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Journal articles on the topic 'Rigid domain'

Author: Grafiati

Published: 14 March 2023

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1

Wang, J. D., D. Zhou, and W. Q. Liu. "Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part II: Lateral Excitation." Shock and Vibration 19, no. 6 (2012): 1205–22. http://dx.doi.org/10.1155/2012/410957.

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Sloshing response of liquid in a rigid cylindrical container with a rigid annual baffle subjected to lateral excitation has been studied. The complicated liquid domain is separated into several simple sub-domains by introducing the artificial interfaces. The analytical solutions of potential function corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The total potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. On the base of the natural frequencies and modes having been obtained by the sub-domain method, the orthogonality among the sloshing modes has been demonstrated. Substituting the potential functions into the free surface wave equation establishes the dynamic response equation of liquid. Then, the generalized coordinates are solved. The sloshing surface displacement, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment are discussed for the containers subjected to harmonic and seismic lateral excitation, respectively.

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2

Wang, J. D., D. Zhou, and W. Q. Liu. "Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part I: Free Vibration." Shock and Vibration 19, no. 6 (2012): 1185–203. http://dx.doi.org/10.1155/2012/346031.

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An analytical approach is presented to obtain the sloshing natural frequencies and modes of ideal liquid in a rigid cylindrical container with a rigid annular baffle. The free surface waves of the liquid are considered in the analysis. The artificial interfaces are introduced to divide the complicated liquid domain into several simple sub-domains. The exact analytical solutions of velocity potential of liquid corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The Eigen-frequency equation is precisely derived by using the Fourier-Bessel expansion on the free surface and the artificial interfaces of the liquid. The convergence study shows high accuracy and fast convergence of the present approach. The comparative studies with those available from literature are made, excellent agreements have been achieved. Numerical results showing the variations of natural frequencies and modes versus position and inner diameter of the annular baffle are provided.

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3

Ostanin, Stepan A., Maxim V. Mokeev, and Vjacheslav V. Zuev. "Influence of Interpenetrating Chains on Rigid Domain Dimensions in Siloxane-Based Block-Copolymers." Polymers 14, no. 19 (September 27, 2022): 4048. http://dx.doi.org/10.3390/polym14194048.

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1H spin-diffusion solid-state NMR was utilized to elucidate the domain size in multiblock-copolymers (BCPs) poly-(block poly(dimethylsiloxane)-block ladder-like poly(phenylsiloxane)) and poly-(block poly((3,3′,3″-trifluoropropyl-methyl)siloxane)-block ladder-like poly(phenylsiloxane). It was found that these BCPs form worm-like morphology with rigid cylinders dispersed in amorphous matrix. By using the combination of solid-state NMR techniques such as 13C CP/MAS, 13C direct-polarization MAS and 2D 1H EXSY, it was shown that the main factor which governs the diameter value of these rigid domains is the presence of interpenetrating segments of soft blocks. The presence of such interpenetrating chains leads to an increase of rigid domain diameter.

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4

Flynn, Emily, and Ileana Streinu. "Matching Multiple Rigid Domain Decompositions of Proteins." IEEE Transactions on NanoBioscience 16, no. 2 (March 2017): 81–90. http://dx.doi.org/10.1109/tnb.2017.2660538.

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5

Ćwikiel, K., B. Fugiel, and M. Mierzwa. "The rigid domain structure in TGS ferroelectric." Physica B: Condensed Matter 293, no. 1-2 (December 2000): 58–66. http://dx.doi.org/10.1016/s0921-4526(00)00532-9.

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6

Сирюк, Ю. А., А. В. Безус, Е. Д. Бондарь, and В. В. Кононенко. "Фазовые переходы в жесткой доменной структуре феррит-гранатовой пленки." Физика твердого тела 61, no. 7 (2019): 1250. http://dx.doi.org/10.21883/ftt.2019.07.47833.338.

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Spontaneous and magnetic field-induced phase transitions in a rigid domain structure of a uniaxial ferrite-garnet film are studied. It is shown that the temperature and field stability intervals of the lattice of cylindrical magnetic domains depend on the structure of the domain boundaries.

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7

Artemovych, O. D. "Rigid left Noetherian rings." International Journal of Mathematics and Mathematical Sciences 2004, no. 46 (2004): 2473–76. http://dx.doi.org/10.1155/s0161171204301250.

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8

Miller, Joia M., Doug Hall, Joanna Robaszewski, Prerna Sharma, Michael F. Hagan, Gregory M. Grason, and Zvonimir Dogic. "All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes." Science Advances 6, no. 31 (July 2020): eaba2331. http://dx.doi.org/10.1126/sciadv.aba2331.

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Using theory and experiments, we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.

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9

Lipshitz, L., and Z. Robinson. "One-dimensional fibers of rigid subanalytic sets." Journal of Symbolic Logic 63, no. 1 (March 1998): 83–88. http://dx.doi.org/10.2307/2586589.

