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

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

Orthogonal Polynomials in Mathematical Physics

This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal polynomials and consider their various generalizations. The review also includes the orthogonal polynomials into a generic framework of ($q$-)hypergeometric functions and their integral representations. In particular, this gives rise to relations with conformal blocks of the Virasoro algebra.Comment: 46 page

The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $\Gamma$ in a Hilbert space $H$. We prove the existence and uniqueness of a strong solution of this problem when $\Gamma$ is a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when $\Gamma=K_\alpha$, where $K_\alpha={f\in L^2 (0,1)|f\geq -\alpha},\alpha\geq0$

Identity, environment and mental wellbeing in the veterinary profession

Mental health and career dissatisfaction are of increasing concern to the veterinary profession. The influence of identity on the psychological wellbeing of veterinarians has not been widely explored. Twelve recent veterinary graduates were enrolled in a private social media discussion group, and their identities investigated through narrative inquiry: a methodology which enables identity priorities to be extrapolated from stories of experience. Two distinct variants of the veterinary identity were identified: an academic, ‘diagnosis-focused’ identity, which prioritised definitive diagnosis and best-evidence treatment; and a broader ‘challenge-focused’ identity, where priorities additionally included engaging with the client, challenging environment or veterinary business. Contextual challenges (such as a client with limited finances or difficult interpersonal interactions) were seen as a source of frustration for those with a diagnosis-focused identity, as they obstructed the realisation of identity goals. Overcoming these challenges provided satisfaction to those with a challenge-focused identity. The employment environment of the graduates (general veterinary practice) provided more opportunities for those with a challenge-focused identity to realise identity goals, and more markers of emotional wellbeing were apparent in their stories. Markers of poor emotional health were evident in the stories of those with a diagnosis-focused identity

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