Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter beta>0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. We prove that the method is strongly stable when beta > -lambda_k where lambda_k is the k'th Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.Comment: 14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 k

Mineralization of an Axially Aligned Collagenous Matrix: A Morphological Study

Bone can be described as a highly ordered composite of type I collagen integrated with an inorganic mineral phase. In vitro models of bone mineralization using collagenous substrates have been reported in the literature. This study reports an in vitro system of mineralized reconstituted collagen fibers, with aligned fibrillar substructure. The collagen fibers were mineralized in a double diffusion chamber saturated with respect to calcium and phosphate. The morphology and ultrastructure of the mineral precipitate were evaluated as a function of the pH of the incubating media. Brushite crystal was observed at acidic pH. Large rectangular crystals formed at pH 5.15 and appear to associate with the collagen fibers. At neutral and alkaline pHs, hydroxyapatite crystals were observed in association with the collagen fibers . Spherical aggregates of hydroxyapatite crystals were seen at neutral and alkaline pHs, but these structures were reduced in size when formed on collagen at alkaline pH. On close examination these spherical structures were found to be hollow when viewed in cross section. The crystals precipitated within the interior of the collagen fiber at neutral and alkaline pHs were comparable in both size and shape to crystals observed in mineralized turkey tendon and skeletal tissues. These preliminary observations indicate that with further refinement the reconstituted collagen fibers may prove useful in model systems for the study of collagen mediated mineralization in vitro. In addition, mineralization of collagenous matrices may lead to the development of biomaterials for bone repair and replacement

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Alignment enhancement of molecules embedded in helium nanodroplets by multiple laser pulses

We show experimentally that field-free one-dimensional (1D) alignment of 1,4-diiodobenzene molecules embedded in helium nanodroplets, induced by a single, linearly polarized 200-fs laser pulse, can be significantly enhanced by using two or four optimally synchronized laser pulses. The strongest degree of 1D alignment is obtained with four pulses and gives ⟨cos2θ⟩>0.60. Besides the immediate implications for molecular frame studies, our results pave the way for more general manipulation of rotational motion of molecules in He droplets

Selection-free predictions in global games with endogenous information and multiple equilibria

Global games with endogenous information often exhibit multiple equilibria. In this paper, we show how one can nevertheless identify useful predictions that are robust across all equilibria and that cannot be delivered in the common-knowledge counterparts of these games. Our analysis is conducted within a flexible family of games of regime change, which have been used to model, inter alia, speculative currency attacks, debt crises, and political change. The endogeneity of information originates in the signaling role of policy choices. A novel procedure of iterated elimination of nonequilibrium strategies is used to deliver probabilistic predictions that an outside observer—an econometrician—can form under arbitrary equilibrium selections. The sharpness of these predictions improves as the noise gets smaller, but disappears in the complete-information version of the model

Multiflavor Correlation Functions in non-Abelian Gauge Theories at Finite Density in two dimensions

We compute vacuum expectation values of products of fermion bilinears for two-dimensional Quantum Chromodynamics at finite flavored fermion densities. We introduce the chemical potential as an external charge distribution within the path-integral approach and carefully analyse the contribution of different topological sectors to fermion correlators. We show the existence of chiral condensates exhibiting an oscillatory inhomogeneous behavior as a function of a chemical potential matrix. This result is exact and goes in the same direction as the behavior found in QCD_4 within the large N approximation.Comment: 28 pages Latex (3 pages added and other minor changes) to appear in Phys.Rev.

Nonlinear ac conductivity of one-dimensional Mott insulators

We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1d band insulator and find good agreement when the number of simultaneously absorbed photons is large.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday. To appear in JSTAT. 5 pages, 2 figure

The use of a MED calendar to increase medication compliance

This study describes the successful design and implementation of a medications calendar to increase medication compliance among Navajo patients who have difficulty complying with prescription instructions. This paper is presented as an example of a successful method for trying to ensure that medications are taken according to instructions. The MED calendar is designed to help non-English speaking and elderly patients in particular.Initially the calendars were hand made by the drivers from the Public Health Nursing Department. Their primary duty was to serve as interpreters for the Public Health Nurse. Poster board (20 x26 ) was used to simulate a monthly calendar. The days of the week were marked on each grid on each board. The boards were then laminated and the laminated surface was used to mark the name and days of the month for which the calendar was being used. The patients medications were then placed in single unit dose packages. The dose packages were then taped to the calendar according to the prescribed schedule. The patient then received a detailed verbal explanation on when and how to take his or her medicine. The calendar was attached to the wall of the patient\\u27s residence with stick pins and medications were placed for 2-4 weeks at a time. The material cost of the original calendars was $1.75 without labor. Now a professional printer produces them at a total cost of$3.00 per unit. There were two primary safety considerations explored with the implementation of the MED calendars. The first was concern for the stability of the medication in a clear package as opposed to opaque bottle. The Chief of Pharmacy indicated that medicine can be kept in unit dose packages up to six months. The benefits of patient compliance were much greater than any small risk of medication instability. The second concern was safety around small children. In most cases the calendar can be placed high enough on the wall to be out of reach of the children. If this is not possible then the use of the MED calendar is not considered.MED calendars were well accepted by the patients. Navajo patients relate well to ordinary monthly calendars, and this does not require knowledge of the English language. Also, the calendars are highly visible making them difficult to ignore. Medication doses are more easily understood with a pictorial association. The calendars are durable and last at least two or three years. From 1985 to 1987, the MED calendars were used with non-compliant patients. Seventy-three percent of the patients showed some improvement. Improvement was measured by 1) improvement in clinical symptoms including decreased hospitalization, 2) accurate or improved pill count, and 3) patient\\u27s and/or doctor\\u27s affirmation of compliance. There are several difficulties noted in the use of the MED calendar. Safety in the presence of small children is a major concern. Some patients become very dependent on the MED calendar, and this becomes time consuming for the Public Health Nurse who must visit every 2-4 weeks to refill the unit dose packages. Sometimes the unit dose packages do not remain secured to the calendar. Finally, the large size of the calendar can create difficulties in transporting them and are therefore objectionable to some of the patients.The study concludes that the benefits of the MED calendar far outweigh the difficulties encountered in using this system of promoting and facilitating patient compliance