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Let K be an algebraically closed field of any characteristic, complete with respect to the non-trivial ultrametric absolute value ∣·∣: K → ℝ+. By R denote the valuation ring of K, and by ℘ its maximal ideal. We work within the class of subanalytic sets defined in [5], but our results here also hold for the strongly subanalytic sets introduced in [11] as well as for those subanalytic sets considered in [6]. Let X ⊂ R1 be subanalytic. In [8], we showed that there is a decomposition of X as a union of a finite number of special sets U ⊂ R1 (see below). In this note, in Theorem 1.6, we obtain a version of this result which is uniform in parameters, thereby answering a question brought to our attention by Angus Macintyre. It follows immediately from Theorem 1.6 that the theory of K in the language (see [5] and [6]) is C-minimal in the sense of [3] and [9]. The analogous uniformity result in the p-adic case was recently proved in [12].Definition 1.1. (i) A disc in R1 is a set of one of the two following forms:A special set in R1 is a disc minus a finite union of discs.(ii) R-domains u ⊂ Rm, and their associated rings of analytic functions, , are defined inductively as follows. Rm is an R-domain and , the ring of strictly convergent power series in X1,…, Xm over K. If u is an R-domain with associated ring , (where K 〈X, Y〉〚ρ〛S is a ring of separated power series, see [5, §2] and [1, §1]) and f, have no common zero on u and ◸ ϵ {<, ≤}, thenis an R-domain andwhere J is the ideal generated by I and f − gZ (Z is a new variable) if ◸ is ≤, andwhere J is the ideal generated by I and f − gτ (τ a new variable) if ◸ is <. (See [8, Definition 2.2].) R-domains generalize the rational domains of [2, §7.2.3]. It is true, but not easy to prove, that only depends on u as a point set, and is independent of the particular representation of u.

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10

Han, Zejun, Mi Zhou, Xiaowen Zhou, and Linqing Yang. "Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain." International Journal of Structural Stability and Dynamics 19, no. 09 (August 28, 2019): 1950106. http://dx.doi.org/10.1142/s0219455419501062.

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Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

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11

Sun, Qinghe. "Rigid Binary Relations on a 4-Element Domain." Order 34, no. 1 (May 20, 2016): 165–83. http://dx.doi.org/10.1007/s11083-016-9394-z.

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12

Ionescu, Ioan R., and Edouard Oudet. "Modeling Ductile Fracture Using the Discontinuous Velocity Domain Splitting Method." Key Engineering Materials 488-489 (September 2011): 69–72. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.69.

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Discontinuous velocity domain splitting method (DVDS) is a mesh free method which focuses on the strain localization and completely neglect the bulk deformations. It considers the kinematic variational principle on a special class of virtual velocity fields to get an upper-bound of the limit load. To construct this class of virtual velocity fields, the rigid-plastic body is splinted into simple connected sub-domains and on each such sub-domain a rigid motion is associated. The discontinuous collapse flow velocity field results in localized deformations only, located at the boundary of the sub-domains. In the numerical applications of the DVDS method we introduce a numerical technique based on a level set description of the partition of the rigid-plastic body and on genetic minimization algorithms. In the case of in-plane deformation of pressure insensitive materials, the internal boundaries of the sub-domains are parts of circles or straight lines, tangent to the collapse velocity jumps. In this case, DVDS reduces to the block decomposition method, which was intensively used to get analytical upper bounds of the limit loads. When applied to the two notched tensile problem of a von Mises material, DVDS gives excellent results with a low computational cost. Furthermore, DVDS was applied to model collapse in pressure sensitive plastic materials. Illustrative examples for homogenous and heterogeneous Coulomb and Cam-Clay materials shows that DVDS gives excellent prediction of limit loads and on the collapse flow.

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13

Beno, Matej, and Bořek Patzák. "FICTITIOUS DOMAIN METHOD FOR NUMERICAL SIMULATION OF INCOMPRESSIBLE VISCOUS FLOW AROUND RIGID BODIES." Acta Polytechnica 57, no. 4 (September 1, 2017): 245. http://dx.doi.org/10.14311/ap.2017.57.0245.

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This article describes the method of efficient simulation of the flow around potentially many rigid obstacles. The finite element implementation is based on the incompressible Navier-Stokes equations using structured, regular, two dimensional triangular mesh. The fictitious domain method is introduced to account for the presence of rigid particles, representing obstacles to the flow. To enforce rigid body constraints in parts corresponding to rigid obstacles, Lagrange multipliers are used. For time discretization, an operator splitting technique is used. The model is validated using 2D channel flow simulations with circular obstacles. Different possibilities of enforcing rigid body constraints are compared to the fully resolved simulations and optimal strategy is recommended.

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14

Arriagada, Waldo. "Parametric rigidity of real families of conformal diffeomorphisms tangent to x→−x." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 1 (August 30, 2018): 261–77. http://dx.doi.org/10.1017/s0308210518000252.

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We prove that one-parameter families of real germs of conformal diffeomorphisms tangent to the involution x ↦−x are rigid in the parameter. We establish a connection between the dynamics in the Poincaré and Siegel domains. Although repeatedly employed in the literature, the dynamics in the Siegel domain does not explain the intrinsic real properties of these germs. Rather, these properties are fully elucidated in the Poincaré domain, where the fixed points are linearizable. However, a detailed study of the dynamics in the Siegel domain is of crucial importance. We relate both points of view on the intersection of the Siegel normalization domains.

