Average Momentum Research Articles

Control of the vortex lattice formation in coupled atom-molecular Bose–Einstein condensate in a double well potential: role of atom-molecule coupling, trap rotation frequency and detuning parameter

We study the vortex formation in coupled atomic and molecular condensates in a rotating double well trap by numerically solving the coupled Gross–Pitaevskii like equations. Starting with the atomic condensate in the double well potential we considered two-photon Raman photo-association for coherent conversion of atoms to molecules. It is shown that the competition between atom-molecule coupling strength and repulsive atom-molecule interaction controls the spacings between atomic and molecular vortices and the rotation frequency of the trap is the key player for controlling the number of visible atomic and molecular vortices. Whereas the Raman detuning controls the spacing between atomic and molecular vortices as well as the number of atomic and molecular vortices in the trap. We have shown by considering the molecular lattices the distance between two molecular vortices can be controlled by varying the Raman detuning. In addition we have found that the Feynman rule relating the total number of vortices and average angular momentum both for atoms and molecules can be satisfied by considering the atomic and molecular vortices those are hidden in density distribution and seen as singularities in phase distribution of the coupled system except for the lattice structure where molecular vortices are overlapped with each other. It is found that although the number of visible/core vortices in atomic and molecular vortex lattices depends significantly on the system parameters the number of atomic and molecular hidden vortices remains constant in most of the cases.

Development of Science Experimental Video: Process of Converting Salt Water to Fresh Water on Classification of Material and Its Change

This study aims to determine the validity and practicality of the video entitled Process of Converting Salt Water to Fresh Water on science subject. In the process of developing this video, STEM elements and critical thinking skills are included. The method used is development research which consists of three stages, namely preliminary research, prototyping stage, and assessment stage. This study used an instrument in the form of a questionnaire in the form of a validity sheet (26 questions), a practical sheet (18 questions), and an interview sheet (5 questions). The validity test was conducted on three education practitioners, while the practicality test was conducted on students at SMPN 2 Padang. The results of the experimental video validity test show very high validity with an average Kappa Momentum (k) value of 0.91. The results of the practicality test through one-to-one evaluation and small group evaluation have a practical value of 91% and 96%, respectively, with a very practical level of practicality. To find out students' interest in the developed video, interviews were carried out which were used as additional data. The results of the interviews obtained student responses to the developed videos, generally students stated that developed videos was very interesting. Also, it is expected that developed videos can help teachers to train students' critical thinking skills.

Hydrodynamic attractors for the speed of sound in holographic Bjorken flow

The time evolution of the averaged energy momentum tensor as well as its variation with energy density are calculated in a far-from-equilibrium state of $\mathcal{N}=4$ SYM theory undergoing a Bjorken expansion. The calculation is carried out holographically where we consider a collection of trajectories of the energy density in the space of solutions by small changes to the initial conditions of the bulk spacetime. We argue that the proper interpretation of the variation of the diagonal energy momentum tensor components with respect to the energy density is that of a far-from-equilibrium speed of sound. We demonstrate remarkable agreement with a corresponding hydrodynamic prediction. We find by Borel resummation that the holographic system has one attractor for this speed of sound longitudinal, and another transverse to the direction of Bjorken expansion. Attractor times for various initial flow conditions show that reaching an attractor does not imply or require local thermal equilibrium. In the cases studied, reaching an attractor implies hydrodynamization (quantities evolve approximately according to hydrodynamics), justifying the name \emph{hydrodynamic attractor }

Orientation of the spins of galaxies in the local volume

ABSTRACT We estimated the angular momentum, J, of 720 galaxies in the Local Volume with distances r < 12 Mpc. The distribution of the average angular momentum along the Hubble sequence has a maximum at the morphological type T = 4 (Sbc), while the dispersion of the J-values for galaxies is minimal. Among the Local Volume population, 27 elite spiral galaxies stand out, with an angular momentum > 0.15 of the Milky Way, J > 0.15JMW, making the main contribution ($\gt 90~{{\ \rm per\ cent}}$ ) to the total angular momentum of galaxies in the considered volume. Using observational data on the kinematics and structure of these galaxies, we determined the direction of their spins. We present the first map of the distribution of the spins of 27 nearby massive spiral galaxies in the sky and note that their pattern does not exhibit significant alignment with respect to the Local Sheet plane. The relationship between the magnitude of the angular momentum and stellar mass of the local galaxies is well represented by a power law with an exponent of (5/3) over an interval of six orders of magnitude of the mass of galaxies.

Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum

This paper addresses the problem concerning the efficient minimization of power losses in asymmetric distribution grids from the perspective of convex optimization. This research’s main objective is to propose an approximation optimization model to reduce the total power losses in a three-phase network using the concept of electrical momentum. To obtain a mixed-integer convex formulation, the voltage variables at each node are relaxed by assuming them to be equal to those at the substation bus. With this assumption, the power balance constraints are reduced to flow restrictions, allowing us to formulate a set of linear rules. The objective function is formulated as a strictly convex objective function by applying the concept of average electrical momentum, by representing the current flows in distribution lines as the active and reactive power variables. To solve the relaxed MIQC model, the GAMS software (Version 28.1.2) and its CPLEX, SBB, and XPRESS solvers are used. In order to validate the effectiveness of load redistribution in power loss minimization, the initial and final grid configurations are tested with the triangular-based power flow method for asymmetric distribution networks. Numerical results show that the proposed mixed-integer model allows for reductions of 24.34%, 18.64%, and 4.14% for the 8-, 15-, and 25-node test feeders, respectively, in comparison with the benchmark case. The sine–cosine algorithm and the black hole optimization method are also used for comparison, demonstrating the efficiency of the MIQC approach in minimizing the expected grid power losses for three-phase unbalanced networks.

Asymptotic Quantization of a Particle on a Sphere

Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space T∗S2 in the limit of large average angular momentum. The cotangent bundle T∗S2 is also the classical manifold for systems with E(3) symmetry group with appropriately fixed Casimir operators. This allows us to employ the asymptotic form of the star-product proper for variable (integer) spin systems to develop a deformation quantization scheme for a particle moving on the two-dimensional sphere, whose observables are elements of e(3) algebra and the corresponding phase-space is T∗S2. We show that the standard commutation relations of the e(3) algebra are recovered from the corresponding classical Poisson brackets and the explicit expressions for the eigenvalues and eigenfunctions of some quantized classical observables (such as the angular momentum operators and their squares) are obtained.

Bejan’s numerical heat and mass flow visualization in turbulent boundary layer regime

Low Reynolds number k-ϵ model is employed to demonstrate the Bejan's numerical heat and mass flow visualization in turbulent boundary layer regime. The governing turbulence kinetic energy and its dissipation rate equations are included along with conservation equations. The turbulent flow equations are highly nonlinear and coupled in nature, hence, an unconditionally stable Crank–Nicolson finite difference approach is deployed. The computer-generated heatlines, masslines, streamlines, and isotherms for different control parameters are analyzed in the turbulent flow regime. Average momentum, thermal, and concentration diffusion rates are increased upon the increment in in laminar regime and are decreasing with rising in turbulent regime. The stream, heat and masslines deviate more in turbulent regime when compared to laminar regime. Further, the kinetic energy and dissipation rate contours are deviated more in turbulent heat and mass flow regime for different values of . Mainly, in this research paper, the authors made an attempt to demonstrate the turbulent heat and mass flow visualization about a vertical plate using boundary layer approximations through LRN k-ϵ turbulence model.

Subinertial Sea Surface Heights Anomalies Estimated Using High Frequency Radar Surface Current Data in the Mississippi Bight

AbstractSea level studies in the Mississippi Bight (MSB) are less abundant than in other coastal waters of USA. This study investigates the subinertial (time scales >2 days) sea level anomalies in the MSB shelf. The diagnostics of the terms in the invariant form of the momentum equation were computed to determine which terms have the most influence on the anomalies in sea level. It was determined that at subinertial scales the geostrophic balance is the dominant balance in the MSB while the non‐linear and time derivative terms are insignificant relative to the Coriolis term. A Least Squares procedure was applied to the subinertial surface currents data from high frequency radar surface currents (filtered with a window of 2‐day Butterworth filter) to extract subinertial sea level anomalies in the MSB shelf using both geostrophic balance and the invariant form of Reynolds' averaged momentum equations. The resulting subinertial sea level anomalies were validated using sea level observations from an offshore buoy and Sentinel‐3 along‐track satellite altimeter data. The estimated sea level anomalies were reasonably close to observations (more than half had root mean square difference of <0.04 m) and mostly influenced by geostrophic balance. Analysis of the empirical orthogonal functions showed that the first two modes explained the majority (85%) of the variance in the sea level anomalies estimated using the geostrophic approximation. Absolute sea level could be estimated if Global Navigation Satellite System buoys are deployed in the radar footprint.

