001.

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Birch, Jonathan. Hamilton’s Rule as an Organizing Framework. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198733058.003.0002.

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Queller’s version of Hamilton’s rule (HRG), derived from the Price equation, states that the mean breeding value for a social character increases if and only if rb > c, where r is the coefficient of relatedness between social partners, b is the benefit conferred on recipients, and c is the cost incurred by actors. The value of HRG lies in its ability to provide an organizing framework for social evolution theory, helping us to interpret, classify, and compare more detailed models of particular scenarios. HRG does this by allowing us to classify causal explanations of positive change by their commitments regarding the sign of rb and c. This leads to a four-part taxonomy of explanations, comprising indirect fitness explanations, direct fitness explanations, hybrid explanations, and wholly or partially non-selective explanations. There are plausible instances of all four categories in the natural world.
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Clarke, Andrew. The Metabolic Theory of Ecology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199551668.003.0012.

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The model of West, Brown & Enquist (WBE) is built on the assumption that the metabolic rate of cells is determined by the architecture of the vascular network that supplies them with oxygen and nutrients. For a fractal-like network, and assuming that evolution has minimised cardiovascular costs, the WBE model predicts that s=metabolism should scale with mass with an exponent, b, of 0.75 at infinite size, and ~ 0.8 at realistic larger sizes. Scaling exponents ~ 0.75 for standard or resting metabolic rate are observed widely, but far from universally, including in some invertebrates with cardiovascular systems very different from that assumed in the WBE model. Data for field metabolic rate in vertebrates typically exhibit b ~ 0.8, which matches the WBE prediction. Addition of a simple Boltzmann factor to capture the effects of body temperature on metabolic rate yields the central equation of the Metabolic Theory of Ecology (MTE). The MTE has become an important strand in ecology, and the WBE model is the most widely accepted physical explanation for the scaling of metabolic rate with body mass. Capturing the effect of temperature through a Boltzmann factor is a useful statistical description but too simple to qualify as a complete physical theory of thermal ecology.
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Book chapters on the topic "B-evolution Equations"

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Banasiak, J. "B-Bounded Semigroups, Existence Families and Implicit Evolution Equations." In Semigroups of Operators: Theory and Applications, 25–34. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8417-4_3.

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Zeidler, Eberhard. "Accretive Operators and Multivalued First-Order Evolution Equations in B-Spaces." In Nonlinear Functional Analysis and its Applications, 581–98. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5020-3_22.

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Celeghini, E., T. D. Palev, and M. Tarlini. "The q-Deformed Creation and Annihilation Operators as a Realization of the Quantum Superalgebra B q(0∣l)." In Nonlinear Evolution Equations and Dynamical Systems, 138–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76172-0_30.

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Triggiani, Roberto. "Min-Max Game Theory and Optimal Control with Indefinite Cost under a Singular Estimate for e At B in the Absence of Analyticity." In Evolution Equations, Semigroups and Functional Analysis, 353–79. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8221-7_19.

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Axelsson, O. "On the B-Convergence of the θ-Method Over Infinite Time for Time Stepping for Evolution Equations." In Trends in The Theory and Practice of Non-Linear Analysis, Proceedings of the VIth International Conference on Trends in the Theory and Practice of Non-Linear Analysis, 33–40. Elsevier, 1985. http://dx.doi.org/10.1016/s0304-0208(08)72685-9.

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Hoffmann, Roald. "Why Buy That Theory?" In Roald Hoffmann on the Philosophy, Art, and Science of Chemistry. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199755905.003.0006.

