Search Results (25 total)

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady state. The method is general enough to accommodate nonlinear transition rates allowing characterization of fluctuations around a delay-induced limit cycle.

The neutron unbound ground state of ²⁵O (Z=8, N=17) was observed for the first time in a proton knockout reaction from a ²⁶F beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of 770_-10⁺²⁰  keV with a total width of 172(30) keV. The N=16 shell gap was established to be 4.86(13) MeV by the energy difference between the ν1s_1/2 and ν0d_3/2 orbitals. The neutron separation energies for ²⁵O agree with the calculations of the universal sd shell model interaction. This interaction incorrectly predicts an ²⁶O ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of ²⁶O. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.

The reliability and validity of professionally written multiple-choice exams have been extensively studied for exams such as the SAT, graduate record examination, and the force concept inventory. Much of the success of these multiple-choice exams is attributed to the careful construction of each question, as well as each response. In this study, the reliability and validity of scores from multiple-choice exams written for and administered in the large introductory physics courses at the University of Illinois, Urbana-Champaign were investigated. The reliability of exam scores over the course of a semester results in approximately a 3% uncertainty in students’ total semester exam score. This semester test score uncertainty yields an uncertainty in the students’ assigned letter grade that is less than 1 / 3 of a letter grade. To study the validity of exam scores, a subset of students were ranked independently based on their multiple-choice score, graded explanations, and student interviews. The ranking of these students based on their multiple-choice score was found to be consistent with the ranking assigned by physics instructors based on the students’ written explanations (r>0.94 at the 95% confidence level) and oral interviews (r=0.94_−0.09^+0.06).

Dark and bright envelope solitons have been generated from a single magnetostatic carrier wave with attractive nonlinearity. The solitons were formed through the mode beating of two microwave input signals with frequency separations of 3–30 MHz for an in-plane magnetized single crystal yttrium-iron-garnet film in the magnetostatic backward volume wave configuration. Numerical modeling based on the Ginzburg-Landau equation model gave good agreement with the data.

The spatial evolution of multi-peaked microwave magnetic envelope solitons in a thin yttrium iron garnet (YIG) film has been measured and analyzed. The experiments were done on a long and narrow 5-μm-thick single-crystal YIG film strip. Double-peaked and triple-peaked magnetostatic backward volume wave soliton pulses were excited at a nominal carrier frequency of 7.0 GHz. The measurements utilized a movable inductive magnetodynamic probe detection system. The formation of these multi-peaked soliton (MPS) pulses is a two step process. First, an initial single large amplitude pulse gradually separates into two or more nonsolitonic peaks. After a certain propagation time, these nonsolitonic peaks evolve, in sequence, into solitonic peaks with constant phase (CP) and an overall stair-like profile. Typically, the larger amplitude peaks lead in time and become solitonic first. As the MPS signals propagate and decay, the peaks lose their CP character in reverse sequence. The region of existence for the “fully formed” MPS pulses for which all the individual peaks have CP character is extremely narrow, typically on the order of a few tenths of a millimeter. The velocities of the individual peaks scale linearly with the peak powers. A nonlinear response analysis of the peak velocity based on the method of envelopes gives a reasonable match to the data.

According to quantum collision theory, scattering amplitudes are complex numbers, which are completely defined by their magnitude and phase. Although the phase information is generally not determined entirely in collision experiments, the phases are well defined and can be used to check computational models. We use four state-of-the-art approaches to calculate the magnitude and phase of the electron-hydrogen ionization amplitude in the Temkin-Poet S-wave model. We demonstrate that the correct phase can be extracted for each method by using the appropriate final-state continuum functions.

The T-matrix approach, as formulated by Pindzola et al. [Phys. Rev. A 62, 062718 (2000)] for calculating the single-differential ionization cross section (SDCS) has been further investigated. Using the “intermediate-energy R-matrix method” to obtain the full scattering wave function needed in the matrix element, we performed several case studies for the Temkin-Poet S-wave model of e-H scattering to study the dependence of the results on the box radius and the number of states included. Despite encouraging results before reaching convergence, we conclude that the method will ultimately not yield the correct form of the SDCS but instead will still suffer from unphysical oscillations.

The self-generation of single, fundamental, stable, spin-wave-envelope black and gray dark solitons has been realized for the first time. These solitons were generated from microwave magnetostatic surface waves (MSSWs) propagated in an in-plane magnetized yttrium iron garnet film MSSW delay line in a resonant ring. These fundamental dark solitons were made possible by a new and general filtering technique for a high gain nonlinear resonant ring. The amplitude and phase profiles together with the power spectra of the self-generated microwave pulses confirm their fundamental dark soliton nature.

It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-Pérot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic field, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom.

The R matrix with pseudostates method has been used to study e^--He collisions at low and intermediate energies up to 80 eV. Since target correlation effects and target continuum states are both accurately represented by this method, the associated program package can now be used to obtain reliable results at intermediate energies for more complex atomic and ionic targets, which are urgently required in many applications.

