Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Simulation of interface dynamics across pore discontinuities

We study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous

Information sharing and social network dynamics : a coevolutionary approach

The capacity to interact socially and share information underlies the success of many animal species, humans included. Researchers of many fields have emphasized the evo¬lutionary significance of how patterns of connections between individuals, or the social networks, and learning abilities affect the information obtained by animal societies. To date, studies have focused on the dynamics either of social networks, or of the spread of information. The present work aims to study them together. We make use of mathematical and computational models to study the dynamics of networks, where social learning and information sharing affect the structure of the population the individuals belong to. The number and strength of the relationships between individuals, in turn, impact the accessibility and the diffusion of the shared information. Moreover, we inves¬tigate how different strategies in the evaluation and choice of interacting partners impact the processes of knowledge acquisition and social structure rearrangement. First, we look at how different evaluations of social interactions affect the availability of the information and the network topology. We compare a first case, where individuals evaluate social exchanges by the amount of information that can be shared by the partner, with a second case, where they evaluate interactions by considering their partners' social status. We show that, even if both strategies take into account the knowledge endowments of the partners, they have very different effects on the system. In particular, we find that the first case generally enables individuals to accumulate higher amounts of information, thanks to the more efficient patterns of social connections they are able to build. Then, we study the effects that homophily, or the tendency to interact with similar partners, has on knowledge accumulation and social structure. We compare the case where individuals who know the same information are more likely to learn socially from each other, to the opposite case, where individuals who know different information are instead more likely to learn socially from each other. We find that it is not trivial to claim which strategy is better than the other. Depending on the possibility of forgetting information, the way new social partners can be chosen, and the population size, we delineate the conditions for which each strategy allows accumulating more information, or in a faster way For these conditions, we also discuss the topological characteristics of the resulting social structure, relating them to the information dynamics outcome. In conclusion, this work paves the road for modeling the joint dynamics of the spread of information among individuals and their social interactions. It also provides a formal framework to study jointly the effects of different strategies in the choice of partners on social structure, and how they favor the accumulation of knowledge in the population. - La capacité d'interagir socialement et de partager des informations est à la base de la réussite de nombreuses espèces animales, y compris les humains. Les chercheurs de nombreux domaines ont souligné l'importance évolutive de la façon dont les modes de connexions entre individus, ou réseaux sociaux et les capacités d'apprentissage affectent les informations obtenues par les sociétés animales. À ce jour, les études se sont concentrées sur la dynamique soit des réseaux sociaux, soit de la diffusion de l'information. Le présent travail a pour but de les étudier ensemble. Nous utilisons des modèles mathématiques et informatiques pour étudier la dynamique des réseaux, où l'apprentissage social et le partage d'information affectent la structure de la population à laquelle les individus appartiennent. Le nombre et la solidité des relations entre les individus ont à leurs tours un impact sur l'accessibilité et la diffusion de l'informa¬tion partagée. Par ailleurs, nous étudions comment les différentes stratégies d'évaluation et de choix des partenaires d'interaction ont une incidence sur les processus d'acquisition des connaissances ainsi que le réarrangement de la structure sociale. Tout d'abord, nous examinons comment des évaluations différentes des interactions sociales influent sur la disponibilité de l'information ainsi que sur la topologie du réseau. Nous comparons un premier cas, où les individus évaluent les échanges sociaux par la quantité d'information qui peut être partagée par le partenaire, avec un second cas, où ils évaluent les interactions en tenant compte du statut social de leurs partenaires. Nous montrons que, même si les deux stratégies prennent en compte le montant de connaissances des partenaires, elles ont des effets très différents sur le système. En particulier, nous constatons que le premier cas permet généralement aux individus d'accumuler de plus grandes quantités d'information, grâce à des modèles de connexions sociales plus efficaces qu'ils sont capables de construire. Ensuite, nous étudions les effets que l'homophilie, ou la tendance à interagir avec des partenaires similaires, a sur l'accumulation des connaissances et la structure sociale. Nous comparons le cas où des personnes qui connaissent les mêmes informations sont plus sus¬ceptibles d'apprendre socialement l'une de l'autre, au cas où les individus qui connaissent des informations différentes sont au contraire plus susceptibles d'apprendre socialement l'un de l'autre. Nous constatons qu'il n'est pas trivial de déterminer quelle stratégie est meilleure que l'autre. En fonction de la possibilité d'oublier l'information, la façon dont les nouveaux partenaires sociaux peuvent être choisis, et la taille de la population, nous déterminons les conditions pour lesquelles chaque stratégie permet d'accumuler plus d'in¬formations, ou d'une manière plus rapide. Pour ces conditions, nous discutons également les caractéristiques topologiques de la structure sociale qui en résulte, les reliant au résultat de la dynamique de l'information. En conclusion, ce travail ouvre la route pour la modélisation de la dynamique conjointe de la diffusion de l'information entre les individus et leurs interactions sociales. Il fournit également un cadre formel pour étudier conjointement les effets de différentes stratégies de choix des partenaires sur la structure sociale et comment elles favorisent l'accumulation de connaissances dans la population.

