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Nonadiabatic coupling between electrons and molecular motion at metal surfaces leads to energy dissipation and dynamical steering effects during chemical surface dynamics. We present a theoretical approach to the scattering of molecules from metal surfaces that incorporates all nonadiabatic and quantum nuclear effects due to the coupling of the molecular degrees of freedom to the electrons in the metal. This is achieved with the hierarchical equations of motion (HEOM) approach combined with a matrix product state representation in twin space. The method is applied to the scattering of nitric oxide from Au(111), for which strongly nonadiabatic energy loss during scattering has been experimentally observed, thus presenting a significant theoretical challenge. Since the HEOM approach treats the molecule-surface coupling exactly, it captures the interplay between nonadiabatic and quantum nuclear effects. Finally, the data obtained by the HEOM approach is used as a rigorous benchmark to assess various mixed quantum-classical methods, from which we derive insights into the mechanisms of energy dissipation and the suitable working regimes of each method.

We explore the role of molecular vibrations in the chirality-induced spin selectivity (CISS) effect in the context of charge transport through a molecular nanojunction. We employ a mixed quantum-classical approach that combines Ehrenfest dynamics for molecular vibrations with the hierarchical equations of motion method for the electronic degrees of freedom. This approach treats the molecular vibrations in a nonequilibrium manner, which is crucial for the dynamics of molecular nanojunctions. To explore the effect of vibrational dynamics on spin selectivity, we also introduce a new figure of merit, the displacement polarization, which quantifies the difference in vibrational displacements for opposing lead magnetizations. We analyze the dynamics of single trajectories, investigating how the spin selectivity depends on voltage and electronic-vibrational coupling. Furthermore, we investigate the dynamics and temperature dependence of ensemble-averaged observables. We demonstrate that spin selectivity is correlated in time with the vibrational polarization, indicating that dynamics of the molecular vibrations is the driving force of CISS in this model within the Ehrenfest approach., Comment: 13 pages, 10 figures

Electronic friction and Langevin dynamics is a popular mixed quantum-classical method for simulating the nonadiabatic dynamics of molecules interacting with metal surfaces, as it can be computationally more efficient than fully quantum approaches. Previous approaches to calculating the electronic friction and other forces, however, have been limited to either noninteracting molecular models or position-independent metal-molecule couplings. In this work, we extend the theory of electronic friction within the hierarchical equations of motion formalism to models with a position-dependent metal-molecule coupling. We show that the addition of a position-dependent metal-molecule coupling adds new contributions to the electronic friction and other forces, which are highly relevant for many physical processes. Our expressions for the electronic forces within the Langevin equation are valid both in and out of equilibrium and for molecular models containing strong interactions. We demonstrate the approach by applying it to different models of interest.

The nearby elliptical galaxy M87 contains one of the only two supermassive black holes whose emission surrounding the event horizon has been imaged by the Event Horizon Telescope (EHT). In 2018, more than two dozen multi-wavelength (MWL) facilities (from radio to gamma-ray energies) took part in the second M87 EHT campaign. The goal of this extensive MWL campaign was to better understand the physics of the accreting black hole M87*, the relationship between the inflow and inner jets, and the high-energy particle acceleration. Understanding the complex astrophysics is also a necessary first step towards performing further tests of general relativity. The MWL campaign took place in April 2018, overlapping with the EHT M87* observations. We present a new, contemporaneous spectral energy distribution (SED) ranging from radio to very high energy (VHE) gamma-rays, as well as details of the individual observations and light curves. We also conduct phenomenological modelling to investigate the basic source properties. We present the first VHE gamma-ray flare from M87 detected since 2010. The flux above 350 GeV has more than doubled within a period of about 36 hours. We find that the X-ray flux is enhanced by about a factor of two compared to 2017, while the radio and millimetre core fluxes are consistent between 2017 and 2018. We detect evidence for a monotonically increasing jet position angle that corresponds to variations in the bright spot of the EHT image. Our results show the value of continued MWL monitoring together with precision imaging for addressing the origins of high-energy particle acceleration. While we cannot currently pinpoint the precise location where such acceleration takes place, the new VHE gamma-ray flare already presents a challenge to simple one-zone leptonic emission model approaches, and emphasises the need for combined image and spectral modelling., Comment: 46 pages, 23 figures, accepted by Astronomy & Astrophysics on August. 29, 2024

A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum-classical methods based on Langevin equations to models containing strong electron-electron or quantum electronic-vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule-metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions.

