Nontrivial Variations Research Articles

Infinitesimally Moebius bendable hypersurfaces

AbstractLi, Ma and Wang have provided in [13] a partial classification of the so-called Moebius deformable hypersurfaces, that is, the umbilic-free Euclidean hypersurfaces $f\colon M^n\to \mathbb{R}^{n+1}$ that admit non-trivial deformations preserving the Moebius metric. For $n\geq 5$, the classification was completed by the authors in [12]. In this article we obtain an infinitesimal version of that classification. Namely, we introduce the notion of an infinitesimal Moebius variation of an umbilic-free immersion $f\colon M^n\to \mathbb{R}^m$ into Euclidean space as a one-parameter family of immersions $f_t\colon M^n\to \mathbb{R}^m$, with $t\in (-\epsilon, \epsilon)$ and $f_0=f$, such that the Moebius metrics determined by ft coincide up to the first order. Then we characterize isometric immersions $f\colon M^n\to \mathbb{R}^m$ of arbitrary codimension that admit a non-trivial infinitesimal Moebius variation among those that admit a non-trivial conformal infinitesimal variation, and use such characterization to classify the umbilic-free Euclidean hypersurfaces of dimension $n\geq 5$ that admit non-trivial infinitesimal Moebius variations.

Nontrivial Variations of Morpho-Anatomical Leaf Traits in Natural South-Eastern Populations of Vaccinium species from Central Balkans

Nontrivial Variations of Morpho-Anatomical Leaf Traits in Natural South-Eastern Populations of Vaccinium species from Central Balkans

Body Forces Drive the Apparent Line Tension of Sessile Droplets.

The line tension of a three-phase contact line is implicated in a wide variety of interfacial phenomena, but there is ongoing controversy, with existing measurements spanning six orders of magnitude in both signs. Here, we show that computationally obtained magnitudes, sign changes, and nontrivial variations of apparent line tension can be faithfully reproduced in a parsimonious model that incorporates only liquid-substrate interactions. Our results suggest that the origin for the remarkable variation lies in the failure of a widely used estimation method to eliminate body forces, leading measured line tensions to behave like an extensive quantity.

Self-Limitations of Heat Release in Coupled Core-Shell Spinel Ferrite Nanoparticles: Frequency, Time, and Temperature Dependencies.

We explored a series of highly uniform magnetic nanoparticles (MNPs) with a core-shell nanoarchitecture prepared by an efficient solvothermal approach. In our study, we focused on the water dispersion of MNPs based on two different CoFe2O4 core sizes and the chemical nature of the shell (MnFe2O4 and spinel iron oxide). We performed an uncommon systematic investigation of the time and temperature evolution of the adiabatic heat release at different frequencies of the alternating magnetic field (AMF). Our systematic study elucidates the nontrivial variations in the heating efficiency of core-shell MNPs concerning their structural, magnetic, and morphological properties. In addition, we identified anomalies in the temperature and frequency dependencies of the specific power absorption (SPA). We conclude that after the initial heating phase, the heat release is governed by the competition of the Brown and Néel mechanism. In addition, we demonstrated that a rational parameter sufficiently mirroring the heating ability is the mean magnetic moment per MNP. Our study, thus, paves the road to fine control of the AMF-induced heating by MNPs with fine-tuned structural, chemical, and magnetic parameters. Importantly, we claim that the nontrivial variations of the SPA with the temperature must be considered, e.g., in the emerging concept of MF-assisted catalysis, where the temperature profile influences the undergoing chemical reactions.

Conformal infinitesimal variations of Euclidean hypersurfaces

In the realm of conformal geometry, we give a parametric classification of the hypersurfaces in Euclidean space that admit nontrivial conformal infinitesimal variations. A parametric classification of the Euclidean hypersurfaces that allow a nontrivial conformal variation was obtained by E. Cartan in 1917. In particular, we show that the class of hypersurfaces studied here is much larger than the one characterized by Cartan.

Time-Domain Adaptive Algorithms for Low- and High-Level Audio Information Processing

Abstract In this paper, we present a set of time-domain algorithms for the low- and high-level analysis of audio streams. These include spectral centroid, noisiness, and spectral spread for the low level, and dynamicity, heterogeneity, and complexity for the high level. The low-level algorithms provide a continuous measure of the features and can operate with short analysis frames. The high-level algorithms, on the other hand, are original designs informed both perceptually and by complexity theory for the analysis of musically meaningful information, both in short sounds or articulated streams with long-term nontrivial variations. These algorithms are suitable for the implementation of real-time audio analysis in diverse live performance setups that require the extraction of information from several streams at the same time. For example, the low-level algorithms can be deployed in large audio networks of adaptive agents, or in small-to-large ensembles for the analysis of various characteristics of the instruments for computer-assisted performance. Furthermore, the high-level algorithms can be implemented as part of fitness functions in music systems based on evolutionary algorithms that follow musically-informed criteria, or as analysis tools to assess the quality of some of the characteristics of a musical output. Musical applications of these algorithms can be found in a companion paper in this issue of Computer Music Journal: “Complex Adaptation in Audio Feedback Networks for the Synthesis of Music and Sounds.”

