Antinodal Points Research Articles

The interplay between a pseudogap and superconductivity in a two-dimensional Hubbard model

Strongly correlated electrons systems may exhibit a variety of interesting phenomena, for instance, superconductivity and pseudogap, as is the case of cuprates and pnictides. In strongly correlated electron systems, it is considered essential to understand, not only the nature of the pseudogap, but also the relationship between superconductivity and the pseudogap. In order to address this question, in the present work, we investigated a one-band Hubbard model treated by the Green's function method within an n-pole approximation. In the strongly correlated regime, antiferromagnetic correlations give rise to nearly flat band regions in the nodal points of the quasiparticle bands. As a consequence, a pseudogap emerges at the antinodal points of the Fermi surface. The obtained results indicate that the same antiferromagnetic correlations responsible for a pseudogap, can also favor superconductivity, providing an increase in the superconducting critical temperature Tc.

SIMULATION OF CRACK EFFECT ON SPECTRUM OF NATURAL OSCILLATIONS DURING MONITORING OF STRENGTH OF LARGE STRUCTURES

This document contains monitoring results of structural strength of bearing beams of two large structures. To conduct the monitoring, beam natural oscillations were excited and their spectrum changes in case of possible defects were analysed. Simulators in the form of small-size plates pressed to the beams were used as possible defects (cracks). The specific feature of such a simulation is that the plate, pressed to the beam in an antinodal point of some mode of natural oscillations and damping it, also damps it in all the other antinodal points. The oscillations were excited and received by special transducers with mechanical filters at their inputs. This enables significant reduction of the spectrum of natural oscillations, reducing it to two or several dominant modes. It is shown that during the flaw detection with such a reduced spectrum, two processes take place – damping of natural oscillations and energy redistribution between their modes, which should be taken into account during the monitoring in automated mode.

Modal analysis of plate to analyze the effect of mass stiffeners using the Chladni plate approach

Modal analysis of mechanical structures or components determines the mode shapes and natural frequencies. The Chladni plate approach is used to demonstrate the mode shapes of plates. Chladni pattern formation depends on plate material, geometry, thickness, and vibration frequency. This paper studies the Chladni figures obtained by sprinkling tea powder on a square acrylic plate mounted on the mechanical vibrator. Frequencies corresponding to each Chladni figure are noted. Further, the effect of adding stiffener at antinode points of the plate is analyzed. The change in the frequency due to the addition of stiffener is also studied. Results show that the Eigenfrequency values have increased. The Chladni patterns are obtained at a higher frequency for the plate with stiffener than the plate without stiffener. Simulation results obtained in the ANSYS workbench are used to validate experimental observations. For the acrylic Chladni plate, the error between the experimental and simulation work is less than 18%.

Wave power extraction by multiple wave energy converters arrayed in a water channel resonator

Abstract The wave power extraction by multiple Wave Energy Converters (WECs) deployed in a Y-shaped Water Channel Resonator (WCR) has been investigated. A WCR consists of a long water channel, and a V-shaped wave guider installed at the entrance of a water channel. If the period of the incident waves coincides with the natural periods of the fluid in a WCR, resonance occurs, as a result, the internal fluid in a WCR is greatly amplified. To estimate the wave power by multiple WECs placed at the antinodal points in a WCR, the heave motion response, time-averaged power, and capture width ratio were calculated for several design parameters. Also, the systematic model tests were conducted in a 2D wave tank. The numerical results are in good agreement with the experimental data. It was verified that a WCR helps the WECs to produce electricity more effectively by amplifying the wave energy in a WCR.

Pairing glue in cuprate superconductors from the self-energy revealed via machine learning

Recently, machine learning was applied to extract both the normal and the anomalous components of the self-energy from photoemission data at the antinodal points in Bi-based cuprate high-temperature superconductors [Y. Yamaji {\it et al.}, arXiv:1903.08060]. It was argued that both components do show prominent peaks near 50 meV, which hold information about the pairing glue, but the peaks are hidden in the actual data, which measure only the total self-energy. We analyze the self-energy within an effective fermion-boson theory. We show that soft thermal fluctuations give rise to peaks in both components of the self-energy at a frequency comparable to superconducting gap, while they cancel in the total self-energy; all irrespective of the nature of the pairing boson. However, in the quantum limit $T \to 0$ prominent peaks survive only for a very restricted subclass of pairing interactions. We argue that the way to potentially nail down the pairing boson is to determine the thermal evolution of the peaks.

