Music Education Transformation: How Orff, Kodaly, and Suzuki Promote Academic Success

We all need Music in our lives. Music education is valued less in the education system, but present data from these literature sources of articles, books, and research, tells us another story. For decades school systems have struggled with whether or not to include Music in the education system. There are many values for Music, including individual growth and development. In this research study, I intend to showcase the central benefits of Music to help show there is a need for these programs and to help promote music programs based on their own merits and not just because of academic success. A change also needs to occur in how to teach Music to the young. We need to preserve music education in schools and create a new music curriculum to help promote Music. The research on the main aspects of the Orff, Kodaly, and Suzuki approaches show that Music engages school children on both a personal and social level, as well as impacting their academic growth. I will then analyze this data, collected from journal articles and books about the values of music and learning approaches, to answer my research questions. I will then use this analytical data in my thesis to explain the significance of Music, the importance of these approaches in music education, and layout guidelines and ideas for a new curriculum. In completing my research, I hope to create more awareness of the values of Music and what it brings to the educational system. I will explain the different teaching approaches and how they promote Music and lead to success in personal, social, and academic areas while generating ideas and guidelines for a new curriculum for young children

Combinatorial approaches to Hopf bifurcations in systems of interacting elements

We describe combinatorial approaches to the question of whether families of real matrices admit pairs of nonreal eigenvalues passing through the imaginary axis. When the matrices arise as Jacobian matrices in the study of dynamical systems, these conditions provide necessary conditions for Hopf bifurcations to occur in parameterised families of such systems. The techniques depend on the spectral properties of additive compound matrices: in particular, we associate with a product of matrices a signed, labelled digraph termed a DSR^[2] graph, which encodes information about the second additive compound of this product. A condition on the cycle structure of this digraph is shown to rule out the possibility of nonreal eigenvalues with positive real part. The techniques developed are applied to systems of interacting elements termed “interaction networks”, of which networks of chemical reactions are a special case

Quasiparticle light elements and quantum condensates in nuclear matter

Nuclei in dense matter are influenced by the medium. In the cluster mean field approximation, an effective Schr\"odinger equation for the $A$-particle cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free neutrons and protons), the light elements ($2 \le A \le 4$, internal quantum state $\nu$) are treated as quasiparticles with energies $E_{A,\nu}(P; T, n_n,n_p)$ that depend on the center of mass momentum $\vec P$, the temperature $T$, and the total densities $n_n,n_p$ of neutrons and protons, respectively. We consider the composition and thermodynamic properties of nuclear matter at low densities. At low temperatures, quartetting is expected to occur. Consequences for different physical properties of nuclear matter and finite nuclei are discussed.Comment: 5 pages, 1 figure, 2 table

Valley Jahn-Teller Effect in Twisted Bilayer Graphene

The surprising insulating and superconducting states of narrow-band graphene twisted bilayers have been mostly discussed so far in terms of strong electron correlation, with little or no attention to phonons and electron-phonon effects. We found that, among the 33 492 phonons of a fully relaxed \u3b8=1.08\ub0 twisted bilayer, there are few special, hard, and nearly dispersionless modes that resemble global vibrations of the moir\ue9 supercell, as if it were a single, ultralarge molecule. One of them, doubly degenerate at \u393 with symmetry A1+B1, couples very strongly with the valley degrees of freedom, also doubly degenerate, realizing a so-called E\ue2\u160-e Jahn-Teller (JT) coupling. The JT coupling lifts very efficiently all degeneracies which arise from the valley symmetry, and may lead, for an average atomic displacement as small as 0.5 m \uc5, to an insulating state at charge neutrality. This insulator possesses a nontrivial topology testified by the odd winding of the Wilson loop. In addition, freezing the same phonon at a zone boundary point brings about insulating states at most integer occupancies of the four ultraflat electronic bands. Following that line, we further study the properties of the superconducting state that might be stabilized by these modes. Since the JT coupling modulates the hopping between AB and BA stacked regions, pairing occurs in the spin-singlet Cooper channel at the inter-(AB-BA) scale, which may condense a superconducting order parameter in the extended s-wave and/or d\ub1id-wave symmetry

Bounded Verification with On-the-Fly Discrepancy Computation

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.Comment: 24 page

Experimental investigations of non-Newtonian/Newtonian liquid-liquid flows in microchannels

The plug flow of a non-Newtonian and a Newtonian liquid was experimentally investigated in a quartz microchannel (200-µm internal diameter). Two aqueous glycerol solutions containing xanthan gum at 1000 and 2000 ppm were the non-Newtonian fluids and 0.0046 Pa s silicone oil was the Newtonian phase forming the dispersed plugs. Two-color particle image velocimetry was used to obtain the hydrodynamic characteristics and the velocity profiles in both phases under different fluid flow rates. The experimental results revealed that the increase in xanthan gum concentration produced longer, bullet-shaped plugs, and increased the thickness of the film surrounding them. From the shear rate and viscosity profiles, it was found that the polymer solution was in the shear-thinning region while the viscosity was higher in the middle of the channel compared to the region close to the wall. Circulation times in the aqueous phase increased with the concentration of xanthan gum

Surfactant effects on the coalescence of a drop in a Hele-Shaw cell

In this work the coalescence of an aqueous drop with a flat aqueous-organic interface was investigated in a thin gap Hele-Shaw cell. Different concentrations of a nonionic surfactant (Span 80) dissolved in the organic phase were studied. We present experimental results on the velocity field inside a coalescing droplet in the presence of surfactants. The evolution of the neck between the drop and the interface was studied with high-speed imaging. It was found that the time evolution of the neck at the initial stages of coalescence follows a linear trend, which suggests that the local surfactant concentration at the neck region for this stage of coalescence can be considered quasiconstant in time. This neck expansion can be described by the linear law developed for pure systems when the surfactant concentration at the neck is assumed higher than in the bulk solution. In addition, velocity and vorticity fields were computed inside the coalescing droplet and the bulk homophase using a high-speed shadowgraphy technique. The significant wall effects in the Hele-Shaw cell in the transverse axis cause the two vertical velocity components towards the singularity rupture point, from the drop and from the bulk homophase, to be of the same order of magnitude. This movement together with the neck expansion creates two pairs of counteracting vortices in the drop and in the bulk phase. The neck velocity is the average of the advection velocities of the two counteracting vortex pairs on each side of the neck. The presence of the surfactant slows down the dynamics of the coalescence, affects the propagation direction of the pair of vortices in the bulk phase, and reduces their size faster compared to the system without surfactant

Transition from stratified to non-stratified oil-water flows using a bluff body

In this paper the effect of a transverse cylindrical rod immersed in water on the flow patterns and interfacial characteristics of an oil-water pipe flow is investigated experimentally. The cylinder is used to passively actuate the transition from stratified to non-stratified flows and to localise the formation of waves and the detachment of drops. The studies are carried out in an acrylic test section with 37 mm ID using as test fluids tap water and Exxsol D140 (density 830 kg m-3 and viscosity 5.5 cP). The rod has 5 mm diameter and is located at 460 mm from the test section inlet. Flow patterns and interface characteristics were studied with high speed imaging. It was found that the presence of the rod generates waves shortly downstream, from which drops detach, and reduces the mixture velocity for the transition from stratified to non-stratified flows. The average interface height and wave amplitude increase with distance from the rod, while the average wave length and frequency remain almost constant. The Strouhal number is found to be equal to 0.24, while the wave velocities are slightly higher than the mixture velocities