Journal articles: 'Higher-gradient theorie'

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Abali, B. Emek, Wolfgang H. Müller, and Francesco dell’Isola. "Theory and computation of higher gradient elasticity theories based on action principles." Archive of Applied Mechanics 87, no. 9 (June 5, 2017): 1495–510. http://dx.doi.org/10.1007/s00419-017-1266-5.

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Surana, Karan S., and Stephen W. Long. "Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality." Entropy 22, no. 4 (April 14, 2020): 443. http://dx.doi.org/10.3390/e22040443.

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This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders n ε as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders n Θ . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works.

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dell’Isola, F., P. Seppecher, and A. Della Corte. "The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2183 (November 2015): 20150415. http://dx.doi.org/10.1098/rspa.2015.0415.

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In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s -order forces.

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GUHA, SUMAN, SANDEEP SANGAL, and SUMIT BASU. "A review of higher order strain gradient theories of plasticity: Origins, thermodynamics and connections with dislocation mechanics." Sadhana 40, no. 4 (June 2015): 1205–40. http://dx.doi.org/10.1007/s12046-015-0369-3.

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Bardenhagen, S., and N. Triantafyllidis. "Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models." Journal of the Mechanics and Physics of Solids 42, no. 1 (January 1994): 111–39. http://dx.doi.org/10.1016/0022-5096(94)90051-5.

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Miandoab, Ehsan Maani, Hossein Nejat Pishkenari, and Aghil Yousefi-Koma. "Dynamic Analysis of Electrostatically Actuated Nanobeam Based on Strain Gradient Theory." International Journal of Structural Stability and Dynamics 15, no. 04 (May 2015): 1450059. http://dx.doi.org/10.1142/s021945541450059x.

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In this study, dynamic response of a micro- and nanobeams under electrostatic actuation is investigated using strain gradient theory. To solve the governing sixth-order partial differential equation, mode shapes and natural frequencies of beam using Euler–Bernoulli and strain gradient theories are derived and then compared with classical theory. Galerkin projection is utilized to convert the partial differential equation to ordinary differential equations representing the system mode shapes. Accuracy of proposed one degree of freedom model is verified by comparing the dynamic response of the electrostatically actuated micro-beam with analogue equation and differential quadrature methods. Moreover, the static pull-in voltages of micro-beams found by one DOF model are compared with the reported data in literature. The main advantage of proposed method based on the Galerkin method is its simplicity and also its low computational cost in analyzing the dynamic and static responses of micro- and nanobeams. Additionally, effect of axial force, beam thickness and applied voltage are analyzed. The results obtained based on strain gradient theory, are compared with classical and modified couple stress theories which are the special cases of the strain gradient theory. It is shown that strain gradient theory leads to higher frequency and lower amplitude in comparison with two other theories.

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Forest, Samuel, and Karam Sab. "Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models." Mathematics and Mechanics of Solids 25, no. 7 (August 1, 2017): 1429–49. http://dx.doi.org/10.1177/1081286517720844.

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Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presented, together with its relation to the second-order micromorphic model. The linearization of the combination of stress and strain gradient models is then shown to deliver formulations related to Eringen’s and Aifantis’s well-known gradient models involving the Laplacians of stress and strain tensors. Finally, the structures of the dynamical equations are given for strain and stress gradient media, showing fundamental differences in the dynamical behaviour of these two classes of generalized continua.

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Panteghini, Andrea, and Lorenzo Bardella. "On the Finite Element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility." Computer Methods in Applied Mechanics and Engineering 310 (October 2016): 840–65. http://dx.doi.org/10.1016/j.cma.2016.07.045.

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Polizzotto, Castrenze. "A note on the higher order strain and stress tensors within deformation gradient elasticity theories: Physical interpretations and comparisons." International Journal of Solids and Structures 90 (July 2016): 116–21. http://dx.doi.org/10.1016/j.ijsolstr.2016.04.001.

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Forest, Samuel. "Continuum thermomechanics of nonlinear micromorphic, strain and stress gradient media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (March 30, 2020): 20190169. http://dx.doi.org/10.1098/rsta.2019.0169.

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A comprehensive constitutive theory for the thermo-mechanical behaviour of generalized continua is established within the framework of continuum thermodynamics of irreversible processes. It represents an extension of the class of generalized standard materials to higher order and higher grade continuum theories. It reconciles most existing frameworks and proposes some new extensions for micromorphic and strain gradient media. The special case of strain gradient plasticity is also included as a contribution to the current debate on the consideration of energetic and dissipative mechanisms. Finally, the stress gradient continuum theory emerges as a new research field for which an elastic-viscoplastic theory at finite deformations is provided for the first time. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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dell’Isola, Francesco, Alessandro Della Corte, and Ivan Giorgio. "Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives." Mathematics and Mechanics of Solids 22, no. 4 (January 14, 2016): 852–72. http://dx.doi.org/10.1177/1081286515616034.

