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Journal articles on the topic 'Two continuum model'

Author: Grafiati
Published: 2 July 2021
Last updated: 1 February 2022

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1

Xiao, Zhiguang, and Zhi-Yong Zhou. "On Friedrichs model with two continuum states." Journal of Mathematical Physics 58, no. 6 (June 2017): 062110. http://dx.doi.org/10.1063/1.4989832.

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2

Deijfen, Maria, and Olle Häggström. "Coexistence in a two-type continuum growth model." Advances in Applied Probability 36, no. 04 (December 2004): 973–80. http://dx.doi.org/10.1017/s0001867800013264.

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We consider a stochastic model describing the growth of two competing infections on ℝ d . The growth takes place by way of spherical outbursts in the infected region, an outburst in the type-1 or -2 infected region causing all previously uninfected points within a stochastic distance from the outburst location to become type-1 or -2 infected, respectively. The main result is that, if the infection types have the same intensity, then there is a strictly positive probability that both infection types grow unboundedly.
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3

Head, A. K., S. D. Howison, J. R. Ockendon, J. B. Titchener, and P. Wilmott. "A continuum model for two-dimensional dislocation distributions." Philosophical Magazine A 55, no. 5 (May 1987): 617–29. http://dx.doi.org/10.1080/01418618708214372.

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4

Anazawa, M., A. Ishikawa, and H. Itoyama. "Continuum annulus amplitudes from the two-matrix model." Physical Review D 52, no. 10 (November 15, 1995): 6016–19. http://dx.doi.org/10.1103/physrevd.52.6016.

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5

Hoyle, Rebecca B., and Anita Mehta. "Two-Species Continuum Model for Aeolian Sand Ripples." Physical Review Letters 83, no. 24 (December 13, 1999): 5170–73. http://dx.doi.org/10.1103/physrevlett.83.5170.

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6

Deijfen, Maria, and Olle Häggström. "Coexistence in a two-type continuum growth model." Advances in Applied Probability 36, no. 4 (December 2004): 973–80. http://dx.doi.org/10.1239/aap/1103662953.

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We consider a stochastic model describing the growth of two competing infections on ℝd. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type-1 or -2 infected region causing all previously uninfected points within a stochastic distance from the outburst location to become type-1 or -2 infected, respectively. The main result is that, if the infection types have the same intensity, then there is a strictly positive probability that both infection types grow unboundedly.
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7

Zdravković, S., S. Zeković, A. N. Bugay, and J. Petrović. "Two component model of microtubules and continuum approximation." Chaos, Solitons & Fractals 152 (November 2021): 111352. http://dx.doi.org/10.1016/j.chaos.2021.111352.

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8

Mi, Qi, David Swigon, and Beatrice Riviere. "Two-dimensional elastic continuum model of enterocyte layer migration." Journal of Critical Care 22, no. 4 (December 2007): 350. http://dx.doi.org/10.1016/j.jcrc.2007.10.034.

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9

Ryś, M., and B. Skoczeń. "Coupled constitutive model of damage affected two-phase continuum." Mechanics of Materials 115 (December 2017): 1–15. http://dx.doi.org/10.1016/j.mechmat.2017.08.015.

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10

Yu, Lei. "A new continuum traffic flow model with two delays." Physica A: Statistical Mechanics and its Applications 545 (May 2020): 123757. http://dx.doi.org/10.1016/j.physa.2019.123757.

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11

Sulem, Jean, and Hans-B. Mühlhaus. "A continuum model for periodic two-dimensional block structures." Mechanics of Cohesive-frictional Materials 2, no. 1 (January 1997): 31–46. http://dx.doi.org/10.1002/(sici)1099-1484(199701)2:1<31::aid-cfm24>3.0.co;2-o.

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12

Zhou, Yahong, Peijun Wei, Yueqiu Li, and Li Li. "Continuum model of two-dimensional crystal lattice of metamaterials." Mechanics of Advanced Materials and Structures 26, no. 3 (August 30, 2017): 224–37. http://dx.doi.org/10.1080/15376494.2017.1341582.

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13

Lämmel, M., D. Rings, and K. Kroy. "A two-species continuum model for aeolian sand transport." New Journal of Physics 14, no. 9 (September 20, 2012): 093037. http://dx.doi.org/10.1088/1367-2630/14/9/093037.