Fully automated peptide mapping multi-attribute method by liquid chromatography–mass spectrometry with robotic liquid handling system

The multi-attribute method (MAM) based on liquid chromatography (LC)–tandem mass spectrometry is emerging as a powerful tool to directly monitor multiple product quality attributes simultaneously. To better implement MAM, either for product characterization or for quality control (QC), there is a need for a robust, universal, and high-throughput workflow that can be broadly adopted in different laboratories with minimal barriers to implementation. Manual preparation of samples for MAM, however, is labor intensive and produces nontrivial variations across analysts and laboratories. We describe the development of a fully automated peptide mapping procedure with a high-throughput robotic liquid handling system to improve sample handling capacity and outcome reproducibility while saving analyst hands-on time. Our procedure features the automation of a “microdialysis” step, an efficient desalting approach prior to proteolytic digestion that optimizes digestion completeness and consistency each time. The workflow is completely hands-free and requires the analyst only to pre-normalize the sample concentrations and to load buffers and reagents at their designated positions on the robotic deck. The robotic liquid handler performs all the subsequent preparation steps and stores the digested samples on a chiller unit to await retrieval for further analysis. We also demonstrate that the manual and automated procedures are comparable with regard to protein sequence coverage, digestion completeness and consistency, and quantification of posttranslational modifications. Notably, in contrast to a previously reported automated sample preparation protocol that relied on customized accessories, all components in our automation procedure are commercial products that are readily available. In addition, we also present the high-throughput data analysis workflow by using Protein Metrics. The automation procedure can be applied cross-functionally in the biopharmaceutical industry and, given its practicality and reproducibility, can pave the way for MAM implementation in QC laboratories.

Conformal infinitesimal variations of submanifolds

This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds are a classical subject in differential geometry. In fact, already in 1917 Cartan classified parametrically the Euclidean hypersurfaces that admit nontrivial conformal variations. Our first main result is a Fundamental theorem for conformal infinitesimal variations. The second is a rigidity theorem for Euclidean submanifolds that lie in low codimension.

Particle Swarm Optimization-Based Metaheuristic Design Generation of Non-Trivial Flat-Foldable Origami Tessellations With Degree-4 Vertices

Abstract Flat-foldable origami tessellations are periodic geometric designs that can be transformed from an initial configuration into a flat-folded state. There is growing interest in such tessellations, as they have inspired many innovations in various fields of science and engineering, including deployable structures, biomedical devices, robotics, and mechanical metamaterials. Although a range of origami design methods have been developed to generate such fold patterns, some non-trivial periodic variations involve geometric design challenges, the analytical solutions to which are too difficult. To enhance the design methods of such cases, this study first adopts a geometric-graph-theoretic representation of origami tessellations, where the flat-foldability constraints for the boundary vertices are considered. Subsequently, an optimization framework is proposed for developing flat-foldable origami patterns with four-fold (i.e., degree-4) vertices, where the boundaries of the unit fragment are given in advance. A metaheuristic using particle swarm optimization (PSO) is adopted for finding optimal solutions. Several origami patterns are studied to verify the feasibility and effectiveness of the proposed design method. It will be shown that in comparison with the analytical approach and genetic algorithms (GAs), the presented method can find both trivial and non-trivial flat-foldable solutions with considerably less effort and computational cost. Non-trivial flat-foldable patterns show different and interesting folding behaviors and enrich origami design.

Intrinsic non-flat-foldability of two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals

Functional origami tessellations have certain geometric or physical properties - such as flat-foldability and rigid-foldability - which make them of particular interest for a broad range of applications in science, engineering, and architecture. While some simple variations of certain functional origami tessellations can be designed trivially, a systematic symmetry-reduction scheme is proved to be productive for the computational generation of more complex, non-trivial variations. Such a scheme has been previously applied to the developable double corrugation (DDC) surface, widely known as the Miura-ori, resulting in the development of novel crystalline derivatives, the symmetry groups of which are subgroups of the parent pattern. Computational algorithms can search for and find flat-foldable solutions for a large number of derivatives of the DDC surface, but fail to find solutions for all of them. In this paper, we exploit the symmetry reduction scheme along with classical plane geometry to analytically demonstrate why some crystallographic derivatives of this pattern do not exist. To this end, by applying the local flat-foldability condition at the vertices of different orbits associated with each tessellation, we show that such patterns are never flat-foldable, regardless of the geometric specifications of their constituting quadrilateral facets. In particular, we prove that two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals are intrinsically non-flat-foldable, resulted from geometric incompatibilities between the properties of certain unit cells and the local flat-foldability condition.

