Specific Momentum Research Articles

Defining and Mitigating Flow Instabilities in Open Channels Subjected to Hydropower Operation: Formulations and Experiments

A thorough literature review was conducted on the effects of free surface oscillation in open channels, highlighting the risks of the occurrence of positive and negative surge waves that can lead to overtopping. Experimental analyses were developed to focus on the instability of the flow due to constrictions, gate blockages, and the start-up and shutdown of hydropower plants. A forebay at the downstream end of a tunnel or canal provides the right conditions for the penstock inlet and regulates the temporary demand of the turbines. In tests with a flow of 60 to 100 m3/h, the effects of a gradually and rapidly varying flow in the free surface profile were analyzed. The specific energy and total momentum are used in the mathematical characterization of the boundaries along the free surface water profile. A sudden turbine stoppage or a sudden gate or valve closure can lead to hydraulic drilling and overtopping of the infrastructure wall. At the same time, a PID controller, if programmed appropriately, can reduce flooding by 20–40%. Flooding is limited to 0.8 m from an initial amplitude of 2 m, with a dissipation wave time of between 25 and 5 s, depending on the flow conditions and the parameters of the PID characteristics.

Dynamic protected states in the non-Hermitian system

The non-Hermitian skin effect and nonreciprocal behavior are sensitive to the boundary conditions, which are unique features of non-Hermitian systems. In such systems, eigenenergies can become complex, and all eigenstates tend to localize at the boundary, a phenomenon that contrasts with Hermitian topologies. In this work, we theoretically study the dynamic behavior of the propagation of Gaussian wavepackets inside a non-Hermitian lattice and analyze the self-acceleration process of bulk state or Gaussian wavepackets toward the system’s boundary. The initial wavepackets will not only propagate toward the side where the eigenstates are localized, but also their momentum will approach to a specific value. This value corresponds to the maximum imaginary components of the energy dispersion. In addition, if the wavepackets in the momentum space cover this specific momentum, they will eventually exhibit exponentially increasing amplitudes with time evolution, maintaining the dynamic protected condition for an extended period of time until they approach the boundary. We also take two widely used toy models as examples in one and two dimensions to verify the correspondence of the non-Hermitian skin effect and the dynamic protected state.

Effects of different momentum ratios and Reynolds number in a T-junction with an upstream elbow

This study focuses on analysing thermal mixing in T-junctions with varying momentum and Reynolds number ratios, utilizing computational fluid dynamics (CFD) simulations. The T-junction is a critical component of the primary nuclear thermal–hydraulic circuit within a pressurized water-cooled reactor (PWR). The T-junction connects the pressurizer (PRZ) with the steam generator (SG) and the reactor pressure vessel (RPV). Water from the PRZ and the SG are at different temperatures and incomplete thermal mixing occurs when these two fluid streams meet at the T-junction. This incomplete thermal mixing can induce thermal stratification of the water within the T-junction as well as thermal striping phenomena. Thermal striping phenomena can lead to fluctuations of the temperature at the inner pipe wall of the T-junction. Thermal stratification and thermal striping phenomena can induce thermo-mechanical fatigue and eventual pipe failure which can affect the safety of the reactor. Therefore, a high-fidelity, mechanistic understanding of the turbulent thermo-fluid mixing within T-junctions of PWRs might lead to improvements in component reliability and safety within nuclear power plants (NPPs).The primary aim of the research, presented in this paper, is to understand and quantify the effect of variations in the momentum ratio on the turbulent fluid flow within T-junctions. This is achieved by either varying the branch pipe diameter while keeping the inlet velocity constant (part one) or by adjusting the branch pipe inlet velocity while maintaining a constant diameter (part two). Despite the different variations in momentum ratios, the specific momentum ratios under consideration in both parts of the study remain consistent (namely 98 and 66.4). It is also noteworthy that the momentum ratios considered in the paper can be classified as wall-jet and impinging-jet, according to the definition in (Hosseini, Yuki, & Hashizume, 2008). It should be noted that the momentum ratio is manipulated by adjusting the flow parameters, leading to variations in the Reynolds number ratio between the main pipe inlet and the upstream branch pipe at the T-junction. The turbulent flows in the cases that are considered are simulated using the Improved delayed detached eddy simulation (IDDES-SST) model. The numerical results from these simulations indicate, for the considered momentum ratios, that maintaining the same momentum ratio does not produce similar mean flow behaviour and turbulent quantities of interest (QoI). For instance, the size of the flow recirculation zone is more likely linked to the diameter of the branch pipe. Moreover, the turbulent QoI and temperature fluctuations at the determined locations are likely affected by the changed flow recirculation zone as well as the Reynolds number of the branch pipe flow.

