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We simulate the charging of a single electrolyte-filled pore using the modified Poisson-Nernst-Planck and Navier-Stokes equations. We find that electroconvection, previously ignored in this context, can substantially speed up the charging dynamics. We derive an analytical model that describes the induced fluid velocity and the electric current arising due to convection. Our findings suggest that convection becomes significant beyond a certain threshold voltage that is an inherent electrolyte property.

Germanium (Ge), the next-in-line group-IV material, bears great potential to add functionality and performance to next-generation nanoelectronics and solid-state quantum transport based on silicon (Si) technology. Here, we investigate the direct epitaxial growth of two-dimensional high-quality crystalline Ge layers on Si deposited at ultra-low growth temperatures ($T_{Ge} = 100^{\circ}\mathrm{C}-350^{\circ}\mathrm{C}$) and pristine growth pressures ($\lesssim 10^{-10}\,\mathrm{mbar}$). First, we show that $T_{Ge}$ does not degrade the crystal quality of homoepitaxial Ge/Ge(001) by comparing the point defect density using positron annihilation lifetime spectroscopy. Subsequently, we present a systematic investigation of the Ge/Si(001) heteroepitaxy, varying the Ge coverage (${\theta}_{Ge}$, 1, 2, 4, 8, 12, and 16 nm) and $T_{Ge}$ ($100^{\circ}\mathrm{C}$ to $300^{\circ}\mathrm{C}$, in increments of $50^{\circ}\mathrm{C}$) to assess the influence of these parameters on the layer's structural quality. Atomic force microscopy revealed a rippled surface topography with superimposed grainy features and the absence of three-dimensional structures, such as quantum dots. Transmission electron microscopy unveiled pseudomorphic, grains of highly crystalline growth separated by defective domains. Thanks to nanobeam scanning x-ray diffraction measurements, we were able to evidence the lattice strain fluctuations due to the ripple-like structure of the layers. We conclude that the heteroepitaxial strain contributes to the formation of the ripples, which originate from the kinetic limitations of the ultra-low temperatures.

Brillouin light scattering spectroscopy (BLS) is applied to study the micromechanics of cellulosic viscose fibers, one of the commercially most important, man-made biobased fibers. Using an equal angle scattering geometry, we provide a thorough description of the procedure to determine the complete transversely isotropic elastic stiffness tensor. From the stiffness tensor the engineering-relevant material parameters such as Young's moduli, shear moduli, and Poisson's ratios in radial and axial fiber direction are evaluated. The investigated fiber type shows that, at ideal conditions, the material exhibits optical waveguide properties resulting in spontaneous Brillouin backscattering which can be used to obtain additional information from the Brillouin spectra, enabling the measurement of two different scattering processes and directions with only one scattering geometry.

LiMn2O4 (LMO), cathodes present large stability when cycled in aqueous electrolytes, contrasting its behavior in conventional organic electrolytes in Lithium-ion batteries (LIBs). To elucidate the mechanisms underlying this distinctive behavior, we employ unconventional characterization techniques, including Variable Energy Positron Annihilation Lifetime Spectroscopy (VEPALS), Tip-Enhanced Raman Spectroscopy (TERS) and macro-Raman Spectroscopy (with mm-size laser spot). These still rather unexplored techniques in the battery field provide complementary information across different length scales, revealing previously hidden features. VEPALS offers atomic-scale insights, uncovering cationic defects and sub-nanometer pores that tend to collapse with cycling. TERS, operating at the nanometric range at the surface, captured the presence of Mn3O4 and its dissolution with cycling, elucidating dynamic changes during operation. Additionally, TERS highlights SO42- accumulation at grain boundaries. Macro-Raman Spectroscopy focuses on the micrometer scale, depicting small changes in the cathode's long-range order, suggesting a slow but progressive loss of crystalline quality under operation. Integrating these techniques provides a comprehensive assessment of LMO cathode stability in aqueous electrolytes, offering multifaceted insights into phase and defect evolution that can help to rationalize the origin of such stability when compared to conventional organic electrolytes. Our findings advance the understanding of LMO behavior in aqueous environments and provide guidelines for its development for next-generation LIBs.

