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River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

We obtain macroscopic equations for average suspension velocity and particle current in a Brownian suspension valid on long time scales for which the memory effects are important. The coefficients in these equations depend solely on local properties of the medium. This formalism allows one to obtain well-defined theoretical expressions for transport coefficients, free of the integrals diverging with the size of the system. As an example, the expression for long-time collective diffusion coefficient is derived and the memory contribution to this coefficient is estimated.

The mobility tensor for many spheres suspended in a viscous fluid is considered. An analytical formula for the divergence of this tensor is derived. It is then applied in calculations of long-time collective diffusion coefficient of hard-sphere suspension by means of Brownian dynamics method.

The problem of memory contribution to the collective diffusion coefficient of interacting Brownian particles is considered. A well-defined theoretical expression for this contribution, free of divergent integrals, is derived. Its value is then estimated for hard sphere suspensions numerically by means of extensive computer simulations.

The virial expansion of the collective mobility (sedimentation) coefficient is considered for hard sphere suspensions at equilibrium. The term of the second order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy. To achieve that we represent the collective mobility coefficient as the sum of convergent integrals over particle configurations. In this way the short-wave-number limit k→0 is avoided. Moreover, an efficient numerical procedure is applied to evaluate the hydrodynamic interactions. The algorithm is based on the multipole expansion, corrected for lubrication. The method allows us to analyze contributions to the collective mobility coefficient from different configurations of three particles and to select the dominant part. This suggests a general approximation scheme.

Rotne-Prager-Yamakawa approximation is a commonly used approach to model hydrodynamic interactions between particles suspended in fluid. It takes into account all the long-range contributions to the hydrodynamic tensors, with the corrections decaying at least as fast as the inverse fourth power of the interparticle distances, and results in a positive definite mobility matrix, which is fundamental in Brownian dynamics simulations. In this communication, we show how to construct the Rotne-Prager-Yamakawa approximation for the bulk system under shear flow, which is modeled using the Lees-Edwards boundary conditions.

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.

The Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equal-sized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, different-sized beads, which we illustrate with an example.

A shoelace can be readily untied by pulling its ends rather than its loops. Attempting to untie a native knot in a protein can also succeed or fail depending on where one pulls. However, thermal fluctuations induced by the surrounding water affect conformations stochastically and may add to the uncertainty of the outcome. When the protein is pulled by the termini, the knot can only get tightened, and any attempt at untying results in failure. We show that, by pulling specific amino acids, one may easily retract a terminal segment of the backbone from the knotting loop and untangle the knot. At still other amino acids, the outcome of pulling can go either way. We study the dependence of the untying probability on the way the protein is grasped, the pulling speed, and the temperature. Elucidation of the mechanisms underlying this dependence is critical for a successful experimental realization of protein knot untying.

The structure of a series of highly Al-doped superconducting Y(RE)-123 (RE = rare earth element) single crystals was investigated by XRD and NMR methods. On the basis of the data obtained by the structural investigations combined with the studies of magnetic and optical properties, the formation of various superstructures in the samples of pseudo-tetragonal symmetry has been discussed. The correlation between the carrier concentration and Tc-values has been determined. The superconductivity (at 70 K) was indicated even at the 2/3 and 1/3 Al substitution for Cu in the basal and CuO2 planes, respectively, in the phase presumably of a perovskite-like structural type.

The bond-valence-sum method is used to calculate the hole distribution in the spin ladders of [M 2 Cu 2 O 3 ] m [CuO 2 ] n -type cuprates with m = n = 1 (where M are divalent or trivalent cations). It is shown that the appearance of superconductivity in this system is related to hole transfer from chain planes to the spin-ladder plane. The role of the valency and size of the M atoms is discussed in detail.

The Drude–Lorentz model of a nonpolar dielectric with the simple cubic, face-centered and body-centered crystal lattice structures is considered. The electrostatic spectral density of the renormalized polarizability is found. The problem is equivalent to the calculation of the electronic density of states in the model. The obtained spectra are analyzed and the critical points are identified. The results are compared with the computer simulation data for a hard-sphere fluid. In the latter, the structure analogous to the transverse and longitudinal polarization modes characteristic for a solid dielectric is shown to exist.

An analytic argument is given to show that the application of the Kirkwood superposition approximation to the description of fluid correlation functions precludes the existence of a critical point. The argument holds irrespective of the dimension of the system and the specific form of the interaction potential and settles a long-standing controversy surrounding the nature of the critical behavior predicted within the approximation.

The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a “near-critical region” where monotonically decaying correlations acquire very long range, although the system never loses stability.

