We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles. The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space. We analyze the singular behavior of the integrals (single-layer and double-layer integrals) appearing in the equations. The int...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

In the present study, we introduce two Neural Network (NN) enhanced methods to approximate local tangent stiffness matrix and internal force computation for a 2D Finite Element. The proposed model is based on Long-Short Term Memory (LSTM), which inherently captures required path-dependent behavior through its parameters. Furthermore, propose an training algorithm where additional loss term corr...

Collagen type I scaffolds are commonly used due to its abundance, biocompatibility, and ubiquity. Most applications require the scaffolds to operate under mechanical stresses. Therefore understanding and being able to control the structural-functional integrity of collagen scaffolds becomes crucial. Using a combined experimental and modeling approach, we studied the structure and function of Ty...

The problem of transient dynamics of highly flexible three-dimensional space-curved beams, undergoing large rotations and stretches, is treated. The case of conservative force loading, which may also lead to configuration-dependent moments on the beam, is considered. Using the three parameters associated with a conformal rotation vector representation of finite rotations, a well-defined Hamilto...

BACKGROUND The Plantaris Longus Tendon (PLT) may be implicated in Achilles (AT) tendinopathy. Different mechanical characteristics may be the cause. This study is designed to measure these. METHODS Six PLT and six AT were harvested from frozen cadavers (aged 65-88). Samples were stretched to failure using a Minimat 2000™ (Rheometric Scientific Inc.). Force and elongation were recorded. Calcul...

Phylogenetic PCA (p-PCA) is a version of for observations that are leaf nodes phylogenetic tree. P-PCA accounts the fact such not independent, due to shared evolutionary history. The method works on Euclidean data, but in biology there need applying it data manifolds, particularly shapes. We provide generalization p-PCA lying Riemannian called Tangent p-PCA. thus makes possible perform dimensio...

in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...