Ion intercalation of perovskite oxides in liquid electrolytes is a very promising method for controlling their functional properties while storing charge, which opens the potential application in different energy and information technologies. Although the role of defect chemistry in the oxygen intercalation in a gaseous environment is well established, the mechanism of ion intercalation in liquid electrolytes at room temperature is poorly understood. In this study, the defect chemistry during ion intercalation of La0.5Sr0.5FeO3-\delta thin films in alkaline electrolytes is studied. Oxygen and proton intercalation into the LSF perovskite structure is observed at moderate electrochemical potentials (0.5 V to -0.4 V), giving rise to a change in the oxidation state of Fe (as a charge compensation mechanism). The variation of the concentration of holes as a function of the intercalation potential was characterized by in-situ ellipsometry and the concentration of electron holes was indirectly quantified for different electrochemical potentials. Finally, a dilute defect chemistry model that describes the variation of defect species during ionic intercalation was developed.

FIB/SEM tomography represents an indispensable tool for the characterization of three-dimensional nanostructures in battery research and many other fields. However, contrast and 3D classification/reconstruction problems occur in many cases, which strongly limits the applicability of the technique especially on porous materials, like those used for electrode materials in batteries or fuel cells. Distinguishing the different components like active Li storage particles and carbon/binder materials is difficult and often prevents a reliable quantitative analysis of image data, or may even lead to wrong conclusions about structure-property relationships. In this contribution, we present a novel approach for data classification in three-dimensional image data obtained by FIB/SEM tomography and its applications to NMC battery electrode materials. We use two different image signals, namely the signal of the angled SE2 chamber detector and the Inlens detector signal, combine both signals and train a random forest, i.e. a particular machine learning algorithm. We demonstrate that this approach can overcome current limitations of existing techniques suitable for multi-phase measurements and that it allows for quantitative data reconstruction even where current state-of the art techniques fail, or demand for large training sets. This approach may yield as guideline for future research using FIB/SEM tomography.

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a new sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.

At first glance the definition of mass and momentum appears to be uniquely defined. We show here, however, that this certainty can be misleading for many coarse grained systems. We show that particularly the fluctuating properties of common definitions of momentum in coarse grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we can give analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.

The excess energy emitted during the positronium (Ps) formation in condensed matter may be released as light. Spectroscopic analysis of this light can be a new method of studying the electronic properties of materials. We report the first experimental attempt, according to our knowledge, to verify the existence of this emission process. As a result, the possibility of the emission of photons during Ps formation is within the experimental uncertainty in two different solids: an n-alkane and porous silica. However, it seems that the Ps formation on the alkane surface is not accompanied by the emission of photons with energy in the detection range of 1.6 - 3.9 eV. Various processes that can influence the energy of the photon emitted during the Ps formation are discussed to elucidate this issue. To aid future experiments, equations were developed to estimate the expected ratio of light emission events to annihilation events with the presence or absence of a photon during the Ps formation.

The n-type doping of Ge is a self-limiting process due to the formation of vacancy-donor complexes (DnV with n <= 4) that deactivate the donors. This work unambiguously demonstrates that the dissolution of the dominating P4V clusters in heavily phosphorus-doped Ge epilayers can be achieved by millisecond-flash lamp annealing at about 1050 K. The P4V cluster dissolution increases the carrier concentration by more than three-fold together with a suppression of phosphorus diffusion. Electrochemical capacitance-voltage measurements in conjunction with secondary ion mass spectrometry, positron annihilation lifetime spectroscopy and theoretical calculations enabled us to address and understand a fundamental problem that has hindered so far the full integration of Ge with complementary-metal-oxide-semiconductor technology.

Machine learning is changing how we design and interpret experiments in materials science. In this work, we show how unsupervised learning, combined with ab initio modeling, improves our understanding of structural metastability in multicomponent alloys. We use the example case of Al-O-N alloys where the formation of aluminum vacancies in wurtzite AlN upon the incorporation of substitutional oxygen can be seen as a general mechanism of solids where crystal symmetry is reduced to stabilize defects. The ideal AlN wurtzite crystal structure occupation cannot be matched due to the presence of an aliovalent hetero-element into the structure. The traditional interpretation of the c-lattice shrinkage in sputter-deposited Al-O-N films from X-ray diffraction (XRD) experiments suggests the existence of a solubility limit at 8at.% oxygen content. Here we show that such naive interpretation is misleading. We support XRD data with a machine learning analysis of ab initio simulations and positron annihilation lifetime spectroscopy data, revealing no signs of a possible solubility limit. Instead, the presence of a wide range of non-equilibrium oxygen-rich defective structures emerging at increasing oxygen contents suggests that the formation of grain boundaries is the most plausible mechanism responsible for the lattice shrinkage measured in Al-O-N sputtered films.