Atomistic and meso scale computer simulations of nanoparticle aggregation are combined to describe the self-assembly of supraparticles in bulk and on surfaces under vacuum conditions. At the nano scale, atomic resolution molecular dynamics simulations provide the structures of 30 nm-diameter nanoparticles bound to each other and to coated hydrophobic surfaces, through the physical contacting of their alkyl coats. This “molecular velcro” has been recently exploited in experiments to direct the aggregation of coated nanoparticles into stable assemblies on electronics platforms. Interaction potentials are extracted from the nano scale simulations and transferred to coarse grained Brownian dynamics simulations that describe multi-nanoparticle aggregation and surface deposition. The simulation results show that the large interaction area between 30 nm nanoparticles provides a strong driving force for assembly of strongly-welded, porous supraparticles under vacuum conditions. Interaction forces are significantly larger than those found in earlier simulations of the aggregation of smaller nanoparticles, indicating that supraparticle assembly using large 30 nm nanoparticles may be kinetically controlled. The porosity programmed into kinetic assembly may potentially benefit emerging applications of nanoparticle assemblies in medicine, in particular the development of nanostructured drug-eluting stent coatings. Future work will involve potential of mean force calculations in a variety of solvents to estimate the porosity obtainable for specific applications.

This article discusses a project where trainee translators were invited to translate and publish Wikipedia articles as part of their formal translator training. The findings suggest that this form of authentic assignment with real-life application is a powerful teaching format well-suited for, and appreciated by, trainee translators. The article discusses the strengths and limitations of the format, concluding that genuine translation projects in formal translation training are a promising practical contribution to the repertoire of social constructivist translator training in that trainees are provided a way of experiencing natural translation challenges in a safe but realistic environment. Piotr Szymczak

Rotne-Prager-Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation is that it includes all long-range terms (i.e. decaying as R^-3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne-Prager-Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne-Prager-Yamakawa approximation can be generalized for other geometries and boundary conditions., Comment: to be published in J. Fluid. Mech

A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system., Comment: to be published in J. Fluid. Mech

We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: as the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant., Comment: to be published in Phys. Rev. E

[1] A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We show that the “inlet” instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g., carbonate cements) is small, the instability in the steady-state equations is dominant.

We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D=3,4,5 and 6, proceeding from the YBG hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurence of a structural transition in the D->Infinity limit ., to be published in J. Chem. Phys

We consider several systems that are confined within a softly repulsive sphere. The first one is a model protein, crambin, which is described by a structure-based coarse grained model. We demonstrate that the folding process is accelerated by the hydrodynamic interactions (HI) in a way that depends on the radius of the sphere. The tighter the encompassing sphere, the smaller the effect, independent of the nature of the starting conformations. The second system is a protein surrounded by protein-like softly repulsive spheres that make the confined space crowded. In this case, the HI shorten the folding times in a way which depends on the degree of crowdedness only weakly. The third system is a collection of spheres that are meant to represent molecules. We show that confinement increases association times. We also observe that the HI either facilitate or obstruct association of two spheres depending on the crowding conditions. The dependence of the association time on crowdedness in the confining sphere is qualitatively distinct from that derived by Wieczorek and Zielenkiewicz for a cube with the periodic boundary conditions.

The solutional origin of limestone caves was recognized over a century ago, but the short penetration length of an undersaturated solution made it seem impossible for long conduits to develop. This is contradicted by field observations, where extended conduits, sometimes several kilometers long, are found in karst environments. However, a sharp drop in the dissolution rate of CaCO_3 near saturation provides a mechanism for much deeper penetration of reactant. The notion of a "kinetic trigger" - a sudden change in rate constant over a narrow concentration range - has become a widely accepted paradigm in speleogenesis modeling. However, it is based on one-dimensional models for the fluid and solute transport inside the fracture, assuming that the dissolution front is planar in the direction perpendicular to the flow. Here we show that this assumption is incorrect; a planar dissolution front in an entirely uniform fracture is unstable to infinitesimal perturbations and inevitably breaks up into highly localized regions of dissolution. This provides an alternative mechanism for cave formation, even in the absence of a kinetic trigger. Our results suggest that there is an inherent wavelength to the erosion pattern in dissolving fractures, which depends on the reaction rate and flow rate, but is independent of the initial roughness. In contrast to one-dimensional models, two-dimensional simulations indicate that there is only a weak dependence of the breakthrough time on kinetic order; localization of the flow tends to keep the undersaturation in the dissolution front above the threshold for non-linear kinetics., to be published in Earth and Planetary Science Letters

Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction {\eta}*~0.718, a value which is in substantial agreement with the packing fraction, {\eta}~0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. We next show that the same method of analysis predicts that exponential damping of oscillations in the hard sphere fluid becomes impossible when \lambda = 4n\pi {\sigma}^3 [1 + H(1)]>/- 34.81, where H(1) is the contact value of the correlation function, n is the number density and {\sigma} is the sphere diameter, in exact agreement with the condition, \lambda >/- 34.8, first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing., Comment: to be published in J. Chem. Phys

We investigate the dissolution of artificial fractures with three-dimensional, pore-scale numerical simulations. The fluid velocity in the fracture space was determined from a lattice-Boltzmann method, and a stochastic solver was used for the transport of dissolved species. Numerical simulations were used to study conditions under which long conduits (wormholes) form in an initially rough but spatially homogeneous fracture. The effects of flow rate, mineral dissolution rate and geometrical properties of the fracture were investigated, and the optimal conditions for wormhole formation determined., Comment: to be published in J. Geophys Res

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. Following Carleson and Makarov [L. Carleson and N. Makarov, J. Anal. Math. 87, 103 (2002)], the evolution of the fingers is studied with use of the deterministic Loewner equation. The method is then extended to study the growth in a linear channel with reflecting sidewalls. One- and two-finger solutions are found and analyzed. It turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.

The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A special diagrammatic method is developed to analyze the structure of the expansion. The concept of irreducibility is discussed in detail and shown to be crucial in obtaining macroscopic equations characterizing the system response with coefficients depending solely on local properties of the medium. Due to the representation of particles by lines in diagrams, irreducibility is given a particularly simple topological interpretation in the diagrammatic language. The method is illustrated by a discussion of response problems in colloidal suspensions in presence of hydrodynamic interactions., Comment: to be published in J. Stat. Mech

The conformational dynamics of a single protein molecule in a shear flow is investigated using Brownian dynamics simulations. A structure-based coarse grained model of a protein is used. We consider two proteins, ubiquitin and integrin, and find that at moderate shear rates they unfold through a sequence of metastable states - a pattern which is distinct from a smooth unraveling found in homopolymers. Full unfolding occurs only at very large shear rates. Furthermore, the hydrodynamic interactions between the amino acids are shown to hinder the shear flow unfolding. The characteristics of the unfolding process depend on whether a protein is anchored or not, and if it is, on the choice of an anchoring point., to be published in J. Chem. Phys

We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they diffuse around and eventually slide off. The waiting times of the jumps are increasingly stochastic as the temperature is raised. Larger knots do not return to their native locations when a protein is released after stretching., 4 pages, 5 figures

We incorporate hydrodynamic interactions in a structure-based model of ubiquitin and demonstrate that the hydrodynamic coupling may reduce the peak force when stretching the protein at constant speed, especially at larger speeds. Hydrodynamic interactions are also shown to facilitate unfolding at constant force and inhibit stretching by fluid flows., to be published in Journal of Physics: Condensed Matter

We report the results of experimental and numerical studies of two-phase flow in a periodic, rectangular network of microfluidic channels. This geometry promotes the formation of anisotropic, dendrite-like structures during viscous fingering experiments. The dendrites then compete with each other for the available flow, which leads to the appearance of hierarchical growth pattern. Combining experiments and numerical simulations, we analyze different growth regimes in such a system, depending on the network geometry and fluid properties. For immiscible fluids, a high degree of screening is present which results in a power-law distribution of finger lengths. Contrastingly, for miscible fluids, strong lateral currents of displaced fluid lead to the detachment of the heads of the longest fingers from their roots, thus preventing their further growth.

In the paper the radial and axial permanent magnet synchronous machines (RPMSM, APMSM) are classified in accordance with the types of design topologies and degree of active electromagnetic materials utilization. To realize an express comparison analysis of these machines the generalized geometric method is presented. Unlike the other methods this approach is distinguished by very small time for calculation of the ratio of radial and axial machines volumes as well as the similar ratio of mechatronic modules based on these machines. Derived a simple analytical expression enables to draw 3D plot of the volume ratio of compared machines at different number of poles and various geometrical sizes. The comparative study shows, that at the increased number of poles and at certain stator and rotor configuration the APMSM confidently exceed the RPMSM in term of torque/power density.

Kinetics of folding of a protein held in a force-clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force-clamp are distinct., Comment: 9 pages, 4 figures, Journal of Chemical Physics (in press)

[1] During dissolution in porous or fractured rock, a positive feedback between fluid transport and chemical reactions at the mineral surfaces may lead to the formation of pronounced, wormhole-like channels. As the dissolution proceeds the channels interact, competing for the available flow, and eventually the growth of the shorter ones ceases. Thus the number of channels decreases with time while the characteristic distance between them increases, which leads to a scale-invariant, power-law distribution of channel lengths. A simple resistor network model of the evolution of dissolving channels is constructed and its properties studied. The results are compared with pore-scale simulations of fracture dissolution using a microscopic, three-dimensional numerical model. Despite its simplicity, the resistor model is found to retain the essential features of the nonlinear interaction between the channels.

The creeping flow along a periodic rough surface is calculated as a series in the slope of the roughness grooves. On a scale much larger than the grooves, this flow is equivalent to that over a smooth plane which is shifted from the top of the riblets. The convergence of the series for the shift distance in term of the slope is accelerated by use of Euler transformation and of the existence of a limit for large slope. The case of a flow along the grooves is presented in detail. The result for the shift is typically valid for a slope up to 2. A flow perpendicular to grooves can be treated in a similar way. Asymptotic behaviour for large slope depends on the profile shape.

Mechanically induced protein unfolding in the force-clamp apparatus is shown, in a coarse-grained model of ubiquitin, to have lognormal statistics above a treshold force and exponential below it. Correspondingly, the mean unfolding time is slowly varying and exponentially decreases as a function of the force. The time dependencies of the end-to-end distances are also distinct. The time sequence of unfolding events weakly depends on force and much of it resembles that for stretching at constant speed. A more complicated time dependence arises for integrin., 14 pages, 6 figures; submitted to J. Phys. Cond. Matt

[1] Microscopic simulations of fracture dissolution are reported, taking account of the explicit topography of the pore space, the transport of reactants and products, and the chemical kinetics at the solid surfaces. A three-dimensional numerical model has been constructed, in which the fluid velocity field is calculated with an implicit lattice-Boltzmann method, and the transport of dissolved species is modeled by an innovative random walk algorithm that incorporates the chemical kinetics at the solid surfaces. The model contains no free parameters or semi-empirical mass-transfer coefficients. The simulated morphological changes in a complex fracture are compared with recent laboratory experiments [Detwiler et al., 2003] with the same initial topography.

From the solution of the creeping-flow equations, the drag force on a sphere becomes infinite when the gap between the sphere and a smooth wall vanishes at constant velocity, so that if the sphere is displaced towards the wall with a constant applied force, contact theoretically may not occur. Physically, the drag is finite for various reasons, one being the particle and wall roughness. Then, for vanishing gap, even though some layers of fluid molecules may be left between the particle and wall roughness peaks, conventionally it may be said that contact occurs. In this paper, we consider the example of a smooth sphere moving towards a rough wall. The roughness considered here consists of parallel periodic wedges, the wavelength of which is small compared with the sphere radius. This problem is considered both experimentally and theoretically. The motion of a millimetre size bead settling towards a corrugated horizontal wall in a viscous oil is measured with laser interferometry giving an accuracy on the displacement of 0.1 m. Several wedge-shaped walls were used, with various wavelengths and wedge angles.From the results, it is observed that the velocity of the sphere is, except for small gaps, similar to that towards a smooth plane that is shifted down from the top of corrugations. Indeed, earlier theories for a shear flow along a corrugated wall found such an equivalent smooth plane. These theories are revisited here. The creeping flow is calculated as a series in the slope of the roughness grooves. The cases of a flow along and across the grooves are considered separately. The shift is larger in the former case. Slightly flattened tops of the wedges used in experiments are also considered in the calculations. It is then demonstrated that the effective shift for the sphere motion is the average of the shifts for shear flows in the two perpendicular directions. A good agreement is found between theory and experiment.

Simulations of heat and mass transport may require complex nonlinear boundary conditions to describe the flow of mass and energy across an interface. Although stochastic methods do not suffer from the numerical diffusion of grid-based methods, they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce ideas and algorithms to account for mass (or energy) transfer at reactive interfaces, with accuracies comparable to the bulk phase. We show how to introduce particles into the system with the correct distribution near the interface, as well as the correct flux through the interface. The algorithms have been tested in a channel flow, for which accurate numerical solutions can be independently calculated.

Magnetization measurements on an amorphous ferro-magnetic magnetic ahoy Fe/sub 78/(SiB)/sub 22/ have been made over the temperature range from 5 to 295 K and in fields to 5 T, using a SQUID magnetometer and a superconducting magnet. As-received and field-annealed samples were measured. Having data over a range of temperatures allows the spin-wave contribution to the magnetization to be determined, and then subtracted. When the spin-wave contribution is removed, a substantial high-field susceptibility remains, which is independent of temperature. Attempts to fit the corrected curves to one of two theoretical equations were not conclusive, but the best fit seems to be to M=M/sub 0/+aH/sup -0.5/+bH. The annealing treatment has no significant effect on the high-field magnetization. >

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection-diffusion equation with accuracies comparable to the bulk phase. The algorithms have been tested in two-dimensional channel flows over a range of Peclet numbers, and compared with independent finite-difference calculations.

We study patterns formed by viscous fingering in a rectangular network of microfluidic channels. Due to the strong anisotropy of such a system, the emerging patterns have a form of thin needle-like fingers, which interact with each other, competing for an available flow. We develop an upscaled description of this system in which only the fingers are tracked and the effective interactions between them are introduced, mediated through the evolving pressure field. Due to the quasi-2d geometry of the system, this is conveniently accomplished using conformal mapping techniques. A complex two-phase flow problem is thus reduced to a much simpler task of tracking evolving shapes in a 2d complex plane. This description, although simplified, turns out to capture all the key features of the system's dynamics and allows for the effective prediction of the resulting growth patterns.

During the dissolution of porous rock, positive feedback between fluid transport and mineral dissolution leads to the spontaneous formation of pronounced wormhole-like channels. In a recent paper, Cohen et al. (2008) analyzed wormhole growth and competition in a dissolving porous rock, using a Darcy-scale numerical model developed by Golfier et al. (2002). In particular, they analyzed the competition between wormholes, which hinders the growth of shorter channels and leads to the emergence of a hierarchical structure, with many short wormholes, and only a few long ones. By analyzing the distribution of wormhole lengths (reproduced in Fig. 1) they found evidence for the existence of a characteristic length d ≈ 5cm, at which a change in slope occurs. They concluded that the wormhole competition process is not completely scale invariant. The length scale d was interpreted as marking a transition to a regime where the interplay of diffusion and convection of reactant within a wormhole plays a decisive role in its growth.

Aggregation of misfolded proteins into amyloid fibrils has been linked to several disorders such as Alzheimer's disease, or diabetes mellitus type II. Factors such as low pH, high temperature, and agitation have been recognized to accelerate this process in vitro. Amyloid fibrils from unrelated proteins share similar features on different levels of structural hierarchy: e.g. cross-beta structure, and tendency of individual fibrils to form intertwined chiral superstructures with defined morphological handedness and optical activity.In this work we investigate this phenomenon numerically with the use of coarse-grained numerical model of chiral fibrils. The aggregate morphologies, chirality and stability are then analyzed as a function of temperature and initial pitch of the fibrils. The simulations show the existence of a critical pitch below which the handedness of the aggregates is opposite to that of the constituting fibrils. We also observe and analyze the process of spontaneous chirality inversion of individual fibrils in the aggregate. This inversion is accompanied by a helical wave propagation along the fibril axis, with a kink separating left-haded and right-handed regions moving along the chain. The frequency of this process is strongly dependent on the initial pitch of the fibrils with a local maximum near the critical pitch.

The formation of aggregates of helical fibrils is analyzed numerically. The aggregate morphology, chirality and stability are studied as a function of temperature and helical pitch of individual fibrils. The simulations show the existence of a critical pitch above which the handedness of the aggregates is opposite to that of the constituting fibrils. We also observe and analyze the process of spontaneous chirality inversion of individual fibrils within the aggregates. This inversion is accompanied by a helical wave propagating along the fibril axis, with a kink separating left-handed and right-handed regions moving along the fibril. The frequency of this process is strongly dependent on the initial pitch of the fibrils with a local maximum near the critical pitch.

We present a theoretical description of linker-mediated self-assembly of gold nanoparticles (Au-NP). Using mesoscale simulations with a coarse-grained model for the Au NPs and dirhenium-based linker molecules, we investigate the conditions under which large clusters can grow and construct a phase diagram that identifies favorable growth conditions in terms of floating and bound linker concentrations. The findings can be considered as generic, as we expect other NP-linker systems to behave in a qualitatively similar way. In particular, we also discuss the case of antibody-functionalised Au NPs connected by the C-reactive proteins (CRPs). We extract some general rules for NP linking that may aid the production of size- and shape-specific NP clusters for technology applications. (Some figures in this article are in colour only in the electronic version)

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Stokesian dynamics simulations of close particles are reported, taking into account lubrication forces and many-body hydrodynamic interactions between spheres. A periodic trajectory of three particles maintaining a permanent proximity to each other has been found and analyzed. This solution is used as a benchmark to study the accuracy and stability of various numerical integration schemes. In particular, different methods of preventing unphysical overlaps of the particles are considered and potential artifacts discussed.