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Journal articles on the topic 'Energy curvature'

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Author: Grafiati

Published: 11 March 2023

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1

Oakley, William S. "Resolving the electron-positron mass annihilation mystery." International Journal of Scientific Reports 1, no. 6 (October 22, 2015): 250. http://dx.doi.org/10.18203/issn.2454-2156.intjscirep20150954.

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<p class="abstract"><span lang="EN-US">Mutual annihilation of low energy electrons and positrons results in two photons of equal energy. The annihilation is consistent with charge conservation but both particles have positive mass, so how do two positive masses annihilate? The issue is resolved by considering particles electromagnetic (EM) energy localized by curvature of the space-time metric. The curvature extends into the surrounding metric forming the particle’s gravitational field, usually attributed as due to mass by the observer, but only the curved space-time metric exists. In principle both positive and negative metric curvatures could exist and display positive and negative masses respectively, but both would possess positive energy. For the electron EM energy circulates in the observer domain and outside but close to an event horizon (EH), the positive metric curvature results in the impression of positive mass. Symmetry suggests positron energy circulates inside an EH and should have negative curvature. It is posited metric field curvature reverses on passage through an event horizon, thus the positron positive mass apparent to the observer arises from negative metric curvature inside the particle EH. The opposite metric curvatures of the electron and positron cancel on annihilation, eliminating their gravitational effects and thereby their apparent masses.</span></p>

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2

Hassan, M. A., Mohd Hamdi Abdul Shukor, Sadjad Naderi, and F. Zahedi. "Effect of Curvature and Thickness of Aluminum Shells on the Energy Absorption in Low Velocity Impact." Advanced Materials Research 488-489 (March 2012): 40–45. http://dx.doi.org/10.4028/www.scientific.net/amr.488-489.40.

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The objective of this study is to investigate the behavior of Aluminum shells AA5083-H116 under low energy impact and the effects of curvature and thickness were assessed under different impact velocities (5.6, 7.5, 9.5, 11.5 m/s). LS-DYNA software was used to evaluate the amount of absorbed energy by the Aluminum shell during impact under different curvature parameter c. The results showed that the amount of absorbed energy incereases with increasing curvature in a linear relationship which make it possible to predict the amount of absorbed energy for this aluminum alloy under different impact energy. Aslo, the amount of absorbed energy has a direct linear relation with the rise of impact energy. The slopes of curves for absorbed energy with respect to the imapct energy are similar for all curvatures. Shell thickness has inverse effect on the amount of absorbed energy and the relation shows similar ternds with diffrent curvatures. However thick shells show significant increase in maximum force and better stability in the dynamic behavior with less fluctuations in the impact force as the cuvature increases.

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3

SIMANCA, SANTIAGO R. "PRECOMPACTNESS OF THE CALABI ENERGY." International Journal of Mathematics 07, no. 02 (April 1996): 245–54. http://dx.doi.org/10.1142/s0129167x96000141.

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For any complex manifold of Kähler type, the L2-norm of the scalar curvature of an extremal Kähler metric is a continuous function of the Kähler class. In particular, if a convergent sequence of Kähler classes are represented by extremal Kähler metrics, the corresponding sequence of L2-norms of the scalar curvatures is convergent. Similarly, the sequence of holomorphic vector fields associated with a sequence of extremal Kähler metrics with converging Kähler classes is convergent.

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4

Wang, Dan, Zhili Hu, Gang Peng, and Yajun Yin. "Surface Energy of Curved Surface Based on Lennard-Jones Potential." Nanomaterials 11, no. 3 (March 9, 2021): 686. http://dx.doi.org/10.3390/nano11030686.

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Although various phenomena have confirmed that surface geometry has an impact on surface energy at micro/nano scales, determining the surface energy on micro/nano curved surfaces remains a challenge. In this paper, based on Lennard-Jones (L-J) pair potential, we study the geometrical effect on surface energy with the homogenization hypothesis. The surface energy is expressed as a function of local principle curvatures. The accuracy of curvature-based surface energy is confirmed by comparing surface energy on flat surface with experimental results. Furthermore, the surface energy for spherical geometry is investigated and verified by the numerical experiment with errors within 5%. The results show that (i) the surface energy will decrease on a convex surface and increase on a concave surface with the increasing of scales, and tend to the value on flat surface; (ii) the effect of curvatures will be obvious and exceed 5% when spherical radius becomes smaller than 5 nm; (iii) the surface energy varies with curvatures on sinusoidal surfaces, and the normalized surface energy relates with the ratio of wave height to wavelength. The curvature-based surface energy offers new insights into the geometrical and scales effect at micro/nano scales, which provides a theoretical direction for designing NEMS/MEMS.

