Acoustic particle separation

A method is described which uses acoustic energy to separate particles of different sizes, densities, or the like. The method includes applying acoustic energy resonant to a chamber containing a liquid of gaseous medium to set up a standing wave pattern that includes a force potential well wherein particles within the well are urged towards the center, or position of minimum force potential. A group of particles to be separated is placed in the chamber, while a non-acoustic force such as gravity is applied, so that the particles separate with the larger or denser particles moving away from the center of the well to a position near its edge and progressively smaller lighter particles moving progressively closer to the center of the well. Particles are removed from different positions within the well, so that particles are separated according to the positions they occupy in the well

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.Comment: 28 pages and 3 figure

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Mass Diffusion Coefficient Of Desiccants For Dehumdification Applications: Silica Aerogels And Silica Aerogel Coatings On Metal Foams

Silica aerogels prepared by the sol-gel process are often used as solid desiccants in enthalpy wheels for dehumidifying ventilation air in air-conditioning systems. These hygroscopic materials have good moisture adsorption and desorption characteristics due to their porous structure. The current study is focused on the evaluation of the mass diffusivity of solid silica aerogels and silica aerogel coatings on substrates, which determines the rate at which a dehumidification process can be performed. The mass diffusivity of silica aerogels is affected by their porous structure which depends on the synthesis technique used to prepare the silica aerogels. The sol-gel process is used to prepared silica aerogels using various basic (ammonium hydroxide, sodium hydroxide, potassium hydroxide) and acidic (hydrofluoric acid, steric acid, hydrogen peroxide) catalysts with the same precipitator (tetra methyl orthosilicate-TMOS) and solvent (methanol). Scanning electron microscopy is used to analyze the microstructure of supercritically dried aerogels. The dynamic vapor sorption method is used to determine the effective mass diffusivity for the different silica aerogels. It is found that the mass diffusivity is related to the microstructure of silica aerogels, which depends on the catalysts used in the sol-gel process; however, the value for mass diffusivities for solid desiccants and desiccant coatings are similar. In addition, a parametric study is conducted to determine the effect of relative humidity and temperature on the adsorption and desorption mass diffusivity

Adsorption and Desorption Isotherms Of Desiccants for Dehumidification Applications: Silica Aerogels and Silica Aerogel Coatings on Metal Foams

Silica aerogels are frequently employed as solid desiccants in enthalpy wheels for dehumidifying the supply stream in air-conditioning systems. These desiccant materials possess good moisture adsorption and desorption characteristics due to their porous structure. Analysis of adsorption and desorption isotherms is critical for performance characterization and is often performed to evaluate the capacity and transient performance of desiccant-based dehumidification systems. The current study is focused on the adsorption and desorption isotherms of solid silica aerogels and silica aerogel coatings on open-cell metal-foam substrates. The sol-gel process is adopted to synthesize silica aerogels using different basic (ammonium hydroxide, sodium hydroxide, potassium hydroxide) and acidic (hydrofluoric acid, steric acid, hydrogen peroxide) catalysts, with the same precipitator (tetra methyl orthosilicate-TMOS) and solvent (methanol). Scanning electron microscopy is used to characterize the microstructure of super-critically dried aerogels and adsorption/desorption isotherms for the different samples are obtained by the dynamic vapor sorption method. The steady-state moisture adsorption and desorption capacity of silica aerogels is affected by their porous structure, which depends on the synthesis technique used to prepare the silica aerogels. For the silica aerogel coatings on metal foams, the substrate structure and surface area also play an important role. The effect of the substrate surface area on adsorption/desorption capacity is analyzed by comparing the isotherms for solid silica aerogel samples, and silica aerogels coatings on flat plates and on metal foams with different pore sizes

Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in the literature to further split up the kinetic part of the Hamiltonian, which lowers the accuracy. The goal of this note is to comment on the best combination of optimized splitting and gradient methods that avoids splitting the kinetic energy. These schemes are generally applicable, but the optimal scheme depends on the desired level of accuracy. For simulations of liquid water it is found that the velocity Verlet scheme is only optimal for crude simulations with accuracies larger than 1.5%, while surprisingly a modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for publication in the Journal of Chemical Physic

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046