In this letter we investigate a class of Hamiltonians which, in addition to the usual center-ofmass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where p and q are coprime integers. Interestingly the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis is the directed movement resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs in bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis and a mathematical model reveals that bacterial rheotaxis is a purely physical phenomenon, in contrast to fish rheotaxis but in the same way as sperm rheotaxis. This previously unrecognized bacterial taxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that alters a bacterium's swimming direction. Because this torque is independent of the presence of a nearby surface, bacterial rheotaxis is not limited to the immediate neighborhood of liquid-solid interfaces, but also takes place in the bulk fluid. We predict that rheotaxis occurs in a wide range of bacterial habitats, from the natural environment to the human body, and can interfere with chemotaxis, suggesting that the fitness benefit conferred by bacterial motility may be sharply reduced in some hydrodynamic conditions. low Reynolds number | directional motion | chirality T he effectiveness and benefit of motility are largely determined by the dependence of movement behavior on environmental stimuli. For example, chemical stimuli may affect the spreading of tumor cells (1) and allow bacteria to increase uptake by swimming toward larger nutrient concentrations (2, 3), whereas hydrodynamic stimuli can stifle phytoplankton migration (4), allow protists to evade predators (5), and change sperm-egg encounter rates for external fertilizers (6). Microorganisms exhibit a broad range of directed movement responses, called "taxes". Whereas some of these responses, such as chemotaxis (7) and thermotaxis (8), are active and require the ability to sense and respond to the stimulus, others, such as magnetotaxis (9) and gyrotaxis (4), are passive and do not imply sensing, instead resulting purely from external forces.Chemotaxis is the best studied among these directional motions: Bacteria measure chemical concentrations and migrate along gradients (Fig. 1A). For instance, chemotaxis guides Escherichia coli to epithelial cells in the human gastrointestinal tract, favoring infection (10); Rhizobium bacteria to legume root hairs in soil, favoring nitrogen fixation (2); and marine bacteria to organic matter, favoring remineralization (3). Equally as pervasive as chemical gradients in microbial habitats are gradients in ambient fluid velocity or "shear" (Fig. 1B). Although nearly every fluid environment experiences velocity gradientsfrom laminar shear in bodily conduits and soil to turbulent shear in streams and oceans-the effect of velocity gradients on bacterial motility has received negligible attention compared with chemical gradients, partly due to the difficulty of studying motility under controlled flow conditi...

Motivated by the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine the swimming of filaments in the nonlinear viscoelastic Upper Convected Maxwell model. We obtain the swimming velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. We use these results to examine the swimming of a simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends to decrease swimming speed, and changes in the beating patterns due to viscoelasticity can reverse swimming direction.The physical environment of the cell places severe constraints on mechanisms for motility. For example, viscous effects dominate inertial effects in water at the scale of a few microns. Therefore, swimming cells use viscous resistance to move, since mechanisms that rely on imparting momentum to the surrounding fluid, such as waving a rigid oar, do not work [1,2]. The fundamental principles of swimming in the low-Reynolds number regime of small-scale, slow flows have been established for many years [2,3,4,5], yet continue to be an area of active research. However, when a sperm cell moves through the viscoelastic mucus of the female mammalian reproductive tract, the theory of swimming in a purely viscous fluid is inapplicable. Observations of sperm show that they are strongly affected by differences between viscoelastic and viscous fluids. In particular, the shape of the flagellar beating pattern as well as swimming trajectories and velocities depend on the properties of the medium [6,7,8].The interplay of medium properties and flagellar motility or transport also arises in other situations, such as spirochetes swimming in a gel [9], and cilia beating in mucus to clear foreign particles in the human airway [10]. Motivated by these phenomena, we develop a theory for swimming filaments in a viscoelastic medium. We begin by analyzing the swimming of an infinite filament with a prescribed beating pattern in a fluid described by the Upper Convected Maxwell (UCM) model [11]. We deduce the hydrodynamic force per unit length acting on the filament and the swimming velocity to leading order in the deformation of the filament. Our results extend the findings of Lauga [12], who considered a variety of fading memory models for the case of a prescribed beat pattern on a planar sheet. We further apply our results to a simple model flagellum with active internal forces, and find that changes in flagellum shapes play a crucial role in distinguishing the effects of viscoelastic media.Newtonian fluids are characterized by a simple constitutive relation, in which stress is proportional to strain rate. Non-newtonian fluids cannot be characterized by a simple universal constitutive relation, and exhibit a range of phenomena such as elasticity, shear thinning, and yield stress behavior. We choose to focus our attention on fluids with fading memory, in which the stress relaxes over time to the viscous stress. We consider small amplitude deflections of an infinite filam...

Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on micro-organisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that a leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates.

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella.

We show that plane parabolic flow in a microfluidic channel causes nonmotile helically-shaped bacteria to drift perpendicular to the shear plane. Net drift results from the preferential alignment of helices with streamlines, with a direction that depends on the chirality of the helix and the sign of the shear rate. The drift is in good agreement with a model based on resistive force theory, and separation is efficient (> 80%) and fast (< 2 s). We estimate the effect of Brownian rotational diffusion on chiral separation and show how this method can be extended to separate chiral molecules.Many biochemically active molecules are naturally chiral and can only bind to target chiral molecules of a specific handedness [1]. The other enantiomer (i.e. the molecule having opposite handedness) may be inactive or cause undesirable effects. Chemical synthesis of chiral molecules usually produces a racemic mixture, with equal amounts of both enantiomers, and their separation based on chirality is of importance in fields ranging from agriculture to food and pharmaceutical industries. Currently favored approaches rely on gas, liquid or capillary electromigration chromatography [2], requiring costly chiral media. Thus, simpler, alternative approaches to chiral separation are desirable.Several alternative proposals for chiral separation exploit hydrodynamic forces. Some of these, yet untested experimentally, rely on the presence of a surface [3] or array of microvortices [4], and there has been successful chiral separation of cm-sized crystals in a rotating drum [5]. Other methods [6,7] stem from the prediction that a chiral particle in a simple shear flow experiences a lateral drift [8]. However, the feasibility of this approach has remained questionable, as measurements in Couette cells reported that the drift of mm-sized chiral objects [9] and the forces on cm-sized ones [10] differ from predictions by two orders of magnitude [9] or even in sign [10].Here we report that microscale chiral objects, three orders of magnitude smaller than previous studies [9,10], experience a lateral drift in a microfluidic shear flow and the magnitude of the drift is in agreement with our theory. Previous work has demonstrated the ability of microfluidics to separate and sort colloids by size [11], spermatozoa by motility [12], and microbes by their preference for dissolved chemicals [13]. Our method uses microchannels to sort particles by chirality. We show that an enantiomer drifts with direction determined by the local shear, demonstrate the feasibility of this method for chiral separation, and indicate how the high shear rates achievable in microchannels (> 10 6 s −1 [14]) allow it to be extended to smaller scales (< 40 nm).The origin of chirality-dependent drift at low Reynolds number can be simply understood for the case of a helix. In a shear flow, objects undergo periodic rotations known as Jeffery orbits [15]: a sphere rotates with constant angular velocity, whereas for an elongated body, such as a helix, the velocity depends on orienta...

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.

Abstract. -Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in the "two-fluid" model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can also enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network. The nature of these boundary conditions significantly impacts swimming speeds.While biological locomotion at low-Reynolds number is a well-established and active field (see [1] for a review), only recently has swimming in complex, non-Newtonian media started to be systematically explored. Indeed, many microorganisms routinely swim through complex or nonNewtonian media. Bacteria in the stomach such as Helicobacter pylori encounter gastric mucus [2]; mammalian sperm swim through viscoelastic mucus in the female reproductive tract [3,4]; and spirochetes burrow into the tissues they infect [5]. Most of the prior theoretical work on swimming in complex media has focused on viscoelastic fluids [6][7][8][9][10][11][12][13][14]. Because prescribed swimming strokes lead to the same swimming speed in linearly viscoelastic fluids as in Newtonian fluids [7,13], these studies have focused on the effects of nonlinear viscoelasticity [6,8,9,[11][12][13][14] and the effect of altered medium response on swimming strokes via fluid-structure interactions [9,10]. However, many biological viscoelastic materials contain crosslinked polymer networks, and are therefore solid rather than fluid. In this paper we focus on swimming in such crosslinked materials, which have a nonzero zero-frequency elastic shear modulus. We use the term "gel" to refer to these types of materials.Generally, viscoelastic materials have frequencydependent response, while the distinction we make between solid and fluid is a zero-frequency property. Some of the issues addressed by studies of viscoelastic fluids carry over straightforwardly to gels. For example, the fluidstructure interactions which determine the beating patterns of sperm flagella depend on the viscoelastic response at the beating frequency, not at zero frequency. However, a simple physical argument demonstrates a fundamental difference between swimming in a gel versus swimming in a fluid. In fluid dynamics, one uses no-slip boundary conditions, but for a swimmer in a solid, no-slip boundary conditions do not allow swimming. Under no-slip boundary ...