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14

Soheili, Ali Reza. "Continuum model of the two-component Becker-Döring equations." International Journal of Mathematics and Mathematical Sciences 2004, no. 49 (2004): 2641–48. http://dx.doi.org/10.1155/s0161171204304084.

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The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.
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15

CAI, YUNHAI, and GEORGE SIOPSIS. "CRITICAL MODELS COUPLED TO TWO-DIMENSIONAL GRAVITY IN THE CONTINUUM." Modern Physics Letters A 06, no. 14 (May 10, 1991): 1261–68. http://dx.doi.org/10.1142/s0217732391001342.

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We discuss minimal conformal field theories M(p,q) coupled to 2-dimensional gravity in the continuum. We find a transformation that enables us to relate all models with p=2 to each other. We identify the Fock space in each model and calculate correlation functions. We thus show that the k-th multi-critical matrix model corresponds to the non-unitary minimal model with q=2k−1.
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16

Brackley, C. A., and M. S. Turner. "Two-point heterogeneous connections in a continuum neural field model." Biological Cybernetics 100, no. 5 (April 7, 2009): 371–83. http://dx.doi.org/10.1007/s00422-009-0308-7.

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17

NGUYEN, VAN LIEN, and ENRIQUE CANESSA. "FINITE-SIZE SCALING IN TWO-DIMENSIONAL CONTINUUM PERCOLATION MODELS." Modern Physics Letters B 13, no. 17 (July 20, 1999): 577–83. http://dx.doi.org/10.1142/s0217984999000737.

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We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of mass M to sample size L as generally accepted for isotropic lattice problems, but with a positive sign of the slope in the ln–ln plot of M versus L. Another interesting aspect of the finite-size 2D models is also suggested by plotting the normalized mass in 2D continuum and lattice bond percolation models versus an effective percolation parameter, independent of the system structure (i.e., lattice or continuum) and of the possible directions allowed for percolation (i.e., isotropic or directed) in regions close to the percolation thresholds. Our study is the first attempt to map the scaling behavior of the mass for both lattice and continuum model systems into one curve.
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18

BLOM, J. G., and M. A. PELETIER. "A continuum model of lipid bilayers." European Journal of Applied Mathematics 15, no. 4 (August 2004): 487–508. http://dx.doi.org/10.1017/s0956792504005613.

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We study a one-dimensional continuum model for lipid bilayers. The system consists of water and lipid molecules; lipid molecules are represented by two ‘beads’, a head bead and a tail bead, connected by a rigid rod. We derive a simplified model for such a system, in which we only take into account the effects of entropy and hydrophilic/hydrophobic interactions. We show that for this simple model membrane-like structures exist for certain choices of the parameters, and numerical calculations suggest that they are stable.
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19

Meeus, Wim. "The Identity Status Continuum Revisited." European Psychologist 23, no. 4 (October 2018): 289–99. http://dx.doi.org/10.1027/1016-9040/a000339.

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Abstract. The developmental continuum of identity status has been a topic of theoretical debate since the early 1980’s. A recent meta-analysis and recent studies with dual cycle models lead to two conclusions: (1) during adolescence there is systematic identity maturation; (2) there are two continuums of identity status progression. Both continuums show that in general adolescents move from transient identity statuses to identity statuses that mark the relative endpoints of development: from diffusion to closure, and from searching moratorium and moratorium to closure and achievement. This pattern can be framed as development from identity formation to identity maintenance. In Identity Status Interview research using Marcia’s model, not the slightest indication for a continuum of identity development was found. This may be due to the small sample sizes of the various studies leading to small statistical power to detect differences in identity status transitions, as well as developmental inconsistencies in Marcia’s model. Findings from this review are interpreted in terms of life-span developmental psychology.
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20

Askes, Harm, Juha Hartikainen, Kari Kolari, Reijo Kouhia, Timo Saksala, and Jani Vilppo. "On the Kachanov-Rabotnov continuum damage model." Rakenteiden Mekaniikka 53, no. 2 (March 30, 2020): 125–44. http://dx.doi.org/10.23998/rm.82528.

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In this paper two partially complementary formulations of the simple phenomenological Kachanov-Rabotnov continuum damage constitutive model are presented. The models are based on a consistent thermodynamic formulation using proper expressions for the Helmholtz free energy or its complementary form of the dissipation potential. Basic features of the models are discussed and the behaviour in tensile test and creep problems is demonstrated.
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21

Verzi, D. W. "A two-dimensional continuum model for the crawling nematode sperm cell." Journal of Interdisciplinary Mathematics 16, no. 1 (February 2013): 59–81. http://dx.doi.org/10.1080/09720502.2013.778505.