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Since the first studies dedicated to the mechanics of deformable bodies (by Euler, D’Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to provide firm guidance to the formulation of novel theories. Gabrio Piola dedicated his scientific life to formulating a continuum theory in order to encompass a large class of deformation phenomena and was the first author to consider continua with non-local internal interactions and, as a particular case, higher-gradient continua. More recent followers of Piola (Mindlin, Sedov and then Richard Toupin) recognized the principle of virtual work (and its particular case, the principle of least action) as the (only!) firm foundation of continuum mechanics. Mindlin and Toupin managed to formulate a conceptual frame for continuum mechanics which is able to effectively model the complex behaviour of so-called architectured, advanced, multiscale or microstructured (meta)materials. Other postulation schemes, in contrast, do not seem able to be equally efficient. The present work aims to provide a historical and theoretical overview of the subject. Some research perspectives concerning this theoretical approach are outlined in the final section.

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Panteghini, Andrea, Lorenzo Bardella, and Christian F. Niordson. "A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2229 (September 2019): 20190258. http://dx.doi.org/10.1098/rspa.2019.0258.

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We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004 J. Mech. Phys. Solids 52 , 2545–2568, doi:10.1016/j.jmps.2003.11.002 ) distortion gradient plasticity, adopting Nye's dislocation density tensor as primal HO variable, we expect our results to hold qualitatively for any HO SGP theory, including crystal plasticity.

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Xu, Lei, Ning Zhang, Liqing Fang, Huadong Chen, Pengfei Lin, and Chunsheng Lin. "Simulation Analysis of Magnetic Gradient Full-Tensor Measurement System." Mathematical Problems in Engineering 2021 (March 19, 2021): 1–13. http://dx.doi.org/10.1155/2021/6688364.

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The magnetic gradient full-tensor measurement system is diverse, and the magnetometer array structure is complex. Aimed at the problem, seven magnetic gradient full-tensor measurement system models are studied in detail. The full-tensor measurement theories of the tensor measurement arrays are analyzed. Under the same baseline distance, the magnetic dipole model is used to simulate the measurement system. Based on different measurement systems, the paper quantitatively compares and analyzes the error of the structure. A more optimized magnetic gradient full-tensor measurement system is suggested. The simulation results show that the measurement accuracy of the planar measurement system is slightly higher than that of the stereo measurement system. Among them, the cross-shaped and square measurement systems have relatively smaller structural errors and higher measurement accuracy.

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14

Triantafyllidis, N., and S. Bardenhagen. "On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models." Journal of Elasticity 33, no. 3 (December 1993): 259–93. http://dx.doi.org/10.1007/bf00043251.

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15

CHALLAMEL, NOËL, GJERMUND KOLVIK, and JOSTEIN HELLESLAND. "PLATE BUCKLING ANALYSIS USING A GENERAL HIGHER-ORDER SHEAR DEFORMATION THEORY." International Journal of Structural Stability and Dynamics 13, no. 05 (May 28, 2013): 1350028. http://dx.doi.org/10.1142/s0219455413500284.

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The buckling of higher-order shear plates is studied in this paper with a unified formalism. It is shown that usual higher-order shear plate models can be classified as gradient elasticity Mindlin plate models, by augmenting the constitutive law with the shear strain gradient. These equivalences are useful for a hierarchical classification of usual plate theories comprising Kirchhoff plate theory, Mindlin plate theory and third-order shear plate theories. The same conclusions were derived by Challamel [Mech. Res. Commun.38 (2011) 388] for higher-order shear beam models. A consistent variational presentation is derived for all generic plate theories, leading to meaningful buckling solutions. In particular, the variationally-based boundary conditions are obtained for general loading configurations. The buckling of the isotropic or orthotropic composite plates is then investigated analytically for simply supported plates under uniaxial or hydrostatic in-plane loading. An analytical buckling formula is derived that is common to all higher-order shear plate models. It is shown that cubic-based interpolation models for the displacement field are kinematically equivalent, and lead to the same buckling load results. This conclusion concerns for instance the plate models of Reddy [J. Appl. Mech.51 (1984) 745] or the one of Shi [Int. J. Solids Struct.44 (2007) 4299] even though these models are statically distinct (leading to different stress calculations along the cross-section). Finally, a numerical sensitivity study is made.

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Dreyer, Wolfgang, and Wolfgang H. Müller. "Toward Quantitative Modeling of Morphology Changes in Solids with Phase Field Theories: Atomistic Arguments for the Determination of Higher Gradient Coefficients." Key Engineering Materials 240-242 (May 2003): 901–14. http://dx.doi.org/10.4028/www.scientific.net/kem.240-242.901.

