Search

A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is enhanced by inertia to induce a non-zero net flow. Building on classical work for simple geometrical forcing and motivated by the complex-shaped oscillations of elastic capsules and bubbles, we develop the mathematical framework to quantify the steady streaming of a spherical body with arbitrary axisymmetric time-periodic boundary conditions. We compute the flow asymptotically for small-amplitude oscillations of the boundary in the limit where the viscous penetration length scale is much smaller than the body. In that case, the flow has a boundary layer structure, and the fluid motion is solved by asymptotic matching. Our results, presented in the case of no-slip boundary conditions and extended to include the motion of vibrating free surfaces, recover classical work as particular cases. We illustrate the flow structure given by our solution and propose one application of our results for small-scale force generation and synthetic locomotion. [ABSTRACT FROM AUTHOR]

A number of micro-scale biological flows are characterized by spatio-temporal chaos. These include dense suspensions of swimming bacteria, microtubule bundles driven by motor proteins and dividing and migrating confluent layers of cells. A characteristic common to all of these systems is that they are laden with active matter, which transforms free energy in the fluid into kinetic energy. Because of collective effects, the active matter induces multi-scale flow motions that bear strong visual resemblance to turbulence. In this study, multi-scale statistical tools are employed to analyse direct numerical simulations (DNS) of periodic two-dimensional (2-D) and three-dimensional (3-D) active flows and to compare the results to classic turbulent flows. Statistical descriptions of the flows and their variations with activity levels are provided in physical and spectral spaces. A scale-dependent intermittency analysis is performed using wavelets. The results demonstrate fundamental differences between active and high-Reynolds-number turbulence; for instance, the intermittency is smaller and less energetic in active flows, and the work of the active stress is spectrally exerted near the integral scales and dissipated mostly locally by viscosity, with convection playing a minor role in momentum transport across scales. [ABSTRACT FROM AUTHOR]

The surface wettability effect on fluid transport in nanoscale slit pores is quantitatively accessed by using non-equilibrium molecular dynamics (NEMD) simulation incorporating with density functional theory (DFT). In particular, the slip lengths of benzene steady flows under various wetting conditions are computed with NEMD simulations and a quasi-general expression is given, while the structural properties are investigated with DFT. By taking into account the inhomogeneity of fluid density inside pore, we find that the conventional flux enhancement rate is associated with both the molecule slipping and geometrical confinement, and it becomes drastically high in solvophobic pores especially when the pore size is of several fluid diameters. In good agreement with experimental results, we further show that the wettability effect competes with pore size effect in determining the flux after pore inner surface modification, and a high flux can be achieved when the deposited layer is solvophobic yet thin. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1704-1714, 2017 [ABSTRACT FROM AUTHOR]

The double-faced Janus micro-motor, which utilizes the heterogeneity between its two hemispheres to generate self-propulsion, has shown great potential in water cleaning, drug delivery in micro/nanofluidics, and provision of power for a novel micro-robot. In this paper, we focus on the self-propulsion of a platinum-silica (Pt-SiO2) spherical Janus micro-motor (JM), which is one of the simplest micro-motors, suspended in a hydrogen peroxide solution (H2O2). Due to the catalytic decomposition of H2O2 on the Pt side, the JM is propelled by the established concentration gradient known as diffusoiphoretic motion. Furthermore, as the JM size increases to O (10 m), oxygen molecules nucleate on the Pt surface, forming microbubbles. In this case, a fast bubble propulsion is realized by the microbubble cavitation-induced jet flow. We systematically review the results of the above two distinct mechanisms: self-diffusiophoresis and microbubble propulsion. Their typical behaviors are demonstrated, based mainly on experimental observations. The theoretical description and the numerical approach are also introduced. We show that this tiny motor, though it has a very simple structure, relies on sophisticated physical principles and can be used to fulfill many novel functions. [ABSTRACT FROM AUTHOR]

We study heterotic backgrounds with non-trivial H-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear [ABSTRACT FROM AUTHOR]

