Journal articles on the topic 'Random polymer models'
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1
Jitomirskaya, S., H. Schulz-Baldes, and G. Stolz. "Delocalization in Random Polymer Models." Communications in Mathematical Physics 233, no. 1 (February 1, 2003): 27–48. http://dx.doi.org/10.1007/s00220-002-0757-5.
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Toninelli, Fabio. "Giambattista Giacomin: Random Polymer Models." Journal of Statistical Physics 130, no. 6 (January 8, 2008): 1219–20. http://dx.doi.org/10.1007/s10955-007-9478-7.
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SEMENOFF, GORDON W., and RICHARD J. SZABO. "POLYMER STATISTICS AND FERMIONIC VECTOR MODELS." Modern Physics Letters A 11, no. 14 (May 10, 1996): 1185–97. http://dx.doi.org/10.1142/s0217732396001211.
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We consider a variation of O(N)-symmetric vector models in which the vector components are Grassmann numbers. We show that these theories generate the same sort of random polymer models as the O(N) vector models and that they lie in the same universality class in the large-N limit. We explicitly construct the double-scaling limit of the theory and show that the genus expansion is an alternating Borel summable series that otherwise coincides with the topological expansion of the bosonic models. We also show how the fermionic nature of these models leads to an explicit solution even at finite-N for the generating functions of the number of random polymer configurations.
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Toninelli, Fabio Lucio. "Correlation Lengths for Random Polymer Models and for Some Renewal Sequences." Electronic Journal of Probability 12 (2007): 613–36. http://dx.doi.org/10.1214/ejp.v12-414.
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E. J. Staggs, John. "Discrete population balance models of random agglomeration and cleavage in polymer pyrolysis." AIMS Materials Science 4, no. 3 (2017): 614–37. http://dx.doi.org/10.3934/matersci.2017.3.614.
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Talyigás, Zsófia, and Bálint Vető. "Borodin–Péché Fluctuations of the Free Energy in Directed Random Polymer Models." Journal of Theoretical Probability 33, no. 3 (May 23, 2019): 1426–44. http://dx.doi.org/10.1007/s10959-019-00919-8.
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Tashkinov, M. A., A. D. Dobrydneva, V. P. Matveenko, and V. V. Silberschmidt. "Modeling the Effective Conductive Properties of Polymer Nanocomposites with a Random Arrangement of Graphene Oxide Particles." PNRPU Mechanics Bulletin, no. 2 (December 15, 2021): 167–80. http://dx.doi.org/10.15593/perm.mech/2021.2.15.
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Сomposite materials are widely used in various industrial sectors, for example, in the aviation, marine and automotive industries, civil engineering and others. Methods based on measuring the electrical conductivity of a composite material have been actively developed to detect internal damage in polymer composite materials, such as matrix cracking, delamination, and other types of defects, which make it possible to monitor a composite’s state during its entire service life. Polymers are often used as matrices in composite materials. However, almost always pure polymers are dielectrics. The addition of nanofillers, such as graphene and its derivatives, has been successfully used to create conductive composites based on insulating polymers. The final properties of nanomodified composites can be influenced by many factors, including the type and intrinsic properties of nanoscale objects, their dispersion in the polymer matrix, and interphase interactions. The work deals with modeling of effective electric conductive properties of the representative volume elements of nanoscale composites based on a polymer matrix with graphene oxide particles distributed in it. In particular, methods for evaluating effective, electrically conductive properties have been studied, finite element modelling of representative volumes of polymer matrices with graphene oxide particles have been performed, and the influence of the tunneling effect and the orientation of inclusions on the conductive properties of materials have been investigated. The possibility of using models of resistive strain gauges operating on the principle of the tunneling effect is studied. Based on the finite-element modeling and graph theory tools, we created approaches for estimating changes in the conductive properties of the representative volume elements of a nanomodified matrix subjected to mechanical loading.
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Zhang, Qing Ping, and Zhi Geng Fan. "Numerical Studies on the Dynamic Performance of Polymer Foams." Advanced Materials Research 287-290 (July 2011): 2256–60. http://dx.doi.org/10.4028/www.scientific.net/amr.287-290.2256.
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Two-dimensional (2D) regular and random cell models composed of circular cells are developed to simulate the microstructure of polymer foams. Two-parameter Mooney-Rivlin strain energy potential model is employed to characterize the hyperelasticity of the solid of which the foams are made. Finite element method is used to simulate the large deformation of the foams. Numerical results show that the strain rate sensitivity of the polymer foam is weak as rate independent constitutive model is introduced to describe the mechanical performance of cell material. ‘X’-, ‘I’-, and ‘V’-shaped bands are observed in regular foam models at a low, high and moderate impact velocities, respectively; whereas ‘I”-shaped modes appear in random cell models at a high impact velocity only.
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GEURTS, BERNARD J., and FREDERIK W. WIEGEL. "SIMULATION OF THE DYNAMICS OF A MACROMOLECULE IN A RANDOM CONSTRAINT CAGE." Modern Physics Letters B 01, no. 01n02 (May 1987): 57–60. http://dx.doi.org/10.1142/s0217984987000089.
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We determine the centre of mass diffusion coefficient D and the chain relaxation time T of a macromolecule diffusing through a random constraint cage. This cage models the average topological constraints on the motion of a particular polymer, imposed by the other polymers in the system. The constraint cage consists of regularly spaced constraint lines on a cubic lattice which are “active” with a probability p and absent with a probability 1−p. To a good approximation D≈A(p)N−α(p) and T≈B(p)Nβ(p) if N≫1. The exponents α and β show two regions of very rapid change at pc,1≈0.30 and at pc,2≈0.98.
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Hoffmann, Falk, Rainhard Machatschek, and Andreas Lendlein. "Analytical model and Monte Carlo simulations of polymer degradation with improved chain cut statistics." Journal of Materials Research 37, no. 5 (March 3, 2022): 1093–101. http://dx.doi.org/10.1557/s43578-022-00495-4.
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AbstractThe degradation of polymers is described by mathematical models based on bond cleavage statistics including the decreasing probability of chain cuts with decreasing average chain length. We derive equations for the degradation of chains under a random chain cut and a chain end cut mechanism, which are compared to existing models. The results are used to predict the influence of internal molecular parameters. It is shown that both chain cut mechanisms lead to a similar shape of the mass or molecular mass loss curve. A characteristic time is derived, which can be used to extract the maximum length of soluble fragments l of the polymer. We show that the complete description is needed to extract the degradation rate constant k from the molecular mass loss curve and that l can be used to design polymers that lose less mechanical stability before entering the mass loss phase. Graphical abstract
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ANDERSON, ARLEN. "SYMMETRIC SPACE TWO-MATRIX MODELS." International Journal of Modern Physics A 07, no. 23 (September 20, 1992): 5781–96. http://dx.doi.org/10.1142/s0217751x92002635.
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The radial form of the partition function of a two-matrix model is formally given in terms of a spherical function for matrices representing any Euclidean symmetric space. An explicit expression is obtained by constructing the spherical function by the method of intertwining. The reduction of two-matrix models based on Lie algebras is an elementary application. A model based on the rank one symmetric space isomorphic to RN is less trivial and is treated in detail. This model may be interpreted as an Ising model on a random branched polymer. It has the unusual feature that the maximum order of criticality is different in the planar and double-scaling limits.