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Guruprasad, Thimmappa Shetty, and Sumit Basu. "Some issues concerning the use of a single, material specific length scale parameter in theories of higher order strain gradient plasticity." Mechanics of Materials 136 (September 2019): 103076. http://dx.doi.org/10.1016/j.mechmat.2019.103076.

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18

Abbasi, Mohammad, and Seyed E. Afkhami. "Resonant Frequency and Sensitivity of a Caliper Formed With Assembled Cantilever Probes Based on the Modified Strain Gradient Theory." Microscopy and Microanalysis 20, no. 6 (September 10, 2014): 1672–81. http://dx.doi.org/10.1017/s1431927614013117.

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AbstractThe resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) is analyzed utilizing strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of strain gradient theory and Hamilton’s principle. The resonant frequency and sensitivity of the proposed AFM microcantilever are then obtained numerically. The proposed ACP includes a horizontal cantilever, two vertical extensions, and two tips located at the free ends of the extensions that form a caliper. As one of the extensions is located between the clamped and free ends of the AFM microcantilever, the cantilever is modeled as two beams. The results of the current model are compared with those evaluated by both modified couple stress and classical beam theories. The difference in results evaluated by the strain gradient theory and those predicted by the couple stress and classical beam theories is significant, especially when the microcantilever thickness is approximately the same as the material length-scale parameters. The results also indicate that at the low values of contact stiffness, scanning in the higher cantilever modes decrease the accuracy of the proposed AFM ACP.

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Bedia, Wafa Adda, Mohammed Sid Ahmed Houari, Aicha Bessaim, Abdelmoumen Anis Bousahla, Abdelouahed Tounsi, Tareq Saeed, and Mohammed S. Alhodaly. "A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams." Journal of Nano Research 57 (April 2019): 175–91. http://dx.doi.org/10.4028/www.scientific.net/jnanor.57.175.

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In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns

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Chen, J. Y., Y. Huang, K. C. Hwang, and Z. C. Xia. "Plane-Stress Deformation in Strain Gradient Plasticity." Journal of Applied Mechanics 67, no. 1 (July 23, 1999): 105–11. http://dx.doi.org/10.1115/1.321155.

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A systematic approach is proposed to derive the governing equations and boundary conditions for strain gradient plasticity in plane-stress deformation. The displacements, strains, stresses, strain gradients and higher-order stresses in three-dimensional strain gradient plasticity are expanded into a power series of the thickness h in the out-of-plane direction. The governing equations and boundary conditions for plane stress are obtained by taking the limit h→0. It is shown that, unlike in classical plasticity theories, the in-plane boundary conditions and even the order of governing equations for plane stress are quite different from those for plane strain. The kinematic relations, constitutive laws, equilibrium equation, and boundary conditions for plane-stress strain gradient plasticity are summarized in the paper. [S0021-8936(00)02301-1]

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Geers, M. G. D., V. Kouznetsova, and W. A. M. Brekelmans. "Multiscale Mechanics in Microelectronics: A Paradigm in Miniaturization." Journal of Electronic Packaging 127, no. 3 (June 24, 2004): 255–61. http://dx.doi.org/10.1115/1.1939007.

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This paper reviews the inherent change in the observed mechanical behavior of electronic components, structures, and multimaterials as a result of the ongoing miniaturization. In general, the size of microstructures is no longer negligible with respect to the component size in micro and submicron applications. Additionally, surface layers start to play a more prominent role in the mechanical response. Microstructural effects, macroscopically triggered gradient effects, and surface effects jointly appear and constitute the various size effects that can be observed. Classical continuum mechanics theories fail to describe these phenomena, and higher-order multiscale theories are required to arrive at an appropriate prediction of the mechanical behavior of miniaturized structures.

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Al‐Furjan, M. S. H., Y. Yang, Ahmad Farrokhian, X. Shen, Reza Kolahchi, and Dipen Kumar Rajak. "Dynamic instability of nanocomposite piezoelectric‐ leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories." Polymer Composites 43, no. 1 (October 30, 2021): 282–98. http://dx.doi.org/10.1002/pc.26373.

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Yin, Shuohui, Zhibing Xiao, Gongye Zhang, Jingang Liu, and Shuitao Gu. "Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis." Crystals 12, no. 9 (September 9, 2022): 1282. http://dx.doi.org/10.3390/cryst12091282.

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This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analysis approach, which conforms to the requirements of higher continuity in gradient elasticity theory. Numerical results are compared with exact solutions to reveal the accuracy of the current isogeometric analysis approach. The influences of length–scale parameter, length-to-thickness ratio, beam thickness and boundary conditions are investigated. Moreover, the difference between the buckling responses obtained by the Timoshenko and Euler–Bernoulli theories shows that the Euler–Bernoulli theory is suitable for slender beams.

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Mareishi, Soraya, Mohsen Mohammadi, and Mohammad Rafiee. "An Analytical Study on Thermally Induced Vibration Analysis of FG Beams Using Different HSDTs." Applied Mechanics and Materials 249-250 (December 2012): 784–91. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.784.

