Weak Dispersion Research Articles

Trapping of two-component light bullets in a gradient waveguide with normal group dispersion.

In this paper we consider the process of the second harmonic generation in a gradient waveguide, taking into account diffraction and relatively weak temporal dispersion. Using the slowly varying envelope approximation and neglecting the dispersion of the nonlinear part of the response of the medium we obtain the system of parabolic equations for the envelopes of both harmonics. We also derive integrals of motion of this system. To solve it numerically we construct a nonlinear finite-difference scheme based on the Crank-Nicolson method preserving the integrals. Primarily, we focus our investigations on the processes of a two-component light bullets generation. We demonstrate that the generation of a coupled pair is possible in a planar waveguide even at normal group velocity dispersion.

Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity

In this work, the KdV equation with conformable derivative and dual-power law nonlinearity is considered. It is exceedingly used as a model to depict the feeble nonlinear long waves in different fields of sciences. Furthermore, it explains the comparable effects of weak dispersion and weak nonlinearity on the evolvement of the nonlinear waves. Using the Jacobi elliptic function expansion method, new exact solutions of that equation have been found. As results, some obtained solutions behave as periodic traveling waves, bright soliton, and dark soliton.

The role of dispersal, selection, and timing of sampling on the false discovery rate of loci under selection during geographic range expansion.

Identifying adaptive loci is important to understand the evolutionary potential of species undergoing range expansion. However, in expanding populations, spatial demographic processes such as allele surfing can create spatial patterns of neutral genetic variation that appear similar to those generated through adaptive processes. As a result, the false discovery rate of adaptive loci may be inflated in landscape genomic analyses. Here, we take a simulation modelling approach to investigate how range expansion affects our ability to correctly distinguish between neutral and adaptive genetic variation, using the mountain pine beetle outbreak system as a motivating example. We simulated the demographic and population genetic dynamics of populations undergoing range expansion using an individual-based genetic model CDMetaPOP. We investigated how the false discovery rate of adaptive loci is affected by (i) dispersal capacity, (ii) timing of sampling, and (iii) the strength of selection on an adaptive reference locus. We found that a combination of weak dispersal, weak selection, and early sampling presents the greatest risk of misidentifying loci under selection. Expanding populations present unique challenges to the reliable identification of adaptive loci. We demonstrate that there is a need for further methodological development to account for directional demographic processes in landscape genomics.

Te-canfieldite from the lunnoe au-u deposit (Aldan region, Republic of Yakutiya)

Te-canfeldite was found in assemblage with pyrite, marcasite, hessite, and Tl sulfosalts in the ores of the Fedorovskaya vein zone of the Lunnoe Au-U deposit, Aldan shield (Yakutia). The mineral forms anhedral inclusions in vein matrix. Its refection spectrum is characterized by weak normal dispersion, the dispersion curve is almost parallel to the canfeldite curve, but the refectivity value is signifcantly higher. A sustained S:Te ratio of Te-canfldite is consistent with the analytical data for most mineral localities (Lengenbach, Sirotan, Nikolayevskoye, Uryakh). It is suggested that Te-canfeldite is formed in a wide range of geological settings.

Linear Schrödinger equation with temporal evolution for front induced transitions.

The nonlinear Schrödinger equation based on slowly varying approximation is usually applied to describe the pulse propagation in nonlinear waveguides. However, for the case of the front induced transitions (FITs), the pump effect is well described by the dielectric constant perturbation in space and time. Thus, a linear Schrödinger equation (LSE) can be used. Also, in waveguides with weak dispersion the spatial evolution of the pulse temporal profile is usually tracked. Such a formulation becomes impossible for optical systems for which the group index or higher dispersion terms diverge as is the case near the band edge of photonic crystals. For the description of FITs in such systems a linear Schrödinger equation can be used where temporal evolution of the pulse spatial profile is tracked instead of tracking the spatial evolution. This representation provides the same descriptive power and can easily deal with zero group velocities. Furthermore, the Schrödinger equation with temporal evolution can describe signal pulse reflection from both static and counter-propagating fronts, in contrast to the Schrödinger equation with spatial evolution which is bound to forward propagation. Here, we discuss the two approaches and apply the LSE with temporal evolution for systems close to the band edge where the group velocity vanishes by simulating intraband indirect photonic transitions. We also compare the numerical results with the theoretical predictions from the phase continuity criterion for complete transitions.