Dual-Gas Quartz-Enhanced Photoacoustic Sensor for Simultaneous Detection of Methane/Nitrous Oxide and Water Vapor.

The development of a dual-gas quartz-enhanced photoacoustic (QEPAS) sensor capable of simultaneous detection of water vapor and alternatively methane or nitrous oxide is reported. A diode laser and a quantum cascade laser (QCL) excited independently and simultaneously both the fundamental and the first overtone flexural mode of the quartz tuning fork (QTF), respectively. The diode laser targeted a water absorption line located at 7181.16 cm-1 (1.392 μm), while the QCL emission wavelength is centered at 7.71 μm and was tuned to target two strong absorption lines of methane and nitrous oxide, located at 1297.47 and 1297.05 cm-1, respectively. Two sets of microresonator tubes were positioned, respectively, at the antinode points of the fundamental and the first overtone flexural modes of the QTF to enhance the QEPAS signal-to-noise ratio. Detection limits of 18 ppb for methane, 5 ppb for nitrous oxide and 20 ppm for water vapor have been achieved at a lock-in integration time of 100 ms.

The t−t′−t″−U Hubbard model and Fermi-level peak

Using the strong-coupling diagram technique, low-temperature spectral properties of the two-dimensional fermionic Hubbard model are considered for strong and moderate Hubbard repulsions U. The electron hopping to the nearest, second and third neighbors is taken into account with hopping constants and , respectively. The nonzero values of and lead to strong asymmetry in magnetic properties with respect to the hole and electron doping—for U = 8t strong antiferromagnetic correlations are retained up to the electron concentration , while they are destroyed completely at . When the temperature is decreased to T ≲ 0.1t, in a wide range of electron concentrations there appear narrow and intensive peaks at the Fermi level (FL) in densities of states. For U ≲ 6t the peaks are seen even at half-filling, while for larger U they arise as the FL leaves the Mott gap. The peaks are connected with a narrow band emerging at low temperatures. We identify states forming the band with spin-polaron excitations—bound states of correlated electrons and mobile spin excitations. Obtained low-temperature spectral functions are used for interpreting the peak-dip-hump structure observed in the photoemission of Nd2−xCexCuO4. In the case of hole doping, the calculated Fermi contour contains arcs near nodal points with pseudogaps near antinodal points, while for electron doping the spectral intensity is suppressed at hot spots, in agreement with experimental observations in cuprate perovskites.

Free vibration analysis for a pipe conveying fluid with intermediate support and carrying multiple concentrated masses

In the present paper, the exact vibration characteristics of multi-span pipe conveying fluid has been studied. A mathematical model and a computer program are used to obtain the results. Results of typical cases have been obtained using the current model and compared with the relevant published results. The effect of intermediate support location on the vibration characteristics of clamped-pinnedpinned pipe carrying concentrated masses is evaluated. Natural frequencies and the critical flow velocity of the selected pipe are determined for different locations of both the intermediate support and the concentrated masses. Nodal and anti-nodal points of the mode shape are investigated due to the change of the intermediate support location for accepted observability and controllability aspects.

Why is the antinodal quasiparticle in the electron-doped cuprate Pr1.3−xLa0.7CexCuO4 immune to the antiferromagnetic band-folding effect?

A recent ARPES measurement on electron-doped cuprate Pr1.3−xLa0.7CexCuO4 finds that the antiferromagnetic (AFM) band-folding gap along the boundary of the antiferromagnetic Brillouin zone (AFBZ) exhibits dramatic momentum dependence. In particular, it vanishes in a finite region around the antinodal point, in which a single broadened peak emerges at the unrenormalized quasiparticle energy. Such an observation is argued to be inconsistent with the AFM band-folding picture, which predicts a constant band splitting along the AFBZ boundary. On the other hand, it is claimed that the experimental results are consistent with the prediction of the cluster dynamical mean-field theory (CDMFT) simulation on the Hubbard model, in which the obserevd spectral gap is interpreted as an s-wave pseudogap between the Hubbard bands and the in-gap states. Here we show that the observed momentum dependence of the spectral gap along the AFBZ boundary is indeed consistent with the AFM band-folding picture, provided that we assume the existence of a strongly momentum-dependent quasiparticle scattering rate. More specifically, we show that the quasiparticle scattering rate acts to reduce the spectral gap induced by the AFM band-folding effect. The new quasiparticle poles corresponding to the AF-split bands can even be totally eliminated when the scattering rate exceeds the bare band-folding gap, leaving the system with a single pole at the unrenormalized quasiparticle energy. We predict that the AFM band-folding gap should close in a square root fashion as we move toward along the AFBZ boundary. Our results illustrate that the quasiparticle scattering rate can play a much more profound role than simply broadening the quasiparticle peak in the quasiparticle dynamics of strongly correlated electron systems.