Roles of astrocytic sodium dynamics in the neurometabolic coupling : a study by cellular imaging

RESUME LARGE PUBLIC Le système nerveux central est principalement composé de deux types de cellules :les neurones et les cellules gliales. Ces dernières, bien que l'emportant en nombre sur les neurones, ont longtemps été considérées comme des cellules sans intérêts par les neuroscientifiques. Hors, les connaissances modernes à leurs sujets indiquent qu'elles participent à la plupart des tâches physiologiques du cerveau. Plus particulièrement, elles prennent part aux processus énergétiques cérébraux. Ceux-ci, en plus d'être vitaux, sont particulièrement intrigants puisque le cerveau représente seulement 2 % de la masse corporelle mais consomme environ 25 % du glucose (substrat énergétique) corporel. Les astrocytes, un type de cellules gliales, jouent un rôle primordial dans cette formidable utilisation de glucose par le cerveau. En effet, l'activité neuronale (transmission de l'influx nerveux) est accompagnée d'une augmentation de la capture de glucose, issu de la circulation sanguine, par les astrocytes. Ce phénomène est appelé le «couplage neurométabolique » entre neurones et astrocytes. L'ion sodium fait partie des mécanismes cellulaires entrant en fonction lors de ces processus. Ainsi, dans le cadre de cette thèse, les aspects dynamiques de la régulation du sodium astrocytaire et leurs implications dans le couplage neurométabolique ont été étudiés par des techniques d'imagerie cellulaires. Ces études ont démontré que les mitochondries, machineries cellulaires convertissant l'énergie contenue dans le glucose, participent à la régulation du sodium astrocytaire. De plus, ce travail de thèse a permis de découvrir que les astrocytes sont capables de se transmettre, sous forme de vagues de sodium se propageant de cellules en cellules, un message donnant l'ordre d'accroître leur consommation d'énergie. Cette voie de signalisation leur permettrait de fournir de l'énergie aux neurones suite à leur activation. RESUME Le glutamate libéré dans la fente synaptique pendant l'activité neuronale, est éliminé par les astrocytes environnants. Le glutamate est co-transporté avec des ions sodiques, induisant une augmentation intracellulaire de sodium (Na+i) dans les astrocytes. Cette élévation de Na+i déclenche une cascade de mécanismes moléculaires qui aboutissent à la production de substrats énergétiques pouvant être utilisés par les neurones. Durant cette thèse, la mesure simultanée du sodium mitochondrial (Na+mit) et cytosolique par des techniques d'imagerie utilisant des sondes fluorescentes spécifiques, a indiqué que les variations de Na+i induites par le transport du glutamate sont transmises aux mitochondries. De plus, les voies d'entrée et de sortie du sodium mitochondrial ont été identifiées. L'échangeur de Na+ et de Ca2+ mitochondrial semble jouer un rôle primordial dans l'influx de Na+mit, alors que l'efflux de Na+mit est pris en charge par l'échangeur de Na+ et de H+ mitochondrial. L'étude du Na+mit a nécessité l'utilisation d'un système de photoactivation. Les sources de lumière ultraviolette (UV) classiques utilisées à cet effet (lasers, lampes à flash) ayant plusieurs désavantages, une alternative efficace et peu coûteuse a été développée. Il s'agit d'un système compact utilisant une diode électroluminescente (LED) à haute puissance et de longueur d'onde de 365nm. En plus de leurs rôles dans le couplage neurométabolique, les astrocytes participent à la signalisation multicellulaire en transmettant des vagues intercellulaires de calcium. Ce travail de thèse démontre également que des vagues intercellulaires de sodium peuvent être évoquées en parallèle à ces vagues calciques. Le glutamate, suite à sa libération par un mécanisme dépendent du calcium, est réabsorbé par les transporteurs au glutamate. Ce mécanisme a pour conséquence la génération de vagues sodiques se propageant de cellules en cellules. De plus, ces vagues sodiques sont corrélées spatialement avec une consommation accrue de glucose par les astrocytes. En conclusion, ce travail de thèse a permis de montrer que le signal sodique astrocytaire, déclenché en réponse au glutamate, se propage à la fois de façon intracellulaire aux mitochondries et de façon intercellulaire. Ces résultats suggèrent que les astrocytes fonctionnent comme un réseau de cellules nécessaire au couplage énergétique concerté entre neurones et astrocytes et que le sodium est un élément clé dans les mécanismes de signalisations cellulaires sous-jacents. SUMMARY Glutamate, released in the synaptic cleft during neuronal activity, is removed by surrounding astrocytes. Glutamate is taken-up with Na+ ions by specific transporters, inducing an intracellular Na+ (Na+i) elevation in astrocytes which triggers a cascade of molecular mechanisms that provides metabolic substrates to neurons. Thus, astrocytic Na+i homeostasis represents a key component of the so-called neurometabolic coupling. In this context, the first part of this thesis work was aimed at investigating whether cytosolic Na+ changes are transmitted to mitochondria, which could therefore influence their function and contribute to the overall intracellular Na+ regulation. Simultaneous monitoring of both mitochondrial Na+ (Na+mit) and cytosolic Na+ changes with fluorescent dyes revealed that glutamate-evoked cytosolic Na+ elevations are indeed transmitted to mitochondria. The mitochondrial Na+/Ca2+ exchangers have a prominent role in the regulation of Na+mit influx pathway, and Na+mit extrusion appears to be mediated by Na+/H+ exchangers. To demonstrate the implication of Na+/Ca2+ exchangers, this study has required the technical development of an UV-flash photolysis system. Because light sources for flash photolysis have to be powerful and in the near UV range, the use of UV lasers or flash lamps is usually required. As an alternative to these UV sources that have several drawbaks, we developped a compact, efficient and lowcost flash photolysis system which employs a high power 365nm light emitting diode. In addition to their role in neurometabolic coupling, astrocytes participate in multicellular signaling by transmitting intercellular Ca2+ waves. The third part of this thesis show that intercellular Na+ waves can be evoked in parallel to Ca2+ waves. Glutamate released by a Ca2+ wave-dependent mechanism is taken up by glutamate transporters, resulting in a regenerative propagation of cytosolic Na+ increases. Na+ waves in turn lead to a spatially correlated increase in glucose uptake. In conclusion, the present thesis demonstrates that glutamate-induced Na+ changes occurring in the cytosol of astrocytes propagate to both the mitochondrial matrix and the astrocytic network. These results furthermore support the view that astrocytic Na+ is a signal coupled to the brain energy metabolism.