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Hordijk, Wim, Mike Steel, and Stuart Kauffman. "Molecular Diversity Required for the Formation of Autocatalytic Sets." Life 9, no. 1 (March 1, 2019): 23. http://dx.doi.org/10.3390/life9010023.
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Systems chemistry deals with the design and study of complex chemical systems. However, such systems are often difficult to investigate experimentally. We provide an example of how theoretical and simulation-based studies can provide useful insights into the properties and dynamics of complex chemical systems, in particular of autocatalytic sets. We investigate the issue of the required molecular diversity for autocatalytic sets to exist in random polymer libraries. Given a fixed probability that an arbitrary polymer catalyzes the formation of other polymers, we calculate this required molecular diversity theoretically for two particular models of chemical reaction systems, and then verify these calculations by computer simulations. We also argue that these results could be relevant to an origin of life scenario proposed recently by Damer and Deamer.
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Chen, Fang-Chung. "Virtual Screening of Conjugated Polymers for Organic Photovoltaic Devices Using Support Vector Machines and Ensemble Learning." International Journal of Polymer Science 2019 (March 31, 2019): 1–7. http://dx.doi.org/10.1155/2019/4538514.
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Herein, we report virtual screening of potential semiconductor polymers for high-performance organic photovoltaic (OPV) devices using various machine learning algorithms. We particularly focus on support vector machine (SVM) and ensemble learning approaches. We found that the power conversion efficiencies of the device prepared with the polymer candidates can be predicted with their structure fingerprints as the only inputs. In other words, no preliminary knowledge about material properties was required. Additionally, the predictive performance could be further improved by “blending” the results of the SVM and random forest models. The resulting ensemble learning algorithm might open up a new opportunity for more precise, high-throughput virtual screening of conjugated polymers for OPV devices.
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BARRETT, JOHN W., CHRISTOPH SCHWAB, and ENDRE SÜLI. "EXISTENCE OF GLOBAL WEAK SOLUTIONS FOR SOME POLYMERIC FLOW MODELS." Mathematical Models and Methods in Applied Sciences 15, no. 06 (June 2005): 939–83. http://dx.doi.org/10.1142/s0218202505000625.
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We study the existence of global-in-time weak solutions to a coupled microscopic–macroscopic bead-spring model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝd, d = 2, 3, for the velocity and the pressure of the fluid, with an extra-stress tensor as right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function which satisfies a Fokker–Planck type degenerate parabolic equation. Upon appropriate smoothing of the convective velocity field in the Fokker–Planck equation, and in some circumstances, of the extra-stress tensor, we establish the existence of global-in-time weak solutions to this regularised bead-spring model for a general class of spring-force-potentials including in particular the widely used FENE (Finitely Extensible Nonlinear Elastic) model.
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Wang, Huai Wen, Hong Wei Ji, Wen Quan Shao, and Hui Miao. "3D Finite Element Modeling for Particle-Reinforced Polymer Composites for Wind Energy Application." Advanced Materials Research 189-193 (February 2011): 2177–80. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.2177.
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A series of numerical meso-mechanical models for different kinds of particle (include spherical, cylindrical and discal) reinforced composites are developed to investigate the effect of microstructural parameters on the elastic properties of composites. In these models, an effective interface concept is adopted. Finite element models with prescribed and random parameters are automatically generated in ABAQUS PDE (Python Development Environment). In the simulative investigations, it is observed that the degree of particle clustering and particle’s shape have strong effects on the elastic mechanical properties of composites.
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MUSACCHIO, STEFANO, and DARIO VINCENZI. "Deformation of a flexible polymer in a random flow with long correlation time." Journal of Fluid Mechanics 670 (February 7, 2011): 326–36. http://dx.doi.org/10.1017/s0022112010006385.
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The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and finitely extensible nonlinear elastic (FENE) dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil–stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.
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MARTELLINI, M., M. SPREAFICO, and K. YOSHIDA. "A FIELD THEORETICAL APPROACH FOR STRINGS AND INTERFACES OF ISING-LIKE MODELS AT d>1." International Journal of Modern Physics B 10, no. 18n19 (August 30, 1996): 2431–40. http://dx.doi.org/10.1142/s0217979296001094.
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Starting from a generalized version of David-Distler-Kawai treatment of 2d-induced quantum gravity, we impose a series of “physical” boundary conditions to obtain an unique field theoretical Lagrangian describing random surface models and strings at given dimensions d>1. Our theory reproduces the critical exponents obtained by numerical simulations on d-dimensional Ising-like models for lower d-values. One observes, at appropriate dimensions d, the transition to the so-called branched polymer phase.
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Peran, Ivan, Alex S. Holehouse, Isaac S. Carrico, Rohit V. Pappu, Osman Bilsel, and Daniel P. Raleigh. "Unfolded states under folding conditions accommodate sequence-specific conformational preferences with random coil-like dimensions." Proceedings of the National Academy of Sciences 116, no. 25 (June 5, 2019): 12301–10. http://dx.doi.org/10.1073/pnas.1818206116.
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Proteins are marginally stable molecules that fluctuate between folded and unfolded states. Here, we provide a high-resolution description of unfolded states under refolding conditions for the N-terminal domain of the L9 protein (NTL9). We use a combination of time-resolved Förster resonance energy transfer (FRET) based on multiple pairs of minimally perturbing labels, time-resolved small-angle X-ray scattering (SAXS), all-atom simulations, and polymer theory. Upon dilution from high denaturant, the unfolded state undergoes rapid contraction. Although this contraction occurs before the folding transition, the unfolded state remains considerably more expanded than the folded state and accommodates a range of local and nonlocal contacts, including secondary structures and native and nonnative interactions. Paradoxically, despite discernible sequence-specific conformational preferences, the ensemble-averaged properties of unfolded states are consistent with those of canonical random coils, namely polymers in indifferent (theta) solvents. These findings are concordant with theoretical predictions based on coarse-grained models and inferences drawn from single-molecule experiments regarding the sequence-specific scaling behavior of unfolded proteins under folding conditions.
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Semenoff, Gordon W., and Richard J. Szabo. "Fermionic Matrix Models." International Journal of Modern Physics A 12, no. 12 (May 10, 1997): 2135–291. http://dx.doi.org/10.1142/s0217751x97001328.
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We review a class of matrix models whose degrees of freedom are matrices with anti-commuting elements. We discuss the properties of the adjoint fermion one-matrix, two-matrix and gauge-invariant D-dimensional matrix models at large N and compare them with their bosonic counterparts, which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behavior. The topological large N expansions are also constructed and their relation to other aspects of modern string theory, such as integrable hierarchies, is discussed. We use these connections to discuss the applications of these matrix models to string theory and induced gauge theories. We argue that as such the fermionic matrix models may provide a novel generalization of the discretized random surface representation of quantum gravity in which the genus sum alternates and the sums over genera for correlators have better convergence properties than their Hermitian counterparts. We discuss the use of adjoint fermions instead of adjoint scalars to study induced gauge theories. We also discuss two classes of dimensionally reduced models, a fermionic vector model and a supersymmetric matrix model, and discuss their applications to the branched polymer phase of string theories in target space dimensions D > 1 and also to the meander problem.
