Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems

We study a liquid film that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We additionally assume that there is a constant temperature gradient along the plate that induces a Marangoni shear stress. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of the temperature gradient significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we obtain numerical solutions of the steady-state equation and analyse the behaviour of the solutions as the plate velocity is changed. We observe that the bifurcation curve exhibits snaking behaviour when the plate inclination angle is beyond a certain critical value. Otherwise, the bifurcation curve is monotonic. The solutions along these curves are characterised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we explain that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.Comment: Final revised version. 18 pages. To be published in Eur. Phys. J.

Analisi della funzione del gene neurale Sox2 nell'ematopoiesi

Il sistema ematopoietico si sviluppa molto precocemente durante l’ontogenesi di un organismo e permette di sostenere, per tutta la vita fetale e adulta, una continua rigenerazione delle cellule del sangue. All’apice di tale processo di rinnovamento risiedono le cellule staminali ematopoietiche (HSCs), dotate di elevata capacità autoreplicativa, proliferativa e differenziativa. Queste cellule, dividendosi, danno origine ad altre cellule staminali e/o progenitori pluripotenti che, a loro volta, generano precursori già destinati verso una specifica filiera ematopoietica. Sono stati identificati numerosi geni implicati nella regolazione della ematopoiesi, codificanti fattori di crescita e loro recettori (come Stem Cell Factor, SCF, e il suo recettore Kit) o fattori di trascrizione (per esempio gli omeogeni e i geni della famiglia GATA), che attivano o reprimono l’espressione di geni bersaglio. In questi ultimi anni, lo studio dei regolatori dello sviluppo embrionale e della differenziazione cellulare ha permesso di evidenziare l’esistenza di meccanismi molecolari comuni che controllano diversi sistemi differenziativi, in particolare l’ematopoiesi e la neurogenesi. A tale proposito, nel nostro laboratorio, abbiamo dimostrato l’importante funzione che Otx1, gene essenziale nella morfogenesi del cervello, ha nella produzione delle cellule del sangue. Attualmente la nostra attenzione è rivolta al gene Sox2 (Sry-type high-mobility-group box 2), il quale codifica un fattore di trascrizione espresso in diversi tipi di cellule staminali, come le embrionali, le germinali e le neurali. Nel nostro laboratorio è stata osservata l’espressione di Sox2, seppure a livelli molto bassi, anche nel midollo osseo murino, principale sede dell’ematopoiesi nella vita adulta. Lo scopo della mia tesi è stato quindi quello di studiare la possibile funzione di questo gene nella produzione delle cellule del sangue; utilizzando topi mutanti Sox2 knock down (dal momento che la completa inattivazione di Sox2 è letale), in cui l’espressione del gene è fortemente diminuita, a seguito della delezione di una sequenza di 2.4 Kb nella regione enhancer. A tal fine, ho analizzato le popolazioni mature attraverso esame emocromocitometrico, mentre i precursori, morfologicamente indifferenziati e rari, sono stati valutati sfruttando la loro capacità clonogenica in vitro. A livello delle cellule mature non ho evidenziato particolari variazioni nei mutanti Sox2 knock down rispetto ai controlli wild type. Al contrario, saggi clonogenici di cellule midollari di topi wild type e Sox2 knock down hanno dimostrato un significativo aumento nella frequenza dei precursori multipotenti (CFU-MIX) nei mutanti. Tale risultato è in accordo con l’osservazione, ottenuta nel nostro laboratorio, che Sox2 è espresso a livello di precursori pluripotenti primitivi, suggerendo quindi che Sox2 abbia ruolo nelle fasi precoci dell’ematopoiesi. In particolare si può quindi ipotizzare che Sox2 sia coinvolto nei meccanismi di autoreplicazione dei precursori pluripotenti e/o di una popolazione limitata di cellule a monte di questi, come le cellule staminali stesse. Per verificare la prima ipotesi, ho effettuato colture secondarie in terreno semisolido di singole colonie CFU-MIX. Anche in questo caso ho osservato un aumento significativo di CFU-Mix secondarie nei topi mutanti rispetto ai controlli wild type. Per studiare il ruolo di Sox2 a livello delle cellule staminali, ho effettuato dei saggi di ripopolazione competitiva in vivo, coiniettando cellule di midollo Sox2 knock down e cellule di midollo osseo wild type, secondo proporzioni predefinite, in animali letalmente irradiati. Questi trapianti hanno mostrato che il midollo osseo proveniente dal topo Sox2 knock down, anche se in condizioni di netto vantaggio rispetto al midollo di topi wild type, presenta un forte svantaggio ripopolativo, condizione che potrebbe essere dovuta a una diminuzione di cellule staminali nei topi mutanti. Queste osservazioni sono in accordo con quanto accade a livello del sistema nervoso, in particolare per le cellule staminali neurali, suggerendo che Sox2 sia coinvolto anche nel controllo di altri tipi di cellule staminali e/o precursori, come quelli ematopoietici

