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Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03Tc). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio Srot/Strans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio Srot/Strans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the “rigid” liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5–11 GPa.

Identifying approaching bifurcations and regime transitions from observations is an important challenge in time series analysis with practical applications in many fields of science. Well-known indicators are the increase in spatial and temporal correlations. However, the performance of these indicators depends on the system under study and on the type of approaching bifurcation, and no indicator provides a reliable warning for any system and bifurcation. Here we propose an indicator that simultaneously takes into account information about spatial and temporal correlations. By performing a bivariate correlation analysis of signals recorded in pairs of adjacent spatial points, and analyzing the distribution of lag times that maximize the cross-correlation, we find that the variance of the lag distribution displays an extreme value that is a consistent early warning indicator of the approaching bifurcation. We demonstrate the reliability of this indicator using different types of models that present different types of bifurcations, including local bifurcations (transcritical, saddle-node, supercritical and subcritical Hopf), and global bifurcations. This work was funded by the Spanish Ministerio de Ciencia, Innovación y Universidades (PGC2018-099443-B-I00 ) and the ICREA ACADEMIA program of Generalitat de Catalunya.

Ensembles with long-range interactions between particles are promising for revealing strong quantum collective effects and many-body phenomena. Here we study the ground-state phase diagram of a two-dimensional Bose system with quadrupolar interactions using a diffusion Monte Carlo technique. We predict a quantum phase transition from a gas to a solid phase. The Lindemann ratio and the condensate fraction at the transition point are $\gamma=0.269(4)$ and $n_0/n=0.031(4)$, correspondingly. We observe the strong rotonization of the collective excitation branch in the vicinity of the phase transition point. Our results can be probed using state-of-the-art experimental systems of various nature, such as quasi-two-dimensional systems of quadrupolar excitons in transition metal dichalcogenide (TMD) trilayers, quadrupolar molecules, and excitons or Rydberg atoms with quadrupole moments induced by strong magnetic fields., Comment: 7 pages, 5 figures

A novel conservative level-set method for saturated liquid-vapor phase change on unstruc-tured meshes is introduced. Transport equations are discretized by the finite-volume method on col-located unstructured grids. Mass transfer promoted by thermal phase change is computed using theenergy jump condition at the interface, as a function of the temperature gradient. The fractional-stepprojection method is used for solving the pressure-velocity coupling, convective terms are discretized byunstructured flux-limiter schemes, central difference scheme is used for discretization of diffusive terms.Verification and validation cases have been undertaken to prove the accuracy and robustness of the nu-merical methods, including simulation of the Stefan problem, and film boiling on a cylindrical surface.Excellent agreement between numerical solutions against analytical solution and empirical correlationsfrom the literature is reported.

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive inter-component and repulsive intra-component interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by DMRG method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state. Finally, we identify conditions for the formation of a solitonic solution., Comment: Main text: 6 pages and 3 figures. Appendix: 2 pages and 2 figures

The design of phase boundaries has now become a consolidated strategy to improve the functional properties of piezoelectric oxides because of the unique properties that may be obtained in their vicinity. In particular, polymorphic phase boundaries (PPBs) have attracted significant interest in recent years because they represent a significant breakthrough in terms of enhanced piezoelectric activity of lead-free piezoelectric oxides. PPBs are temperature-driven phase transitions where both intrinsic and extrinsic contributions maximize, thereby enhancing the macroscopic properties of piezoelectric materials. This tutorial discusses potassium–sodium–niobate-based systems as model materials to reveal some of the most relevant advances in the design of PPBs through compositional modifications. We focus on how PPBs can be modulated by engineered doping and also discuss the direct relation between PPBs and the enhancement of piezoelectric activity. Finally, we briefly describe the main experimental techniques for detecting PPBs.