Вплив детонаційної хвилі на перерозширений надзвуковий потік газу в со-плі

This paper proposes to use the detonation process to solve the problem of controlling highly maneuverable flying vehicles. The goal of the work is to study a new way of the thrust vector control of a rocket engine using the effect of a detonation shock wave on the gas flow in the nozzle. It is known that the method of thrust vector control by gas injection into the supersonic nozzle area of a rocket engine features one of the lowest losses of specific momentum and a high response speed and produces a significant lateral force. However, for the current level of rocket technology, there is a need to improve these characteristics. Detonation is considered as a method to intensify processes that affect the main gas flow and produce a lateral force. Its features make it possible to develop a system for pulse trajectory correction. In order to study the features of such a system, experimental studies of the detonation wave effect on a supersonic nozzle flow were conducted. A nozzle model and a gas generator for initiating a detonation wave interacting with the main supersonic air flow were developed and made. In the course of experiments, the effect of separation of the main flow from the nozzle wall by the detonation wave during the nozzle operation in the overexpansion mode was revealed. The duration of this effect was much longer than that of the detonation product effect on the main air flow in the nozzle, thus allowing it to be used in the development of a new thrust vector control method. To better understand the experimental results, a numerical simulation of the detonation wave propagation in a supersonic flow was carried out for the test conditions. The simulation was carried out in a non-stationary 2D formulation using the Solid Works software package. The goal of the simulation was to estimate the flow structure and the value of the relative lateral force produced by the change of this structure during detonation product injection into the supersonic nozzle area. The time evolution of the pressure field was obtained. The relative lateral force produced by detonation product injection into the supersonic air flow in the nozzle was determined. The presented features and method of jet engine thrust vector control may be used in unmanned systems operating in a wide range of speeds.

Deuteron system in finite volume with particle-dimer picture

This article delves into the application of Dimer images in addressing two-body problems within lattice quantum chromodynamics (LQCD), providing the finite volume energy spectrum of deuterons in the context of S13-D13 coupled-channels. The author commences by introducing the Dimer-particle method and formulating the Lagrangian for the scattering of two fermions. Additionally, the author defines the relativistic high partial zeta-function in a moving reference system and outlines a method for its rapid convergence calculation. The article further scrutinizes zeta-function representations across various momentum shells and discusses issues related to symmetry breakdown in specific momentum configurations. In sum, this work presents innovative methods for incorporating spin and isospin indices into dimer models, thereby establishing closer relevance to LQCD and deuteron studies.

Theoretical study of double oscillating fields induced electron-positron pairs creation process

<sec>We investigate an important aspect of electron-positron pair creation from vacuum in the presence of a strong background field, where the combined field plays a key role in the pair creation process. By utilizing computational quantum field theory, we explore electron-positron pair creation induced by double-located oscillating electric fields by numerically solving the Dirac equation in full spacetime dimensions. We demonstrate theoretically that computational quantum field theory is equivalent to the first-order time-dependent perturbation theory for single-photon transition pair creation in a spatially inhomogeneous and time-dependent electric field, and verify their equivalence through numerical simulations of pair creation in double-located oscillating fields. We show some interesting results about the periodic oscillation of the momentum spectrum structure of the created particle and the asymmetric multi-photon pair creation process due to the interference between two fields. By using first-order time-dependent perturbation theory, we find that the periodic oscillation in the momentum distribution of the created particle is affected by the field width, the field frequency and the distance between two fields. The period of the oscillation of momentum spectrum structure is changed by the distance between two fields, while the field width has an influence on both the difference between the peak and valley of the momentum spectra and the width of the momentum space available to the created particle. Increasing the frequency of the electric field results in larger momentum for the created particle pairs, while correspondingly reducing the coupling matrix element <inline-formula><tex-math id="M1">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.png"/></alternatives></inline-formula> and diminishing the probability of electron-positron pair creation.</sec><sec>The interference between two fields significantly enhances the yield of pair numbers for small distances between two fields. When the distance is too large, the number of pairs created by double oscillating fields is twice that created by a single field, and the enhancement is vanished. When the distance between two fields increases, the period of oscillation decreases. In turn, the creation of electron-positron pairs can become more monochromatic in momentum (energy), while the number of pairs created remains almost constant. As the electric field broadens, the yield of the created pairs decreases for constant potential height. Increasing the field width will reduce the number of particles for each momentum and narrow the momentum space of the created particle. Increasing the field frequency leads to the reduction of the coupling matrix element <inline-formula><tex-math id="M2">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.png"/></alternatives></inline-formula> and subsequently reduces the total number of electron-positron pairs created. The field profile parameters such as frequency, width, and distance between two fields can be utilized to select a specific momentum (energy) of particles in future electron-positron pair creation experiments.</sec>