Superlattice (SL) thin films composed of refractory ceramics unite extremely high hardness and enhanced fracture toughness; a material combination often being mutually exclusive. While the hardness enhancement obtained whentwo materials form a superlattice is well described by existing models based on dislocation mobility, the underlying mechanisms behind the increase in fracture toughness are yet to be unraveled. Here we provide a model based on linear elasticity theory to predict the fracture toughness enhancement in (semi-)epitaxial nanolayers due to coherency stresses and formation of misfit dislocations. We exemplarily study a superlattice structure composed of two cubic transition metal nitrides (TiN, CrN) on a MgO (100) single-crystal substrate. Minimization of the overall strain energy, each time a new layer is added on the nanolayered stack, allows estimating the density of misfit dislocations formed at the interfaces. The evolving coherency stresses, which are partly relaxed by the misfit dislocations, are then used to calculate the apparent fracture toughness of respective SL architectures by applying the weight function method. The results show that the critical stress intensity increases steeply with increasing bilayer period for very thin (essentially dislocation-free) SLs, before the K_IC values decline more gently along with the formation of misfit dislocations. The characteristic K_IC vs. bilayer-period-dependence nicely matches experimental trends. Importantly, all critical stress intensity values of the superlattice films clearly exceed the intrinsic fracture toughness of the constituting layer materials, evincing the importance of coherency stresses for increasing the crack growth resistance.

A recently discovered modified low-temperature baking leads to reduced surface losses and an increase of the accelerating gradient of superconducting TESLA shape cavities. We will show that the dynamics of vacancy-hydrogen complexes at low-temperature baking lead to a suppression of lossy nanohydrides at 2\u2009K and thus a significant enhancement of accelerator performance. Utilizing Doppler broadening Positron Annihilation Spectroscopy, Positron Annihilation Lifetime Spectroscopy and instrumented nanoindentation, samples made from European XFEL niobium sheets were investigated. We studied the evolution of vacancies in bulk samples and in the sub-surface region and their interaction with hydrogen at different temperature levels during \it in-situ and \it ex-situ annealing.

So far, magneto-ionics, understood as voltage-driven ion transport in magnetic materials, has largely relied on controlled migration of oxygen ion/vacancy and, to a lesser extent, lithium and hydrogen. Here, we demonstrate efficient, room-temperature, voltage-driven nitrogen transport (i.e., nitrogen magneto-ionics) by electrolyte-gating of a single CoN film (without an ion-reservoir layer). Nitrogen magneto-ionics in CoN is compared to oxygen magneto-ionics in Co3O4, both layers showing a nanocrystalline face-centered-cubic structure and reversible voltage-driven ON-OFF ferromagnetism. In contrast to oxygen, nitrogen transport occurs uniformly creating a plane-wave-like migration front, without assistance of diffusion channels. Nitrogen magneto-ionics requires lower threshold voltages and exhibits enhanced rates and cyclability. This is due to the lower activation energy for ion diffusion and the lower electronegativity of nitrogen compared to oxygen. These results are appealing for the use of magneto-ionics in nitride semiconductor devices, in applications requiring endurance and moderate speeds of operation, such as brain-inspired computing.

The transition from insulator to conductor can be achieved in some materials but requires modification of both the arrangement of atoms and their electronic configurations. This is often achieved by doping. Here we reveal a mechanism the lattice may adopt to induce such a transition. We show that limited exposure to sub-bandgap light caused a permanent transition from an insulator state to a conductor state in the insulating oxide Ga2O3 with 9-orders of magnitude increase in electronic conduction. Photoexcitation modifies the charge state of an O-vacancy and the redistribution of the localized electrons, leading to a massive structural distortion in the lattice that is shown to be the underlying mechanism. It modifies density of states and introduces new stable states with shallower energy levels, leading to this intriguing behavior. We suggest that this mechanism may occur in other wide bandgap metal oxides leading to drastic modification in their electronic properties.