Many-body effects in twisted bilayer graphene at low twist angles

We study the zero-temperature many-body properties of twisted bilayer graphene with a twist angle equal to the so-called `first magic angle'. The system low-energy single-electron spectrum consists of four (eight, if spin label is accounted) weakly-dispersing partially degenerate bands, each band accommodating one electron per Moir{\'{e}} cell per spin projection. This weak dispersion makes electrons particularly susceptible to the effects of interactions. Introducing several excitonic order parameters with spin-density-wave-like structure, we demonstrate that (i)~the band degeneracy is partially lifted by the interaction, and (ii)~the details of the low-energy spectrum becomes doping-dependent. For example, at or near the undoped state, interactions separate the eight bands into two quartets (one quartet is almost filled, the other is almost empty), while for two electrons per Moir\'{e} cell, the quartets are pulled apart, and doublets emerge. When the doping is equal to one or three electrons per cell, the doublets split into singlets. Hole doping produces similar effects. As a result, electronic properties (e.g., the density of states at the Fermi energy) demonstrate oscillating dependence on the doping concentration. This allows us to reproduce qualitatively the behavior of the conductance observed recently in experiments [Cao et al., Nature {\bf 556}, 80 (2018)]. Near half-filling, the electronic spectrum loses hexagonal symmetry indicating the appearance of a many-body nematic state.

Global Patterns of Aquatic Macroinvertebrate Dispersal and Functional Feeding Traits in Aridland Rock Pools

Rock pools are important desert ecosystems that provide rare sources of surface water in arid regions. Hydroperiod is one of the primary limiting factors on aquatic macroinvertebrates living in rock pools. Resident macroinvertebrates must complete their life cycles before drying, and may employ active or passive dispersal strategies to survive drying. Quantifying dispersal and functional feeding traits across rock pool macroinvertebrate communities in multiple regions could provide insight into how rock pool ecosystems will respond to shorter hydroperiods predicted by climate change models. Here, we analyze taxonomic data (26 species lists) obtained from 24 published studies of rock pools to assess the dispersal and feeding strategies of macroinvertebrates, and how ecosystem functions may change with shorter hydroperiods. On average across all data sets, taxa were equally comprised of active dispersers and passive dispersers. Most active disperser taxa were predators (60%) and gatherers (33%). In contrast, passive disperser taxa were generally filterers (39%), gatherers (29%), and scrapers (21%). Climate change scenarios may result in shorter rock pool hydroperiods in many regions, which could reduce habitat availability for passive dispersers with weak overland dispersal abilities. If passive disperser populations decrease, their associated ecosystem functions, such as fine organic matter processing, could be disrupted. These results provide a foundation for future work investigating changes in rock pool ecosystem function due to altered hydroperiods.

Ducting of upper-hybrid waves by density depletions in a magnetoplasma with weak spatial dispersion

The effects of wave trapping and ducting inside a plasma density depletion are studied in a large laboratory magnetoplasma in the upper-hybrid (UH) range of frequencies. A field-aligned density depletion is generated via localized rf plasma heating and subsequent plasma thermal diffusion. Test UH waves are emitted and detected by small-size electric monopole antennas. For a given set of experimental parameters, propagation of UH waves can be considered as collisionless. At the same time, wave surface topology in the UH range is determined by weak spatial dispersion, which is conditioned by the thermal motion of electrons and the ambient magnetic field. For various density depletion depths and diameters, ducting of UH waves belonging to different characteristic parts of the “dumbbell-shaped” wave surface can be observed. Particularly, quasiparallel Langmuir (L-mode) waves and oblique resonance cone (X-mode) waves can be ducted in different regimes. A qualitative explanation of ducting regimes is given based on ray tracing analysis.

Research on the sediment acoustic properties based on a water coupled laboratory measurement system

The high-frequency acoustic properties of seafloor sediments are very significant in seafloor study and underwater acoustic study field. In order to measure the sound speed and the attenuation for the small-scale sediment cores more accurately, this study developed a water coupled acoustic laboratory measurement system based on Richardson-Briggs technique. This method used the correlation comparison of waveforms received in sediment core and in identical reference tubes filled with water to measure sound speed and attenuation. The sound speed and attenuation of a clayey silt sediment sample were measured using the water coupled acoustic laboratory measurement system. This frequency dependence of the sound speed and attenuation showed that the clayey silt sediment has a weak positive sound speed dispersion, while the attenuation increases with a strong positive gradient within the measurement frequency range. This study also noted that the measured sound speed ratio match well with the empirical equations from literature. The measured attenuation factor data can fall in the Hamilton’s empirical prediction range.