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15

Prakash, Om, and Ashish Khare. "Tracking of Non-Rigid Object in Complex Wavelet Domain." Journal of Signal and Information Processing 02, no. 02 (2011): 105–11. http://dx.doi.org/10.4236/jsip.2011.22014.

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16

Laxminarsimha Rao, V., and Sovan Lal Das. "Drag force on a liquid domain moving inside a membrane sheet surrounded by aqueous medium." Journal of Fluid Mechanics 779 (August 18, 2015): 468–82. http://dx.doi.org/10.1017/jfm.2015.434.

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We compute the drag on a circular and liquid microdomain diffusing in a two-dimensional fluid lipid bilayer membrane surrounded by a fluid above and below. Under the assumptions that the liquids are incompressible and the flow is of low Reynolds number, Stokes’ equations describe the flow in the two-dimensional membrane as well as in the surrounding three-dimensional fluid. The expression for the drag force on the liquid domain involves Fredholm integral equations of the second kind, which we numerically solve using discrete collocation method based on Chebyshev polynomials. We observe that when the domain is more viscous than the surrounding membrane (including the rigid domain case), the drag force is almost independent of the viscosity contrast between the domain and the surrounding membrane, as also observed earlier in experiments by other researchers. The mobility also varies logarithmically with Boussinesq number${\it\beta}$for large${\it\beta}$. On the other hand, for a less viscous domain the dimensionless drag force reduces with increasing viscosity contrast, and a significant change in the drag force, from that when there is no viscosity contrast or when the domain is rigid, has been observed. Further, the logarithmic behaviour of the mobility no longer holds for less viscous domains. Our method of computing the drag force and diffusion coefficient is valid for arbitrary viscosity contrast between the domain and membrane and any domain size (subject to${\it\beta}\geqslant 5$).

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17

Tuitman, Johan T., Šime Malenica, and Riaan van't Veer. "Generalized Modes in Time-Domain Seakeeping Calculations." Journal of Ship Research 56, no. 04 (December 1, 2012): 215–33. http://dx.doi.org/10.5957/jsr.2012.56.4.215.

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The concept of "generalized modes" is to describe all degrees of freedom by mode shapes and not using any predefined shape, like rigid body modes. Generalized modes in seakeeping computations allow one to calculate the response of a single ship, springing, whipping, multibody interaction, etc., using a uniform approach. The generalized modes have already been used for frequency-domain seakeeping calculations by various authors. This article extents the generalized modes methodology to be used for time-domain seakeeping computations, which accounts for large-amplitude motions of the rigid-body modes. The time domain can be desirable for seakeeping computations because it is easy to include nonlinear load components and to compute transient response, like slamming and whipping. Results of multibody interaction, two barges connected by a hinge, whipping response of a ferry resulting from slamming loads, and the response of a flexible barge are presented to illustrate the theory.

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18

Hamed, Gary R. "Reinforcement of Rubber." Rubber Chemistry and Technology 73, no. 3 (July 1, 2000): 524–33. http://dx.doi.org/10.5254/1.3547603.

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Abstract One of the most important phenomenon in material science is the reinforcement of rubber by rigid entities, such as dispersed particulate filler or phase-separated organic domains. In order to impart significant reinforcement, the size of the hard phase must be small, much less than a micron. The basis of this requirement is a major focus of this short review. Furthermore, the roles of energy dissipation and crack deflection in rubber reinforcement are considered. The final part of the review deals with nano-composite rubbers, in which rigid domain size is in the range of 1–10 nm.

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19

Wang, Kang, Zhong Ke Wu, and Jun Li Zhao. "Curve Correspondence in Two-Dimensional Space." Applied Mechanics and Materials 556-562 (May 2014): 4651–54. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4651.

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Curve or contour correspondence has been extensively explored. Previous work was mainly concentrated on the rigid correspondence or alignment. This paper presents a spectral analysis method to resolve the problem of curves correspondence with non-rigid deformation. Using the embedding of original affinity matrix to the spectral domain, we can build the point correspondence of no-rigid deformation shapes.

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20

HUNG, TIN-KAN, and TOMMY M. C. TSAI. "NONLINEAR PULSATILE FLOWS IN RIGID AND DISTENSIBLE ARTERIES." Journal of Mechanics in Medicine and Biology 04, no. 04 (December 2004): 419–34. http://dx.doi.org/10.1142/s0219519404001168.

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Blood flow in distensible arteries is nonlinear and time-dependent. The radial motion of the wall alters the dimension and geometry of the flow field. The nonlinear pulsating flow processes are successfully computed by mapping the wavy flow field to a fixed domain and by casting the geometric, kinematic and dynamic parameters of the flow into a dimensionless form of the Navier–Stokes equations. The complexity of the equations is compensated by a significant advantage in finite difference solutions. It is accomplished by using a fixed regular mesh network to model time-dependent irregular meshes in the physical domain for boundary layer development and vortices in pulsatile flows.

