Using the Franck-Hertz Experiment To Illustrate Quantization Energy States of the Neon Atom by Electron Impact

na provide students with motivation for the study of quantum mechanics. That microscopic matter exists in quantized states can be demonstrated with modem versions of historic experiments: atomic line spectra (I), resonance potentials, and blackbody radiation. The resonance potentials of mercury were discovered by Franck and Hertz in 1914 (2). Their experiment consisted of bombarding atoms by electrons, and detecting the kinetic energy loss of the scattered electrons (3). Prior to the Franck-Hertz experiment, spectroscopic work bv Balmer and Rvdbere revealed that atoms emitted radiatibn at discrete ekergiis. The Franck-Hertz experiment showed directly that auantized enerm levels in an atom are real, not jist optiEal artifacts. atom can be raised to excited states by inelastic collisions with electrons as well as lowered from excited states by emission of photons. The classic Franck-Hertz experiment is carried out with mercury (4-7). Here we present an experiment for the study of resonance potentials using neon.

Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Fastener-Based Computational Models of Cold-Formed Steel Shear Walls

Cold-formed steel (CFS) combined with wood sheathing, such as oriented strand board (OSB), forms shear walls that can provide lateral resistance to seismic forces. The ability to accurately predict building deformations in damaged states under seismic excitations is a must for modern performance-based seismic design. However, few static or dynamic tests have been conducted on the non-linear behavior of CFS shear walls. Thus, the purpose of this research work is to provide and demonstrate a fastener-based computational model of CFS wall models that incorporates essential nonlinearities that may eventually lead to improvement of the current seismic design requirements. The approach is based on the understanding that complex interaction of the fasteners with the sheathing is an important factor in the non-linear behavior of the shear wall. The computational model consists of beam-column elements for the CFS framing and a rigid diaphragm for the sheathing. The framing and sheathing are connected with non-linear zero-length fastener elements to capture the OSB sheathing damage surrounding the fastener area. Employing computational programs such as OpenSees and MATLAB, 4 ft. x 9 ft., 8 ft. x 9 ft. and 12 ft. x 9 ft. shear wall models are created, and monotonic lateral forces are applied to the computer models. The output data are then compared and analyzed with the available results of physical testing. The results indicate that the OpenSees model can accurately capture the initial stiffness, strength and non-linear behavior of the shear walls.

Isospectrality and Heat Content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrodinger operators acting in L-2[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S-4 (q, t). Both cases, elastic (epsilon = 1) and inelastic (epsilon < 1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6 <= phi <= 0.805, scaling is shown to hold: S-4 (q, t)/chi(4)(t) = s(q xi(t)). Both the dynamic susceptibility chi(4)(tau(alpha)) and the dynamic correlation length xi(tau(alpha)) evaluated at the alpha relaxation time tau(alpha) can be fitted to a power law divergence at a critical packing fraction. The measured xi(tau(alpha)) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, chi(4)(tau(alpha)) approximate to xi(d-p) (tau(alpha)), with an exponent d - p approximate to 1.6. This scaling is remarkably independent of epsilon, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on epsilon.