Chaotic scattering in solitary wave interactions: A singular iterated-map description

We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. Unlike previous analyses, this map allows one to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a ``multi-pulse'' Melnikov integral and allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The family of maps derived exhibits singular behavior, including regions of infinite winding. This problem is shown to be a singular version of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics.Comment: 29 pages, 17 figures, submitted to Chaos, higher-resolution figures available at author's website: http://m.njit.edu/goodman/publication

Studies on nucleic acid reassociation kinetics: empirical equations describing DNA reassociation

The rate of appearance of duplex DNA renaturation, measured with single strand specific nuclease, deviates significantly from a second order reaction. Measurements reported in paper I of this series indicate an inhibition in the rate of reassociation of single strand tails on partially reassociated molecules by a factor of at least two. Equations are derived that describe the observed form of reassociation kinetics as measured with hydroxyapatite and with single strand specific nuclease. The free parameter that describes the extent of inhibition of nucleation with single strand tails in these equations has been evaluated by least squares methods and agrees with the experimentally measured value

Sensitivity design technique for optimal control, part C Final report

Optimal sensitivity design techniques to design feedback control system for large, flexible booste

Allelopathic Observations in Rice (Oryza sativa L.) to Ducksalad (Heteranthera limosa)

More than 50 weed species infest drill-seeded rice in the U.S. and one of the most prevalent aquatic weeks is ducksalad (Heteranthera limosa). During the summer of 1988, a field experiment was conducted to identify rice accessions from the USDA/ARS rice germplasm collection for allelopathic effects to ducksalad. In this field experiment, 5,000 accessions were evaluated for allelopathic activity. Five to seven seeds of each rice accession were planted in hills about 75cm apart in two replications. Allelopathic activity was recorded as 1) radius of the area affected by allelochemical from the base of the rice plant and 2) percentage of weed control within the affected area. Ducksalad was rated at the panicle initiation stage of rice development. Of the 5,000 accessions that were evaluated, approximately 191 were identified as having evident allelopathic activity. The accessions that demonstrated allelopathic activity originated in 26 countries (Afghanistan, Argentina, Australia, Brazil, Columbia, Dominican Republic, France, India, Iran, Iraq, Israel, Italy, Japan, Malaysia, Mexico, Pakistan, Peru, Philippines, Portugal, Republic of Korea, People Republic of China, Soviet Union, Taiwan, Thailand, Turkey, and United States)

Nonlinear Propagation of Light in One Dimensional Periodic Structures

We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion), the periodic structure (photonic band dispersion) and nonlinearity. We present a detailed discussion of the role of these effects individually and in concert. We derive the nonlinear coupled mode equations (NLCME) which govern the envelope of the coupled backward and forward components of the electromagnetic field. We prove the validity of the NLCME description and give explicit estimates for the deviation of the approximation given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known to have gap soliton states. A consequence of our results is the existence of very long-lived {\it gap soliton} states of AMLE. We present numerical simulations which validate as well as illustrate the limits of the theory. Finally, we verify that the assumptions of our model apply to the parameter regimes explored in recent physical experiments in which gap solitons were observed.Comment: To appear in The Journal of Nonlinear Science; 55 pages, 13 figure

ALERT: FARMERS NEED TO SIGN UP FOR ACRE!

Corn, soybean and wheat producers are facing serious financial challenges. And it is even worse for livestock producers, most of who are also crop producers and are therefore eligible for ACRE. Crops are behind in maturity, some areas of the state need rain, product prices have fallen substantially, and USDA Counter Cyclical payments do not start until $2.35 on corn,$5.36 soybeans and $3.40 on wheat. Chances of prices that low are around 10-15%, but at that point ACRE payments would be much, much bigger. Many producers do not understand ACRE and the benefits available; most of the reasons given for not participating are invalid.Crop Production/Industries, Farm Management,

Nonlinear photon transport in a semiconductor waveguide-cavity system containing a single quantum dot: Anharmonic cavity-QED regime

We present a semiconductor master equation technique to study the input/output characteristics of coherent photon transport in a semiconductor waveguide-cavity system containing a single quantum dot. We use this approach to investigate the effects of photon propagation and anharmonic cavity-QED for various dot-cavity interaction strengths, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down, even in the weak coupling regime. As a measure of the anharmonic multiphoton-correlations, we compute the Fano factor and the correlation error associated with making a semiclassical approximation. We also explore the role of electron--acoustic-phonon scattering and find that phonon-mediated scattering plays a qualitatively important role on the light propagation characteristics. As an application of the theory, we simulate a conditional phase gate at a phonon bath temperature of $20$K in the strong coupling regime.Comment: To appear in PR

Studies on Nucleic Acid Reassociation Kinetics: Retarded Rate of Hybridization of RNA with Excess DNA

The rate of reaction of excess double-stranded bacteriophage phi X174 and plasmid RSF2124 DNA drivers with enzymatically synthesized asymmetric RNA tracers was measured. Other reactions were carried out with excess Escherichia coli DNA and E. coli RNA labeled in vivo. RNA and DNA fragment lengths were held approximately equal. For each case it was shown that in DNA excess the rate constant for RNA· DNA hybridization is 3- to 4.5-fold lower than that of the renaturation rate constant for the driver DNA. This retardation was also observed in pseudo-first-order hybridization reactions driven by excess strand-separated RSF2124 DNA. It was concluded that the rate constant for RNA· DNA hybridization depends partially on which species is in excess

Methods for Evaluating Respondent Attrition in Web-Based Surveys

Background: Electronic surveys are convenient, cost effective, and increasingly popular tools for collecting information. While the online platform allows researchers to recruit and enroll more participants, there is an increased risk of participant dropout in Web-based research. Often, these dropout trends are simply reported, adjusted for, or ignored altogether. Objective: To propose a conceptual framework that analyzes respondent attrition and demonstrates the utility of these methods with existing survey data. Methods: First, we suggest visualization of attrition trends using bar charts and survival curves. Next, we propose a generalized linear mixed model (GLMM) to detect or confirm significant attrition points. Finally, we suggest applications of existing statistical methods to investigate the effect of internal survey characteristics and patient characteristics on dropout. In order to apply this framework, we conducted a case study; a seventeen-item Informed Decision-Making (IDM) module addressing how and why patients make decisions about cancer screening. Results: Using the framework, we were able to find significant attrition points at Questions 4, 6, 7, and 9, and were also able to identify participant responses and characteristics associated with dropout at these points and overall. Conclusions: When these methods were applied to survey data, significant attrition trends were revealed, both visually and empirically, that can inspire researchers to investigate the factors associated with survey dropout, address whether survey completion is associated with health outcomes, and compare attrition patterns between groups. The framework can be used to extract information beyond simple responses, can be useful during survey development, and can help determine the external validity of survey results

Time Dependent Effects and Transport Evidence for Phase Separation in La_{0.5}Ca_{0.5}MnO_{3}

The ground state of La_{1-x}Ca_{x}MnO_{3} changes from a ferromagnetic metallic to an antiferromagnetic charge-ordered state as a function of Ca concentration at x ~ 0.50. We present evidence from transport measurements on a sample with x = 0.50 that the two phases can coexist, in agreement with other observations of phase separation in these materials. We also observe that, by applying and then removing a magnetic field to the mainly charge-ordered state at some temperatures, we can "magnetically anneal" the charge order, resulting in a higher zero-field resistivity. We also observe logarithmic time dependence in both resistivity and magnetization after a field sweep at low temperatures.Comment: 9 pages, LATEX, 3 postscript figure