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21

Zhang, Yuan, Liyi Zhang, and Yunshan Sun. "Rigid motion artifact reduction in CT using frequency domain analysis." Journal of X-Ray Science and Technology 25, no. 5 (October 19, 2017): 721–36. http://dx.doi.org/10.3233/xst-16193.

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22

Dong, Wei-Li, Li Liu, Si-Da Zhou, and Shu-Lin Chen. "Substructure Synthesis in Time Domain with Rigid–Elastic Hybrid Joints." AIAA Journal 53, no. 2 (February 2015): 504–10. http://dx.doi.org/10.2514/1.j053630.

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23

Cheng, Tammy MK, Tom L. Blundell, and Juan Fernandez-Recio. "Structural assembly of two-domain proteins by rigid-body docking." BMC Bioinformatics 9, no. 1 (2008): 441. http://dx.doi.org/10.1186/1471-2105-9-441.

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24

Overholt, Marius. "The area of the complement of a conformally rigid domain." Proceedings of the American Mathematical Society 103, no. 2 (February 1, 1988): 448. http://dx.doi.org/10.1090/s0002-9939-1988-0943064-3.

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25

Ahn, Hyeong-Joon, Sang-Wook Lee, Sang-Ho Lee, and Dong-Chul Han. "Frequency domain control-relevant identification of MIMO AMB rigid rotor." Automatica 39, no. 2 (February 2003): 299–307. http://dx.doi.org/10.1016/s0005-1098(02)00203-0.

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26

Wilson, D. Keith, David F. Aldridge, Neill P. Symons, Vladimir E. Ostashev, Sandra L. Collier, and David H. Marlin. "Time‐domain calculations of acoustic interactions with rigid porous surfaces." Journal of the Acoustical Society of America 116, no. 4 (October 2004): 2493–94. http://dx.doi.org/10.1121/1.4808646.

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27

Blasco, Jordi, M. Carmen Calzada, and Mercedes Marín. "A Fictitious Domain, parallel numerical method for rigid particulate flows." Journal of Computational Physics 228, no. 20 (November 2009): 7596–613. http://dx.doi.org/10.1016/j.jcp.2009.07.010.

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28

Guo, Yong Ming. "Computer Modeling of Extrusion by the Rigid-Plastic Hybrid Element Method." Materials Science Forum 505-507 (January 2006): 703–8. http://dx.doi.org/10.4028/www.scientific.net/msf.505-507.703.

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In this paper, a rigid-plastic hybrid element method is formulated, which is a mixed approach of the rigid-plastic domain-BEM and the rigid-plastic FEM based on the theory of slightly compressible plasticity. Since compatibilities of velocity and velocity's derivative between adjoining boundary elements and finite elements can be met, the velocity and the derivative of velocity can be calculated with the same precision for this hybrid element method. While, the compatibility of the velocity's derivative cannot be met for the rigid-plastic FEMs.

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29

Xia, Jinzhu, and Zhaohui Wang. "Time-Domain Hydroelasticity Theory of Ships Responding to Waves." Journal of Ship Research 41, no. 04 (December 1, 1997): 286–300. http://dx.doi.org/10.5957/jsr.1997.41.4.286.

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A time-domain linear theory of fluid-structure interaction between floating structures and the incident waves is presented. The structure is assumed to be elastic and represented by general separation of variables, whereas the fluid is described as an initial boundary value problem of potential free surface flow. The general interface boundary condition is used in the mathematical formulation of the fluid motion around the flexible structure. The general time-domain theory is simplified to a slender-body theory for the analysis of wave-induced global responses of monohull ships. The structure is represented by a nonuniform beam, while the generalized hydrodynamic coefficients can be obtained from two-dimensional potential flow theory. The linear slender body theory is generalized to treat the nonlinear loading effects of rigid motion and structural response of ships traveling in rough seas. The nonlinear hydrostatic restoring force and hydrodynamic momentum action are considered. A numerical solution is presented for the slender body theory. Numerical examples are given for two ship cases with different geometry features, a warship hull and the S175 containership with two different bow flare forms. The predicted results include linear and nonlinear rigid motions and structural responses of ships advancing in regular and irregular waves. The results clearly demonstrate the importance and the magnitude of nonlinear effects in ship motions and internal forces. Numerical calculations are compared with experimental results of rigid and elastic material ship model tests. Good agreement is obtained.

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30

Xin, Weiyue, Hao Wu, Gregory M. Grason, and Maria M. Santore. "Switchable positioning of plate-like inclusions in lipid membranes: Elastically mediated interactions of planar colloids in 2D fluids." Science Advances 7, no. 14 (April 2021): eabf1943. http://dx.doi.org/10.1126/sciadv.abf1943.

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We demonstrate how manipulating curvature in an elastic fluid lamella enables the reversible relative positioning of flat, rigid, plate-like micrometer-scale inclusions, with spacings from about a micrometer to tens of micrometers. In an experimental model comprising giant unilamellar vesicles containing solid domain pairs coexisting in a fluid membrane, we adjusted vesicle inflation to manipulate membrane curvature and mapped the interdomain separation. A two-dimensional model of the pair potential predicts the salient experimental observations and reveals both attractions and repulsions, producing a potential minimum entirely a result of the solid domain rigidity and bending energy in the fluid membrane. The impact of vesicle inflation on domain separation in vesicles containing two solid domains was qualitatively consistent with observations in vesicles containing many domains. The behavior differs qualitatively from the pure repulsions between fluid membrane domains or interactions between nanoscopic inclusions whose repulsive or attractive character is not switchable.

