Stokes theorem for the first presented in 1854 as a research questionin Cambridge University of England by George Gabriel Irishmathematician (1819-1903). is generalized form Green’stheorem, since Green’s connects double integral plane region D tocurve line which bounded this surface ...
 

Following Part I, this paper continues to describe the calculation of the reach sets and tubes for linear control systems with time-varying coe cients and ellipsoidal hard bounds on the controls and initial states. It deals with parametrized families of internal ellipsoidal approximations constructed such that they touch the reach sets at every point of their boundary at any instant of time (bo...

Nano-sized polymersomes functionalized with peptides or proteins are being increasingly studied for targeted delivery of diagnostic and therapeutic molecules. Earlier computational studies have suggested that ellipsoidal nanoparticles, compared to spherical ones, display enhanced binding efficiency with target cells, but this has not yet been experimentally validated. We hypothesize that hydrop...

We numerically investigate the mechanical properties of static packings of frictionless ellipsoidal particles in two and three dimensions over a range of aspect ratio and compression Δφ. While amorphous packings of spherical particles at jamming onset (Δφ=0) are isostatic and possess the minimum contact number z_{iso} required for them to be collectively jammed, amorphous packings of ellipsoida...

In noncommutative spaces, it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define “Instanton number” by the size of Bα in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of Pontrjagin class (instanton charge) with the Foc...

In noncommutative spaces it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define “Instanton number” by the size of Bα in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of Pontrjagin class (instanton charge) in the Fock s...

The ‘triad interactions’, arising from the spectral resolution of the nonlinear terms in the Navier-Stokes equations, have so far not been substantially modified in the wavelet representation. In this paper, the multiscale interactions are captured by exact expressions evaluated at a single scale of the Mexican hat wavelet coefficients: the larger-scale terms as a volume integral of nearby wave...

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...

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer funct...

Centrifugal sedimentation of particles suspended in a fluid is a well known method (1, 2) to measure the size distribution of particles in the range of about 0.02 micron to about 20 microns. The sedimentation velocity of any particle can be calculated if the particle density, fluid density, fluid viscosity, and centrifugal acceleration are known, using the well known Stokes' Equation (3). Stoke...