Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

FLUCTUATION OF THE INITIAL CONDITIONS AND ITS CONSEQUENCES ON SOME OBSERVABLES

We show effects of the event-by-event fluctuation of the initial conditions (IC) in hydrodynamic description of high-energy nuclear collisions on some observables. Such IC produce not only fluctuations in observables but, due to their bumpy structure, several non-trivial effects appear. They enhance production of isotropically distributed high-p(T) particles, making upsilon(2) smaller there. Also, they reduce upsilon(2) in the forward and backward regions where the global matter density is smaller, so where such effects become more efficacious. They may also produce the so-called ridge effect in the two large-p(T) particle correlation.

Importance of granular structure in the initial conditions for the elliptic flow

We show the effects of the granular structure of the initial conditions of a hydrodynamic description of high-energy nucleus-nucleus collisions on some observables, especially on the elliptic-flow parameter upsilon(2). Such a structure enhances production of isotropically distributed high-p(T) particles, making upsilon(2) smaller there. Also, it reduces upsilon(2) in the forward and backward regions where the global matter density is smaller and, therefore, where such effects become more efficacious.

Hydro-kinetic approach to relativistic heavy ion collisions

We develop a combined hydro-kinetic approach which incorporates a hydrodynamical expansion of the systems formed in A + A collisions and their dynamical decoupling described by escape probabilities. The method corresponds to a generalized relaxation time (tau(rel)) approximation for the Boltzmann equation applied to inhomogeneous expanding systems; at small tau(rel) it also allows one to catch the viscous effects in hadronic component-hadron-resonance gas. We demonstrate how the approximation of sudden freeze-out can be obtained within this dynamical picture of continuous emission and find that hypersurfaces, corresponding to a sharp freeze-out limit, are momentum dependent. The pion m(T) spectra are computed in the developed hydro-kinetic model, and compared with those obtained from ideal hydrodynamics with the Cooper-Frye isothermal prescription. Our results indicate that there does not exist a universal freeze-out temperature for pions with different momenta, and support an earlier decoupling of higher p(T) particles. By performing numerical simulations for various initial conditions and equations of state we identify several characteristic features of the bulk QCD matter evolution preferred in view of the current analysis of heavy ion collisions at RHIC energies.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

f t value of the 0(+)-> 0(+) beta(+) decay of (32)Ar: A measurement of isospin symmetry breaking in a superallowed decay

We determined the absolute branch of the T=2 superallowed decay of (32)Ar by detecting the beta(+)-delayed protons and gamma decays of the daughter state. We obtain b(SA)(beta)=(22.71 +/- 0.16)%, which represents the first determination of a proton branch to better than 1%. Using this branch along with the previously determined (32)Ar half-life and energy release, we determined ft=(1552 +/- 12) s for the superallowed decay. This ft value, together with the corrected Ft value extracted from previously known T=1 superallowed decays, yields a measurement of the isospin symmetry breaking correction in (32)Ar decay delta(exp)(C)=(2.1 +/- 0.8)%. This can be compared to a theoretical calculation delta(C)=(2.0 +/- 0.4)%. As by-products of this work, we determined the gamma and proton branches for the decay of the lowest T=2 state of (32)Cl, made a precise determination of the total proton branch and relative intensities of proton groups that leave (31)S in its first excited state and deduced an improved value for the (32)Cl mass.