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31

ANTÓNIO, J., A. TADEU, and P. AMADO MENDES. "A 2.5D TRACTION BOUNDARY ELEMENT METHOD FORMULATION APPLIED TO THE STUDY OF WAVE PROPAGATION IN A FLUID LAYER HOSTING A THIN RIGID BODY." Journal of Computational Acoustics 16, no. 02 (June 2008): 177–98. http://dx.doi.org/10.1142/s0218396x08003567.

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This paper models three-dimensional wave propagation around two-dimensional rigid acoustic screens, with minimal thickness (approaching zero), and placed in a fluid layer. Rigid or free boundaries are prescribed for the flat fluid surfaces. The problem is computed using the Traction Boundary Element Method (TBEM), which is appropriate for modeling thin-body inclusions, overcoming the difficulty posed by the conventional direct Boundary Element Method (BEM). The problem is solved as a summation of two-dimensional problems for different wave numbers along the direction for which the geometry does not vary. The source in each problem is a spatially sinusoidal harmonic line load. The influence of the horizontal boundaries of the fluid medium on the final wave field is computed analytically using appropriate 2.5D Green's functions for each model developed. Thus, only the boundary of the rigid acoustic screen needs to be discretized by boundary elements. The computations are performed in the frequency domain and are subsequently inverse Fourier transformed to obtain time domain results. Complex frequencies are used to avoid aliasing phenomena in the time domain results.

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32

BRANCO, FERNANDO J. F. G., LUÍS GODINHO, and ANTÓNIO TADEU. "ACOUSTIC INSERTION LOSS PROVIDED BY RIGID ACOUSTIC BARRIERS OF DIFFERENT SHAPES." Journal of Computational Acoustics 11, no. 04 (December 2003): 503–19. http://dx.doi.org/10.1142/s0218396x03002073.

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The present article studies what effect the shape of a rigid acoustic barrier has on the acoustic insertion loss provided by the barrier. The Boundary Element Method (BEM), formulated in the frequency domain, is used to evaluate the sound propagation around acoustic screens in the vicinity of a tall building. The acoustic screen is assumed to be non-absorbing, and the building is modeled as an infinite barrier. Signals in the time domain are obtained from the frequency domain computations by applying inverse Fourier transforms. In the examples provided, the height of the acoustic barrier remains constant, but different geometric shapes are modeled. The results obtained for a vertical barrier are used as a reference.

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33

Zhong, Yan Hui, Bei Zhang, Xiao Li Xie, Fu Ming Wang, and Cheng Chao Guo. "Numerical Simulation of GPR Electromagnetic Wave Propagation in Rigid Pavement with Voids Based on FDTD." Advanced Materials Research 250-253 (May 2011): 2765–68. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2765.

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Two-dimension finite difference time domain (FDTD) update equations are established, and the GPR electromagnetic wave propagation in rigid pavement with voids beneath slabs is numerical simulated by using effective CPML boundary conditions, and then the two-Dimension GPR images for voids beneath slab are obtained. Moreover, the relationship between characteristics of voids beneath rigid slabs and GPR data is analyzed. The achievements of this paper will provide a theoretical basis for the use of GPR to rapidly detect voids beneath rigid slab.

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34

Wriggers, Willy, and Klaus Schulten. "Protein domain movements: detection of rigid domains and visualization of hinges in comparisons of atomic coordinates." Proteins: Structure, Function, and Genetics 29, no. 1 (September 1997): 1–14. http://dx.doi.org/10.1002/(sici)1097-0134(199709)29:1<1::aid-prot1>3.0.co;2-j.

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35

Liu, Y. J., N. Nishimura, Y. Otani, T. Takahashi, X. L. Chen, and H. Munakata. "A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model." Journal of Applied Mechanics 72, no. 1 (January 1, 2005): 115–28. http://dx.doi.org/10.1115/1.1825436.

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A new boundary element method (BEM) is developed for three-dimensional analysis of fiber-reinforced composites based on a rigid-inclusion model. Elasticity equations are solved in an elastic domain containing inclusions which can be assumed much stiffer than the host elastic medium. Therefore the inclusions can be treated as rigid ones with only six rigid-body displacements. It is shown that the boundary integral equation (BIE) in this case can be simplified and only the integral with the weakly-singular displacement kernel is present. The BEM accelerated with the fast multipole method is used to solve the established BIE. The developed BEM code is validated with the analytical solution for a rigid sphere in an infinite elastic domain and excellent agreement is achieved. Numerical examples of fiber-reinforced composites, with the number of fibers considered reaching above 5800 and total degrees of freedom above 10 millions, are solved successfully by the developed BEM. Effective Young’s moduli of fiber-reinforced composites are evaluated for uniformly and “randomly” distributed fibers with two different aspect ratios and volume fractions. The developed fast multipole BEM is demonstrated to be very promising for large-scale analysis of fiber-reinforced composites, when the fibers can be assumed rigid relative to the matrix materials.

