Escherization with Large Deformations Based on As-Rigid-As-Possible Shape Modeling

Escher tiling is well known as a tiling that consists of one or a few recognizable figures, such as animals. The Escherization problem involves finding the most similar shape to a given goal figure that can tile the plane. However, it is easy to imagine that there is no similar tile shape for complex goal shapes. This article devises a method for finding a satisfactory tile shape in such a situation. To obtain a satisfactory tile shape, the tile shape is generated by deforming the goal shape to a considerable extent while retaining the characteristics of the original shape. To achieve this, both goal and tile shapes are represented as triangular meshes to consider not only the contours but also the internal similarity of the shapes. To measure the naturalness of the deformation, energy functions based on traditional as-rigid-as-possible shape modeling are incorporated into a recently developed framework of the exhaustive search of the templates for the Escherization problem. The developed algorithms find satisfactory tile shapes with natural deformations for fairly complex goal shapes.

Comment on Inverse problem from discrete spectrum in the D = 2 dimensional space (2014 Phys. Scr. 989 085201)

We analyse a method for the construction of the potential-energy function from the moments of the ground-state density. The sum rule on which some expressions are based appear to be wrong, as well as the moments and potential-energy functions derived for some illustrative examples.

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.

Quantum harmonic free energies for biomolecules and nanomaterials

Obtaining the free energy of large molecules from quantum mechanical energy functions is a longstanding challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of unprecedented size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where the exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

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.

ENTIRE-REGION CONSTITUTIVE RELATION FOR TRELOAR'S DATA

ABSTRACT Hyperelastic materials can experience a large deformation process. A constitutive relation suitable for an entire region from small, moderate, to large deformations is of great importance for practical applications such as fracture problems. Treloar's data are first investigated, and the tension curve is divided into three regimes: small-to-moderate regime, strain-hardening regime, and limiting-chain regime. Next, the modeling theory of hyperelastic materials is introduced, and the tensile behaviors of basic energy functions are analyzed for different deformation regimes. Finally, a successive procedure is suggested to establish an entire-region constitutive relation and then applied to Treloar's data. The present constitutive relation can maintain the initial shear modulus while the experimental data are satisfactorily predicted. The present procedure is simple and feasible and hence applicable to other hyperelastic materials when their entire-region constitutive relations are studied based on experimental data.

Roll on two: Ambiguous energies in Stephen King’s The Shining, The Green Mile and Revival

This article positions King as both heir to the literary romantics and arbiter of contemporary issues as located specifically within his representation of energy, and electricity in particular. Writing both within and beyond horror, King both characterizes and creates energic structures that reflect both romantic aesthetic conceptualizations of electricity and modern concerns regarding its generation and fuel consumption more generally. By examining how The Shining (1977), The Green Mile (1996) and Revival (2014) present energy and also formally generate it, I will explore a little attended to element of King’s work and identify how energy functions ambiguously within these texts, materializing both horror and hope, bringing about both the conclusion and continuation of human life. I will also explore how the particular spaces this power is located within both channel and amplify it, King’s work here a surprising textual conduit for our fascination with, reliance on and fear of energy and the ongoing problems and potentialities alive within it.

ACTUAL PROBLEMS OF TRAINING OF HIGHLY QUALIFIED BASKETBALL PLAYERS

The work presents the study results of the technical and physical preparation level of highly qualified basketball players, as well as the level of development of their aerobic and anaerobic functions, taking into account play functions. According to the study results, the need was found out to increase the efficiency of the high-level players' training system, that, despite positive changes, the training system used in basketball does not fully ensure any sufficient impact upon the energy functions of highly qualified basketball players.