Total Momentum Research Articles

Moduli Space for Kink Collisions with Moving Center of Mass

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.

Oscillations of the total kinematic momentum vector for viscous fluid dynamics in pipes of arbitrary section

We derive the oscillatory exact solutions to the Navier–Stokes equations that describe z-invariant viscous fluid flows in a general cylindrical pipe C=D×ℝ1 with section D having an arbitrary geometry and a piece-wise smooth boundary ∂D. Exact viscous fluid flows are presented that satisfy the no-slip boundary condition at the pipe's boundary ∂D×ℝ1 and have an arbitrary number of oscillations of the total kinematic momentum vector on any given interval of time [T1,T2]. The stability of the oscillations with respect to small perturbations of infinitely many parameters is proven. The new method for the generation of a hierarchy of exact solutions with oscillating kinematic momentum is developed. Exact solutions to the Navier–Stokes equations without external forces (in addition to the friction forces at the pipes's boundary ∂D×ℝ1) are derived, which have any number of oscillations of the average shift of viscous fluid.

Theoretical Study of Antihydrogen Formation Reactions in the Three Body $${{e}^{ + }}{{e}^{ - }}\bar {p}$$ System via Faddeev–Merkuriev Equations in Total Orbital Momentum Representation

Theoretical Study of Antihydrogen Formation Reactions in the Three Body $${{e}^{ + }}{{e}^{ - }}\bar {p}$$ System via Faddeev–Merkuriev Equations in Total Orbital Momentum Representation

Theoretical study of antihydrogen formation reactions in the three body <span class="inline-formula"><span class="math">\({{e}^{ + }}{{e}^{ - }}\bar {p}\)</span></span> system via Faddeev–Merkuriev equations in total orbital momentum representation

The results of calculations of low-energy reaction in the three body \({{e}^{ + }}{{e}^{ - }}\bar {p}\) system with the emphasis on the process of the antihydrogen formation from the ground and excited states of the positronium are presented. This reaction is important for some of the current antimatter experiments. The multi-channel scattering calculations are based on a new highly efficient method of solving the Faddeev–Merkuriev equations in total orbital momentum representation. We discuss the effects that originate from the long-range dipole interaction between the excited atom and the spectator particle.

The Sensitivity of Large Eddy Simulations to Grid Resolution in Tropical Cyclone High Wind Area Applications

The question of at what resolution the large eddy simulations (LESs) of a tropical cyclone (TC) high wind area may converge largely remains unanswered. To address this issue, LESs with five resolutions of 300 m, 100 m, 60 m, 33 m, and 20 m are performed in this study to simulate a high wind area near the radius of maximum wind of Typhoon Chanthu (2021) using the Weather Research and Forecasting (WRF) model. The results show that, for a limited area LES, model grid resolution may alter the local turbulence structure to generate significantly different extreme values of temperature, moisture, and winds, but it only has a marginal impact on the median values of these variables throughout the vertical column. All simulations are able to capture the turbulent roll vortices in the TC boundary layer, but the structure and intensity of the rolls vary substantially in different resolution simulations. Local hectometer-scale eddies with vertical velocities exceeding 10 m s−1 are only observed in the 20 m resolution simulation but not in the coarser resolution simulations. The ratio of the resolved turbulent momentum fluxes and turbulent kinetic energies (TKEs) to the total momentum fluxes and TKEs appears to show some convergence of LESs when the grid resolution reaches 100 m or finer, suggesting that it is an acceptable grid resolution for LES applications in TC simulations.

On the Global Minimum of the Energy–Momentum Relation for the Polaron

For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.

Hinge-like Co2S3and Co2Te3Nanosheets: Promising Two-Dimensional Optical, Thermoelectric, and Spintronic Materials

In this study, the structural and physical properties of hinge-like Co2S3 and Co2Te3 nanosheets are predicted using spin-polarized density functional theory. Our calculations show that Co2S3 and Co2Te3 nanosheets are ferromagnetic semiconductors and antiferromagnetic metals in the ground state, respectively, and these nanosheets are dynamically and thermodynamically stable. According to the mean-field theory, Co2S3 and Co2Te3 nanosheets have the Néel temperature of 933 K and the Curie temperature of 285 K. Also, Co2Te3 nanosheets have unique properties such as significant total magnetic momentum (5.07 μB) and high magnetic anisotropy energy (2.62 meV). The examination of optical properties shows that Co2S3 and Co2Te3 nanosheets can be used in optoelectronic devices such as strong far- ultraviolet and ultraviolet absorbers, respectively. Calculating thermoelectric properties using Boltzmann’s theory shows that the Co2S3 nanosheet not only has ZT = 1 at 100 K but has significant thermoelectric efficiency at temperatures higher than room temperature (ZT = 0.97 at 700 K). Based on spin-dependent transport calculations, the current passing through Co2S3 (37.55 μA) and Co2Te3 (75 μA) nanosheets is higher than many 2D nanostructures, and the transport properties of these nanosheets are anisotropic. Therefore, Co2S3 and Co2Te3 nanosheets can be promising candidates for the development of nanoscale thermoelectric and spintronic devices.