Exploring Shades of Corruption Tolerance: Tentative Lessons from Iceland and Sweden

The aim of this paper is to explore the effects of corruption tolerance on corruption levels. Strong claims are made in the literature to the effect that tolerance of corruption is universally low. We show, however, that there are non-trivial variations in tolerance of corruption, and that these are significantly related to commonly used indices of corruption. This suggests that understanding which factors shape corruption tolerance is important. Here, our concern is with the effects of elite structures on corruption. We first ask if closeness to power affects corruption tolerance and if the general population is less tolerant than elite groups. We then ask if different elite groups — e. g., politicians and civil servants respectively — are likely to form different standards regarding corruption. To hold certain external variables constant, the paper focuses on two relatively homogeneous, low-corruption countries: Sweden and Iceland. Our findings suggest that whereas little supports the closeness to power hypothesis — the general population is not less tolerant of corruption than elites — there may be important differences in how different elite groups within these countries view corrupt activities. This has implications for how corruption can be contained.

No chiral light bending by clumps of axion-like particles

Abstract We study the propagation of light in the presence of a parity-violating coupling between photons and axion-like particles (ALPs). Naively, this interaction could lead to a split of light rays into two separate beams of different polarization chirality and with different refraction angles. However, by using the eikonal method we explicitly show that this is not the case and that ALP clumps do not produce any spatial birefringence. This happens due to non-trivial variations of the photon’s frequency and wavevector, which absorb time-derivatives and gradients of the ALP field. We argue that these variations represent a new way to probe the ALP-photon coupling with precision frequency measurements.

Flow around a squirmer in a shear-thinning fluid

Many biological fluids display shear-thinning rheology, where the viscosity decreases with an increasing shear rate. To better understand how this non-Newtonian rheology affects the motion of biological and artificial micro-swimmers, recent efforts have begun to seek answers to fundamental questions about active bodies in shear-thinning fluids. Previous analyses based on a squirmer model have revealed non-trivial variations of propulsion characteristics in a shear-thinning fluid via the reciprocal theorem. However, the reciprocal theorem approach does not provide knowledge about the flow surrounding the squirmer. In this work, we fill in this missing information by calculating the non-Newtonian correction to the flow analytically in the asymptotic limit of small Carreau number. In particular, we investigate the local effect due to viscosity reduction and the non-local effect due to induced changes in the flow; we then quantify their relative importance to locomotion in a shear-thinning fluid. Our results demonstrate cases where the non-local effect can be more significant than the local effect. These findings suggest that caution should be exercised when developing physical intuition from the local viscosity distribution alone around a swimmer in a shear-thinning fluid.

Hydrodynamic Interaction Enhances Colonization of Sinking Nutrient Sources by Motile Microorganisms.

In this study, we document hydrodynamics-mediated trapping of microorganisms around a moving spherical nutrient source such as a settling marine snow aggregate. There exists a range of size and excess density of the nutrient source, and motility and morphology of the microorganism under which hydrodynamic interactions enable the passive capture of approaching microorganisms onto a moving nutrient source. We simulate trajectories of chemotactic and non-chemotactic bacteria encountering a sinking marine snow particle effusing soluble nutrients. We calculate the average nutrient concentration to which the bacteria are exposed, under regimes of strong and weak hydrodynamic trapping. We find that hydrodynamic trapping can significantly amplify (by ≈40%) the nutrient exposure of bacteria, both chemotactic and non-chemotactic. The subtle interactions between hydrodynamic and chemotactic effects reveal non-trivial variations in this “hydrodynamic amplification,” as a function of relevant biophysical parameters. Our study provides a consistent description of how microorganism motility, fluid flow and nutrient distribution affect foraging by marine microbes, and the formation of biofilms on spherical nutrient sources under the influence of fluid flow.

On the extraction of the boundary conditions and the boundary ports in second-order field theories

In this paper, we consider second-order field theories in a variational setting. From the variational principle, the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This also has consequences on the derivation of the boundary conditions when non-trivial variations are allowed on the boundary. By posing extra conditions on the set of possible boundary terms, we exploit the degree of freedom in the Cartan form to extract physical meaningful boundary expressions. The same mathematical machinery will be applied to derive the boundary ports in a Hamiltonian representation of the partial differential equations which is crucial for energy based control approaches. Our results will be visualized for mechanical systems such as beam and plate models.

Swimming efficiency in a shear-thinning fluid.

