Stability of Liquid Bridges between Unequal Disks under Zero-Gravity Conditions

The stability, of axisymmetric equilibrium shapes of a liquid bridge between two coaxial disks of different radii under zero-gravity conditions is investigated. The stability regions have been evaluated for different values of the ratio of the disk radii in terms of the dimensionless parameters which characterize the length and the volume of the bridge. It has been found that disk radii unequality radically changes the upper boundary of the stability region. The analysis of the shape of marginally stable equilibrium surfaces has been carried out. Relationships between the critical values of the parameters have been deduced for some particular cases, which are of special interest for the materials purification processes and growing of single crystals by the floating zone method: for typical values of the growing angle for semiconductor materials and for liquid volumes close to that of the cylinder having a radius equal to the mean radius of the disk

Mechanical Imperfections Effect on the Minimum Stability Limit of Liquid Bridges

The bifurcation to unstable equilibrium shapes in the neighborhood of the minimum volume stability limit of liquid bridges has been described by using the Lyapunov–Schmidt technique. Prior to the bifurcation analysis, the stability limits of axisymmetric liquid bridges (both that of maximum and that of minimum volume) have been analytically calculated when the liquid bridge supports are two circular, coaxial disks. The interface shapes have been parametrically described and the parameters corresponding to the marginally stable shapes have been determined in terms of elliptic variables. Bifurcation equations have been obtained analytically describing the behavior near the critical points previously calculated and the effect of small axisymmetric imperfections has been considered. The considered imperfections are inequality in the diameter of the supporting disks, small body forces due to an axial gravity, and liquid bridge rotation as a solid bod

On the Stability Limit Change due to Imperfections

The minimum volume stability limit of axisymmetric liquid bridges has been obtained in the past for zero Bond number, no solid body rotation and equal disks. When gravity, rotation or different disk diameters are considered, only a few numerical results are available and the singular case of small values of these parameters have been only partly considered. An analytical study using the Lyapunov-Schmidt method considering small values of gravity, disk diameter ratio and rotation rate is presented and the variation of the stability limit determined

Anisotropic Atom-Surface Interactions in the Casimir-Polder Regime

The distance-dependence of the anisotropic atom-wall interaction is studied. The central result is the 1/z^6 quadrupolar anisotropy decay in the retarded Casimir-Polder regime. Analysis of the transition region between non-retarded van der Waals regime (in 1/z^3) and Casimir-Polder regime shows that the anisotropy cross-over occurs at very short distances from the surface, on the order of 0.03 Lambda, where Lambda is the atom characteristic wavelength. Possible experimental verifications of this distance dependence are discussed.Comment: 5 pages, 2 figure

Stormwater to Groundwater: How California can increase groundwater storage and build climate resilience.

California is predicted to have more intense and frequent changes in weather patterns within the next 50 years. Historical and current groundwater use for residential and agricultural use is unsustainable and is creating significant deficits in groundwater aquifers throughout the state. To better adapt to potential damages caused by atmospheric rivers, better stormwater management and capture could increase California’s Climate adaptability. This study is focused on the means and methods to capture stormwater and increase groundwater recharge. Nature-based infrastructure (NBI), or Green Infrastructure (GI), has been used in urban areas throughout the country to mitigate harmful stormwater effects by replicating the natural hydrological cycle for groundwater recharge. A GIS analysis revealed roughly 5,000 square milesof groundwater potential areas were identified for NBI implementation. Further adaptation of the GIS model could target critically low aquifers. Six NBI methods were identified as means to retain and filter stormwater for groundwater recharge. The noted NBI methods were also found to be a substantially cheaper alternative to standard stormwater management utilizing gray infrastructure. This study also found a varying degree of municipal data regarding NBI/GI. Of the 3 California cities analyzed, each city heavily invested in more expensive gray infrastructure projects over NBI/GI projects in FY22. The state of California would greatly benefit from adapting the model created for this project (or something similar) to better manage urban stormwater and recharge critically low groundwater aquifers. Doing so could considerably increase the state’s groundwater storage and sustain California’s water needs in dry/drought years

Effects of Axial and Centrifugal Forces on the Stability of Liquid Bridges

The equilibrium and stability equations for liquid bridges are well known, but they are nonlinear and it is difficult to guess real behavior, such as the sensitivity of the shape to axial and rotational forces (measured by Bond and Weber numbers, respectively) or to the geometry of the solid supports that support the bridge. A parametric study by numerical methods of the different effects and the analytical solutions at the bifurcation points in the stability diagrams is presented. The well known shooting method to numerically compute equilibrium shapes of liquid bridges, and their stability limits, is applied to a five parameter case, when different disc sizes (measured by H), bridge lengths (Lr), liquid volumes (Vr), residual axial acceleration (Bo), and solid body centrifugation (We) are contemplated. The bundle of diagrams presented give an idea of the complexities of such a multiparametric analysis and may help in further research to delimitate other forms of instability. The numerical results were used to check the validity of several analytical asymptotic expressions, with perfect agreement over the range of interest (long liquid bridges), but these models only take into consideration the subset (Lr, Vr = 1, H = 0, Bo, We) of the five parameter family. These results will be of great help to plan future space experiments on liquid columns and floating zones in space and in particular will show a method to easily measure very weak residual forces in microgravity platforms

Negative-index media for matter-wave optics

We consider the extension of optical meta-materials to matter waves. We show that the generic property of pulsed comoving magnetic fields allows us to fashion the wave-number dependence of the atomic phase shift. It can be used to produce a transient negative group velocity of an atomic wave packet, which results into a negative refraction of the matter wave. Application to slow metastable argon atoms Ar*(3P2) shows that the device is able to operate either as an efficient beam splitter or an atomic meta-lens. Implications of "meta-media" in atom optics are considered.Comment: 4 pages, 4 figures, submitted at PRL 4 November 200

Synchronization of the Frenet-Serret linear system with a chaotic nonlinear system by feedback of states

A synchronization procedure of the generalized type in the sense of Rulkov et al [Phys. Rev. E 51, 980 (1995)] is used to impose a nonlinear Malasoma chaotic motion on the Frenet-Serret system of vectors in the differential geometry of space curves. This could have applications to the mesoscopic motion of biological filamentsComment: 12 pages, 7 figures, accepted at Int. J. Theor. Phy

HUMAN MOTION ANALYSIS AND SYNTHESIS USING GRAPHICAL BIOMECHANICS MODELS IN SPORTS ACTIVITIES

In many applications the study of human movement using a computer is very useful. One such application is the three-dimensional reconstruction of the structure of the human body and its movement using sequences of images and graphic models. For this reconstruction to be accurate and precise the person analyzed and the virtual human (humanoid) must have similar anthropometric characteristics. A process is therefore defined that attempts to adjust the humanoid to the morphology of the person, a process which can be very laborious and subjective if done manually or by selection of points. This article presents a process of semiautomatic matching between person and humanoid. Once this process is carried out we are ready to analyze and represent the movements under study. The study is adapted to specific sports activities. In these cases the adjustment process can be assisted by the computer. At present, it is used in indoor spaces, but its use in outdoor spaces is also intended. The system requires no markers or special clothing to be worn by the athlete or sports participant, and its range of application is therefore very wide. Also very important are its portability into domestic environments using VRML 2.0 and the H-anim standard for specification of virtual humanoids. This advantage is very important because experts can visualize movements on any personal computer with a commercial Internet browser