Search Results (9)

Precise 3D shape correspondence is a fundamental prerequisite for critical applications ranging from medical anatomical modeling to visual recognition. However, non-isometric 3D shape matching remains a challenging task due to the limited sensitivity of traditional Laplace–Beltrami (LB) bases to local geometric deformations such as stretching and bending. To address these limitations, this paper proposes a Sinkhorn-Regularized Elastic Functional Map framework (SRE-FMaps) that integrates entropy-regularized optimal transport with an elastic thin-shell energy basis. First, a sparse Sinkhorn transport plan is adopted to initialize a bijective correspondence with linear computational complexity. Then, a non-orthogonal elastic basis, derived from the Hessian of thin-shell deformation energy, is introduced to enhance high-frequency feature perception. Finally, correspondence stability is quantified through a cosine-based elastic distance metric, enabling retrieval and classification. Experiments on the SHREC2015, McGill, and Face datasets demonstrate that SRE-FMaps reduces the correspondence error by a maximum of 32% and achieves an average of 92.3% classification accuracy (with a peak of 94.74% on the Face dataset). Moreover, the framework exhibits superior robustness, yielding a recall of up to 91.67% and an F1-score of 0.94, effectively handling bending, stretching, and folding deformations compared with conventional LB-based functional map pipelines. The proposed framework provides a scalable solution for non-isometric shape correspondence in medical modeling, 3D reconstruction, and visual recognition. Full article

Data-driven simulations are gaining popularity in mechanics of biomaterials since they do not require explicit form of constitutive relations. Data-driven modeling based on neural networks lacks interpretability. In this study, we propose an interpretable data-driven finite element modeling for hyperelastic materials. This approach employs the Laplace stretch as the strain measure and utilizes response functions to define constitutive equations. To validate the proposed method, we apply it to inflation of anisotropic membranes on the basis of synthetic data for porcine skin represented by Holzapfel-Gasser-Ogden model. Our results demonstrate applicability of the method and show good agreement with reference displacements, although some discrepancies are observed in the stress calculations. Despite these discrepancies, the proposed method demonstrates its potential usefulness for simulation of hyperelastic biomaterials. Full article

Response functions completely define the constitutive equations for a hyperelastic material. A strain measure providing an orthogonal stress response, grants response functions directly from experimental curves. One of these strain measures is the Laplace stretch based on QR-decomposition of the deformation gradient. Such a recovery of response functions from experimental data fits the paradigm of data-driven modeling. The set of independent conjugate stress–strain base pairs were proposed as a simple alternative for constitutive modeling and thus might be efficient for data-driven modeling. In the present paper we explore applicability of the conjugate pairs approach for data-driven modeling. The analysis is based on representation of the conjugate pairs in terms of the response functions due to the Laplace stretch. Our analysis shows that one can not guarantee independence of these pairs except in the case of infinitesimal strain. Full article

The invention of carbon nanotubes (CNT) has a wide range of industrial and medical applications. The notion of boundary layer flow is used in medicine, particularly in nanomedicine, and the use of magnetic fields is used to treat cancer tumour growth. The governing PDEs are altered into ODEs with the help of suitable transformations. The mass transfer of a chemically reactive species and the flow of MHD over a stretching plate subjected to an inclined magnetic field are investigated, and analytical solutions for velocity in terms of exponential function and temperature field in terms of incomplete Gamma function are obtained using the Laplace transformation. We investigate the variation of physically important parameters with varying suction, magnetic field, and slip using the analytical results. The differences in velocity and temperature profiles are explored in relation to a number of physical parameters. MWCNT nanofluids have higher effective velocities than the SWCNT deferred nanofluids, and this might assist in industrial applications and medical benefits. Earlier research tells us that carbon nanotubes are likely quicker than nanoparticles at achieving the same tumour instance. As a result, in the presence of CNTs or nanoparticles, the magnetic field can also act as a source. We found that SWCNTs nanofluids are better nanofluids than MWCNTs nanofluids. Full article

