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The ability to traverse an unknown environment is crucial for autonomous robot operations. However, due to the limited sensing capabilities and system constraints, approaching this problem with a single robot agent can be slow, costly, and unsafe. For example, in planetary exploration missions, the wear on the wheels of a rover from abrasive terrain should be minimized at all costs as reparations are infeasible. On the other hand, utilizing a scouting robot such as a micro aerial vehicle (MAV) has the potential to reduce wear and time costs and increasing safety of a follower robot. This work proposes a novel cooperative IPP framework that allows a scout (e.g., an MAV) to efficiently explore the minimum-cost-path for a follower (e.g., a rover) to reach the goal. We derive theoretic guarantees for our algorithm, and prove that the algorithm always terminates, always finds the optimal path if it exists, and terminates early when the found path is shown to be optimal or infeasible. We show in thorough experimental evaluation that the guarantees hold in practice, and that our algorithm is 22.5% quicker to find the optimal path and 15% quicker to terminate compared to existing methods., Comment: 8 pages, 9 figures, code will be available at https://github.com/ethz-asl/scouting-ipp

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted locally, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, away from or towards fuel source and waste sink, depending on the product molecules' affinity towards fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

The use of modern software-defined radio (SDR) devices enables the implementation of efficient communication systems in numerous scenarios. Such technology comes especially handy in the context of search and rescue (SAR) systems, enabling the incorporation of additional communication data transmission into the otherwise sub-optimally used SAR bands at 121.5 and 243~MHz. In this work, we propose a novel low-complexity, energy-efficient modulation scheme that allows transmission of additional data within chirped homing signals, while still meeting the standards of international SAR systems such as COSPAS-SARSAT. The proposed method modulates information onto small deviations of the chirp slope with respect to the required unmodulated chirp, which can be easily detected at the receiver side using digital signal processing.

The rising demand for high-performing batteries requires new technological concepts. To facilitate fast charge and discharge, hierarchically structured electrodes offer short diffusion paths in the active material. However, there are still gaps in understanding the influences on the cell performance of such electrodes. Here, we employed a cell model to demonstrate that the morphology of the hierarchically structured electrode determines which electrochemical processes dictate the cell performance. The potentially limiting processes include electronic conductivity within the porous secondary particles, solid diffusion within the primary particles, and ionic transport in the electrolyte surrounding the secondary particles. Our insights enable a goal-oriented tailoring of hierarchically structured electrodes for high-power applications.

In order to operate in human environments, a robot's semantic perception has to overcome open-world challenges such as novel objects and domain gaps. Autonomous deployment to such environments therefore requires robots to update their knowledge and learn without supervision. We investigate how a robot can autonomously discover novel semantic classes and improve accuracy on known classes when exploring an unknown environment. To this end, we develop a general framework for mapping and clustering that we then use to generate a self-supervised learning signal to update a semantic segmentation model. In particular, we show how clustering parameters can be optimized during deployment and that fusion of multiple observation modalities improves novel object discovery compared to prior work. Models, data, and implementations can be found at https://github.com/hermannsblum/scim, Comment: accepted at ISRR 2022

We grafted polyacrylic acid brushes containing cysteine side chains at a defined surface density on planar lipid membranes. Specular X-ray reflectivity data indicated that the addition of Cd2+ ions induces the compaction of the polymer brush layer and modulates the adhesion of lipid vesicles. The critical threshold level inducing the switch from non-wetting to partial wetting state, [Cd2+] = 0.25 mM, was determined by microinterferometry. The interactions between vesicles and brushes were evaluated by height fluctuations of the membrane in contact with brushes and the shape of vesicles near the surface. To analyze these experiments, we have studied adhesion of axially symmetric vesicles for finite-range membrane-substrate interaction and buoyancy through simulations. We found that the local transversality condition that relates the maximal curvature at the edge of the adhesion zone to the adhesion strength remains rather accurate. Thus, although it is not experimentally possible to prepare vesicles at zero buoyancy, we can use the transversality condition to estimate the adhesion strength. However, the adhesion diagram is significantly modified by a finite range of membrane-substrate interaction and buoyancy. For downward buoyancy, vesicles merely sediment onto the substrate and there is no mean-field adhesion transition. For upward buoyancy, adhered vesicles are metastable at best. Thus, a mean-field adhesion transition can only occur at vanishing buoyancy. Only for zero-range membrane-substrate interaction does a second-order adhesion transition occur at finite interaction strength. For any finite-range interaction, the transition occurs when the membrane-substrate interaction changes from repulsive to attractive. We present a adhesion diagram as a function of adhesion strength and buoyancy and compare the adhesion behavior of vesicles to the wetting behavior of droplets of liquids., Comment: 15 pages, 17 figures