Partially molten rock is a densely packed, melt-saturated, granular medium, but it has seldom been considered in these terms. In this manuscript, we extend the continuum theory of partially molten rock to incorporate the physics of granular media. Our formulation includes dilatancy in a viscous constitutive law and introduces a non-local fluidity. We analyse the resulting poro-viscous--granular theory in terms of two modes of liquid--solid segregation that are observed in published torsion experiments: localisation of liquid into high-porosity sheets and radially inward liquid flow. We show that the newly incorporated granular physics brings the theory into agreement with experiments. We discuss these results in the context of grain-scale physics across the nominal jamming fraction at the high homologous temperatures relevant in geological systems., Comment: 31 pages, 9 figures, 4 appendicies

Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid-dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community., Comment: 29 pages, 10 figures, 3 supplementary tables. Minor edits from initial submission including new figure 1

From core to atmosphere, the oxidation states of elements in a planet shape its character. Oxygen fugacity (fO$_2$) is one parameter indicating these likely oxidation states. The ongoing search for atmospheres on rocky exoplanets benefits from understanding the plausible variety of their compositions, which depends strongly on their oxidation states -- and if derived from interior outgassing, on the fO$_2$ at the top of their silicate mantles. This fO$_2$ must vary across compositionally-diverse exoplanets, but for a given planet its value is unconstrained insofar as it depends on how iron (the dominant multivalent element) is partitioned between its 2+ and 3+ oxidation states. Here we focus on another factor influencing how oxidising a mantle is -- a factor modulating fO$_2$ even at fixed Fe$^{3+}$/Fe$^{2+}$ -- the planet's mineralogy. Only certain minerals (e.g., pyroxenes) incorporate Fe$^{3+}$. Having such minerals in smaller mantle proportions concentrates Fe$^{3+}$, increasing fO$_2$. Mineral proportions change within planets according to pressure, and between planets according to bulk composition. Constrained by observed host star refractory abundances, we calculate a minimum fO$_2$ variability across exoplanet mantles, of at least two orders of magnitude, due to mineralogy alone. This variability is enough to alter by a hundredfold the mixing ratio of SO$_2$ directly outgassed from these mantles. We further predict that planets orbiting high-Mg/Si stars are more likely to outgas detectable amounts of SO$_2$ and H$_2$O; and for low-Mg/Si stars, detectable CH$_4$, all else equal. Even absent predictions of Fe$^{3+}$ budgets, general insights can be obtained into how oxidising an exoplanet's mantle is., Comment: 16 pages, 7 figures, accepted for publication in MNRAS

A new approach to calculating current-induced forces in charge transport through nanosystems is introduced. Starting from the fully quantum mechanical hierarchical equations of motion formalism, a timescale separation between electronic and vibrational degrees of freedom is used to derive a classical Langevin equation of motion for the vibrational dynamics as influenced by current-induced forces, such as the electronic friction. The resulting form of the friction is shown to be equivalent to previously derived expressions. The numerical exactness of the hierarchical equations of motion approach, however, allows the investigation of transport scenarios with strong intrasystem and system-environment interactions. As a demonstration, the electronic friction of three example systems is calculated and analyzed: a single electronic level coupled to one classical vibrational mode, two electronic levels coupled to one classical vibrational mode, and a single electronic level coupled to both a classical and quantum vibrational mode.

Nominally anhydrous minerals in rocky planet mantles can sequester oceans of water as a whole, giving a constraint on bulk water inventories. Here we predict mantle water capacities from the thermodynamically-limited solubility of water in their constituent minerals. We report the variability of mantle water capacity due to (i) host star refractory element abundances that set mineralogy, (ii) realistic mantle temperature scenarios, and (iii) planet mass. We find that planets large enough to stabilise perovskite almost unfailingly have a dry lower mantle, topped by a high-water-capacity transition zone which may act as a bottleneck for water transport within the planet's interior. Because the pressure of the ringwoodite-perovskite phase boundary defining the lower mantle is roughly insensitive to planet mass, the relative contribution of the upper mantle reservoir will diminish with increasing planet mass. Large rocky planets therefore have disproportionately small mantle water capacities. In practice, our results would represent initial water concentration profiles in planetary mantles where their primordial magma oceans are water-saturated. We suggest that a considerable proportion of massive rocky planets' accreted water budgets would form surface oceans or atmospheric water vapour immediately after magma ocean solidification, possibly diminishing the likelihood of these planets hosting land. This work is a step towards understanding planetary deep water cycling, thermal evolution as mediated by rheology and melting, and the frequency of waterworlds., Comment: 20 pages, 7 figures; this version accepted for publication in MNRAS

