On the new translational shape invariant potentials

Recently, several authors have found new translational shape invariant potentials not present in classic classifications like that of Infeld and Hull. For example, Quesne on the one hand and Bougie, Gangopadhyaya and Mallow on the other have provided examples of them, consisting on deformations of the classical ones. We analyze the basic properties of the new examples and observe a compatibility equation which has to be satisfied by them. We study particular cases of such equation and give more examples of new translational shape invariant potentials.Comment: 9 pages, uses iopart10.clo, version

Clinical Considerations of BRCA1- and BRCA2-Mutation Carriers: A Review

Individuals who carry an inherited mutation in the breast cancer 1 (BRCA1) and BRCA2 genes have a significant risk of developing breast and ovarian cancer over the course of their lifetime. As a result, there are important considerations for the clinician in the counseling, followup and management of mutation carriers. This review outlines salient aspects in the approach to patients at high risk of developing breast and ovarian cancer, including criteria for genetic testing, screening guidelines, surgical prophylaxis, and chemoprevention

Continuum simulations of shocks and patterns in vertically oscillated granular layers

We study interactions between shocks and standing-wave patterns in vertically oscillated layers of granular media using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order. We simulate a layer of grains atop a plate that oscillates sinusoidally in the direction of gravity. Standing waves form stripe patterns when the accelerational amplitude of the plate's oscillation exceeds a critical value. Shocks also form with each collision between the layer and the plate; we show that pressure gradients formed by these shocks cause the flow to reverse direction within the layer. This reversal leads to an oscillatory state of the pattern that is subharmonic with respect to the plate's oscillation. Finally, we study the relationship between shocks and patterns in layers oscillated at various frequencies and show that the pattern wavelength increases monotonically as the shock strength increases.Comment: 12 pages, 9 figure

Conservation Laws and Energy Transformations in a Class of Common Physics Problems

We analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated parts that exchange energy, eventually reaching a shared equilibrium with a loss of mechanical or electrical energy. Such systems can be constrained by a constant of the system (e.g., mass, charge, momentum, or angular momentum) that uniquely determines the mechanical or electrical energy of the equilibrium state, regardless of the dissipation mechanism. A representative example would be a perfectly inelastic collision between two objects in one dimension, for which momentum conservation requires that some of the initial kinetic energy is dissipated by conversion to thermal or other forms as the two objects reach a common final velocity. We discuss how this feature manifests in a suite of four well-known and disparate problems that all share a common mathematical formalism. These examples, in which the energy dissipated during the process can be difficult to solve directly from dissipation rates, can be approached by students in a first-year physics class by considering conservation laws and can therefore be useful for teaching about energy transformations and conserved quantities. We then illustrate how to extend this method by applying it to a final example

Effects of Thermal Noise on Pattern Onset in Continuum Simulations of Shaken Granular Layers

The author investigates the onset of patterns in vertically oscillated layers of dissipative particles using numerical solutions of continuum equations to Navier-Stokes order. Above a critical accelerational amplitude of the cell, standing waves form stripe patterns which oscillate subharmonically with respect to the cell. Continuum simulations neglecting interparticle friction yield pattern wavelengths consistent with experiments using frictional particles. However, the critical acceleration for standing wave formation is approximately 10% lower in continuum simulations without added noise than in molecular dynamics simulations. This report incorporates fluctuating hydrodynamics theory into continuum simulations by adding noise terms with no fit parameters; this modification yields a critical acceleration in agreement with molecular dynamics simulations.Comment: 5 pages, 4 figure

Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations

We study the onset of patterns in vertically oscillated layers of frictionless dissipative particles. Using both numerical solutions of continuum equations to Navier-Stokes order and molecular dynamics (MD) simulations, we find that standing waves form stripe patterns above a critical acceleration of the cell. Changing the frequency of oscillation of the cell changes the wavelength of the resulting pattern; MD and continuum simulations both yield wavelengths in accord with previous experimental results. The value of the critical acceleration for ordered standing waves is approximately 10% higher in molecular dynamics simulations than in the continuum simulations, and the amplitude of the waves differs significantly between the models. The delay in the onset of order in molecular dynamics simulations and the amplitude of noise below this onset are consistent with the presence of fluctuations which are absent in the continuum theory. The strength of the noise obtained by fit to Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in fluid convection experiments, and is comparable to the noise found in experiments with oscillated granular layers and in recent fluid experiments on fluids near the critical point. Good agreement is found between the mean field value of onset from the Swift-Hohenberg fit and the onset in continuum simulations. Patterns are compared in cells oscillated at two different frequencies in MD; the layer with larger wavelength patterns has less noise than the layer with smaller wavelength patterns.Comment: Published in Physical Review

Optical diagnostics of diesel spray injections and combustion in a high-pressure high-temperature cell

We report on spatially and temporally resolved optical diagnostic measurements of propagation and combustion of diesel sprays introduced through a single-hole fuel injector into a constant volume, high-temperature, high-pressure cell. From shadowgraphy images in non-reacting environments of pure nitrogen, penetration lengths and dispersion angles were determined for non-vaporizing and vaporizing conditions, and found to be in reasonable agreement with standard models for liquid jet propagation and break-up. Quasi-simultaneous two-dimensional images were obtained of laser elastic light scattering, shadowgraphs and spectrally integrated flame emission in a reacting environment (cell temperature 850 K). In addition laser-induced incandescence was employed for the identification of soot-loaded regions. The simultaneously recorded spray images exhibit remarkable structural similarity and provide complementary information about the spray propagation and combustion process. The measurements also reveal the fuel vapor cloud extending well beyond the liquid core and close to the nozzle tip. Ignition takes place close to the tip of the spray within the mixing layer of fuel vapor and surrounding air. Soot is formed in the vapor core region at the tip of the liquid fuel jet. Our results support recently developed phenomenological model on diesel spray combustio

A First-Year Research Experience: The Freshman Project in Physics at Loyola University Chicago

Undergraduate research has become an essential mode of engaging and retaining students in physics. At Loyola University Chicago, first-year physics students have been participating in the Freshman Projects program for over twenty years, which has coincided with a period of significant growth for our department. In this paper, we describe how the Freshman Projects program has played an important role in advancing undergraduate research at Loyola and the profound impact it has made on our program. We conclude with suggestions for adoption of similar programs at other institutions

Time resolved particle dynamics in granular convection

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays and important role, and the branches of the bifurcation do not diverge as the control parameter is increased. We quantify the friction of the beads against the walls, showing that this interaction is the underlying mechanism responsible for the dynamics of the flow observed near the lateral wall

Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must include also the corresponding associated functions. In the specific case of anharmonic second-plus-fourth order interaction, expressions for the wave functions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wave functions is given.Comment: 17 p.