Dipole Glass Phase in an Isolated Hydrogen-Bonded Mixed Crystal [(NH4)1−x Rbx]3H(SO4)2 (x = 0.58)

[(NH4)1−xRbx]3H(SO4)2 mixed crystals were investigated by dielectric constant measurement and Raman spectroscopy from room temperature to 7 K. In contrast to the result of (NH4)3H(SO4)2 (x = 0) showing multiple phase transitions, [(NH4)1−xRbx]3H(SO4)2 (x = 0.58) mixed crystal does not show any remarkable dielectric anomaly but a weak dielectric dispersion below 40 K, which is characterized by the Arrhenius law. From the measurement of the Raman spectra of both crystals, it is confirmed that the [(NH4)1−xRbx]3H(SO4)2 (x = 0.58) mixed crystal shows a global symmetry conservation between the two spectra measured at room temperature and at 20 K while the (NH4)3H(SO4)2 crystal exhibits drastic structural changes associated with the sequence of the phase transitions. It is concluded that [(NH4)1−xRbx]3H(SO4)2 (x = 0.58) mixed crystal shows a new dipole glass phase in the isolated hydrogen-bonded system.

A Metal-organic Framework with Paddle-wheel Zn2(CO2)4 Secondary Building Units and Cubane-1,4-dicarboxylic Acid Linkers

A new crystal structure of catena-(bis((µ4-cubane-1,4-dicarboxylato)-(N-methyl-2-pyrrolidone)-zinc(II)) N-methyl-2-pyrrolidone solvate) (1) was prepared by solvothermal method. The crystal structure of the compound was analyzed by single-crystal X-ray diffraction. It has a P1 space group, with lattice parameters a = 10.7190(4) Å, b = 10.8245(5) Å, c = 10.8403(8) Å, α = 80.291(5)°, β = 70.0015(5)°, γ = 77.531(4)°, V = 1147.97(12) Å3. The secondary building units of 1 consist of 2 central Zn ions, coordinated by 4 carboxylate groups in a bis-monodentate way, forming a square planar configuration of Zn2(CO2)4, known as paddle-wheel units. The paddle-wheels are connected by cubane-1,4-dicarboxylic acid linkers at the edges, resulting in a two-dimensional coordination polymer with a square lattice (sql) underlying network topology. The axial sites of the zinc atoms are occupied by N-methyl-2-pyrrolidone molecules. In this new crystal structure the two-dimensional polymer planes are interstacked by weak dispersion bonds. The axial N-methyl-2-pyrrolidone solvent molecules determine the distances of planar polymer planes. The thermal properties of this new structure were studied by thermogravimetry/mass spectrometry in inert atmosphere. It was found, that the organic linkers in the framework structure do not decompose below 200 °C. The stochiometry of the activated compound is Zn2[C8H6(COO)2]2(C5H9NO)2, as determined by thermogravimetry in oxidative atmosphere.

MXene-based saturable absorber for femtosecond mode-locked fiber lasers.

We report simple and compact all-fiber erbium-doped soliton and dispersion-managed soliton femtosecond lasers mode-locked by the MXene Ti3C2Tx. A saturable absorber device fabricated by optical deposition of Ti3C2Tx onto a microfiber exhibits strong saturable absorption properties, with a modulation depth of 11.3%. The oscillator operating in the soliton regime produces 597.8 fs-pulses with 5.21 nm of bandwidth, while the cavity with weak normal dispersion (~0.008 ps2) delivers 104 fs pulses with 42.5 nm of bandwidth. Our results contribute to the growing body of work studying the nonlinear optical properties of MXene that underpin new opportunities for ultrafast photonic technology.