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Chhillar, Ajay, and Rajender Singh. "Rigid Plastic Analysis of Metal Parts using Meshless Approach." International Journal of Advance Research and Innovation 3, no. 3 (2015): 34–44. http://dx.doi.org/10.51976/ijari.331506.

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Plastic deformation of metal parts has been a matter of concern for investigators in academia, industry and research institutions all over the world. Literature reveals that earlier researchers have applied efforts for predicting plastic deformations using mesh based approach. A truly meshless formulation for rigid plastic analysis of metal parts has been developed in the present study for both plane stress and plane strain cases. In the present formulation, the governing equations are obtained for different set of scattered nodes over the problem domain and the integral equation for rigid plastic behavior is obtained through weak form over a local sub-domain. The meshless solution functions are obtained for different set of scattered nodes through moving least square technique. Essential boundary conditions are enforced through Penalty approach. The rigid plastic constitutive relationships incorporate only small deformation. Material constitutive relationship include Von-Mises yield criterion with rate independent associative flow theory. The solution algorithm for rigid plastic analysis of metal parts using meshless approach is discussed in the present work. Numerical results have been computed through two test functions using both linear and quadratic basis function which shows that presented formulation is accurate and robust for carrying out the rigid plastic analysis of metal parts.

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Zhao, Tingting, Nischal Karki, Brian D. Zoltowski, and Devin A. Matthews. "Allosteric regulation in STAT3 interdomains is mediated by a rigid core: SH2 domain regulation by CCD in D170A variant." PLOS Computational Biology 18, no. 12 (December 21, 2022): e1010794. http://dx.doi.org/10.1371/journal.pcbi.1010794.

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Signal Transducer and Activator of Transcription 3 (STAT3) plays a crucial role in cancer development and thus is a viable target for cancer treatment. STAT3 functions as a dimer mediated by phosphorylation of the SRC-homology 2 (SH2) domain, a key target for therapeutic drugs. While great efforts have been employed towards the development of compounds that directly target the SH2 domain, no compound has yet been approved by the FDA due to a lack of specificity and pharmacologic efficacy. Studies have shown that allosteric regulation of SH2 via the coiled-coil domain (CCD) is an alternative drug design strategy. Several CCD effectors have been shown to modulate SH2 binding and affinity, and at the time of writing at least one drug candidate has entered phase I clinical trials. However, the mechanism for SH2 regulation via CCD is poorly understood. Here, we investigate structural and dynamic features of STAT3 and compare the wild type to the reduced function variant D170A in order to delineate mechanistic differences and propose allosteric pathways. Molecular dynamics simulations were employed to explore conformational space of STAT3 and the variant, followed by structural, conformation, and dynamic analysis. The trajectories explored show distinctive conformational changes in the SH2 domain for the D170A variant, indicating long range allosteric effects. Multiple analyses provide evidence for long range communication pathways between the two STAT3 domains, which seem to be mediated by a rigid core which connects the CCD and SH2 domains via the linker domain (LD) and transmits conformational changes through a network of short-range interactions. The proposed allosteric mechanism provides new insight into the understanding of intramolecular signaling in STAT3 and potential pharmaceutical control of STAT3 specificity and activity.

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Bhat, Vijay Kumar, Pradeep Singh, and Sunny Sharma. "On weak (σ, δ)-rigid rings over Noetherian rings." Acta Universitatis Sapientiae, Mathematica 12, no. 1 (July 1, 2020): 5–13. http://dx.doi.org/10.2478/ausm-2020-0001.

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AbstractLet R be a Noetherian integral domain which is also an algebra over ℚ (ℚ is the field of rational numbers). Let σ be an endo-morphism of R and δ a σ-derivation of R. We recall that a ring R is a weak (σ, δ)-rigid ring if a(σ(a)+ δ(a)) ∈ N(R) if and only if a ∈ N(R) for a ∈ R (N(R) is the set of nilpotent elements of R). With this we prove that if R is a Noetherian integral domain which is also an algebra over ℚ, σ an automorphism of R and δ a σ-derivation of R such that R is a weak (σ, δ)-rigid ring, then N(R) is completely semiprime.

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Kumar, Narveen, and Neelam Choudhary. "Sloshing mitigation using vertical cylindrical baffle." 59th International Conference on Vibroengineering in Dubai, United Arab Emirates, October 22, 2022 45 (October 22, 2022): 41–45. http://dx.doi.org/10.21595/vp.2022.22960.

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This study has looked into the phenomenon of liquid vibrations in a rigid cylindrical container. The impacts of rigid vertical baffle positioned in the container on frequencies have been examined. The container is partially filled with an impermeable and non-viscous fluid. ANSYS software is used to report the mode shapes of the baffle and fluid domain.