This paper focuses on the comfort properties of graduated and preventive compression stockings for people who work long hours in standing postures and for athletes for proper blood circulation. The present study was conducted in order to investigate the effects of the yarn insertion density and inlaid stitches on the performance of the compression stockings. The effects of these parameters on the thermo-physiological comfort properties were tested with standard and developed methods of testing. All compression stockings were maintained with class 1 pressure as per German standards. The structural parameters of the knitted fabric structures were investigated. The stretching and recovery properties were also investigated to determine the performance properties. The theoretical pressure was predicated using the Laplace’s law by testing the stockings’ tensile properties. The compression interface pressures of all stockings were also investigated using a medical stocking tester (MST) from Salzmann AG, St. Gallen, Switzerland. Correlation between the theoretical pressures and pressures measured using the MST system were also assessed. The current research used a multi-response optimization technique, i.e., principal component analysis (PCA), to identify the best structure based on the optimalization of the above-mentioned properties. The results also revealed that samples with higher insertion density levels exhibit better comfort properties. The results showed that sample R1 was the best sample, followed by R2 and P. In addition, all developed stocking samples exhibited better comfort properties than the control sample from the market. Full article

The aim of this study is to develop a mathematical model for the prediction of compression pressure based on fabric parameters, such as engineering stress, engineering strain and engineering modulus of elasticity. Four knitted compression fabrics with different fibrous compositions and knit structures were used. Rectangular-cut strips were employed for the force–elongation characterization of the fabrics. The experimental pressure values between the fabric and rigid cylinder were assessed using a Picopress pressure measuring device. The mechanical and physical parameters of the fabric that influence the interface pressure, such as strain, elasticity modulus/stress and thickness, were determined and integrated into Laplace’s law. A good correlation was observed between the experimental and calculated pressure values for all combinations of fabrics, mounted with variable tension on the cylinder. Over the considered range of pressures, the difference between the two datasets was generally less than 0.5 mmHg. The effect of washing after five, ten and fifteen washing cycles on the fabric–cylinder interface pressure was found to be significant. Full article

Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R_∞-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain. Full article

Plasmon-enhanced photothermal and optomechanical effects on deforming and reshaping a gold nanoparticle (NP) are studied theoretically. A previous paper (Wang and Ding, ACS Nano 13, 32–37, 2019) has shown that a spherical gold nanoparticle (NP) irradiated by a tightly focused laser beam can be deformed into an elongated nanorod (NR) and even chopped in half (a dimer). The mechanism is supposed to be caused by photothermal heating for softening NP associated with optical traction for follow-up deformation. In this paper, our study focuses on deformation induced by Maxwell’s stress provided by a linearly polarized Gaussian beam upon the surface of a thermal-softened NP/NR. We use an elastic model to numerically calculate deformation according to optical traction and a viscoelastic model to theoretically estimate the following creep (elongation) as temperature nears the melting point. Our results indicate that a stretching traction at the two ends of the NP/NR causes elongation and a pinching traction at the middle causes a dent. Hence, a bigger NP can be elongated and then cut into two pieces (a dimer) at the dent due to the optomechanical effect. As the continuous heating process induces premelting of NPs, a quasi-liquid layer is formed first and then an outer liquid layer is induced due to reduction of surface energy, which was predicted by previous works of molecular dynamics simulation. Subsequently, we use the Young–Laplace model to investigate the surface tension effect on the following deformation. This study may provide an insight into utilizing the photothermal effect associated with optomechanical manipulation to tailor gold nanostructures. Full article

The C library libkww provides functions to compute the Kohlrausch–Williams– Watts function, i.e., the Laplace–Fourier transform of the stretched (or compressed) exponential function exp(-t^β ) for exponents β between 0.1 and 1.9 with double precision. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies, the numeric integration is enormously accelerated by using the Ooura–Mori double exponential transformation. The primitive of the cosine transform needed for the convolution integrals is also implemented. The software is hosted at http://apps.jcns.fz-juelich.de/kww; version 3.0 is deposited as supplementary material to this article. Full article