Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Nullification of small knots

in the paper we consider the nullification number of small knots with at most 9 crossings. We establish two inequalities (Corollary 2.1) relating the nullification number to other knot invariants and properties of the knot diagram. We show that these inequalities allow us to settle the nullification number for all of the 84 prime knots with at most 9 crossings.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

A partial ordering of knots and links through diagrammatic unknotting

In this paper we de. ne a partial ordering of knots and links using a special property derived from their minimal diagrams. A link K' is called a predecessor of a link K if Cr(K') < Cr(K) and a diagram of K' can be obtained from a minimal diagram D of K by a single crossing change. In such a case, we say that K' < K. We investigate the sets of links that can be obtained by single crossing changes over all minimal diagrams of a given link. We show that these sets are specific for different links and permit partial ordering of all links. Some interesting results are presented and many questions are raised.

Decision-theoretic reflections on processing a fingermark

A recent publication in this journal [Neumann et al., Forensic Sci. Int. 212 (2011) 32-46] presented the results of a field study that revealed the data provided by the fingermarks not processed in a forensic science laboratory. In their study, the authors were interested in the usefulness of this additional data in order to determine whether such fingermarks would have been worth submitting to the fingermark processing workflow. Taking these ideas as a starting point, this communication here places the fingermark in its context of a case brought before a court, and examines the question of processing or not processing a fingermark from a decision-theoretic point of view. The decision-theoretic framework presented provides an answer to this question in the form of a quantified expression of the expected value of information (EVOI) associated with the processed fingermark, which can then be compared with the cost of processing the mark.

Distribution of events of positive selection and population differentiation in a metabolic pathway: the case of asparagine N-glycosylation

Asparagine N-Glycosylation is one of the most important forms of protein post-translational modification in eukaryotes. This metabolic pathway can be subdivided into two parts: an upstream sub-pathway required for achieving proper folding for most of the proteins synthesized in the secretory pathway, and a downstream sub-pathway required to give variability to trans-membrane proteins, and involved in adaptation to the environment and innate immunity. Here we analyze the nucleotide variability of the genes of this pathway in human populations, identifying which genes show greater population differentiation and which genes show signatures of recent positive selection. We also compare how these signals are distributed between the upstream and the downstream parts of the pathway, with the aim of exploring how forces of population differentiation and positive selection vary among genes involved in the same metabolic pathway but subject to different functional constraints. Our results show that genes in the downstream part of the pathway are more likely to show a signature of population differentiation, while events of positive selection are equally distributed among the two parts of the pathway. Moreover, events of positive selection are frequent on genes that are known to be at bifurcation points, and that are identified as being in key position by a network-level analysis such as MGAT3 and GCS1. These findings indicate that the upstream part of the Asparagine N-Glycosylation pathway has lower diversity among populations, while the downstream part is freer to tolerate diversity among populations. Moreover, the distribution of signatures of population differentiation and positive selection can change between parts of a pathway, especially between parts that are exposed to different functional constraints. Our results support the hypothesis that genes involved in constitutive processes can be expected to show lower population differentiation, while genes involved in traits related to the environment should show higher variability. Taken together, this work broadens our knowledge on how events of population differentiation and of positive selection are distributed among different parts of a metabolic pathway.

Block structured dynamics and neuronal coding

When certain control parameters of nervous cell models are varied, complex bifurcation structures develop in which the dynamical behaviors available appear classified in blocks, according to criteria of dynamical likelihood. This block structured dynamics may be a clue to understand how activated neurons encode information by firing spike trains of their action potentials.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.

Paisatge, poblament, cultura material i història de l'Ager Tarraconensis. Resultats i comparacions

Síntesi dels primers resultats del Projecte Ager Tarraconensis i de les aportacions al simposi, de les quals s’extreuen reflexions i coneixements nous sobre el tema de l’estudi entorn del conjunt de l’espai de la ciutat romana, del paisatge, tractat com un sistema. Les aportacions se centren en la varietat de les primeres estratègies de control romà del territori, de les tipologies i evolució dels establiments, dels aspectes econòmics i de la dinàmica del poblament. Tot plegat fa referència molt especialment al territori de Tarraco, per bé que es fan nombroses comparacions amb altres territoris de l’àrea catalana i saguntina i també d’altres províncies romanes. Tarraco es va perfilant com una ciutat amb un territorium molt productiu, no sols en agricultura, sinó també en indústries, producció tèxtil, explotacions de recursos minerals com les pedreres i el ferro, i amb un comerç molt actiu que la devia convertir en un port important de la Mediterrània occidental romana. La jerarquia dels hàbitats rurals també s’està demostrant més complexa gràcies al coneixement de noves aglomeracions. L’evolució posterior al període romà també ha entrat en discussió, especialment pel que fa a l’època islàmica, sobre la qual es discuteix si el camp va quedar poblat o despoblat, tema que resol en sentit positiu el diagrama pol·línic realitzat dins del marc del projecte.