This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse Gaussian Processes (GPs). We prove theoretically that DNNs can be seen as a special case of sparse GPs, namely mixtures of GP experts (MoE-GP), and we devise a learning algorithm that brings the derived theory into practice. In experiments from two different robotic tasks -- inverse dynamics of a manipulator and object detection on a micro-aerial vehicle (MAV) -- we show the effectiveness of our approach in terms of predictive uncertainty, improved scalability, and run-time efficiency on a Jetson TX2. We thus argue that our approach can pave the way towards reliable and fast robot learning systems with uncertainty awareness., Comment: 12 pages, 6 figures and 1 table. Accepted at the 5th Conference on Robot Learning (CORL 2021), London, UK

In the future, extraterrestrial expeditions will not only be conducted by rovers but also by flying robots. The technical demonstration drone Ingenuity, that just landed on Mars, will mark the beginning of a new era of exploration unhindered by terrain traversability. Robust self-localization is crucial for that. Cameras that are lightweight, cheap and information-rich sensors are already used to estimate the ego-motion of vehicles. However, methods proven to work in man-made environments cannot simply be deployed on other planets. The highly repetitive textures present in the wastelands of Mars pose a huge challenge to descriptor matching based approaches. In this paper, we present an advanced robust monocular odometry algorithm that uses efficient optical flow tracking to obtain feature correspondences between images and a refined keyframe selection criterion. In contrast to most other approaches, our framework can also handle rotation-only motions that are particularly challenging for monocular odometry systems. Furthermore, we present a novel approach to estimate the current risk of scale drift based on a principal component analysis of the relative translation information matrix. This way we obtain an implicit measure of uncertainty. We evaluate the validity of our approach on all sequences of a challenging real-world dataset captured in a Mars-like environment and show that it outperforms state-of-the-art approaches., Comment: Accepted to IROS 2021. Updated version corresponding to IROS camera-ready. The source code is publicly available at: https://github.com/DLR-RM/granite

A hierarchical (triple scale) simulation methodology is presented for the prediction of the dynamical and rheological properties of high molecular weight entangled polymer melts. The methodology consists of atomistic, moderately coarse-grained (mCG), and highly coarse-grained slip-spring (SLSP) simulations. At the mCG level, a few chemically bonded atoms are lumped into one coarse-grained bead. At this level, the chemical identity of the atomistic system, and the interchain topological constraints (entanglements) are preserved. The mCG potentials are derived by matching local structural distributions of the mCG model to those of the atomistic model through iterative Boltzmann inversion. For matching mCG and atomistic dynamics, the mCG time is scaled by a time scaling factor, which compensates for the lower monomeric friction coefficient of the mCG model than that of the atomistic one. At the SLSP level, multiple Kuhn segments of a polymer chain are represented by one coarse-grained bead. The very soft nonbonded interactions between beads do not prevent chain crossing and, hence, can not capture entanglements. The topological constraints are represented by slip-springs. A compensating pair potential is used in the SLSP model, to keep the static macromolecular properties unaltered upon the introduction of slip-springs. The static and kinetic parameters of the SLSP model are determined based on the lower level simulation models. Particularly, matching the orientational autocorrelation of the end-to-end vector, we determine the number of slip-springs and calibrate the timescale of the SLSP model. As the test case, the hierarchical methodology is applied to $cis$-1,4-polybutadiene (cPB) at 413 K. Dynamical properties of cPB melts are calculated for a broad range of molecular weights. The calculations are compared, and found in good agreement, with experimental data from the literature.