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Marshall, W. F., A. F. Straight, A. Murray, J. C. Fung, J. Marko, D. A. Agard, and J. W. Sedat. "Direct measurement of chromatin diffusion and constraint in living cells using a gfp-lac repressor fusion protein." Proceedings, annual meeting, Electron Microscopy Society of America 54 (August 11, 1996): 740–41. http://dx.doi.org/10.1017/s0424820100166166.
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The polymer dynamics of interphase chromatin is at present a poorly understood aspect of nuclear organization, but one with profound consequences on events within the nucleus. The rates of many important processes, such as meiotic homolog pairing, site-specific recombination, and chromatin condensation, all involve the motion of chromatin within the nucleus. How fast can such rearrangements occur? Because interphase chromatin is likely to behave as a tangle of random-walk polymers, there is likely to be a substantial hindrance to diffusion. Therefore, the rate at which a given site on a chromosome can diffuse within the nucleus may limit the rate at which events requiring chromatin motion can occur. Furthermore, the polymer physics of interphase chromatin is an interesting line of theoretical research in its own right, and knowledge of diffusion rates is an important experimental parameter to consider when evaluating physical models. Finally, a fundamental aspect of nuclear architecture is the extent to which chromatin is anchored to a nuclear skeleton. Such matrix attachments would result in constrained diffusion, which can be detected by analysis of chromatin motion.
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Supriya, S., J. Selwinrajadurai, and P. Anshul. "MICROSTRUCTURE BASED FINITE ELEMENT ANALYSIS OF PARTICLE FILLED POLYMER COMPOSITE." Transactions of the Canadian Society for Mechanical Engineering 41, no. 5 (December 2017): 681–90. http://dx.doi.org/10.1139/tcsme-2017-503.
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Particle filled polymer composites are widely used because of its tailor-made properties and ease of manufacturability. Existing micro mechanical models to characterize heterogeneous material are based on the Representative Volume Element (RVE). The assumptions made in the RVE model, play a crucial role in the exact prediction of effective properties of the composites. In this work, microstructure based RVE is utilized to predict the effective properties of Solid Glass Microsphere (SGM) filled epoxy composite. The Scanning Electron Microscope (SEM) image obtained from the specimens fabricated at different loading fractions is processed in MATLAB. Canny edge detection algorithm is utilized for processing the images. The random dispersion of the particle is exactly modeled in ANSYS from the MATLAB output. The effective Young’s modulus of the SGM filled epoxy composite is determined. The numerically predicted values are compared with the experimental value and analytical models.
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KIM, HA-YOUNG, FREDERI G. VIENS, and ANDREW B. VIZCARRA. "LYAPUNOV EXPONENTS FOR STOCHASTIC ANDERSON MODELS WITH NON-GAUSSIAN NOISE." Stochastics and Dynamics 08, no. 03 (September 2008): 451–73. http://dx.doi.org/10.1142/s0219493708002408.
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The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian spacetime potentials W as solutions u to the multiplicative stochastic heat equation [Formula: see text] with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponential behavior of u is studied via its almost sure Lyapunov exponent λ = lim t→∞ t-1 log u(t, x), which is proved to exist, and is estimated as a function of β and κ for β2κ-1 bounded below: positivity and nontrivial upper bounds are established, generalizing and improving existing results. In discrete space λ is of order β2/ log (β2/κ) and in continuous space it is between β2(κ/β2)H/(H+1) and β2(κ/β2)H/(1+3H).
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Ahmadi, M., R. Ansari, and H. Rouhi. "Free Vibration Analysis of Carbon Fiber-Carbon Nanotube-Polymer Matrix Composite Plates by a Finite Element-Based Multi-Scale Modeling Approach." Journal of Multiscale Modelling 09, no. 02 (June 2018): 1850002. http://dx.doi.org/10.1142/s1756973718500026.
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The vibrational behavior of polymer matrix nanocomposite plates reinforced with carbon fibers (CFs) and carbon nanotubes (CNTs) is studied using the finite element method based on a multi-scale modeling approach. The influences of nano- and micro-scale are coupled through a two-step procedure. First, CNTs are dispersed into the polymer matrix. In the selected representative volume element (RVE), interphase due to chemical interaction between CNT and polymer matrix is considered. Also, the state of dispersion of CNTs into the matrix is assumed to be random. In the second step, CFs are randomly distributed in the reinforced polymer with CNTs. The reinforcement is carried out for various volume fractions of CFs and CNTs. Two three-dimensional models including the brick and shell ones are used to generate the results. Moreover, the analysis is presented for square plates under different types of boundary conditions. The effect of nanocomposite thickness on its vibrational response is also investigated.
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Kaliraj, M., P. Narayanasamy, M. Rajkumar, M. Mohammed Mohaideen, and I. Neethi Manickam. "Design, Fabrication and Analysis of Advanced Polymer Based Kevlar-49 Composite Material." Applied Mechanics and Materials 592-594 (July 2014): 122–27. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.122.
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The fatigue behavior of reinforced composites is complex and the present knowledge of fatigue study still needs extensive investigation of the micromechanical composite behavior. In fiber reinforced composites mechanical properties are highly dependent on their compositions, the matrix type as well as the volume fraction of the reinforcement and their arrangements such as random orientation and distribution, which increase the complexity in the study of fatigue damage behavior. There exist several classes of models to predict the fatigue life or the fatigue degradation of fiber reinforced composites but there exists so far no fatigue model that can be applied to a wide range of fiber reinforced composites. Thus, modifications of fatigue models are always needed in accordance with the micromechanical behavior of different fiber/matrix composites. In this paper the fatigue failure is rectified by using polymer based Kevlar composite material. The design and fabrication involves the design of polymer matrix like as fiber and resin, hardener etc. Kevlar-49 is chosen for as fabricating material to carry out this work. The fabrication set up is made by Vacuum Bag and it is demonstrated satisfactorily.
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Li, Jing, Liwen Zhang, Yanggui Deng, and Junping Zhang. "A Research on Modification Method for NSM FRP-Concrete Bonded Joints Strength Models." Advances in Polymer Technology 2020 (March 12, 2020): 1–15. http://dx.doi.org/10.1155/2020/1973626.
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A modification method was proposed for near-surface mounted (NSM) fiber-reinforced polymer (FRP)-concrete bonded joints strength prediction models considering model uncertainty. A database consisting of 246 test records was involved. Three bonded joints strength prediction models for NSM FRP reinforcement system were selected for modification. All the three selected models have model uncertainty factors associated with input design parameters. Spearman correlation analysis was used to prove the systematic correlation of the model uncertainty factors. For each model, a regression function f was established to eliminate the systematic nonrandom part of the model uncertainty factor. Then, the model uncertainty factors could be described by random variables obeying logarithmic normal distribution. A reliability analysis using the JC method was carried out to validate the practical significance and value of model modification. This study improves the predictability of FRP NSM reinforcement systems and provides valuable references for model calibration in practical engineering.
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Barrett, John W., and Endre Süli. "Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers." Mathematical Models and Methods in Applied Sciences 26, no. 03 (February 10, 2016): 469–568. http://dx.doi.org/10.1142/s0218202516500093.