Dark breather waves, dark lump waves and lump wave–soliton interactions for a [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation in a fluid

Fluids are seen in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, astrophysics and biology. In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation for the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Breather-wave, lump-wave and lump wave–soliton solutions are derived under certain conditions via the Hirota method. With h1h2−1<0, where h1 and h2 represent the coefficients of dispersion and nonlinearity, respectively, we obtain the dark breather wave and lump wave. We observe the effects of h1, h2, h4, h6 and h8 on the dark breather wave and lump wave, where h6 is the perturbed effect, h4 and h8 stand for the disturbed wave velocity effects corresponding to the y and z coordinates: h1 and h2 influence the amplitude of the dark breather wave; h1, h4 and h8 influence the distance between the adjacent valleys of the dark breather wave; h1, h4, h6 and h8 influence the location of the dark breather wave; h2, h4, h6 and h8 influence the amplitude of the dark lump wave; h1, h4 and h8 influence the width of the dark lump wave; h4, h6 and h8 influence the location of the dark lump wave. When h1h2−1>0, we present the fusion between a bright lump wave and one bright soliton as well as fission of one bright soliton. We also observe the fusion between a dark lump wave and one dark soliton as well as fission of one dark soliton with h1h2−1>0.

Equation of State of Fluid Methane from First Principles with Machine Learning Potentials.

The predictive simulation of molecular liquids requires potential energy surface (PES) models that are not only accurate but also computationally efficient enough to handle the large systems and long time scales required for reliable prediction of macroscopic properties. We present a new approach to the systematic approximation of the first-principles PES of molecular liquids using the GAP (Gaussian Approximation Potential) framework. The approach allows us to create potentials at several different levels of accuracy in reproducing the true PES and thus to determine the level of quantum chemistry that is necessary to accurately predict macroscopic properties. We test the approach by building a series of many-body potentials for liquid methane (CH4), which is difficult to model from first principles because its behavior is dominated by weak dispersion interactions with a significant many-body component. The increasing accuracy of the potentials in predicting the bulk density correlates with their fidelity to the true PES, whereas the trend with the empirical potentials tested is surprisingly the opposite. We conclude that an accurate, consistent prediction of its bulk density across wide ranges of temperature and pressure requires not only many-body dispersion but also quantum nuclear effects to be modeled accurately.

Towards understanding π-stacking interactions between non-aromatic rings.

The first systematic study of π interactions between non-aromatic rings, based on the authors' own results from an experimental X-ray charge-density analysis assisted by quantum chemical calculations, is presented. The landmark (non-aromatic) examples include quinoid rings, planar radicals and metal-chelate rings. The results can be summarized as: (i) non-aromatic planar polyenic rings can be stacked, (ii) interactions are more pronounced between systems or rings with little or no π-electron delocalization (e.g. quinones) than those involving delocalized systems (e.g. aromatics), and (iii) the main component of the interaction is electrostatic/multipolar between closed-shell rings, whereas (iv) interactions between radicals involve a significant covalent contribution (multicentric bonding). Thus, stacking covers a wide range of interactions and energies, ranging from weak dispersion to unlocalized two-electron multicentric covalent bonding ('pancake bonding'), allowing a face-to-face stacking arrangement in some chemical species (quinone anions). The predominant interaction in a particular stacked system modulates the physical properties and defines a strategy for crystal engineering of functional materials.

Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

Under investigation is a generalized Kadomtsev–Petviashvili equation with variable coefficients, which describes the long water waves and small-amplitude surface waves with weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics. Stripe solitons and lump solutions are obtained by proposing an improved positive quadratic function based on Hirota’s bilinear form and symbolic computation. The dynamical properties of the obtained solutions are demonstrated in some 3D and contour plots by setting the values of the parameters.

Fluorinated carbon nanofiber/polyimide composites: Electrical, mechanical, and hydrophobic properties

The poor multifunction of polyimide (PI) based composites and the weak dispersion of nanofillers in PI matrix greatly limits their broad industrial application. In this paper, fluorine element doping carbon nanofiber (FCNF) was designed, and the FCNF can disperse and embed into the PI matrix commendably, compared with pure PI, even at a very low contents of FCNF (1 wt%), the FCNF/PI composite can endow the PI matrix with a dramatic increment on mechanical strength (77.9%), volume resistivity (77.9%), and hydrophobic properties (35.0%), this can be attributed to the doping of F element in carbon nanofiber, the uniform dispersion of FCNF in composite and strong interfacial interaction between FCNF and the matrix. Meanwhile, TEM and XPS results further proved the doping of fluorine element, and the SEM results also confirmed the uniform distribution of FCNF in the FCNF/PI composites. Moreover, the interface existence the FCNF/PI composite was proved by the synchrotron radiation small angle x-ray scattering (SAXS) experiments. This method provides a novel route for improving the electrical, mechanical, and hydrophobic of PI based composites and a new thought to carry out the application of the FCNF as an advanced nano-material.