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5

Smith, Keith T. "Curvature with interacting dark energy." Science 371, no. 6536 (March 25, 2021): 1329.5–1330. http://dx.doi.org/10.1126/science.371.6536.1329-e.

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6

Cárdenas, Víctor H., and Roberto G. Perez. "Holographic dark energy with curvature." Classical and Quantum Gravity 27, no. 23 (November 8, 2010): 235003. http://dx.doi.org/10.1088/0264-9381/27/23/235003.

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7

Balakin, Alexander B., Diego Pav n, Dominik J. Schwarz, and Winfried Zimdahl. "Curvature force and dark energy." New Journal of Physics 5 (July 4, 2003): 85. http://dx.doi.org/10.1088/1367-2630/5/1/385.

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8

Durand, M., P. Schuck, and X. Vi�as. "On the nuclear curvature energy." Zeitschrift f�r Physik A Hadrons and Nuclei 346, no. 2 (June 1993): 87–100. http://dx.doi.org/10.1007/bf01294624.

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9

Zhang, Xuhui, Yan Guo, Fulin Zhu, Xiaoyu Chen, Hao Tian, and Hengtao Xu. "A Linear-Arc Composite Beam Piezoelectric Energy Harvester Modeling and Finite Element Analysis." Micromachines 13, no. 6 (May 29, 2022): 848. http://dx.doi.org/10.3390/mi13060848.

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To improve the output performance of the piezoelectric energy harvester, this paper proposed the design of a linear-arc composite beam piezoelectric energy harvester (PEH-C). First the nonlinear restoring force model of a composite beam was obtained by the numerical simulation method. Afterwards, the corresponding coupled governing equations were derived by using the generalized Hamilton principle, laying the foundation for subsequent in-depth research. After this, a finite element simulation was performed in the COMSOL software to simulate the output voltage, stress distribution, and resonance frequency of the PEH-C under different curvatures. In this way, the effect of curvature change on the PEH-C was analyzed. Finally, the PEH-C with a curvature of 40 m−1 was prepared, and an experimental platform was built to verify the correctness of the relevant analysis. The results showed that the resonant frequency of the PEH-C can be changed by changing the curvature, and that the stress on the composite beam will increase after the arc segment is introduced. When the curvature of the PEH-C was 40 m−1, the open-circuit output voltage was 44.3% higher than that of the straight beam.

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10

Saffari, H., R. Tabatabaei, and S. H. Mansouri. "Vibration Analysis of Circular Arch Element Using Curvature." Shock and Vibration 15, no. 5 (2008): 481–92. http://dx.doi.org/10.1155/2008/149393.

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In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.

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11

Seibi, A. C., and A. M. Al-Shabibi. "Pipe Bending and Running Forces in Medium to High-Curvature Wells Using Finite Element Analysis." Journal of Energy Resources Technology 120, no. 4 (December 1, 1998): 263–67. http://dx.doi.org/10.1115/1.2795046.

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The present paper describes the running process in horizontal wells and studies the effect of some factors on running forces required to push pipes through curved holes with short to medium radii of curvatures. Estimation of the running forces was performed using a general-purpose finite element program called ANSYS. The effect of pipe bending stiffness, hole radius of curvature, and hole clearance are investigated. Finite element results showed that the pipe bending stiffness becomes insignificant for medium curvatures (i.e., radius of curvature greater than 80 m). It was also found that the running force at the kick-off point (k.o.p) increases as the radius of curvature shortens (severe doglegs) and as the pipe stiffness increases. In addition, FE results revealed that the effect of hole clearance on the running force is negligible.

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12

Centelles, M., X. Viñas, and P. Schuck. "Nuclear curvature energy in relativistic models." Physical Review C 53, no. 2 (February 1, 1996): 1018–21. http://dx.doi.org/10.1103/physrevc.53.1018.

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13

Martinez, J. C., and M. B. A. Jalil. "Gaussian curvature energy of graphene sheets." Physics Letters A 375, no. 24 (June 2011): 2437–40. http://dx.doi.org/10.1016/j.physleta.2011.05.002.