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Thermo-mechanical vibrations of functionally graded (FG) beams are developed. Governing equations of functionally graded beams are obtained based on higher-order variation of transverse shear strain through the depth of the beam. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary condition are derived from Hamilton’s principle. Beam is assumed under uniform thermal loading and simply supported boundary condition. Analytical solution is presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Numerical computations are performed for a functionally graded simply supported beam with a gradient index obeying power law and the results are displayed graphically and tabular to show the effects of the gradient index, temperature rise, and geometrical parameters on the fundamental natural frequency of FG beams, indicating that natural frequency is sensitive to the gradient variation of material properties, geometrical parameters, shear deformations and temperature rise.

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Markolefas, Stylianos, and Dimitrios Fafalis. "Strain Gradient Theory Based Dynamic Mindlin-Reissner and Kirchhoff Micro-Plates with Microstructural and Micro-Inertial Effects." Dynamics 1, no. 1 (July 31, 2021): 49–94. http://dx.doi.org/10.3390/dynamics1010005.

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In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).

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Gümrükçüoğlu, A. Emir, and Kazuya Koyama. "Gravitational wave interactions in Λ₃ models of dark energy." Journal of Cosmology and Astroparticle Physics 2022, no. 10 (October 1, 2022): 025. http://dx.doi.org/10.1088/1475-7516/2022/10/025.

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Abstract We argue that cubic order interactions between two scalar gravitons and one tensor graviton are ubiquitous in models of dark energy where the strong coupling scale is Λ3. These interactions can potentially provide efficient decay channels for gravitational waves. They can also lead to gradient instabilities of the scalar perturbations in the presence of large amplitude gravitational waves, e.g. those detected by LIGO/Virgo. In contrast with models in scalar-tensor theories, there is an infinite number of higher order interactions in generic Λ3 models, which make it difficult to predict the fate of these instabilities inferred from cubic order interactions.

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Chang, Han Soo, Masahiro Joko, Naoki Matsuo, Sang Don Kim, and Hiroshi Nakagawa. "Subarachnoid pressure—dependent change in syrinx size in a patient with syringomyelia associated with adhesive arachnoiditis." Journal of Neurosurgery: Spine 2, no. 2 (February 2005): 209–14. http://dx.doi.org/10.3171/spi.2005.2.2.0209.

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✓ The pathophysiology of syringomyelia is still not well understood. Current prevailing theories involve the assumption that cerebrospinal fluid (CSF) flows into the syrinx from the subarachnoid space through the perivascular space of Virchow—Robin. Reported here is the case of a patient with syringomyelia in which this course is clearly contradicted. This patient with a holocord syrinx associated with adhesive arachnoiditis was treated 3 years previously with insertion of a subarachnoid—peritoneal shunt and had recently experienced worsening myelopathy. On surgical exploration, the shunt system was functioning normally. The medium-pressure shunt valve was replaced with an adjustable valve with a higher closing pressure setting, thus increasing the CSF pressure in the subarachnoid space. Contrary to prevailing theories, this procedure markedly reduced the size of the syrinx. This case provides direct evidence that the syrinx size is inversely related to subarachnoid CSF pressure and supports the hypothesis that the pressure gradient across the spinal cord parenchyma is the force that generates syringes in syringomyelia.

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Nyul, Dávid, Levente Novák, Mónika Kéri, and István Bányai. "A Simple Elimination of the Thermal Convection Effect in NMR Diffusiometry Experiments." Molecules 27, no. 19 (September 27, 2022): 6399. http://dx.doi.org/10.3390/molecules27196399.

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Thermal convection is always present when the temperature of an NMR experiment is different from the ambient one. Most often, it falsifies the value of the diffusion coefficient determined by NMR diffusiometry using a PGSE NMR experiment. In spite of common belief, it acts not only at higher temperatures but also at temperatures lower than in the laboratory. Sodium alkyl-sulfate monomers and micelles in D2O solvent were used as model molecules measured at T = 319 K in order to show that thermal convection sometimes remains hidden in experiments. In this paper, we demonstrate that the increase in apparent diffusion coefficient with increasing diffusion time is a definite indicator of thermal convection. Extrapolation to zero diffusion time can also be used to obtain the real diffusion coefficient, likewise applying the less sensitive pulse sequences designed for flow compensation or the expensive hardware, e.g., sapphire or Shigemi NMR tubes, to decrease the temperature gradient. Further, we show experiments illustrating the effect of a long diffusion time in which the periodic changes of the echo intensity with gradient strength appear as predicted by theories.

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Cai, Lei, Mohamed Jebahi, and Farid Abed-Meraim. "Strain Localization Modes within Single Crystals Using Finite Deformation Strain Gradient Crystal Plasticity." Crystals 11, no. 10 (October 13, 2021): 1235. http://dx.doi.org/10.3390/cryst11101235.

