Modelling Nonlinear Optics in the CERN SPS

Nonlinear fields arising from eddy currents in the vac-uum chamber and remanent fields in the magnets of the CERN SPS vary with time and with the acceleration cycle. We describe a procedure of constructing a nonlinear op-tics model for the SPS, by considering sextupolar, octupo-lar, and decapolar field errors in the dipole and quadrupole magnets, respectively, whose strengths are adjusted so as to best reproduce the measured nonlinear chromaticities up to third order in the momentum deviation. Applying this procedure to SPS chromaticity measurements taken at 26 GeV/c, we have obtained a refined optics model. The tune shifts with the transverse amplitude predicted by this model are consistent with a direct measurement

Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love kinematics. Their governing equation is a vector-valued, fourth-order, nonlinear, partial differential equation (PDE) that requires at least $C^1$-continuity within a displacement-based finite element formulation. The second class are surface phase separations modeled by a phase field. Their governing equation is the Cahn-Hilliard equation - a scalar, fourth-order, nonlinear PDE - that can be coupled to the thin shell PDE. The third class are brittle fracture processes modeled by a phase field approach. In this work, these are described by a scalar, fourth-order, nonlinear PDE that is similar to the Cahn-Hilliard equation and is also coupled to the thin shell PDE. Using a direct finite element discretization, the two phase field equations also require at least a $C^1$-continuous formulation. Isogeometric surface discretizations - often composed of multiple patches - thus require constraints that enforce the $C^1$-continuity of displacement and phase field. For this, two numerical strategies are presented: For this, two numerical strategies are presented: A Lagrange multiplier formulation and a penalty method. The curvilinear shell model including the geometrical constraints is taken from Duong et al. (2017) and it is extended to model the coupled phase field problems on thin shells of Zimmermann et al. (2019) and Paul et al. (2020) on multi-patches. Their accuracy and convergence are illustrated by several numerical examples considering deforming shells, phase separations on evolving surfaces, and dynamic brittle fracture of thin shells.Comment: In this version, typos were fixed, Chapter 6.4 is added, Table 1 is updated, and clarifying explanations and remarks are added at several place

Different Transport Pathways of Individual Precursor Proteins in Mitochondria

Transport of mitochondrial precursor proteins into mitochondria of Neurospora crassa was studied in a cellfree reconstituted system. Precursors were synthesized in a reticulocyte lysate programmed with Neurospora mRNA and transported into isolated mitochondria in the absence of protein synthesis. Uptake of the following precursors was investigated: apocytochrome c, ADP/ATP carrier and subunit 9 of the oligomycin-sensitive ATPase. Addition of high concentrations of unlabelled chemically prepared apocytochrome c (1–10 μM) inhibited the appearance in the mitochondrial of labelled cytochrome c synthesized in vitro because the unlabelled protein dilutes the labelled one and because the translocation system has a limited capacity [apparent V is 1–3 pmol × min−1× (mg mitochondrial protein)−1]. Concentrations of added apocytochrome c exceeding the concentrations of precursor proteins synthesized in vitro by a factor of about 104 did not inhibit the transfer of ADP/ATP carrier or ATPase subunit 9 into mitochondria. Carbonylcyanide m-chlorophenylhydrazone, an uncoupler of oxidative phosphorylation, inhibited transfer in vitro of ADP/ATP carrier and of ATPase subunit 9, but not of cytochrome c. These findings suggest that cytochrome c and the other two proteins have different import pathways into mitochondria. It can be inferred from the data presented that different 'receptors' on the mitochondrial surface mediate the specific recognition of precursor proteins by mitochondria as a first step in the transport process

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$\alpha$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.Comment: In this version, typos were fixed, Fig. 16 is added, the literature review is extended and clarifying explanations and remarks are added at several places. Supplementary movies are available at https://av.tib.eu/series/641/supplemental+videos+of+the+paper+an+adaptive+space+time+phase+field+formulation+for+dynamic+fracture+of+brittle+shells+based+on+lr+nurb

No evidence for retinal damage evolving from reduced retinal blood flow in carotid artery disease

