Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion

We present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce continuity of the solution field across geometric patches in a multi-patch setting, which yields a mass matrix with convenient block diagonal structure. Over each patch, we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight-adjusted approximation of the mass matrix inverse. This approximation restores a tensor product structure while retaining provable high order accuracy and semi-discrete energy stability. We also estimate the maximum stable timestep for spline-based finite elements and show that the use of spline spaces result in less stringent CFL restrictions than equivalent piecewise continuous or discontinuous finite element spaces. Finally, we explore the use of optimal knot vectors based on L2 n-widths. We show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep, and present a simple heuristic method for approximating optimal knot positions. Numerical experiments confirm the accuracy and stability of the proposed methods

Spatial learning and memory in the tortoise (Geochelone carbonaria)

A single tortoise (Geochelone carbonaria) was trained in an eight-arm radial maze, with the apparatus and general procedures modeled on those used to demonstrate spatial learning in rats. The tortoise learned to perform reliably above chance, preferentially choosing baited arms, rather than returning to arms previously visited on a trial. Test sessions that examined control by olfactory cues revealed that they did not affect performance. No systematic, stereotyped response patterns were evident. In spite of differences in brain structure, the tortoise showed spatial learning abilities comparable to those observed in mammals

Complementation between mouse Mfn1 and Mfn2 protects mitochondrial fusion defects caused by CMT2A disease mutations

Mfn2, an oligomeric mitochondrial protein important for mitochondrial fusion, is mutated in Charcot-Marie-Tooth disease (CMT) type 2A, a peripheral neuropathy characterized by axonal degeneration. In addition to homooligomeric complexes, Mfn2 also associates with Mfn1, but the functional significance of such heterooligomeric complexes is unknown. Also unknown is why Mfn2 mutations in CMT2A lead to cell type–specific defects given the widespread expression of Mfn2. In this study, we show that homooligomeric complexes formed by many Mfn2 disease mutants are nonfunctional for mitochondrial fusion. However, wild-type Mfn1 complements mutant Mfn2 through the formation of heterooligomeric complexes, including complexes that form in trans between mitochondria. Wild-type Mfn2 cannot complement the disease alleles. Our results highlight the functional importance of Mfn1–Mfn2 heterooligomeric complexes and the close interplay between the two mitofusins in the control of mitochondrial fusion. Furthermore, they suggest that tissues with low Mfn1 expression are vulnerable in CMT2A and that methods to increase Mfn1 expression in the peripheral nervous system would benefit CMT2A patients

Emergence of Gapped Bulk and Metallic Side Walls in the Zeroth Landau level in Dirac and Weyl semimetals

Recent transport experiments have revealed the activation of longitudinal magnetoresistance of Weyl semimetals in the quantum limit, suggesting the breakdown of chiral anomaly in a strong magnetic field. Here we provide a general mechanism for gapping the zeroth chiral Landau levels applicable for both Dirac and Weyl semimetals. Our result shows that the zeroth Landau levels anticross when the magnetic axis is perpendicular to the Dirac/Weyl node separation and when the inverse magnetic length $l_B^{-1}$ is comparable to the node separation scale $\Delta k$. The induced bulk gap increases rapidly beyond a threshold field in Weyl semimetals, but has no threshold and is non-monotonic in Dirac systems due to the crossover between $l_B^{-1}>\Delta k$ and $l_B^{-1}<\Delta k$ regions. We also find that the Dirac and possibly Weyl systems host counterpropagating edge states between the zeroth Landau levels, leading to a state with metallic side walls and zero Hall conductance.Comment: 8 pages, 4 figure

Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is ``fixed domain'' (or ``infill'') asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat richer than in the Gaussian case (the latter is recovered when g is affine), in part because estimators of the type considered may have an asymptotic variance which is random in the limit. Broadly, when g is smooth and nonaffine, three types of limit distributions can arise, types (i), (ii) and (iii), say. Each type can be represented as a random integral. More specifically, type (i) can be represented as the integral of a certain random function with respect to Lebesgue measure; type (ii) can be represented as the integral of a second random functio

Proton translocation in proteins

The active transport of protons across the low dielectric barrier imposed by biological membranes is accomplished by a plethora of proteins that span the ca. 40 Å of the phospholipid bilayer. The free energy derived from the proton electrochemical potential established by the translocation of these protons can subsequently be used to drive vital chemical reactions of the cell, such as ATP synthesis and cell locomotion. Membrane-bound proton translocating proteins have now been found for a variety of organisms and tissues (1). The driving force for proton pumping in these proteins is supplied by numerous mechanisms, including light absorption (e.g. bacteriorhodopsin) (2a,b), ligand binding (e.g. ATPase) (3), and electrochemistry (e.g. electron transfer through cytochrome c oxidase) (4). Thus nature has devised a variety of methods for supplying the energy required for proton pumping by these proteins. Such diversity notwithstanding, the proteins most likely share some common elements of structure and mechanism that allow them to function as proton pumps. A number of theoretical mechanisms have been put forth for both general proton translocation (5-7) and for energy coupling in specific proton pumps. However, despite almost three decades of intensive research, the details of the mechanism(s) and structural requirements for proton pumping remain largely unresolved. To some extent this is the result of the paucity of structural information available for integral membrane proteins. This situation may soon improve as a result of advances in protein methodologies that have allowed several integral membrane proteins to be successfully crystalized (8), and the increased use of genetic engineering to obtain recombinant proton translocating proteins that will offer an opportunity to assess the importance of specific amino acids for the proton translocation process (9)