Momentum Research Articles

Theoretical and experimental study of linear momentum contours in pristine and aged nafion 117 membranes

Theoretical and experimental study of linear momentum contours in pristine and aged nafion 117 membranes

Complete 3D photoelectron momentum vector reconstruction from time-position charged particle imaging

Abstract Many charged particle imaging techniques exist which directly measure, at a detector, the transverse position (x, y) and time-of-flight (t) of individual events in order to obtain a full set of 3D coordinates. Where curved velocity-mapping electric field lines are implemented, as in the case of 3D Velocity Map Imaging (3D VMI) and certain COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) instruments, the general transformation of (x, y, t)-data into initial 3D recoil momentum vectors (px , py , pz ) is challenging and has not yet been fully addressed. Here we present a detailed and general method for this transformation, illustrated using our 3D VMI spectrometer and the well-known narrow-band photoionization of nitric oxide, for which we demonstrate quantitative agreement with reported values. We additionally show how to measure and correct (i) small errors in the laser polarization axis alignment at the interaction region of a 3D charged particle imaging spectrometer, and (ii) the spatial variation of gain on a microchannel plate (MCP) detector. Improvements to and characterization of our 3D VMI spectrometer yield an electron time-of-flight resolution of 72 ps across the full 40 mm MCP, in combination with pixel-level spatial resolution.

Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order

Abstract We compute the gravitational radiation-reaction force on a compact binary source at the fourth-and-a-half post-Newtonian (4.5PN) order of general relativity, i.e., 2PN order beyond the leading 2.5PN radiation reaction. The calculation is valid for general orbits in a general frame, but in a particular coordinate system which is an extension of the Burke-Thorne coordinate system at the lowest order. With the radiation-reaction acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass position, in a general frame and up to 4.5PN order. Restricting our attention to the frame of the center of mass, we point out that the equations of motion acquire a non-local-in-time contribution at the 4.5PN order, made of the integrated flux of linear momentum (responsible for the recoil of the source) together with the instantaneous flux of center-of-mass position. The non-local contribution was overlooked in the past literature, which assumed locality of the radiation-reaction force in the center of mass frame at 4.5PN order. We discuss the consequences of this non-local effect and obtain consistent non-local equations of motion and flux balance laws at 4.5PN order in the center-of-mass frame.

Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations

The Lie group method is a powerful technique for obtaining analytical solutions for various nonlinear differential equations. This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical properties using Lie group invariants. We derived eight-dimensional symmetry algebra for the (3+1)-dimensional nonlinear elastic wave equation, which was used to obtain the optimal system. Group-invariant solutions were obtained using this optimal system. The same analysis was conducted for the damped version of this equation. For the conservation laws, we applied Noether’s theorem to the nonlinear elastic wave equations owing to the availability of a classical Lagrangian. However, for the damped version, we cannot obtain a classical Lagrangian, which makes Noether’s theorem inapplicable. Instead, we used an extended approach based on the concept of a partial Lagrangian to uncover conservation laws. Both techniques account for the conservation laws of linear momentum and energy within the model. These novel approaches add an application of variational calculus to the existing literature. This offers valuable insights and potential avenues for further exploration of the elastic wave equations.

Current-induced spin polarisation in Rashba–Dresselhaus systems under different point groups

Abstract Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin–orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, we demonstrate that electrically induced spin polarisation in non-magnetic materials, for example, electronic systems within quantum-well geometries, can significantly be influenced by the system’s point-group symmetries, such as Cn and C nv . These symmetries allow various linear and higher-order momentum, k − varying SOC Hamiltonian. Specifically, we show that surfaces having C n point-group symmetry, which permits specific linear and cubic Rashba and Dresselhaus SOC terms, can lead to both orthogonal and non-orthogonal spin polarisations with respect to the applied field. In contrast, surfaces with C nv symmetry exhibit only transverse spin polarisation, regardless of the linear and cubic SOC terms. We further find contrasting spin polarisation for cubic-in-k SOC as compared to the linear-in-k SOC when energy is varied, for example, through doping. Additionally, we show that the surfaces with C n symmetry may exhibit persistent spin current, depending on the relative strength between different momentum-dependent SOC terms. Our finding emphasizes the significance of crystal symmetry in understanding and manipulating induced spin polarisation in noncentrosymmetric materials, especially in surface/interface systems.