Introduction. Carotid artery disease (CAD) comprising high-grade internal carotid artery stenosis (CAS) or carotid artery occlusion (CAO) may lead to ipsilateral impaired cerebral blood flow and reduced retinal blood supply. Objective. To examine the influence of chronic CAD on retinal blood flow, retinal morphology, and visual function. Methods. Patients with unilateral CAS ≥ 50% (ECST criteria) or CAO were grouped according to the grade of the stenosis and to the flow direction of the ophthalmic artery (OA). Retinal perfusion was measured by transorbital duplex ultrasound, assessing central retinal artery (CRA) blood flow velocities. In addition, optic nerve and optic nerve sheath diameter were measured. Optical coherence tomography (OCT) was performed to study retinal morphology. Visual function was assessed using high- and low-contrast visual paradigms. Results. Twenty-seven patients were enrolled. Eyes with CAS ≥ 80%/CAO and retrograde OA blood flow showed a significant reduction in CRA peak systolic velocity (no-CAD side: 0.130 ± 0.035 m/s, CAS/CAO side: 0.098 ± 0.028; p = 0.005; n = 12). OCT, optic nerve thicknesses, and visual functional parameters did not show a significant difference. Conclusion. Despite assessable hemodynamic effects, chronic high-grade CAD does not lead to gaugeable morphological or functional changes of the retina

Alcohol Approach Bias Is Associated With Both Behavioral and Neural Pavlovian-to-Instrumental Transfer Effects in Alcohol-Dependent Patients

BACKGROUND: Even after qualified detoxification, alcohol-dependent (AD) patients may relapse to drinking alcohol despite their decision to abstain. Two mechanisms may play important roles. First, the impact of environmental cues on instrumental behavior (i.e., Pavlovian-to-instrumental transfer [PIT] effect), which was found to be stronger in prospectively relapsing AD patients than in abstaining patients. Second, an automatic approach bias toward alcohol stimuli was observed in AD patients, and interventions targeting this bias reduced the relapse risk in some studies. Previous findings suggest a potential behavioral and neurobiological overlap between these two mechanisms. METHODS: In this study, we examined the association between alcohol approach bias and both behavioral and neural non–drug-related PIT effects in AD patients after detoxification. A total of 100 AD patients (17 females) performed a PIT task and an alcohol approach/avoidance task. Patients were followed for 6 months. RESULTS: A stronger alcohol approach bias was associated with both a more pronounced behavioral PIT effect and stronger PIT-related neural activity in the right nucleus accumbens. Moreover, the association between alcohol approach bias and behavioral PIT increased with the severity of alcohol dependence and trait impulsivity and was stronger in patients who relapsed during follow-up in the exploratory analysis. CONCLUSIONS: A stronger alcohol approach bias was associated with both a more pronounced behavioral PIT effect and stronger PIT-related neural activity in the right nucleus accumbens. Moreover, the association between alcohol approach bias and behavioral PIT increased with the severity of alcohol dependence and trait impulsivity and was stronger in patients who relapsed during follow-up in the exploratory analysis

Average Case Analysis of Unification Algorithms

International audienceUnification in first-order languages is a central operation in symbolic computation and logic programming. Many unification algorithms have been proposed in the past, however there is no consensus on which algorithm is the best to use in practice. While Paterson and Wegman's linear unification algorithm has the lowest time complexity in the worst case, it requires an important overhead to be implemented. This is true also, although less importantly, for Martelli and Montanari's algorithm [MM82], and Robinson's algorithm [Rob71] is finally retained in many applications despite its exponential worst-case time complexity. There are many explanations for that situation: one important argument is that in practice unification subproblems are not independent, and linear unification algorithms do not perform well on sequences of unify-deunify operations [MU86]. In this paper we present average case complexity theoretic arguments. We first show that the family of unifiable pairs of binary trees is exponentially negligible with respect to the family of arbitrary pairs of binary trees formed over l binary function symbols, c constants and v variables. We analyze the different reasons for failure and get asymptotical and numerical evaluations. We then extend the previous results of [DL89] to these families of trees, we show that a slight modification of Herbrand-Robinson's algorithm has a constant average cost on random pairs of trees. On the other hand, we show that various variants of Martelli and Montanari's algorithm all have a linear average cost on random pairs of trees. The point is that failures by clash are not sufficient to lead to a constant average cost, an efficient occur check (i.e. without a complete traversal of subterms) is necessary. In the last section we extend the results on the probability of the occur check in presence of an unbounded number of variables