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.

Remaining rod activity mediates visual behavior in adult Rpe65-/- mice.

Purpose: C57/Bl6, Cpfl1-/- (Cone photoreceptors function loss 1; pure rod function), Gnat1alpha-/- (rod alpha-transducin; pure cone function) and Rpe65-/-;Rho-/- double knock-out mice were studied in order to distinguish the respective contributions of the different photoreceptor (PR) systems that enable light perception and mediate a visual reflex in adult Rpe65-/- mice using a simple behavioural procedure. Methods: Visual function was estimated using a rotating automatized optomotor drum covered with vertical black and white stripes at spatial frequencies of 0.025 to 0.5 cycles per degree (cpd) in both photopic and scotopic conditions. To evaluate the contribution as well as the light intensity threshold of each PR system, we tested the mouse strains with different luminances. Results: Stripe rotation elicits head movements in wild-type (WT) animals in photopic and scotopic conditions depending on the spatial frequency, whereas Cpfl1-/- mice show a reduced activity in the photopic condition and Gnat1alpha-/- mice an almost absent response in the scotopic condition. Interestingly, a robust visual response is obtained with Rpe65-/- knockout mice at 0.075 cpd and 0.1 cpd in the photopic condition. The residual rod function in the Rpe65-/- animals was demonstrated by testing Rpe65-/-;Rho-/- mice that present no response in photopic conditions. Conclusions: The optomotor test is a simple method to estimate the visual function, and to evaluate the respective contributions of rod and cone systems. Using this test, we demonstrate that in Rpe65-/- mice, devoid of functional cones and of detectable 11-cis-retinal protein, rods mimic in part the cone function by mediating vision in photopic conditions.

Controlling anomalous stresses in soft field-responsive systems

We report a phenomenon occurring in field-responsive suspensions: shear-induced anomalous stresses. Competition between a rotating field and a shear flow originates a multiplicity of anomalous stress behaviors in suspensions of bound dimers constituted by induced dipoles. The great variety of stress regimes includes nonmonotonic behaviors, multiresonances, negative viscosity effect, and blockades. The reversibility of the transitions between the different regimes and the self-similarity of the stresses make this phenomenon controllable and therefore applicable to modify macroscopic properties of soft condensed matter phases.

Temporal changes of an alfalfa succession and related soil physical properties on the Loess Plateau, China

The objective of this work was to investigate the relationship between changes in the plant community and changes in soil physical properties and water availability, during a succession from alfalfa (Medicago sativa L.) to natural vegetation on the Loess Plateau, China. Data from a succession sere spanning 32 years were collated, and vegetative indexes were compared to changes related to soil bulk density and soil water storage. The alfalfa yield increased for approximately 7 years, then it declined and the alfalfa was replaced by a natural community dominated by Stipa bungeana that began to thrive about 10 years after alfalfa seeding. Soil bulk density increased over time, but the deterioration of the alfalfa was mainly ascribed to a severe reduction in soil water storage, which was lowest around the time when degradation commenced. The results indicated that water consumption by alfalfa could be reduced by reducing plant density. The analysis of the data also suggested that soil water recharge could be facilitated by rotating the alfalfa with other crops, natural vegetation, or bare soil.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Microwave spectrometry for the Evaluation of the structural integrity of metallic stents

Purpose: To assess the feasibility of a method based on microwave spectrometry to detect structural distortions of metallic stents in open air conditions and envisage the prospects of this approach toward possible medical applicability for the evaluation of implanted stents. Methods: Microwave absorbance spectra between 2.0 and 18.0 GHz were acquired in open air for the characterization of a set of commercial stents using a specifically design setup. Rotating each sample over 360º, 2D absorbance diagrams were generated as a function of frequency and rotation angle. To check our approach for detecting changes in stent length (fracture) and diameter (recoil), two specific tests were performed in open air. Finally, with a few adjustments, this same system provides 2D absorbance diagrams of stents immersed in a water-based phantom, this time over a bandwidth ranging from 0.2 to 1.8 GHz. Results: The authors show that metallic stents exhibit characteristic resonant frequencies in their microwave absorbance spectra in open air which depend on their length and, as a result, may reflect the occurrence of structural distortions. These resonances can be understood considering that such devices behave like dipole antennas in terms of microwave scattering. From fracture tests, the authors infer that microwave spectrometry provides signs of presence of Type I to Type IV stent fractures and allows in particular a quantitative evaluation of Type III and Type IV fractures. Recoil tests show that microwave spectrometry seems able to provide some quantitative assessment of diametrical shrinkage, but only if it involves longitudinal shortening. Finally, the authors observe that the resonant frequencies of stents placed inside the phantom shift down with respect to the corresponding open air frequencies, as it should be expected considering the increase of dielectric permittivity from air to water. Conclusions: The evaluation of stent resonant frequencies provided by microwave spectrometry allows detection and some quantitative assessment of stent fracture and recoil in open air conditions. Resonances of stents immersed in water can be also detected and their characteristic frequencies are in good agreement with theoretical estimates. Although these are promising results, further verifica tion in a more relevant phantom is required in order to foresee the real potential of this approach.