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The theory of theories goes like this: A theory will be accepted by a scientific community if it explains better (or more of) what is known, fits at its fringes with what is known in other parts of our universe, and makes verifiable, preferably risky, predictions. Sometimes it does go like that. So the theory that made my name (and added to the already recognized greatness of the man with whom I collaborated, the synthetic chemist of the 20th century, R. B. Woodward) did make sense of many disparate and puzzling observations in organic chemistry. And “orbital symmetry control,” as our complex of ideas came to be called, made some risky predictions. I remember well the day that Jerry Berson sent us his remarkable experimental results on the stereochemistry of the so- called 1,3-sigmatropic shift . It should proceed in a certain way, he reasoned from our theory—a non-intuitive way. And it did. But much that goes into the acceptance of theories has little to do with rationalization and prediction. Instead, I will claim, what matters is a heady mix of factors in which psychological attitudes figure prominently. A simple equation describing a physical phenomenon (better still, many), the molecule shaped like a Platonic solid with regular geometry, the simple mechanism (A→B, in one step)—these have tremendous aesthetic appeal, a direct beeline into our soul. They are beautifully simple, and simply beautiful. Theories of this type are awesome in the original sense of the word—who would deny this of the theory of evolution, the Dirac equation or general relativity? A little caution might be suggested from pondering the fact that political ads patently cater to our psychobiological predilection for simplicity. Is the world simple? Or do we just want it to be such? In the dreams of some, the beauty and simplicity of equations becomes a criterion for their truth. Simple theories seem to validate that idol of science, Ockham’s Razor. In preaching the poetic conciseness and generality of orbital explanations, I have succumbed to this, too.
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Conference papers on the topic "B-evolution Equations"

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Kosztolowicz, Tadeusz, and Katarzyna D. Lewandowska. "Application of Scaling and Quasistatic Methods to Study Nonlinear Subdiffusion-Reaction Equations With Fractional Time Derivative." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87215.

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We consider a subdiffusive system where transported particles of spieces A and B chemically react according to the formula A + B → 0̸. This process is described by the nonlinear subdiffusion-reaction equations with fractional time derivatives. We show that the scaling method, which is commonly used to study diffusion-reaction equations of natural order, is not applicable to the subdiffusion case due to the specific properties of fractional derivatives, unless very special assumptions are taken into account. Contrary to the scaling method, the quasistatic one provides the explicite solutions in the diffusion region and the time evolution of reaction front xf, which reads xf = Ktα/2, where α is the subdiffusion parameter and K is uniquely determined. We also present the numerical solutions of subdiffusion-reaction equations and show that the numerical results coincide with the analytical ones.
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de Souza, Rodolfo F., and Claudio Ruggieri. "Revised η-Factors for 3P SE(B) Fracture Specimens Incorporating 3-D Effects." In ASME 2014 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/pvp2014-28135.

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Standardized procedures to measure cleavage fracture toughness of ferritic steels in the DBT region most commonly employ three-point bend fracture specimens, conventionally termed SE(B) or SENB specimens. The evaluation protocol of fracture toughness for these crack configurations builds upon laboratory records of load and crack mouth opening displacement (CMOD) to relate plastic work with J (or, equivalently, CTOD). The experimental approach employs a plastic η-factor to relate the macroscale crack driving force to the area under the load versus crack mouth opening displacement for cracked configurations. This work provides revised η-factors derived from CMOD records applicable to estimate the J-integral and CTOD in SE(B) specimens with varying crack size and specimen configuration. Non-linear finite element analyses for plane-strain and 3-D models provide the evolution of load with increased CMOD which is required for the estimation procedure. The analysis matrix considers SE(B) specimens with W = 2B and W = B configurations with and without side grooves covering a wide range of specimen thickness, including precracked Charpy (PCVN) specimens. Overall, the present results provide further validation of the J and CTOD evaluation procedure currently adopted by ASTM 1820 while, at the same time, giving improved estimation equations for J incorporating 3-D effects which enter directly into more accurate testing protocols for experimental measurements of fracture toughness values using 3P SE(B) specimens.
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Colac¸o, Marcelo J., George S. Dulikravich, and Thomas J. Martin. "Reducing Convection Effects in Solidification by Applying Magnetic Fields Having Optimized Intensity Distribution." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47308.

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This paper presents a numerical procedure for achieving desired features of a melt undergoing solidification by applying an external magnetic field whose intensity and spatial distribution are obtained by the use of a hybrid optimization algorithm. The intensities of the magnets along the boundaries of the container are described as B-splines. The inverse problem is then formulated as to find the magnetic boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the gravity direction are minimized. For this task, a hybrid optimization code was used that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). Transient Navier-Stokes and Maxwell equations were discretized using finite volume method in a generalized curvilinear non-orthogonal coordinate system. For the phase change problems, an enthalpy formulation was used. The code was validated against analytical and numerical benchmark results with very good agreements in both cases.
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Colac¸o, Marcelo J., George S. Dulikravich, and Thomas J. Martin. "Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection Effects During Solidification." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41703.