In this thesis we develop and analyse mathematical models describing phase change phenomena linked with novel technological applications. The models are based on modifications to standard phase change theory. The mathematical tools used to analyse such models include asymptotic analysis, similarity solutions, the Heat Balance Integral Method and standard numerical techniques such as finite differences. In chapters 2 and 3 we study the melting of nanoparticles. The Gibbs-Thomson relation, accounting for melting point depression, is coupled to the heat equations for the solid and liquid and the associated Stefan condition. A perturbation approach, valid for large Stefan numbers, is used to reduce the governing system of partial differential equations to a less complex one involving two ordinary differential equations. Comparison between the reduced system and the numerical solution shows good agreement. Our results reproduce interesting behaviour observed experimentally such as the abrupt melting of nanoparticles. Standard analyses of the Stefan problem impose constant physical properties, such as density or specific heat. We formulate the Stefan problem to allow for variation at the phase change and show that this can lead to significantly different melting times when compared to the standard formulation. In chapter 4 we study a mathematical model describing the solidification of supercooled liquids. For Stefan numbers larger than unity the classical Neumann solution provides an analytical expression to describe the solidification. For Stefan numbers equal or smaller than unity, the Neumann solution is no longer valid. Instead, a linear relationship between the phase change temperature and the front velocity is often used. This allows solutions for all values of the Stefan number. However, the linear relation is an approximation to a more complex, nonlinear relationship, valid for small amounts of supercooling. We look for solutions using the nonlinear relation and demonstrate the inaccuracy of the linear relation for large supercooling. Further, we show how the classical Neumann solution significantly over-predicts the solidification rate for values of the Stefan number near unity. The Stefan problem is often reduced to a 'one-phase' problem (where one of the phases is neglected) in order to simplify the analysis. When the phase change temperature is variable it has been claimed that the standard reduction loses energy. In chapters 5 and 6, we examine the one-phase reduction of the Stefan problem when the phase change temperature is time-dependent. In chapter 5 we derive a one-phase reduction of the supercooled Stefan problem, and test its performance against the solution of the two-phase model. Our model conserves energy and is based on consistent physical assumptions, unlike one-phase reductions from previous studies. In chapter 6 we study the problem from a general perspective, and identify the main erroneous assumptions of previous studies leading to one-phase reductions that do not conserve energy or, alternatively, are based on non-physical assumptions. We also provide a general one-phase model of the Stefan problem with a generic variable phase change temperature, valid for spherical, cylindrical and planar geometries., En aquesta tesi desenvolupem i analitzem models matemàtics que descriuen processos de transició de fase vinculats a noves tecnologies. Els models es basen en modificacions de la teoria estàndard de canvis de fase. Les tècniques matemàtiques per resoldre els models es basen en l'anàlisi asimptòtic, solucions autosimilars, el mètode de la integral del balanç de la calor i mètodes numèrics estàndards com ara el mètode de les diferències finites. En els capítols 2 i 3 estudiarem la transició solid-liquid d'una nanopartícula, acoblant la relació de Gibbs-Thomson, que descriu la depressió de la temperatura de fusió en una superfície corba, amb l'equació de la calor per la fase sòlida i líquida, i la condició de Stefan. Mitjançant el mètode de pertorbacions, per a valors grans del nombre de Stefan, el problema d'equacions en derivades parcials inicial és reduït a un sistema més senzill de dues equacions diferencials ordinàries. La solució del sistema reduït concorda perfectament amb la solució numèrica del sistema inicial d'equacions en derivades parcials. Els resultats confirmen la transició ultra ràpida de sòlid a líquid observada en experiments amb nanopartícules. Els anàlisis estàndards del problema de Stefan consideren propietats físiques com la densitat i el calor específic constants en la fase sòlida i líquida. En aquesta tesi, formularem el problema de Stefan relaxant la condició de densitat constant, el que portarà a diferències molt significatives en els temps totals de fusió al comparar-los amb els temps obtinguts mitjançant la formulació habitual del problema de Stefan. En el capítol 4 estudiarem un model matemàtic que descriu la solidificació de líquids sota-refredats. Per nombres de Stefan més grans que la unitat la solució clàssica de Neumann dona una expressió analítica que descriu el procés. Per valors del nombre de Stefan més petits o iguals que la unitat, la solució de Neumann no es vàlida i, habitualment, per tal de trobar solucions en aquest règim, s'estableix una relació lineal entre la temperatura de canvi de fase i la velocitat del front de solidificació. Aquesta relació lineal però, és una aproximació per sota-refredaments moderats d'una relació no lineal més complexa. En aquest capítol, buscarem solucions del problema incorporant la relació no lineal al model, i demostrarem la poca precisió a l'utilitzar l'aproximació lineal. A més a més, veurem com la solució de Neumann sobreestima de manera significativa la velocitat del procés per valors propers a la unitat. Habitualment, el problema de Stefan és simplificat a un problema d'una fase (on una de les fases es desestimada) per tal de reduir la dificultat de l'anàlisi. En casos on la temperatura de transició de fase és variable s'ha reclamat que la simplificació d'una fase del problema no conserva l'energia. En els capítols 5 i 6, examinarem les diferents reduccions d'una fase del problema de Stefan en el cas on la temperatura de transició depèn del temps. En el capítol 5 derivarem el problema de Stefan d'una fase associat a la solidificació de líquids sota-refredats, i compararem la solució del sistema resultant amb la solució del problema de Stefan estàndard de dues fases. A diferència dels models d'una fase descrits en estudis previs, el nostre model reduït conserva l'energia i està basat en suposicions físiques consistents. En el capítol 6 estudiarem el problema des d'una perspectiva més general i identificarem les suposicions errònies d'estudis previs que porten a la no conservació de l'energia o que, alternativament, estan basades en suposicions físiques poc consistents. A més a més, derivarem un model d'una fase amb temperatura de canvi de fase variable, vàlid per geometries esfèriques, cilíndriques i planes.