Development of the Acoustic Emission Based Diagnostics Concept for the Rotary Lime Kiln

Reaaliaikainen, ennakoiva kunnonvalvonta on erittäin tärkeä osa modernin tehtaan tai tuotantolinjan toimintaa. Diplomityön teettäjä haluaa edelleen kehittää akustiseen emissioon perustuvaa kunnonvalvonta järjestelmäänsä, jotta siitä olisi enemmän hyötyä asiakkaalle. Diplomityö sisältää johdannonakustiseen emissioon ja akustisiin emissio sensoreihin. Työn tavoitteena oli kehittää päätöksentekojärjestelmä, jota käytettäisiin työn teettäjän valmistamien sensoreiden antaman tiedon automatisoituun analysointiin. Työssä on vertailtu kolmea eri ohjelmistotoimittajaa ja heidän ohjelmiaan, ja tehty ehdotus hankittavasta ohjelmistosta. Lisäksi työssä on kehitetty ohjeita, joiden avulla ohjelmisto ohjelmoidaan tuottamaan reaaliaikaista tietoa ja huolto-ohjeita sen käyttäjille. Lisäksi työssä annetaan ehdotuksia kunnonvalvonta- ja päätöksentekojärjestelmän edelleen kehittämiseen.

Design of a Condition Monitoring System for a Glass Wool Production Line

Työn tarkoituksena oli suunnitella kunnonvalvontajärjestelmä kahdelle lasivillan tuotantolinjalle. Suunnitteluprosessin lisäksi työssä on esitelty erilaisia kunnonvalvontamenetelmiä. Työn alussa on kerrottu erilaisista kunnonvalvontamenetelmistä, joilla voidaan seurata erilaisten laitteiden ja koneiden toimintakuntoa.Erityisesti työssä on tarkasteltu teollisuudessa yleistyviä kunnonvalvonnan värähtelymittauksia. Työssä suunniteltu kunnonvalvontajärjestelmä perustuu viiteen eri menetelmään, jotka ovat värähtelymittaus, lämpötilanmittaus lämpökameralla, lämpötilanmittaus kannettavalla mittarilla, kuuntelu elektronisella stetoskoopilla ja pyörivien osien kunnontarkkailu stroboskoopilla. Kunnonvalvontajärjestelmän suunnittelu on tehty useassa eri vaiheessa. Ensin työssä on kartoitettu tuotannon kannalta tärkeimmät laitteet ja niiden mahdolliset vikaantumistavat. Seuraavaksi on valittu sopivat kunnonvalvontamenetelmät ja tehty mittaussuunnitelma, jossa on esitetty eri laitteille suoritettavat mittaukset ja mittausten aikavälit.Lopuksi työssä on esitelty muutama esimerkkitapaus kunnonvalvontamenetelmien käytöstä sekä kerrottu mahdollisista tulevaisuuden kehitysmahdollisuuksista.

Adaptive changes in a radial maze task: Efficient selection of baited arms with reduced foraging in senescent hooded rats

Qualitative differences in strategy selection during foraging in a partially baited maze were assessed in young and old rats. The baited and non-baited arms were at a fixed position in space and marked by a specific olfactory cue. The senescent rats did more re-entries during the first four-trial block but were more rapid than the young rats in selecting the reinforced arms during the first visits. Dissociation between the olfactory spatial cue reference by rotating the maze revealed that only few old subjects relied on olfactory cues to select the baited arms and the remainder relied mainly on the visuo-spatial cues.

Permanent magnet synchronous motor for industrial inverter applications - analysis and design

During the latest few years the need for new motor types has grown, since both high efficiency and an accurate dynamic performance are demanded in industrial applications. For this reason, new effective control systems such as direct torque control (DTC) have been developed. Permanent magnet synchronous motors (PMSM) are well suitable for new adjustable speed AC inverter drives, because their efficiency and power factor are not depending on the pole pair number and speed to the same extent as it is the case in induction motors. Therefore, an induction motor (IM) with a mechanical gearbox can often be replaced with a direct PM motor drive. Space as well as costs will be saved, because the efficiency increases and the cost of maintenance decreases as well. This thesis deals with design criterion, analytical calculation and analysis of the permanent magnet synchronous motor for both sinusoidal air-gap flux density and rectangular air-gapflux density. It is examined how the air-gap flux, flux densities, inductances and torque can be estimated analytically for salient pole and non-salient pole motors. It has been sought by means of analytical calculations for the ultimate construction for machines rotating at relative low 300 rpm to 600 rpm speeds, which are suitable speeds e.g. in Pulp&Paper industry. The calculations are verified by using Finite Element calculations and by measuring of prototype motor. The prototype motor is a 45 kW, 600 rpm PMSM with buried V-magnets, which is a very appropriate construction for high torque motors with a high performance. With the purposebuilt prototype machine it is possible not only to verify the analytical calculations but also to show whether the 600 rpm PMSM can replace the 1500 rpm IM with a gear. It can also be tested if the outer dimensions of the PMSM may be the same as for the IM and if the PMSM in this case can produce a 2.5 fold torque, in consequence of which it may be possible to achieve the same power. The thesis also considers the question how to design a permanent magnet synchronous motor for relatively low speed applications that require a high motor torqueand efficiency as well as bearable costs of permanent magnet materials. It is shown how a selection of different parameters affects the motor properties. Key words: Permanent magnet synchronous motor, PMSM, surface magnets, buried magnets