The Earth's ellipticity of figure has an effect on the travel times of seismic waves over teleseismic distances. Tables of ellipticity corrections and coefficients have been used by seismologists for several decades, however due to the increasing variety and complexity of seismic phases in use, current tables of ellipticity coefficients are now outmoded and incomplete. We present a Python package, EllipticiPy, for the calculation of ellipticity corrections that removes the dependence on pre-calculated coefficients at discrete source depths and epicentral distances. EllipticiPy also facilitates the calculation of ellipticity corrections on other planetary bodies. When applied to both Earth and Mars, the magnitudes of ellipticity corrections are on the order of single seconds and are significant for some seismic studies on Earth but remain negligible on Mars due to other greater sources of uncertainty., Comment: Main paper of 11 pages, 4 figures and 1 table plus a supplement of 12 pages and 1 table

Topography on a wet rocky exoplanet could raise land above its sea level. Although land elevation is the product of many complex processes, the large-scale topographic features on any geodynamically-active planet are the expression of the convecting mantle beneath the surface. This so-called "dynamic topography" exists regardless of a planet's tectonic regime or volcanism; its amplitude, with a few assumptions, can be estimated via numerical simulations of convection as a function of the mantle Rayleigh number. We develop new scaling relationships for dynamic topography on stagnant lid planets using 2D convection models with temperature-dependent viscosity. These scalings are applied to 1D thermal history models to explore how dynamic topography varies with exoplanetary observables over a wide parameter space. Dynamic topography amplitudes are converted to an ocean basin capacity, the minimum water volume required to flood the entire surface. Basin capacity increases less steeply with planet mass than does the amount of water itself, assuming a water inventory that is a constant planetary mass fraction. We find that dynamically-supported topography alone could be sufficient to maintain subaerial land on Earth-size stagnant lid planets with surface water inventories of up to approximately $10^{-4}$ times their mass, in the most favourable thermal states. By considering only dynamic topography, which has ~1-km amplitudes on Earth, these results represent a lower limit to the true ocean basin capacity. Our work indicates that deterministic geophysical modelling could inform the variability of land propensity on low-mass planets., Comment: 33 pages, 9 figures, submitted to The Planetary Science Journal

Solid polycrystalline materials undergoing diffusion creep are usually described by Cauchy continuum models with a Newtonian viscous rheology dependent on the grain size. Such a continuum lacks the rotational degrees of freedom needed to describe grain rotation. Here we provide a more general continuum description of diffusion creep that includes grain rotation, and identifies the deformation of the material with that of a micropolar (Cosserat) fluid. We derive expressions for the micropolar constitutive tensors by a homogenisation of the physics describing a discrete collection of rigid grains, demanding an equivalent dissipation between the discrete and continuum descriptions. General constitutive laws are derived for both Coble (grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep. Detailed calculations are performed for a two-dimensional tiling of irregular hexagonal grains, which illustrates a potential coupling between the rotational and translational degrees of freedom. If only the plating out or removal of material at grain boundaries is considered, the constitutive laws are degenerate: modes of deformation that involve pure tangential motion at the grain boundaries are not resisted. This degeneracy can be removed by including the resistance to grain-boundary sliding, or by imposing additional constraints on the deformation., Comment: 28 pages, 3 figures

One of the long-standing goals of quantum transport is to use the noise, rather than the average current, for information processing. However, achieving this requires on-demand control of quantum fluctuations in the electric current. In this paper, we demonstrate theoretically that transport through a molecular spin-valve provides access to many different statistics of electron tunneling events. Simply by changing highly tunable parameters, such as electrode spin-polarization, magnetization angle, and voltage, one is able to switch between Poisson behavior, bunching and anti-bunching of electron tunnelings, and positive and negative temporal correlations. The molecular spin-valve is modeled by a single spin-degenerate molecular orbital with local electronic repulsion coupled to two ferromagnetic leads with magnetization orientations allowed to rotate relative to each other. The electron transport is described via Born-Markov master equation and fluctuations are studied with higher-order waiting time distributions. For highly magnetized parallel-aligned electrodes, we find that strong positive temporal correlations emerge in the voltage range where the second transport channel is partially open. These are caused by a spin-induced electron-bunching, which does not manifest in the stationary current alone.

