Let P be a set of n points in R, and k ≤ n an integer. A sphere σ is k-rich with respect to P if |σ ∩ P | ≥ k, and is η-nondegenerate, for a fixed fraction 0 < η < 1, if no circle γ ⊂ σ contains more than η|σ ∩ P | points of P . We improve the previous bound given in [1] on the number of k-rich η-nondegenerate spheres in 3space with respect to any set of n points inR, from O(n/k+n/k), which hol...

In this work, the behavior of charged micron-sized particles in DC glow discharge stratum at low pressure a crossed magnetic and electric field was experimentally studied. The experiment conducted vertically oriented gas-discharge glass tube. A homogeneous created using two-section Helmholtz coil. results showed that dust move opposite direction to ExB drift as induction increases. Once reaches...

In electric-field-responsive soft-matter systems, the suspended particles respond to the Lorentz local field (LLF), yielding abundant important phenomena. Even though the particles can easily rotate, the LLF was conventionally adopted as a quantity that is independent of rotations in the literature. In contrast, here we design an experiment to measure the LLF between two metallic spheres, one o...

We present a density functional theory for a model colloidal mixture of hard spheres and infinitely thin hard rods. For these freely rotating particles, we use a fundamental measures approach to obtain a functional that features the correct dimensional crossover and the exact low density limit. For isotropic bulk fluid mixtures, the free energy, and hence the demixing phase diagram, are identic...