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22

Asikainen, J., and T. Ala-Nissila. "Percolation and spatial correlations in a two-dimensional continuum deposition model." Physical Review E 61, no. 5 (May 1, 2000): 5002–8. http://dx.doi.org/10.1103/physreve.61.5002.

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23

Sidis, V., D. Grimbert, and C. Courbin-Gaussorgues. "An exponential two-state model for collisional excitation via a continuum." Journal of Physics B: Atomic, Molecular and Optical Physics 21, no. 16 (August 28, 1988): 2879–87. http://dx.doi.org/10.1088/0953-4075/21/16/013.

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24

Rotureau, J., J. Okołowicz, and M. Płoszajczak. "Theory of the two-proton radioactivity in the continuum shell model." Nuclear Physics A 767 (March 2006): 13–57. http://dx.doi.org/10.1016/j.nuclphysa.2005.12.005.

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25

Zhang, Jin. "A nonlocal continuum model for the piezopotential of two-dimensional semiconductors." Journal of Physics D: Applied Physics 53, no. 4 (November 25, 2019): 045303. http://dx.doi.org/10.1088/1361-6463/ab56ce.

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26

Iliuta, I., C. F. Petre, and F. Larachi. "Hydrodynamic continuum model for two-phase flow structured-packing-containing columns." Chemical Engineering Science 59, no. 4 (February 2004): 879–88. http://dx.doi.org/10.1016/j.ces.2003.11.020.

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27

Zakharov, S. A., V. V. Pisarev, and V. V. Chudanov. "One-dimensional continuum model of two-phase flows in porous media." Journal of Physics: Conference Series 1556 (May 2020): 012064. http://dx.doi.org/10.1088/1742-6596/1556/1/012064.

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28

Panga, Mohan K. R., Murtaza Ziauddin, and Vemuri Balakotaiah. "Two-scale continuum model for simulation of wormholes in carbonate acidization." AIChE Journal 51, no. 12 (September 6, 2005): 3231–48. http://dx.doi.org/10.1002/aic.10574.

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29

Giorgio, I., P. Harrison, F. dell'Isola, J. Alsayednoor, and E. Turco. "Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2216 (August 2018): 20180063. http://dx.doi.org/10.1098/rspa.2018.0063.

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We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics.
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30

Español, Malena I., Dmitry Golovaty, and J. Patrick Wilber. "Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (January 2018): 20170612. http://dx.doi.org/10.1098/rspa.2017.0612.

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In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.
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31

Weitsman, Y. "A Continuum Damage Model for Viscoelastic Materials." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 773–80. http://dx.doi.org/10.1115/1.3173721.

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This paper presents a continuum damage model for viscoelastic materials. “Damage” is expressed by two symmetric, second rank tensors which are related to the total areas of “active” and “passive” microcracks within a representative volume element of the multifractured material. Viscoelasticity is introduced through scalar valued internal state variables that represent the internal degrees-of-freedom associated with the motions of long chain polymeric molecules. The constitutive relations are established from basic considerations of continuum mechanics and irreversible thermodynamics, with detailed expressions derived for the case of initially isotropic materials. It is shown that damage causes softening of the material moduli as well as changes in material symmetry. The special cases of uniaxial damage under uniaxial stress and the interaction of damage with moisture diffusion are also considered.
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32

ALVAREZ-GAUMÉ, L., H. ITOYAMA, J. L. MAÑES, and A. ZADRA. "SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY." International Journal of Modern Physics A 07, no. 21 (August 20, 1992): 5337–67. http://dx.doi.org/10.1142/s0217751x92002441.

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We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.
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33

DEMETERFI, KREŠIMIR. "TWO-DIMENSIONAL QUANTUM GRAVITY, MATRIX MODELS AND STRING THEORY." International Journal of Modern Physics A 08, no. 07 (March 20, 1993): 1185–244. http://dx.doi.org/10.1142/s0217751x93000497.

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We review some results of the recent progress in understanding two-dimensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exactly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the one-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative results. We compare the results obtained from matrix models to the results in the continuum approach to string theory.
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34

Obara, Paulina. "Analysis of orthotropic tensegrity plate strips using a continuum two-dimensional model." MATEC Web of Conferences 262 (2019): 10010. http://dx.doi.org/10.1051/matecconf/201926210010.