Graphene-based nanostructured systems and van-der-Waals heterostructures comprise a material class of growing technological and scientific importance. Joining materials with vastly different properties, polymer-graphene heterosystems promise diverse applications in surface- and nanotechnology, including photovoltaics or nanotribology. Fundamentally, molecular adsorbates are prototypical systems to study confinement-induced phase transitions exhibiting intricate dynamics, which require a comprehensive understanding of the dynamical and static properties on molecular time and length scales. Here, we investigate the dynamics and the structure of a single polyethylene chain on free-standing graphene by means of molecular dynamics simulations. In equilibrium, the adsorbed polymer is orientationally linked to the graphene as two-dimensional folded-chain crystallites or, at elevated temperatures, as a floating solid. The associated superstructure can be reversibly melted on a picosecond time scale upon quasi-instantaneous substrate heating, involving ultrafast heterogeneous melting via a transient floating phase. Our findings elucidate time-resolved molecular-scale ordering and disordering phenomena in individual polymers interacting with solids, yielding complementary information to collective friction and viscosity, and linking to recent experimental observables from ultrafast electron diffraction. We anticipate that the approach will help in resolving non-equilibrium phenomena of hybrid polymeric systems over a broad range of time and length scales.

In equilibrium the interface potential that describes the interaction between two AB interfaces in a binary blend of A and B homopolymers is attractive at all distances, resulting in coarsening of the blend morphology even in the absence of interface curvature. We demonstrate that the dissipative assembly in response to a time-periodic variation of the blend incompatibility qualitatively alters this behavior, i.e., for suitable parameters the interface potential exhibits a periodic spatial modulation and AB interfaces adopt a well-defined distance. We explore for which oscillation periods and amplitudes an interface repulsion occurs and demonstrate that we can control the preferred interface distance over a wide range by varying the oscillation period. Using particle-based simulations we explicitly demonstrate that this dissipative assembly of a homopolymer blend results in a lamellar structure with multiple planar interfaces in a thin film geometry.

Multi-component polymer systems are important for the development of new materials because of their ability to phase-separate or self-assemble into nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction with a soft, coarse-grained polymer model is an established technique to investigate these soft-matter systems. Here we present an im- plementation of this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is suitable to simulate large system sizes with up to billions of particles, yet versatile enough to study properties of different kinds of molecular architectures and interactions. We achieve efficiency of the simulations commissioning accelerators like GPUs on both workstations as well as supercomputers. The implementa- tion remains flexible and maintainable because of the implementation of the scientific programming language enhanced by OpenACC pragmas for the accelerators. We present implementation details and features of the program package, investigate the scalability of our implementation SOMA, and discuss two applications, which cover system sizes that are difficult to reach with other, common particle-based simulation methods.

Carnivores are important components of ecosystems with wide-ranging effects on ecological communities.We studied the carnivore community in the Apostle Islands National Lakeshore (APIS), where the presence, distribution, and populations of carnivores was largely unknown. We developed a systematic method to deploy camera traps across a grid while targeting fine-scale features to maximize carnivore detection (Appendix 1), including systematic methods for organizing and tagging the photo data (Appendix 2). We deployed 88 cameras on 13 islands from 2014-2016. We collected 92,694 photographs across 18,721 trap nights, including 3,591 wildlife events and 1,070 carnivore events. We had a mean of 6.6 cameras per island (range 2-30), and our camera density averaged 1.23 (range 0.74-3.08) cameras/ km2. We detected 27 species and 10 terrestrial carnivores, including surprising detections of American martens (Martes americana) and gray wolves (Canis lupus). The mean richness of carnivores on an island was 3.23 (range 0-10). The best single variable to explain carnivore richness on the Apostle Islands was island size, while the best model was island size (positive correlation) and distance from mainland (negative correlation) (R2 = 0.92). Relative abundances for carnivores ranged from a low of 0.01 for weasels (Mustela spp.) to a high of 2.64 for black bears (Ursus americanus), and the relative abundance of a species was significantly correlated with the number of islands on which they were found. Carnivore occupancy ranged from lows of 0.09 for gray wolves and 0.11 for weasels to a high of 0.82 for black bears. Fuller understanding of APIS ecology will require on-going monitoring of carnivores to evaluate temporal dynamics as well as related ecological evaluations (e.g. small mammal dynamics, plant community dynamics) to understand trophic effects.

