An iterative adaptive finite element method for elliptic eigenvalue problems

We consider the task of resolving accurately the n$n$th eigenpair of a generalized eigenproblem rooted in some elliptic partial differential equation (PDE), using an adaptive finite element method (FEM). Conventional adaptive FEM algorithms call a generalized eigensolver after each mesh refinement step. This is not practical in our situation since the generalized eigensolver needs to calculate n$n$ eigenpairs after each mesh refinement step, it can switch the order of eigenpairs, and for repeated eigenvalues it can return an arbitrary linear combination of eigenfunctions from the corresponding eigenspace. In order to circumvent these problems, we propose a novel adaptive algorithm that only calls a generalized eigensolver once at the beginning of the computation, and then employs an iterative method to pursue a selected eigenvalue–eigenfunction pair on a sequence of locally refined meshes. Both Picard’s and Newton’s variants of the iterative method are presented. The underlying partial differential equation (PDE) is discretized with higher-order finite elements (hp$hp$-FEM) but the algorithm also works for standard low-order FEM. The method is described and accompanied with theoretical analysis and numerical examples. Instructions on how to reproduce the results are provided.     

Nearest Neighbor Distances on a Circle: Multidimensional Case

We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for various choices of E, particularly when E goes to infinity. Primarily, we study the case in which the spring constant is a badly approximable vector. We first give the proof by Boshernitzan-Dyson that the number of distinct spacings has a uniform bound independent of E. Then, if the spring constant has components forming a basis of an algebraic number field, we show that, when normalized up to a unit, the spacings are from a finite set. Moreover, in the specific case that the field has one fundamental unit, the probability distribution of these spacings behaves quasiperiodically in logE. We conclude by studying the spacings in the case that the spring constant is not badly approximable, providing examples for which the number of distinct spacings is unbounded.     

Counterion condensation in short cationic peptides: limiting mobilities beyond the Onsager-Fuoss theory

We investigated the effect of the background electrolyte (BGE) anions on the electrophoretic mobilities of the cationic amino acids arginine and lysine and the polycationic peptides tetraarginine, tetralysine, nonaarginine, and nonalysine. BGEs composed of sodium chloride, sodium propane-1,3-disulfonate, and sodium sulfate were used. For the amino acids, determination of the limiting mobility by extrapolation, using the Onsager-Fuoss (OF) theory expression, yielded consistent estimates. For the peptides, however, the estimates of the limiting mobilities were found to spuriously depend on the BGE salt. This paradox was resolved using molecular modeling. Simulations, on all-atom as well as coarse-grained levels, show that significant counterion condensation, an effect not accounted for in OF theory, occurs for the tetra- and nonapeptides, even for low BGE concentrations. Including this effect in the quantitative estimation of the BGE effect on mobility removed the discrepancy between the estimated limiting mobilities in different salts. The counterion condensation was found to be mainly due to electrostatic interactions, with specific ion effects playing a secondary role. Therefore, the conclusions are likely to be generalizable to other analytes with a similar density of charged groups and OF theory is expected to fail in a predictable way for such analytes.     

Rapid testing of clopidogrel resistance by genotyping of CYP2C19 and CYP2C9 polymorphisms using denaturing on-chip capillary electrophoresis

Antiplatelet therapy is a cornerstone of cardiovascular treatment in patients with coronary artery disease and after myocardial infarction. Clopidogrel has become a popular antiplatelet agent due to its fast action and low frequency of adverse effects. Kinetics of clopidogrel metabolism is driven by enzymatic activity of the Cytochrome P450 system. Genotyping of CYP2C19 and CYP2C9 polymorphisms allows to identify slow metabolizers showing resistance to clopidogrel therapy. Today, a number of PCR-based techniques for single nucleotide polymorphism genotyping directed at clopidogrel resistance polymorphisms are in use. Here, we describe a new alternative genotyping approach combining the separation power of denaturing capillary electrophoresis with the analysis speed and ease of use of Bioanalyzer chipCE platform. Using an upgraded heater control, we present an optimization for allele separation of CYP2C19 I331V, CYP2C9 R144C, and CYP2C9 I359L polymorphisms employing run temperatures of up to 55°C. We demonstrate rapid and accessible approach to reproducible clopidogrel resistance with feasibility and low cost.     

Hyperbolic subalgebras of hyperbolic Kac–Moody algebras

We investigate regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras via their Weyl groups. We classify all subgroup relations between Weyl groups of hyperbolic Kac–Moody algebras, and show that for every pair of a group and subgroup there exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for a given hyperbolic Kac–Moody algebra, and present a finite algorithm classifying all embeddings.     

Phonemic restoration effect reversed in a reverberant room

Classic demonstrations of the phonemic restoration effect show increased intelligibility of interrupted speech when the interruptions are caused by a plausible masking sound rather than by silent periods. Previous studies of this effect have been conducted exclusively under anechoic or nearly anechoic listening conditions. This study demonstrates that the effect is reversed when sounds are presented in a realistically simulated reverberant room (broadband T(60) = 1.1 s): intelligibility is greater for silent interruptions than for interruptions by unmodulated noise. Additional results suggest that the reversal is primarily due to filling silent intervals with reverberant energy from the speech signal.     

Preparation of well-dispersed magnetorheological fluids and effect of dispersion on their magnetorheological properties

In this work, we describe methods for the preparation of suspensions of micron-sized iron particles grafted with different surfactants. The aim is to obtain well-dispersed magnetorheological (MR) fluids. The effectiveness of the surfactants as dispersants was analyzed quantitatively by means of rheological measurements. With this objective, the viscosity of the suspensions was measured, and the results were compared with the prediction of the Batchelor’s formula (Batchelor, J Fluid Mech 83:97–117, 1977). The effect of dispersion on the MR properties of the suspensions was also studied. It was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field. It was also found that the transition from the solid-like state to the liquid-like one happens very smoothly for well-dispersed suspensions, contrarily to the abrupt transition for poorly dispersed suspensions.     

Derived subgroups of fixed points

LetA be an elementary abelianq-group acting on a finiteq′-groupG. We show that ifA has rank at least 3, then properties ofC _G(a)′, 1 ≠a ∈A restrict the structure ofG′. In particular, we consider exponent, order, rank and number of generators. This author was supported by the NSF. This author was supported by CNP_q-Brazil.     

Remarks Relative to the Use of Atmospheric Plasma-Pulsed Discharge for PET Bottles Instant Sterilization

Plasma Chemistry and Plasma Processing -