Organic matter processing and soil evolution in a braided river system

Traditionally, braided river research has considered flow, sediment transport processes and, recently, vegetation dynamics in relation to river morphodynamics. However, if considering the development of woody vegetated patches over a time scale of decades, we must consider the extent to which soil forming processes, particularly related to soil organic matter, impact the alluvial geomorphic-vegetation system. Here we quantify the soil organic matter processing (humification) that occurs on young alluvial landforms. We sampled different geomorphic units, ranging from the active river channel to established river terraces in a braided river system. For each geomorphic unit, soil pits were used to sample sediment/soil layers that were analysed in terms of grain size (<2mm) and organic matter quantity and quality (RockEval method). A principal components analysis was used to identify patterns in the dataset. Results suggest that during the succession from bare river gravels to a terrace soil, there is a transition from small amounts of external organic matter supply provided by sedimentation processes (e.g. organic matter transported in suspension and deposited on bars), to large amounts of autogenic in situ organic matter production due to plant colonisation. This appears to change the time scale and pathways of alluvial succession (bio-geomorphic succession). However, this process is complicated by: the ongoing possibility of local sedimentation, which can serve to isolate surface layers via aggradation from the exogenic supply; and erosion which tends to create fresh deposits upon which organic matter processing must re-start. The result is a complex pattern of organic matter states as well as a general lack of any clear chronosequence within the active river corridor. This state reflects the continual battle between deposition events that can isolate organic matter from the surface, erosion events that can destroy accumulating organic matter and the early ecosystem processes necessary to assist the co-evolution of soil and vegetation. A key question emerges over the extent to which the fresh organic matter deposited in the active zone is capable of significantly transforming the local geochemical environment sufficiently to accelerate soil development.