Summary: This is a series of four lectures presented at the 2015 Enrico Fermi Summer School in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low-Reynolds-number examples such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of single active particles, covering the Stokes equation and the Scallop Theorem, and stressing the link between autonomous activity and the dipolar symmetry of the far flow field. In lecture 2 I discuss applications of this mathematics to the behaviour of microswimmers at surfaces and in external flows, and describe our current understanding of how swimmers stir the surrounding fluid. Lecture 3 concentrates on the collective behaviour of active particles, modelled as an active nematic. I write down the equations of motion and motivate the form of the active stress. The resulting hydrodynamic instability leads to a state termed "active turbulence" characterised by strong jets and vortices in the flow field and the continual creation and annihilation of pairs of topological defects. Lecture 4 compares simulations of active turbulence to experiments on suspensions of microtubules and molecular motors. I introduce lyotropic active nematics and discuss active anchoring at interfaces. [ABSTRACT FROM AUTHOR]

The shape and size distribution of micro- and nanoscale particles of a magnetoactive filler in an elastomeric matrix on the surface of a magnetorheological composite are determined by SEM and AFM methods. With the aid of AFM, the phenomena of the restructuring of particles of filler aggregates on the surface of elastomers under the action of a weak external constant magnetic field are directly visualized. A model is proposed for the interaction of the magnetoactive filler with the elastomeric matrix of a composite, which explains the observed experimental results. [ABSTRACT FROM AUTHOR]

In this study, an improved indirect cell coculture system was constructed by using a polyelectrolyte complex membrane generated by alginate (A) and chitosan (C). Methodologies of characterizing thickness and permeability of flat AC membrane were first established due to the importance of these two parameters in determining intercellular distance and degree of contact between cocultured cells. Compared to reaction time, both alginate concentration and molecular weight (Mw) of chitosan play more dominant roles in determining the membrane thickness and diffusion coefficients. Moreover, cells in the alginate gel and on the AC membrane could maintain high cell viability. Thus, an improved indirect cell coculture system constructed by flat AC membrane was fabricated and characterized, which provides a robust tool to study the effect of intercellular distance and degree of contact between cocultured cells on cell-cell interactions. [ABSTRACT FROM AUTHOR]

The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems. [ABSTRACT FROM AUTHOR]

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components. [ABSTRACT FROM AUTHOR]

Microdischarge-induced reaction processes working at atmospheric pressure create fractal-like network structure of metal nano-particles which shows variable electric and optical properties. Due to their smallness, microdischarges or microplasmas can be installed in a gas-tubing system, and they enable us to create a compact chemical reduction reactor which includes decomposers of molecules, gas flows, and aqueous solutions with metallic ions at atmospheric pressure. Ammonia (NH) gas is successfully decomposed in this reactor, and its products which include mainly hydrazine (NH) and flow in the downstream induce reduction reactions for AgNO solution. Various parameters in the reactor trigger formation of functional patterns of silver nano-particles like partially transparent layers whose conductivity is variable. Optical properties of this equivalent films show some absorption spectra coming from structure resonances, which can be an optical metamaterials in this self-assembly process. [ABSTRACT FROM AUTHOR]

Thermo-sensitive colloidal crystals were prepared simply and conveniently by mixing of colloidal silica spheres with a series of thermo-sensitive gel spheres, poly ( N-isopropyl acrylamide) (pNIPAm, 225~1500 nm in hydrodynamic diameter, 0.5~5 mol% in degree of cross-linking and at 20~45 °C) in the deionized aqueous suspension. The thermo-reversible change in the lattice spacing of colloidal crystals of monodispersed silica spheres (CS83, 103 nm in diameter) depends on the size of the admixed pNIPAm. For gel spheres with similar or less than that of the silica spheres, the lattice spacing decreased with rising temperature. On the other hand, the spacing increased with temperature for the mixtures with pNIPAm spheres of larger than the size of the silica spheres. A mechanism, which is able to explain properly the several experiments including the present work, is proposed, i.e., balancing between the weak adsorption and segregation effects of silica with gel spheres. [ABSTRACT FROM AUTHOR]

Myxococcus xanthus cells self-organize into aligned groups, clusters, at various stages of their lifecycle. Formation of these clusters is crucial for the complex dynamic multi-cellular behavior of these bacteria. However, the mechanism underlying the cell alignment and clustering is not fully understood. Motivated by studies of clustering in self-propelled rods, we hypothesized that M. xanthus cells can align and form clusters through pure mechanical interactions among cells and between cells and substrate. We test this hypothesis using an agent-based simulation framework in which each agent is based on the biophysical model of an individual M. xanthus cell. We show that model agents, under realistic cell flexibility values, can align and form cell clusters but only when periodic reversals of cell directions are suppressed. However, by extending our model to introduce the observed ability of cells to deposit and follow slime trails, we show that effective trail-following leads to clusters in reversing cells. Furthermore, we conclude that mechanical cell alignment combined with slime-trail-following is sufficient to explain the distinct clustering behaviors observed for wild-type and non-reversing M. xanthus mutants in recent experiments. Our results are robust to variation in model parameters, match the experimentally observed trends and can be applied to understand surface motility patterns of other bacterial species. [ABSTRACT FROM AUTHOR]

The solid-phase diagram of binary systems consisting of particles of diameter σA =σ and σB =γσ (γ ≤1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential. In addition to the diameter ratio γ that characterizes hard-sphere models, the phase diagram is a function of an additional parameter that controls the relative interaction strength between the different particle types. Phase diagrams are determined from extremes of thermodynamic functions by considering 15 candidate lattices. In general, it is shown that the phase diagram of a soft repulsive potential leads to the morphological diversity observed in experiments with binary nanoparticles, thus providing a general framework to understand their phase diagrams. Particular emphasis is given to the two most successful crystallization strategies so far: evaporation of solvent from nanoparticles with grafted hydrocarbon ligands and DNA programmable self-assembly. [ABSTRACT FROM AUTHOR]

Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties-such as density and temperature-through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state. Their mechanical pressure exhibits anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of L-fuzzy semi-topogenous order, L-fuzzy topogenous (cotopogenuous) space, L-fuzzy topology (cotopology),L-fuzzy quasi-uniform space and theL-fuzzy quasi-proximity space. We study some relationships between previous spaces. The notions of their continuities are investigated. [ABSTRACT FROM AUTHOR]

Crystallization is almost always initiated at an interface to a solid. This observation is classically explained by the assumption of a reduced barrier for crystal nucleation at the interface. However, an interface can also induce crystallization by prefreezing (i.e., the formation of a crystalline layer that is already stable above the bulk melting temperature). We present an atomic force microscopy (AFM)-based in situ observation of a prefreezing process at the interface of a polymeric model system and a crystalline solid. Explicitly, we show an interfacial ordered layer that forms well above the bulk melting temperature with thickness that increases on approaching melt-solid coexistence. Below the melting temperature, the ordered layer initiates crystal growth into the bulk, leading to an oriented, homogeneous semicrystalline structure. [ABSTRACT FROM AUTHOR]

Chitosan, the cationic polysaccharide derived from the natural polysaccharide chitin, has been studied as a biomaterial for more than two decades. As a polycationic polymer with favorable properties, it has been widely used to form polyelectrolyte complexes with polyanions for various applications in drug delivery fields. In recent years, a growing number of studies have been focused on the preparation of polyelectrolyte complexes based on chitosan and its water soluble derivatives. They have been considered well-suited as biomaterials for a number of vital drug carriers with targeted/controlled release profiles, e.g., films, capsules, microcapsules. In this work, an overview highlights not only the favorable properties of chitosan and its water soluble derivatives but also the good performance of the polyelectrolyte complexes produced based on chitosan. Their various types of applications as drug carriers are reviewed in detail. [ABSTRACT FROM AUTHOR]

Exclusion zone (EZ) formation at water-membrane interfaces was studied via bright- and dark-field microscopy. Various aqueous colloids including suspensions of charged microspheres, silicon dioxide particles, and raw whole milk were studied with Nafion® hydrophilic membranes. Interfacial formations observed included EZs and more complex patterns including striations, double layers, banding, dendritic aggregates of particles, and double-stranded structures resembling Birkeland current filaments in cold plasmas. A complex three-dimensional dynamic structure and continuous flow patterns persist in and around EZs, maintaining movement of the colloidal particles even after EZs are fully formed, for which a schematic is proposed. Since radiant energy is critical for EZ formation, we hypothesize that these interfacial phenomena are non-equilibrium dissipative structures that self-organize and self-maintain due to ongoing dynamic processes that may involve hydrodynamic interactions. Another experimental approach undertaken involved the construction of a microscope flow cell to measure the kinetics of EZ formation using sequential microphotography analyzed with macro-programmed ImageJ software to investigate effects of different types of conditioned water. No significant difference was found between spring water and the same water treated by a magnetic vortexer. A significant difference was found for municipal tap water compared to electrolyzed alkaline tap water from the same source. [ABSTRACT FROM AUTHOR]

Anatase titanium dioxide nanoparticles (TiO-NPs) were synthesized with and without gelatin via the sol-gel method. The TiO-NPs were characterized by a number of techniques, such as thermogravimetric analysis (TGA), X-ray diffraction analysis (XRD), transmission electron microscopy (TEM), fourier transform infrared spectroscopy (FT-IR) and ultraviolet visible spectroscopy (UV-Vis). The particle sizes of the TiO-NPs prepared with and without gelatin were ∼13 and ∼17 nm, respectively. The main advantage of using gelatin as a stabilizing agent is that it provides long-term stability for nanoparticles by preventing particles agglomeration. The results indicated that gelatin was a reliable green stabilizer, which can be used as a polymerization agent in the sol-gel method for synthesis of tiny size TiO-NPs. Moreover, the composite film was prepared by synthesized TiO-NPs nanoparticles and multi wall carbon nanotube (MWNT) on glassy carbon electrode (TiO-MWNT/GCE). The TiO-MWNT/GCE responded linearly to L-tryptophan (L-Trp) in the concentration of 1.0 × 10 to 1.5 × 10 M with detection limit of 5.2 × 10 M at 3 using amperometry. The studied sensor exhibited good reproducibility and long-term stability. [ABSTRACT FROM AUTHOR]

Colloidal crystallization and amorphous solidification of deionized suspensions of the polydispersed cationic gel spheres of lightly cross-linked poly(2-vinylpyridine), CAIBA-P2VP (107∼113 nm in diameter, ±19∼22 nm in dispersity), have been studied from the reflection spectroscopy, morphology, phase diagram, and elastic property. Crystallization takes place even for the polydispersed cationic gel spheres by the significant contribution of the extended electrical double layers formed around the spheres. Critical concentrations of melting coexisted with ion exchange resins were around 0.02 in volume fraction and high compared with those of other cationic and anionic gel crystals examined hitherto. The densities ( ρ) of CAIBA-P2VP in suspension state, i.e., weight percent of the gel spheres divided by the corresponding volume percent, was around 0.3. The ρ values decreased sharply with decreasing size of P2VP gel spheres, which supports the small gel spheres containing much water inside and being softer than the large ones. The closest intersphere distances of the crystals and/or amorphous solids were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. Fluctuation parameters ( b) evaluated from the rigidities of CAIBA-P2VP (0.15∼0.28) were large compared with those of gel crystals of large-sized P2VP-based cationic gel spheres, anionic thermosensitive gel spheres of poly( N-isopropylacrylamide) (0.05∼0.09) and further much larger than those of typical colloidal hard spheres (around 0.03). The dispersity in sphere size played an important role for distinguishing crystal and amorphous solid. Importance of the extended electrical double layers around the cationic gel spheres is supported in addition to the excluded volume effect of the sphere themselves on the crystallization and/or solidification. [ABSTRACT FROM AUTHOR]

We have studied the effect of additions of both anionic and cationic spherical silica colloids of different sizes on the rheology of dispersions of a well-characterised montmorillonite clay, SWy-2. The systems have been studied above and below the critical hydrodynamic overlap concentration, c*, of the clay. For dispersions at c < c* on replacement of ∼10 % w/w of the clay content by silica, it was found that whereas a cationic silica additive transformed a liquid-like, non-gelling montmorillonite dispersion into a substantial gel, anionic silica destroyed any nascent structure in the fluids, reducing the effective viscosity and virtually eliminating the rheological hysteresis characteristic of structured fluids. On the other hand, in the regime of c > c*, replacement of ∼10 % w/w of the clay content by silica leads to enhancements of all the rheological parameters characteristic of a gelling system, for the addition of both anionic and cationic silica. A simple tentative microstructural model for this complex behaviour is presented. This work, alongside our previous studies, confirms significant rheological modification by the addition of small quantities of nanoparticles as a general phenomenon of clay-colloid systems. It further suggests that viscosity enhancement and control of the rates of sol-gel transitions for product applications can be achieved using relatively low-cost, commercially available materials, such as silica nanoparticles and natural clays of different mineralogy. [ABSTRACT FROM AUTHOR]

String theory constructions towards the MSSM allow us to identify some general properties that could be relevant for tests at the LHC. They originate from the geometric structure of compactification and the location of fields in extra-dimensional space. Within the framework of the heterotic MiniLandscape we extract some generic lessons for supersymmetric model building. Among them is a specific pattern of SUSY breakdown based on mirage mediation and remnants of extended supersymmetry. This leads to a split spectrum with heavy scalars of the first two families of quarks and leptons and suppressed masses for gauginos, top partners and Higgs bosons. The models exhibit some specific form of hidden supersymmetry consistent with the high mass of the Higgs boson and all presently available experimental constraints. The most compelling picture is based on precision gauge coupling unification that might be in the kinematic reach of the LHC. [ABSTRACT FROM AUTHOR]

Star polymers with sulfonyl groups in the central core were prepared by ATRP and the degradation of their cores was investigated. The core of the star polymer was efficiently and selectively decomposed by piperidine. Furthermore, the star polymer with mesogens in the side chain showed almost the same LC-isotropic phase transition temperature as the resulting degradation product, demonstrating the independence of polymer architecture on LC properties. [ABSTRACT FROM PUBLISHER]

Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction, resulting in a transition from short-time ballistic dynamics to effective long-time diffusion. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and so-called run-and-tumble dynamics in orientation space. The latter process characterizes the manner in which the orientation of many bacteria decorrelates during their swimming motion. In contrast to rotary diffusion, the decorrelation occurs by means of large and impulsive jumps in orientation (tumbles) governed by a Poisson process. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily swimming particle in three canonical linear flows (extension, simple shear and solid-body rotation). We then show how to extend our results to the case where the swimmer orientation also decorrelates on account of run-and-tumble dynamics. Self-propulsion in general leads to the same long-time temporal scalings as for passive particles in linear flows but with increased coefficients. In the particular case of solid-body rotation, the effective long-time diffusion is the same as that in a quiescent fluid, and we clarify the lack of flow dependence by briefly examining the dynamics in elliptic linear flows. By comparing the new active terms with those obtained for passive particles we see that swimming can lead to an enhancement of the mean-square displacements by orders of magnitude, and could be relevant for biological organisms or synthetic swimming devices in fluctuating environmental or biological flows. [ABSTRACT FROM PUBLISHER]

Colloidal crystallization of highly monodisperse spindle-shaped hematite particles coated with poly(poly(ethylene oxide) methyl ether methacrylate) brush (SHB) was studied by reflection spectroscopy and optical microscopy. SHB suspensions were deionized exhaustively with the mixtures of cation- and anion-exchange resins more than 6 months. The liquid thin film along the vertical cell wall above the horizontal air-liquid interface showed the strong color bands. Furthermore, the reflection spectra composed of many sharp peaks shifted continuously toward shorter wavelengths with time. These observations support the presence of thin film of SHB suspension, where the width is thickened downward by the gravity and the layered liquid further flow downward with time. The rigidities of SHB crystals in the bulk phase estimated from the optical microscopy in the sedimentation equilibrium were 0.007 to 0.7 Pa as SHB concentration increased from 0.006 to 0.35 wt.%. The fluctuation parameter, b-factors of the anisotropic crystals, was from 0.025 to 0.035 and decreased slightly as particle concentration increased. Rigidities and the fluctuation parameters of SHB suspensions support that the elastic properties of the anisotropic-shaped colloidal crystals are close to those of typical crystals of colloidal spheres. Compression of the SHB crystals by the gravity is also suggested in the sedimentation equilibrium state. [ABSTRACT FROM AUTHOR]

We applied the complex scaling method to study the resonances of a Dirac particle in the Yukawa potential, and obtained the corresponding energies and widths. In the non-relativistic limit, our results are in excellent agreement with those by non-relativistic calculations with J-matrix approach. Furthermore, we found that the energies and widths of spin doublets are approximately degenerate, and preserve a good spin symmetry. The quality of spin symmetry is correlated with the parameters of the Yukawa potential. [ABSTRACT FROM AUTHOR]

A three-stage model is presented for the electrostatic repulsion between two parallel plates covered with polyelectrolyte brushes (i.e., plate-like soft particles) in an electrolyte solution. This is an extension of a previous theory (Ohshima, Colloid Polym Sci 277: 535, ), which assumes that when the two brushes come into contact, they are squeezed against each other but they do not interdigitate. The present theory covers the case where interdigitation between brushes occurs and proceeds until full interdigitation occurs. Then, compression of the polyelectrolyte brushes starts. That is, in the present model, the interaction process consists of three stages, i.e., interaction before contact of the polyelectrolyte brushes (stage 1), interdigitation (stage 2), and compression (stage 3). It is found that for highly charged polyelectrolyte brushes, the repulsive force between the two plates becomes almost constant independent of the plate separation during interdigitation. [ABSTRACT FROM AUTHOR]