Seminars 2018

In mathematics, the metric $g$ and the affine connection $\Gamma$ of a manifold are two independent fields, each with their own mathematical structure. However, for every metric $g$, there is a special connection $\mathring \Gamma$, called the Levi-Civita connection, which is entirely determined as a function of $g$. In Riemannian geometry and standard General Relativity, the geometrical properties of spacetime are described using this Levi-Civita connection. However, one version of modified theories of gravity is to consider other possible affine connections and investigate their dynamics and their physical influences. This class of theories are usually called metric-affine gravities, the first-order formalism or the Palatini formalism. In this talk we will investigate the Palatini formalism for the Einstein-Hilbert action, Einstein-Dirac theory and the Gauss-Bonnet action and point out its relation to the projective symmetries of these actions.

It is well known that universality does not hold in general in antiferromagnetic (AF) models: the phase diagram depends strongly on the microscopic structure of the lattice. However, for the two-dimensional q-state Potts model, some sort of universal behavior can be recovered, at least for some classes of lattices and certain values of q. In this talk, I will introduce some unusual and interesting properties of Potts AF such as non-zero ground-state entropy density (without frustration!) and the existence of zero-temperature critical points and height representations for certain models. These ideas will be needed in order to understand a recent conjecture that predicts the universality class of the 3-state Potts AF on (periodic) plane quadrangulations.

Random number generators (RNG) are key in many areas: data security, numerical simulations, online games of chance, etc. Classical generators can be either insecure or slow. Recent solutions that avoid both problems include doped weakly coupled semiconductor superlattices which, operated at room temperature [1] can produce spontaneous chaotic oscillations. This can be exploited to generate true random numbers fast enough and with little post-processing.
Under DC voltage bias, idealized superlattices [2] show self-sustained chaotic behavior for certain voltage intervals. If external and internal noise is taken into account, these voltage intervals can be made broader and the chaotic response enhanced. Thus, establishing superlattices as a robust physical entropy source.
Another feature seen both in experiments [3] and numerical simulations [4] is coherence resonance: external band limited voltage noise of sufficient amplitude induces regular current self-oscillations in states that are stationary in the absence of noise. Furthermore, when a weak AC voltage signal is applied, coherence resonance triggers a stochastic resonance. That is, the current response is both phase locked to the AC signal and amplified, in the sense of a higher signal to noise ratio.

[1] ‍ W. Li, I. Reidler, Y. Aviad, Y. Huang, H. Song, Y. Zhang, M. Rosenbluth and I. Kanter, Phys. Rev. Lett. 111 044102 (2013)
[2] ‍ M. Alvaro, M. Carretero, and L.L. Bonilla, Europhys. Lett. 107, 37002 (2014)
[3] ‍ Z. Shao, Z. Yin, H. Song, W. Liu, X. Li, J. Zhu, K. Biermann, L.L. Bonilla, H.T. Grahn, and Y. Zhang, Phys. Rev. Lett. 121 086806 (2018)
[4] ‍ E. Mompo, M. Ruiz-Garcia, M. Carretero, H.T. Grahn, Y. Zhang, and L.L. Bonilla, Phys. Rev. Lett. 121 086805 (2018)

Microrheology was introduced more than 20 years ago as a novel technique to measure the viscosity at microscopic scales. Here, a colloidal tracer is introduced in the sample, and its dynamics is monitored as it explores the bath. When no external force acts on the tracer, so-called passive microrheology, it diffuses freely and the system is in equilibrium; on the other hand, when an external force drives the tracer, the system falls out of equilibrium. In the latter case, an effective friction coefficient can be obtained from the steady-state relation $F_\text{ext}=\gamma_\text{eff}\, \langle v \rangle$. For a viscoelastic medium, this coefficient is constant for small forces (within the linear regime) and decreases as the force increases (force-thinning regime). However, studying the dynamics of the tracer provides much more information than just the friction coefficient; it reflects the bath dynamics in the linear regime, and a complicated interaction of the pulled tracer and bath dynamics for large forces.
In this talk, we will present simulations from Langevin dynamics simulations of quasi-hard colloidal spheres (see snapshot). We focus on the behaviour of the probe particle for increasing volume fraction of the host fluid, up to densities beyond the glass transition. The effective friction coefficient, as well as other dynamical quantities are studied and compared with a theoretical model based on the mode-coupling approximation to describe the bath dynamics. Beyond the glass transition, a localized regime is found for small forces, where the tracer is trapped. The tracer breaks free beyond a critical force, entering an intriguing super-diffusive behaviour. Finally, we will study the connection between microrheology and bulk rheology using a "large" tracer.
 