Piezoelectric effect and diode effect in anapole and monopole superconductors

Superconductors lacking both inversion symmetry and time-reversal symmetry have been attracting much attention as a platform for exotic superconducting phases and anomalous phenomena, including the superconducting diode effect. Recent studies revealed intrinsic phases with this symmetry, named anapole superconductivity and monopole superconductivity, which are $PT$-symmetric superconducting states with and without Cooper pairs' total momentum, respectively. To explore characteristic phenomena in these states, we calculate and predict the superconducting piezoelectric effect and superconducting diode effect. A close relationship with the finite-$q$ pairing, asymmetric Bogoliubov spectrum, and quantum geometry is discussed. This study reveals the piezoelectric and diode effects as potential probes to elucidate exotic superconducting phases.

An entropy consistent and symmetric seven-equation model for compressible two-phase flows

We propose new seven-equation model and related solution methods for compressible two-phase flows. The model is built on new closure laws for the interaction between the coexisting two phases. It takes a symmetric form for the two phases and shares some favorable properties with the well-known Baer-Nunziato model [4]: the equations system is unconditionally hyperbolic and is conservative for the total momentum and energy; the interfacial interaction between phases is an isentropic process for each phase. Moreover, it permits to obtain a linear degenerate field associated with the wave which separates the mixture, and the full set of the associated Riemann invariants can be derived explicitly. The pressure and velocity relaxation terms are included for the additional interaction between phases. Numerical approximation of the entire model is performed in an operator splitting manner – two Godunov-type schemes utilizing respectively a HLL solver and a composite approximate Riemann solver are used to discretize the homogeneous system; stable implicit algorithms are explored for the non-instantaneous pressure and velocity relaxations. Several examples are provided to illustrate the property of the new model and the capability of the solution methods.

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

Experimental Study on the Interaction of an Impulse Water Jet with Molten Metal

The impingement of a short-duration water jet on a pool of molten Rose’s metal is studied experimentally herein. Short-duration water jet impacting on the free surface of a molten metal pool with a temperature of 300 °C are generated with a pneumatic water delivery system, with two-camera high-speed video registration. A total of 14 experimental series, each containing 5 repeated tests, are performed for a water volume of 0.2–1 mL and a jet impact velocity of 4.1–9.0 m/s. The cavity development in the melt layer is studied, with the main stages described herein. Despite the significantly higher density of melt in comparison with water, the cavity can reach the melt pool bottom; furthermore, its further collapse results in the formation of a central jet rising to the height of a few centimeters. The maximum height of the central jet is shown to depend linearly on the total momentum of the water jet, and a semi-logarithmic correlation is found for the maximum diameter of the cavity. Repeatability analysis is performed within each experimental series, and the relative standard deviation for the melt splash height is shown to be from 8.8% to 26.8%. The effects of the pool depth, the vessel shape, and the water temperature are weaker in the range of the experimental parameters used here.

Theory of superdiffusive spin transport in noncollinear magnetic multilayers

Ultrafast demagnetization induced by femtosecond laser pulses in thin metallic layers is caused by the outflow of spin-polarized hot-electron currents describable by the superdiffusive transport model. These laser-generated spin currents can cross the interface into another magnetic layer and give rise to magnetization dynamics in magnetic spin valves with noncollinear magnetizations. To describe ultrafast transport and spin dynamics in such nanostructures, we develop here the superdiffusive theory for general noncollinear magnetic multilayers. Specifically, we introduce an Al/Ni/Ru/Fe/Ru multilayer system with noncollinear Ni and Fe magnetic moments and analyze how the ultrafast demagnetization and spin-transfer torque depend on the noncollinearity. We employ ab initio calculations to compute the spin- and energy-dependent transmissions of hot electrons at the interfaces of the multilayer. Taking into account multiple electron scattering at interfaces and spin mixing in the spacer layer, we find that the laser-induced demagnetization of the Ni layer and the magnetization change of the Fe layer strongly depend on the angle between their magnetizations. Similarly, the spin-transfer torques on the Ni and Fe layers and the total spin momentum absorbed in the Ni and Fe layer are found to vary markedly with the amount of noncollinearity. These results suggest that by changing the amount of noncollinearity in magnetic multilayers, one can efficiently control the hot-electron spin transport, which may open a way toward achieving fast, laser-driven spintronic devices.