Voltage control of magnetism through electric field-induced oxygen motion (magneto-ionics) could represent a significant breakthrough in the pursuit for new strategies to enhance energy efficiency in a large variety of magnetic devices, such as magnetic micro-electro-mechanical systems (MEMS), magnetic logics, spin electronics, or neuromorphic computing, i.e., envisaging ultra-low power emulation of the biological synapse. Boosting the induced changes in magnetization, magneto-ionic motion and cyclability (endurance) continue to be key challenges to turn magneto-ionic phenomena into real applications. Here, we demonstrate that, without degrading cyclability, room temperature magneto-ionic motion in electrolyte-gated paramagnetic and fairly thick (> 100 nm) Co3O4 films largely depends on the configuration used to apply the electric field. In particular, magneto-ionic effects are significantly increased both in terms of generated magnetization (6 times larger: from 118.5 to 699.2 emu cm-3) and speed (35 times faster: from 33.1 to 1170.8 emu cm-3 h-1) if the electric field is applied across a conducting buffer layer (grown underneath the Co3O4 films), instead of directly contacting Co3O4. This is attributed to a greater uniformity and strength of the applied electric field when using the conducting layer. These results may trigger the use of oxygen magneto-ionics into promising new technologies, such as magnetic MEMS or brain-inspired computing, which require endurance and moderate speeds of operation.

Advancement of optoelectronic and high-power devices is tied to the development of wide band gap materials with excellent transport properties. However, bipolar doping (n-type and p-type doping) and realizing high carrier density while maintaining good mobility have been big challenges in wide band gap materials. Here P-type and n-type conductivity was introduced in beta-Ga2O3, an ultra-wide band gap oxide, by controlling hydrogen incorporation in the lattice without further doping. Hydrogen induced a 9-order of magnitude increase of n-type conductivity with donor ionization energy of 20 meV and resistivity of 10-4 Ohm.cm. The conductivity was switched to p-type with acceptor ionization energy of 42 meV by altering hydrogen incorporation in the lattice. Density functional theory calculations were used to examine hydrogen location in the Ga2O3 lattice and identified a new donor type as the source of this remarkable n-type conductivity. Positron annihilation spectroscopy confirmed this finding and the interpretation of the results. This work illustrates a new approach that allows a tunable and reversible way of modifying the conductivity of semiconductors and it is expected to have profound implications on semiconductor field. At the same time it demonstrates for the first time p-type and remarkable n-type conductivity in Ga2O3 which should usher in the development of Ga2O3 devices and advance optoelectronics and high-power devices

Using the recently introduced Molecular Dynamics Lattice Gas (MDLG) approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse-graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a non-ideal equation of state. The MDLG method gives a guidance to the exact nature of the fluctuation in such systems.

We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.

Outstanding crystalline perfection is a key requirement for the formation of new forms of electronic order in a vast number of widely different materials. Whereas excellent sample quality represents a standard claim in the literature, there are, quite generally, no reliable microscopic probes to establish the nature and concentration of lattice defects such as voids, dislocations and different species of point defects on the level relevant to the length and energy scales inherent to these new forms of order. Here we report an experimental study of the archetypical skyrmion-lattice compound MnSi, where we relate the characteristic types of point defects and their concentration to the magnetic properties by combining different types of positron spectroscopy with ab-initio calculations and bulk measurements. We find that Mn antisite disorder broadens the magnetic phase transitions and lowers their critical temperatures, whereas the skyrmion lattice phase forms for all samples studied underlining the robustness of this topologically non-trivial state. Taken together, this demonstrates the unprecedented sensitivity of positron spectroscopy in studies of new forms of electronic order.

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

We study the ground-state phase diagram of spinless and spin-1 bosons in optical superlattices using a Bose-Hubbard Hamiltonian that includes spin-dependent interactions. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second-order for spinless bosons and second- or first-order for spin-1 bosons. Anti-ferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of single-atom tunneling resonances which surprisingly survives well into the superfluid regime.

In this paper we show that standard implementations of fluctuating Lattice Boltzmann methods do not obey Galilean invariance at a fundamental level. In trying to remedy this we are led to a novel kind of multi-relaxation time lattice Boltzmann methods where the collision matrix depends on the local velocity. This new method is conceptually elegant but numerically inefficient. With a small numerical trick, however, this method recovers nearly the original efficiency and allows the practical implementation of fluctuating lattice Boltzmann methods with significantly improved Galilean invariance. This will be important for applications of fluctuating lattice Boltzmann for non-equilibrium systems involving strong flow fields.