On the Reversed Brayton Cycle with High Speed Machinery

This work was carried out in the laboratory of Fluid Dynamics, at Lappeenranta University of Technology during the years 1991-1996. The research was a part of larger high speed technology development research. First, there was the idea of making high speed machinery applications with the Brayton cycle. There was a clear need to deepen theknowledge of the cycle itself and to make a new approach in the field of the research. Also, the removal of water from the humid air seemed very interesting. The goal of this work was to study methods of designing high speed machinery to the reversed Brayton cycle, from theoretical principles to practical applications. The reversed Brayton cycle can be employed as an air dryer, a heat pump or a refrigerating machine. In this research the use of humid air as a working fluid has an environmental advantage, as well. A new calculation method for the Braytoncycle is developed. In this method especially the expansion process in the turbine is important because of the condensation of the water vapour in the humid air. This physical phenomena can have significant effects on the level of performance of the application. Also, the influence of calculating the process with actual, achievable process equipment efficiencies is essential for the development of the future machinery. The above theoretical calculations are confirmed with two different laboratory prototypes. The high speed machinery concept allows one to build an application with only one rotating shaft including all the major parts: the high speed motor, the compressor and the turbine wheel. The use of oil free bearings and high rotational speed outlines give several advantages compared to conventional machineries: light weight, compact structure, safe operation andhigher efficiency at a large operational region. There are always problems whentheory is applied to practice. The calibrations of pressure, temperature and humidity probes were made with care but still measurable errors were not negligible. Several different separators were examined and in all cases the content of the separated water was not exact. Due to the compact sizes and structures of the prototypes, the process measurement was slightly difficult. The experimental results agree well with the theoretical calculations. These experiments prove the operation of the process and lay a ground for the further development. The results of this work give very promising possibilities for the design of new, commercially competitive applications that use high speed machinery and the reversed Brayton cycle.

Nitrogen replacement value of alfalfa to corn and wheat under irrigated Mediterranean conditions

In crop rotations that include alfalfa (Medicago sativa L.), agronomic and environmental concerns mean that it is important to determine the N fertilizer contribution of this legume for subsequent crops in order to help to increase the sustainability of cropping systems. To determine the N fertilizer replacement value (FRV) of a 2-yr alfalfa crop on subsequent crops of corn (Zea mays L.) followed by wheat (Triticum aestivum L.) under irrigated Mediterranean conditions, two 4-yr rotations (alfalfa-corn-wheat and corn-corn-corn-wheat) were conducted from 2001 to 2004 in a Typic Xerofluvent soil. Corn yields were compared after two years of alfalfa and a third year of corn under monoculture and wheat yields were also compared after both rotations. Corn production after alfalfa outyielded monoculture corn at all four rates of N fertilizer application analyzed (0, 100, 200 and 300 kg N/ha). The FRV of 2-yr alfalfa for corn was about 160 kg N/ha. Wheat grown after the alfalfa-corn rotation outyielded that grown after corn under monoculture at both the rates of N studied (0 and 100 kg N/ha). The FRV of alfalfa for wheat following alfalfa-corn was about 76 kg N/ha. Soil NO3 -N content after alfalfa was greater than with the corn monoculture at all rates of N fertilizer application and this higher value persisted during the second crop after alfalfa. This was probably one of the reasons for the better yields associated with the alfalfa rotation. These results make a valuable contribution to irrigated agriculture under mediterranean conditions, show reasons for interest in rotating alfalfa with corn, and explain how it is possible to make savings when applying N fertilizer.