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14

Strzelecki, Paweł, and Heiko von der Mosel. "Menger curvature as a knot energy." Physics Reports 530, no. 3 (September 2013): 257–90. http://dx.doi.org/10.1016/j.physrep.2013.05.003.

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15

França, Urbano. "Dark energy, curvature, and cosmic coincidence." Physics Letters B 641, no. 5 (October 2006): 351–56. http://dx.doi.org/10.1016/j.physletb.2006.08.070.

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16

Stocker, W., J. Bartel, J. R. Nix, and A. J. Sierk. "Anomaly in the nuclear curvature energy." Nuclear Physics A 489, no. 2 (November 1988): 252–68. http://dx.doi.org/10.1016/0375-9474(88)90152-2.

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17

Rabha, Chayanika, and Sanjeev Kalita. "Cosmic expansion with curved dark energy cosmology: Inevitability of cosmic doomsday." International Journal of Modern Physics D 30, no. 07 (April 8, 2021): 2150048. http://dx.doi.org/10.1142/s0218271821500486.

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In this work, we have constructed deceleration–acceleration and future evolution of cosmic expansion with curved dynamical dark energy models. Closed and open spatial curvatures are calculated by assuming that dark energy density does not exceed 85% of the closure density and by obtaining lower bounds on the ratio of dark energy to matter density, in terms of equation of state of dark energy. The range of transition epoch [Formula: see text] realized for spatial curvature [Formula: see text] is consistent with model independent estimations coming from galactic ages, strong lensing, Type Ia supernovae and recent constraints coming from [Formula: see text] measurements in non-flat dynamical dark energy models. Two novel parametrizations of dark energy equation of state namely the logarithmic and oscillatory, which are singularity free at future point [Formula: see text] are used to study the deceleration parameter q(z). Irrespective of spatial curvature, cosmic doomsday has been found inevitable for both the parametrizations. The time evolution of logarithmic parametrization, being reminiscent of a quintom field (canonical[Formula: see text]phantom), is converted into dynamics of a canonical quintessence and a phantom field for the redshift range ([Formula: see text],[Formula: see text]) and ([Formula: see text], [Formula: see text]). It is found that irrespective of spatial curvature, the quintessence component becomes sub-dominant in future giving it’s way to the phantom component.

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18

CUEVAS, J., E. B. STARIKOV, J. F. R. ARCHILLA, and D. HENNIG. "MOVING BREATHERS IN BENT DNA WITH REALISTIC PARAMETERS." Modern Physics Letters B 18, no. 25 (October 30, 2004): 1319–26. http://dx.doi.org/10.1142/s0217984904007840.

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Recent papers have considered moving breathers (MB) in DNA models including long range interaction due to the dipole moments of the hydrogen bonds. We have recalculated the value of the charge transfer when hydrogen bonds stretch using quantum chemical methods which takes into account the whole nucleoside pairs. We explore the consequences of this value on the properties of MBs, including the range of frequencies for which they exist and their effective masses. They are able to travel through bending points with fairly large curvatures, provided that their kinetic energy is larger than a minimum energy which depends on the curvature. These energies and the corresponding velocities are also calculated in function of the curvature.

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19

Bulnes, Francisco. "Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy." Science Journal of Circuits, Systems and Signal Processing 4, no. 5 (2015): 41. http://dx.doi.org/10.11648/j.cssp.20150405.12.

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20

Saffari, H., M. J. Fadaee, and R. Tabatabaei. "Developing a Formulation Based upon Curvature for Analysis of Nonprismatic Curved Beams." Mathematical Problems in Engineering 2007 (2007): 1–19. http://dx.doi.org/10.1155/2007/46215.

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A new element with three nodal curvatures has been considered for analysis of the nonprismatic curved beams by finite element method. In the formulation developed, the force-curvature relationships in polar coordinate system have been obtained first, then the curvature of the element has been assumed to have a second-order polynomial function form and the radial, tangential displacements, and rotation of the cross section have been found as a function of the curvature accounting for the effects of the cross section variation. Moreover, the relationship between nodal curvatures and nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force-deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. The results obtained have been compared with the results of some other references through several numerical examples. The comparison indicates that the present formulation has enough accuracy in analysis of thin and thick nonprismatic curved beams.