Horizontal vestibulo-ocular reflex dynamics in acute vestibular neuritis and viral labyrinthitis: evidence of otolith-canal interaction.

OBJECTIVE: To evaluate the dynamic properties of the horizontal vestibulo-ocular reflex (h-VOR) in the acute stage of two common labyrinthine diseases that provoke severe attacks of vertigo with spontaneous nystagmus: vestibular neuritis (vestibular loss alone) and viral labyrinthitis (cochleovestibular loss). MATERIAL AND METHODS: Sixty-three patients were investigated: 42 were diagnosed with vestibular neuritis and 21 with viral labyrinthitis. The h-VOR function was evaluated by conventional caloric and impulsive testing. A simplified model of vestibular function was used to analyze the vestibulo-ocular response to rotational stimulation. RESULTS: The results showed a significant difference in h-VOR characteristics between the two pathologies. Patients with vestibular neuritis exhibited a strong horizontal semicircular canal deficit, but no h-VOR asymmetry between the two rotational directions. In contrast, patients with viral labyrinthitis demonstrated moderate canal paresis and a marked h-VOR deficit in rotation toward the affected ear. CONCLUSION: These findings support the hypothesis that the h-VOR dynamic asymmetry that occurs after an acute unilateral inner ear lesion is not due to canal dysfunction alone, but involves complex adaptive changes in the central VOR that may implicate the otolith system. Based on histopathologic and clinical differences in the two pathologies reported in the literature, we postulate that this otolith-canal interaction is mainly linked to the loss of saccular function.

Silene as a model system in ecology and evolution.

The genus Silene, studied by Darwin, Mendel and other early scientists, is re-emerging as a system for studying interrelated questions in ecology, evolution and developmental biology. These questions include sex chromosome evolution, epigenetic control of sex expression, genomic conflict and speciation. Its well-studied interactions with the pathogen Microbotryum has made Silene a model for the evolution and dynamics of disease in natural systems, and its interactions with herbivores have increased our understanding of multi-trophic ecological processes and the evolution of invasiveness. Molecular tools are now providing new approaches to many of these classical yet unresolved problems, and new progress is being made through combining phylogenetic, genomic and molecular evolutionary studies with ecological and phenotypic data.

Ising critical behavior of a non-Halmiltonian lattice system

We study steady states in d-dimensional lattice systems that evolve in time by a probabilistic majority rule, which corresponds to the zero-temperature limit of a system with conflicting dynamics. The rule satisfies detailed balance for d=1 but not for d>1. We find numerically nonequilibrium critical points of the Ising class for d=2 and 3.

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

A quantitative analysis of L-glutamate-regulated Na+ dynamics in mouse cortical astrocytes: implications for cellular bioenergetics.

The mode of Na+ entry and the dynamics of intracellular Na+ concentration ([Na+]i) changes consecutive to the application of the neurotransmitter glutamate were investigated in mouse cortical astrocytes in primary culture by video fluorescence microscopy. An elevation of [Na+]i was evoked by glutamate, whose amplitude and initial rate were concentration dependent. The glutamate-evoked Na+ increase was primarily due to Na+-glutamate cotransport, as inhibition of non-NMDA ionotropic receptors by 6-cyano-7-nitroquinoxiline-2,3-dione (CNQX) only weakly diminished the response and D-aspartate, a substrate of the glutamate transporter, produced [Na+]i elevations similar to those evoked by glutamate. Non-NMDA receptor activation could nevertheless be demonstrated by preventing receptor desensitization using cyclothiazide. Thus, in normal conditions non-NMDA receptors do not contribute significantly to the glutamate-evoked Na+ response. The rate of Na+ influx decreased during glutamate application, with kinetics that correlate well with the increase in [Na+]i and which depend on the extracellular concentration of glutamate. A tight coupling between Na+ entry and Na+/K+ ATPase activity was revealed by the massive [Na+]i increase evoked by glutamate when pump activity was inhibited by ouabain. During prolonged glutamate application, [Na+]i remains elevated at a new steady-state where Na+ influx through the transporter matches Na+ extrusion through the Na+/K+ ATPase. A mathematical model of the dynamics of [Na+]i homeostasis is presented which precisely defines the critical role of Na+ influx kinetics in the establishment of the elevated steady state and its consequences on the cellular bioenergetics. Indeed, extracellular glutamate concentrations of 10 microM already markedly increase the energetic demands of the astrocytes.