The fluctuation behavior of triple quantum dots (TQDs) has, so far, largely focused on current cumulants in the long-time limit via full counting statistics. Given that (TQDs) are non-trivial open quantum systems with many interesting features, such as Aharonov-Bohm interference and coherent population blocking, new fluctuating-time statistics, such as the waiting time distribution (WTD), may provide more information than just the current cumulants alone. In this paper, we use a Born-Markov master equation to calculate the standard and higher-order WTDs for coherentlycoupled TQDs arrayed in triangular ring geometries for several transport regimes. In all cases we find that the WTD displays coherent oscillations that correspond directly to individual time-dependent dot occupation probabilities, a result also reported recently in Ref.[1]. Our analysis, however, goes beyond the single-occupancy and single waiting time regimes, investigating waiting time behavior for TQDs occupied by multiple electrons and with finite electron-electron interactions. We demonstrate that, in these regimes of higher occupancy, quantum coherent effects introduce correlations between successive waiting times, which we can tune via an applied magnetic field. We also show that correlations can be used to distinguish between TQD configurations that have identical FCS and that dark states can be tuned with Aharonov-Bohm interference for more complicated regimes than single-occupancy.

Convection in fluid layers at high Rayleigh number (Ra $\sim 10^6$) have a spoke pattern planform. Instabilities in the bottom thermal boundary layer develop into hot rising sheets of fluid, with a component of radial flow towards a central upwelling plume. The sheets form the "spokes" of the pattern, and the plumes the "hubs". Such a pattern of flow is expected to occur beneath plate interiors on Earth, but it remains a challenge to use observations to place constraints on the convective planform of the mantle. Here we present predictions of key surface observables (gravity, topography, and rates of melt generation) from simple 3D numerical models of convection in a fluid layer. These models demonstrate that gravity and topography have only limited sensitivity to the spokes, and mostly reflect the hubs (the rising and sinking plumes). By contrast, patterns of melt generation are more sensitive to short wavelength features in the flow. There is the potential to have melt generation along the spokes, but at a rate which is relatively small compared with that at the hubs. Such melting of spokes can only occur when the lithosphere is sufficiently thin ($\lesssim 80$ km) and mantle water contents are sufficiently high ($\gtrsim 100$ ppm). The distribution of volcanism across the Middle East, Arabia and Africa north of equator suggests that it results from such spoke pattern convection., Comment: Very minor changes from previous submission

Partial melting of asthenospheric mantle generates magma that supplies volcanic systems. The timescale of melt extraction from the mantle has been hotly debated. Microstructural measurements of permeability typically suggest relatively slow melt extraction (1 m/yr) whereas geochemical (Uranium-decay series) and geophysical observations suggest much faster melt extraction (100 m/yr). The deglaciation of Iceland triggered additional mantle melting and magma flux at the surface. The rapid response has been used to argue for relatively rapid melt extraction. However, this episode must, at least to some extent, be unrepresentative, because the rates of magma eruption at the surface increased about thirty-fold relative to the steady state. Our goal is to quantify this unrepresentativeness. We develop a one-dimensional, time-dependent and nonlinear (far from steady-state), model forced by the most recent, and best mapped, Icelandic deglaciation. We find that 30 m/yr is the best estimate of the steady-state maximum melt velocity. This is a factor of about 3 smaller than previously claimed, but still relatively fast. We translate these estimates to other mid-ocean ridges accounting for differences in passive and active upwelling and degree of melting. We find that fast melt extraction greater than about 10 m/yr prevails globally., Comment: Accepted for publication in Earth and Planetary Science Letters (2020). Total 17 pages and 5 figures (including Supplementary Material)