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21

Chen, Lei, Yong Xiang Hu, Gang Fang, Zhen Qiang Yao, and Xing Wei Zheng. "The Effect of Elastic Pre-Bending on the Laser Peen Forming of 2024-T351 Aluminum Alloy Plate." Applied Mechanics and Materials 496-500 (January 2014): 133–36. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.133.

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Laser peen forming, is a purely mechanical forming method achieved through the use of laser energy to form metal plate with small curvatures. Experiments were performed to investigate the effect of pre-bending on the plate bending deformation induced by laser peen forming. The pre-bending of plate was accomplished by a fixture with the cambered top surface. The pre-bending curvature radius is calculated and is used to design cambered surface. The LPF experiments are performed with Nd: YAG laser with overlapping laser spots. It is found that the convex deformation can be induced after laser shocks. And its curvature radius in the elastically elongated direction can be greatly increased by applying pre-bending, while in the perpendicular direction, the curvature radius is decreased.

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22

CAPOZZIELLO, SALVATORE. "CURVATURE QUINTESSENCE." International Journal of Modern Physics D 11, no. 04 (April 2002): 483–91. http://dx.doi.org/10.1142/s0218271802002025.

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The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic fourth order theory and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth order theories so that we get an alternative scheme to the standard quintessence scalar field, minimally coupled to gravity, usually adopted. We discuss also conformal transformations in order to see the links of quintessence between the Jordan and Einstein frames.

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23

HELMERS, MICHAEL. "SNAPPING ELASTIC CURVES AS A ONE-DIMENSIONAL ANALOGUE OF TWO-COMPONENT LIPID BILAYERS." Mathematical Models and Methods in Applied Sciences 21, no. 05 (May 2011): 1027–42. http://dx.doi.org/10.1142/s0218202511005234.

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In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes, we consider planar curves that are made of a material with two phases. Each phase induces a preferred curvature to the curve, and these curvatures as well as phase boundaries may lead to the development of kinks. We introduce a family of energies for smooth curves and phase fields, and we show that these energies Γ-converge to an energy for curves with a finite number of kinks. The theoretical result is illustrated by some numerical examples.

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24

FEROZE, TOOBA. "NEW CONSERVED QUANTITIES FOR THE SPACES OF DIFFERENT CURVATURES." Modern Physics Letters A 25, no. 13 (April 30, 2010): 1107–14. http://dx.doi.org/10.1142/s021773231003241x.

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It is known that corresponding to each isometry there exists a conserved quantity. It is also known that the Lagrangian of the line element of a space is conserved. Here we investigate the possibility of the existence of "new" conserved quantities, i.e. other than the Lagrangian and associated with the isometries, for spaces of different curvatures. It is found that there exist new conserved quantities only for the spaces of zero curvature or having a section of zero curvature.

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25

Mucci, Domenico. "On the Curvature Energy of Cartesian Surfaces." Journal of Geometric Analysis 31, no. 8 (February 5, 2021): 8460–519. http://dx.doi.org/10.1007/s12220-020-00601-0.

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26

Yao, Wen Wei. "Curvature Elastic Energy Model for Carbon Nanotubes." Advanced Materials Research 906 (April 2014): 185–89. http://dx.doi.org/10.4028/www.scientific.net/amr.906.185.

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Since carbon nanotubes (CNTs) were discovered, due to their unique and novel physical and chemical characteristics, many studies focus on them. In this article, a two-dimensional (2D) curvature elastic energy model for isotropic tube is presented, and reduced to a one-dimensional (1D) continuous model which is in accordance with Kirchhoff elastic rod theory. The problems remaining to be solved are discussed.

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27

Clarkson, Chris, Marina Cortês, and Bruce Bassett. "Dynamical dark energy or simply cosmic curvature?" Journal of Cosmology and Astroparticle Physics 2007, no. 08 (August 9, 2007): 011. http://dx.doi.org/10.1088/1475-7516/2007/08/011.

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28

Hall, G. S., and Lucy MacNay. "Sectional curvature and the energy–momentum tensor." Classical and Quantum Gravity 22, no. 9 (April 6, 2005): 1493–502. http://dx.doi.org/10.1088/0264-9381/22/9/001.

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29

Joshi, Pushkar, and Carlo Séquin. "Energy Minimizers for Curvature-Based Surface Functionals." Computer-Aided Design and Applications 4, no. 5 (January 2007): 607–17. http://dx.doi.org/10.1080/16864360.2007.10738495.

