BRST–BFV and BRST–BV descriptions for bosonic fields with continuous spin on R1,d−1

Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a [Formula: see text]-dimensional Minkowski space–time using a metric-like formulation are constructed on the basis of a constrained BRST–BFV approach we propose. The resulting BRST–BFV equations of motion for a scalar field augmented by ghost operators contain different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded constrained equations of motion with the initial irreducible Poincaré group conditions of a Bargmann–Wigner type, it is demonstrated that one should replace the field in these conditions by a class of gauge-equivalent configurations. Triplet-like, doublet-like constrained descriptions, as well as an unconstrained quartet-like non-Lagrangian and Lagrangian formulations, are derived using both Fronsdal-like and new tensor fields. In particular, the BRST–BV equations of motion and Lagrangian using an appropriate set of Lagrangian multipliers in the minimal sector of the respective field and antifield configurations are constructed in a manifest way.

Geometrically nonlinear analysis by the generalized finite element method

Purpose The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations. Design/methodology/approach An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments. Findings The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted. Originality/value This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.

Quasi-optimal and pressure-robust discretizations of the Stokes equations by new augmented Lagrangian formulations

We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is quasi-optimal and pressure-robust, in the sense that the velocity $H^1$-error is proportional to the best velocity $H^1$-error. This shows that such a property can be achieved without using conforming and divergence-free pairs. We also bound the pressure $L^2$-error, only in terms of the best velocity $H^1$-error and the best pressure $L^2$-error. Our construction can be summarized as follows. First, a linear operator acts on discrete velocity test functions, before the application of the load functional, and maps the discrete kernel into the analytical one. Second, in order to enforce consistency, we employ a new augmented Lagrangian formulation, inspired by discontinuous Galerkin methods.

Analysis of cylindrical cavity expansion in anisotropic critical state soils under drained conditions

This paper presents a semi-analytical solution for the drained cylindrical cavity expansion problem using the well-known anisotropic modified Cam clay model proposed by Dafalias in 1987. The prominent feature of this elastoplastic model, i.e., its capability to describe both the initial fabric anisotropy and stress-induced anisotropy of soils, makes the anisotropic elastoplastic solution derived herein for the cavity problem a more realistic one. Following the development by Chen and Abousleiman in 2013 of a novel solution scheme that establishes a link between the Eulerian and Lagrangian formulations of the condition of radial equilibrium, the plastic zone solution can eventually be obtained by solving a system of eight partial differential equations with the three stress components, three anisotropic hardening parameters, specific volume, and preconsolidation pressure being the basic unknowns. Parametric studies have been conducted to explore the influences of K0 consolidation anisotropy and overconsolidation ratio (OCR), and their pronounced impacts on the stress patterns outside the cavity as well as on the development of stress-induced anisotropy are clearly observed.

Mathematical Modeling of a Brain-on-a-Chip: A Study of the Neuronal Nitric Oxide Role in Cerebral Microaneurysms

Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. While the physics and biochemistry of brain’s cell types and their interactions within their networks have been studied extensively, only recently the interactions of and feedback among the networks have started to capture the attention of the research community. Thus, a good understanding of the coupled mechano-electrochemical processes that either provide or diminish brain’s functions is still lacking. One way to increase the knowledge on how the brain yields its functions is by developing a robust controlled feedback engineering system that uses fundamental science concepts to guide and interpret experiments investigating brain’s response to various stimuli, aging, trauma, diseases, treatment and recovery processes. Recently, a mathematical model for an implantable neuro-glial-vascular unit, named brain-on-a-chip, was proposed that can be optimized to perform some fundamental cellular processes that could facilitate monitoring and supporting brain’s functions, and highlight basic brain mechanisms. In this paper we use coupled elastic, viscoelastic and mass elements to model a brain-on-a-chip made of a neuron and its membrane, and astrocyte’s endfeet connected to an arteriole’s wall. We propose two constrained Lagrangian formulations that link the Hodgkin-Huxley model of the neuronal membrane, and the mechanics of the neuron, neuronal membrane, and the glia’s endfeet. The effects of the nitric oxide produced by neurons and endothelial cells on the proposed brain-on-a-chip are investigated through numerical simulations. Our numerical simulations suggest that a non-decaying synthesis of nitric oxide may contribute to the onset of a cerebral microaneurysm.