The string method is a general and flexible strategy to compute the most probable transition path for an activated process (rare event). We apply here the atomistic string method in the density field to the Cassie-Wenzel transition, a central problem in the field of superhydrophobicity. We discuss in detail the mechanism of wetting of a submerged hydrophobic cavity of nanometer size and its dependence on the geometry of the cavity. Furthermore, we discuss the algorithmic analogies between the string method and CREaM [Giacomello et al., Phys. Rev. Lett. 109, 226102 (2012)], a method inspired by the string that allows for a faster and simpler computation of the mechanism and of the free-energy profiles of the wetting process. This approach is general and can be employed in mesoscale and macroscopic calculations.

Using Molecular Dynamics simulations of a coarse-grained polymer liquid we investigate the transport of droplets on asymmetrically structured (saw-tooth shaped), vibrating substrates. Due to a continuous supply of power by substrate vibrations and the asymmetry of its topography, the droplets are driven in a preferred direction. We study this directed motion as a function of the size of the droplets, the linear dimensions of the substrate corrugation, and the period of vibrations. Two mechanisms of driven transport are identified: (i) one that relies on the droplet's contact lines and (ii), in a range of vibration periods, the entire contact area contributes to the driving. In this latter regime, the set-up may be used in experiments for sorting droplets according to their size. Additionally, we show that the linear dimension of the substrate corrugation affects the flux inside the droplet. While on a substrate with a fine corrugation droplets mostly slide, on a more coarsely corrugated substrate the flux may exhibit an additional rotation pattern., Comment: 24 pages, 17 figures, 2 tables

Using Molecular Dynamics simulations of a polymer liquid flowing past flat and patterned surfaces, we investigate the influence of corrugation, wettability and pressure on slippage and friction at the solid-liquid interface. For one-dimensional, rectangular grooves, we observe a gradual crossover between the Wenzel state, where the liquid fills the grooves, and the Cassie state, where the corrugation supports the liquid and the grooves are filled with vapor. Using two independent flow set-ups, we characterize the near-surface flow by the slip length, $\delta$, and the position, $z_\textrm{h}$, at which viscous and frictional stresses are balanced according to Navier's partial slip boundary condition. This hydrodynamic boundary position depends on the pressure inside the channel and may be located above the corrugated surface. In the Cassie state, we observe that the edges of the corrugation contribute to the friction., Comment: 13 pages, 13 figures

We study equilibrium properties of polymer films and droplets on a solid substrate employing particle-based simulation techniques (Molecular Dynamics) and a continuum description. Parameter-passing techniques are explored that facilitate a detailed comparison of the two models. In particular, the liquid-vapor, solid-liquid and solid-vapor interface tensions, and the Derjaguin or disjoining pressure are determined by Molecular Dynamics simulations. This information is then introduced into continuum descriptions accounting for (i) the full curvature and (ii) a long-wave approximation of the curvature (thin film model). A comparison of the dependence of the contact angle on droplet size indicates that the theories agree well if the contact angles are defined in a compatible manner., Comment: 34 pages, 13 figures

Coarse-grained theories of dense polymer liquids such as block copolymer melts predict a universal dependence of equilibrium properties on a few dimensionless parameters. For symmetric diblock copolymer melts, such theories predict a universal dependence on only chi N and Nbar, where chi is an effective interaction parameter, N is a degree of polymerization, and Nbar is a measure of overlap. We test whether simulation results for the structure factor S(q) obtained from several different simulation models are consistent with this two-parameter scaling hypothesis. We compare results from three models: (1) a lattice Monte Carlo model, the bond-fluctuation model, (2) a bead-spring model with harsh repulsive interactions, similar to that of Kremer and Grest, and (3) a bead-spring model with very soft repulsion between beads, and strongly overlapping beads. We compare results from pairs of simulations of different models that have been designed to have matched values of Nbar, over a range of values of chi N and N, and devise methods to test the scaling hypothesis without relying on any prediction for how the phenomenological interaction parameter chi depends on more microscopic parameters. The results strongly support the scaling hypothesis, even for rather short chains, confirming that it is indeed possible to give an accurate universal description of simulation models that differ in many details., Comment: 22 pages, 6 figures, submitted to Soft Matter