gamma Cassiopeiae: an X-ray Be star with personality

An exciting unsolved problem in the study of high energy processes of early type stars concerns the physical mechanism for producing X-rays near the Be star gamma Cassiopeiae. By now we know that this source and several ""gamma Cas analogs"" exhibit an unusual hard thermal X-ray spectrum, compared both to normal massive stars and the non-thermal emission of known Be/X-ray binaries. Also, its light curve is variable on almost all conceivable timescales. In this study we reanalyze a high dispersion spectrum obtained by Chandra in 2001 and combine it with the analysis of a new (2004) spectrum and light curve obtained by XMM-Newton. We find that both spectra can be fit well with 3-4 optically thin, thermal components consisting of a hot component having a temperature kT(Q) similar to 12-14 keV, perhaps one with a value of similar to 2.4 keV, and two with well defined values near 0.6 keV and 0.11 keV. We argue that these components arise in discrete (almost monothermal) plasmas. Moreover, they cannot be produced within an integral gas structure or by the cooling of a dominant hot process. Consistent with earlier findings, we also find that the Fe abundance arising from K-shell ions is significantly subsolar and less than the Fe abundance from L-shell ions. We also find novel properties not present in the earlier Chandra spectrum, including a dramatic decrease in the local photoelectric absorption of soft X-rays, a decrease in the strength of the Fe and possibly of the Si K fluorescence features, underpredicted lines in two ions each of Ne and N (suggesting abundances that are similar to 1.5-3x and similar to 4x solar, respectively), and broadening of the strong NeXLy alpha and OVIII Ly alpha lines. In addition, we note certain traits in the gamma Cas spectrum that are different from those of the fairly well studied analog HD110432 - in this sense the stars have different ""personalities."" In particular, for gamma Cas the hot X-ray component remains nearly constant in temperature, and the photoelectric absorption of the X-ray plasmas can change dramatically. As found by previous investigators of gamma Cas, changes in flux, whether occurring slowly or in rapidly evolving flares, are only seldomly accompanied by variations in hardness. Moreover, the light curve can show a ""periodicity"" that is due to the presence of flux minima that recur semiregularly over a few hours, and which can appear again at different epochs.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Insulin and leptin relations in obesity: a multimedia approach

Obesity has been recognized as a worldwide public health problem. It significantly increases the chances of developing several diseases, including Type II diabetes. The roles of insulin and leptin in obesity involve reactions that can be better understood when they are presented step by step. The aim of this work was to design software with data from some of the most recent publications on obesity, especially those concerning the roles of insulin and leptin in this metabolic disturbance. The most notable characteristic of this software is the use of animations representing the cellular response together with the presentation of recently discovered mechanisms on the participation of insulin and leptin in processes leading to obesity. The software was field tested in the Biochemistry of Nutrition web-based course. After using the software and discussing its contents in chatrooms, students were asked to answer an evaluation survey about the whole activity and the usefulness of the software within the learning process. The teaching assistants (TA) evaluated the software as a tool to help in the teaching process. The students' and TAs' satisfaction was very evident and encouraged us to move forward with the software development and to improve the use of this kind of educational tool in biochemistry classes.

Bayesian updating rules in continuous opinion dynamics models

Here, I investigate the use of Bayesian updating rules applied to modeling how social agents change their minds in the case of continuous opinion models. Given another agent statement about the continuous value of a variable, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a uniform distribution. This represents the idea that the other agent might have no idea about what is being talked about. The effect of updating only the first moments of the distribution will be studied, and we will see that this generates results similar to those of the bounded confidence models. On also updating the second moment, several different opinions always survive in the long run, as agents become more stubborn with time. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Characterization and greenhouse evaluation of Brazilian calcined nonapatite phosphate rocks for rice