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A continuum two-dimensional model of orthotropic moderately thick plate strip is proposed in this paper. The model considers the different reference planes (lower, middle and upper) thus the different planes of support may be taken into account. The linear six-parameter and five-parameter shell theories are applied to the analysis. In case of a considered plate strip a number of parameters are reduced to four and to three respectively. The closed form of displacements and internal forces for any orthotropic plate strips are determined. As an example a continuum model of orthotropic tensegrity plate strip is considered. The influence of the self-stress state and some geometrical parameters on displacements are analyzed. The proposed approach can be used for all orthotropic systems.
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35

Holland, Edward N., and Andrew W. Woods. "A continuum model for the dispersion of traffic on two-lane roads." Transportation Research Part B: Methodological 31, no. 6 (November 1997): 473–85. http://dx.doi.org/10.1016/s0191-2615(97)00009-x.

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36

Vries, Hylke De, and Theo Opsteegh. "Interpretation of discrete and continuum modes in a two-layer Eady model." Tellus A: Dynamic Meteorology and Oceanography 59, no. 2 (January 2007): 182–97. http://dx.doi.org/10.1111/j.1600-0870.2006.00219.x.

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37

Ricoeur, Andreas, and Dimitri Henneberg. "Two Scale-Based Continuum Damage Model for Brittle Materials under Thermomechanical Loading." Key Engineering Materials 525-526 (November 2012): 589–92. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.589.

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Ceramic refractory materials initially contain a multitude of defects such as voids, microcracks, grain boundaries etc. Particularly being exposed to high temperatures above 1000 °C the macroscopic properties such as effective compliance, strength and lifetime are essentially determined by microscopic features of the material. The deformation process and failure mechanisms are going along with the creation of new microdefects as well as the growth and coalescence of cracks. A brittle material damage model for dynamic thermomechanical loading conditions is presented in this paper. Representative volume elements (RVE) include microcrack initiation and growth. The material laws are formulated on the continuum level using appropriate homogenisation methods. To demonstrate the potential of the numerical tools, two examples are presented which are taken from applications. Based on experiments, cyclic thermal shock tests at refractory plates are simulated by FEM. To quantify the thermal shock resistance of ceramics, experiments suggested by Hasselman are simulated numerically supplying a critical temperature slope.
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38

Adhikary, Deepak P., and Hua Guo. "A Coupled Model of Two-Phase Diffusion and Flow through Deforming Porous Cosserat Media." Defect and Diffusion Forum 297-301 (April 2010): 281–93. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.281.

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Simulation of mining induced rock deformation, rock fracture enhanced permeability and fluid and gas diffusion and flow process is a complex task. A new three dimensional coupled mechanical two-phase double porosity desorption and diffusion finite element code called COSFLOW has been recently developed by CSIRO Exploration and Mining to service the mining industry’s need. A unique feature of COSFLOW is the incorporation of Cosserat continuum theory in its formulation. In the Cosserat model, inter-layer interfaces (joints, bedding planes) are considered to be smeared across the mass, i.e. the effects of interfaces are incorporated implicitly in the choice of stress-strain model formulation. An important feature of the Cosserat model is that it incorporates bending rigidity of individual layers in its formulation and this makes it different from other conventional implicit models. The Cosserat continuum formulation has a major advantage over conventional continuum models in that it can efficiently simulate rock breakage and slip as well as separation along the bedding planes. Any opening/closure along a bedding plane may introduce a strong anisotropy in fluid flow properties of the porous medium. This, in turn, will impact on the fluid/gas flow behaviour of the porous medium. This paper will briefly describe the Cosserat continuum theory, the treatment of permeability changes with rock deformation and the coupling of the two-phase dual porosity fluid diffusion- flow model and present a number of examples highlighting the capability of the developed code in simulating the mining induced rock deformation, permeability changes and fluid diffusion and flow will be presented.
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39

Degond, Pierre, Angelika Manhart, and Hui Yu. "An age-structured continuum model for myxobacteria." Mathematical Models and Methods in Applied Sciences 28, no. 09 (August 2018): 1737–70. http://dx.doi.org/10.1142/s0218202518400043.