Momentum dependent nucleon-nucleon contact interaction from a relativistic Lagrangian

A complete set of parity- and time-reversal conserving relativistic nucleon-nucleon contact operators is identified up to the order O(p4) of the expansion in soft momenta p. A basis is also provided for the corresponding non-relativistic operators contributing in the general reference frame. We show that the non-relativistic expansions of the relativistic operators involve twenty-six independent combinations, two starting at O(p0), seven at order O(p2) and seventeen at order O(p4). This gives supporting evidence to the existence of two free low-energy constants which parametrize an interaction depending on the total nucleon pair momentum P, and were recently found to be instrumental for the resolution of the long standing Ay problem in low-energy p−d scattering. Furthermore, all remaining P-dependent interactions at the same order are uniquely determined as relativistic corrections.

Effect of Physically Realistic Potential Energy Form on Spatial Pattern Complexity in a Collective Motion Model

Collective motion models most often use self-propelled particles, which are known to produce organized spatial patterns via their collective interactions. However, there is less work considering the possible organized spatial patterns achievable by non-self-propelled particles (nondriven), i.e., those obeying energy and momentum conservation. Moreover, it is not known how the potential energy interaction between the particles affects the complexity of the patterns. To address this, in this paper, a collective motion model with a pairwise potential energy function that conserved the total energy and momentum of the particles was implemented. The potential energy function was derived by generalizing the Lennard–Jones potential to reduce to gravity-like and billiard-ball-like potentials at the extremes of its parameter range. The particle model was simulated under a number of parameterizations of this generalized potential, and the average complexity of the spatial pattern produced by each was computed. Complexity was measured by tracking the information needed to describe the particle system at different scales (the complexity profile). It was found that the spatial patterns of the particles were the most complex around a specific ratio in the parameters. This parameter ratio described a characteristic shape of the potential energy function that is capable of producing complex spatial patterns. It is suggested that the characteristic shape of the potential energy produces complex behavior by balancing the likelihood for particles to bond. Furthermore, these results demonstrate that complex spatial patterns are possible even in an isolated system.

Singularity-robust full-pose workspace control of space manipulators with non-zero momentum

We address the end-effector full-pose tracking control problem in free-floating space manipulators, experiencing constant non-zero linear and angular momentum. The aim is to develop an output-tracking (workspace) control law free of singularities due to parameterizing the end-effector motion and being robust against singularities of the input–output decoupling matrix (generalized Jacobian matrix). Space manipulators are modeled as open-chain multi-body systems with single- and multi-degree-of-freedom joints, whose kinematics and dynamics are formulated on the Special Euclidean group SE(3). Such systems exhibit conserved (not necessarily zero) total momentum when operating in the free-floating regime, which we use to systematically reduce their dynamical equations by eliminating the base spacecraft’s motion. To avoid parameterizing the end-effector motion, we consider its full pose as the system output and develop a novel feedback linearization technique on the matrix Lie group SE(3) in the reduced phase space of the space manipulator. We then propose an intrinsic feedforward, feedback proportional–integral–derivative workspace controller involving a coordinate-free pose error function on SE(3) and velocity error on its Lie algebra. Using a Lyapunov candidate, this controller is proven to stabilize the end-effector pose to a feasible desired trajectory. The input–output decoupling matrix in the proposed control law can lose rank at some regions of the configuration space; hence, we implement a singularity-robust inverse, derived from the damped least squares method, to avoid impractical joint torques in these regions. The developed controller is implemented on a 7-degree-of-freedom manipulator onboard a spacecraft and its efficacy and robustness are demonstrated through a series of simulations.

Single-particle properties of topological Wannier excitons in bismuth chalcogenide nanosheets

We analyze the topology, dispersion, and optical selection rules of bulk Wannier excitons in nanosheets of Bi2Se3, a topological insulator in the family of the bismuth chalcogenides. Our main finding is that excitons also inherit the topology of the electronic bands, quantified by the skyrmion winding numbers of the constituent electron and hole pseudospins as a function of the total exciton momentum. The excitonic bands are found to be strongly indirect due to the band inversion of the underlying single-particle model. At zero total momentum, we predict that the s-wave and d-wave states of two exciton families are selectively bright under left- or right-circularly polarized light. We furthermore show that every s-wave exciton state consists of a quartet with a degenerate and quadratically dispersing nonchiral doublet, and a chiral doublet with one linearly dispersing mode as in transition metal dichalcogenides. Finally, we discuss the potential existence of topological edge states of chiral excitons arising from the bulk-boundary correspondence.