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30

Hobill, D., and W. Guo. "Cosmology without dark energy: Weyl curvature solutions." Canadian Journal of Physics 86, no. 4 (April 1, 2008): 571–77. http://dx.doi.org/10.1139/p08-002.

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To reconcile recent observations that the cosmological expansion has a positive acceleration with the standard Friedmann–Lemaitre–Robertson–Walker models of our Universe, as yet unseen sources of energy and (or) momentum are required for an explanation. This is due to the particular nature of spacetimes that assume homogeneity and isotropy where the curvature of the spacetime is linked to the energy-momentum content of the matter and fields in the spacetime. It is shown that more general cosmological models where Weyl (or vacuum) curvature is present can produce effects that might be responsible for the observed acceleration and other phenomena.PACS Nos.: 95.30.sf, 95.36.+x, 98.80.jk

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31

Savelyev, Yasha. "Mean curvature versus diameter and energy quantization." Annales mathématiques du Québec 44, no. 2 (October 18, 2019): 291–97. http://dx.doi.org/10.1007/s40316-019-00127-0.

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32

KAHNG, B., and K. PARK. "DYNAMICS OF THE CURVATURE-ENERGY-DRIVEN SURFACES." International Journal of Modern Physics B 10, no. 05 (February 28, 1996): 543–61. http://dx.doi.org/10.1142/s0217979296000222.

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The dynamics of the curvature-energy-driven surfaces such as the dynamics of the orientational roughening (OR) transition and the dynamics of the molecular beam epitaxial (MBE) growth with the lattice pinning force are studied. For the dynamics of the OR transition, we first derive the lattice pinning force of the sine-Gordon model, which is in a peculiar form of [Formula: see text] where {êk} (k =1, 2, 3) are the basis vectors of the triangular lattice. The lattice pinning force is renormalized and contributes to the coarse-grained curvature force under the dynamic renormalization group transformation introduced by Nozières and Gallet [J. Phys. (Paris) 48, 353 (1987)]. The dynamic exponent is obtained as z =4 − ∊ with ∊ =2 − d and the mobility is scaled as r−2.51 ∊ in general dimension d ≤ 2. The tilt-tilt correlation function behaves logarithmically with spatial and temporal changes of scales in two dimensions. Next, we study the dynamic equation of the OR transition with the addition of the growth-induced nonlinear term proportional to ∇2 (∇ϕ)2. It is obtained that the OR transition occurs even in the presence of the growth-induced nonlinear term, but the nature of the phase transition changes by the nonlinear term. We compare our analysis with the recent study of the growth-induced roughening transition by Hwa, Kardar and Paczuski [Phys. Rev. Lett.66, 441 (1991)]. It is also found that the lattice pinning force is irrelevant to the MBE growth.

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33

Gaspard, P., S. A. Rice, H. J. Mikeska, and K. Nakamura. "Parametric motion of energy levels: Curvature distribution." Physical Review A 42, no. 7 (October 1, 1990): 4015–27. http://dx.doi.org/10.1103/physreva.42.4015.

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34

Daneshfaraz, Rasoul, and Amir Ghaderi. "Numerical Investigation of Inverse Curvature Ogee Spillway." Civil Engineering Journal 3, no. 11 (December 10, 2017): 1146. http://dx.doi.org/10.28991/cej-030944.

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Design of water structures and their segments including spillways play an important role in water resources management and agricultural activities. In the the linear body part of an ogee spillway, for speeding up the flow rate, the flow should be transferred to the stilling basin by inverse curve so that the water energy can be reduced. This study aims to evaluate the effect of the inverse profile curvature on the pressure of spillway surface using Fluent software. For this purpose, five different curvatures of inverse profile were considered to be equal to no-curvature (zero), 1, 1.5, 2 and 2.5 of the spillway design head. The results indicated that by increasing the curvature radius, the maximum pressure dramatically reduced. And for this purpose, some relationships were given to predict the pressure reduction. Pressure increment in zero curvature is caused by sudden collision of flow lines and turbulence caused by it. By increase in inverse profile curvature, the turbulence is created in flow lines and the maximum pressure shows a lower value than before. In general, there was little change in the average absolute pressure.