El fenómeno de la vida envuelve varias escalas de tamaño: desde las moléculas hasta los objetos que manejamos con nuestras manos. Pero la vida va más allá de las descripciones fenomenológicas o de las explicaciones químicas, que cubren buena parte del conocimiento básico que tenemos hasta hoy: la vida obedece a las leyes de la Física, como cualquier otro proceso en el universo. La vida se desarrolla fuera del equilibrio termodinámico e implica el consumo de energía química, principalmente, y la producción de actividades diversas que van desde el trabajo mecánico hasta el procesamiento de información. Por último, y no menos relevante en nuestros días, la vida supone un paradigma para la Nanotecnología puesto que la maquinaria que hace funcionar a una célula o a un virus es de sólo unos cuantos nanómetros.
En esta charla nos adentraremos en el estudio de dicha maquinaria nanoscópica desde los puntos de vista del físico y del ingeniero, y presentaremos las metodologías experimentales que en los últimos veinte años nos están permitiendo manipular y medir la actividad de los constituyentes fundamentales de la materia animada. Exploraremos, a continuación, las nanopartículas, que posibilitan el control de fenómenos estímulo-respuesta en medios fisiológicos y en escalas biomoleculares, y que, por tanto, resuenan en Nanomedicina. Por último, hablaremos del software en nuestras células, así como del hardware implicado en el procesamiento de la información genética. En lo segundo, nos centraremos en la mecano-química de los motores biomoleculares, que los dota de una eficiencia termodinámica muy por encima de la de los motores macroscópicos, y en los mecanismos de transferencia de información de alta fidelidad, que permiten conciliar el mantenimiento de la identidad genética con la evolución y adaptabilidad de las especies.
El conjunto nos acercará a la imagen moderna que la Nanociencia proyecta sobre el fenómeno de la vida y a la investigación en Biología como fuente de inspiración en Nanotecnología.

Active matter represents a fundamentally new nonequilibrium regime within statistical mechanics. In contrast to traditional nonequilibrium systems, where directional driving forces emerge as a result of global changes in the thermodynamic variables (such as temperature and pressure), active systems are intrinsically out of equilibrium at the single-particle level. In our recent work, we have focused on studying the collective behaviour and assembly in dilute suspensions of spherical self-propelled particles, unraveling the role played by the particle-particle interactions (whether short-range or long-range, isotropic or anisotropic) and by the hydrodynamics.

In this talk I will present some recent results on the thermodynamic properties of a series of minerals that are important constituents of the Earth's mantle. Beyond presenting those results and describing the techniques used to obtain them, I will aim to illustrate the fact that there are many interesting questions relevant to the fields of geology and geophysics that are ultimately materials questions, questions that can begin to be addressed, if not fully at least partially, with the techniques of computational materials science.

During the airframe assembly process it is important to control both gap between joined parts and stresses caused by installed fixture elements. The main goal of the presented work is to develop special tool for numerical simulations of assembly process in order to check and optimize the assembly technology.

The main challenge for simulation the assembly process is necessity to solve the contact problem for determination of deformed stress state of the assembly loaded by the forces from fastening elements. This contact problem has some peculiarities that were taken into account in order to derive efficient algorithm: The developed mathematical model combines dimension reduction with use of state-of-the-art optimization algorithms for solving of derived quadratic programming problem.

The described above algorithm was realized in software code and thoughtfully tested in the framework of joint project between Saint Petersburg Polytechnic University and Airbus Operations S.A.S. The verification of obtained results is made against analytic solution and number of physical experiments on real aircraft junctions. Simulation results have been already successfully implemented for optimization of Airbus assembly chain. Application examples and respective challenges are to be discussed during the presentation.