We examine spinor Bose-Einstein condensates in optical superlattices theoretically using a Bose-Hubbard Hamiltonian that takes spin effects into account. Assuming that a small number of spin-1 bosons is loaded in an optical potential, we study single-particle tunneling that occurs when one lattice site is ramped up relative to a neighboring site. Spin-dependent effects modify the tunneling events in a qualitative and quantitative way. Depending on the asymmetry of the double well different types of magnetic order occur, making the system of spin-1 bosons in an optical superlattice a model for mesoscopic magnetism. We use a double-well potential as a unit cell for a one-dimensional superlattice. Homogeneous and inhomogeneous magnetic fields are applied and the effects of the linear and the quadratic Zeeman shifts are examined. We also investigate the bipartite entanglement between the sites and construct states of maximal entanglement. The entanglement in our system is due to both orbital and spin degrees of freedom. We calculate the contribution of orbital and spin entanglement and show that the sum of these two terms gives a lower bound for the total entanglement.

6H-SiC (silicon carbide) single crystals containing VSi-VC divacancies are investigated with respect to magnetic and structural properties. We found that an initial increase of structural disorder leads to pronounced ferromagnetic properties at room temperature. Further introduction of disorder lowers the saturation magnetization and is accompanied with the onset of lattice amorphization. Close to the threshold of full amorphization, also divacancy clusters are formed and the saturation magnetization nearly drops to zero.

A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very regular, non-equilibrium structures. We present here a numerical study of these fronts using a lattice Boltzmann method. In two dimensions these structures are regular stripes or droplet arrays. In general the kind and orientation of the selected morphology and the size of the domains depends on the speed of the front as well as the composition of the material overtaken by the phase-separation front. We present a survey of morphologies as a function of these two parameters. We show that the resulting morphologies are initial condition dependent. We then examine which of the potential morphologies is the most stable. An analytical analysis for symmetrical compositions predicts the transition point from orthogonal to parallel stripes.

A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without explicitly moving into a moment space representation. The corresponding 'moments' are derived as left eigenvectors of said collision operator in velocity space. Consequently we can, in a representation independent of the chosen base velocity set, generate the conservation equations. We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant. Therefore we can explain why MRT implementations in the literature reproduce identical hydrodynamics despite being based on different orthogonalization relations.

We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett. 71, 473 (2005)] and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered. This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths. In particular cross correlators vanish to less than 0.5%. For larger mean velocities, however, Galilean invariance violations manifest themselves through errors of a magnitude similar to those of the earlier implementations.

Background: A metabolic genotype comprises all chemical reactions an organism can catalyze via enzymes encoded in its genome. A genotype is viable in a given environment if it is capable of producing all biomass components the organism needs to survive and reproduce. Previous work has focused on the properties of individual genotypes while little is known about how genome-scale metabolic networks with a given function can vary in their reaction content. Results: We here characterize spaces of such genotypes. Specifically, we study metabolic genotypes whose phenotype is viability in minimal chemical environments that differ in their sole carbon sources. We show that regardless of the number of reactions in a metabolic genotype, the genotypes of a given phenotype typically form vast, connected, and unstructured sets -- genotype networks -- that nearly span the whole of genotype space. The robustness of metabolic phenotypes to random reaction removal in such spaces has a narrow distribution with a high mean. Different carbon sources differ in the number of metabolic genotypes in their genotype network; this number decreases as a genotype is required to be viable on increasing numbers of carbon sources, but much less than if metabolic reactions were used independently across different chemical environments. Conclusions: Our work shows that phenotype-preserving genotype networks have generic organizational properties and that these properties are insensitive to the number of reactions in metabolic genotypes.

We show that an enslaved phase-separation front moving with diffusive speeds U = C T^(-1/2) can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

For the realisation of scalable solid-state quantum-bit systems, spins in semiconductor quantum dots are promising candidates. A key requirement for quantum logic operations is a sufficiently long coherence time of the spin system. Recently, hole spins in III-V-based quantum dots were discussed as alternatives to electron spins, since the hole spin, in contrast to the electron spin, is not affected by contact hyperfine interaction with the nuclear spins. Here, we report a breakthrough in the spin coherence times of hole ensembles, confined in so called natural quantum dots, in narrow GaAs/AlGaAs quantum wells at temperatures below 500 mK. Consistently, time-resolved Faraday rotation and resonant spin amplification techniques deliver hole-spin coherence times, which approach in the low magnetic field limit values above 70 ns. The optical initialisation of the hole spin polarisation, as well as the interconnected electron and hole spin dynamics in our samples are well reproduced using a rate equation model.