3D quantum Hall effect in a topological nodal-ring semimetal

A quantized Hall conductance (not conductivity) in three dimensions has been searched for more than 30 years. Here we explore it in 3D topological nodal-ring semimetals, by employing a minimal model describing the essential physics. In particular, the bulk topology can be captured by a momentum-dependent winding number, which confines the drumhead surface states in a specific momentum region. This confinement leads to a surface quantum Hall conductance in a specific energy window in this 3D system. The winding number for the drumhead surface states and Chern number for their quantum Hall effect form a two-fold topological hierarchy. We demonstrate the one-to-one correspondence between the momentum-dependent winding number and wavefunction of the drumhead surface states. More importantly, we stress that breaking chiral symmetry is necessary for the quantum Hall effect of the drumhead surface states. The analytic theory can be verified numerically by the Kubo formula for the Hall conductance. We propose an experimental setup to distinguish the surface and bulk quantum Hall effects. The theory will be useful for ongoing explorations on nodal-ring semimetals.

Application of Momentum Strategy to S&P 500: A Five-Year Retrospective Analysis

Momentum strategy, a popular approach since the 1990s, has seen various successful iterations over the years. However, with the market environment evolving considerably in recent times, this study seeks to explore the efficacy of a specific momentum strategy on the S&P 500 in the past five years. The hypothesis centers on the correlation between returns and the moving average, serving as a momentum indicator. A simple linear model relating the two is trained using historical data, and the subsequent strategy is formed based on the model's parameters. Different lookback periods are considered, leading to an evaluation of diverse strategies. Despite the strategy's simplicity, findings suggest that it might struggle to thrive in real market conditions. There are some strategies that beat the benchmark under ideal conditions, but all of them loss when the transection fees are taken into account. The analysis uncovers situations where momentum strategies can indeed be effective. This underlines the potential for further research and the development of a more sophisticated, precise strategy that mirrors real market dynamics with greater accuracy.

Observation of flat-band localized state in a one-dimensional diamond momentum lattice of ultracold atoms

We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple two- and four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.

Breakdown of one-to-one correspondence between the photoelectron emission angle and the tunneling instant in the attoclock scheme

Attoclock is a promising chronoscopy of the ultrafast dynamics of atoms and molecules in intense laser fields. The attoclock procedure is established based on the one-to-one correspondence between the photoelectron emission angle and the tunneling instant at each photoelectron kinetic energy for ionization of atoms and molecules subject to elliptically polarized strong laser fields. In this work, our joint theoretical and experimental study demonstrates that this correspondence could be broken down for photoelectrons emitted in a direction close to the minimum yield. Two trajectories with different tunneling instants and different initial velocities are found to correspond to a specific final momentum of the photoelectron in this direction, and a multi-peak structure appears in the photoelectron kinetic energy spectrum that can be attributed to interference between these two trajectories. Our work is essential for a deeper understanding and further development of the attoclock scheme.

Observational Characteristics of Radiation-mediated Shocks in Photospheric Gamma-Ray Burst Emission