Weakening of Tropical Free-Tropospheric Temperature Gradients with Global Warming

Abstract The weak temperature gradients in the tropical free troposphere due to the vanishing Coriolis force near the equator lead to a strong dynamical coupling over the entire tropics. Using theory and a suite of targeted model experiments, we show that the weak temperature gradients further weaken under global warming. We show that the temperature gradient is set by the circulation strength, with a weaker circulation being associated with weaker gradients. Thus, the known scaling difference between atmospheric radiative cooling and static stability that leads to a slowdown of the circulation under warming also leads to a weakening of the temperature gradients in the tropical free troposphere. The impact from the weakening circulation on the weakening of temperature gradients is shown to dominate over the impact of masked CO2 forcing and the El Niño–like tropical Pacific warming pattern in model projections. Key to the result is the nonlinear zonal momentum advection term. Using the well-known Matsuno–Gill model with the correct scaling of heating and static stability may give the correct sign of the response in the temperature gradients, but inaccurate scaling, due to the linear momentum damping in that model. The robust scaling of the magnitude of the tropical quasi-stationary structure with temperature opens possibilities for theoretical advances on questions of societal relevance, ranging from changes in tropical cloudiness to heat stress under climate change.

Quantifying the Chirality of Vibrational Modes in Helical Molecular Chains.

Chiral phonons have been proposed to be involved in various physical phenomena, yet the chirality of molecular normal modes has not been well defined mathematically. Here we examine two approaches for assigning and quantifying the chirality of molecular normal modes in double-helical molecular wires with various levels of twist. First, associating with each normal mode a structure obtained by imposing the corresponding motion on a common origin, we apply the continuous chirality measure (CCM) to quantitatively assess the relationship between the chirality-weighted normal mode spectrum and the chirality of the underlying molecular structure. We find that increasing the amount of twist in the double helix shifts the mean normal mode CCM to drastically higher values, implying that the chirality of molecular normal modes is strongly correlated with that of the underlying molecular structure. Second, we assign to each normal mode a pseudoscalar defined as the product of atomic linear and angular momentum summed over all atoms, and we analyze the handedness of the normal mode spectrum with respect to this quantity. We find that twisting the double-chain structure introduces asymmetry between right- and left-handed normal modes so that in twisted structures different frequency bands are characterized by distinct handedness. This may give rise to global phenomena such as thermal chirality.

Orbital angular momentum at the tight focus of a circularly polarized Gaussian beam

When tightly focusing a circularly polarized optical vortex, a phenomenon of spin-to-orbit conversion has been known to occur. As a rule, the longitudinal component of the spin angular momentum (SAM) vector is assumed to be converted into the longitudinal component of the orbital angular momentum (OAM) vector. In this work, we show that, due to the focusing, the original longitudinal SAM component, averaged over the beam cross-section, is partly converted to the transverse SAM component. In a similar way, the original longitudinal energy flow is partly converted, upon focusing, to the azimuthal component. Meanwhile, the longitudinal component of the OAM vector, averaged over the entire beam cross-section at the focus, increases exactly by the magnitude of the (canonical) averaged azimuthal orbital energy flow at the focus. We show that, upon focusing, the azimuthal energy flow is formed at the focus due to the fact that a right-handed circularly polarized light wave generates two optical vortices: a transverse left-handed circularly polarized vortex with topological charge 2 and a longitudinal vortex with topological charge 1.

Dynamical implications of the Kerr multipole moments for spinning black holes

Previously the linearized stress tensor of a stationary Kerr black hole has been used to determine some of the values of gravitational couplings for a spinning black hole to linear order in the Riemann tensor in the action (worldline or quantum field theory). In particular, the couplings on operators containing derivative structures of the form (\U0001d446 ∙ ∇)\U0001d45b acting on the Riemann tensor were fixed, with \U0001d446\U0001d707 the spin vector of the black hole. In this paper we find that the Kerr solution determines all of the multipole moments in the sense of Dixon of a stationary spinning black hole and that these multipole moments determine all linear in \U0001d445 couplings. For example, additional couplings beyond the previously mentioned are fixed on operators containing derivative structures of the form \U0001d4462\U0001d45b(\U0001d45d ∙ ∇)2\U0001d45b acting on the Riemann tensor with \U0001d45d\U0001d707 the momentum vector of the black hole. These additional operators do not contribute to the three-point amplitude, and so do not contribute to the linearized stress tensor for a stationary black hole. However, we find that they do contribute to the Compton amplitude. Additionally, we derive formal expressions for the electromagnetic and gravitational Compton amplitudes of generic spinning bodies to all orders in spin in the worldline formalism and evaluated expressions for these amplitudes to \U0001d4aa(\U0001d4463) in electromagnetism and \U0001d4aa(\U0001d4465) in gravity.

