[4] **viXra:1112.0074 [pdf]**
*submitted on 2011-12-26 01:57:02*

**Authors:** Giuliano Bettini

**Comments:** 7 Pages.

The electron is interpreted as a small electric current carrying the elementary charge and the elementary mass. The equivalent circuit is a quarter-wave short circuited transmission line, the line having characteristic impedance 25812.807449 Ohm, the von Klitzing constant.
A similar line, closed on itself after a twist (as in a Moebius strip), not only justifies the charge and mass, but also the angular momentum of the electron.

**Category:** Condensed Matter

[3] **viXra:1112.0069 [pdf]**
*replaced on 2012-01-29 15:09:21*

**Authors:** Armando V.D.B. Assis

**Comments:** 13 pages. English.

This brief paper is part of my research on the origins of turbulence. Since the derivations of the Navier-Stokes equation are frequently cumbersome, I would like to provide this pedagogical derivation (I hope), discussing the properties of the continuum fluids under a heuristical approach, viz., we provide a heuristical derivation of the so-called Navier-Stokes equation. We turn out to be concerned with the physical insight regarding the system under consideration, a system of continuum. Derivations of the Navier-Stokes equation are, frequently, pedagogically cumbersome, loosing the main heuristics one should grasp under the transition to the continuum. This transition turns out to naturally encapsulate neglected degrees of freedom due to the intrinsically thermodynamic domain. This pedagogical derivation discusses the properties of the continuum fluids and the relation to the taken limit encapsulating the continuum hypothesis, which turns out to raise the question of lack of validity over extremely distorted subdomains, once a grown rarefied subdomain may not provide sufficient large statistics to a smooth description via its center of mass, which is the main hypothesis of the infinitesimal limit process for the local description under the continuum hypothesis. Such transient, albeit not presented here, once it would change the characteristic of this paper to the research one connected to the important question of unicity of the (3+1)-dimensional Navier-Stokes differential equation, is to be pointed out, once it provides ansatz for research on the unicity of description of fluids by the Navier-Stokes equation.

**Category:** Condensed Matter

[2] **viXra:1112.0066 [pdf]**
*replaced on 2012-01-30 11:37:16*

**Authors:** Armando V.D.B. Assis

**Comments:** 5 pages. English.

Through a convenient mathematical approach for the Navier-Stokes equation, we obtain the quadratic dependence $v^{2}$ of the drag force $F_{D}$ on a falling sphere, and the drag coefficient, $C_{D}$, as a function of the Reynolds number. Viscosity effects related to the turbulent boundary layer under transition, from laminar to turbulent, lead to the tensorial integration related to the flux of linear momentum through a conveniently choosen control surface in the falling reference frame. This approach turns out to provide an efficient route for the drag force calculation, since the drag force turns out to be a field of a non-inertial reference frame, allowing an arbitrary and convenient control surface, finally leading to the quadratic term for the drag force.

**Category:** Condensed Matter

[1] **viXra:1112.0027 [pdf]**
*submitted on 2011-12-07 19:38:19*

**Authors:** Mohit Shridhar

**Comments:** 19 Pages.

Particles on a plate form Chladni patterns when the plate is acoustically excited. To better understand these patterns and their possible real-world applications, I present a new analytical and numerical study of the transition between standard and inverse Chladni patterns on an adhesive surface at any magnitude of acceleration. By spatial autocorrelation analysis, I examine the effects of surface adhesion and friction on the rate of pattern formation. Next, I explore displacement models of particles translating on a frictional surface with both adhesive and internal particle-plate frictions. In addition, I find that both adhesion and damping forces serve as exquisite particle sorting mechanisms. Finally, I discuss the possible real-world applications of these sorting mechanisms, such as separating nanoparticles, organelles, or cells.

**Category:** Condensed Matter