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We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier–Stokes system in a bounded domain [Formula: see text] in [Formula: see text], [Formula: see text] or [Formula: see text], for the density [Formula: see text], the velocity [Formula: see text] and the pressure [Formula: see text] of the fluid, with an equation of state of the form [Formula: see text], where [Formula: see text] is a positive constant and [Formula: see text]. The right-hand side of the Navier–Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. The elastic extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term.
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Kyu, Thein, Hak-Soo Lee, Avi Gadkari, Joseph P. Kennedy, and Jar-Shyong Lin. "Structural and Rheo-Optical Characterization of Random Bicomponent Networks Prepared of Hydroxyl-Telechelic Polyisobutylene and Polytetrahydrofuran." Rubber Chemistry and Technology 68, no. 1 (March 1, 1995): 110–23. http://dx.doi.org/10.5254/1.3538722.
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Abstract The structure of a bicomponent network prepared of hydroxyl-telechelic polyisobutylene (HO—PIB—OH) and polytetrahydrofuran (HO—PTHF—OH) has been characterized by small-angle and wide-angle x-ray scattering, birefringence, and differential scanning Calorimetry. A single phase random network was obtained by endlinking HO—PIB—OH/HO—PTHF—OH mixtures using triphenyl methane triisocyanate (TTI) as a crosslinking agent. A small-angle x-ray scattering peak was observed in the PIB networks as well as in the PIB/PTHF bicomponent networks. The glass transition temperature of the random bicomponent network increased with decreasing PTHF molecular weight as the network became tighter. Network tensile properties were analyzed in terms of Gaussian and non-Gaussian network models. The stress-optical law was tested for random networks by measuring the variation of birefringence and stress as a function of elongation. Author to whom correspondence should be addressed. Present Address: Exxon Chemical Co. , Baytown Polymer Research Center, Baytown, TX 77520.
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Gerbuz, Vitalii. "Transport exponents of states with large support." Reviews in Mathematical Physics 31, no. 09 (October 2019): 1950029. http://dx.doi.org/10.1142/s0129055x19500296.
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We investigate spreading rates of one-dimensional quantum states under the Schrödinger time-evolution. The focus of this paper is on the states that either have finite support or decay exponentially at [Formula: see text]. In particular, we extend results of Damanik and Tcheremchantsev on estimating transport exponents that were originally proved to hold for the initial states supported on a single site. These general upper and lower estimates are then applied to several classes of models, including Sturmian, quasi-periodic and substitution-generated potentials, and the random polymer model.
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Miao, Fengyang, Weiguo Li, Jianguo Xu, Zhihao Chen, and Xiaoyu Feng. "Dynamic Response Analysis of Buried Drainage Pipes for Polymer Grouting Trenchless Rehabilitation under the Traveling Wave Effect." Advances in Civil Engineering 2022 (September 29, 2022): 1–15. http://dx.doi.org/10.1155/2022/2129573.
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The polymer grouting nonexcavation repair technology has been widely used in the repair of underground pipeline leaks, but the seismic response to the polymer repair pipeline is currently using a consistent excitation of seismic input without considering the influence of the traveling wave effect. This paper establishes the longitudinal and transverse vibration models of the polymer grout repair pipeline considering the traveling wave effect based on the elastic foundation beam theory. The seismic input uses artificially generated random seismic waves and solves the differential equations for pipeline vibration to carry out seismic response analysis of long-buried pipelines under three conditions: normal, vacant, and polymer grouting repair. The results show that after considering the traveling wave effect, the reaction of each measuring point on the pipeline has obvious phase characteristics, and the waveform of the distant measuring point has an obvious hysteresis phenomenon; the seismic wave velocity has a great influence on the deformation of the pipeline, and the displacement amplitude of the pipeline increases with the increase of the seismic wave velocity. The peak of pipeline displacement after vacancy will increase by 100%∼300% more than normal, while the difference in pipeline deformation after high polymer grouting is about 25% compared with normal, which means that the bottom vacant will have a great influence on pipeline deformation, and high polymer repair can restore the pipeline mechanical properties to normal levels.
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Kos, Pavel I., Aleksandra A. Galitsyna, Sergey V. Ulianov, Mikhail S. Gelfand, Sergey V. Razin, and Alexander V. Chertovich. "Perspectives for the reconstruction of 3D chromatin conformation using single cell Hi-C data." PLOS Computational Biology 17, no. 11 (November 18, 2021): e1009546. http://dx.doi.org/10.1371/journal.pcbi.1009546.
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Construction of chromosomes 3D models based on single cell Hi-C data constitute an important challenge. We present a reconstruction approach, DPDchrom, that incorporates basic knowledge whether the reconstructed conformation should be coil-like or globular and spring relaxation at contact sites. In contrast to previously published protocols, DPDchrom can naturally form globular conformation due to the presence of explicit solvent. Benchmarking of this and several other methods on artificial polymer models reveals similar reconstruction accuracy at high contact density and DPDchrom advantage at low contact density. To compare 3D structures insensitively to spatial orientation and scale, we propose the Modified Jaccard Index. We analyzed two sources of the contact dropout: contact radius change and random contact sampling. We found that the reconstruction accuracy exponentially depends on the number of contacts per genomic bin allowing to estimate the reconstruction accuracy in advance. We applied DPDchrom to model chromosome configurations based on single-cell Hi-C data of mouse oocytes and found that these configurations differ significantly from a random one, that is consistent with other studies.
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Zhu, Jing-Ang, Yetong Jia, Jincheng Lei, and Zishun Liu. "Deep Learning Approach to Mechanical Property Prediction of Single-Network Hydrogel." Mathematics 9, no. 21 (November 4, 2021): 2804. http://dx.doi.org/10.3390/math9212804.
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Hydrogel has a complex network structure with inhomogeneous and random distribution of polymer chains. Much effort has been paid to fully understand the relationship between mesoscopic network structure and macroscopic mechanical properties of hydrogels. In this paper, we develop a deep learning approach to predict the mechanical properties of hydrogels from polymer network structures. First, network structural models of hydrogels are constructed from mesoscopic scale using self-avoiding walk method. The constructed model is similar to the real hydrogel network. Then, two deep learning models are proposed to capture the nonlinear mapping from mesoscopic hydrogel network structural model to its macroscale mechanical property. A deep neural network and a 3D convolutional neural network containing the physical information of the network structural model are implemented to predict the nominal stress–stretch curves of hydrogels under uniaxial tension. Our results show that the end-to-end deep learning framework can effectively predict the nominal stress–stretch curves of hydrogel within a wide range of mesoscopic network structures, which demonstrates that the deep learning models are able to capture the internal relationship between complex network structures and mechanical properties. We hope this approach can provide guidance to structural design and material property design of different soft materials.
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Lee, Franklin Langlang, Jaehong Park, Sushmit Goyal, Yousef Qaroush, Shihu Wang, Hong Yoon, Aravind Rammohan, and Youngseon Shim. "Comparison of Machine Learning Methods towards Developing Interpretable Polyamide Property Prediction." Polymers 13, no. 21 (October 23, 2021): 3653. http://dx.doi.org/10.3390/polym13213653.