Standard and inverse microscale Chladni figures in liquid for dynamic patterning of microparticles on chip

We report on experimental demonstrations of the first sub-100 μm scale standard and inverse Chladni figures in both one- (1D) and two-dimensional (2D) fashions in liquid, and on exploiting these micro-Chladni figures for patterning microparticles on chip, via engineering multimode micromechanical resonators with rich, reconfigurable 1D and 2D mode shapes. Silica microparticles (1–8 μm in diameter) dispersed on top of resonating doubly-clamped beams (100 × 10 × 0.4 μm3) are observed to aggregate at antinodal points, forming 1D inverse Chladni figures, while microbeads atop square trampoline resonators (50 × 50 × 0.2 μm3) cluster at nodal lines/circles, creating 2D standard Chladni figures such as “,” “○,” “×,” and “\.” These observations suggest two distinct micro-Chladni figure patterning mechanisms in liquid. Combining analytical and computational modeling, we elucidate that streaming flow dominates the inverse Chladni pattern formation in the 1D beam experiments, while vibrational acceleration dictates the standard Chladni figure generation in the 2D trampoline experiments. We further demonstrate dynamical patterning, switching, and removal of 2D micro-Chladni figures in swift succession by simply controlling the excitation frequency. These results render new understandings of Chladni patterning genuinely at the microscale, as well as a non-invasive, versatile platform for manipulating micro/nanoparticles and biological objects in liquid, which may enable microdevices and functional device-liquid interfaces toward relevant sensing and biological applications.

Ultrasound-assisted extraction of hemicellulose and phenolic compounds from bamboo bast fiber powder.

Ultrasound-assisted extraction of hemicellulose and phenolic compounds from bamboo bast fibre powder was investigated. The effect of ultrasonic probe depth and power input parameters on the type and amount of products extracted was assessed. The results of input energy and radical formation correlated with the calculated values for the anti-nodal point (λ/4; 16.85 mm, maximum amplitude) of the ultrasonic wave in aqueous medium. Ultrasonic treatment at optimum probe depth of 15 mm improve 2.6-fold the extraction efficiencies of hemicellulose and phenolic lignin compounds from bamboo bast fibre powder. LC-Ms-Tof (liquid chromatography-mass spectrometry-time of flight) analysis indicated that ultrasound led to the extraction of coniferyl alcohol, sinapyl alcohol, vanillic acid, cellobiose, in contrast to boiling water extraction only. At optimized conditions, ultrasound caused the formation of radicals confirmed by the presence of (+)-pinoresinol which resulted from the radical coupling of coniferyl alcohol. Ultrasounds revealed to be an efficient methodology for the extraction of hemicellulosic and phenolic compounds from woody bamboo without the addition of harmful solvents.

Complementary views on electron spectra: From fluctuation diagnostics to real-space correlations

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation diagnostics" approach, to extract the dominant wave vector dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes, to render its connection with resonance valence bond (RVB) fluctuations more transparent. Secondly, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity and RVB-like real space correlations, broadening the analysis of an earlier work [Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K-points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-like state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath-couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.

Correlation between Fermi arc and charge order resulting from the momentum-dependent self-energy correction in cuprates

We calculate momentum-dependent self-energies due to self-consistent spin and charge-density fluctuations within a single-band Hubbard model for hole-doped cuprates. We find that the dynamical density instability (mainly paramagnonlike spin fluctuations) arising from the van Hove singularity at the antinodal point produces strongly anisotropic mass renormalization, increasing from the nodal direction to the antinodal one. This gives rise to a coherent Fermi arc pattern in which although the self-energy dressed Green's function has poles at all Fermi momenta, the corresponding spectral weight decreases from the nodal to the antinodal direction. We study the feedback effects of the anisotropic self-energy and Fermi arc on the charge-density wave (CDW) instability by direct computations of charge susceptibility and the quasiparticle interference pattern. We find that that due to the loss of spectral weight at the antinodal points, the CDW nesting weakens, and the corresponding hot spot shifts from the antinodal region to the tip of the Fermi arc below the magnetic Brillouin zone. The results are in good agreement with experiments, reproducing the observed slow doping dependence of the CDW wave vector. Our investigation therefore provides a mechanism for the Fermi arc in cuprates, with various testable predictions such as a sharp, first-order-like phase transition of the CDW order on the higher-doping side.