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35

Chabanon, Morgan, and Padmini Rangamani. "Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks." Soft Matter 14, no. 12 (2018): 2281–94. http://dx.doi.org/10.1039/c8sm00035b.

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36

Liu, Ze Qin, Zhen Jing Wu, and Ze Peng Feng. "Experimental Investigation of Dust Amount from Free Falling Particle Stream Effected by Deflector Curvature of Dust Suppression." Advanced Materials Research 864-867 (December 2013): 1789–92. http://dx.doi.org/10.4028/www.scientific.net/amr.864-867.1789.

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This paper focuses on the study of the curvatures of deflector installed on the below receiving device to effect the dust amount from the free falling particle stream. The deflector curvature was artificially controlled to limit the fugitive dust direction which was generated by the collision between the free falling bulk materials and the receiving device. This method was used to improve efficiency of the dust control system to exhaust fugitive dust, and to achieve the targets of energy conservation and emissions reduction. The experimental method was adopted to explore the relationship between the deflector curvature and the producing dust quantity. The experimental results indicated that, the dust suppression effect containing deflector contained a certain radian was more remarkable, when the height of the free falling of bulk materials was constant. The producing dust quantity decreased slightly with the deflector curvature increasing, and then increased rapidly. When the deflector curvature was 0.045 cm-1 or 0.060cm-1, the minimum of producing dust quantity could be obtained, and the dust removal effect might be significant.

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37

Cooperstock, F. I. "The essence of gravitational waves and energy." International Journal of Modern Physics D 24, no. 12 (October 2015): 1543005. http://dx.doi.org/10.1142/s0218271815430051.

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In this paper, we discuss the essential element of gravity as spacetime curvature and a gravitational wave as the propagation of spacetime curvature. Electromagnetic waves are necessarily localized carriers of spacetime curvature and hence are also gravitational waves. Thus, electromagnetic waves have dual character and detection of gravitational waves is the routine of our everyday experience. Regarding the transferring energy from a gravitational wave to an apparatus, both Rosen and Bondi waves lack the essential characteristic of inducing a gradient of acceleration between detector elements. We discuss our simple invariant energy expression for general relativity and its extension. If the cosmological term is present in the field equations, its universal presence characteristic implies that gravitational waves would necessarily have an energy aspect in their propagation in every case.

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38

Saffari, H., M. J. Fadaee, and R. Tabatabaei. "A new formulation based upon trigonometric function for finite circular arch elements." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 8 (August 1, 2008): 1371–80. http://dx.doi.org/10.1243/09544062jmes487.

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In this paper, the formulation of the curved beam element by trigonometric functions for the curvature, which is an alternative to the displacement function is presented. Trigonometric function is chosen for the curvature to avoid the shear and membrane locking phenomena. In the developed formulation, the force—curvature relationships in polar coordinate system have been obtained first; then the curvature of the element has been assumed to have a trigonometric function form; and the radial and tangential displacements, and rotation of the cross-section have been found to be a function of the curvature. Moreover, the relationship between the nodal curvatures and the nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force—deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. In such an equilibrium equation, the locking phenomenon is eliminated. The formulation is applied to six examples to verify its capabilities. The results demonstrate that the presented element is capable of representing the behaviour of the curved beam with adequate accuracy and efficiency as compared with the previous methods.

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39

Sun, Zeyang, Yang Yang, Wenlong Yan, Gang Wu, and Xiaoyuan He. "Moment-Curvature Behaviors of Concrete Beams Singly Reinforced by Steel-FRP Composite Bars." Advances in Civil Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/1309629.

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A steel-fiber-reinforced polymer (FRP) composite bar (SFCB) is a kind of rebar with inner steel bar wrapped by FRP, which can achieve a better anticorrosion performance than that of ordinary steel bar. The high ultimate strength of FRP can also provide a significant increase in load bearing capacity. Based on the adequate simulation of the load-displacement behaviors of concrete beams reinforced by SFCBs, a parametric analysis of the moment-curvature behaviors of concrete beams that are singly reinforced by SFCB was conducted. The critical reinforcement ratio for differentiating the beam’s failure mode was presented, and the concept of the maximum possible peak curvature (MPPC) was proposed. After the ultimate curvature reached MPPC, it decreased with an increase in the postyield stiffness ratio (rsf), and the theoretical calculation method about the curvatures before and after the MPPC was derived. The influence of the reinforcement ratio, effective depth, and FRP ultimate strain on the ultimate point was studied by the dimensionless moment and curvature. By calculating the envelope area under the moment-curvature curve, the energy ductility index can obtain a balance between the bearing capacity and the deformation ability. This paper can provide a reference for the design of concrete beams that are reinforced by SFCB or hybrid steel bar/FRP bar.