Full textAbstract:
Polyamides are often used for their superior thermal, mechanical, and chemical properties. They form a diverse set of materials that have a large variation in properties between linear to aromatic compounds, which renders the traditional quantitative structure–property relationship (QSPR) challenging. We use extended connectivity fingerprints (ECFP) and traditional QSPR fingerprints to develop machine learning models to perform high fidelity prediction of glass transition temperature (Tg), melting temperature (Tm), density (ρ), and tensile modulus (E). The non-linear model using random forest is in general found to be more accurate than linear regression; however, using feature selection or regularization, the accuracy of linear models is shown to be improved significantly to become comparable to the more complex nonlinear algorithm. We find that none of the models or fingerprints were able to accurately predict the tensile modulus E, which we hypothesize is due to heterogeneity in data and data sources, as well as inherent challenges in measuring it. Finally, QSPR models revealed that the fraction of rotatable bonds, and the rotational degree of freedom affects polyamide properties most profoundly and can be used for back of the envelope calculations for a quick estimate of the polymer attributes (glass transition temperature, melting temperature, and density). These QSPR models, although having slightly lower prediction accuracy, show the most promise for the polymer chemist seeking to develop an intuition of ways to modify the chemistry to enhance specific attributes.
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BARRETT, JOHN W., and ENDRE SÜLI. "EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS II: HOOKEAN-TYPE MODELS." Mathematical Models and Methods in Applied Sciences 22, no. 05 (April 8, 2012): 1150024. http://dx.doi.org/10.1142/s0218202511500242.
Full textAbstract:
We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain in ℝd, d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker–Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum ṵ0 for the Navier–Stokes equation and a non-negative initial probability density function ψ0 for the Fokker–Planck equation, which has finite relative entropy with respect to the Maxwellian M, we prove, via a limiting procedure on certain regularization parameters, the existence of a global-in-time weak solution t ↦ (ṵ(t), ψ(t)) to the coupled Navier–Stokes–Fokker–Planck system, satisfying the initial condition (ṵ(0), ψ(0)) = (ṵ0, ψ0), such that t ↦ ṵ(t) belongs to the classical Leray space and t ↦ ψ(t) has bounded relative entropy with respect to M and t ↦ ψ(t)/M has integrable Fisher information (with respect to the measure [Formula: see text]) over any time interval [0, T], T>0. If the density of body forces [Formula: see text] on the right-hand side of the Navier–Stokes momentum equation vanishes, then a weak solution constructed as above is such that t ↦ (ṵ(t), ψ(t)) decays exponentially in time to [Formula: see text] in the [Formula: see text]-norm, at a rate that is independent of (ṵ0, ψ0) and of the center-of-mass diffusion coefficient. Our arguments rely on new compact embedding theorems in Maxwellian-weighted Sobolev spaces and a new extension of the Kolmogorov–Riesz theorem to Banach-space-valued Sobolev spaces.
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Spanos, P., P. Elsbernd, B. Ward, and T. Koenck. "Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1993 (June 28, 2013): 20120494. http://dx.doi.org/10.1098/rsta.2012.0494.
Full textAbstract:
This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective stress–strain curve and thermal conductivity of the composite material, finite-element analysis (FEA), in conjunction with the embedded fibre method (EFM), is used. Variable nanotube geometry, alignment and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, incremental and iterative FEA approaches are used for the determination of the nonlinear properties of the nanocomposite. For the determination of the electrical properties, a spanning network identification algorithm is used. First, a realistic nanotube morphology is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in a representative volume element. Then, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's current law is used in conjunction with FEA to solve for the voltages and currents in the system and thus calculate the effective electrical conductivity of the nanocomposite. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone and determines the effective conductivity. Monte Carlo analysis of 500 random microstructures is performed to capture the stochastic nature of the fibre generation and to derive statistically reliable results. The models are validated by comparison with various experimental datasets reported in the recent literature.
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BARRETT, JOHN W., and ENDRE SÜLI. "EXISTENCE OF GLOBAL WEAK SOLUTIONS TO DUMBBELL MODELS FOR DILUTE POLYMERS WITH MICROSCOPIC CUT-OFF." Mathematical Models and Methods in Applied Sciences 18, no. 06 (June 2008): 935–71. http://dx.doi.org/10.1142/s0218202508002917.
Full textAbstract:
We study the existence of global-in-time weak solutions to a coupled microscopic–macroscopic bead-spring model with microscopic cut-off, which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝd, d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function ψ that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term and a cut-off function βL(ψ) = min (ψ,L) in the drag term, where L ≫ 1. We establish the existence of global-in-time weak solutions to the model for a general class of spring-force potentials including, in particular, the widely used finitely extensible nonlinear elastic potential. A key ingredient of the argument is a special testing procedure in the weak formulation of the Fokker–Planck equation, based on the convex entropy function [Formula: see text]. In the case of a corotational drag term, passage to the limit as L → ∞ recovers the Navier–Stokes–Fokker–Planck model with centre-of-mass diffusion, without cut-off.
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Cariapa, V., R. J. Stango, L. Chen, and R. Hermann. "Aspects of Process Model for Automatic Control of Edge-Deburring with Filamentary Brush." Journal of Engineering for Industry 114, no. 3 (August 1, 1992): 294–300. http://dx.doi.org/10.1115/1.2899795.
Full textAbstract:
In this paper, process models are reported for a dynamic system consisting of a polymer/mineral abrasive filamentary brush during an orthogonal deburring operation. Dynamic process models are generated by employing both a viscoelastic representation and Dynamic Data Systems approach for predicting brush response under random penetration depth operating conditions. A process model for material removal is obtained by the use of a multiple regression method in conjunction with experimental results for burr material removal under various brushing conditions. Time constants for both the viscoelastic dynamic system and material removal characteristics of brushes are reported and discussed. An examination of system transfer functions indicates that the system is stable. In addition, generally good agreement is obtained when comparison is made between the process model for burr removal and actual measurement of machined burrs.
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Zeki, Mousa, and Shakir Al-Busaltan. "Developing Laboratory Performance Models for Thin Asphalt Overlay Mixtures." Journal of University of Babylon for Engineering Sciences 27, no. 1 (February 11, 2019): 382–95. http://dx.doi.org/10.29196/jubes.v27i1.2186.
Full textAbstract:
Statistical modeling is utilized effectively to development relation/s between the dependent variables and independent variables. In other words, it describes how one or more random variables are related to one more other variables. Building verified models can help in predicting performance characteristics, and saving time and money. This study aims to present a statistical models which help to understand the significance of the different parameters in characterizing the performance of the Thin Asphalt Overlay (TAO). The experimental program included: design the thin asphalt overlay mixtures using one gradation type (9.5 Nominal Maximum Aggregate Size NMAS), three filler types (conventional mineral filler, Ordinary Portland Cement, and Quick lime), and five percentages of asphalt content to identify the optimum asphalt content. Then, Styrene Butadiene Styrene (SBS) modified polymer binder was introduced for performance enhancement. Performance tests were used to evaluate TAO mixture in term of some main namely, volumetric, mechanical, and durability properties are (bulk density, indirect tensile strength and tensile strength ratio). Statistical Product and Service Solutions (SPSS) software (Version 24) was used as a tool for models building. To find the most accurate statistical models, linear and nonlinear regression was achieved. This study demonstrates that the using statistical modeling is achievable and offer a vital tool to describe the characteristics and performance of the TAO mixture in term volumetric, mechanical and durability properties.
