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We confirm that for vanishingly small loading and large impact condition, it may be possible to generate solitons in a chain of grains that are characterized by Hertzian contacts. For uniform or progressive loading conditions throughout the chain, one generates soft-solitons which are weakly dispersive in space and time. Under conditions of weak impact, one generates acoustic pulses through the chain. We describe the displacements, velocities and accelerations suffered by the individual grains when subjected to solitons, soft-solitons and acoustic pulses and describe the effects of restitution on the propagating pulse.

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Physica A: Statistical Mechanics and its Applications

Propagation and backscattering of soliton-like pulses in a chain of quartz beads and related problems. (I). Propagation

We consider a model dilute ferrofluid with the grains suspended in water (e.g., γ-Fe2O3) and subject the system to a strong, homogeneous magnetic field directed perpendicular to the surface such that there is chain formation along the field direction. We show that an appropriate impulse initiated at the base of the container might travel as a nondispersive soliton pulse with sufficient energy to overcome surface tension and eject the ferrofluid grain nearest to the liquid-air interface. The proposed mechanism, if successfully realized in the laboratory, could help design a nozzle-free, ink-jet printer of unparalleled resolution. © 1999 American Institute of Physics.

Applied Physics Letters

Ejection of ferrofluid grains using nonlinear acoustic impulses - A particle dynamical study

We demonstrate that the propagation of solitons, soliton-like excitations and acoustic pulses discussed in the preceding article (M. Manciu, S. Sen and A.J. Hurd, Physica A, preceding article) can be used to detect buried impurities in a chain of elastic grains with Hertzian contacts. We also present preliminary data for 3D granular beds, where soliton-like objects can form and can be used to probe for buried impurities, thus suggesting that soliton-pulse spectroscopy has the potential to become a valuable tool for probing the structural properties of granular assemblies. The effects of restitution are briefly discussed. We refer to available experiments which support our contention.

Propagation and backscattering of soliton-like pulses in a chain of quartz beads and related problems. (II). Backscattering

We used the monoclonal antibody SMI-32 to label pyramidal cells of sensorimotor cortex in two chimpanzees. The majority of the pyramidal cells had typical vertically oriented apical dendrites that extended towards the pial surface. A small population of pyramidal cells varied from this orientation, so that the apical dendrites were 20°or more from radial, and were often inverted, extending away from the pial surface. When numbers of non-inverted and inverted pyramidal cells were compared, less than 1% were found to be inverted.

Somatosensory and Motor Research

Inverted pyramidal neurons in chimpanzee sensorimotor cortex are revealed by immunostaining with monoclonal antibody SMI-32

Neuron

Subcortical contributions to massive cortical reorganizations

We consider elastic grains which repel upon contact according to the Hertz potential V = aδn, n &gt; 2, where δ is the overlap between adjacent grains and report numerical and analytical studies for the case of a 1-D chain of spherical grains to show that an impulse initiated at an end of a chain of Hertzian grains in contact, eventually propagates as a soliton for all n &gt; 2.

Discrete hertzian chains and solitons

The ipsilateral and contralateral cortical connections of visual cortex of tree shrews (Tupaia belangeri) were investigated by placing restricted injections of fluorochrome tracers, wheat germ agglutinin-horseradish peroxidase, or biotinylated dextran amine into area 17 (V1), area 18 (V2), or the adjoining temporal dorsal area (TD). As previously reported, V1 was characterized by a widespread, patchy pattern of intrinsic connections; ipsilateral connections with V2, TD, and to a lesser extent, other areas of the temporal cortex; and contralateral connections with V1, V2, and TD. A surface-view of the myelin pattern in V1 revealed a patchwork of light and dark module-like regions. The ipsilateral connections with V2 and TD were roughly topographic, whereas heterotopic locations in V1 were callosally connected. Injections in V2 labeled as much as one third of V2 in a patchy pattern, and portions of ipsilateral V1 and TD in roughly topographic patterns. In addition, connections with several other visual areas in the temporal lobe were revealed. Contralaterally, most of the label was in V2, with some in V1 and TD. Injections in TD demonstrated connections within the region, and with adjoining portions of the temporal cortex, V2, and V1. There were sparse connections with an oval of densely myelinated cortex, which we have termed the temporal inferior area (TI). Callosal connections were concentrated in TD, but also included V2. The results provide further evidence for modular organizations within V1 and V2, and reveal for the first time the complete patterns of cortical connections of V2 and TD. The results are consistent with the proposal that at least three visual areas, the temporal anterior area, TA, the temporal dorsal area, TD, and the temporal posterior area, TP, exist along the rostrolateral border of V2 in tree shrews; suggest visual involvement of at least three other areas, the temporal inferior area, TI, the temporal anterior lateral area, and the temporal posterior inferior area located more ventrally in the temporal cortex; and fortify the conclusion that TD is the likely homologue of the middle temporal visual area of primates. Because tree shrews are considered close relatives of primates, the evidence for several visual areas along the border of V2 is more compatible with theories that propose a series of visual areas along V2 in primates, rather than a single visual area, V3.

Journal of Comparative Neurology

Cortical connections of striate and extrastriate visual areas in tree shrews

We present detailed numerical studies on the motion of an initial perturbation in a chain of spheres which are characterized by Hertzian contacts. We consider the propagation of the perturbation in the presence and in the absence of gravitational compaction in the chain [see R. S. Sinkovits and S. Sen, Phys. Rev. Lett. 74, 2686 (1995)]. Our results show that robust solitonlike pulses carry the initial perturbation from the surface to the depths of the Hertzian chains for various magnitudes of the initial perturbation at finite loadings of the column. In addition, we probe the structural characteristics of the solitonlike pulse as a function of the magnitude of the initial impact, of loading, and of the gravitational field. Our results suggest that the solitonlike features, while altered, persist at finite gravitational fields when the compaction of grains with increasing depth becomes important. In the presence of light mass impurities in the Hertzian chain, we present evidence of backscattering of the solitonlike pulse and suggest that acoustic backscattering can be a possible probe of buried light mass impurities in granular beds. In closing, we discuss the propagation of perturbations in finite Hertzian chains when the surface grain is coupled to a transducer which vibrates with very low amplitude and frequency, and we report the formation of metastable standing-wave-like patterns in finite Hertzian chains. © 1998 The American Physical Society.

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities

We use the continued fraction formalism to show that a weakly bound, S = 1/2, impurity spin, in a S = 1/2 XY chain exhibits slow relaxation. The dynamical xx-correlation of the impurity spin, at different couplings to the rest of the chain, is best described by a non-universal stretched-exponential-like (SEL) decay at large times. The zz-correlation for that spin shows exponential-like decay. The host spins relax faster than the impurity spin. To our knowledge, this is the first study which introduces a simple 1D spin Hamiltonian and solves the Heisenberg equation of motion for the impurity spin to obtain SEL relaxation. © 1998 Elsevier Science B.V. All rights reserved.

Stretched exponential-like impurity relaxation in the S = 1/2 XY chain: A numerical study

Somatotopic maps in the mature brain reorganize in response to deafferentation by peripheral nerve cut, amputations, or spinal lesions. Mechanisms underlying these changes may range from altered tonic inhibition and synaptic efficacy to neuronal sprouting. An understanding of these mechanisms could guide interventions that potentiate recovery from such injuries. © 1998 Int. Union Physiol. Sci./Am.Physiol. Soc.