Force, relative-displacement, and work networks in granular materials subjected to quasistatic deformation

To describe the heterogeneous nature of stress transmission in granular materials, the concept of the “strong” network consisting of contacts with large normal forces has been proposed by Radjaï et al. [Phys. Rev. Lett. 80, 61 (1998)]. The shear stress is mainly determined by this strong network. The dual viewpoint is adopted here, by not only considering the forces at contacts, but also the deformation. It is shown that the strain increments are determined by the tangential component of the relative displacements at the contacts. A “mobile” network consisting of contacts with large tangential relative displacements is defined that primarily accounts for the strain increments. The investigation of the relation between the strong and the mobile networks shows that these networks are largely unrelated. An alternative network is defined that consists of contacts at which the contribution to the work input is large. It is found that this work input occurs primarily through the tangential forces and tangential relative displacements

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

The deformation characteristics of idealized granular materials have been studied from the micro-mechanical viewpoint, using Bagi’s three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165–177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles. Bagi’s formulation expresses the continuum, macro-scale strain as an average over all edges, of their relative displacements (between two successive states) and the complementary-area vectors. This latter vector is a geometrical quantity determined from the set of edges, i.e. from the structure of the particle packing.\ud \ud Results from Discrete Element Method simulations of isotropic and triaxial loading of a three-dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary-area vectors of edges (subdivided into physical and virtual contacts) and of the relative displacements of edges. The investigated statistics are probability density functions and averages over groups of edges with the same orientation. It is shown that these averages can be represented by second-order Fourier series in edge orientation.\ud \ud Edge orientations are distributed isotropically, contrary to contact orientations. The average lengths of the branch vectors and the normal component of the complementary-area vectors are distributed isotropically (with respect to the edge orientation) and their average values are related to each other and to the volume fraction of the assembly. The other two components of the complementary-area vector are zero on average.\ud \ud The total deformation of the assembly, as given by the average of the relative displacements of the edges of the Delaunay tessellation follows the uniform-strain prediction. However, neither the deformation of the physical contact network nor of the virtual contact network has this property. The average relative displacement of physical edges in the normal direction (determined by the branch vector) is smaller than that according to the uniform-strain assumption, while that of virtual contacts is larger. This is caused by the high interparticle stiffness that hinders compression. The reverse observation holds for the tangential component of the relative displacement vector. The contribution of the deformation of the empty space between physical contacts to the continuum, macro-scale strain tensor is therefore very important for the understanding and the prediction of the macro-scale deformation of granular materials

A note on tsunamis: their generation and propagation in an ocean of uniform depth

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion. Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion during propagation and the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and more recently advocated by Benjamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case

Displacement of Histones at Promoters of \u3ci\u3eSaccharomyces cerevisiae\u3c/i\u3e Heat Shock Genes Is Differentially Associated with Histone H3 Acetylation

Chromatin remodeling at promoters of activated genes spans from mild histone modifications to outright displacement of nucleosomes in trans. Factors affecting these events are not always clear. Our results indicate that histone H3 acetylation associated with histone displacement differs drastically even between promoters of such closely related heat shock genes as HSP12, SSA4, and HSP82. The HSP12 promoter, with the highest level of histone displacement, showed the highest level of H3 acetylation, while the SSA4 promoter, with a lower histone displacement, showed only modest H3 acetylation. Moreover, for the HSP12 promoter, the level of acetylated H3 is temporarily increased prior to nucleosome departure. Individual promoters in strains expressing truncated versions of heat shock factor (HSF) showed that deletion of either one of two activating regions in HSF led to the diminished histone displacement and correspondingly lower H3 acetylation. The deletion of both regions simultaneously severely decreased histone displacement for all promoters tested, showing the dependence of these processes on HSF. The level of histone H3 acetylation at individual promoters in strains expressing truncated HSF also correlated with the extent of histone displacement. The beginning of chromatin remodeling coincides with the polymerase II loading on heat shock gene promoters and is regulated either by HSF binding or activation of preloaded HSF

Space as an invention of biological organisms

The question of the nature of space around us has occupied thinkers since the dawn of humanity, with scientists and philosophers today implicitly assuming that space is something that exists objectively. Here we show that this does not have to be the case: the notion of space could emerge when biological organisms seek an economic representation of their sensorimotor flow. The emergence of spatial notions does not necessitate the existence of real physical space, but only requires the presence of sensorimotor invariants called `compensable' sensory changes. We show mathematically and then in simulations that na\"ive agents making no assumptions about the existence of space are able to learn these invariants and to build the abstract notion that physicists call rigid displacement, which is independent of what is being displaced. Rigid displacements may underly perception of space as an unchanging medium within which objects are described by their relative positions. Our findings suggest that the question of the nature of space, currently exclusive to philosophy and physics, should also be addressed from the standpoint of neuroscience and artificial intelligence

Evolution of displacements and strains in sheared amorphous solids

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval $\Delta \gamma$ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small $\Delta \gamma$ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as $\Delta \gamma$ increases to about .03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest $\Delta \gamma$ studied.Comment: Submitted to J. Phys. Cond. Mat. special volume for PITP Conference on Mechanical Behavior of Glassy Materials. 16 Pages, 8 figure

Dynamics and Structure of Three-Dimensional Poloidally Magnetized Supermagnetosonic Jets

A set of 3D MHD simulations of magnetized jets has been performed. The jets contain an equipartition primarily poloidal magnetic field and the effect of jet density on jet dynamics and structure is evaluated. The jet is precessed at the origin to excite Kelvin-Helmholtz unstable helical modes. We extensively compare the structure in these simulations with linear stability theory. The jet that is dense with respect to the external medium develops a high speed core surrounded by a less dense sheath consisting of slower moving jet fluid. These simulations suggest that extended extragalactic jets propagate to such large distances because they are surrounded by a lobe or cocoon whose density is less than the jet density. (Abridged abstract.)Comment: 30 pages, AASTeX, to appear in ApJ, much better versions of Figures 2-5 are available at http://crux.astr.ua.edu/~rosen/hcr/hcr.htm

An optimized tuned mass damper/harvester device

Much work has been conducted on vibration absorbers, such as tuned mass dampers (TMD), where significant energy is extracted from a structure. Traditionally, this energy is dissipated through the devices as heat. In this paper, the concept of recovering some of this energy electrically and reuse it for structural control or health monitoring is investigated. The energy-dissipating damper of a TMD is replaced with an electromagnetic device in order to transform mechanical vibration into electrical energy. That gives the possibility of controlled damping force whilst generating useful electrical energy. Both analytical and experimental results from an adaptive and a semi-active tuned mass damper/harvester are presented. The obtained results suggest that sufficient energy might be harvested for the device to tune itself to optimise vibration suppression