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Myxobacteria are social bacteria, that can glide in two dimensions and form counter-propagating, interacting waves. Here, we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules that can be formulated as a particle-based model and set within the Self-Organized Hydrodynamics (SOH) framework. The strength of this combined approach is that microscopic knowledge or data can be incorporated easily into the particle model, whilst the continuous model allows for easy numerical analysis of the different effects. However, we found that the derived macroscopic model lacks a diffusion term in the density equations, which is necessary to control the number of waves, indicating that a higher order approximation during the derivation is crucial. Upon ad hoc addition of the diffusion term, we found very good agreement between the age-structured model and the biology. In particular, we analyzed the influence of a refractory (insensitivity) period following a reversal of movement. Our analysis reveals that the refractory period is not necessary for wave formation, but essential to wave synchronization, indicating separate molecular mechanisms.
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40

Li, Cheng. "Torsional vibration of carbon nanotubes: Comparison of two nonlocal models and a semi-continuum model." International Journal of Mechanical Sciences 82 (May 2014): 25–31. http://dx.doi.org/10.1016/j.ijmecsci.2014.02.023.

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41

Savu, Anamaria. "Hydrodynamic scaling limit of continuum solid-on-solid model." Journal of Applied Mathematics 2006 (2006): 1–37. http://dx.doi.org/10.1155/jam/2006/69101.

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A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of the hydrodynamic scaling limit of nongradient models. What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor interaction. Along the way, a few steps have to be adapted to our new context. As a byproduct of our main result, we also derive the hydrodynamic scaling limit of a perturbation of the continuum solid-on-solid model, a model that incorporates both surface diffusion and surface electromigration.
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42

VYCHYTIL, J., and M. HOLEČEK. "GRID CONTINUUM DESCRIPTION: A NOVEL APPROACH IN TWO-SCALE HYPERELASTICITY." Journal of Multiscale Modelling 04, no. 01 (March 2012): 1250004. http://dx.doi.org/10.1142/s1756973712500047.

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In this paper, a generalization of the standard continuum theory is proposed in order to describe materials with a more complex microstructure. The key idea consists in dividing the studied body onto a set of small but finite disjunct cells whose boundaries form what is called the grid. The state of the grid is described by macroscopically smooth functions. The interior of each cell, on the other hand, is described by an additional field that may be discontinuous or highly oscillating. Such an approach allows us to include non-trivial effects of the microstructure in resulting material models of macroscopic bodies. The theory is illustrated on two examples of two-scale hyperelastic models. The first one represents a crystalline material with a failure of the Cauchy-Born rule. The second one, motivated by an arrangement of soft tissues, includes prestress at the reference state as well as non-trivial response caused by a collapse of micro-constituents. Transparent physical meaning of several material parameters of the latter model provides for their direct identification instead of the least-squares fitting.
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43

VON PFEIL, KARL, MICHAEL D. GRAHAM, DANIEL J. KLINGENBERG, and JEFFREY F. MORRIS. "A TWO-FLUID MODEL FOR ELECTRO- AND MAGNETORHEOLOGICAL SUSPENSIONS." International Journal of Modern Physics B 16, no. 17n18 (July 20, 2002): 2669–75. http://dx.doi.org/10.1142/s0217979202012827.

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A two-fluid continuum model is developed to describe mass transport in electro- and magnetorheological suspensions. The particle flux is related to the field-induced stresses. Solutions of the resulting mass balance show column formation in the absence of flow, and stripe formation when a suspension is subjected simultaneously to an applied electric field and shear flow.
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44

Ospina Holguín, Javier Humberto. "The Cobb-Douglas function for a continuum model." Cuadernos de Economía 36, no. 70 (January 1, 2017): 1–18. http://dx.doi.org/10.15446/cuad.econ.v36n70.49052.

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This paper introduces two formal equivalent definitions of the Cobb-Douglas function for a continuum model based on a generalization of the Constant Elasticity of Substitution (CES) function for a continuum under not necessarily constant returns to scale and based on principles of product calculus. New properties are developed, and to illustrate the potential of using the product integral and its functional derivative, it is shown how the profit maximization problem of a single competitive firm using a continuum of factors of production can be solved in a manner that is completely analogous to the one used in the discrete case.
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45

Vorobiev, Oleg, Eric Herbold, Souheil Ezzedine, and Tarabay Antoun. "A continuum model for concrete informed by mesoscale studies." International Journal of Damage Mechanics 27, no. 10 (September 18, 2017): 1451–81. http://dx.doi.org/10.1177/1056789517730884.