Standing Waves in One-Dimensional Resonator Containing an Ideal Isothermal Gas Affected by the Constant Mass Force

Abstract The study is devoted to standing acoustic waves in one-dimensional planar resonator which containing an ideal gas. A gas is affected by the constant mass force. Two types of physically justified boundary conditions are considered: zero velocity or zero excess pressure at both boundaries. The variety of nodal and antinodal points is determined. The conclusion is that the nodes of pressure and antinodes of velocity do not longer coincide, as well as antinodes of pressure and nodes of velocity. The entropy mode may contribute to the total field in a resonator. It is no longer isobaric, in contrast to the case when the external force is absent. Examples of perturbations inherent to the entropy mode in the volume of a resonator are discussed.

Cardinal and anti-cardinal points, equalities and chromatic dependence.

Cardinal points are used for ray tracing through Gaussian systems. Anti-principal and anti-nodal points (which we shall refer to as the anti-cardinal points), along with the six familiar cardinal points, belong to a much larger set of special points. The purpose of this paper is to obtain a set of relationships and resulting equalities among the cardinal and anti-cardinal points and to illustrate them using Pascal's ring. The methodology used relies on Gaussian optics and the transference T. We make use of two equations, obtained via the transference, which give the locations of the six cardinal and four anti-cardinal points with respect to the system. We obtain equalities among the cardinal and anti-cardinal points. We utilise Pascal's ring to illustrate which points depend on frequency and their displacement with change in frequency. Pascal described a memory schema in the shape of a hexagon for remembering equalities among the points and illustrating shifts in these points when an aspect of the system changes. We modify and extend Pascal's ring to include the anti-cardinal points. We make use of Pascal's ring extended to illustrate which points are dependent on the frequency of light and the direction of shift of the equalities with change in frequency. For the reduced eye the principal and nodal points are independent of frequency, but the focal points and the anti-cardinal points depend on frequency. For Le Grand's four-surface model eye all six cardinal and four anti-cardinal points depend on frequency. This has implications for definitions, particularly of chromatic aberrations of the eye, that make use of cardinal points and that themselves depend on frequency. Pascal's ring and Pascal's ring extended are novel memory schema for remembering the equalities among the cardinal and anti-cardinal points. The rings are useful for illustrating changes among the equalities and direction of shift of points when an aspect of a system changes. Care should be taken when defining concepts that rely on cardinal points that depend on frequency.

Double antinode excited quartz-enhanced photoacoustic spectrophone

A double antinode excited quartz-enhanced photoacoustic spectroscopy (DAE-QEPAS) spectrophone, employing a custom-made quartz tuning fork (QTF) and operating at the 1stt overtone resonance mode is reported. The signal phase variation along the QTF prong was investigated, and a piezoelectric transducer was introduced to compensate the phase shift between two QTF separated 1st overtone antinode points. Two sets of acoustic micro-resonators were optimized and assembled at two antinode points to improve the spectrophone performance. With the two antinodes excited by one laser source, the DAE-QEPAS spectrophone attained a sensitivity gain factor of ∼100 times and ∼3 times with respect to the 1st overtone resonances of a bare custom QTF and a standard on-beam QEPAS spectrophone, respectively. H2O was selected as the target analyte and a detection limit of ∼230 ppb was obtained by the DAE-QEPAS spectrophone for a 1 s integration time, corresponding to a normalized noise equivalent absorption coefficient of 1.73 × 10-9 cm−1·W·Hz−1/2.

Application of Computational Fluid Dynamics in Simulating Film Boiling of Cryogens

This paper presents a computational fluid dynamic (CFD) model, simulating film boiling based on Rayleigh–Taylor (R-T) instability, using the volume of fluid (VOF) method to track the liquid/vapor interface. Film boiling of cryogenic liquids (e.g., LNG and liquid nitrogen) is simulated to estimate the vapor generation rate during an accidental spill. The simulated heat fluxes were compared with heat fluxes obtained from Berenson and Klimenko correlations. The effects of wall superheats on the bubble generation frequency were studied. This study helps researchers to understand the physics of film boiling that are useful during the risk assessment of a cryogenic spill scenario. For example, it was found that the bubble released from the node and the antinode points between the consecutive bubble generations cycles do not follow the alternating nature under the realistic film boiling conditions. Therefore, empirical expressions assuming alternating bubble generation might be unsuitable for cryogenic vaporization source term estimation.