Hidden diversity in pebble beaches - a thus far unrecognized radiation of the cryptobenthic fish genus Gouania (Gobiesocidae)

Event Abstract Back to Event Hidden diversity in pebble beaches - a thus far unrecognized radiation of the cryptobenthic fish genus Gouania (Gobiesocidae) Maximilian Wagner1* 1 University of Graz, Institute of Biology, Austria Gouania willdenowi (Risso 1810), the sole representative of the monotypic clingfish genus Gouania, is endemic to the Mediterranean Sea where it lives a very cryptic and secretive life in the interstices of pebble beaches. With its wormlike body and small eyes, it is perfectly adapted to this extreme environment. Because of a reduced swim bladder and a very patchy distribution of suitable habitats, adult G. willdenowi are very weak active dispersers and dispersal likely happens passively during the pelagic larval phase. Despite being quite common in pebble beaches throughout the Mediterranean, hardly anything is known about its biology, behaviour, phylogeny or taxonomy. However, DNA-barcoding, species tree analysis (*BEAST) including 9 nuclear and one mitochondrial marker, as well as geometric morphometric analyses (GEMO) and MicroCT imaging across the whole Mediterranean Sea, yielded unexpected results regarding the evolutionary history of this genus. Molecular data suggests that the genus Gouania underwent a thus far unrecognized radiation into five highly divergent species that started around three million years ago. Furthermore, GEMO revealed two parallelly evolved morphotypes characterized by a slender (smaller eyes, increased vertebrae number) and a stout (larger eyes, smaller number of vertebrae) body shape. Whereas in the Adriatic and the Eastern Mediterranean basins “slender” and “stout” Gouania occur sympatrically, only the “stout” morphotype was found in the Western Mediterranean. To conclude, the radiation of Gouania represents a promising model system for studying radiation and the independent origin of eco-morphologically similar species pairs, and the role of water currents and ecological potential for driving diversification in the marine environment. Keywords: Gobiesocidae, Cryptic diversity, Cryptobenthic fishes, Gouania, phylogeny Conference: XVI European Congress of Ichthyology, Lausanne, Switzerland, 2 Sep - 6 Sep, 2019. Presentation Type: Oral Topic: TAXONOMY, PHYLOGENY AND ZOOGEOGRAPHY Citation: Wagner M (2019). Hidden diversity in pebble beaches - a thus far unrecognized radiation of the cryptobenthic fish genus Gouania (Gobiesocidae). Front. Mar. Sci. Conference Abstract: XVI European Congress of Ichthyology. doi: 10.3389/conf.fmars.2019.07.00099 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 10 May 2019; Published Online: 14 Aug 2019. * Correspondence: Mr. Maximilian Wagner, University of Graz, Institute of Biology, Graz, Austria, maximilian.wagner@uni-graz.at Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Maximilian Wagner Google Maximilian Wagner Google Scholar Maximilian Wagner PubMed Maximilian Wagner Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Weak dispersion for the Dirac equation on asymptotically flat and warped product spaces

In this paper we prove local smoothing estimates for the Dirac equation on some non-flat manifolds; in particular, we will consider asymptotically flat and warped products metrics. The strategy of the proofs relies on the multiplier method.

Low RCS Antennas Based on Dispersion Engineering of Spoof Surface Plasmon Polaritons

In this paper, we propose the design of antennas with low radar cross section (RCS) based on dispersion engineering of spoof surface plasmon polaritons (SSPPs). The antenna consists of a feeding monopole and SSPPs guiding structure placed vertically on a metal ground. By comprehensively engineering the weak and strong dispersion regimes of the SSPPs structure, the cutoff frequency of SSPPs can be made close to the upper operating frequency of the feeding monopole. In this way, the SSPPs structure serves as a high-efficiency radiator in the operating band and as a broadband absorber out of band, leading to low RCS out of band. As an example, a C -band antenna with low RCS in the X -band was designed, simulated, and measured. Both the simulation and experiment results show that the antenna can radiate in the C -band, with average gain 6 dB and fractional bandwidth 28%. In order to evaluate the RCS reduction performances, a $5\times 5$ antenna array was fabricated and the mono-static RCS was measured. The measured results show that the mono-static RCS is reduced by more than 10 dB in the whole X -band (8.0–12.5 GHz), with a maximal reduction above 30 dB. The design method provides an effective alternative to low-RCS antennas.