Micro-organisms expend energy moving through complex media. While propulsion speed is an important property of locomotion, efficiency is another factor that may determine the swimming gait adopted by a micro-organism in order to locomote in an energetically favorable manner. The efficiency of swimming in a Newtonian fluid is well characterized for different biological and artificial swimmers. However, these swimmers often encounter biological fluids displaying shear-thinning viscosities. Little is known about how this nonlinear rheology influences the efficiency of locomotion. Does the shear-thinning rheology render swimming more efficient or less? How does the swimming efficiency depend on the propulsion mechanism of a swimmer and rheological properties of the surrounding shear-thinning fluid? In this work, we address these fundamental questions on the efficiency of locomotion in a shear-thinning fluid by considering the squirmer model as a general locomotion model to represent different types of swimmers. Our analysis reveals how the choice of surface velocity distribution on a squirmer may reduce or enhance the swimming efficiency. We determine optimal shear rates at which the swimming efficiency can be substantially enhanced compared with the Newtonian case. The nontrivial variations of swimming efficiency prompt questions on how micro-organisms may tune their swimming gaits to exploit the shear-thinning rheology. The findings also provide insights into how artificial swimmers should be designed to move through complex media efficiently.

Photon-assisted and spin-dependent shot noise in magnetic-field tunable ZnSe/Zn1−xMnxSe structures**Project supported by the National Natural Science Foundation of China (Grant No. 11574173), the National Basic Research Program of China (Grant No. 2011CB606405), and the General Program of Science and Technology Development Project of Beijing Municipal Education Commission of China (Grant No. KM201410028021).

We have investigated the photon-assisted shot noise properties in the magnetic field tunable heterostructures. Transport properties of the model structure are strongly dependent on the oscillatory field and the magnetic field. In this structure, electrons can absorb or emit one or multi-photons to reach the quasi-bound state. As a result, the transmission properties are affected considerably by photon-assisted tunneling and these features cause the nontrivial variations in the shot noise and Fano factor. It is found that the shot noise becomes spin-dependent and can be modulated not only by the magnetic field, but also by the oscillatory field. Both the spin-up and spin-down components of the shot noise can be greatly suppressed by the magnetic field, and can also be drastically enhanced by the harmonically driven field. Furthermore, with increasing external magnetic field, it is important to note that the enhanced intensity is decreased, even suppressed. These results suggest another method to suppress the shot noise via modulating the oscillatory field at a diluted-magnetic semiconductors/semiconductor structure.

Mixed brush made of 4-arm stars and linear chains: MD simulations.

We investigate the structural properties of binary polymer brushes, composed of functional 4-armed star polymers and chemically identical linear polymers of different molecular weights. The molecular dynamics simulations confirm recent self-consistent field studies, in which a considerable potential of these systems for the design of switchable surfaces has been claimed. The length of the linear chains serves as a control parameter, which, while passing over a critical value, induces a sharp transition of the molecular conformation. We investigate these transitions at different grafting densities and summarize our findings in a phase diagram. The temperature dependence of the brush structure is investigated in a non-selective solvent, and non-trivial variations of the surface composition are observed. The quantity of these latter effects would be insufficient to build switchable systems, and we argue that a minor quantity of solvent selectivity would suffice to enable the desired feature of an environment-responsive coating.

A critical look into effects of electrode pore morphology in solid oxide fuel cells

Knudsen diffusion, an important form of gas transport in sub‐micro/nanoscale porous electrodes of solid oxide fuel cells (SOFCs), is evaluated typically based on the assumption of isotropic cross‐sections of electrode pores. As a consequence, errors are induced in the evaluation of gas transport and polarization loss of SOFCs with irregular, anisotropic pore morphology. Here, a numerical model is derived to investigate the impact of pore morphology on Knudsen diffusivity and effective total diffusivity in porous SOFC electrodes. Based on the model, the correlation between pore morphology and important parameters of SOFCs, including limiting current density (LCD) and concentration polarization (CP), is evaluated. As the aspect ratio of pore cross‐section increases, the gas diffusivity in SOFC electrodes decreases, and then nontrivial variations in LCD and CP are induced. This work facilitates the accurate evaluation of gas transport in SOFCs as well as the rational design of electrode microstructure of SOFCs. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2312–2317, 2017

Analyzing optical properties of thin vanadium oxide films through semiconductor-to-metal phase transition using spectroscopic ellipsometry

We investigated the optical behaviors of vanadium dioxide (VO2) films through the semiconductor-to-metal (STM) phase transition using spectroscopic ellipsometry. Correlations between film thickness and refractive index were observed resulting from the absorbing nature of these films. Simultaneously analyzing data at multiple temperatures using Kramers-Kronig consistent oscillator models help identify film thickness. Nontrivial variations in resulting optical constants were observed through STM transition. As temperature increases, a clear increase is observed in near infrared absorption due to Drude losses that accompany the transition from semiconducting to metallic phases. Thin films grown on silicon and sapphire substrate present different optical properties and thermal hysteresis due to lattice stress and compositional differences.