Synthetic Jet Actuators for Active Flow Control: A Review

A synthetic jet actuator (SJA) is a fluidic device often consisting of a vibrating diaphragm that alters the volume of a cavity to produce a synthesized jet through an orifice. The cyclic ingestion and expulsion of the working fluid leads to a zero-net mass-flux and the transfer of linear momentum to the working fluid over an actuation cycle, leaving a train of vortex structures propagating away from the orifice. SJAs are a promising technology for flow control applications due to their unique features, such as no external fluid supply or ducting requirements, short response time, low weight, and compactness. Hence, they have been the focus of many research studies over the past few decades. Despite these advantages, implementing an effective control scheme using SJAs is quite challenging due to the large parameter space involving several geometrical and operational variables. This article aims to explain the working mechanism of SJAs and provide a comprehensive review of the effects of SJA design parameters in quiescent conditions and cross-flow.

A diffusion-based wind turbine wake model

Describing the evolution of a wind turbine's wake from a top-hat profile near the turbine to a Gaussian profile in the far wake is a central feature of many engineering wake models. Existing approaches, such as super-Gaussian wake models, rely on a set of tuning parameters that are typically obtained from fitting high-fidelity data. In the current study, we present a new engineering wake model that leverages the similarity between the shape of a turbine's wake normal to the streamwise direction and the diffusion of a passive scalar from a disk source. This new wake model provides an analytical expression for a streamwise scaling function that ensures the conservation of linear momentum in the wake region downstream of a turbine. The model also considers the different rates of wake expansion that are known to occur in the near- and far-wake regions. Validation is presented against high-fidelity numerical data and experimental measurements from the literature, confirming a consistent good agreement across a wide range of turbine operating conditions. A comparison is also drawn with several existing engineering wake models, indicating that the diffusion-based model consistently provides more accurate wake predictions. This new unified framework allows for extensions to more complex wake profiles by making adjustments to the diffusion equation. The derivation of the proposed model included the evaluation of analytical solutions to several mathematical integrals that can be useful for other physical applications.

MULTI-USE APPARATUS IN MECHANICS AND HEAT

The equipment, which has versatile applications in mechanics and heat, consists of a base, a detachable upright post, a bottom level adjuster, and a top holder. It is applicable for conducting experiments on several subjects including uniform acceleration, friction, moment of inertia, conservation of linear momentum, center-of-gravity, principle of moments, simple harmonic motion, Bernoulli's principle, heat expansion, and heat conductivity. Throughout the execution of an experiment, its crucial components are systematically assembled. The holder is fitted with a locking mechanism that ensures the secure fastening of interchangeable accessories. The tests can be tailored to suit the intended results. The components of the apparatus are detachable, facilitating easy assembly and disassembly, while also allowing for increased storage capacity, transportation convenience, and inventory management. To facilitate and expedite the process of assembling and disassembling, all components are meticulously and systematically stored in a container. The current concept provides a multitude of advantages through the optimization of mechanics and the implementation of heat-efficient testing.