Many molecular junctions display stochastic telegraphic switching between two distinct current values, which is therefore an important source of fluctuations in nanoscale quantum transport. We investigate electronic fluctuations arising via Markovian master equations; identifying regions of non-renewal behavior due to telegraphic switching. Non-renewal behavior is characterized by the emergence of correlations between successive first-passage times of detection in one of the leads. Our method of including telegraphic switching is general for any source-molecule-drain setup, but we consider three specific cases. In the first, we model stochastic transitions between an Anderson impurity with and without an applied magnetic field $B$. The last two scenarios couple the electronic level to a single vibrational mode via the Holstein model. We then stochastically switch between two vibrational conformations, with different electron-phonon coupling and vibrational frequency, which corresponds to different molecular conformations. Finally, we model the molecule attaching and detaching from an electrode by switching between two different molecule-electrode coupling strengths. We find, for all three cases, that including the telegraph process in the master equation induces relatively strong positive correlations, with Pearson coefficient $p \approx 0.5$, between successive first-passage times. These correlations only appear, however, when there is telegraphic switching between two significantly different transport scenarios, and we show that it arises from the underlying physics of the model. We also find that, in order for correlations to appear, the switching rate $\nu$ must be much smaller than the rate of electron transfer $\gamma$., Comment: 14 pages, 16 figures

The number of ribosomes in a cell is considered as limiting, and gene expression is thus largely determined by their cellular concentration. In this work we develop a toy model to study the trade-off between the ribosomal supply and the demand of the translation machinery, dictated by the composition of the transcript pool. Our equilibrium framework is useful to highlight qualitative behaviours and new means of gene expression regulation determined by the fine balance of this trade-off. We also speculate on the possible impact of these mechanisms on cellular physiology.

In quantum transport through nanoscale devices, fluctuations arise from various sources: the discreteness of charge carriers, the statistical non-equilibrium that is required for device operation, and unavoidable quantum uncertainty. As experimental techniques have improved over the last decade, measurements of these fluctuations have become available.} They have been accompanied by a plethora of theoretical literature using many different fluctuation statistics to describe the quantum transport. In this paper, we overview three prominent fluctuation statistics: full counting, waiting time, and first-passage time statistics. We discuss their weaknesses and strengths, and explain connections between them in terms of renewal theory. In particular, we discuss how different information can be encoded in different statistics when the transport is non-renewal, and how this behavior manifests in the measured physical quantities of open quantum systems. All theoretical results are illustrated via a demonstrative transport scenario: a Markovian master equation for a molecular electronic junction with electron-phonon interactions. {{} We demonstrate that to obtain non-renewal behavior, and thus to have temporal correlations between successive electron tunneling events, there must be a strong coupling between tunneling electrons and out-of-equilibrium quantized molecular vibrations., Comment: 24 pages, 8 figures

The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect non-renewal behaviour in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of first-passage times. Rather than the time between successive electron tunnelings, the first-passage refers to the first time the number of extra electrons in the drain reaches $+1$. Here, we demonstrate the differences between first-passage time statistics and waiting time statistics in transport scenarios where the waiting time either cannot correctly reproduce the higher order current cumulants or cannot be calculated at all. To this end, we examine electron transport through a molecule coupled to two macroscopic metal electrodes. We model the molecule with strong electron-electron and electron-phonon interactions in three regimes: (i) sequential tunneling and cotunneling for a finite bias voltage through the Anderson model, (ii) sequential tunneling with no temperature gradient and a bias voltage through the Holstein model, and (iii) sequential tunneling at zero bias voltage and a temperature gradient through the Holstein model. We show that, for each transport scenario, backtunneling events play a significant role; consequently, the waiting time statistics do not correctly predict the renewal and non-renewal behaviour, whereas the first-passage time distribution does., Comment: 16 pages, 8 figures total

Observations of the time lag between the last deglaciation and a surge in volcanic activity in Iceland constrain the average melt ascent velocity to be $\geq50$ $\mathrm{m/yr}$. Although existing theoretical work has explained why the surge in eruption rates increased $5$-$30$ fold from the steady-state rates during the last deglaciation, they cannot account for large variations of Rare Earth Element (REE) concentrations in the Icelandic lavas. Lavas erupted during the last deglaciation are depleted in REEs by up to $70\%$; whereas, existing models, which assume instantaneous melt transport, can only produce at most $20\%$ depletion. Here, we develop a numerical model with finite melt ascent velocity and show that the variations of REEs are strongly dependent on the melt ascent velocity. When the average melt ascent velocity is $100$ $\mathrm{m/yr}$, the variation of $\mathrm{La}$ calculated by our model is comparable to that of the observations. In contrast, when the melt ascent velocity is $1,000$ $\mathrm{m/yr}$ or above, the model variation of $\mathrm{La}$ becomes significantly lower than observed, which explains why previous models with instantaneous melt transport did not reproduce the large variations. We provide the first model that takes account of the diachronous response of volcanism to deglaciation. We show by comparing our model calculations of the relative volumes of different eruption types (subglacial, finiglacial and postglacial) and the timing of the bursts in volcanic eruptions with the observations across different volcanic zones that the Icelandic average melt ascent velocity during the last deglaciation is likely to be $\sim100$ $\mathrm{m/yr}$.