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The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

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Cai, Lei, Mohamed Jebahi, and Farid Abed-Meraim. "Strain Localization Modes within Single Crystals Using Finite Deformation Strain Gradient Crystal Plasticity." Crystals 11, no. 10 (October 13, 2021): 1235. http://dx.doi.org/10.3390/cryst11101235.

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The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

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Kim, Meelae. "Linearised Moser-Trudinger inequality." Bulletin of the Australian Mathematical Society 62, no. 3 (December 2000): 445–57. http://dx.doi.org/10.1017/s0004972700018967.

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As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtained for functions in with resulting exponential class integrability. Here we prove this inequality again and at the same time get sharper information for the bound. We also generalise the Linearised Moser inequality to higher dimensions, which was first introduced by Beckner for functions on the unit disc. Both of our results are obtained by using the method of Carleson and Chang. The last section introduces an analogue of each inequality for the Laplacian instead of the gradient under some restricted conditions.

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HRENYA, C. M., J. E. GALVIN, and R. D. WILDMAN. "Evidence of higher-order effects in thermally driven rapid granular flows." Journal of Fluid Mechanics 598 (February 25, 2008): 429–50. http://dx.doi.org/10.1017/s0022112007000079.

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Molecular dynamic (MD) simulations are used to probe the ability of Navier–Stokes-order theories to predict each of the constitutive quantities – heat flux, stress tensor and dissipation rate – associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect)

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Thomsen, Jens-Peter. "Test-Based Admission to Selective Universities: A Lever for First-Generation Students or a Safety Net for the Professional Classes?" Sociology 52, no. 2 (June 21, 2016): 333–50. http://dx.doi.org/10.1177/0038038516653097.

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This article examines whether the existence of a secondary higher education admission system honouring more qualitative and extra-curricular merits has reduced the social class gap in access to highly sought-after university programmes in Denmark. I use administrative data to examine differences in the social gradient in the primary admission system, admitting students on the basis of their high school grade point average, and in the secondary admission system, admitting university students based on more qualitative assessments. I find that the secondary higher education admission system does not favour first-generation students; further, the system serves as an access route for low-achieving children from the privileged professional classes. Drawing mainly on theories in the social closure tradition, I argue that children with highly educated parents will be favoured when qualitative merits are honoured, and that professional-class families will be especially vigilant in pursuing educational pathways that will secure the reproduction of their class.

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Camacho-Sanchez, Miguel, Melissa T. R. Hawkins, Fred Tuh Yit Yu, Jesus E. Maldonado, and Jennifer A. Leonard. "Endemism and diversity of small mammals along two neighboring Bornean mountains." PeerJ 7 (October 8, 2019): e7858. http://dx.doi.org/10.7717/peerj.7858.

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Mountains offer replicated units with large biotic and abiotic gradients in a reduced spatial scale. This transforms them into well-suited scenarios to evaluate biogeographic theories. Mountain biogeography is a hot topic of research and many theories have been proposed to describe the changes in biodiversity with elevation. Geometric constraints, which predict the highest diversity to occur in mid-elevations, have been a focal part of this discussion. Despite this, there is no general theory to explain these patterns, probably because of the interaction among different predictors with the local effects of historical factors. We characterize the diversity of small non-volant mammals across the elevational gradient on Mount (Mt.) Kinabalu (4,095 m) and Mt. Tambuyukon (2,579 m), two neighboring mountains in Borneo, Malaysia. We documented a decrease in species richness with elevation which deviates from expectations of the geometric constraints and suggests that spatial factors (e.g., larger diversity in larger areas) are important. The lowland small mammal community was replaced in higher elevations (from above ~1,900 m) with montane communities consisting mainly of high elevation Borneo endemics. The positive correlation we find between elevation and endemism is concordant with a hypothesis that predicts higher endemism with topographical isolation. This supports lineage history and geographic history could be important drivers of species diversity in this region.

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dell’Isola, Francesco, and Pierre Seppecher. "“Hypertractions and hyperstresses convey the same mechanical information Continuum Mech. Thermodyn. (2010) 22:163–176” by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories." Continuum Mechanics and Thermodynamics 23, no. 5 (November 27, 2010): 473–78. http://dx.doi.org/10.1007/s00161-010-0176-3.

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Al-shujairi, Mohammed, and Çağrı Mollamahmutoğlu. "Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect." Composites Part B: Engineering 154 (December 2018): 292–312. http://dx.doi.org/10.1016/j.compositesb.2018.08.103.

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Weniger, Ernst Joachim. "The Spherical Tensor Gradient Operator." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1225–71. http://dx.doi.org/10.1135/cccc20051225.

