Volume Charge Density in Geometric Product Lorentz Transformation

Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

Electromagnetohydrodynamic peristaltic flow of a couple stress nanofluid through a vertical annulus in the presence of Hall currents and thermal radiation

This paper investigates the electric properties of gold nanoparticles mixed with a convection dielectric couple stress fluid inside a vertical cylindrical tube with moving endoscope in the presence of Hall currents and thermal radiation. Under the long wavelength approximation and the use of appropriate conversion relationships between fixed and moving frame coordinates, the exact solutions have been evaluated for temperature distribution, gold nanoparticles concentration, electrical potential function and nanofluid pressure, while analytical solution is found for the axial velocity using the homotopy analysis method. The results show that the presence of the electric field enhances the effects of Brownian motion parameter, thermophoresis parameter, radiation parameter, Hall currents and wave amplitude ratio on the axial nanofluid velocity, while it was found that its presence reduces the effects of couple stress parameter, thermophoresis diffusion constant and Brownian diffusion constant.

The dual Yamada–Watanabe theorem for mild solutions to stochastic partial differential equations

We provide the dual result of the Yamada–Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called “method of the moving frame”, which allows us to reduce the proof to infinite dimensional stochastic differential equations.

Lagrangian Data Assimilation for Improving Model Estimates of Velocity Fields and Residual Currents in a Tidal Estuary

Numerical models are associated with uncertainties that can be reduced through data assimilation (DA). Lower costs have driven a recent tendency to use Lagrangian instruments such as drifters and floats to obtain information about water bodies. However, difficulties emerge in their assimilation, since Lagrangian data are set out in a moving frame of reference and are not compatible with the fixed grid locations used in models to predict flow variables. We applied a pseudo-Lagrangian approach using OpenDA, an open-source DA tool to assimilate Lagrangian drifter data into an estuarine hydrodynamic model. Despite inherent challenges with using drifter datasets, the work showed that low-cost, low-resolution drifters can provide a relatively higher improvement over the Eulerian dataset due to the larger area coverage of the drifter. We showed that the assimilation of Lagrangian data obtained from GPS-tracked drifters in a tidal channel for a few hours can significantly improve modelled velocity fields (up to 30% herein). A 40% improvement in residual current direction was obtained when assimilating both Lagrangian and Eulerian data. We conclude that the best results are achieved when both Lagrangian and Eulerian datasets are assimilated into the hydrodynamic model.

Wear and Breakage Detection of Integral Spiral End Milling Cutters Based on Machine Vision

Tool wear and breakage detection technologies are of vital importance for the development of automatic machining systems and improvement in machining quality and efficiency. The monitoring of integral spiral end milling cutters, however, has rarely been investigated due to their complex structures. In this paper, an image acquisition system and image processing methods are developed for the wear and breakage detection of milling cutters based on machine vision. The image acquisition system is composed of three light sources and two cameras mounted on a moving frame, which renders the system applicable in cutters of different dimensions and shapes. The images captured by the acquisition system are then preprocessed with denoising and contrast enhancing operations. The failure regions on the rake face, flank face and tool tip of the cutter are extracted with the Otsu thresholding method and the Markov Random Field image segmentation method afterwards. Eventually, the feasibility of the proposed image acquisition system and image processing methods is demonstrated through an experiment of titanium alloy machining. The proposed image acquisition system and image processing methods not only provide high quality detection of the integral spiral end milling cutter but can also be easily converted to detect other cutting systems with complex structures.

How Do Broken Bones Heal?

The human skeleton is truly amazing. It is a moving frame that protects soft tissues and organs, while simultaneously storing minerals and producing blood cells and immune cells. Bones also have an amazing ability to rebuild and repair themselves. There is no need to worry much if you break a bone because, with the support of your doctors and therapists, the bone should heal itself. Bones have a flexible structure that serves as the scaffolding for the minerals that create a strong and stable skeleton. Unfortunately, bone strength may decrease with age or due to food or hormonal deficiencies. When you experience pain, swelling, or bruising following a fall, you should go to the doctor to see if you have a bone fracture. But do not worry—remember that bones can repair themselves! Have you ever wondered how bone healing happens? You can find the answers in this article.

Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Simulation of the frequency split of the fundamental air cavity mode of a loaded and rolling tire by using steady-state transport analysis

It has been found that when a tire deforms due to loading, the fundamental air cavity mode splits into two due to the break in geometrical symmetry. The result is the creation of fore-aft and vertical acoustic modes near 200 Hz for typical passenger car tires. When those modes couple with structural, circumferential modes having similar natural frequencies, the oscillatory force transmitted to the suspension can be expected to increase, hence causing increased interior noise levels. Further, when the tire rotates, the frequency split is enlarged owing to the Doppler effect resulting from the airflow within the tire cavity. The current research is focused on determining the influence of rotation speed on the frequency split by using FE simulation. In particular, the analysis was performed by using steady-state transport analysis which enables vibroacoustic analysis in a moving frame attached to tire in the frequency domain. The details of the modeling are described and results are given for a tire under different rotation speeds, presented in terms of dispersion curves that illustrate the interaction between structural and acoustical modes. The results are compared to those for static tires and tires spinning without translational velocity to highlight the effects of rolling.