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Wei, Shao-Wen, Yu-Xiao Liu, Chun-E. Fu, and Hai-Tao Li. "Geometric Curvatures of Plane Symmetry Black Hole." Advances in High Energy Physics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/734138.

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We study the properties and thermodynamic stability of the plane symmetry black hole from the viewpoint of geometry. We find that the Weinhold curvature gives the first-order phase transition atN=1, whereNis a parameter of the plane symmetry black hole while the Ruppeiner one shows first-order phase transition points for arbitraryN≠1. Considering the Legendre invariant proposed by Quevedo et al., we obtain a unified geometry metric, which contains the information of the second-order phase transition. So, the first-order and second-order phase transitions can be both reproduced from the geometry curvatures. The geometry is also found to be curved, and the scalar curvature goes to negative infinity at the Davie phase transition points beyond semiclassical approximation.

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Akopyan, Arsenyi, and Herbert Edelsbrunner. "The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram." Computational and Mathematical Biophysics 8, no. 1 (August 12, 2020): 74–88. http://dx.doi.org/10.1515/cmb-2020-0101.

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AbstractThe morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.

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42

MALEKJANI, M., and A. KHODAM-MOHAMMADI. "AGEGRAPHIC DARK ENERGY MODEL IN THE NON-FLAT UNIVERSE: STATEFINDER DIAGNOSTIC AND w–w′ ANALYSIS." International Journal of Modern Physics D 19, no. 11 (September 2010): 1857–71. http://dx.doi.org/10.1142/s0218271810018086.

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We study the interacting agegraphic dark energy (ADE) model in the non-flat universe by means of the statefinder diagnostic and an w–w′ analysis. First, the evolution of EoS parameter (wd) and deceleration parameter (q) are calculated in terms of scale-factor for interacting ADE models in the non-flat universe. The dependency of wd on the ADE model parameters n and α in different spatial curvatures is investigated. We show that the evolution of q is dependent on the type of spatial curvature, besides dependening on parameters n and α. The accelerated expansion takes place sooner in the open universe and latter in the closed universe as compared with the flat universe. Then, we plot the evolutionary trajectories of the interacting ADE models for different values of the parameters n and α, as well as for different contributions of spatial curvature, in the plane of statefinder parameters. In addition to the statefinder, we also investigate the ADE model in the non-flat universe with w–w′ analysis.

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Chen, Hao, and Chenyu Jin. "Competition brings out the best: modelling the frustration between curvature energy and chain stretching energy of lyotropic liquid crystals in bicontinuous cubic phases." Interface Focus 7, no. 4 (June 16, 2017): 20160114. http://dx.doi.org/10.1098/rsfs.2016.0114.

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It is commonly considered that the frustration between the curvature energy and the chain stretching energy plays an important role in the formation of lyotropic liquid crystals in bicontinuous cubic phases. Theoretic and numeric calculations were performed for two extreme cases: parallel surfaces eliminate the variance of the chain length; constant mean curvature surfaces eliminate the variance of the mean curvature. We have implemented a model with Brakke's Surface Evolver which allows a competition between the two variances. The result shows a compromise of the two limiting geometries. With data from real systems, we are able to recover the gyroid–diamond–primitive phase sequence which was observed in experiments.

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Tsui, Yeng-Yung, and Hong-Ping Cheng. "Tumbling Flow in Loop-Scavenged Two-Stroke Engines." Journal of Fluids Engineering 117, no. 4 (December 1, 1995): 628–32. http://dx.doi.org/10.1115/1.2817314.

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A multidimensional calculation procedure is used to investigate the flow in loop-scavenged two-stroke engine with curved cylinder heads. Five different cylinder heads are considered. The curvature of cylinder head increases from case I to case IV. In case V the head curvature is further increased, but it is shaped in the radially outer region. Calculations reveal that a tumbling vortex forms after the exhaust port is closed and the vortex constantly dominates the flow structure in the cylinder throughout the compression period. With high head curvatures the vortex is well organized and occupies the entire cylinder volume in the late compression stage. Due to compression of the better organized tumbling vortex by the moving piston more energy cascades from mean flow to turbulence in the high curvature cases III and IV. As for case V, the larger clearance in the bowl center region leads to lower shear stresses and, thus, the turbulence augmentation phenomenon is less prominent than that for cases III and IV.