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The spherical tensor gradient operator Ylm(∇), which is obtained by replacing the Cartesian components of r by the Cartesian components of ∇ in the regular solid harmonic Ylm(r), is an irreducible spherical tensor of rank l. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank l. Thus, it is in principle sufficient to consider only multicenter integrals of scalar functions: Higher angular momentum states can be generated by differentiation with respect to the nuclear coordinates. Many of the properties of Ylm(∇) can be understood easily with the help of an old theorem on differentiation by Hobson [Proc. Math. London Soc. 24, 54 (1892)]. It follows from Hobson's theorem that some scalar functions of considerable relevance as for example the Coulomb potential, Gaussian functions, or reduced Bessel functions produce particularly compact results if Ylm(∇) is applied to them. Fourier transformation is very helpful in understanding the properties of Ylm(∇) since it produces Ylm(-ip). It is also possible to apply Ylm(∇) to generalized functions, yielding for instance the spherical delta function δlm(r). The differential operator Ylm(∇) can also be used for the derivation of pointwise convergent addition theorems. The feasibility of this approach is demonstrated by deriving the addition theorem of rvYlm(r) with v ∈ πR.

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Xi, Jianjun, Yongliang Liu, and Dandan Cui. "Research on 3D SIP Conjugate Gradient Inversion Algorithm with Parameter Range Constraints." Mathematical Problems in Engineering 2021 (June 14, 2021): 1–8. http://dx.doi.org/10.1155/2021/6617794.

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3D SIP inversion algorithm involves multiple parameters, and the key is the calculating speed and memory. A whole set of quasi-linear (QL) theories has taken shape in recent years, including the QL approximation method proposed by Zhdanov, quasi-analytic approximation, and localized quasi-linear (LQL) approximation. They are characterized by high speed and accuracy in electromagnetic field numerical modeling. The above-based 3D QL inversion algorithm, boasting quicker calculating speed plus more stable and favorable inversion effect, has been adopted profoundly in electromagnetic prospecting, whereas its frequent source conversion requires recalculating the dyadic Green’s function and primary field each time, thus delaying the 3D SIP modeling speed. This study makes use of the spatial symmetry in the primary field and Green function to propose an effective and quicker QL forward modeling method, which has the hallmark of higher calculating speed owing to less calculating times, and makes feasible the 3D SIP conjugate gradient inversion algorithm with Cole–Cole parameter range constraints.

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Matta, Anjanna, and G. Nagaraju. "The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction." International Journal of Computing Science and Mathematics 14, no. 3 (2021): 301. http://dx.doi.org/10.1504/ijcsm.2021.10043445.

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Matta, Anjanna, and G. Nagaraju. "The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction." International Journal of Computing Science and Mathematics 14, no. 3 (2021): 301. http://dx.doi.org/10.1504/ijcsm.2021.119903.

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Rawat, Angel, Raghu Piska, A. Rajagopal, and Mokarram Hossain. "Nonlocal plasticity-based damage modeling in quasi-brittle materials using an isogeometric approach." Engineering Computations 38, no. 6 (January 27, 2021): 2604–30. http://dx.doi.org/10.1108/ec-12-2019-0562.

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Purpose This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented. Design/methodology/approach In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented. Findings The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables. Research limitations/implications The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work. Practical implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Social implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Originality/value The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

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Wang, Chunxia, Jun Bi, Qiuyue Sai, and Zun Yuan. "Analysis and Prediction of Carsharing Demand Based on Data Mining Methods." Algorithms 14, no. 6 (June 5, 2021): 179. http://dx.doi.org/10.3390/a14060179.

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With the development of the sharing economy, carsharing is a major achievement in the current mode of transportation in sharing economies. Carsharing can effectively alleviate traffic congestion and reduce the travel cost of residents. However, due to the randomness of users’ travel demand, carsharing operators are faced with problems, such as imbalance in vehicle demand at stations. Therefore, scientific prediction of users’ travel demand is important to ensure the efficient operation of carsharing. The main purpose of this study is to use gradient boosting decision tree to predict the travel demand of station-based carsharing users. The case study is conducted in Lanzhou City, Gansu Province, China. To improve the accuracy, gradient boosting decision tree is designed to predict the demands of users at different stations at various times based on the actual operating data of carsharing. The prediction results are compared with results of the autoregressive integrated moving average. The conclusion shows that gradient boosting decision tree has higher prediction accuracy. This study can provide a reference value for user demand prediction in practical application.

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Lurie, Sergey A., Dmitrii B. Volkov-Bogorodskii, and Petr A. Belov. "Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures." Mathematics 10, no. 1 (December 27, 2021): 90. http://dx.doi.org/10.3390/math10010090.