Design and implementation of FPGA-based LQ control of active magnetic bearings

The need for high performance, high precision, and energy saving in rotating machinery demands an alternative solution to traditional bearings. Because of the contactless operation principle, the rotating machines employing active magnetic bearings (AMBs) provide many advantages over the traditional ones. The advantages such as contamination-free operation, low maintenance costs, high rotational speeds, low parasitic losses, programmable stiffness and damping, and vibration insulation come at expense of high cost, and complex technical solution. All these properties make the use of AMBs appropriate primarily for specific and highly demanding applications. High performance and high precision control requires model-based control methods and accurate models of the flexible rotor. In turn, complex models lead to high-order controllers and feature considerable computational burden. Fortunately, in the last few years the advancements in signal processing devices provide new perspective on the real-time control of AMBs. The design and the real-time digital implementation of the high-order LQ controllers, which focus on fast execution times, are the subjects of this work. In particular, the control design and implementation in the field programmable gate array (FPGA) circuits are investigated. The optimal design is guided by the physical constraints of the system for selecting the optimal weighting matrices. The plant model is complemented by augmenting appropriate disturbance models. The compensation of the force-field nonlinearities is proposed for decreasing the uncertainty of the actuator. A disturbance-observer-based unbalance compensation for canceling the magnetic force vibrations or vibrations in the measured positions is presented. The theoretical studies are verified by the practical experiments utilizing a custom-built laboratory test rig. The test rig uses a prototyping control platform developed in the scope of this work. To sum up, the work makes a step in the direction of an embedded single-chip FPGA-based controller of AMBs.

Nelitietrukin ohjausjärjestelmän suunnittelu QFD-laatutyökalua hyväksikäyttäen

Tämä työ käsittelee tuotekehitysprojektia, jonka tarkoituksena on suunnitella uusi nelitietyöntömastotrukki asiakaslähtöisesti QFD-laatutyökalua hyväksi käyttäen. Työ esittelee QFD-laatutyökalun, sekä varsinkin sen nelivaiheisen ASI:n toimintamallin. Työ antaa myös perusvalmiudet ASI:n toimintamallin käyttöön tuotekehitysprojektissa. Työssä keskitytään tarkastelemaan uuden ohjausjärjestelmän mekaanista kehittelyä. Suunnittelutyössä käytetään hyväksi ASI:n (American Supplier Institute) nelivaiheista QFD-laatutyökalua, joka on autoteollisuuden toimintatapoihin perustuva QFD-tekniikka. QFD tulee sanoista Quality Funcktion Deployment ja vapaasti suomennettuna se merkitsee asiakaslähtöinen tuotesuunnittelu. Nelivaiheinen QFD-malli koostuu seuraavista matriiseista: 1. Tuotteen suunnittelu, 2. osien suunnittelu ja kehittäminen, 3. prosessin suunnittelu sekä 4. tuotannon suunnittelu. Matriisin tulokset muodostavat aina seuraavan matriisin lähtökohdat. Ensimmäisen matriisin lähtökohdat muodostuvat asiakastarvekuvauksesta, joka saadaan haastatteluista, tutkimuksista yms. Tuotekehitysprojektissa kehitetty TEM-monitietrukki, jossa rajattomasti ympäripyöriviä tukipyöriä ohjataan CAN-väylän kautta älykkäällä ohjauslogiikalla, on markkinoilla erittäin kilpailukykyinen sekä ominaisuuksiensa että hintansa puolesta. QFD yhdessä huolellisesti analysoidun asiakastarvekuvauksen kanssa selkeyttää ja priorisoi tuotteen spesifikaation määrittelyä sekä ohjaa tuotteen kehittelyä ja tuotannollistamista. Tuotekehitysprojekti pysyy aikataulussaan ja tuotannollistamisen kynnyksellä tehtävät muutokset vähenevät selkeän jäsentelyn ansiosta.

Monitelakalanterin ulosottotelan analysointi ja kehittäminen

Työn tarkoituksena on selvittää uusien ulosottotelaratkaisujen käyttömahdollisuutta sekä levitystelojen tarvetta on-line-monitelakalanterissa. Uusia ratkaisuja tutkitaan teoreettisesti. On-line-konseptissa ajonopeus on suuri. Tällöin paperirata liikkuu sileillä teloilla yleensä ilmafilmialueella. Ilmafilmi paperiradan ja telan välissä mahdollistaa radan ja telan nopeuden riippumattomuuden toisistaan. Ilmafilmikerros toimii liukulaakerin tavoin radan ja telan välissä. Ilmafilmin muodostumiseen vaikuttavat useat muuttujat. Ilmafilmiä, sileän telan pitoa sekä ilmanpainetta radan ja telan välissä mitattiin koeajossa Metso Paper Oy:n Järvenpään WEB3000-tutkimuslaitoksessa. Saatujen teoreettisten tulosten perusteella uudet ulosottotelaratkaisut ovat mahdollisia. Ulosottotelaa voidaan pyörittää tietyissä olosuhteissa paperirataa hitaammin tai ulosottotela voidaan korvata palkkityyppisellä radankääntölaitteella. Samoin levitystelojen poisto alimmista positioista on mahdollista.