Solving Systems of Non-Linear Equations by Broyden's Method with Projected Updates

We introduce a modification of Broyden's method for finding a zero of n nonlinear equations in n unknowns when analytic derivatives are not available. The method retains the local Q-superlinear convergence of Broyden's method and has the additional property that if any or all of the equations are linear, it locates a zero of these equations in n+1 or fewer iterations. Limited computational experience suggests that our modification often improves upon Eroyden's method.

The finite mass beamsplitter in high power interferometers

The beamplitter in high-power interferometers is subject to significant radiation-pressure fluctuations. As a consequence, the phase relations which appear in the beamsplitter coupling equations oscillate and phase modulation fields are generated which add to the reflected fields. In this paper, the transfer function of the various input fields impinging on the beamsplitter from all four ports onto the output field is presented including radiation-pressure effects. We apply the general solution of the coupling equations to evaluate the input-output relations of the dual-recycled laser-interferometer topology of the gravitational-wave detector GEO600 and the power-recycling, signal-extraction topology of advanced LIGO. We show that the input-output relation exhibits a bright-port dark-port coupling. This mechanism is responsible for bright-port contributions to the noise density of the output field and technical laser noise is expected to decrease the interferometer's sensitivity at low frequencies. It is shown quantitatively that the issue of technical laser noise is unimportant in this context if the interferometer contains arm cavities.Comment: 10 pages, 7 figure

Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities

We investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and non-monotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and non-icosahedral low-energy polymer morphologies.Comment: 9 pages, 17 figure

Changes in union membership over time : a panel analysis for West Germany

Despite the apparent stability of the wage bargaining institutions in West Germany, aggregate union membership has been declining dramatically since the early 90's. However, aggregate gross membership numbers do not distinguish by employment status and it is impossible to disaggregate these sufficiently. This paper uses four waves of the German Socioeconomic Panel in 1985, 1989, 1993, and 1998 to perform a panel analysis of net union membership among employees. We estimate a correlated random effects probit model suggested in Chamberlain (1984) to take proper account of individual specfic effects. Our results suggest that at the individual level the propensity to be a union member has not changed considerably over time. Thus, the aggregate decline in membership is due to composition effects. We also use the estimates to predict net union density at the industry level based on the IAB employment subsample for the time period 1985 to 1997. JEL - Klassifikation: J

Experimental demonstration of continuous variable purification of squeezed states

We report on the first experimental demonstration of purification of nonclassical continuous variable states. The protocol uses two copies of phase-diffused states overlapped on a beam splitter and provides Gaussified, less mixed states with the degree of squeezing improved. The protocol uses only linear optical devices such as beam splitters and homodyne detection, thereby proving these optical elements can be used for successful purification of this type of state decoherence which occurs in optical transmission channels

The Impact of Traditional and Alternative University Teacher Preparation Program Options on Secondary Teacher Candidates’ Knowledge, Skills, Dispositions, and Employment

The preparation of secondary teacher candidates through traditional (n = 13) or alternative (n = 15) options did not statistically significantly impact knowledge, skills or dispositions. Results for content knowledge, as measured at entrance to the program based on the Pre-Professional Skills Test, indicate that candidates who entered the traditional secondary teacher preparation program begin their studies with measured content knowledge in reading, writing, and mathematics that was congruent with the content knowledge of post-baccalaureate candidates who entered the alternative secondary teacher preparation program. Furthermore, content knowledge, based on cumulative grade point averages calculated upon completion of all content area coursework in the arts and sciences\u27 discipline just prior to student teaching results indicated that traditionally prepared candidates entered the student teaching experience with an overall measured cumulative grade point average that was congruent with the alternatively prepared candidates. The traditional candidates\u27 cumulative grade point average, 3.39 was .39 mean points above the cut score of 3.00 for admission to graduate school. The alternative candidates\u27 cumulative grade point average, 3.42 was .42 mean points above the cut score of 3.00 for admission to graduate school. Traditional and alternative candidates had congruent mastery of required content knowledge in subject matter and successful course completion for both groups of candidates as they begin their student teaching capstone experience. The overall pretest-posttest results for traditional and alternative candidates\u27 initial mid-term student teaching evaluation ratings compared to final student teaching evaluation ratings of teacher effectiveness based on cooperating teacher judgments, indicated statistically improved in all six domains: knowledge base, instructional skills, assessment and evaluation skills, classroom management skills, communication and interpersonal skills and disposition/professionalism. The overall pretest-posttest results for traditional and alternative candidates\u27 initial mid-term student teaching evaluation ratings compared to final student teaching evaluation ratings of teacher effectiveness based on university supervisor judgments, indicated statistically improved in five of the six domains. Positive statistical growth of this magnitude suggests real world mastery of teaching effectiveness based on the observations of cooperating teachers and university supervisors. Finally, the overall, observed levels of fulltime teaching employment six months after program completion for traditionally (85%) and alternatively (73%) prepared candidates represents a commendable level of employment for both groups

Demonstration of 3-port grating phase relations

We experimentally demonstrate the phase relations of 3-port gratings by investigating 3-port coupled Fabry-Perot cavities. Two different gratings which have the same 1st order diffraction efficiency but differ substantially in their 2nd order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities we could validate the results of an earlier theoretical description of the phases at a three port grating

Preparing the bound instance of quantum entanglement

Among the possibly most intriguing aspects of quantum entanglement is that it comes in "free" and "bound" instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no pure maximally entangled pairs can be regained. Their existence hence certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with thermodynamics. In this work, we present a first experimental unconditional preparation and detection of a bound entangled state of light. We consider continuous-variable entanglement, use convex optimization to identify regimes rendering its bound character well certifiable, and realize an experiment that continuously produced a distributed bound entangled state with an extraordinary and unprecedented significance of more than ten standard deviations away from both separability and distillability. Our results show that the approach chosen allows for the efficient and precise preparation of multimode entangled states of light with various applications in quantum information, quantum state engineering and high precision metrology.Comment: The final version accounts for a recent comment in Nature Physics [24] clarifying that a previous claim of having generated bound entanglement [23] was not supported by the authors' data. We also extended our introduction and discussion and also added reference

Heat transfer and pressure drop correlations for laminar flow in an in-line and staggered array of circular cylinders

Enhanced heat transfer surfaces based on cylindrically shaped pin fins with wire diameters in the range of 100 µm were analyzed. The design is based on a high pin length to diameter ratio in the range of 20–100. Correlations for thermal and fluid dynamic characteristics of these fine wire structures are not available in literature. An in-line and staggered arrangement of pins were simulated for a variety of operational and geometrical conditions with a twodimensional computational thermal and fluid dynamics model. Correlations for Nusselt number and friction factor with respect to Reynolds number and geometry were derived thereby. Reynolds numbers based on the wire diameter are in the range of 3–60. The correlations for the Nusselt number and friction factor can predict 93% and 97% of the simulated data within ±10%

Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.Comment: 4 pages, 3 figure