Geometric origin of mechanical properties of granular materials

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list of contacts is known- is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to load increments, even though grains are rigid. This sets an uuper bound on the contact coordination number. The approximation of small displacements (ASD) allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation. Plasticity and hysteresis are due to the lack of such uniqueness and may stem, apart from intergranular friction, from small, but finite, rearrangements, in which the system jumps between two distinct potential energy minima, or from bounded tensile contact forces. The response to load increments is discussed. On the basis of past numerical studies, we argue that, if the ASD is valid, the macroscopic displacement field is the solution to an elliptic boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and minor errors correcte

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

We introduce a model for charge and heat transport based on the Landauer-Buttiker scattering approach. The system consists of a chain of $N$ quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T_L,\mu_L) and (T_R,mu_R), and adjust the parameters (T_i,mu_i), for i = 1,...,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.Comment: Minor changes (45 pages

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a $t^{-3/2}$ long time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations.Comment: 8 pages, 6 figur

Analysis of shared heritability in common disorders of the brain

Paroxysmal Cerebral Disorder

Bi-allelic Loss-of-Function CACNA1B Mutations in Progressive Epilepsy-Dyskinesia.

The occurrence of non-epileptic hyperkinetic movements in the context of developmental epileptic encephalopathies is an increasingly recognized phenomenon. Identification of causative mutations provides an important insight into common pathogenic mechanisms that cause both seizures and abnormal motor control. We report bi-allelic loss-of-function CACNA1B variants in six children from three unrelated families whose affected members present with a complex and progressive neurological syndrome. All affected individuals presented with epileptic encephalopathy, severe neurodevelopmental delay (often with regression), and a hyperkinetic movement disorder. Additional neurological features included postnatal microcephaly and hypotonia. Five children died in childhood or adolescence (mean age of death: 9 years), mainly as a result of secondary respiratory complications. CACNA1B encodes the pore-forming subunit of the pre-synaptic neuronal voltage-gated calcium channel Cav2.2/N-type, crucial for SNARE-mediated neurotransmission, particularly in the early postnatal period. Bi-allelic loss-of-function variants in CACNA1B are predicted to cause disruption of Ca2+ influx, leading to impaired synaptic neurotransmission. The resultant effect on neuronal function is likely to be important in the development of involuntary movements and epilepsy. Overall, our findings provide further evidence for the key role of Cav2.2 in normal human neurodevelopment.MAK is funded by an NIHR Research Professorship and receives funding from the Wellcome Trust, Great Ormond Street Children's Hospital Charity, and Rosetrees Trust. E.M. received funding from the Rosetrees Trust (CD-A53) and Great Ormond Street Hospital Children's Charity. K.G. received funding from Temple Street Foundation. A.M. is funded by Great Ormond Street Hospital, the National Institute for Health Research (NIHR), and Biomedical Research Centre. F.L.R. and D.G. are funded by Cambridge Biomedical Research Centre. K.C. and A.S.J. are funded by NIHR Bioresource for Rare Diseases. The DDD Study presents independent research commissioned by the Health Innovation Challenge Fund (grant number HICF-1009-003), a parallel funding partnership between the Wellcome Trust and the Department of Health, and the Wellcome Trust Sanger Institute (grant number WT098051). We acknowledge support from the UK Department of Health via the NIHR comprehensive Biomedical Research Centre award to Guy's and St. Thomas' National Health Service (NHS) Foundation Trust in partnership with King's College London. This research was also supported by the NIHR Great Ormond Street Hospital Biomedical Research Centre. J.H.C. is in receipt of an NIHR Senior Investigator Award. The research team acknowledges the support of the NIHR through the Comprehensive Clinical Research Network. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR, Department of Health, or Wellcome Trust. E.R.M. acknowledges support from NIHR Cambridge Biomedical Research Centre, an NIHR Senior Investigator Award, and the University of Cambridge has received salary support in respect of E.R.M. from the NHS in the East of England through the Clinical Academic Reserve. I.E.S. is supported by the National Health and Medical Research Council of Australia (Program Grant and Practitioner Fellowship)

Scattering of elastic waves by small surface-breaking or subsurface cracks in three dimensions

The long-wavelength limit of elastic wave scattering by surface cracks in 3d is considered. It is shown that, if the crack is normal to the surface, the scattering can be described by two real parameters, one of which may be taken to be the crack size. The other therefore depends on shape, orientation, and burial depth. Many computed illustrations are given. It is concluded that the amount of information about cracks obtainable by low frequency elastic wave scattering is very limited

Application of MOOT to scattering of elastic waves from compound inclusions

It is shown how MOOT (method of optimal truncation, a convergent T-matrix scheme) can be used to calculate elastic wave scattering from compound inclusions, i.e., inclusions which themselves contain flaws - inclusions, voids, or cracks. The general equations are derived, and they are solved for a particular axially-symmetric case - a cracked spherical inclusion immersed in fluid. The crack edge is a circle on the equatorial plane; the crack can extend either inward to the center or outward to the surface of the sphere. Numerical results are given for scattering of acoustic waves from cracked spheres of various materials. Cracked spheres can be fabricated relatively easily, and may be useful in NDE calibrations

Acoustic wave scattering from a circular crack: comparison of different computational methods

The work reported was motivated by disagreement between the results obtained from two computations of scattering of an axially incident elastic p-wave on a circular crack. One calculation involves the direct solution of the Helmholtz integral equation, showing an oscillating total cross section. The other uses a program called MOOT, in which the elastic displacement near the crack is expanded in regular spherical eigenfunctions of the elastic wave equation. This calculation shows that the oscillations in total cross section disappear rapidly at high wave numbers. The conjecture that the basis for the MOOT expansion was inappropriate is examined by application to a test problem. Results indicate that there is no inadequacy in the spherical basis set. (LEW

The influence of hybridization on epidermal properties of birch species and the consequences for palaeoclimatic interpretations

The Fennoscandian birch population primarily consists of Betula nana, B. pendula and B. pubescens ssp. czerepanovii, the Mountain birch. Frequent hybridization between the Mountain birch and B. nana generates a wide range of genotypic and phenotypic plasticity in the subarctic birch zone of Fennoscandia. Phases of subarctic conditions prevailed during the Late Glacial in large parts of NW - Europe, and palynological as well as macrofossil analysis provide some evidence for the occurrence of birch hybrids during these intervals. Leaves from genetically controlled specimens of Betula pendula, B. pubescens ssp. czerepanovii, B. nana and the hybrids B. pubescens ssp. czerepanovii x nana and B. nana x pubescens ssp. czerepanovii are investigated for their specific characteristics of the epidermis morphology. Frequency and size of epidermal cells and stomata reveal a close affinity of both hybrids to B. nana and allow a differentiation of the intermediate forms between B. nana and the Mountain birch. With respect to palaeoatmospheric CO2 reconstructions based on stomatal index, epidermal analysis shows that a possible occurrence of hybrids in fossil leaf assemblages has no profound consequences for combined species records. However, the significant differences observed in B. nana demand the separation of this species. A comparison of the cuticle properties of B. pendula and B. pubescens from Finnish Lappland and leaf material from The Netherlands reveals a divergence of the stomatal index that may be due to differences in day light length