Dopant site occupancies in YBa₂Cu_3-xM_xO_7-δ, with M=Fe (x=0.3 and x=0.5), Co (x=0.2 and x=0.5), Ni (x=0.3), and Zn (x=0.3) have been found using differential anomalous x-ray scattering. The Ni and Zn atoms were found to occupy the Cu(1) (‘‘chains’’) site and the Cu(2) (‘‘planes’’) site in a nearly random distribution. The Fe and Co atoms were found to occupy the Cu(1) site predominantly at low x, with an increasing fraction on the Cu(2) sites as the total amount of dopant increases. In all cases, our results appear to have high statistical significance, with very little sensitivity to expected uncertainties in oxygen content, total dopant content, anomalous corrections to the atomic scattering factor of the dopant, and to relative atomic coordinates assumed in the modeling. We have also discussed the results in the context of existing extended x-ray-absorption fine-structure and neutron-diffraction results, thermogravimetric analysis, and Mössbauer spectra, and T_c and Hall-effect studies.

We investigate proton spin-lattice relaxation in two powdered organic molecular solids with reorienting methyl (CH₃) and tert-butyl [C(CH₃)₃] groups: 3,5-di-tert-butylphenol (DTBP) and 1,3,5-tri-tert-butylbenzene (TTBZ). The temperature and Larmor frequency dependence of the relaxation rate is considerably more complicated than would be expected on the basis of random reorientations of the CH₃ and C(CH₃)₃ groups. The spectral densities describing the relaxation are broader, and show more structure, than those customarily used to interpret relaxation data. Assuming that the spectral densities may be expressed as linear superpositions of Lorentzians, we are able to obtain a single, nonexponential correlation function which leads to satisfactory fits of the data. Assuming also the validity of the Arrhenius relation, τ=τ_∞exp(E/kT), with a constant τ_∞, we find that the barriers to rotation for the CH₃ and C(CH₃)₃ groups may be characterized by a distribution of activation energies consisting of a wide background and one (DTBP) or two (TTBZ) δ functions.

The small angle scattering of π⁺ from ¹²C was measured at 115, 167, and 242 MeV from 3 to 10°. These measurements covered the Coulomb-nuclear interference region. New values of the π⁺-¹²C total cross section have been used to extract the real part of the forward-scattering amplitude.

[NUCLEAR REACTION ¹²C(π⁺,π⁺), E=115-242 MeV; measured σ(θ_π); deduced Ref_N(0^∘) / Imf_N(0^∘).]

The small-angle scattering of π⁺ from ¹²C was measured at 115, 167, and 242 MeV. The measurements covered the Coulomb-nuclear interference region from 3° to 10°. The real part of the forward nuclear amplitude was extracted from the data.

The polarization of protons elastically scattered from alpha particles was observed by measuring the asymmetry obtained by doubly scattering protons in helium. Protons from the Brookhaven National Laboratory Van de Graaff generator entered a helium-filled double-scattering chamber through a 50-microinch nickel window. The first scattering was at either 104° 29′ (c.m.) or 73° 38′ (c.m.) and the second scattering was to left and right at 73° 38′ (c.m.). The doubly scattered protons were detected by 50-μ Ilford C-2 plates. The polarization product, P_aP_b, was calculated from the left-right ratio (R) using the formula R=(1+P_aP_b) / (1-P_aP_b), where P_a and P_b are the polarizations at the first and second scatterings, respectively. Three interdependent measurements, in which P_aP_b was equal to P₁P₂, P₁P₃, or P₂P₃, yielded values for P₁[3.580 Mev, 104° 29^′ (c.m.)], P₂[2.020 Mev, 73° 38^′ (c.m.)], and P₃[1.375 Mev, 73° 38^′ (c.m.)]. The calculated polarizations are in the direction of the normal n (n=k₀×k|k₀×k|) to the scattering plane. The following results were obtained: Polarization measured Experimental value (%) Calculated value (%) P₁ 54±2 +59±13 P₂ 85±3 +80±4 P₃ 62±2 +59±16

Thin thallium-activated potassium iodide crystals were exposed to monoenergetic neutrons ranging in energy from 2.0 to 5.5 Mev. Pulse-height spectra were taken of the scintillations in the crystal. Five charged particle groups were observed, three (n, p) reactions leading to states in A³⁹, and two (n, α) reactions leading to states in Cl³⁶. A new level was discovered at 2.46±0.1 Mev in A³⁹, and the level at about 1.25 Mev in A³⁹ confirmed. Yield curves were measured for three of the groups.

Highly monoergic electrons from a 22-Mev betatron have been used to study the Cu⁶² activity in a pair of 2-mil copper foils separated by a 10-mil copper radiator. The ratio of the photodisintegration to electro-disintegration in the foils decreases by less than 10% in the region from 14 to 20 Mev. The measured value of F at 20 Mev is 8.6 in reasonable agreement with the extrapolation of previous measurements at higher energies and with the value of 8.38 expected on the basis of simple virtual photon calculations. Analysis of the excitation curves gave a Cu⁶³(γ, n) cross section of 80×10^-27 cm² which is 20% below most previous measurements.