Emission from the photosphere in gamma-ray burst jets can be substantially affected by subphotospheric energy dissipation, which is typically caused by radiation-mediated shocks. We study the observational characteristics of such emission, in particular the spectral signatures. Relevant shock initial conditions are estimated using a simple internal collision framework, which then serve as inputs for a radiation-mediated shock model that generates synthetic photospheric spectra. Within this framework, we find that if the free fireball acceleration starts at r 0 ∼ 1010 cm, in agreement with hydrodynamical simulations, then the typical spectrum consists of a broad, soft power-law segment with a cutoff at high energies and a hardening in X-rays. The synthetic spectra are generally well fitted with a standard cutoff power-law (CPL) function, as the hardening in X-rays is commonly outside the observable energy range of current detectors. The CPL-fits yield values for the low-energy index, α, and the peak energy, E peak, that are centered around ∼ −0.8 and ∼220 keV, respectively, similar to typical observed values. We also identify a nonnegligible parameter region for what we call optically shallow shocks: shocks that do not accumulate enough scatterings to reach a steady-state spectrum before decoupling and thereby produce more complex spectra. These occur for optical depths , where u u = γ u β u is the dimensionless specific momentum of the upstream as measured in the shock rest frame.

Causal perturbative QFT and white noise

In this paper, we present the Bogoliubov’s causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared — and ultraviolet — divergences in the transition to the adiabatic limit for interacting fields. We present here the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators.

Four-dimensional electron energy-loss spectroscopy

Recent advances in scanning transmission electron microscopy have enabled atomic-scale focused, coherent, and monochromatic electron probes, achieving nanoscale spatial resolution, meV energy resolution, sufficient momentum resolution, and a wide energy detection range in electron energy-loss spectroscopy (EELS). A four-dimensional EELS (4D-EELS) dataset can be recorded with a slot aperture selecting the specific momentum direction in the diffraction plane and the beam scanning in two spatial dimensions. In this paper, the basic principle of the 4D-EELS technique and a few examples of its application are presented. In addition to parallelly acquired dispersion with energy down to a lattice vibration scale, it can map the real space variation of any EELS spectrum features with a specific momentum transfer and energy loss to study various locally inhomogeneous scattering processes. Furthermore, simple mathematical combinations associating the spectra at different momenta are feasible from the 4D dataset, e.g., the efficient acquisition of a reliable electron magnetic circular dichroism (EMCD) signal is demonstrated. This 4D-EELS technique provides new opportunities to probe the local dispersion and related physical properties at the nanoscale.

On the Need for Patent Speed

The “Million Milestone” chart found on the website of The United States Patent and Trademark Office (USPTO) is a timeline of the eleven million patents that the office has granted since 1836: a visual depiction of patenting as expeditious and accelerating. With the chart as the backdrop, the narrative focus of this essay is on the third marker on the timeline, patent 3 million, granted to Kenneth R. Eldredge for “Automatic Reading System” on September 12, 1961. Two overlapping lines of inquiry are pursued. First, looking behind the chart in order to locate the history of patent three million as it happened, which is in conjunction with the 125th anniversary of the 1836 Patent Act, the moment when the “Million Milestone” begins. Second, looking at the chart to unpack how “Automatic Reading System” became part of an evidentiary chain that in 2023 seeks to convince us that accumulation and quantification stand as proof of technological progress. The overall objective of this essay is to show how the patent system synchronizes time and numbers in order to create knowledge about itself as a system, introducing the term tempo-metrics in order to account for the specific intersection of calculation and commemoration where such self-fashioning gains specific momentum.

Dynamics of direct impact accretion in degenerate binary systems

ABSTRACTWe consider the gas dynamics in an accreting binary system of degenerate stars within the framework of the Newtonian approximation. In such a system, the accretion stream can impact the surface of a white dwarf (WD) or neutron star (NS) as a result of the very compact orbit. This causes a loss of angular momentum from the orbit and spin-up of the accretor. We construct an approximation for the specific angular momentum of the accreting matter, which goes to spin up the accretor and approximations for some other parameters of the system. It is shown that the obtained approximation of the specific momentum is qualitatively different from the widely used Keplerian formula. It should affect the boundary between scenarios of immediate tidal disruption and slow mass-loss of the donor in WD–WD and NS–NS binaries, as well as the time of stable mass transfer in the stripping scenario.

Crystal-Momentum-Resolved Contributions to Harmonics in Laser-Driven Graphene

We investigate the crystal-momentum-resolved contributions to high-order harmonic generation in laser-driven graphene by semi-conductor Bloch equations in the velocity gauge. It is shown that each harmonic is generated by electrons with the specific initial crystal momentum. The higher harmonics are primarily contributed by the electrons of larger initial crystal momentum because they possess larger instantaneous energies during the intra-band motion. Particularly, we observe circular interference fringes in the crystal-momentum-resolved harmonics spectrum, which result from the inter-cycle interference of harmonic generation. These circular fringes will disappear if the inter-cycle interference is disrupted by the strong dephasing effect. Our findings can help to better analyze the mechanism of high harmonics in graphene.