Molecular Orientation Resolved (e, 2e) Cross Sections for CF4 at 67 eV Impact Energy

In this investigation, the fully differential cross sections (FDCS) for ionization of electron impact at low energy (E<sub>0</sub> = 67 eV) were measured for the specific orientations of the molecules and around it axis. In the full perpendicular plane (FPP), the FDCS for CF<sub>4</sub> were experimentally figured out by using reaction microscope (REMI) for different kinematics such as two ejection electron energies of 5 eV and 8 eV, scattering angles of -25° and 30°, and two molecular axis directions of ϕ<sub>Mol</sub> = 0° and 45°, also their relative orientations such as 180° and 225°. The momentum vectors of the two ejected electrons (with energies E<sub>e1</sub>, and E<sub>e2</sub>) and the fragment ions (e, 2e+ ions) were detected by the triple coincidence method. For the duration of dissociation, the time of flight (TOF) of CF<sub>3</sub><sup>+</sup>, CF<sub>2</sub><sup>+</sup>, CF<sup>+</sup>, F<sup>+</sup>, and C<sup>+</sup> are observed in the TOF diagram. During the dissociation of the final fragment of CF<sub>3</sub><sup>+</sup> ion and its electronic ground state neutral F, the momentum vector of CF<sub>3</sub><sup>+</sup> allows us to draw conclusions about the orientation of the molecule in the course of the collision. Finally, it was remarked that concerning molecular orientation, electrons are highly sensitive at low energy and low scattering angle.

Time-Dependent Retarded Microwave Electromagnetic Motors

In a previous work, we showed that Newton’s third law does not strictly hold in a system with remote elements due the finite speed of signal propagation, and thus force imbalance occurs at the system’s center of mass. As the said system is affected by a total force for a finite time interval, mechanical energy and momentum are gained by the system. In early works, we assumed that the bodies were macroscopically charge-neutral. Later, we removed this restriction, thus analyzing the consequences of a possible electrically charged relativistic motor. In the first published paper on this subject, we studied this phenomenon in general but gave only an example of a system reaching a stationary state. In this paper, we shall analyze a charged retarded electromagnetic motor in a more general time-dependent setting, giving specific examples in which the system never reaches a stationary state yet produces steady linear momentum nonetheless. We show that the device is more efficient in the microwave (or higher) frequencies.

Hybrid approach to perfect and dissipative spin hydrodynamics

A hybrid framework of spin hydrodynamics is proposed that combines the results of kinetic theory for particles with spin 1/2 with the Israel-Stewart method of introducing nonequilibrium dynamics. The framework of kinetic theory is used to define the perfect-fluid description that conserves baryon number, energy, linear momentum and spin part of angular momentum. This leads to the entropy conservation although, in the presence of spin degrees of freedom, the perfect-fluid formalism includes extra terms whose structure is usually attributed to dissipation. The genuine dissipative terms appear from the condition of positive entropy production in nonequilibrium processes. They are responsible for the transfer between the spin and orbital parts of angular momentum, with the total angular momentum being conserved. Published by the American Physical Society 2024

Particles and their fluids in nontrivial matter extensions to general relativity

According to the standard von Laue condition, the volume-averaged pressure inside particles of fixed mass and structure vanishes in the Minkowski limit of general relativity. Here we show that this condition is in general not fulfilled in the context of f(R,T) gravity, or of other theories of gravity in which the linear momentum is not conserved in this limit (here, R and T represent the Ricci scalar and the trace of the energy-momentum tensor, respectively). We derive a generalized von Laue condition valid for the R(R)+F(T) subclass of f(R,T) theories of gravity and discuss its cosmological implications. In particular, we show that the standard radiation and matter era evolution of the universe is recovered in the context R+F(T) gravity independently of the specific properties of the function F(T). We also find that dust — a perfect fluid whose particles are at rest in the fluid's proper frame — cannot in general be described as pressureless in the context of these theories. We further discuss the implications of our findings for the form of the on-shell Lagrangian of an ideal gas.