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This paper presents a numerical procedure to reduce and possibly control the natural convection effects in a cavity filled with a molten material by applying an external electric field whose intensity and spatial distributions are obtained by the use of a hybrid optimizer. This conceptually new approach to manufacturing could be used in creation of layered and functionally graded materials and objects. In the case of steady electro-hydrodynamics (EHD), the flow-field of electrically charged particles in a solidifying melt is influenced by an externally applied electric field while the existence of any magnetic field is neglected. Solidification front shape, distribution of the charged particles in the accrued solid, and the amount of accrued solid phase in such processes can be influenced by an appropriate distribution and orientation of the electric field. The intensities of the electrodes along the boundaries of the cavity were described using B-splines. The inverse problem was then formulated to find the electric boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the horizontal direction are minimized. For this task we used a hybrid optimization algorithm which incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). The transient Navier-Stokes and Maxwell equations were discretized using the finite volume method in a generalized curvilinear non-orthogonal coordinate system. For the phase change problems, we used the enthalpy method.
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Lang, Jinhua, Wuli Chu, Haoguang Zhang, Shan Ma, and Xiangyi Chen. "Investigation of In-Stall Behavior in a Transonic Compressor Rotor." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63759.

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This paper shows the results of three-dimensional multi-passage numerical simulations on a transonic compressor, NASA compressor Rotor 37. The aim is to investigate the unsteady flow on the stall condition and elucidate the dynamic evolution mechanism of the rotating stall. Three-dimensional Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model were solved to analyze the fluid flow in the transonic axial compressor. Before the study of the stall flow, grid independence and data correctness were well validated. A new parameter B is defined to assess the blockage effect during the stall development. As shown in the results, with the development of the rotating stall, the blockage effect increases slowly before the 18th revolution in unsteady numerical simulation, and then increases dramatically in the following revolutions. Thus, the whole process of stall evolution can be divided into two stages, i.e. stall stage I and stall stage II. The stall stage I is the first 18th revolutions, while the stall stage II refers to the period after the18th revolution. Further analyses of the instantaneous flow field show that the interaction between the tip leakage flow and the detached shock wave induces the breakdown of the leakage vortex. As the broken leakage vortex moves downstream, the low energy flow is rolled up. At the middle of the channel, the trajectory of the vortex core inclines to the PS of adjacent blade under the influence of the adverse pressure gradient, and an obvious new vortex is formed. During the development process of the rotating stall, the blockage is primarily induced by the tip leakage vortex and the new vortex. In the stall stage I, the evolution of the blockage area near the tip is periodic affected by the self-sustaineed process of tip leakage vortex. The self-sustained phenomenon will be illustrated in detail later. In the stall stage II, the whole passage is blocked at 99% blade span, and the spillage flow is observed throughout the whole stage. These flow charicteristics are regarded as signs of a rapid deterioration of the flow field. A vicious cycle is seen as the main reason for the rapid deterioration of the flow field, and the vicious cycle will be explained in detail later.
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Tian, Shuqing, Zhi Tao, Shuiting Ding, and Guoqiang Xu. "Investigation of Flow and Heat Transfer Instabilities in a Rotating Cavity With Axial Throughflow of Cooling Air." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-53525.