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Bulnes, Francisco, Isaías Martínez, and Isaí M. Martínez. "Water Manipulation through Curvature Energy on Humidity Microparticles." Electrical Science & Engineering 4, no. 1 (April 21, 2022): 21. http://dx.doi.org/10.30564/ese.v4i1.4529.

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The electric field created in a curvature energy sensor on air microparticles is used to obtain a temperature-humidity map by stereoradially of the sensor design to detect and measure the temperature and humidity of certain local region of the environment space. Likewise,considering the curvature energy as the deviation of any field interaction,even the obstruction to its proper flow, is designed and created a humidityresistor sensor to the control and optimization of humidity in a space with different gradients of humidity, pressure and temperature in a radial detection and measuring. Then the sensing problem is a problem of free boundary conditions where is satisfied an energy functional of norm ,to curvature functions that satisfy in the temperature and humidity function the change limit condition This carries to that the temperature-humidity sensor must be designed on a length gauge to measure the changes of humidity and temperature in the space.

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TÜKEL, Gözde Özkan, and Ahmet YÜCESAN. "A Curvature Energy Problem on a Timelike Surface." International Electronic Journal of Geometry 11, no. 2 (November 30, 2018): 120–25. http://dx.doi.org/10.36890/iejg.545141.

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Bargiacchi, G., M. Benetti, S. Capozziello, E. Lusso, G. Risaliti, and M. Signorini. "Quasar cosmology: dark energy evolution and spatial curvature." Monthly Notices of the Royal Astronomical Society 515, no. 2 (July 22, 2022): 1795–806. http://dx.doi.org/10.1093/mnras/stac1941.

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ABSTRACT We analyse some open debates in cosmology in light of the most updated quasar (QSO) sample, covering a wide redshift range up to $\mathit{ z}$ ∼ 7.5, combined with type Ia supernovae (SNe) and baryon acoustic oscillations (BAOs). Indeed, extending the cosmological analyses with high-redshift data is key to distinguishing between different cosmological models that are degenerate at low redshifts, and allowing better constraints on a possible dark energy (DE) evolution. Also, we discuss combinations of BAO, SNe, and QSO data to understand their compatibility and implications for extensions of the standard cosmological model. Specifically, we consider a flat and non-flat ΛCDM cosmology, a flat and non-flat DE model with a constant DE equation of state parameter (w), and four flat DE models with variable w, namely the Chevallier–Polarski–Linder and Jassal–Bagla–Padmanabhan models, and an ‘exponential’, and Barboza–Alcaniz parametrizations. We find that a joint analysis of QSO+SNe with BAO is only possible in the context of a flat Universe. Indeed BAO confirms the flatness condition assuming a curved geometry, whilst SNe + QSO show evidence of a closed space. We also find ΩM,0 = 0.3 in all data sets assuming a flat ΛCDM model. Yet, all the other models show a statistically significant deviation at 2-3 σ with the combined SNe + SO + BAO data set. In the models where DE density evolves with time, SNe + QSO + BAO data always prefer ΩM,0 > 0.3, w0 < −1 and wa > 0. This DE phantom behaviour is mainly driven by SNe + QSO, while BAO are closer to the flat ΛCDM model.

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Hafez, Youssef I. "Excess energy theory for river curvature and meandering." Journal of Hydrology 608 (May 2022): 127604. http://dx.doi.org/10.1016/j.jhydrol.2022.127604.

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Gilbert, L. P., M. Belloni, M. A. Doncheski, and R. W. Robinett. "Piecewise zero-curvature energy eigenfunctions in one dimension." European Journal of Physics 27, no. 6 (September 6, 2006): 1331–39. http://dx.doi.org/10.1088/0143-0807/27/6/007.

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Capozziello, S., V. F. Cardone, and A. Troisi. "Dark energy and dark matter as curvature effects?" Journal of Cosmology and Astroparticle Physics 2006, no. 08 (August 3, 2006): 001. http://dx.doi.org/10.1088/1475-7516/2006/08/001.

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