The enigmatic origin of two dormant BH binaries: Gaia BH1 and Gaia BH2

Abstract The two systems, namely, Gaia BH1 and Gaia BH2, that have been confirmed as dormant (i.e., no X-ray emission detected) black hole (BH) - low-mass star binaries in the latest Gaia mission data release (DR3) are intriguing in the context of their formation and evolution. Both systems consist of $\sim 9\, \mathrm{{\rm M}_{\odot }}$ BH and $\sim 1\, \mathrm{{\rm M}_{\odot }}$ star orbiting each other on a wide, eccentric orbit (e ∼ 0.5). We argue that formation of such Gaia BH-like systems through the isolated binary evolution (IBE) channel, under the standard common envelope assumptions, and from dynamical interactions in young massive and open clusters are equally probable, and that the formation rate of such binaries is of the order of $10^{-7}\, \mathrm{{\rm M}_{\odot }}^{-1}$ for both channels. We estimate that, according to our models, there are at most ∼900 detectable Gaia BH-like binaries in the Milky Way thin disc. What plays an important role in formation of Gaia BH-like systems via the IBE channel is the mutual position of the natal kick velocity vector and the binary angular momentum vector. We find that natal kicks with a median magnitude of ∼40 km/s are preferred for the formation of Gaia BH1-like binaries. Approximately 94% of those binaries are formed with the BH spin misaligned to the orbital axis by less than 40○. Gaia BH2-like binaries form if the low velocity natal kick (of median magnitude ∼20 km/s) is directed within 15○ about the orbital plane. In addition to natal kick, we also discuss the influence of tidal interaction and the adopted common envelope λce parameter prescription on the evolution of Gaia BH-like binaries. We follow the subsequent evolution of the binaries, once formed as Gaia BH1 and Gaia BH2 systems, to investigate their connection with the low-mass X-ray binary population.

Leaning Sideways: VHS 1256−1257 b is a Super-Jupiter with a Uranus-like Obliquity

We constrain the angular momentum architecture of VHS J125601.92-125723.9, a 140 ± 20 Myr old hierarchical triple system composed of a low-mass binary and a widely separated planetary-mass companion, VHS 1256 b. VHS 1256 b has been a prime target for multiple characterization efforts, revealing the highest measured substellar photometric variability to date and the presence of silicate clouds and disequilibrium chemistry. Here we add a key piece to the characterization of this super-Jupiter on a Tatooine-like orbit: we measure its spin-axis tilt relative to its orbit, i.e., the obliquity of VHS 1256 b. We accomplish this by combining three measurements. We find a projected rotation rate vsinip=8.7±0.1kms−1 for VHS 1256 b using near-infrared high-resolution spectra from Gemini/IGRINS. Combining this with a published photometric rotation period indicates that the companion is viewed edge on, with a line-of-sight spin axis inclination of i p = 90° ± 18°. We refit available astrometry measurements to confirm an orbital inclination of io=23−13+10 degrees. Taken together, VHS 1256 b has a large planetary obliquity of ψ = 90° ± 25°. In total, we have three measured angular momentum vectors for the system: the binary orbit normal, companion orbit normal, and companion spin axis. All three are misaligned with respect to each other. Although VHS 1256 b is tilted like Uranus, their origins are distinct. We rule out planet-like scenarios including collisions and spin–orbit resonances, and suggest that top-down formation via core/filament fragmentation is promising.

Investigation of a Theoretical Model for the Rotational Shot Put Technique.

The biomechanics of the rotational shot put technique have been demonstrated. However, the causal relationships among kinematics and kinetics for achieving higher release velocity remain poorly understood. This study investigated these causal relationships among biomechanical variables for achieving a higher release velocity in the rotational shot put technique. The study included 22 male shot putters whose 3-dimensional motion was captured during official competitions. Key kinematic and kinetic variables throughout the shot put motion were calculated, as suggested by previous studies. Path analysis was used to explore a hierarchical model that postulates both direct and indirect effects among variables. The findings revealed that the impulse of the shot, system angular momentum, and system linear momentum were critical kinetic variables contributing directly to release velocity. Additionally, 8 kinematic variables significantly affected the impulse of the shot, including shoulder rotation, shot path length, and trunk tilt, while movements such as swings and extensions of the lower extremities were related to system momentum. This model not only provides a detailed understanding of the mechanics involved in the rotational technique but also informs technical coaching strategies in the shot put.

An inverse problem for the system modeling nonhomogeneous asymmetric fluids

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with a smooth boundary. The direct problem is an initial boundary value problem for a system where the unknowns are the velocity field of the fluid particles, the angular velocity of rotation of the fluid particles, the mass density of the fluid, and the pressure distribution. The inverse problem consists of recovering external forces to the linear and angular momentum equations by assuming a set of measurements as an integral overspecified condition. We introduce and prove several a priori estimates. We characterize the inverse problem solutions using an operator equation of a second kind, deduced from applying the Helmholtz decomposition. We prove several properties of the associated operator, which implies that the Tikhonov fixed point theorem hypothesis is valid. Then, we deduce the local unique solvability of the inverse problem.