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Herrmann, Jonathan, Po-Nan Li, Fatemeh Jabbarpour, Anson C. K. Chan, Ivan Rajkovic, Tsutomu Matsui, Lucy Shapiro, et al. "A bacterial surface layer protein exploits multistep crystallization for rapid self-assembly." Proceedings of the National Academy of Sciences 117, no. 1 (December 17, 2019): 388–94. http://dx.doi.org/10.1073/pnas.1909798116.

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Surface layers (S-layers) are crystalline protein coats surrounding microbial cells. S-layer proteins (SLPs) regulate their extracellular self-assembly by crystallizing when exposed to an environmental trigger. However, molecular mechanisms governing rapid protein crystallization in vivo or in vitro are largely unknown. Here, we demonstrate that theCaulobacter crescentusSLP readily crystallizes into sheets in vitro via a calcium-triggered multistep assembly pathway. This pathway involves 2 domains serving distinct functions in assembly. The C-terminal crystallization domain forms the physiological 2-dimensional (2D) crystal lattice, but full-length protein crystallizes multiple orders of magnitude faster due to the N-terminal nucleation domain. Observing crystallization using a time course of electron cryo-microscopy (Cryo-EM) imaging reveals a crystalline intermediate wherein N-terminal nucleation domains exhibit motional dynamics with respect to rigid lattice-forming crystallization domains. Dynamic flexibility between the 2 domains rationalizes efficient S-layer crystal nucleation on the curved cellular surface. Rate enhancement of protein crystallization by a discrete nucleation domain may enable engineering of kinetically controllable self-assembling 2D macromolecular nanomaterials.

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Li, Wei, Jan-Michael Y. Carrillo, John Katsaras, Bobby G. Sumpter, Rana Ashkar, and Rajeev Kumar. "The influence of curvature on domain distribution in binary mixture membranes." Soft Matter 15, no. 33 (2019): 6642–49. http://dx.doi.org/10.1039/c9sm01262a.

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Curvature-induced domain sorting is investigated in two types of binary mixture membranes. Two contrasting sorting behaviors are revealed, showing that rigid species can also be accommodated in the high curvature regions.

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Zhou, Si-Da, Li Liu, and Wei-Li Dong. "Time-Domain Substructure Synthesis with Hybrid Rigid and Nonlinear-Elastic Joints." AIAA Journal 54, no. 8 (August 2016): 2545–51. http://dx.doi.org/10.2514/1.j054466.

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Cortelazzo, G. M., L. Lucchese, and C. M. Monti. "Frequency domain analysis of general planar rigid motion with finite duration." Journal of the Optical Society of America A 16, no. 6 (June 1, 1999): 1238. http://dx.doi.org/10.1364/josaa.16.001238.

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Pandit, S. M., and Z. Q. Hu. "Determination Of Rigid Body Characteristics From Time Domain Modal Test Data." Journal of Sound and Vibration 177, no. 1 (October 1994): 31–41. http://dx.doi.org/10.1006/jsvi.1994.1414.

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Kumar, M. Arul. "Microstructural Modeling of Banding in Single Crystals: 'Stack of Domains' Model." Materials Science Forum 702-703 (December 2011): 200–203. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.200.

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A rigid-plastic rate-independent crystal plasticity based `stack of domains' model of a single crystal is developed to capture local deformation inhomogeneity and sub-structure formation when subjected to macroscopically homogeneous imposed deformation. This model regards the single crystal as a linear stack of domains with planar shaped domain boundaries. The domains of the model single crystal collectively accommodate the imposed deformation and individual domains maintain velocity and traction continuity with its neighbors. The lattice orientation of individual domains perturbed and that perturbation triggers the inhomogeneity of plastic slip amongst domains. Mobility of domain boundaries relative to the material and a differential hardening law that accounts for the orientational instability of individual domains are also considered in the model. The developed model is applied to predict the formation of banding in initially copper (C), rotated cube (RC) and Goss (G) orientated single crystals when subjected to plane strain deformation and the predictions are compared with the experimental literature.

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Adams, Thorsten M., Alexander Wentzel, and Harald Kolmar. "Intimin-Mediated Export of Passenger Proteins Requires Maintenance of a Translocation-Competent Conformation." Journal of Bacteriology 187, no. 2 (January 15, 2005): 522–33. http://dx.doi.org/10.1128/jb.187.2.522-533.2005.

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ABSTRACT Intimins from pathogenic bacteria promote intimate bacterial adhesion to epithelial cells. Several structurally similar domains form on the bacterial cell surface an extended rigid rod that exposes the carboxy-terminal domain, which interacts with the translocated intimin receptor. We constructed a series of intimin-derived fusion proteins consisting of carboxy-terminally truncated intimin and the immunoglobulin light-chain variable domain REIv, ubiquitin, calmodulin, β-lactamase inhibitor protein, or β-lactamase. By systematically investigating the intimin-mediated cell surface exposure of these passenger domains in the presence or absence of compounds that interfere with outer membrane stability or passenger domain folding, we acquired experimental evidence that intimin-mediated protein export across the outer membrane requires, prior to export, the maintenance of a translocation-competent conformation that may be distinct from the final protein structure. We propose that, during export, competition exists between productive translocation and folding of the passenger domain in the periplasm into a stable conformation that is not compatible with translocation through the bacterial outer membrane. These results may expand understanding of the mechanism by which intimins are inserted into the outer membrane and expose extracellular domains on the cell surface.