Quantized momentum eigenstates and thermodynamic properties of the Feinberg–Horodecki equation for the time-dependent Wei-Hua oscillator

In this study, we obtained exact solutions of the Feinberg–Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtained the partition function for the system and studied other thermodynamic properties that include vibrational mean momentum ( U), vibrational specific heat capacity ( C), vibrational entropy ( s), and vibrational free momentum ( F) as a signature in the momentum space.

Momentum-selective orbital hybridisation

When a molecule interacts chemically with a metal surface, the orbitals of the molecule hybridise with metal states to form the new eigenstates of the coupled system. Spatial overlap and energy matching are determining parameters of the hybridisation. However, since every molecular orbital does not only have a characteristic spatial shape, but also a specific momentum distribution, one may additionally expect a momentum matching condition; after all, each hybridising wave function of the metal has a defined wave vector, too. Here, we report photoemission orbital tomography measurements of hybrid orbitals that emerge from molecular orbitals at a molecule-on-metal interface. We find that in the hybrid orbitals only those partial waves of the original orbital survive which match the metal band structure. Moreover, we find that the conversion of the metal’s surface state into a hybrid interface state is also governed by momentum matching constraints. Our experiments demonstrate the possibility to measure hybridisation momentum-selectively, thereby enabling deep insights into the complicated interplay of bulk states, surface states, and molecular orbitals in the formation of the electronic interface structure at molecule-on-metal hybrid interfaces.

Exclusive semileptonic B → πℓνℓ and Bs → Kℓνℓ decays through unitarity and lattice QCD

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element ∣Vub∣ is obtained from exclusive semileptonic B → πℓνℓ and Bs→ Kℓνℓ decays adopting the unitarity-based dispersion matrix approach for the determination of the hadronic form factors (FFs) in the whole kinematical range. We use lattice computations of the relevant susceptibilities and of the FFs in the large-q2 regime in order to derive their behavior in the low-q2 region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address the extraction of |Vub| from the experimental data, obtaining |Vub| = (3.62 ± 0.47) · 10−3 from B → π and |Vub| = (3.77 ± 0.48) · 10−3 from Bs→ K, which after averaging yield |Vub| = (3.69 ± 0.34) · 10−3. These results are compatible with the most recent inclusive value |Vub|incl = 4.13 (26) · 10−3 at the 1σ level. We also present purely theoretical estimates of the ratio of the τ/μ decay rates {R}_{pi (K)}^{tau /mu } , the normalized forward-backward asymmetry {overline{mathcal{A}}}_{FB}^{ell, pi (K)} and the normalized lepton polarization asymmetry {overline{mathcal{A}}}_{mathrm{polar}}^{ell, pi (K)} .

Tsunami-Induced Bores Propagating over a Canal, Part II: Numerical Experiments Using the Standard k-ε Turbulence Model

This companion paper presents the results of a series of numerical experiments examining the effects of a mitigation canal on the hydrodynamics of a tsunami-like turbulent bore proceeding over a horizontal bed. The hydraulic bores were generated by a dam-break setup which employed impoundment depths of do = 0.20 m, 0.30 m, and 0.40 m. The bore propagated downstream of the impoundments in the flume and interacted with a canal with varying geometry located downstream. The bore then left the flume through a drain located further downstream of the canal. In this study, the effect of the canal depth on the specific momentum and specific energy of hydraulic bores passing over a rectangular canal is numerically studied. The canal width was kept constant, at w = 0.6 m, while the canal depths were varied as follows: d = 0.05 m, 0.10 m, and 0.15 m. The time history of mean flow energy during the bore’s passing over the mitigation canal indicates that the jet stream of the maximum mean flow energy is controlled by the canal depth. The time required to dissipate the jet stream of the maximum vorticity, the turbulent kinetic energy, and the energy dissipation rate all increased as the canal depth decreased. The effect of canal orientation on the bore hydrodynamics was also numerically investigated, and it was found that the impulsive momentum and specific energy reached the highest values for canal orientations of 45 and 60 degrees. For the same canal depth, the highest peak specific momentum occurred with the highest degree of canal orientation (θ = 60°).