A model for a flywheel automatic assistedmanual transmission

This paper is focused on the model and dynamical analysis of a flywheel assisted transmis- sion aiming at reducing the torque gap during gear shift manoeuvres. A completely passive device, consisting of a planetary gear set mounting a flywheel on the sun gear shaft, allows to continuously connect the engine to the load shaft. Depending on the operating condi- tions, it can either absorb energy from the engine or deliver the previously stored kinetic energy to the wheels when the clutch is disengaged, thus allowing better vehicle performances and/or ride comfort through a suitable coordinated control of engine and clutc

Modelling of driven free surface liquid films

In several types of coating processes a solid substrate is removed at a controlled velocity U from a liquid bath. The shape of the liquid meniscus and the thickness of the coating layer depend on U. These dependencies have to be understood in detail for non-volatile liquids to control the deposition of such a liquid and to lay the basis for the control in more complicated cases (volatile pure liquid, solution with volatile solvent). We study the case of non-volatile liquids employing a precursor film model that describes partial wettability with a Derjaguin (or disjoining) pressure. In particular, we focus on the relation of the deposition of (i) an ultrathin precursor film at small velocities and (ii) a macroscopic film of thickness h ∝ U^(2/3) (corresponding to the classical Landau Levich film). Depending on the plate inclination, four regimes are found for the change from case (i) to (ii). The different regimes and the transitions between them are analysed employing numerical continuation of steady states and saddle-node bifurcations and simulations in time. We discuss the relation of our results to results obtained with a slip model. In connection with evaporative processes, we will study the pinning of a droplet due to a sharp corner. The approach employs an evolution equation for the height profile of an evaporating thin film (small contact angle droplet) on a substrate with a rounded edge, and enables one to predict the dependence of the apparent contact angle on the position of the contact line. The calculations confirm experimental observations, namely that there exists a dynamically produced critical angle for depinning that increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs criterion for pinning that accounts for the non-equilibrium effect of evaporation

Epicyclic gear train dynamics including mesh efficiency

The paper presents an epicyclic gear train dynamic mathematical model including mesh efficiency, bearings/seals losses and inertial effects

Correspondence in anticipation of The question concernig technology

A continuación, presentamos la traducción comentada de un intercambio epistolar entre Werner Heisenberg y Martin Heidegger: una carta fechada en octubre de 1953 que cobra importancia en tanto se relaciona estrechamente con la conferencia que Heisenberg dictaría pocos meses después y que luego aparecería referida por Heidegger en La pregunta por la técnica [Die Frage nach der Technik] (1954). Esta carta, aunque brevísima, es densa en referencias a cuestiones que aparecerían poco después en La pregunta por la técnica; cuestiones tales como el peligro que está en germen en que los aspectos científicos del mundo sean considerados como los únicos, esa “unilateralidad peligrosa” [gefährlichen Einseitigkeit]. De las poquísimas referencias en La pregunta por la técnica, las dos menciones a Heisenberg en el texto quedan en relieve. Es, por esto, interesante mostrar que antes de la publicación de La pregunta por la técnica Heidegger había debatido sobre estas cuestiones con lo más granado de la comunidad científica de su espacio y su tiempo.Herein, we present a commented translation of an epistolary exchange between Werner Heisenberg and Martin Heidegger: a letter dated October 1953, which results important in that it is closely related to the lecture that Heisenberg would deliver a few months later and which would later appear to be referred to by Heidegger in The Question Concerning Technology (Die Frage nach der Technik) (1954). This letter, although very brief, is dense in references to issues that would appear soon after in The Question Concerning Technology; questions such as the danger of the scientific aspects of the world being considered as the only ones, that "dangerous one-sidedness" (gefährlichen Einseitigkeit). Of the very few references in The Question Concerning Technology, the two references to Heisenberg are highlighted that text. It is, therefore, interesting to show that before the publication of The Question Concerning Technology, Heidegger had debated these questions with the best of the scientific community of his space and time

Dynamic unbinding transitions and deposition patterns in dragged meniscus problems

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We sketch main results of our recent work on the transfer of a thin liquid film onto a flat plate that is extracted from a bath of pure non-volatile liquid. Employing a long-wave hydrodynamic model, that incorporates wettability via a Derjaguin (disjoining) pressure, we analyse steady-state meniscus profiles as the plate velocity is changed. We identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of equilibrium unbinding transitions. The conclusion briefly discusses how the gradient dynamics formulation of the problem allows one to systematically extend the employed one-component model into thermodynamically consistent two-component models as used to describe, e.g., the formation of line patterns during the Langmuir-Blodgett transfer of a surfactant layer

Luis Santaló and classical field theory

Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950’s and the 1970’s, he wrote a series of papers on general relativity and on the attempts at generalizing Einstein’s theory to formulate a unified field theory. His main contribution in this subject was to provide a classification theorem for the plethora of tensors that were populating Einstein’s generalized theory. This paper revisits his work on theoretical physics.Fil: Galvagno, Mariano. Technion - Israel Institute of Technology; IsraelFil: Giribet, Gaston Enrique. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Abdus Salam International Centre for Theoretical Physics; Itali