The observed variability of trace-element concentration in basaltic lavas and melt inclusions carries information about heterogeneity in the mantle. The difficulty is to disentangle the contributions of source heterogeneity (i.e., spatial variability of mantle composition before melting) and process heterogeneity (i.e., spatial and temporal variability in melt transport). Here we investigate the end-member hypothesis that variability arises due to source heterogeneity alone. We model the attenuation of trace-element variability introduced into the bottom of a one-dimensional, steady-state melting column. Our results show that the melting column can be considered to be a filter that attenuates variability according to the wavelength of heterogeneity, the partition coefficient of the trace element, melt productivity and the efficiency of melt segregation. We further show that while the model can be fit to the observations, this requires assumptions inconsistent with constraints on the timescales of magma assembly. Hence, we falsify the end-member hypothesis and, instead, conclude that observed variability requires heterogeneity of melt transport. This might take the form of channels or waves and would almost certainly interact with source heterogeneity., Comment: 44 pages, 13 figures, to be published in G-cubed

Partially molten materials resist shearing and compaction. This resistance is described by a fourth-rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective bulk viscosity. Here, calculations are presented of the effective viscosity tensor during diffusion creep for a 2D tiling of hexagonal unit cells and a 3D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2D tiling is isotropic, but that for the 3D tessellation is anisotropic. Two parameters control the effect of melt on the viscosity tensor: the porosity and the dihedral angle. Calculations for both Nabarro-Herring (volume diffusion) and Coble (surface diffusion) creep are presented. For Nabarro-Herring creep the bulk viscosity becomes singular as the porosity vanishes. This singularity is logarithmic, a weaker singularity than typically assumed in geodynamic models. The presence of a small amount of melt (0.1% porosity) causes the effective shear viscosity to approximately halve. For Coble creep, previous modelling work has argued that a very small amount of melt may lead to a substantial, factor of 5, drop in the shear viscosity. Here, a much smaller, factor of 1.4, drop is obtained for tetrakaidecahedrons. Owing to a Cauchy relation symmetry, the Coble creep bulk viscosity is a constant multiple of the shear viscosity when melt is present., Comment: 36 pages, 13 figures. Revised version accepted by Journal of Geophysical Research: Solid Earth. One figure added from original submission to show comparison with previous models for Coble creep

In the resonant tunneling regime sequential processes dominate single electron transport through quantum dots or molecules that are weakly coupled to macroscopic electrodes. In the Coulomb blockade regime, however, cotunneling processes dominate. Cotunneling is an inherently quantum phenomenon and thus gives rise to interesting observations, such as an increase in the current shot noise. Since cotunneling processes are inherently fast compared to the sequential processes, it is of interest to examine the short time behaviour of systems where cotunneling plays a role, and whether these systems display nonrenewal statistics. We consider three questions in this paper. Given that an electron has tunneled from the source to the drain via a cotunneling or sequential process, what is the waiting time until another electron cotunnels from the source to the drain? What are the statistical properties of these waiting time intervals? How does cotunneling affect the statistical properties of a system with strong inelastic electron-electron interactions? In answering these questions, we extend the existing formalism for waiting time distributions in single electron transport to include cotunneling processes via an $n$-resolved Markovian master equation. We demonstrate that for a single resonant level the analytic waiting time distribution including cotunneling processes yields information on individual tunneling amplitudes. For both a SRL and an Anderson impurity deep in the Coulomb blockade there is a nonzero probability for two electrons to cotunnel to the drain with zero waiting time inbetween. Furthermore, we show that at high voltages cotunneling processes slightly modify the nonrenewal behaviour of an Anderson impurity with a strong inelastic electron-electron interaction., Comment: 16 pages, 6 figures

