A generalized strain approach to anisotropic elasticity

This work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton’s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton’s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.

Real-time unstructured road detection based on CNN and Gibbs energy function

Road detection algorithms with high robustness as well as timeliness are the basis for developing intelligent assisted driving systems. To improve the robustness as well as the timeliness of unstructured road detection, a new algorithm is proposed in this paper. First, for the first frame in the video, the homography matrix H is estimated based on the improved random sample consensus (RANSAC) algorithm for different regions in the image, and the features of H are automatically extracted using convolutional neural network (CNN), which in turn enables road detection. Secondly, in order to improve the rate of subsequent similar frame detection, the color as well as texture features of the road are extracted from the detection results of the first frame, and the corresponding Gaussian mixture models (GMMs) are constructed based on Orchard-Bouman, and then the Gibbs energy function is used to achieve road detection in subsequent frames. Finally, the above algorithm is verified in a real unstructured road scene, and the experimental results show that the algorithm is 98.4% accurate and can process 58 frames per second with 1024×960 pixels.

Eigensolution to Morse potential for Scandium and Nitrogen monoiodides

The solutions for Morse potential energy function under the influence of Schr¨odinger equation are examined using supersymmetric approach. The energy equation obtained was used to generate eigenvalues forX1 +state of scandium monoiodide (ScI) and X3 state of nitrogen monoiodide (NI) respectively were obtained by imputing their respective spectroscopic parameters. The calculated results for the two molecules aligned excellently with the predicted/observed values.

The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts (GRBs) are brief, intense, gamma-ray flashes in the universe, lasting from a few milliseconds to a few thousand seconds. For short gamma-ray bursts (sGRBs) with duration less than 2 seconds, the isotropic energy (E iso) function may be more scientifically meaningful and accurately measured than the luminosity (L p) function. In this work we construct, for the first time, the isotropic energy function of sGRBs and estimate their formation rate. First, we derive the L p – E p correlation using 22 sGRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi sGRBs. Then, we adopt the Lynden-Bell c − method to study isotropic energy functions and formation rate of sGRBs without any assumption. A strong evolution of isotropic energy E iso ∝ (1+z)5.79 is found, which is comparable to that between L p and z. After removing effect of the cosmic evolution, the isotropic energy function can be reasonably fitted by a broken power law, which is ϕ ( E iso , 0 ) ∝ E iso , 0 − 0.45 for dim sGRBs and ϕ ( E iso , 0 ) ∝ E iso , 0 − 1.11 for bright sGRBs, with the break energy 4.92 × 1049 erg. We obtain the local formation rate of sGRBs is about 17.43 events Gpc−3 yr−1. If assuming a beaming angle is 6° to 26°, the local formation rate including off-axis sGRBs is estimated as ρ 0,all = 155.79 – 3202.35 events Gpc−3 yr−1.