The yield of π⁰ mesons from gamma rays on protons has been measured as a function of center-of-mass angle for gamma-ray energies from 170 Mev to 340 Mev. The results are shown to be consistent with a model of production predominantly through a J=3 / 2, isotopic spin, 3 / 2, state, which is resonant at about 300 Mev gamma-ray energy. There is evidence for S-state production and possibly electric quadrupole, P-wave production through the resonant state.

The differential scattering cross section for electron-electron scattering has been measured at relativistic energies. A focused beam of 15.7-Mev monokinetic electrons from the 22-Mev betatron was scattered by 1- and 2-mil Nylon foils in a 20-inch scattering chamber. The incident current was collected by a faraday cage after it had passed through the scattering foil and was measured by a vibrating reed electrometer. The scattered beam was defined by gold-lined slits at a known angle to the incident beam. The number of scattered electrons in a given momentum interval chosen by a magnetic analyzer was counted by a Geiger counter.

Energy analysis of the scattered electrons made it possible to separate the nuclear scattering events from the electron scattering events. The energy of the scattered electrons was measured as a function of the scattering angle and was found to be in agreement with the laws of relativistic mechanics within an experimental accuracy of 0.4 percent.

For the electron-electron collisions the relative scattering cross sections agree with the Møller formula. For the electron-nuclear collisions they agree with the relativistic Mott theory (Born approximation) corrected for the radiative losses as calculated by Schwinger (3 to 8 percent). The experimental consistency of the cross sections was about 4 percent.

The absolute differential scattering cross sections for the electron-nuclear scattering were measured at angles between 10° and 43°. The average of the absolute values was 2 percent lower than theory. This is probably due to systematic errors in the solid angle, and in the collection and counting efficiencies.

The absolute differential scattering cross sections for electron-electron scattering were measured at the same set of angles, which correspond to the angular interval of 70° to 150° in the center-of-mass system. The average of these absolute cross sections was 7 percent lower than theory predicts. The bulk of the 5 percent additional departure from theory may be due to a systematic error in the measurement of the momentum interval defined by the counter.

The angular distribution of electrons scattered by thin Be and Au foils has been measured for angles where the multiple scattering is important. The 1 / e widths of the distributions obtained with Au foils of 18.66 and 37.28 mg/cm² are 2.58° and 3.76°, respectively. These widths are about 10 percent narrower than those calculated from the theories of Williams or of Goudsmit and Saunderson but are in good agreement with the calculations of Molière.

The 1 / e widths obtained with Be foils of 257 and 495 mg/cm² are 3.06° and 4.25°. These widths are about 5 percent smaller than those given by Molière's theory increased by (1+1 / Z)^{1 / 2} for the contribution of electron-electron collisions. The discrepancy may be qualitatively explained by the fact that the Thomas-Fermi screening used in the calculation is different from the effective screening in the Be metal.

The scattering from the two Au foils was measured for larger angles where the scattering can be considered as single scattering modified by the effect of multiple scattering. The ratio of the scattering from the thick to the thin foil can be represented by the relation 2+95 / θ² from 9° to 30°, and is in fair agreement with theoretical expressions for this ratio.

Electrons removed from the 20-Mev betatron are focused to a 0.08-inch spot about 10 feet from the betatron by a magnetic lens. The electrons impinge on thin foils at the center of a highly evacuated scattering chamber having a diameter of 20 inches. Elastically scattered electrons, selected by a 3 / 8 inch×2 inch aperture, are focused by means of a 75° magnetic analyzer with 3 percent energy resolution and are detected by coincidence Geiger counters. Corrections are applied for multiple scattering and for energy losses which remove the electrons from the range of energies accepted by the detector arrangement. The scattering cross section for gold at 150° is found to be about 2.6 times that given by Mott's formula in the Born approximation and about one-half of that expected for the scattering by a point nucleus. This result is in good agreement with the calculations for electrons of this energy if the nuclear charge is assumed to be distributed uniformly throughout the nuclear volume.

The results for the scattering from C, Al, Cu, and Ag are also in agreement with the assumption of a uniformly distributed nuclear charge within the uncertainties involved in the theory and the experimental results.

Striking potential in the low-voltage mercury arc.—(1) Variation with vapor pressure. A tube with a thoriated tungsten filament and a nickel anode over a reservoir of mercury was heated in an electric furnace. When a constriction was placed in the tube leading to the pump so as practically to eliminate streaming of the vapor, and the temperature raised, the striking potential decreased to a minimum of approximately 5.3 volts for a pressure corresponding to a mercury surface temperature of 160°C and then increased. When no constriction was present, a similar curve was obtained except that on account of the streaming the pressure for a given furnace temperature was lower and hence the minimum was not reached below 320°C. If the fact that the vapor was fresher in the second case had any influence, it was not evident. (2) Variation with the distance away of mercury surface. When streaming was prevented, the same striking potentials were obtained for the same vapor pressures whether the surface was 5 cm or 80 cm from the arc. These results are somewhat at variance with those of Yao and suggest that further investigation is necessary.