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The paper describes a novel computational approach to refine continuum models for penetration calculations which involves two stages. At the first stage, a trial continuum model is used to model penetration into a concrete target. Model parameters are chosen to match experimental data on penetration depth. Deformation histories are recorded at few locations in the target around the penetrator. In the second stage, these histories are applied to the boundaries of a representative volume comparable to the element size in large scale penetration simulation. Discrete-continuum approach is used to model the deformation and failure of the material within the representative volume. The same deformation histories are applied to a single element which uses the model to be improved. Continuum model may include multiple parameters or functions which cannot be easily found using experimental data. We propose using mesoscale response to constrain such parameters and functions. Such tuning of the continuum model using typical deformation histories experienced by the target material during the penetration allows us to minimize the parameter space and build better models for penetration problems which are based on physics of penetration rather than intuition and ad hoc assumptions.
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46

FUKUMA, MASAFUMI, HIKARU KAWAI, and RYUICHI NAKAYAMA. "CONTINUUM SCHWINGER-DYSON EQUATIONS AND UNIVERSAL STRUCTURES IN TWO-DIMENSIONAL QUANTUM GRAVITY." International Journal of Modern Physics A 06, no. 08 (March 30, 1991): 1385–406. http://dx.doi.org/10.1142/s0217751x91000733.

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We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model are explicitly derived and turn out to be a formal Virasoro condition on the square root of the partition function, which is conjectured to be the τ function of the KdV hierarchy. Furthermore, we argue that general multi-matrix models are related to the W algebras and suitable reductions of KP hierarchy and its generalizations.
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47

MIGNACO, J. A., C. SIGAUD, F. J. VANHECKE, and A. R. DA SILVA. "CONNES–LOTT MODEL BUILDING ON THE TWO-SPHERE." Reviews in Mathematical Physics 13, no. 01 (January 2001): 1–28. http://dx.doi.org/10.1142/s0129055x01000582.

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In this work we examine generalized Connes–Lott models, with C⊕C as finite algebra, over the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure (magnetic monopoles). The finitely generated projective module over the full algebra is also taken as topologically non-trivial, which is possible over S2. We also construct a real spectral triple enlarging this Hilbert space to include "particle" and "anti-particle" fields.
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48

Hudson, Thomas, Patrick van Meurs, and Mark Peletier. "Atomistic origins of continuum dislocation dynamics." Mathematical Models and Methods in Applied Sciences 30, no. 13 (December 15, 2020): 2557–618. http://dx.doi.org/10.1142/s0218202520500505.

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This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.
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49

Willatzen, Morten, Lok C. Lew Yan Voon, Appala Naidu Gandi, and Udo Schwingenschlögl. "3D continuum phonon model for group-IV 2D materials." Beilstein Journal of Nanotechnology 8 (June 30, 2017): 1345–56. http://dx.doi.org/10.3762/bjnano.8.136.

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A general three-dimensional continuum model of phonons in two-dimensional materials is developed. Our first-principles derivation includes full consideration of the lattice anisotropy and flexural modes perpendicular to the layers and can thus be applied to any two-dimensional material. In this paper, we use the model to not only compare the phonon spectra among the group-IV materials but also to study whether these phonons differ from those of a compound material such as molybdenum disulfide. The origin of quadratic modes is clarified. Mode coupling for both graphene and silicene is obtained, contrary to previous works. Our model allows us to predict the existence of confined optical phonon modes for the group-IV materials but not for molybdenum disulfide. A comparison of the long-wavelength modes to density-functional results is included.
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50

Wang, Xiaolong, Haodong Wang, Zhijiang Du, and Wenlong Yang. "Kinematics modeling of a two DOFs continuum manipulator with uniform notches." MATEC Web of Conferences 309 (2020): 05006. http://dx.doi.org/10.1051/matecconf/202030905006.

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Continuum manipulators have been widely adopted for single-port laparoscopy (SPL). A novel continuum manipulator with uniform notches which has two degrees of freedom (DOFs) is presented in this paper. The arrangement of flexible beams makes it own a higher load capacity. Its kinematic model is coupled with the mechanical model. The comprehensive elliptic integral solution (CEIS) is more practical in the actual deformation of the flexible beams. Based on that method, kinematics modeling is established from the driven space to the Cartesian space. The friction coefficient is an important factor which can affect the kinematic modeling. Therefore, an experimental platform is established to obtain the friction coefficient. The kinematic modeling is verified through the prototype. Experimental results show that the model has high precision.
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