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A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

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Vivenzi, N., G. Spizzo, M. Veranda, D. Bonfiglio, and S. Cappello. "Kinematic viscosity estimates in reversed-field pinch fusion plasmas." Journal of Physics: Conference Series 2397, no. 1 (December 1, 2022): 012010. http://dx.doi.org/10.1088/1742-6596/2397/1/012010.

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Abstract This paper concerns the kinematic viscosity in reversed-field pinch fusion plasmas, including both the study of numerical magneto-hydrodynamics (MHD) simulations and the analysis of RFX-mod experimental data. In the first part, we study the role of non-uniform time-constant radial viscosity profiles in 3D non-linear visco-resistive MHD simulations. The new profiles induce a moderate damp (for the velocity field) and a correspondent enhancement (for the magnetic field) of the spectral components resonating in the regions where the viscosity is higher. In the second part, we evaluate the kinematic viscosity coefficient on a wide database of RFX-mod shots according to the transport theories of Braginskii (considering parallel, perpendicular and gyro viscosity coefficients), considering the action on viscosity of ITG modes (ion temperature gradient) and according to the transport theory of Finn. We then exploit the comparison with the visco-resistive MHD simulations (where the visco-resistive dissipation rules the MHD activity) to show that the classical Braginskii perpendicular viscosity produces the best agreement between simulations and data, followed by the Braginskii gyro-viscosity.

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Kantrao Kulkarni, Sanjay, and Yuwaraj Marotrao Ghugal. "FLEXURAL ANALYSIS OF THERMALLY LOADED SYMMETRIC SANDWICH BEAM." Journal of the Serbian Society for Computational Mechanics 16, no. 1 (November 1, 2022): 29–42. http://dx.doi.org/10.24874/jsscm.2022.16.01.03.

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In the present paper, an attempt has been made to study the effect of temperature gradient on simply supported symmetric sandwich beam. A Navierâ€™s solution technique is used. The temperature profile is assumed to be linear across the thickness of a sandwich beam. A higher order beam theory (HBT) is used to include the effect of shear deformation on thermal flexural response of the sandwich beam. The theory satisfies the shear stress free boundary condition at the top and bottom surfaces of the sandwich beam. No shear correction factor is required. The principle of virtual work is used to obtain the governing equations and boundary conditions. A program has been developed in FORTRAN-77 to obtain thermal stresses and displacements in the sandwich beam for various aspect ratios. The numerical results are presented for moderately thick and thin sandwich beams to assess the performance of the theory. The validity of the present theory is verified by comparing the results with the results available in the literature. The present results are in good agreement with the results of other theories.

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Zhong, Yi, Kai Zhang, and Xin Juan Zheng. "A Compressed Sensing Improvement Algorithm Based on Power Quality Transient Disturbance Signal." Applied Mechanics and Materials 610 (August 2014): 407–13. http://dx.doi.org/10.4028/www.scientific.net/amm.610.407.

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Traditional power quality signal samples are based on the Nyquist sampling theory. Because of the existence of disturbance signal for the presence of power, it requires two times higher than the sampling frequency of the original signal, resulting in many problems, such as a high cost of hardware. Compressed sensing algorithm abandoned the characteristics of Shannon theorem, using a lower sampling frequency and the less amount of the signal to reconstruct the signal, with the method of a loss compression, which can effectively solve this problem. A team in Beijing University of Chemical Technology has done a deep research in this direction and proposed the total variation gradient reduction algorithm, which has good effects on reduction. But the algorithm runs slower and needs higher sample volumes of signal. Therefore, this paper presents a modified algorithm based on Nesta algorithm to reduce the amount of data sampled of power quality signal, the complexity of the algorithm to improve the algorithm’s speed. The modified algorithm has a very important value in practical applications. This paper has carried out simulations in matlab, the results of the simulation show that this method is accurate and applied.

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Qu, Lixin, and Robert Hetland. "Nongeostrophic Baroclinic Instability over Sloping Bathymetry: Buoyant Flow Regime." Journal of Physical Oceanography 50, no. 7 (July 1, 2020): 1937–56. http://dx.doi.org/10.1175/jpo-d-19-0145.1.

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AbstractBaroclinic instabilities are important processes that enhance mixing and dispersion in the ocean. The presence of sloping bathymetry and the nongeostrophic effect influence the formation and evolution of baroclinic instabilities in oceanic bottom boundary layers and in coastal waters. This study explores two nongeostrophic baroclinic instability theories adapted to the scenario with sloping bathymetry and investigates the mechanism of the instability suppression (reduction in growth rate) in the buoyant flow regime. Both the two-layer and continuously stratified models reveal that the suppression is related to a new parameter, slope-relative Burger number Sr ≡ (M2/f2)(α + αp), where M2 is the horizontal buoyancy gradient, α is the bathymetry slope, and αp is the isopycnal slope. In the layer model, the instability growth rate linearly decreases with increasing Sr {the bulk form Sr = [U0/(H0f)](α + αp)}. In the continuously stratified model, the instability suppression intensifies with increasing Sr when the regime shifts from quasigeostrophic to nongeostrophic. The adapted theories are intrinsically applicable to deep ocean bottom boundary layers and could be conditionally applied to coastal buoyancy-driven flow. The slope-relative Burger number is related to the Richardson number by Sr = δrRi−1, where the slope-relative parameter is δr = (α + αp)/αp. Since energetic fronts in coastal zones are often characterized by low Ri, that implies potentially higher values of Sr, which is why baroclinic instabilities may be suppressed in the energetic regions where they would otherwise be expected to be ubiquitous according to the quasigeostrophic theory.