Pseudogap and singlet formation in organic and cuprate superconductors

The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation approach to the Hubbard model. In this method a cluster embedded in a self-consistent bath is studied. With increasing Coulomb repulsion, $U$, the antinodal point [$\mathbf{k}=(\ensuremath{\pi},0)$] displays a gradual suppression of spectral density of states around the Fermi energy which is not observed at the nodal point [$\mathbf{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$]. The opening of the antinodal pseudogap is found to be related to the internal structure of the cluster and the much weaker bath-cluster couplings at the antinodal than nodal point. The role played by internal cluster correlations is elucidated from a simple four-level model. For small $U$, the cluster levels form Kondo singlets with their baths leading to a peak in the spectral density. As $U$ is increased a localized state is formed localizing the electrons in the cluster. If this cluster localized state is nondegenerate, the Kondo effect is destroyed and a pseudogap opens up in the spectra at the antinodal point. The pseudogap can be understood in terms of destructive interference between different paths for electrons hopping between the cluster and the bath. However, electrons at the nodal points remain in Kondo states up to larger $U$ since they are more strongly coupled to the bath. The strong correlation between the $(\ensuremath{\pi},0)$ and the $(0,\ensuremath{\pi})$ cluster levels in the localized state leads to a large correlation energy gain, which is important for localizing electrons and opening up a pseudogap at the antinodal point. Such a scenario is in contrast with two independent Mott transitions found in two-band systems with different bandwidths in which the localized cluster electron does not correlate strongly with any other cluster electron for intermediate $U$. The important intracluster sector correlations are associated with the resonating valence bond character of the cluster ground state containing $d$-wave singlet pairs. The low-energy excitations determining the pseudogap have suppressed $d$-wave pairing, indicating that the pseudogap can be related to breaking very short-range $d$-wave pairs. Geometrical frustration on the anisotropic triangular lattice relevant to $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}X$ leads to a switch in the character of the ground state of the cluster at intermediate hopping ratios ${t}^{\ensuremath{'}}/t\ensuremath{\sim}0.7$. Electron doping of the frustrated square lattice destroys the pseudogap, in agreement with photoemission experiments on cuprates, due to a larger Schrieffer-Wolff exchange coupling, ${J}_{K}$, and a stronger cluster-bath coupling for the antinodal point.

Specific heat of a non-local attractive Hubbard model

The specific heat of an attractive (interaction $G<0$) non-local Hubbard model is investigated. We use a two-pole approximation which leads to a set of correlation functions. In particular, the correlation function $\ <\vec{S}_i\cdot\vec{S}_j\ >$ plays an important role as a source of anomalies in the normal state of the model. Our results show that for a giving range of $G$ and $\delta$ where $\delta=1-n_T$ ($n_T=n_{\uparrow}+n_{\downarrow}$), the specific heat as a function of the temperature presents a two peak structure. Nevertehelesss, the presence of a pseudogap on the anti-nodal points $(0,\pm\pi)$ and $(\pm\pi,0)$ eliminates the two peak structure, the low temperature peak remaining. The effects of the second nearest neighbor hopping on the specific heat are also investigated.

플립칩 접합용 초음파 혼의 목표 주파수와 모드를 고려한 2차원 및 3차원 위상최적화 설계

Ultrasonic flip-chip bonding needs a precise bonding tool which delivers ultrasonic energy into chip bumps effectively to use the selected resonance mode and frequency of the horn structure. The bonding tool is excited at the resonance frequency and the input and output ports should locate at the anti-nodal points of the resonance mode. In this study, we propose new design method with topology optimization for ultrasonic bonding tools. The SIMP(solid isotropic material with penalization) method is used to formulate topology optimization and OC(optimal criteria) algorithm is adopted for the update scheme. MAC(modal assurance criterion) tracking is used for the target frequency and mode. We fabricate two prototypes of ultrasonic tools which are based on 3D optimization models after reviewing 2D and 3D topology optimization results. The prototypes are satisfied with the ultrasonic frequency and vibration amplitude as the ultrasonic bonding tools.