Among the different competing mechanisms involved in granular segregation, thermal diffusion becomes the most relevant one when an external energy input drives the system into rapid flow conditions. In this regime, granular matter flows like a fluid and kinetic theory tools (conveniently adapted to account for the inelastic character of collisions between grains) can be quite useful to analyze thermal diffusion segregation. Thermal diffusion is caused by the relative motion of the components of a mixture due to the presence of both gravity and a temperature gradient. Due to this motion, a steady state is reached where the separation effect arising from thermal diffusion is balanced by the remixing effect of ordinary diffusion. The aim of this contribution is determine the so-called thermal diffusion factor $\Lambda$ of a moderately dense granular binary mixture (with coefficients of normal restitution $\alpha_{ij}$ for collisions between particles of species $i$ with $j$) described by the (inelastic) Enskog kinetic equation. A segregation criterion is derived from the knowledge of $\Lambda$, which is explicitly obtained in terms of the parameters of the system (masses and sizes of particles, concentration, solid volume fraction and coefficients of normal restitution) [1]. The sign of $\Lambda$ determines the tendency of the large particles to drift toward the cooler or warmer plate. To test the i reliability of the theoretical calculations, the factor $\Lambda$ is also obtained by computer simulations [Monte Carlo (DSMC) and molecular dynamics (MD) simulations] carried out for a granular impurity (species 1) in a driven low-density granular gas [2]. As an illustration, Fig. 1 shows the marginal segregation curve ($\Lambda=0$) for a system with $\alpha_{22} = 0.9$ and $\alpha_{12} = 0.7$. It is quite apparent that theory reproduces very well the phase diagram obtained from simulations.

[1] ‍ Garzó, V. Phys. Rev. E, 78, pp. 020301 (R), 2008; Eur. Phys. J. E, 29, pp. 261-274, 2009; New J. Phys., 13, pp. 055020, 2011.
[2] ‍ Vega Reyes, F., Garzó, V. and Khalil, N., Phys. Rev. E, 89, pp. 055206, 2014.

Complex material structures are inherently interesting for the curious scientific mind due to the challenge their in depth understanding constitutes. Periodicity greatly simplifies their understanding and adds interesting new properties. Self-assembled nanostructures usually develop ordered patterns in three dimensions [1]. When disorder is dominant, some interesting new phenomena may appear, as random lasing [2]. Artificial opals are one of such possible arrangements usually forming fcc structures with promising photonic properties. Often, and undesirably, unwanted defects are present spoiling the optical properties of such nanostructures [3]. On the other hand, and contrary to intuition, the introduction of arbitrarily high amounts of disorder is, in some cases, an equally difficult task but the resulting material presents intriguing new optical properties. We have grown novel nanophotonic materials, photonic glasses, which are solid, disordered assembly of monodisperse dielectric spheres [4], in which novel devices such as resonant random lasing may be observed [5].

In this talk, I will summarize our latest results regarding self-assembled photonic materials and, in particular, I will focused on the transition from order to disorder, and vice versa, when understanding self-assembly can be approached by studying colloidal crystallization.

[1] ‍ J.F. Galisteo-López, M. Ibisate, R. Sapienza, L. Froufe-Pérez, A. Blanco, and C. López, Adv. Mater. 23, 30-69 (2011).
[2] ‍ M. Leonetti, C. Conti, C. López, Nat. Photonics 5, 615 (2011).
[3] ‍ X. Checoury, S. Enoch, C. López, and A. Blanco, Appl. Phys. Lett. 90, 161131 (2007)
[4] ‍ P. D. García, R. Sapienza, A. Blanco, and C. López, Adv. Mater. 19, 2597, (2007)
[5] ‍ S. Gottardo, R. Sapienza, P. D. García, A. Blanco, D. S. Wiersma, C. López, Nat. Photonics 2008, 2, 429.

Fluctuations are strong in mesoscopic systems and have to be taken into account for the description of transport. We show that they can even be used as a resource for the operation of a system as a device. We use the physics of single-electron tunneling to propose a bipartite device [1,2] working as a thermal transistor [3]. Charge and heat currents in a two terminal conductor can be gated by thermal fluctuations from a third terminal to which it is capacitively coupled. The gate system can act as a switch that injects neither charge nor energy into the conductor hence achieving huge amplification factors. Non-thermal properties of the tunneling electrons can be exploited to operate the device with no energy consumption.

[1] ‍ R. Sánchez, M. Büttiker, Optimal energy quanta to current conversion, Phys. Rev. B 83, 085428 (2011).
[2] ‍ H. Thierschmann et al., Three-terminal energy harvester with coupled quantum dots, Nature Nanotech. 10, 854 (2015).
[3] ‍ R. Sánchez, H. Thierschmann, and L.W. Molenkamp, Phys. Rev. B 95, 241401 (2017); New J. Phys. 19, 113040 (2017).

En esta charla revisamos algunos resultados teóricos recientes que predicen el camino de desplegamiento de proteínas simples, como sistemas modulares, como función de la velocidad y la dirección de tracción. Estos resultados teóricos se obtienen a partir de una descripción mesoscópica, en que las extensiones de los distintos módulos que componen la proteína obedecen ecuaciones de evolución escolásticas (Langevin). Las predicciones de este enfoque teórico se comparan tanto con resultados experimentales como con simulaciones de Dinámica Molecular.

En esta charla se abordarán de una manera sencilla los vidrios de espín en dimensión finita. Para ello describiremos la obtención del modelo de Edwards-Anderson a partir de primeros principios. Posteriormente detallaremos las propiedades físicas de las solución en el regimen de campo medio basada en la rotura de la simetria de las réplicas y teorías alternativas como el modelo de los droplets y la de los pares caóticos. A continuación estudiaremos los problemas que presenta el límite termodinámico en estos modelos (por ejemplo, la definición de estados) y el concepto de metaestado. Finalmente presentaré resultados recientes sobre la construcción numérica del metaestado y sus implicaciones sobre las diferentes teorías que pretenden describir los vidrios de espín en dimensión finita.

Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and on several pathological scenarios such as cancer progression or diabetic retinopathy. In this seminar we will present different mathematical approaches to model sprouting angiogenesis. We will focus on the role of cell migration and cell proliferation in determining the morphology of the resulting network. We will present mathematical models that take into account the role of mechanics in regulating endothelial cell proliferation and migration. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an existing functional mature vessel or with another growing sprout. This process is called anastomosis. We will present a systematic 2D and 3D study of vessel growth in a tissue to address the capability of angiogenic factor gradients to drive anastomose formation. We will demonstrate that the production of angiogenic factors by hypoxic cells is able to promote vessel anastomoses events in both 2D and 3D. We also verify that the morphology of these networks has an increased resilience toward variations in the endothelial cell's proliferation and chemotactic response.

We review the main features of the dynamics of a quasi-2D thin granular layer. The system consists in a densely packed set of identical spheres (metallic spheres with a diameter $\sim$ 1mm) that is conned in a vibrating box. The layer is horizontal and the shaking is performed vertically. The box has a width $h \in [1.25\sigma,1.9\sigma]$ so that the geometry forbids vertical particle overlapping. We consider only sine-shaped vibration signals, with amplitude $A$ and angular frequency $\omega$ so that the input acceleration is typically greater than gravitational acceleration: $\Gamma \equiv A\omega^2/g \gt 1$. As energy input is gradually increased the system undergoes over a series of phase transitions, including a quasi-2D hexatic-like phase that can be described in the context of the KTHNY theory [1,2,3]. The observed phase diagram changes considerably as a function of the layer width $h$ and particle collision inelasticity. In fact, we show that under the appropriate conditions a suciently strong inelasticity may suppress any kind of ordering/clustering in the system.

[1] ‍ J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6 (1973) 1181.
[2] ‍ D.R. Nelson and B.I. Halperin, Phys. Rev. B 19 (1979) 2457.
[3] ‍ A.P. Young, Phys. Rev. B 19 (1979) 1855.