We have investigated spin and carrier dynamics of resident holes in high-mobility two-dimensional hole systems in GaAs/Al$_{0.3}$Ga$_{0.7}$As single quantum wells at temperatures down to 400 mK. Time-resolved Faraday and Kerr rotation, as well as time-resolved photoluminescence spectroscopy are utilized in our study. We observe long-lived hole spin dynamics that are strongly temperature dependent, indicating that in-plane localization is crucial for hole spin coherence. By applying a gate voltage, we are able to tune the observed hole g factor by more than 50 percent. Calculations of the hole g tensor as a function of the applied bias show excellent agreement with our experimental findings.

Phase-separation fronts leave in their wakes morphologies that are substantially different from the morphologies formed in homogeneous phase-separation. In this paper we focus on fronts in binary mixtures that are enslaved phase-separation fronts, i.e. fronts that follow in the wake of a control-parameter front. In the one-dimensional case, which is the focus of this paper, the formed morphology is deceptively simple: alternating domains of a regular size. However, determining the size of these domains as a function of the front speed and other system parameters is a non-trivial problem. We present an analytical solution for the case where no material is deposited ahead of the front and numerical solutions and scaling arguments for more general cases. Through these enslaved phase-separation fronts large domains can be formed that are practically unattainable in homogeneous one-dimensional phase-separation.

Simulations of liquid-gas systems with extended interfaces are observed to fail to give accurate results for two reasons: the interface can get ``stuck'' on the lattice or a density overshoot develops around the interface. In the first case the bulk densities can take a range of values, dependent on the initial conditions. In the second case inaccurate bulk densities are found. In this communication we derive the minimum interface width required for the accurate simulation of liquid gas systems with a diffuse interface. We demonstrate this criterion for lattice Boltzmann simulations of a van der Waals gas. When combining this criterion with predictions for the bulk stability we can predict the parameter range that leads to stable and accurate simulation results. This allows us to identify parameter ranges leading to high density ratios of over 1000. This is despite the fact that lattice Boltzmann simulations of liquid-gas systems were believed to be restricted to modest density ratios of less than 20.

We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical potential of each component and the pressure of the overall system, are incorporated in the model. We derived a symmetrical convection diffusion equation for each component as well as the Navier Stokes equation and continuity equation for the overall system. The algorithm was verified through simulations of binary and ternary systems. The equilibrium concentrations of components of binary and ternary systems simulated with our algorithm agree well with theoretical expectations.

Lattice Boltzmann simulations of liquid-gas systems are believed to be restricted to modest density ratios of less than 10. In this article we show that reducing the speed of sound and, just as importantly, the interfacial contributions to the pressure allows lattice Boltzmann simulations to achieve high density ratios of 1000 or more. We also present explicit expressions for the limits of the parameter region in which the method gives accurate results. There are two separate limiting phenomena. The first is the stability of the bulk liquid phase. This consideration is specific to lattice Boltzmann methods. The second is a general argument for the interface discretization that applies to any diffuse interface method.

We present theoretical work in which the degree of electrostatic coupling across a charged lipid bilayer in aqueous solution is analyzed on the basis of nonlinear Poisson-Boltzmann theory. In particular, we consider the electrostatic interaction of a single, large macroion with the two apposed leaflets of an oppositely charged lipid bilayer where the macroion is allowed to optimize its distance to the membrane. Three regimes are identified: a weak and a high macroion charge regime, separated by a regime of close macroion-membrane contact for intermediate charge densities. The corresponding free energies are used to estimate the degree of electrostatic coupling in a lamellar cationic lipid-DNA complex. That is, we calculate to what extent the one-dimensional DNA arrays in a sandwich-like lipoplex interact across the cationic membranes. We find that, in spite of the low dielectric constant inside a lipid membranes, there can be a significant electrostatic contribution to the experimentally observed cross-bilayer orientational ordering of the DNA arrays. Our approximate analytical model is complemented and supported by numerical calculations of the electrostatic potentials and free energies of the lamellar lipoplex geometry. To this end, we solve the nonlinear Poisson-Boltzmann equation within a unit cell of the lamellar lipoplex using a new lattice Boltzmann method.