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Kumar, Archana, and Kamal Prasad. "Effective Complex Permittivity of Random Composite Media: PVDF/(Na<sub>1/2</sub>Bi<sub>1/2</sub>)TiO<sub>3</sub>." Materials Science Forum 1074 (November 8, 2022): 47–52. http://dx.doi.org/10.4028/p-8k3qus.
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The present study discusses the fabrication of non-lead ceramic/polymer composites employing (Na1/2Bi1/2)TiO3 (NBT) ceramic powder as a filler and poly(vinylidene fluoride); PVDF as a polymer matrix. The NBT (volume fraction, ϕ = 1) ceramics were synthesized using the conventional mixed-oxide method followed by the high-energy ball milling method whereas (1-ϕ)PVDF/ϕ(Na1/2Bi1/2)TiO3; 0 ≤ ϕ ≤ 0.3 composites were prepared from a melt-mixing process. It was observed that the real and imaginary parts of dielectric permittivity, ac conductivity, and longitudinal piezoelectric charge coefficient increase with the increase in NBT-content. Different dielectric mixing models were presented to determine the effective complex permittivity of the composites. Five dielectric mixture equations have been chosen to test the acceptability of experimental data. It was revealed that theoretical models as given by Bruggman, Rother-Lichtenecker, and modified Rother-Lichtenecker show good agreement with the experimental results of filler-concentration dependent alteration of effective relative permittivity and loss factor of the PVDF/NBT composite. A mathematical model of first-order exponential growth has also been proposed, which fitted excellently the experimental data (r2 > 0.998).
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Pandiyan, Vigneashwara, Wahyu Caesarendra, Adam Glowacz, and Tegoeh Tjahjowidodo. "Modelling of Material Removal in Abrasive Belt Grinding Process: A Regression Approach." Symmetry 12, no. 1 (January 5, 2020): 99. http://dx.doi.org/10.3390/sym12010099.
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This article explores the effects of parameters such as cutting speed, force, polymer wheel hardness, feed, and grit size in the abrasive belt grinding process to model material removal. The process has high uncertainty during the interaction between the abrasives and the underneath surface, therefore the theoretical material removal models developed in belt grinding involve assumptions. A conclusive material removal model can be developed in such a dynamic process involving multiple parameters using statistical regression techniques. Six different regression modelling methodologies, namely multiple linear regression, stepwise regression, artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), support vector regression (SVR) and random forests (RF) have been applied to the experimental data determined using the Taguchi design of experiments (DoE). The results obtained by the six models have been assessed and compared. All five models, except multiple linear regression, demonstrated a relatively low prediction error. Regarding the influence of the examined belt grinding parameters on the material removal, inference from some statistical models shows that the grit size has the most substantial effect. The proposed regression models can likely be applied for achieving desired material removal by defining process parameter levels without the need to conduct physical belt grinding experiments.
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Wang, Zhenqing, Fang Liu, Wenyan Liang, and Limin Zhou. "Study on Tensile Properties of Nanoreinforced Epoxy Polymer: Macroscopic Experiments and Nanoscale FEM Simulation Prediction." Advances in Materials Science and Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/392450.
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The effect of nanosilica contents on mechanical properties of the epoxy matrix with some nanoparticle aggregations was studied in macroscopic experiments and nanoscale simulation, particularly with regard to the effective modulus and ultimate stress. Three analytical models were used to obtain the effective elastic modulus of nanoparticle-reinforced composites. Based on Monte-Carlo method, the special program for the automatic generation of 2D random distribution particles without overlapping was developed for nanocomposite modeling. Weight fractions of nanoparticles were converted to volume fractions, in order to coordinate the content unit in the simulation. In numerical analysis, the weak interface strengthening and toughening mechanism was adopted. Virtual crack closure technique (VCCT) and extended finite element method (XFEM) were used to simulate phenomena of nanoparticle debonding and matrix crack growth. Experimental and simulation results show a good agreement with each other. By way of simulation, the weak interface toughening and strengthening mechanism of nanocomposites is confirmed.
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Cao, Zheng, Boguslaw Kruczek, and Jules Thibault. "Monte Carlo Simulations for the Estimation of the Effective Permeability of Mixed-Matrix Membranes." Membranes 12, no. 11 (October 27, 2022): 1053. http://dx.doi.org/10.3390/membranes12111053.
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Recent years have seen the explosive development of mixed-matrix membranes (MMMs) for a myriad of applications. In gas separation, it is desired to concurrently enhance the permeability, selectivity and physicochemical properties of the membrane. To help achieving these objectives, experimental characterization and predictive models can be used synergistically. In this investigation, a Monte Carlo (MC) algorithm is proposed to rapidly and accurately estimate the relative permeability of ideal MMMs over a wide range of conditions. The difference in diffusivity coefficients between the polymer matrix and the filler particle is used to adjust the random progression of the migrating species inside each phase. The solubility coefficients of both phases at the polymer–filler interface are used to control the migration of molecules from one phase to the other in a way to achieve progressively phase equilibrium at the interface. Results for various MMMs were compared with the results obtained with the finite difference method under identical conditions, where the results from the finite difference method are used in this investigation as the benchmark method to test the accuracy of the Monte Carlo algorithm. Results were found to be very accurate (in general, <1% error) over a wide range of polymer and filler characteristics. The MC algorithm is simple and swift to implement and provides an accurate estimation of the relative permeability of ideal MMMs. The MC method can easily be extended to investigate more readily non-ideal MMMs with particle agglomeration, interfacial void, polymer-chain rigidification and/or pore blockage, and MMMs with any filler geometry.
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Yoshida, Eri. "Neuron-like tubule extension of giant polymer vesicles." Chemical Reports 3, no. 1 (2021): 195–202. http://dx.doi.org/10.25082/cr.2021.01.004.
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Giant polymer vesicles consisting of amphiphilic diblock copolymers are helpful as artificial biomembrane models based on many similarities in their size, structure, morphological transformation, membrane permeability, etc. This paper describes the creation of neuron-like tubule extension employing the polymer vesicles. The polymerization-induced self-assembly was performed in the presence of micron-sized spherical vesicles consisting of poly(methacrylic acid)-block-poly(methyl methacrylate-random-methacrylic acid), PMAA-b-P(MMA-r-MAA), through the photo nitroxide-mediated controlled/living radical polymerization (photo-NMP) using 4-methoxy-2,2,6,6-tetramethylpiperidine-1-oxyl (MTEMPO) as the mediator. The photo-NMP of methyl methacrylate (MMA) and methacrylic acid (MAA) was carried out in an aqueous methanol solution (CH3OH/H2O = 3/1 v/v) using poly(methacrylic acid) (PMAA) end-capped with MTEMPO and the spherical vesicles of PMAA141-b-P(MMA0.831-r-MAA0.169)368 with an 11.7-mm diameter. The vesicles projected many processes on their surface during the early stage of the polymerization. As the polymerization progressed, only one or two of the processes extended to thick tubules, accompanied by the slow growth of thin tubules. Further progress of the polymerization elongated the thick tubules and caused branching of the tubules. The tubules had a vesicular structure because cup-like vesicles joined in line were formed during the initial stage of the extension. The polymerization livingness supported the tubule extension based on a linear increase in the molecular weight of the component copolymer and a negligible change in the molecular weight distribution versus the monomer conversion. The spherical vesicles were similar to the neurons in the tubule extension for the initial projection, followed by the elongation and branching. This similarity implies that the neurite extension in the neurons is related to the inherent property of the bilayer membrane.