Little information is available on the agronomic effectiveness of calcined nonapatite phosphate rock (PR) sources containing crandallite minerals in the form of Ca-Fe-Al-P for flooded and upland rice (Oryza sativa L.). We conducted laboratory and greenhouse studies to (i) characterize the mineralogical composition, (ii) investigate the solubility and dissolution behavior, and (iii) evaluate the agronomic effectiveness of two nonapatite PR sources (Juquia and Sapucaia) from Brazil and compared them with (i) a highly reactive Gafsa PR (Tunisia) containing apatite in the form of Ca-P and (ii) a reference water-soluble triple superphosphate (TSP) for flooded and upland rice. After calcination at 500 degrees C for 4 h, the solubility of Juquia PR and Sapucaia PR in neutral ammonium citrate (NAC) significantly increased from almost nil to a maximum of 39.3 and 114 g P kg(-1), respectively. X-ray diffraction showed that crystalline crandallite mineral was transformed to an amophorus form after calcination. The solubility behavior of the two calcined PR sources followed the same trend as Gafsa PR, that is, P release decreased with increasing equilibrium pH in the 0.01 M KCl solution (PH 3.0-8.0). At PH 3, the solubility followed: Gafsa PR > calcined Sapucaia PR > calcined Juquia PR. No P release was detected from any of the PR sources at pH >= 5.0 in the solution, indicating the Ca-P characteristic of the Ca-Fe-Al-P mineral controlled P dissolution of the calcined PR. Without calcination, both Juquia PR and Sapucaia PR were totally ineffective for upland rice grown on a Hiwassee clay loam (fine, kaolinitic, thermic Rhodic Kanhapludult) with pH 5.4 whereas a significant P response was observed with the calcined PR samples. For flooded rice grown on Hiwassee soil, the calcined Juquia PR and Sapucaia PR were 66 and 72%, respectively, as effective as TSP in increasing rice grain yield whereas Gafsa PR was ineffective. For upland rice grown on the unlimed soil, Gafsa PR was as effective as TSP in increasing rice grain yield whereas calcined Juquia PR and Sapucaia PR were 89 and 83% of TSP. The effectiveness of Gafsa PR was reduced to 0% after the soil was limed to pH 7.0 whereas the two calcined PR sources were reduced to 49% of TSP. Soil available P extracted by iron oxide impregnated filter paper (Pi test) or anion-exchange resin after rice harvest correlated well with P uptake by rice grain for flooded and upland rice.

Profiles of xylose reductase, xylitol dehydrogenase and xylitol production under different oxygen transfer volumetric coefficient values

BACKGROUND: Xylitol is a sugar alcohol (polyalcohol) with many interesting properties for pharmaceutical and food products. It is currently produced by a chemical process, which has some disadvantages such as high energy requirement. Therefore microbiological production of xylitol has been studied as an alternative, but its viability is dependent on optimisation of the fermentation variables. Among these, aeration is fundamental, because xylitol is produced only under adequate oxygen availability. In most experiments with xylitol-producing yeasts, low oxygen transfer volumetric coefficient (K(L)a) values are used to maintain microaerobic conditions. However, in the present study the use of relatively high K(L)a values resulted in high xylitol production. The effect of aeration was also evaluated via the profiles of xylose reductase (XR) and xylitol clehydrogenase (XD) activities during the experiments. RESULTS: The highest XR specific activity (1.45 +/- 0.21 U mg(protein)(-1)) was achieved during the experiment with the lowest K(L)a value (12 h(-1)), while the highest XD specific activity (0.19 +/- 0.03 U mg(protein)(-1)) was observed with a K(L)a value of 25 h(-1). Xylitol production was enhanced when K(L)a was increased from 12 to 50 h(-1), which resulted in the best condition observed, corresponding to a xylitol volumetric productivity of 1.50 +/- 0.08 g(xylitol) L(-1) h(-1) and an efficiency of 71 +/- 6.0%. CONCLUSION: The results showed that the enzyme activities during xylitol bioproduction depend greatly on the initial KLa value (oxygen availability). This finding supplies important information for further studies in molecular biology and genetic engineering aimed at improving xylitol bioproduction. (C) 2008 Society of Chemical Industry

EFFECT OF CULTIVATION CONDITIONS ON GLUCOSE-6-PHOSPHATE DEHYDROGENASE PRODUCTION BY GENETICALLY MODIFIED Saccharomyces cerevisiae

The objective of this research was to improve Glucose-6-phosphate dehydrogenase (G6PD) production by Saccharomyces cerevisiae W303-181, which carry the plasmid YEpPGK-G6PD, by varying the following cultivation conditions: pH value (4.8, 5.7 and 6.6); inoculum concentration (0.1, 0.6 and 1.1 g/L) and initial glucose concentration (20.0, 30.0 and 40.0 g/L). The effect of those variables on G6PD production capability was studied by the application of response surface statistical analysis. The results showed that the highest G6PD production (1594.2 U/L), specific activity (1189.7 U/g(cell)) and productivity (45.6 U/L.h) occurred at pH 4.8, inoculum concentration of 0.1 g/L and initial glucose concentration of 20.0 g/L, under agitation of 150 rpm at 30 degrees C after 36 h. In this work, the strain expressed about 21 fold more activity than the wild S. cerevisiae strain, being an attractive and promising new source of this enzyme.