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency, i.e. to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of non-ideal lattice Boltzmann methods of sufficient order to identify those higher order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.

Polarized and unpolarized neutron diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems Cu2Te2O5X2 (X=Cl, Br). A model of the magnetic structure associated with the propagation vectors k'Cl ~ -0.150,0.422,1/2 and k'Br ~ -0.172,0.356,1/2 and stable below TN=18 K for X=Cl and TN=11 K for X=Br is proposed. A feature of the model, common to both the bromide and chloride, is a canted coplanar motif for the 4 Cu2+ spins on each tetrahedron which rotates on a helix from cell to cell following the propagation vector. The Cu2+magnetic moment determined for X=Br, 0.395(5)muB, is significantly less than for X=Cl, 0.88(1)muB at 2K. The magnetic structure of the chloride associated with the wave-vector k' differs from that determined previously for the wave vector k~0.150,0.422,1/2 [O. Zaharko et.al. Phys. Rev. Lett. 93, 217206 (2004)].

We describe some scaling issues that arise when using lattice Boltzmann methods to simulate binary fluid mixtures -- both in the presence and in the absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) lattice Boltzmann cannot fully resolve the hierarchy of length, energy and time scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed; an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale up simulations to very large lattice sizes? The problem is acute for systems undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimising such effects are discussed.

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is the main source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to an order of magnitude. Surprisingly incorporating this correction term can also noticeably increase the range of stability for multi-phase algorithms. We found that this is true for methods in which the non-ideality is incorporated by a forcing term as well as methods in which non-ideality is directly incorporated in a non-ideal pressure tensor.

We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy.

The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors $k$. Unlike previous work, which recovers FDT only as $k\to 0$, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversion of the density which can lead to fluid motion; although isothermal, this is somewhat like the Benard problem (a single-phase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important.

We investigate by Lattice Boltzmann methods the effect of inertia on the deformation and break-up of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is \em necessary for break-up, so that at zero Reynolds number the droplet deforms indefinitely without breaking. We identify two different routes to breakup via two-lobed and three-lobed structures respectively, and give evidence for a sharp transition between these routes as parameters are varied.

The structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several large-throughput datasets. Understanding the underlying evolutionary dynamics is crucial for discerning random parts of the network from biologically important properties shaped by natural selection. We present a detailed statistical analysis of the protein interactions in Saccharomyces cerevisiae based on several large-throughput datasets. Protein pairs resulting from gene duplications are used as tracers into the evolutionary past of the network. From this analysis, we infer rate estimates for two key evolutionary processes shaping the network: (i) gene duplications and (ii) gain and loss of interactions through mutations in existing proteins, which are referred to as link dynamics. Importantly, the link dynamics is asymmetric, i.e., the evolutionary steps are mutations in just one of the binding parters. The link turnover is shown to be much faster than gene duplications. According to this model, the link dynamics is the dominant evolutionary force shaping the statistical structure of the network, while the slower gene duplication dynamics mainly affects its size. Specifically, the model predicts (i) a broad distribution of the connectivities (i.e., the number of binding partners of a protein) and (ii) correlations between the connectivities of interacting proteins.

Stationary droplets simulated by multi-phase lattice Boltzmann methods lead to spurious velocities around them. In this article I report the origin of these spurious velocities for one example and show how they can be avoided.

Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short time scales. For instance, more than 100 interactions may be added to the yeast network every million years, a substantial fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain ? without natural selection on global network structure ? the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d) of proteins with d neighbors, which is a broad-tailed distribution. This distribution is independent of the experimental approach providing nformation on network structure.

I calculate the hydrodynamic limit of the BGK approximation of the Boltzmann equation for the case of a long stress relaxation time and find that the stress obeys a viscoelastic constitutive equation. The constitutive equation is different from standard constitutive equations used for polymeric liquids in that it is not ``objective'' because inertial effects are important. I calculate the exact solution for the stresses for simple shear flow and elongational flow.

By performing lattice Boltzmann simulations of a binary mixture, we scrutinize the dynamical scaling hypothesis for the spinodal decomposition of binary mixtures for the crossover region, i.e. the region of parameters in the growth curve where neither inertia nor viscous forces dominate the coarsening process. Our results give no evidence for a breakdown of scaling in this region, as might arise if the process were limited by molecular scale physics at the point of fluid pinch-off between domains. A careful data analysis allows us to refine previous estimates on the width of the crossover region which is somewhat narrower than previously reported.

