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

Modeling of time-resolved laser-induced incandescence transients for particle sizing in high-pressure spray combustion environments: a comparative study

In this study experimental single-pulse, time-resolved laser-induced incandescence (TIRE-LII) signal intensity profiles acquired during transient Diesel combustion events at high pressure were processed. Experiments were performed between 0.6 and 7MPa using a high-temperature high-pressure constant volume cell and a heavy-duty Diesel engine, respectively. Three currently available LII sub-model functions were investigated in their performance for extracting ensemble mean soot particle diameters using a least-squares fitting routine, and a "quick-fit” interpolation approach, respectively. In the calculations a particle size distribution as well as the temporal and spatial intensity profile of the heating laser was taken into account. For the poorly characterized sample environments of this work, some deficiencies in these state-of-the-art data evaluation procedures were revealed. Depending on the implemented model function, significant differences in the extracted particle size parameters are apparent. We also observe that the obtained "best-fit” size parameters in the fitting procedure are biased by the choice of their respective "first-guess” initial values. This behavior may be caused by the smooth temporal profile of the LII cooling curve, giving rise to shallow local minima on the multi-parameter least squares residuals, surface sampled during the regression analysis procedure. Knowledge of the gas phase temperature of the probed medium is considered important for obtaining unbiased size parameter information from TIRE-LII measurement

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

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

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

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.

Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability

Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter, will be studied by means of supersymmetrical intertwining relations. The Hamiltonian does not allow the conventional separation of variables, but the supercharge operator does allow, leading to the partial solvability of the model. This approach, which can be called as the first variant of SUSY-separation, together with shape invariance of the model, provides analytical calculation of the part of spectrum and corresponding wave functions (quasi-exact-solvability). The model is shown to obey two different variants of shape invariance which can be combined effectively in construction of energy levels and wave functions.Comment: 6 p.p., accepted for publication in EP

2-Oxo-N-aryl-1,2,3,4-tetrahydroquinoline-6-sulfonamides as activators of the tumor cell specific M2 isoform of pyruvate kinase

Compared to normal differentiated cells, cancer cells have altered metabolic regulation to support biosynthesis and the expression of the M2 isozyme of pyruvate kinase (PKM2) plays an important role in this anabolic metabolism. While the M1 isoform is a highly active enzyme, the alternatively spliced M2 variant is considerably less active and expressed in tumors. While the exact mechanism by which decreased pyruvate kinase activity contributes to anabolic metabolism remains unclear, it is hypothesized that activation of PKM2 to levels seen with PKM1 may promote a metabolic program that is not conducive to cell proliferation. Here we report the third chemotype in a series of PKM2 activators based on the 2-oxo-N-aryl-1,2,3,4-tetrahydroquinoline-6-sulfonamide scaffold. The synthesis, structure activity relationships, selectivity and notable physiochemical properties are described.National Human Genome Research Institute (U.S.) (Molecular Libraries Initiative of the NIH Roadmap for Medical Research

NMR Experiments on a Three-Dimensional Vibrofluidized Granular Medium

A three-dimensional granular system fluidized by vertical container vibrations was studied using pulsed field gradient (PFG) NMR coupled with one-dimensional magnetic resonance imaging (MRI). The system consisted of mustard seeds vibrated vertically at 50 Hz, and the number of layers N_ell <= 4 was sufficiently low to achieve a nearly time-independent granular fluid. Using NMR, the vertical profiles of density and granular temperature were directly measured, along with the distributions of vertical and horizontal grain velocities. The velocity distributions showed modest deviations from Maxwell-Boltzmann statistics, except for the vertical velocity distribution near the sample bottom which was highly skewed and non-Gaussian. Data taken for three values of N_ell and two dimensionless accelerations Gamma=15,18 were fit to a hydrodynamic theory, which successfully models the density and temperature profiles including a temperature inversion near the free upper surface.Comment: 14 pages, 15 figure

Small interfering RNA targeting mcl-1 enhances proteasome inhibitor-induced apoptosis in various solid malignant tumors

<p>Abstract</p> <p>Background</p> <p>Targeting the ubiquitin-proteasome pathway is a promising approach for anticancer strategies. Recently, we found Bik accumulation in cancer cell lines after they were treated with bortezomib. However, recent evidence indicates that proteasome inhibitors may also induce the accumulation of anti-apoptotic Bcl-2 family members. The current study was designed to analyze the levels of several anti-apoptotic members of Bcl-2 family in different human cancer cell lines after they were treated with proteasome inhibitors.</p> <p>Methods</p> <p>Different human cancer cell lines were treated with proteasome inhibitors. Western blot were used to investigate the expression of Mcl-1 and activation of mitochondrial apoptotic signaling. Cell viability was investigated using SRB assay, and induction of apoptosis was measured using flow cytometry.</p> <p>Results</p> <p>We found elevated Mcl-1 level in human colon cancer cell lines DLD1, LOVO, SW620, and HCT116; human ovarian cancer cell line SKOV3; and human lung cancer cell line H1299, but not in human breast cancer cell line MCF7 after they were treated with bortezomib. This dramatic Mcl-1 accumulation was also observed when cells were treated with other two proteasome inhibitors, MG132 and calpain inhibitor I (ALLN). Moreover, our results showed Mcl-1 accumulation was caused by stabilization of the protein against degradation. Reducing Mcl-1 accumulation by Mcl-1 siRNA reduced Mcl-1 accumulation and enhanced proteasome inhibitor-induced cell death and apoptosis, as evidenced by the increased cleavage of caspase-9, caspase-3, and poly (ADP-ribose) polymerase.</p> <p>Conclusions</p> <p>Our results showed that it was not only Bik but also Mcl-1 accumulation during the treatment of proteasome inhibitors, and combining proteasome inhibitors with Mcl-1 siRNA would enhance the ultimate anticancer effect suggesting this combination might be a more effective strategy for cancer therapy.</p