Temporal dynamics of auditory what and where processing in humans

Recent evidence suggests the human auditory system is organized,like the visual system, into a ventral 'what' pathway, devoted toidentifying objects and a dorsal 'where' pathway devoted to thelocalization of objects in space w1x. Several brain regions have beenidentified in these two different pathways, but until now little isknown about the temporal dynamics of these regions. We investigatedthis issue using 128-channel auditory evoked potentials(AEPs).Stimuli were stationary sounds created by varying interaural timedifferences and environmental real recorded sounds. Stimuli ofeach condition (localization, recognition) were presented throughearphones in a blocked design, while subjects determined theirposition or meaning, respectively.AEPs were analyzed in terms of their topographical scalp potentialdistributions (segmentation maps) and underlying neuronalgenerators (source estimation) w2x.Fourteen scalp potential distributions (maps) best explained theentire data set.Ten maps were nonspecific (associated with auditory stimulationin general), two were specific for sound localization and two werespecific for sound recognition (P-values ranging from 0.02 to0.045).Condition-specific maps appeared at two distinct time periods:;200 ms and ;375-550 ms post-stimulus.The brain sources associated with the maps specific for soundlocalization were mainly situated in the inferior frontal cortices,confirming previous findings w3x. The sources associated withsound recognition were predominantly located in the temporal cortices,with a weaker activation in the frontal cortex.The data show that sound localization and sound recognitionengage different brain networks that are apparent at two distincttime periods.References1. Maeder et al. Neuroimage 2001.2. Michel et al. Brain Research Review 2001.3. Ducommun et al. Neuroimage 2002.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Relation between sequence and structure of HIV-1 protease inhibitor complexes: a model system for the analysis of protein flexibility.

The flexibility of different regions of HIV-1 protease was examined by using a database consisting of 73 X-ray structures that differ in terms of sequence, ligands or both. The root-mean-square differences of the backbone for the set of structures were shown to have the same variation with residue number as those obtained from molecular dynamics simulations, normal mode analyses and X-ray B-factors. This supports the idea that observed structural changes provide a measure of the inherent flexibility of the protein, although specific interactions between the protease and the ligand play a secondary role. The results suggest that the potential energy surface of the HIV-1 protease is characterized by many local minima with small energetic differences, some of which are sampled by the different X-ray structures of the HIV-1 protease complexes. Interdomain correlated motions were calculated from the structural fluctuations and the results were also in agreement with molecular dynamics simulations and normal mode analyses. Implications of the results for the drug-resistance engendered by mutations are discussed briefly.

Experimental insights into deformation dynamics and intermittency in rapid granular shear flows

This work concerns the experimental study of rapid granular shear flows in annular Couette geometry. The flow is induced by continuous driving of the horizontal plate at the top of the granular bed in an annulus. The compressive pressure, driving torque, instantaneous bed height and rotational speed of the shearing plate are measured. Moreover, local stress fluctuations are measured in a medium made of steel spheres 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity in intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of spherical steel balls. The shearing granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus using a piezoelectric sensor. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations are then investigated by different means through monodisperse and bidisperse packings. Another important feature of rapid granular shear flows is the formation of ordered structures upon shearing. It requires a certain range for the amount of granular material (uniform size distribution) loaded in the system in order to obtain stable flows. This is studied more deeply in this thesis. The results of the current work bring some new insights into deformation dynamics and intermittency in rapid granular shear flows. The experimental apparatus is modified in comparison to earlier investigations. The measurements produce data for various quantities continuously sampled from the start of shearing to the end. Static failure and dynamic shearing ofa granular medium is investigated. The results of this work revealed some important features of failure dynamics and structure formation in the system. Furthermore, some computer simulations are performed in a 2D annulus to examine the nature of kinetic energy dissipation. It is found that turbulent flow models can statistically represent rapid granular flows with high accuracy. In addition to academic outcomes and scientific publications our results have a number of technological applications associated with grinding, mining and massive grain storages.

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)10.1088/1751-8113/44/39/395004]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.