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Papantoniou, Dimitris, and E. John List. "Large-scale structure in the far field of byoyant jets." Journal of Fluid Mechanics 209 (December 1989): 151–90. http://dx.doi.org/10.1017/s002211208900306x.

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The flow structure and entrainment mechanisms in the far field of a round vertical buoyant jet have been studied experimentally by use of an optical technique based on laser-induced fluorescence (LIF). A large number of essentially instantaneous tracer concentration profiles were recorded for each experimental run by combining LIF with linear photodiode array imaging and high-speed digital data acquisition. Analysis of the resulting high-resolution flow images indicates that the far-field region is dominated by the periodic passage of structures spanning the entire radial flow extent. Ambient fluid is entrained by vortical motions and is transported to regions deep into the flow interior. Correlation analysis discloses that the passage frequency of the structures scales with the local mean velocity and flow width. Conditional averaging of the data indicates that the downstream frontal region of the structure is well mixed and at higher concentration level than the back and side regions where ambient fluid is intermittently present. This results in an axial concentration gradient within the structure, analogous to the ramp-like pattern previously observed in heated air jets. In comparison to the momentum-driven flow the ambient fluid presence in the flow interior is greatly increased when body forces are the driving mechanism. This appears to result from the influence of buoyancy forces in the production of turbulent vortices at the integral scale. An important feature of both the momentum-driven and buoyancy-driven flows investigated is the strongly intermittent character of the concentration field. This raises the issue of the appropriateness of gradient-diffusion theories for the description of such flows.

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Shahabodini, A., R. Ansari, and H. Rouhi. "A three-dimensional surface elastic model for vibration analysis of functionally graded arbitrary straight-sided quadrilateral nanoplates under thermal environment." Journal of Mechanics 37 (December 10, 2020): 72–99. http://dx.doi.org/10.1093/jom/ufaa011.

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AbstractIn this paper, a three-dimensional (3D) size-dependent formulation is developed for the free vibrations of functionally graded quadrilateral nanoplates subjected to thermal environment. The plate model is constructed within the frameworks of the Gurtin–Murdoch surface and the 3D elasticity theories. In this way, the effect of surface free energy and all the components of stress and strain tensors are considered without any initial assumption on them as there is no need to assume the variation of transverse normal stress inside the bulk material in advance. The variational differential quadrature approach and the mapping technique are applied to derive a discretized weak form of the governing equations. The present solution method bypasses the transformation and discretization of the higher order derivatives appearing in the equations of the strong form. The effects of surface stress, thermal environment, material gradient index and geometrical properties on the size-dependent vibrational behavior of quadrilateral nanoplates are investigated. It is observed that the thermal load intensifies the effect of surface free energy on the natural frequency of the nanoplates. The present model is exact in the extent of the continuum models and can be employed for structures with any thickness–span ratios.

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Chung, Bong Jae, Benjamin De Bari, James Dixon, Dilip Kondepudi, Joseph Pateras, and Ashwin Vaidya. "On the Thermodynamics of Self-Organization in Dissipative Systems: Reflections on the Unification of Physics and Biology." Fluids 7, no. 4 (April 14, 2022): 141. http://dx.doi.org/10.3390/fluids7040141.

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In this paper, we discuss some well-known experimental observations on self-organization in dissipative systems. The examples range from pure fluid flow, pattern selection in fluid–solid systems to chemical-reaction-induced flocking and aggregation in fluid systems. In each case, self-organization can be seen to be a function of a persistent internal gradient. One goal of this article is to hint at a common theory to explain such phenomena, which often takes the form of the extremum of some thermodynamic quantity, for instance the rate of entropy production. Such variational theories are not new; they have been in existence for decades and gained popularity through the Nobel Prize-winning work of theorists such as Lars Onsager and Ilya Prigogine. The arguments have evolved since then to include systems of higher complexity and for nonlinear systems, though a comprehensive theory remains elusive. The overall attempt is to bring out examples from physics, chemistry, engineering, and biology that reveal deep connections between variational principles in physics and biological, or living systems. There is sufficient evidence to at least raise suspicion that there exists an organization principle common to both living and non-living systems, which deserves deep attention.

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Journal articles on the topic 'Higher-gradient theorie'

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