Bound states in nonuniform superconductors

This paper shows that the WKB quantization rule is suitable for the Andreev bound states in nonuniform superconductors. We consider nonhomogeneous superconductivity gap functions $\mathrm{\ensuremath{\Delta}}(x)$ in superconductors with the Bogoliubov quasiparticle energy $E$, the Fermi level ${E}_{F}$, and the total momentum $\mathbf{p}$ at ${E}_{F}+E$. The Andreev bound states in the well of slowly varying $|\mathrm{\ensuremath{\Delta}}(x)|$ are studied, and the well may also be induced by the phase variation of $\mathrm{\ensuremath{\Delta}}(x)$ for massless Dirac fermions. By applying the WKB method to the Bogoliubov--de Gennes equation, we obtain two main results: (i) For ${E}_{F}\ensuremath{\sim}0$, the bound states are determined by ${\ensuremath{\int}}_{{L}_{E}}^{{R}_{E}}|\mathbf{p}\phantom{\rule{0.16em}{0ex}}d\mathbf{x}|=(\frac{1}{2}+n)\ensuremath{\pi}\ensuremath{\hbar}$, where $n\ensuremath{\in}{\mathbb{N}}_{0}$ and ${L}_{E}$ and ${R}_{E}$ are the boundary points between the classically allowed region and forbidden regions, and (ii) for ${E}_{F}\ensuremath{\gg}E$ and $|\mathrm{\ensuremath{\Delta}}(x)|$, the bound states are given by ${\ensuremath{\int}}_{{L}_{E}}^{{R}_{E}}|\mathbf{p}\ifmmode\pm\else\textpm\fi{}{\mathbf{p}}_{F}|dx=(\frac{1}{2}+n)\ensuremath{\pi}\ensuremath{\hbar}$ with small ${p}_{y(z)}$. Empirical quantization conditions are provided for broader parameter regions. In addition to applying the traditional WKB method, we also develop a generalized WKB method to tackle semimetals with parabolic dispersion relationships. The applications of our results are discussed, for example, Dirac $\ensuremath{\pi}$ junctions or nonchiral Majorana wires, SNS junctions, the excitation threshold, and the tunneling rate in NSN junctions. In the $\ensuremath{\pi}$ junction, the Majorana zero modes correspond to the zero-point energy in the WKB formalism. This observation may provide insights into the Majorana bound state in a vortex and the Majorana fermions in high-energy physics.

Superposition of AC-DBD plasma actuator outputs for three-dimensional disturbance production in shear flows

This investigation explores the utility of Alternating Current, Dielectric Barrier Discharge (AC-DBD) plasma actuators for producing three-dimensional disturbances of a desired spanwise wavelength via superposition. The technique utilizes two pairs of exposed and covered electrodes on a single dielectric layer arranged in streamwise succession. Two-dimensional forcing is achieved through operation of the upstream, spanwise uniform electrode pair, while three-dimensional forcing at a prescribed spanwise wavelength is attained by operating both electrode pairs simultaneously, with the downstream actuator spanwise modulating the upstream, two-dimensional output. The ability to produce disturbances of different spanwise wavelengths but with equal streamwise wavelength, frequency and total momentum is established through a combined characterization effort that considers quiescent and in-flow conditions. A demonstration of the technique in an exemplary wall-bounded shear flow, a laminar separation bubble, is provided, revealing spanwise wavelength dependent disturbance growth in the flow that could be exploited for performance gains in future flow control endeavours.Graphical abstract

Electron scattering cross sections from NH3: a comprehensive study based on R-matrix method

In this study, a comprehensive cross-sectional computation on the electron scattering from NH3 was performed using the frame of the R-matrix method. Cross section sets for total elastic, differential, momentum transfer, total ionization, and electronic excitation are presented. The electron-impact dissociation of NH3 to NHH and NH+H2 was considered by summing up the cross sections for the molecular dissociative excitations to the correlated dissociation channels. The reported cross sections for vibrational excitation of NH3 remain controversial and are unable to distinguish the N–H symmetric and asymmetric stretching modes of close frequencies. Here, the excitation cross section for each vibrational mode of NH3 was computed by applying the theoretical approach combining the fixed-nuclei R-matrix method, normal mode approximation and the vibrational frame transformation. The uncertainties of the cross section sets computed in this study were estimated for convenience of use in the plasma modeling.

Convergent close-coupling calculations of positron scattering from atomic carbon

We report on the extension of the single-center convergent close-coupling method to positron scattering on multielectron atoms, along with the development of a technique for separating the direct ionization and positronium-formation channels in single-center calculations. We have performed calculations of positron scattering on carbon and present total elastic, momentum transfer, excitation, direct ionization, total ionization, total inelastic, positronium-formation, stopping power, and total cross sections from threshold to 5000 eV. We also present oscillator strengths, the scattering length, the hidden Ramsauer-Townsend minimum, the energy of the positron-carbon virtual state, and the mean excitation energy. Agreement with electron-scattering experiment and positron-scattering theory for several cross sections has been demonstrated for high energies. However, discrepancies exist between different theoretical methods at lower energies and for the ionization and positronium-formation processes.