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To study the instability of flow and heat transfer within the rotation frame, a rotating cavity with air axial throughflow was studied numerically and efforts were focused upon the flow structure evolution with the increase of Rayleigh number. The cavity can be divided into two typical zones: the Rayleigh_Benard-like convection zone occupying the upper cavity and the forced convection zone down under. These two zones interact with each other via the exchange of mass, momentum and energy. Numerical analysis indicated that, for a fixed inlet Reynolds number, there always exists a critical Rayleigh number Rac, below which the flow is stable and over which the flow becomes unstable and time-dependent. Among all the forces in momentum equations, the centrifugal induced buoyancy force was found to be the key factor leading to instability, while the Coriolis force pays its contribution to instability by inducing its occurrence earlier and the flow structure more complicated though it may not lead to instable by itself. The instability originated in the upper R-B-like convection zone develops into the whole region with the increase of Rayleigh number. For the heat transfer, the characteristic distribution of local Nur along the disk surface is remarkably different before and right after the occurrence of instability due to flow structure variation though the averaged Nuav varies slightly. It was found that the heat transfer, however, does experience a sudden increase when the flow instability develops further with Ra increase.
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Roy, Samit, Priyank Upadhyaya, Mohammad H. Haque, and Hongbing Lu. "A Multi-Scale Viscoelastic Cohesive Layer Model for Predicting Delamination in HTPMC." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36397.

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In this paper, a novel numerical-experimental methodology is outlined to predict delamination in pristine as well as isothermally aged (in air) polymer matrix composites. A rate-dependent viscoelastic cohesive layer model was implemented in an in-house test-bed finite element analysis (FEA) code to simulate the delamination initiation and propagation in unidirectional polymer composites before and after aging. This unified model is fully rate-dependent and does not require a pre-assigned traction-separation law. The actual shape of traction separation law depends on: (a) the strain rate via the viscoelastic constitutive relationship, (b) the degree of thermo-oxidative aging via the changes in the experimentally measured creep compliance due to oxidation, and (c) the evolution of the internal state variable defining the state of damage. To determine the model parameters, double cantilever beam (DCB) experiments were conducted on both pristine and isothermally aged IM-7/bismaleimide (BMI) composite specimens. The J-Integral approach was adapted to extract cohesive stresses near the crack tip. A principal-stretch dependent internal damage state variable defines the damage in the cohesive layer. Within the cohesive layer, pristine and cohesive stresses were compared to estimate the damage parameters. Once the damage parameters had been characterized, the test-bed FEA code employed a micromechanics based viscoelastic cohesive layer model to simulate interlaminar delamination. From a numerical stability standpoint, the viscous regularization effect of the viscoelastic constitutive equations in the cohesive layer helps mitigate numerical instabilities caused by elastic energy released due to crack growth, thereby enabling the FEA model to simulate the load-deflection response of the composite structure well beyond peak load. The present cohesive-layer based FEA model was able to accurately predict not only the macro level load-displacement curve, but also the micro level crack growth history in IM-7/BMI laminate before and after thermal aging, using only three parameters.
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Teymouri, Mehdi, and Zoya Heidari. "AN ADVANCED PETROPHYSICAL ORIENTED NUMERICAL METHOD FOR RELIABLE ASSESSMENT OF MECHANICAL PROPERTIES IN CARBONATE FORMATIONS AT THE PORE-SCALE DOMAIN." In 2021 SPWLA 62nd Annual Logging Symposium Online. Society of Petrophysicists and Well Log Analysts, 2021. http://dx.doi.org/10.30632/spwla-2021-0005.

