An instrument for studying granular media in low-gravity environment.

A new experimental facility has been designed and constructed to study driven granular media in a low-gravity environment. This versatile instrument, fully automatized, with a modular design based on several interchangeable experimental cells, allows us to investigate research topics ranging from dilute to dense regimes of granular media such as granular gas, segregation, convection, sound propagation, jamming, and rheology-all without the disturbance by gravitational stresses active on Earth. Here, we present the main parameters, protocols, and performance characteristics of the instrument. The current scientific objectives are then briefly described and, as a proof of concept, some first selected results obtained in low gravity during parabolic flight campaigns are presented.

Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space.

Solids are distinguished from fluids by their ability to resist shear. In equilibrium systems, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern that is persistent, which in turn results from minimizing the free energy. In this work, we focus on a class of systems where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled by the constraints of mechanical equilibrium. We argue that these constraints can lead to a persistent pattern in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this persistent pattern. We investigate the structure and behavior of patterns both in real space and the dual space as the system evolves through the rigidity transition for a range of packing fractions and in two different shear protocols. We show that, in the protocol that creates homogeneous jammed states without shear bands, measures of shear jamming do not depend on strain and packing fraction independently but obey a scaling form with a packing-fraction-dependent characteristic strain that goes to zero at the isotropic jamming point ϕ_{J}. We demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which provides a quantitative measure of the rigidity of shear-jammed states.

How the ideal jamming point illuminates the world of granular media.

The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.

Origin of rigidity in dry granular solids.

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern. In this work, we focus on the emergence of shear rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.

Microstructure evolution during impact on granular matter.

We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.

Early embryonic lethality in genetically engineered mice: diagnosis and phenotypic analysis.

Embryonic lethality is a common phenotype that occurs in mice that are homozygous for genetically engineered mutations. These phenotypes highlight the time and place that a gene is first required during embryogenesis. Early embryonic lethality (ie, before and up to mid-gestation) can be straightforward to analyze because the stage at which death occurs suggests why an embryo has failed. Here we summarize general strategies for analyzing early embryonic lethal phenotypes in genetically engineered mouse mutants.

Jamming by shear.

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu-Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order-disorder transition.

Force networks and elasticity in granular silos.

We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. We use photoelastic particles to obtain information not available in previous silo experiments --the internal force structure. We directly compare various predictions with the results obtained by averaging ensembles of experimentally obtained force networks. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a nonlinear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported "giant overshoot" effect where overload pressure decays only after an initial increase (G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)). For smaller overloads we find that additional pressure propagates to great depth. Analysis of the differences between the inter-grain contact and force networks suggests that, for our system, when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing deep propagation. For larger loads, the force network rearranges, resulting in the expected, Janssen-like behavior. Thus, a meso-scale network phenomenon results in an observable nonlinearity in the mean pressure profile.

Phenotypic characterization of epiphycan-deficient and epiphycan/biglycan double-deficient mice.

OBJECTIVE: To characterize the in vivo role epiphycan (Epn) has in cartilage development and/or maintenance. METHODS: Epn-deficient mice were generated by disrupting the Epn gene in mouse embryonic stem cells. Epn/biglycan (Bgn) double-deficient mice were produced by crossing Epn-deficient mice with Bgn-deficient mice. Whole knee joint histological sections were stained using van Gieson or Fast green/Safranin-O to analyze collagen or proteoglycan content, respectively. Microarray analysis was performed to detect gene expression changes within knee joints. RESULTS: Epn-deficient and Epn/Bgn double-deficient mice appeared normal at birth. No significant difference in body weight or femur length was detected in any animal at 1 month of age. However, 9-month Epn/Bgn double-deficient mice were significantly lighter and had shorter femurs than wild type mice, regardless of gender. Male Epn-deficient mice also had significantly shorter femurs than wild type mice at 9 months. Most of the deficient animals developed osteoarthritis (OA) with age; the onset of OA was observed earliest in Epn/Bgn double-deficient mice. Message RNA isolated from Epn/Bgn double-deficient knee joints displayed increased matrix protein expression compared with wild type mice, including other small leucine-rich proteoglycan (SLRP) members such as asporin, fibromodulin and lumican. CONCLUSION: Similar to other previously studied SLRPs, EPN plays an important role in maintaining joint integrity. However, the severity of the OA phenotype in the Epn/Bgn double-deficient mouse suggests a synergy between these two proteins. These data are the first to show a genetic interaction involving class I and class III SLRPs in vivo.

Genetic regulation of mammalian diversity.

Mammals have evolved a variety of morphological adaptations that have allowed them to compete in their natural environments. The developmental genetic basis of this morphological diversity remains largely unknown. Bats are mammals that have the unique ability of powered flight. We have examined the molecular embryology of bats and investigated the developmental genetic basis for their highly derived limbs used for flight. Initially, we developed an embryo staging system for a model chiropteran, Carollia perspicillata, the short-tailed fruit bat that has subsequently been used for staging other bat species. Expression studies focusing on genes that regulate limb development indicate that there are similarities and differences between bats and mice. To determine the consequences of these expression differences, we have conducted an enhancer switch assay by gene targeting in mouse embryonic stem cells to create mice whose genes are regulated by bat sequences. Our studies indicate that cis-regulatory elements contribute to the morphological differences that have evolved among mammalian species.

Probing dense granular materials by space-time dependent perturbations.

The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping.

Fetal Leydig cell origin and development.