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different contact angles and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupr\'e wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies., Comment: 13 pages, 11 figures

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation \lambda. Upon increasing the incompatibility \chi\ (by decreasing temperature) in the disordered state, the known ordered phases form: for \lambda\ > \lambda_c, two coexisting macroscopic A- and B-rich phases, for \lambda\ < \lambda_c, a microstructured (lamellar) phase with wave number k(\lambda). In addition, we find a fourth region in the \lambda-\chi\ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. The three-phase region is reached, either, from the macroscopic phases, via a third lamellar phase that is rich in alternating sequences, or, starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (\lambda_c, \chi_c), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (\lambda_c, \chi_c). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M -> \infty are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation., Comment: 24 pages, 19 figures, version published in PRE, main changes: Sec. IIIA, Fig. 14, Discussion

We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The non-bonded interactions take the form of a weighted-density functional which allows us to describe the thermodynamics of self-assembly and packing effects of the coarse-grained beads in terms of a density expansion of the equation of state and the weighting functions that regularize the microscopic bead densities, respectively. Identifying the length and energy scales via the bilayer thickness and the thermal energy scale, kT, the model qualitatively reproduces key characteristics (e.g., bending rigidity, area per lipid molecules, and compressibility) of lipid membranes. We employ this model to study the main phase transition between the liquid and the gel phase of the bilayer membrane. We accurately locate the phase coexistence using free energy calculations and also obtain estimates for the bare and the thermodynamic line tension., Comment: 21 pages, 12 figures. Submitted to J. Chem. Phys

Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the mean-field approach and information about the distribution of distance between different molecules is lost. Based on the knowledge of the exact equilibrium single-chain properties in contact with solid substrates, we generate multi-chain configurations that serve as nearly equilibrated starting configurations for molecular dynamics simulations by utilizing the packing algorithm of Auhl and co-workers [J. Chem. Phys. 119, 12718 (2003)] for spatially inhomogeneous systems, i.e., a thin polymer film confined between two solid substrates. The single-chain conformations are packed into the thin film conserving the single-chain properties and simultaneously minimizing local fluctuations of the density. The extent to which enforcing the near-incompressibility of a dense polymer liquid during the packing process is able to re-establish intermolecular correlations is investigated by monitoring intermolecular correlation functions and the structure function of density fluctuations as a function of the distance from the confining solid substrates., Comment: 10 pages, 8 figures

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter $q=Q^{*4} /T^*$, $Q^*$ is the reduced quadrupole moment of the molecule and $T^*$ the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of Perturbation Theory (PT) in the Mean Spherical Approximation (MSA). As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures., Comment: J. Chem. Phys. (2008), to appear

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ simple and soft effective potentials, coarse-grained models can provide rather direct insight into collective phenomena in membranes on large time and length scales. We present a summary of recent progress in this rapidly evolving field, and pay special attention to model development and computational techniques. Applications of coarse-grained models to changes of the membrane topology are illustrated with studies of membrane fusion utilizing simulations and self-consistent field theory., Comment: 88 pages, 39 figures, accepted to Physics Reports, version with higher resolution figures available at http://www.mrl.ucsb.edu/~katsov/pubs/pub024.pdf

We describe two distinct approaches to obtaining cloud point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand canonical ensemble. The first method determines the chemical potential distribution $\mu(\sigma)$ (with $\sigma$ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution $\rho(\sigma)$ matches a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p(n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns $\mu(\sigma)$ such that an equal peak weight criterion is satisfied for p(n)$ for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining $\mu(\sigma)$. We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are {\em exponentially small} in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a novel polydisperse lattice gas model near its cloud curve, the results showing excellent quantitative agreement with the theory., Comment: 8 pages, 6 figures

Molecular dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model with Lennard-Jones interactions between the beads and a FENE potential between nearest neighbors along the backbone of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and non-equilibrium Molecular Dynamics simulations at constant temperature and volume using the Dissipative Particle Dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The viscosity and slippage at the interface are calculated as functions of grafting density and shear velocity., Comment: 12 pages, submitted to J Chem Phys

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first paper of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with system architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few $k_BT$ over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway.