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Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using a Cosserat model we derive, through variational principles, the equations of motion for two special cases: one in which the system is confined inside a frictionless channel, and one in which it is placed in an anisotropic frictional environment, modeling the dynamical setting of the slithering of snakes on flat surfaces. The presence of constraints in both cases leads to non-standard boundary conditions, that allow us to close the equations of motion reducing them to a differential and an integro-differential equation, respectively, for one end point (the tail) of the active rod. For the snake-like case we also provide analytic solutions for a special class of motions. We highlight the role of the spontaneous curvature in the pushing (and the steering, in the snake-like setting) needed to power locomotion. Comparisons with available experiments confirm that the model is able to capture many of the essential findings in the zoological literature. The complete solvability and the existence of analytic solutions offers a tool that may prove valuable for the design of bio-inspired soft robots.

We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. 'breathing-like' deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.

In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding 'along the grain', and high resistance when sliding 'against the grain'. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots., Comment: 20 pages, 7 figures

We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamics flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number., Comment: 5 pages, 3 figures

We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by M\"uller and Sver\'ak in the context of crystalline solids.

In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost., Comment: 25 pages, 11 figures

Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix---ferronematics--- as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and, simultaneously, cause reorientation of the nematic molecules, greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in a physical literature.

We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-differential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Differentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fixed sink and trim., Comment: 39 pages, 12 figures. Addressed reviewers comments from v1

We investigated the effects of particle shape on shear thickening in densely packed suspensions. Rods of different aspect ratios and non-convex hooked rods were fabricated. Viscosity curves and normal stresses were measured using a rheometer for a wide range of packing fractions for each shape. Suspensions of each shape exhibit qualitatively similar Discontinuous Shear Thickening. The logarithmic slope of the stress/shear-rate relation increases dramatically with packing fraction and diverges at a critical packing fraction phi_c which depends on particle shape. The packing fraction dependence of the viscosity curves for different convex shapes can be collapsed when the packing fraction is normalized by phi_c. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. The value of phi_c is found to coincide with the onset of a yield stress at the jamming transition, suggesting the jamming transition also controls shear thickening. The yield stress is found to correspond with trapped air in the suspensions, and the scale of the stress can be attributed to interfacial tension forces which dramatically increase above phi_c due to the geometric constraints of jamming. The relationship between shear and normal stresses is found to be linear in both the shear thickening and jammed regimes, indicating that the shear stresses come from friction. In the limit of zero shear rate, normal stresses pull the rheometer plates together due to the surface tension of the liquid below phi_c, but push the rheometer plates apart due to jamming above phi_c., Comment: 13 pages, 13 figures. published in Physical Review E

We report the first observation of the rare eta->e+e-e+e- decay based on 1.7 fb^{-1} collected by the KLOE experiment at the DAFNE phi-factory. The selection of the e+e-e+e- final state is fully inclusive of radiation. We have identified 362 +- 29 events resulting in a branching ratio of (2.4 +- 0.2_stat+bckg +- 0.1_syst) x 10^{-5}., Comment: 12 pages, 3 figures, to be published on PLB

The LHCb Muon system performance is presented using cosmic ray events collected in 2009. These events allowed to test and optimize the detector configuration before the LHC start. The space and time alignment and the measurement of chamber efficiency, time resolution and cluster size are described in detail. The results are in agreement with the expected detector performance., Comment: Submitted to JINST and accepted

We study self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail., Comment: 32 pages, 9 figures

Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3., Comment: 21 pages, 8 figures

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming., Comment: 21 pages, 14 figures. submitted to the Journal of Rheology

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response., Comment: 11 pages, 9 figures, accepted for publication in Nature Materials

We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms., Comment: 34 pages, 15 figures. v2: Fixed a reference and eliminated journal style file. v3: Addressed referee's comments.

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response., Comment: 43 pages

This report, the third in a series of reports from the longitudinal evaluation of the Eisenhower Professional Development Program, examines the effects of professional development on improving classroom teaching practice. The Eisenhower Professional Development Program, Title II of the Elementary and Secondary Education Act, is the federal government's largest investment that focuses solely on developing the classroom teachers' knowledge and skills. Drawing on longitudinal data from approximately 300 teachers, this report discusses the impact of the types of professional development activities supported by the Eisenhower Professional Development Program. Results indicate that professional development focused on specific, higher order teaching strategies increased teachers' uses of these strategies in the classroom. This effect was even stronger when the professional development activity was a reform type, rather than traditional. Teachers in the sample did not consistently receive high quality professional development, and teachers in the same school tended to have quite different professional development experiences. There was little change in overall teaching practice from 1996-99. Despite little average change over time in teaching practice, individual teachers varied in their classroom practices, and moderate variation occurred in the classroom practices of individual teachers from year to year. (SM)

Comprehensive school reform (CSR) has the potential to help overcome inequities in education, to provide a vehicle for a combination of state and local control, and to allow reform to permeate the classroom. It is instructive and timely to survey the research on CSR models to determine how well the programs are performing. This monograph does not attempt to synthesize the results of evaluations of individual CSR designs. Instead, it focuses on principles learned from evaluations of CSR, especially large-scale implementation of efforts of CSR designs. A section about CSR implementation reviews what is known about: (1) variations in implementation; (2) design choice; (3) principal leadership; (4) politics; (5) support from design teams; (6) resources; and (7) context. The third section considers preliminary findings from research about the effects of comprehensive school reform on student outcomes. Recommendations for implementation of CSR are synthesized, and recommendations are presented for future research. Most of the conclusions that can be drawn about CSR at present focus on implementation. They stress the importance of teacher participation, principal leadership, adequate resources, and contextual factors. An appendix describes CSR models. (Contains 173 references.) (SLD)

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples., Comment: 58 pages, 4 figures

The professional development of teachers is a crucial element of the nation's efforts to improve education. In recent years, these efforts have sought to foster high standards for teaching and learning for all of the nation's children, and almost all states have met federal requirements for developing challenging statewide content standards. Such standards seek a fundamental shift in what students learn. However, children's learning will be transformed only if high standards are reflected in teachers' classroom practice. Education reforms will not succeed without teachers who are immersed in the subjects they teach and who know how to foster both basic knowledge and advanced thinking and problem solving among their students. The Eisenhower Professional Development Program, Title II of the Elementary and Secondary Education Act (ESEA), is the federal government's largest investment that is solely focused on developing the knowledge and skills of classroom teachers. This is the second report of the National Evaluation of the Eisenhower Professional Development Program, Part B (State and Local Activities), a multi-year evaluation being conducted by the American Institutes for Research (AIR) under a contract with the U.S. Department of Education's Planning and Evaluation Service. The first report was based on six exploratory case studies of school districts conducted during the first months of the evaluation. This second report describes the current status of the program, based primarily on data from national probability samples of districts, SAHE grantees (i.e., the institutions of higher education and nonprofit organizations supported through the SAHE component of the program), and teachers, as well as on data from 10 in-depth case studies in 5 states. Contains 140 references. (Author/WRM)