Male sexual differentiation is a complex process requiring the hormone-producing function of somatic cells in the gonad, including Sertoli cells and fetal Leydig cells (FLCs). FLCs are essential for virilization of the male embryo, but despite their crucial function, relatively little is known about their origins or development. Adult Leydig cells (ALCs), which arise at puberty, have been studied extensively and much of what has been learned about this cell population has been extrapolated to FLCs. This approach is problematic in that prevailing dogma in the field asserts that these 2 populations are distinct in origin. As such, it is imprudent to assume that FLCs arise and develop in a similar manner to ALCs. This review provides a critical assessment of studies performed on FLC populations, rather than those extrapolated from ALC studies to assemble a model for FLC origins and development. Furthermore, we underscore the need for conclusive identification of the source population of fetal Leydig cells.

Stress correlations in granular materials: an entropic formulation.

We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively.

Experimental measures of affine and nonaffine deformation in granular shear.

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces a mean azimuthal flow, smooth affine deformations, and irreversible so-called nonaffine particle displacements. We find that these processes are all of comparable magnitude and depend on the local shear rate. We compute the parameter of Falk and Langer characterizing nonaffine motion, Dmin2, and find that it is reasonably well described in terms of collections of single particles making locally nearly isotropic random steps, delta ri. Distributions for single particle nonaffine displacements, delta ri, satisfy P1(delta ri) proportional, variantexp[-|delta ri/Delta r|alpha] (alpha < or approximately 2).

Gas-driven subharmonic waves in a vibrated two-phase granular material.

Vibrated powders exhibit striking phenomena: subharmonic waves, oscillons, convection, heaping, and even bubbling. We demonstrate novel rectangular profile subharmonic waves for vibrated granular material, that occur uniquely in the two-phase case of grains, and a fluid, such as air. These waves differ substantially from those for the gas-free case, exhibit different dispersion relations, and occur for specific shaking parameters and air pressure, understandable with gas-particle flow models. These waves occur when the gas diffusively penetrates the granular layer in a time comparable to the shaker period. As the pressure is lowered towards P =0, the granular-gas system exhibits a Knudsen regime. This instability provides an opportunity to quantitatively test models of two-phase flow.

Functional redundancy of TGF-beta family type I receptors and receptor-Smads in mediating anti-Mullerian hormone-induced Mullerian duct regression in the mouse.

Amniotes, regardless of genetic sex, develop two sets of genital ducts: the Wolffian and Müllerian ducts. For normal sexual development to occur, one duct must differentiate into its corresponding organs, and the other must regress. In mammals, the Wolffian duct differentiates into the male reproductive tract, mainly the vasa deferentia, epididymides, and seminal vesicles, whereas the Müllerian duct develops into the four components of the female reproductive tract, the oviducts, uterus, cervix, and upper third of the vagina. In males, the fetal Leydig cells produce testosterone, which stimulates the differentiation of the Wolffian duct, whereas the Sertoli cells of the fetal testes express anti-Müllerian hormone, which activates the regression of the Müllerian duct. Anti-Müllerian hormone is a member of the transforming growth factor-beta (TGF-beta) family of secreted signaling molecules and has been shown to signal through the BMP pathway. It binds to its type II receptor, anti-Müllerian hormone receptor 2 (AMHR2), in the Müllerian duct mesenchyme and through an unknown mechanism(s); the mesenchyme induces the regression of the Müllerian duct mesoepithelium. Using tissue-specific gene inactivation with an Amhr2-Cre allele, we have determined that two TGF-beta type I receptors (Acvr1 and Bmpr1a) and all three BMP receptor-Smads (Smad1, Smad5, and Smad8) function redundantly in transducing the anti-Müllerian hormone signal required for Müllerian duct regression. Loss of these genes in the Müllerian duct mesenchyme results in male infertility due to retention of Müllerian duct derivatives in an otherwise virilized male.

Why do granular materials stiffen with shear rate? Test of novel stress-based statistics.

Recent experiments exhibit a rate dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, gamma. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence of (ln(gamma))(1/2).

Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system.

In this work, we first review some general properties of dense granular materials. We are particularly concerned with a statistical description of these materials, and it is in this light that we briefly describe results from four representative studies. These are: experiment 1: determining local force statistics, vector forces, force distributions and correlations for static granular systems; experiment 2: characterizing the jamming transition, for a static two-dimensional system; experiment 3: characterizing plastic failure in dense granular materials; and experiment 4: a dynamical transition where the material 'freezes' in the presence of apparent heating for a sheared and shaken system.

Effects of surface friction on a two-dimensional granular system: numerical model of a granular collider experiment.

We present numerical results from a simulation of a granular collider experiment [B. Painter, M. Dutt, and R. P. Behringer, Physica D 175, 43 (2003)] using a numerical model which accounts for substrate frictional effects [M. Dutt and R. P. Behringer, Phys. Rev. E 70, 061304 (2004)]. We find the gradual birth and growth of a central cluster for the final state of the particles that depends on the system size, the substrate frictional dissipation, and the initial average kinetic energy. For systems where a central cluster is observed in the final state, the autocorrelation function C(r) of the interparticle spacing satisfies a Gaussian functional form C(r)=Ae-(r/sigma)2. We also find that the fluctuation speed distributions adhere to a Maxwell-Boltzmann distribution for times in the vicinity of collapse. Our results strongly indicate that the principal mechanism responsible for the energy and momentum dissipation is the particle-substrate kinetic friction. Our findings reiterate the importance of considering the effects of substrate friction in particle-substrate systems, as shown by the agreement between our numerical results with experimental findings of Painter, Dutt, and Behringer.