We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class of nonequilibrium phase transitions that characterizes a vast set of systems including conserved threshold transfer processes and stochastic sandpile models., Comment: RevTeX, 4 pages, 3 EPS figures

Avrami’s model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami’s model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov–Johnson–Mehl–Avrami transformation rate equation. The corresponding non-isothermal Kolmogorov–Johnson–Mehl–Avrami transformation rate equation differs from the one obtained under isothermal conditions only by a constant parameter, which depends only on the ratio between nucleation and growth rate activation energies. Consequently, a minor correction allows us to extend the Kolmogorov–Johnson–Mehl–Avrami transformation rate equation to continuous heating conditions.

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the physical laws. Here, we study the behavior of two basic reaction-diffusion processes ($B \to A$ and $A+B \to 2B$) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density driven phase transitions, whereas phase transition and critical points, independent of the particle density, are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic meta-populations models and agent-based models that include the complex features of real world networks., 22 pages, 4 figures. For related work and info, visit the Cx-Nets webpage at http://cxnets.googlepages.com/. Nature Physics, in press (2007)

En este trabajo se ha realizado una simulación numérica detallada del fenómeno de cambio de fase sólido-líquido, por ser esta fenomenología de gran interés en diferentes áreas industriales. La simulación realizada implica problemas de no linealidad, fuertes acoplamientos y frontera móvil. Como resultado de esto, solo para las configuraciones más simples se pueden utilizar herramientas analíticas, mientras que para resolver la mayoría de problemas de interés se requiere el uso de métodos numéricos. Estos métodos consisten en discretizar las ecuaciones que definen la fenomenología que nos ocupa en pequeñas celdas o volúmenes de control. En este estudio se ha optado por utilizar el Método de Volúmenes Finitos (FVM) para la discretización de las ecuaciones gobernantes utilizando mallas cartesianas. Se utiliza una malla desplazada; esto quiere decir que las componentes del vector velocidad se calculan en las caras de los volúmenes de control, lo que permite un acoplamiento adecuado entre la ecuación de conservación de la masa y momentum. Tanto el código como las soluciones numéricas han sido convenientemente verificados. La verificación del código consiste en comprobar que éste está libre de errores de programación y que el comportamiento de los esquemas numéricos implementados está acorde con su comportamiento teórico. Para la verificación de la solución numérica se han utilizado métodos de extrapolación de Richardson o realizando un estudio de refinamiento de malla y observando la evolución de algunas magnitudes características del problema como pueden ser la fracción de líquido en el dominio o el número de Nusselt en la pared caliente.Una vez que el código y las soluciones numéricas han sido convenientemente verificados, la validación final de la simulación del proceso es la que se obtiene de comparar los resultados predecidos con los datos experimentales.El problema de la fusión del galio en una cavidad rectangular calentada por un lado ha sido ampliamente utilizado por investigadores con el fin de evaluar los métodos numéricos para la resolución del cambio de fase. Si bien comentar que este material tiene las ventajas de que sus propiedades termofísicas están bien establecidas, que tiene una temperatura de cambio de fase cercana a la temperatura ambiente y que es un material con gran interés industrial, también presenta algunas desventajas como es el hecho de que tiene un comportamiento anisotrópico en cuanto a la conductividad térmica de la fase sólida. No obstante, el gran número de trabajos experimentales que se encuentran en la literatura relacionados con este material nos ha conducido a escoger este material para la realización de un estudio detallado del cambio de fase sólido-líquido en este trabajo.Si bien en la literatura aparece este problema con diferentes configuraciones, en este trabajo nos hemos centrado en el estudio del caso en que la relación de aspecto (alto/ancho) es de 0,5.Existen diferentes métodos numéricos pararesolver problemas de cambio de fase sólido líquido: métodos que siguen la frontera móvil, métodos que fijan la frontera móvil, etc. En este trabajo utilizaremos el Método Entálpico pues nos permite utilizar una malla fija en todo el dominio, la condición de Stefan queda impuesta de manera implícita, permite la coexistencia de más de un frente de cambio de fase y permite que la interfase tenga un cierto grosor. El caso que nos ocupa tiene la singularidad de encontrarse en un rango de Prandtl muy bajo. Esto provoca que se alcance el régimen turbulento para números de Rayleigh relativamente bajos. Esto nos ha hecho pensar sobre la conveniencia de realizar un estudio más detallado para determinar para que valor de Rayleigh se produce la transición de régimen permanente a flujo oscilatorio y de éste a un régimen caótico. Los problemas que han ido surgiendo a lo largo de la realización de este trabajo nos han conducido a la utilización del método multibloc, también conocido como método de descomposición de subdominios. El método se emplea considerando flujos incompresibles y mallas desplazadas. En este trabajo se explicarán las modificaciones que han sido necesarias para la utilización de este método en la fenomenología del cambio de fase sólido líquido. Se han utilizado dos aproximaciones: una conservativa y otra basada en la presión. Para la obtención de la solución de referencia se ha empleado los métodos de subdominios basados en la presión, pues con el método conservativo se han observado discrepancias entre la solución obtenida con un único subdominio y la obtenida con varios subdominios. Finalmente, se ha realizado un estudio parámetrico del caso, para el cual se han considerado diferentes relaciones de aspecto, diferentes condiciones de contorno y variaciones de ±10% en las propiedades termofísicas con respecto al caso de referencia, con el objetivo de ver como afectan estas modificaciones sobre la fenomenología que nos ocupa., In this thesis a detailed numerical simulation of liquid-solid phase change phenomena has been made, because this phenomenology is of great interest in different industrial areas. The simulation done implies problems of nonlinearity, strong couplings and movable interphase. Like a result, only for the simplest configurations analytical tools can be used, whereas to solve the most of interest problems numerical methods are needed. These methods consist in the discretisation of the equations that define the phenomenology in small cells or control volumes. In this study the Finite Volume Method (FVM) has been used for the governing equations discretisation using Cartesian meshes. A displaced mesh is used; this means that the components of the speed vector are calculated in the faces of the control volumes, which allows a correct coupling between the continuity and momentum equations. So the code as the numerical solutions have been properly verified. The code verification consist of verifying that this is free of programming errors and that the behaviour of the numerical schemes is agreed with the theoretical one. For the verification of the numerical solution the Richardson Extrapolation Method or a mesh refinement study have been used. Once the code and the numerical solutions have been properly verified, the final validation of the process simulation is obtained comparing the numerical results with experimental ones.The Gallium melting problem in a square cavity heated by a side has been widely used by investigators with the objective of evaluatingthe numerical methods used for solving the phase change phenomena. Although this material have the advantages of its thermophysical properties are well established, the phase change temperature is near the room temperature and is a material with a great industrial interest, also presents some disadvantages like having an anisotropic thermal conductivity of the solid phase. However, the great number of experimental works that can been found in the literature, lead us to choose this material for doing a detailed study of the solid liquid phase change in this work. Although in the literature this problem appears with different configurations, in this thesis we have centered in the study of the case with an aspect ratio (height/width) of 0.5. Different numerical methods exist to solve solid-liquid phase change problems: methods that follow the moving interphase, methods that fix the moving interphase, etc. In this work we have used the Enthalpy Method because it allows us to use a fixed mesh in all the domain, the Stefan condition is imposed implicitly, it allows the coexistence of more than one front of phase change and allows the interphase has a thickness.This case has the singularity of being in a low Prandtl number range. This causes that a turbulent state has been reached for relatively low Rayleigh numbers. This has made think us on the convenience of making a detailed study to determine the transition of permanent regime to oscillating flow and from oscillating flow to chaotic regime. The problems than have been found in the accomplishment of this work have lead us to the use of multiblock method. This method is used considering incompressible flows and moved meshes. We will explain the modifications that have been necessary for using this method in the phase change phenomena. Two approaches have been used: a conservative one and a pressure based one. For obtaining the reference solution has been use the pressure based method, because the conservative method presents discrepancies between the obtained solution with an only subdomain and the obtained with several subdomains. Finally, a parametric study has been done, considering different aspect ratios, boundary conditions and variations of ±10% in the thermophysical properties with respect to the reference case, with the objective to see as these changes affect on the phenomenology that occupies to us.

We review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to exhibit an absorbing state transition with critical properties coinciding with those of the corresponding sandpile model. We propose a set of Langevin equations capturing the relevant features of this transition. These equations characterize the universality class of systems with an infinite number of absorbing states and a static conserved field coupled to the order parameter. Different models in this class are identified, and strong evidence is presented showing that the Manna sandpile, as well as some other stochastic sandpiles, belong in this universality class. Finally some open problems and questions are discussed., Comment: 10 pages. Latex (aipproc.sty). To appear in the Proceedings of the 6th Granada Seminar on Computational Physics, Ed. J. Marro and P. L. Garrido, American Institute of Physics, 2001

Understanding the glass transition requires getting the picture of the dynamical processes that intervene in it. Glass-forming liquids show a characteristic decoupling of relaxation processes when they are cooled down towards the glassy state. The faster (βJG) process is still under scrutiny, and its full explanation necessitates information at the microscopic scale. To this aim, nuclear γ-resonance time-domain interferometry (TDI) has been utilized to investigate 5-methyl-2-hexanol, a hydrogen-bonded liquid with a pronounced βJG process as measured by dielectric spectroscopy. TDI probes in fact the center-of-mass, molecular dynamics at scattering-vectors corresponding to both inter- and intra-molecular distances. Our measurements demonstrate that, in the undercooled liquid phase, the βJG relaxation can be visualized as a spatially-restricted rearrangement of molecules within the cage of their closest neighbours accompanied by larger excursions which reach out at least the inter-molecular scale and are related to cage-breaking events. In-cage rattling and cage-breaking processes therefore coexist in the βJG relaxation.