The nuclear magnetic resonance (NMR) spin relaxation rate constant in the rotating frame of reference R1 provides information on microsecond to millisecond ( s-ms) timescale kinetic processes that stochastically modulate the resonance frequencies of nuclear spins in molecules. Expressions for R1 are presented for two-site chemical exchange using both the conventional perturbation approach for e...

1 Time-dependent perturbation theory 1 1.1 Rotating frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Perturbation expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Periodic perturbations . . . . . . . . . . . . . . . . . ....

This work aims to explore some dynamic aspects of the problem star motion that is impacted by rotation galaxy, which we model as a bisymmetric potential based on two-dimensional harmonic oscillator with sextic perturbations. We demonstrate analytically non-integrable when certain conditions are met. The analytical results for non-integrability confirmed showing irregularity behavior through uti...

Multidimensional spectroscopies correlate the oscillation frequencies of an atomic or molecular resonance during at least two different time periods. For two-dimensional (2D) optical spectroscopy, oscillations in the first coherence period are sampled in the time domain point-by-point. We present a general method for accelerating this often lengthy task, the quasi-rotating frame (QRF), through ...

In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence any Sagnac effect for these observers. Nevertheless, we argue that on a global scale only physically meaningful concept is relative rotation. The argument substantiated solving Einstein’s equations approximate thin shell...

A phenomenological and electron-theoretical study of the electrodynamics of rotating systems is developed in the threedimensional form. In the former part of the present paper, the electromagnetic field equations in an isotropic and homogeneous medium performing arbitrary accelerated motion relative to an inertial reference frame are derived from the phenomenological viewpoint, under the assump...

Several fundamental concepts with respect to the second-law analysis (SLA) of the turbulent flows in gas turbines are discussed in this study. Entropy and exergy equations for compressible/incompressible flows in a rotating/non-rotating frame have been derived. The exergy transformation efficiency of a gas turbine as well as the exergy transformation number for a single process step have been p...

The movie shows the nucleation of spheres in the shear cell. For visualization the spheres that are in a crystalline state are shown in a rotating side view. Color indicates the crystal symmetry. At the top right the current state is specified by the global packing fraction, shear cycle, and the number of crystalline spheres. The end of the plateau in the packing fraction is marked by the appea...

For rotating-tool machining, such as milling, line boring, and cylinder boring, the tool rotation causes the machining force on each tooth to rotate repetitively relative to the inertial coordinate frame. This is quite different than stationary-tool machining, such as turning or boring with a stationary boring bar, in which the force directions are fixed relative to the inertial frame. Although...