In textural equilibrium, partially molten materials minimise the total surface energy bound up in grain boundaries and grain-melt interfaces. Here, numerical calculations of such textural equilibrium geometries are presented for a space-filling tessellation of grains with a tetrakaidecahedral (truncated octahedral) unit cell. Two parameters determine the nature of the geometries: the porosity and the dihedral angle. A variety of distinct melt topologies occur for different combinations of these two parameters, and the boundaries between different topologies has been determined. For small dihedral angles, wetting of grain boundaries occurs once the porosity has exceeded 11%. An exhaustive account is given of the main properties of the geometries: their energy, pressure, mean curvature, contiguity, and areas on cross-sections and faces. Their effective permeabilities have been calculated, and demonstrate a transition between a quadratic variation with porosity at low porosities to a cubic variation at high porosities., Comment: 27 pages, 20 figures. Only minor changes from the original submission. A diagram was added describing the dihedral angle, and some justification given for the assumed tetrakaidecahedral unit cell. This version is the one accepted by Proc Roy Soc A

Magmatism in subduction zones builds continental crust and causes most of Earth's subaerial volcanism. The production rate and composition of magmas are controlled by the thermal structure of subduction zones. A range of geochemical and heat flow evidence has recently converged to indicate that subduction zones are hotter at lithospheric depths beneath the arc than predicted by canonical thermomechanical models, which neglect magmatism. We show that this discrepancy can be resolved by consideration of the heat transported by magma. In our one- and two-dimensional numerical models and scaling analysis, magmatic transport of sensible and latent heat locally alters the thermal structure of canonical models by $\sim$300 K, increasing predicted surface heat flow and mid-lithospheric temperatures to observed values. We find the advection of sensible heat to be larger than the deposition of latent heat. Based on these results we conclude that thermal transport by magma migration affects the chemistry and the location of arc volcanoes., Comment: Revised version. 10 pages, 9 figures (plus Supplementary Material: 5 pages, 4 figures). Changes: slightly expanded description of model and discussion of results

Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunnelling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper, we used the quantum master equation to consider the following questions: (i) Given that an electron has tunnelled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("the" tunnelling path)? (ii) Given that an electron has tunnelled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("an" tunnelling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between "the" and "an" electron tunnelling paths., Comment: 5 pages, 2 figures

In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a practical approach for calculating it, where the environment is described by the general Markovian master equation. We illustrate the theory by using the rate equation to compute the tunnelling time distribution for electron transport through a molecular junction. The tunnelling time distribution is exponential, which indicates that Markovian quantum tunnelling is a Poissonian statistical process. The tunnelling time distribution is used not only to study the quantum statistics of tunnelling along the average electric current but also to analyse extreme quantum events where an electron jumps against the applied voltage bias. The average tunnelling time shows distinctly different temperature dependance for p- and n-type molecular junction and therefore provides a sensitive tool to probe the alignment of molecular orbitals relative to the electrode Fermi energy.

The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate three-dimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory experiments show emergence of melt-rich bands throughout the rock sample, and pressure shadows around the inclusion. The numerical model displays similar melt-rich bands only for a small bulk-to-shear-viscosity ratio (five or less). The results are consistent with earlier two-dimensional numerical simulations; however, we show that it is easier to form melt-rich bands in three dimensions compared to two. The addition of strain-rate dependence of the viscosity causes a distinct change in the shape of pressure shadows around the inclusion. This change in shape presents an opportunity for experimentalists to identify the strain-rate dependence and therefore the dominant deformation mechanism in torsion experiments with inclusions.

A high quality beam of linearly polarized photons of several GeV will become available with the coherent bremsstrahlung technique at JLab. We have developed a polarimeter which requires about two meters of the beam line, has an analyzing power of 20% and an efficiency of 0.02%. The layout and first results of a polarimeter test on the laser back-scattering photon beam at SPring-8/LEPS are presented.

Dynamics of magnetic vortex core switching in nanometer-scale permalloy disk, having a single vortex ground state, was investigated by micromagnetic modeling. When an in-plane magnetic field pulse with an appropriate strength and duration is applied to the vortex structure, additional two vortices, i.e., a circular- and an anti-vortex, are created near the original vortex core. Sequentially, the vortex-antivortex pair annihilates. A spin wave is created at the annihilation point and propagated through the entire element; the relaxed state for the system is the single vortex state with a switched vortex core., Comment: to appear in Appl. Phys. Lett

Synaptic vesicle (SV) exocytosis mediating neurotransmitter release occurs spontaneously at low intraterminal calcium concentrations and is stimulated by a rise in intracellular calcium. Exocytosis is compensated for by the reformation of vesicles at plasma membrane and endosomes. Although the adaptor complex AP-3 was proposed to be involved in the formation of SVs from endosomes, whether its function has an indirect effect on exocytosis remains unknown. Using mocha mice, which are deficient in functional AP-3, we identify an AP-3-dependent tetanus neurotoxin-resistant asynchronous release that can be evoked at hippocampal mossy fiber (MF) synapses. Presynaptic targeting of the tetanus neurotoxin-resistant vesicle soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) is lost in mocha hippocampal MF terminals, whereas the localization of synaptobrevin 2 is unaffected. In addition, quantal release in mocha cultures is more frequent and more sensitive to sucrose. We conclude that lack of AP-3 results in more constitutive secretion and loss of an asynchronous evoked release component, suggesting an important function of AP-3 in regulating SV exocytosis at MF terminals.