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Alkhatib, A. M., and P. R. King. "The Use of the Least-Squares Probabilistic-Collocation Method in Decision Making in the Presence of Uncertainty for Chemical-Enhanced-Oil-Recovery Processes." SPE Journal 20, no. 04 (August 20, 2015): 747–66. http://dx.doi.org/10.2118/170587-pa.
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Summary The least-squares Monte Carlo method (LSM) is a decision-evaluation method that can capture the value of flexibility of a process. This method was shown to provide us with some insight into the effect of uncertainty on decision making and to help us capture the upside potential or mitigate the downside effects for a chemical enhanced-oil-recovery (EOR) process. The method is a stochastic approximate dynamic programming approach to decision making. It is modeled after a forward simulation coupled with a recursive algorithm, which produces the near-optimal policy. It relies on Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir-engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the LSM by improving the sampling method used to generate the technical uncertainties used in producing the production profiles and to extend its application to different chemical EOR processes. The probabilistic-collocation method has been proved to be a robust and efficient uncertainty-quantification method. It approximates the random input distributions by use of polynomial-chaos expansions and produces a proxy polynomial for the output parameter requiring a limited number of model responses that is conditional on the number of random inputs and the order of the approximation desired. The resulting proxy can then be used to generate the different statistical moments with negligible computational requirement. By use of the sampling methods of the probabilistic-collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision-evaluation method. This is known as the least-squares probabilistic-collocation method (LSPCM). Both methods were demonstrated on a chemical EOR problem by use of a number of stylized reservoir models. The technical uncertainties considered were the residual oil saturation to chemical flooding, surfactant and polymer adsorption, and the viscosity multiplier of the polymer. The economic uncertainties considered were the oil price and the surfactant and polymer price. Both methods were applied by use of three reservoir case studies: a simple homogeneous model, the PUNQ-S3 (2010) model, and a modified portion of the SPE10 model (Christie and Blunt 2001). The results show that the use of the sampling techniques of the probabilistic-collocation method produced relatively accurate responses compared with the original method. For instance, it was possible to produce the same output for the modified SPE10 model by use of the second-order quadrature nodes—81 realizations—rather than the 103 realizations used for the LSM, thus achieving an order-of-magnitude reduction in computational time. The scalability limits of both methods and the different possible enhancements to practically adapt the LSPCM to more-realistic and more-complex reservoir models were discussed. The application was extended to other chemical EOR processes, such as alkaline/surfactant/polymer flooding and polymer flooding, and to more-complex decision problems. The results show that the use of the LSPCM produced accurate results compared with the LSM.
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Alkhatib, A., and M. Babaei. "Applying the Multilevel Monte Carlo Method for Heterogeneity-Induced Uncertainty Quantification of Surfactant/Polymer Flooding." SPE Journal 21, no. 04 (August 15, 2016): 1192–203. http://dx.doi.org/10.2118/172635-pa.
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Summary Reservoir heterogeneity can be detrimental to the success of surfactant/polymer enhanced-oil-recovery (EOR) processes. Therefore, it is important to evaluate the effect of uncertainty in reservoir heterogeneity on the performance of surfactant/polymer EOR. Usually, a Monte Carlo sampling approach is used, in which a number of stochastic reservoir-model realizations are generated and then numerical simulation is performed to obtain a certain objective function, such as the recovery factor. However, Monte Carlo simulation (MCS) has a slow convergence rate and requires a large number of samples to produce accurate results. This can be computationally expensive when using large complex reservoir models. This study applies a multiscale approach to improve the efficiency of uncertainty quantification. This method is known as the multilevel Monte Carlo (MLMC) method. This method comprises performing a small number of expensive simulations on the fine-scale model and a large number of less-expensive simulations on coarser upscaled models, and then combining the results to produce the quantities of interest. The purpose of this method is to reduce computational cost while maintaining the accuracy of the fine-scale model. The results of this approach are compared with a reference MCS, assuming a large number of simulations on the fine-scale model. Other advantages of the MLMC method are its nonintrusiveness and its scalability to incorporate an increasing number of uncertainties. This study uses the MLMC method to efficiently quantify the effect of uncertainty in heterogeneity on the recovery factor of a chemical EOR process, specifically surfactant/polymer flooding. The permeability field is assumed to be the random input. This method is first demonstrated by use of a Gaussian 3D reservoir model. Different coarsening algorithms are used and compared, such as the renormalization method and the pressure-solver method (PSM). The results are compared with running Monte Carlo for the fine-scale model while equating the computational cost for the MLMC method. Both of these results are then compared with the reference case, which uses a large number of runs of the fine-scale model. The method is then extended to a channelized non-Gaussian generated 3D reservoir model incorporating multiphase upscaling The results show that it is possible to robustly quantify spatial uncertainty for a surfactant/polymer EOR process while greatly reducing the computational requirement, up to two orders of magnitude compared with traditional Monte Carlo for both the Gaussian and non-Gaussian reservoir models. The method can be easily extended to other EOR processes to quantify spatial uncertainty, such as carbon dioxide (CO2) EOR. Other possible extensions of this method are also discussed.
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PEKCAN, ÖNDER, and SELIM KARA. "GELATION MECHANISMS." Modern Physics Letters B 26, no. 27 (September 24, 2012): 1230019. http://dx.doi.org/10.1142/s0217984912300190.
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In this paper, we survey the gelation mechanisms for various polymeric systems which are classified by the type and the strength of the cross-linkages. These are the "irreversible" gels that are cross-linked chemically by covalent bonds and the "reversible" gels that are cross-linked physically by hydrogen or ionic bonds and by the physical entanglement of polymer chains. Some of the natural polymer gels fall into the class of physical gels, among which the red algae that has attracted attention for various applications is discussed in detail. Various composite gels, formed from mixture of physical and chemical gels are also discussed in the last section of the article. Theoretical models describe the gelation as a process of random linking of subunits to larger and larger molecules by formation of an infinite network, where no matter what type of objects are linked, there is always a critical "gel point" at which the system behaves neither as a liquid nor as a solid on any length scale. The Flory–Stockmayer theory and percolation theory provide bases for modeling this sol–gel phase transition. The experimental techniques for measuring the critical exponents for sol–gel phase transitions in different polymeric systems are introduced and the validation of various theoretical predictions are surveyed.
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Huang, Li Hong, Xiaoxiang Yang, and Jianhong Gao. "Study on Microstructure Effect of Carbon Black Particles in Filled Rubber Composites." International Journal of Polymer Science 2018 (October 11, 2018): 1–11. http://dx.doi.org/10.1155/2018/2713291.
