Invalidation of the Kelvin Force in Ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)Comment: 4 pages, 4 figure

Spectral Dynamics of the Velocity Gradient Field in Restricted Flows

We study the velocity gradients of the fundamental Eulerian equation, $\partial_t u +u\cdot \nabla u=F$, which shows up in different contexts dictated by the different modeling of $F$'s. To this end we utilize a basic description for the spectral dynamics of $\nabla u$, expressed in terms of the (possibly complex) eigenvalues, $\lambda=\lambda(\nabla u)$, which are shown to be governed by the Ricatti-like equation $\lambda_t+u\cdot \nabla\lambda+\lambda^2=$. We address the question of the time regularity of four prototype models associated with different forcing $F$. Using the spectral dynamics as our essential tool in these investigations, we obtain a simple form of a critical threshold for the linear damping model and we identify the 2D vanishing viscosity limit for the viscous irrotational dusty medium model. Moreover, for the $n$-dimensional restricted Euler equations we obtain $[n/2]+1$ global invariants, interesting for their own sake, which enable us to precisely characterize the local topology at breakdown time, extending previous studies in the $n=3$-dimensional case. Finally, as a forth model we introduce the $n$-dimensional restricted Euler-Poisson (REP)system, identifying a set of $[n/2]$ global invariants, which in turn yield (i) sufficient conditions for finite time breakdown, and (ii) characterization of a large class of 2-dimensional initial configurations leading to global smooth solutions. Consequently, the 2D restricted Euler-Poisson equations are shown to admit a critical threshold

A visual analysis of the usage efficiency of library books

The monographic collections in academic libraries have undergone a period of tremendous growth in volume, in subject diversity, and in formats during the recent several decades. Readers may find it difficult to prioritize which book(s) should be borrowed for a specific purpose. The log data of book loan record may serve as a visible indicator for the more sought-after books by the readers. This paper describes our experimental efforts in works in a university library setting. The visual analysis is thought to provide an effective way to extract the book usage information, which may yield new insights into a host of other related technical as well as user behavior issues. Initial experiment has demonstrated that the proposed approach as articulated in this article can actually benefit end-users as well as library collection development personnel in their endeavor of book selections with effective measure.</p

Synchronization of dissipative dynamical systems driven by non-Gaussian Lévy noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation, and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under a class of Lévy noises is considered. After discussing cocycle property, stationary orbits, and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in some asymptotic sense

Scattering invisibility with free-space field enhancement of all-dielectric nanoparticles

Simultaneous scattering invisibility and free-space field enhancement have been achieved based on multipolar interferences among all-dielectric nanoparticles. The scattering properties of all-dielectric nanowire quadrumers are investigated and two sorts of scattering invisibilities have been identified: the trivial invisibility where the individual nanowires are not effectively excited; and the nontrivial invisibility with strong multipolar excitations within each nanowire, which results in free-space field enhancement outside the particles. It is revealed that such nontrivial invisibility originates from not only the simultaneous excitations of both electric and magnetic resonances, but also their significant magnetoelectric cross-interactions. We further show that the invisibility obtained is both polarization and direction selective, which can probably play a significant role in various applications including non-invasive detection, sensing, and non-disturbing medical diagnosis with high sensitivity and precision.Comment: 7 pages, 4 figures and comments are welcom