We consider accretion discs in close binary systems. We show that heating of a disc at the impact point of the accretion stream contributes significantly to the local energy budget at its outer edge. As a result the thermal balance relation between local accretion rate and surface density (the `S-curve') changes; the critical mass transfer rate above which no dwarf nova outbursts occur can be up to 40% smaller than without impact heating. Standstills in ZCam systems thus occur at smaller mass transfer rates than otherwise expected, and are rather fainter than the peak luminosity during the dwarf nova phase as a result., Comment: 3 pages, 3 figures. Accepted for publication in MNRAS

In unified models of active galaxies the direct line of sight to the nucleus is unobscured only within a certain cone of directions. An opening angle for this cone is usually estimated by methods such as the overall ratio of Seyfert 1s to Seyfert2s, the latter assumed to be obscured versions of the former. Here we shall show, as has often been suspected, that the opening angle of the cone depends on the luminosity of the central source, with higher luminosities corresponding to larger opening angles. This conclusion depends only on the assumption that the width of the broad emission lines at a given luminosity is a measure of inclination angle, an assumption that is supported by observation in radio-loud systems. On the other hand we show that the scatter in X-ray spectral index is not primarily an effect of viewing angle, in contrast to what might be expected if the scatter on the spectral index versus luminosity relation were a consequence of absorption in the obscuring material. The observed correlation between linewidth and spectral index appears to be a further consequence of the dependence of opening angle on luminosity., Comment: 8 pages, 7 figures, uses mn.sty. Accepted for publication in MNRAS

We have previously shown that the linewidth distribution in AGN can be accounted for by an axisymmetric broad emission line region. In this paper we show that the linewidth distribution changes with redshift and that these changes are dependent on H_0 and q_0. We show that relatively small samples of AGN at high redshift with measured linewidth at half maximum can be used to distinguish between values of H_0 and q_0. Furthermore larger low redshift samples can be used to distinguish between luminosity functions and hence different models of quasar evolution., Comment: Accepted for publication in MNRAS. 8 pages LaTeX, uses mn.sty

We propose that the scatter in line width versus luminosity of the BLR of AGN arises from a dependence on the line of sight to an axially symmetric BLR. Adopting a simple model for the line width as a function of luminosity and angle, and convolving this with the observed luminosity function, allows us to predict a line width distribution consistent with the available data. Furthermore, we use the relation between the equivalent width of a line and the luminosity in the continuum to predict an observed correlation between line width and equivalent width. The scatter on this correlation is again provided by angular dependence. We also show a viewing angle dependence can produce the X-ray spectral index distribution. The results have applications as diagnostics of models of the broad line region and in cosmology., Comment: To appear in PASP conference proceedings "Structure and Kinematics of the Quasar Broad Line Region", includes latex .sty file

The nuclei of a wide class of active galaxies emit broad emission lines with widths at half maximum (FWHM) in the range $10^{3}-10^{4}$ km s$^{-1}$. This spread of widths is not solely a consequence of the range of the luminosities of these sources since a plot of width versus luminosity shows a large scatter. We propose that the broad line emission region (BLR) is axially symmetric and that this scatter in line width arises from an additional dependence on the angle of the line of sight to the axis of the emission region. Such a relation is natural in unified models of active nuclei which link a variety of observed properties to viewing angle. Adopting a simple form for the line width as a function of luminosity and angle, and convolving this with the observed luminosity function, allows us to predict a line width distribution consistent with the available data. Furthermore, we use the relation between the equivalent width of a line and the luminosity in the continuum (the `Baldwin Effect') to predict an observed correlation between line width and equivalent width. The scatter on this correlation is again provided by angular dependence. The results have applications as diagnostics of models of the broad line emission region and in cosmology., Comment: 8 pages including 4 figures. Accepted for publication in MNRAS Letters