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The cross sections of blended natural/styrene-butadiene (NSBR) composites filled with different volume fractions of carbon particles were observed using a Quanta 250 scanning electron microscope. In addition, the sizes and distributions of the carbon particles were analyzed using Nano Measurer. A two-dimensional representative volume element model (RVE) for a rubber composite reinforced with circular carbon particles was established, and the uniaxial tensile behaviors of polymer nanocomposites with different particle size distribution patterns were simulated using the ABAQUS software. The results showed the following. (1) For the random models, if the difference of particle size was larger and particle distance was closer, stress distribution would be denser as well as the stress concentration would become greater. However, if the difference of particle size was small, for the case of same particle volume fraction, the particle size has little influence on the macromechanical properties whether the average size is large or small. (2) The correlation between the volume fraction and distribution of the carbon particles revealed that when the volume fraction of carbon black particles was larger than 12%, clusters between carbon particles in the polymer nanocomposites could not be avoided and the modulus of the composites increased with an increase in the cluster number.
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Du, Jlng-Long, and Robert C. Thompson. "Antiferromagnetic exchange in manganese(II) monophenylphosphinate and the effects of cadmium doping." Canadian Journal of Chemistry 67, no. 7 (July 1, 1989): 1239–43. http://dx.doi.org/10.1139/v89-188.
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Mn[H(C6H5)PO2]2, its cadmium analogue, and mixed metal materials of composition Mn1−xCdx[H(C6H5)PO2]2 (x = 0.005, 0.01, 0.09, 0.27, and 0.47) have been synthesized and characterized by X-ray powder diffraction, infrared spectroscopy, differential scanning calorimetry and low-temperature (4.2 to 80 K) magnetic susceptibility studies. The materials are shown to be isomorphous and are considered to have polymeric structures in which chains of metal atoms are linked by bridging phosphinate groups. The pure manganese compound is antiferromagnetic (maximum in xm at ~35 K) and the magnetic data for the compound have been analyzed according to two theoretical models for linear chains of antiferromagnetically coupled manganese(II) (d5, spin-free) ions. The Wagner and Friedberg model gives J = −3.00 cm−1 and the Weng model gives J = −2.78 cm−1. The effects of replacing Mn2+ by Cd2+ ions in the polymer is to increase the magnetic susceptibility (per mol of Mn) at all temperatures. Analysis of the data as a function of Cd doping indicates the incorporation of a paramagnetic component to the susceptibility which increases with increasing Cd content. In addition, the absolute value of the exchange coupling constant appears to decrease as the Cd content increases. These effects are considered in terms of a random defect model in which the replacement of Mn ions in the polymer by Cd ions results in the formation of Cd ion separated finite magnetic chain fragments. Keywords: manganese(II) monophenylphosphinate, magnetic properties, coordination polymer, cadmium doped antiferromagnet.
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Chen, Kai, Yunhai Cheng, Mingsheng Yu, Long Liu, Yonggang Wang, and Junfei Zhang. "Predicting the Geopolymerization Process of Fly-Ash-Based Geopolymer Using Machine Learning." Buildings 12, no. 11 (October 26, 2022): 1792. http://dx.doi.org/10.3390/buildings12111792.
Full textAbstract:
The process of geopolymerization affects the freshness and hardening properties of fly ash base polymer. The prediction of geological polymerization parameters, such as DPT, DPH, GPT, and GPH, is very important for the mixing optimization of FA base polymer. In this study, machine learning models such as backpropagation neural network, support vector regression, random forest, K-nearest neighbor, logistic regression, and multiple linear regression were used to predict the above geological polymerization parameters and explain the influence of composition on the geological polymerization of FA base polymer. Results show that RF was the most stable ML model and had the best predictive performance on the test sets of GPT, GPH, DPT, and DPH, with correlation coefficients of 0.88, 0.95, 0.92, and 0.95, respectively. The variable importance and sensitivity were analyzed by SHapley Additive exPlanations. Results indicate that temperature is the most significant input variable affecting the DPT, DPH, and GPH with SHAP values of 0.09, 4.83, and 1.03, respectively. For GPT, the SHAP value of temperature is 6.89, slightly lower than that of LFR (6.95); yet it is a still significantly important input variable. The mole ratio and alkaline solution concentration were also important and negatively contributed to DPT and DPH, respectively. Besides, both GPT and GPH were sensitive to the mass ratio of liquid-to-fly ash which can promote the geopolymerization extent and shorten the geopolymerization time at a small content. The results of this study pave the way for automatic mixture optimization of FA-based geopolymers.
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Chen, Wei, Yiping Liu, Zhenyu Jiang, Liqun Tang, Zejia Liu, and Licheng Zhou. "Modeling of Compressive Strength for Unidirectional Fiber Reinforced Composites with Nanoparticle Modified Epoxy Matrix." Materials 12, no. 23 (November 26, 2019): 3897. http://dx.doi.org/10.3390/ma12233897.
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Incorporation of nanoparticles into polymer matrix was found to considerably improve the compressive performance of unidirectional fiber reinforced composites. In our experimental study, an increase by 62.7% in the longitudinal compressive strength of unidirectional carbon fiber reinforced composites is attained by dispersing 8.7 vol.% SiO2 nanoparticles into epoxy matrix. A compressive strength model is established to quantitatively describe the reinforcing effects of nanoparticles, which combines a modified microbuckling model for unidirectional fiber reinforced composites and a constitutive model for nanocomposite matrices under compression. In the two models, the coupling of damage and plasticity is considered to contribute to the nonlinear response of nanocomposite matrix. The proposed strength model demonstrates excellent prediction capability in experimental verification. A small relative deviation below 8.2% is achieved between the predicted compressive strength of unidirectional fiber reinforced composites and the measured values, which is at the same level of random error in experiments.
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Needleman, Daniel J., Aaron Groen, Ryoma Ohi, Tom Maresca, Leonid Mirny, and Tim Mitchison. "Fast Microtubule Dynamics in Meiotic Spindles Measured by Single Molecule Imaging: Evidence That the Spindle Environment Does Not Stabilize Microtubules." Molecular Biology of the Cell 21, no. 2 (January 15, 2010): 323–33. http://dx.doi.org/10.1091/mbc.e09-09-0816.
Full textAbstract:
Metaphase spindles are steady-state ensembles of microtubules that turn over rapidly and slide poleward in some systems. Since the discovery of dynamic instability in the mid-1980s, models for spindle morphogenesis have proposed that microtubules are stabilized by the spindle environment. We used single molecule imaging to measure tubulin turnover in spindles, and nonspindle assemblies, in Xenopus laevis egg extracts. We observed many events where tubulin molecules spend only a few seconds in polymer and thus are difficult to reconcile with standard models of polymerization dynamics. Our data can be quantitatively explained by a simple, phenomenological model—with only one adjustable parameter—in which the growing and shrinking of microtubule ends is approximated as a biased random walk. Microtubule turnover kinetics did not vary with position in the spindle and were the same in spindles and nonspindle ensembles nucleated by Tetrahymena pellicles. These results argue that the high density of microtubules in spindles compared with bulk cytoplasm is caused by local enhancement of nucleation and not by local stabilization. It follows that the key to understanding spindle morphogenesis will be to elucidate how nucleation is spatially controlled.