Ohutlevytuotteenvalmistusteknisten piirteiden tunnistaminen ja käyttö suunnittelun apuna

Suunnittelu- ja valmistustoiminnot ovat eriytymässä myös ohutlevyteollisuudessa. Kilpailukyvyn parantamiseksi, valmistusta siirretään alihankkijoille maihin, jossa työvoima on halpaa ja suuret markkinat lähellä, tuotekehityksen ja suunnittelun jäädessä Suomeen tai muualle Länsi-Eurooppaan. Tällöin vanhan lokaalin toimintamallin synergiaedut eivät ole enää mahdollisia ja tuotteen valmistettavuuden arviointi, laadunhallinta ja komponenttien yhteensopivuuden varmistaminen on erittäin haasteellista. Tässä tutkimuksessa etsittiin uuden toimintamallin tuomiin haasteisiin vastauksia piirrepohjaisesta mallintamisesta. Tavoitteen mukaisesti, tutkimuksessa tunnistettiin ohutlevytuotteen valmistusteknilliset piirteet ja luotiin niiden mukainen piirrekaavio. Piirteiden tunnistus vaati tutkimustyötä sekä nykyaikaisten suunnittelumetodien että valmistusmenetelmien ja ohutlevymateriaalien parissa. Lisäksitarkasteltiin, millaisia vaikutuksia piirteillä on tuotteen valmistettavuuteen ja miten nämä tulee huomioida tuotteen suunnittelussa.

Extension of Murray's law using a non-Newtonian model of blood flow.

BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Lämmöntalteenotto kosteasta poistoilmasta prosessiteollisuudessa

Tämän diplomityön päämääränä on tehdä prosessiteollisuuden tarpeisiin Excel-taulukkolaskentaohjelmassa toimiva putkilämmönsiirtimen mitoitusohjelma. Prosessiteollisuudessa lämmönvaihtimien toimintaympäristöt ja olosuhteet vaihtelevat merkittävästi ja niinpä jokaisen vaihtimen suunnittelu ja mitoitus on toteutettava tapauskohtaisesti. Työssä käsitellään rekuperatiivisen ristivirtaputkilämmönvaihtimen yleinen lämpötekninen mitoitus sisältäen putken sisäpinnalle tapahtuvan mahdollisen lauhtumisen. Mitoitettava vaihdinkoostuu pystysuorista putkista, joissa lämmin ja kostea ilma virtaa putkien sisäpuolella ja kylmä kuiva ilma vaippapuolella vaakasuoraan. Vaihdinmateriaalina käytetään ruostumatonta AISI 304 -tai haponkestävää AISI 316 terästä. Kuuman ilman tila vaihtelee tarkasteltavan kohteen mukaan. Paperiteollisuuden kuivausyksiköiltä poistuva ilma on usein lämmintä ja kosteaa, ja infrakuivaimilta poistuva ilma on kuumaa. Mitoitettavalle lämmönvaihtimelle tulevan kuuman ilman lämpötila tapauksesta riippuen voi vaihdella 30°C, maksimissaan +300°C:een saakka, vesisisällön ollessa välillä 0,010...0,200 kg/kg ki tai jopa tämän ylikin. Vaihtimen mitoitus perustuu energiataseyhtälöiden käyttöön. Laskennassa määritetään vaihtimen pintalämpötila sekä mahdollinen kostean ilman lauhtuminen putken sisäpinnalle. Lisäksi teoria käsittää molempien virtausten tilanmuutosten laskennan. Työssä on esitetty esimerkkilaskelma, jossa on laskettu ilma- kostea ilma lämmönsiirrinkonstruktio. Esimerkissä on tarkasteltu vaihtimen hyötysuhdetta, virtausten lämpö- ja kosteuskäyttäytymistä ulkoilman lämpötilan funktiona. Ohjelmasta saadaan tulostettua mitoitettavanvaihtimen dimensiot; putkien lukumäärät syvyys- ja pituussuunnassa sekä kokonaisputkilukumäärä, putkien väliset etäisyydet toisiinsa nähden sekä syvyys, että pituussuunnassa, putkipituus ja putken sisä- ja ulkohalkaisijat. Nämä tiedot suunnittelija itse syöttää ohjelmalle alkuarvoina. Laskettuna tietona ohjelma antaa molempien virtausten poistolämpötilat, kuuman ilman poistuvan absoluuttisen kosteuden, kondenssivesimäärän, vaihtimen tehon ja painehäviöt vaippa- ja putkipuolelle. Lisäksi ohjelma laskee kuuman ilman ominaisentalpiat vaihtimen sisään- ja ulostulossa. Tämä mahdollistaa ilman tilapisteiden piirtämisen Mollier-piirrokseen.

The Lin28/let-7 axis regulates glucose metabolism.

The let-7 tumor suppressor microRNAs are known for their regulation of oncogenes, while the RNA-binding proteins Lin28a/b promote malignancy by inhibiting let-7 biogenesis. We have uncovered unexpected roles for the Lin28/let-7 pathway in regulating metabolism. When overexpressed in mice, both Lin28a and LIN28B promote an insulin-sensitized state that resists high-fat-diet induced diabetes. Conversely, muscle-specific loss of Lin28a or overexpression of let-7 results in insulin resistance and impaired glucose tolerance. These phenomena occur, in part, through the let-7-mediated repression of multiple components of the insulin-PI3K-mTOR pathway, including IGF1R, INSR, and IRS2. In addition, the mTOR inhibitor, rapamycin, abrogates Lin28a-mediated insulin sensitivity and enhanced glucose uptake. Moreover, let-7 targets are enriched for genes containing SNPs associated with type 2 diabetes and control of fasting glucose in human genome-wide association studies. These data establish the Lin28/let-7 pathway as a central regulator of mammalian glucose metabolism.

Obstructive pulmonary artery sarcoma.

A 68 year-old woman presented with increasing dyspnoea (NYHA II) and systolic murmur at auscultation. Echocardiography showed thickened pulmonary valve leaflets, a systolic prolapsing mass provoking severe pulmonary stenosis (peak systolic pulmonary pressure: 42 mmHg), no regurgitation, minimal right ventricular dilatation but normal ventricular function. CT scan showed a dense structure extending from the right ventricular outflow tract (RVOT) up to the pulmonary bifurcation infiltrating the pulmonary valve (PV).