Lees Edwards boundary conditions (LEbc) for Molecular Dynamics simulations are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maxinum shear rate that is limited to less than 1/Ly (with Ly the transverse system size) in traditional lattice Boltzmann implementations of shear flow.

The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains itself, throughout the viscous hydrodynamic regime, by a `coalescence-induced coalescence' mechanism. Scaling is recovered (with length scale $l \sim t$, as in $d=3$). The crossover to the inertial hydrodynamic regime is delayed even longer than in $d=3$; on entering it, full symmetry is finally restored and we find $l\sim t^{2/3}$, regardless of the initial state.

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdoes-Renyi random graphs and synthetic small world networks of the same connectivity, the metabolic network has a particularly large number of triangles and a deficit in large cycles. Short cycles reduce the length of detours when a connection is clipped, so we propose that long cycles in metabolism may have been selected against in order to shorten transition times and reduce the likelihood of oscillations in response to external perturbations.

In this article we show that the phase-ordering scaling state for binary fluids is not necessarily unique and that local correlations in the initial conditions can be responsible for selecting the scaling state. We describe a new scaling state for symmetric volume fractions that consists of drops of the one component suspended in a matrix of the other. The underlying reason for the existence of the newly observed scaling state is that the main coarsening mechanism of binary fluids which is the deformation of interfaces by flow is not acting, and this leads to a new scaling law. An initial droplet state can be formed by a number of physical phenomena. In a unified description this can be undestood as local correlations in the initial conditions. Local correlations with length $\xi$ are believed to be irrelevant when the typical length scale L of the system is large ($L\gg \xi$). Our result shows that these initial correlations, contrary to current thinking, can be important even at late times.

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier-Motzkin elimination, provides an important tool for visualizing the state space of lattice Boltzmann algorithms that conserve a given set of moments of the distribution function. We show how such models can be endowed with a Lyapunov functional, analogous to Boltzmann's H, resulting in unconditional numerical stability. Using the Chapman-Enskog analysis and numerical simulation, we demonstrate that such entropically stabilized lattice Boltzmann algorithms, while fully explicit and perfectly conservative, may achieve remarkably low values for transport coefficients, such as viscosity. Indeed, the lowest such attainable values are limited only by considerations of accuracy, rather than stability. The method thus holds promise for high-Reynolds number simulations of the Navier-Stokes equations.

In this letter we show that the late-time scaling state in spinodal decomposition is not unique. We performed lattice Boltzmann simulations of the phase-ordering of a 50%-50% binary mixture using as initial conditions for the phase-ordering both a symmetric morphology that was created by symmetric spinodal decomposition and a morphology of one phase dispersed in the other, created by viscoelastic spinodal decomposition. We found two different growth laws at late times, although both simulations differ only in the early time dynamics. The new scaling state consists of dispersed droplets. The growth law associated with this scaling state is consistent with a $L\sim t^{1/2}$ scaling law.

We use lattice Boltzmann simulations to study the effect of shear on the phase ordering of a two-dimensional binary fluid. The shear is imposed by generalising the lattice Boltzmann algorithm to include Lees-Edwards boundary conditions. We show how the interplay between the ordering effects of the spinodal decomposition and the disordering tendencies of the shear, which depends on the shear rate and the fluid viscosity, can lead to a state of dynamic equilibrium where domains are continually broken up and re-formed.

We developed a new lattice Boltzmann method that allows the simulation of two-phase flow of viscoelastic liquid mixtures. We used this new method to simulate a bubble rising in a viscoelastic fluid and were able to reproduce the experimentally observed cusp at the trailing end of the bubble.

The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lattice Boltzmann scheme must satisfy in order to obey an H-theorem and show why on a lattice, unlike the continuous case, dynamics that decrease an H-functional do not necessarily lead to a unique ground state.

We present evidence, based on lattice Boltzmann simulations, to show that the coarsening of the domains in phase separating binary fluids is not a scale-invariant process. Moreover we emphasise that the pathway by which phase separation occurs depends strongly on the relation between diffusive and hydrodynamic time scales.

In this article we use a lattice-Boltzmann simulation to examine the effects of shear flow on a equilibrium droplet in a phase separated binary mixture. We find that large drops break up as the shear is increased but small drops dissolve. We also show how the tip-streaming, observed for deformed drops, leads to a state of dynamic equilibrium.