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Liu, Zhihao, and Qinhe Gao. "In-plane vibration response of time and frequency domain with rigid-elastic coupled tire model with continuous sidewall." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 232, no. 4 (December 5, 2017): 429–45. http://dx.doi.org/10.1177/1464419317744681.

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The in-plane vibration characteristic of time and frequency domain for heavy-loaded radial tire with a larger flat ratio (close to 1) is researched by utilizing the rigid-elastic coupled tire model with continuous sidewall. The sidewall bending stiffness is considered and the flexible beam on the elastic continuous beam tire model is proposed and investigated analytically to simulate the in-plane vibration of the heavy-loaded radial tire within more wider frequency band. The rigid-elastic coupled tire model is derived with finite difference method and the analytical stiffness matrix; mass matrix is formed based on the geometrical and structural parameters of heavy-loaded radial tire. Structural parameters are identified utilizing genetic algorithm based on the error between the analytical and experimental modal frequency. In-plane frequency domain transfer function and time domain dynamics response of heavy-loaded radial tire is investigated and compared with the experimental result. Experimental and theoretical results show that in-plane rigid-elastic coupled tire model with sidewall bending stiffness can be used to precisely predict the transfer function and vibration feature within the frequency band of 300 Hz, compared with the tire model with the distributed independent sidewall element. The flexible beam on the elastic continuous beam tire model and rigid-elastic coupled tire model with continuous sidewall can be extended to the dynamic analysis of the tire with larger flat ratio or the tire under the impulsive loading conditions.

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48

Bretagnon, P. "Rotation of the Rigid Earth." International Astronomical Union Colloquium 165 (1997): 295–300. http://dx.doi.org/10.1017/s0252921100046704.

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AbstractWe present the results of a solution of the Earth’s rotation built with analytical solutions of the planets and of the Moon’s motion. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth for the zonal harmonics Cj,0 for j from 2 to 5, and also for the tesseral harmonics C2,2, S2,2C3,k, S3,k for k from 1 to 3 and C4,1, S4,1. We determine three Euler angles ψ, ω, and φ by calculating the components of the torque of the external forces with respect to the geocenter in the case of the rigid Earth. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900–2050. The differences do not exceed 16 μas for ψ and 8 μas for ω whereas the contribution of the tesseral harmonics reaches 150 μas in the time domain.

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Kusanovic, Danilo S., Elnaz Seylabi, and Domniki Asimaki. "Optimization of frequency domain impedances for time-domain response analyses of building structures with rigid shallow foundations." Earthquake Spectra 37, no. 3 (January 19, 2021): 1955–79. http://dx.doi.org/10.1177/8755293020981994.

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The effects of dynamic soil–structure interaction (SSI) have been extensively studied in the last few decades, and proper analysis for the linear elastic case in frequency domain has been established successfully. However, SSI is rarely considered in the design of building structures, and instead, buildings are frequently analyzed using a rigid base assumption and quasi-static loading conditions that ignore SSI and its dynamic nature. Acknowledging these shortcomings, the National Institute of Standards and Technology (NIST) published in 2012 a set of recommendations on time-domain analyses of SSI for building structures compatible with standard finite element packages for consideration in engineering design. The so-called NIST GCR 12-917-21 report introduced a major simplification to enable frequency domain tools to be implemented in time domain analyses. That is, replacing the frequency-dependent soil impedance functions by a single-valued functions read at the flexible-base structure frequency; This work seeks to quantify the accuracy of this simplification considering fully coupled two-dimensional (2D) finite element models (FEM) as the reference. Using a Bayesian approach based on ensemble Kalman inversion (EnKI) and a range of numerical simulations of soil–foundation–building interaction, we estimate the optimal frequency that can be used to estimate soil impedance for time domain analyses; and we evaluate the improvement that the corresponding impedance offers relative to the full FEM results when compared to time domain analyses performed in accordance to the NIST recommendations outlined above.

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Yin, Fengwei, Guanwei Luo, and Xueming Wang. "Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops." Shock and Vibration 2021 (February 11, 2021): 1–21. http://dx.doi.org/10.1155/2021/6624205.

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The mechanical model of a two-degree-of-freedom vibration system with multiple rigid stops was established, and the effects of the multiple rigid stops to dynamic characteristics of two mass blocks of the system were studied. The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. Based on the multiparameter and multiobjective collaborative simulation analysis, the correlation between the dynamic characteristics of the vibration system and the model parameters is studied. The basic periodic and subharmonic impact motions are analyzed with emphasis on the influences of dynamical parameters on the mode diversity and the distribution characteristics, and the law of emergence and competition of various periodic impact motions on the parametric plane is revealed. The singular points, the hysteresis transition domains, and the accompanying codimension-two bifurcations, caused by the irreversibility of the transition between adjacent basic periodic impact motions in the low-frequency domain, are analyzed. The reasonable parameter matching range, associated with dynamic characteristic optimization of the system, is determined.

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