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Assessment of effective mechanical properties such as elastic properties and brittleness can be challenging in the presence of complex rock composition, pore structure, and spatial distribution of minerals, especially in the absence of acoustic measurements. Conventional methods such as effective medium modeling, are not reliable for assessments of mechanical properties in complex formations such as carbonates, because solid skeleton of carbonates does not consist of granular minerals with ideal shapes. The effective medium models also overlook both the spatial distribution of petrophysical properties, and the coupled hydraulic and mechanical (HM) processes, which causes significant uncertainties in geomechanical evaluations. The objective of this paper is to develop a numerical method to enhance assessment of effective mechanical properties of anisotropic and heterogenous carbonate formations by modeling the variation of effective stress and the evolution of corresponding strain. The developed method takes into account the coupled HM processes, the realistic spatial distribution of rock inclusions (i.e., rock fabrics), dynamic fluid flow, pore pressure, and pore structure. To achieve this objective, we develop a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM phenomena. We adopt peridynamic theory to discretize the micro-scale medium. The inputs to our numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock inclusion. We perform image processing on micro-CT scan images of rock samples to obtain a realistic micro-scale structure of both rock matrix (i.e., concentration, spatial distribution, and shape of rock constituents) and pore space. We then assign realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical/hydraulic properties of rock inclusions caused by their spatial distribution, pore pressure, pore structure, natural fractures, and dynamic fluid flow at the micro-scale domain. We then compare the outcomes of numerical models with the mechanical properties estimated based on effective medium models. We performed sensitivity analyses to quantify the effects of concentration and spatial distribution of rock constituents, divergence in spatial distribution of petrophysical, mechanical, and hydraulic properties of inclusions, pore structure and natural micro-fractures, and pore pressure on variations in effective elastic properties of rock samples. We estimated the elastic properties from the stress/strain curves obtained from numerical simulations. We observed significant errors (more than 30.6% relative error depending on the content and distribution of rock constituents) in estimated effective elastic properties by the effective medium models. These errors are due to overlooking the coupled HM analysis, the spatial distribution, actual shape and size of inclusions, pore-structure, and natural micro-fractures by such effective medium models. The presented advanced pore-scale numerical analysis will (a) enhance reliable assessments of effective elastic/mechanical properties of carbonates or any other rock type in the presence of pore pressure and dynamic flow, and (b) assist upscaling techniques for reliable geomechanical evaluation and assessment of fracture propagation in these formations at larger scales.
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9

Smith, Charles E., and Michael R. von Spakovsky. "Time Evoultion of Entropy in a System Comprised of a Boltzmann Type Gas: An Application of the Beretta Equation of Motion." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42933.

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Basing his work on a new formulation of thermodynamics called the Unified Quantum Theory of Mechanics and Thermodynamics first published in a series of four ground breaking papers in 1976 (Hatsopoulos and Gyftopoulos, 1976a, b, c, d), Beretta develops a dynamical postulate (Beretta et al. 1984; Beretta, Gyftopoulos, and Park, 1985) consistent both with the non-dynamical quantum mechanical postulates of the Unified Theory as well as with its thermodynamic ones (the 2nd Law in particular). The theory itself simply and elegantly extends in a unified fashion the concepts of thermodynamics to quantum mechanics and the concepts of quantum mechanics to thermodynamics. It does so without the bridge traditionally used, i.e. statistical mechanics, eliminating a number of the ambiguities, tautologies, and inconsistencies (including a built-in violation of the 2nd Law) inherent in the presentations of both Classical and Statistical Thermodynamics. This new formulation generalizes thermodynamics so that it applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. The Beretta equation of motion describes the time evolution of the state of a system via a density operator which is uniquely based on an unambiguous preparation of an ensemble of identical systems, i.e. the so-called homogenous or irreducible ensemble, and does so both for unitary and non-unitary reversible as well as irreversible processes. In this paper, we present a simple application of this general equation of motion to the time evolution of the entropy of a closed system comprised of a Boltzmann type gas consisting of one or of many particles undergoing an irreversible process. A number of different energy eigenlevels and initial states and their effects on entropy generation and the final state of maximum entropy, i.e. stable equilibrium, are examined. A simple time-dependent work interaction is introduced into the formulation to show how this in turn affects the evolution of the state of the system.
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10

Ruggeri, Felipe, Rafael A. Watai, and Alexandre N. Simos. "A Higher Order Time Domain Rankine Panel Method for Linear and Weakly Non-Linear Computation." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-42234.

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This paper presents a higher order time domain boundary elements method based on the Rankine sources for the computation of both linear and weakly non-linear effects for both fixed and free floating bodies. The geometry is described based on surfaces in a standard iges file, considering a NURBS (Non Uniform Rational Basis-Spline) description. The potential function, velocity, free-surface elevation and other quantities are defined using b-splines of arbitrary degree and the floating body interaction is solved using the potential acceleration approach on a Runge-Kutta scheme for time evolution. The integral equation is obtained and solved considering several possibilities for the collocation points, leading to an over-determined system. The integration over the panels is performed using a mixed desingularized-numerical method over Gaussian points. The results comparison are performed with WAMIT solution for a floating sphere concerning wave runup, body motions, velocity field, mean drift components in time domain.
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