Systematic Errors of Electric Field Measurements in Ferroelectrics by Unit Cell Averaged Momentum Transfers in STEM.

When using the unit cell average of first moment data from four-dimensional scanning transmission electron microscopy (4D-STEM) to characterize ferroelectric materials, a variety of sources of systematic errors needs to be taken into account. In particular, these are the magnitude of the acceleration voltage, STEM probe semi-convergence angle, sample thickness, and sample tilt out of zone axis. Simulations show that a systematic error of calculated electric fields using the unit cell averaged momentum transfer originates from violation of point symmetry within the unit cells. Thus, values can easily exceed those of potential polarization-induced electric fields in ferroelectrics. Importantly, this systematic error produces deflection gradients between different domains seemingly representing measured fields. However, it could be shown that for PbZr0.2Ti0.8O3, many adjacent domains exhibit a relative crystallographic mistilt and in-plane rotation. The experimental results show that the method gives qualitative domain contrast. Comparison of the calculated electric field with the systematic error showed that the domain contrast of the unit cell averaged electric fields is mainly caused by dynamical scattering effects and the electric field plays only a minor role, if present at all.

Factorized Electron-Nuclear Dynamics with an Effective Complex Potential.

We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.

Free streaming length of axion-like particle after oscillon/I-ball decays

Axion-like particles (ALPs) are pseudoscalar bosons predicted by string theory.The ALPs have a shallower potential than a quadratic one, which induces the instability and can form the solitonic object called oscillon/I-ball.Although the lifetime of oscillons can be very long for some type of potentials, they finally decay until the present.We perform the numerical lattice simulations to investigate the decay process of oscillons and evaluate the averaged momentum of ALPs emitted from the oscillon decay.It is found that, if oscillons decay in the early universe, the free-streaming length of ALPs becomes too long to explain the small-scale observations of the matter power spectrum.We show that oscillons with long lifetimes can change the density fluctuations on small scales, which leads to stringent constraints on the ALP mass and the oscillon lifetime.

Lasting effects of static magnetic field on classical Brownian motion.

The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: There is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy, and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.

The medium-modified gto coverline{c} splitting function in the BDMPS-Z formalism

The formalism of Baier-Dokshitzer-Mueller-Peigné-Schiff and Zakharov determines the modifications of parton splittings in the QCD plasma that arise from medium-induced gluon radiation. Here, we study medium-modifications of the gluon splitting into a quark-anti-quark pair in this BDMPS-Z formalism. We derive a compact path-integral formulation that resums effects from an arbitrary number of interactions with the medium to leading order in the 1/{N}_c^2 expansion. Analyses in the N = 1 opacity and the saddle point approximations reveal two phenomena: a medium-induced momentum broadening of the relative quark-anti-quark pair momentum that increases the invariant mass of quark-anti-quark pairs, and a medium-enhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium is comparable to the quark mass. In ultra-relativistic heavy-ion collisions, this condition is satisfied for charm quarks. We therefore focus our numerical analysis on the medium modification of gto coverline{c} , although our derivation applies equally well to gto boverline{b} and to gluons splitting into light-flavoured quark-anti-quark pairs.

Effect of global momentum conservation on longitudinal flow decorrelation

We calculate the longitudinal flow decorrelation coefficients, i.e., $r_n(\eta,\eta_r)$ for $n=2,3$, in the presence of hydro-like flow and the global momentum conservation (GMC) constraint. The longitudinal flow decorrelation is weakened due to the GMC constraint. The GMC effect is sensitive to the total number of particles involved in GMC, the average longitudinal momentum, the transverse momentum, and the reference pseudorapidity. Our results of the $r_2(\eta,\eta_{rA})/r_2(\eta,\eta_{rB})$ ratio between two reference pseudorapidity bins are consistent with the experimental measurements. We predict that the modification effect of GMC on longitudinal flow decorrelation is more noticeable at BNL Relativistic Heavy Ion Collider energies than at CERN Large Hadron Collider energies. Our finding provides a new perspective for understanding the longitudinal flow decorrelation in relativistic heavy-ion collisions.

Natural convective turbulent heat flow visualization around a vertical plate using low Reynolds number k-ϵ model

The authors of this present paper used the low Reynolds number (LRN) k-ϵ model to introduce the notion of turbulent heat function for visualization of average heat flow direction in a natural convective flow in the vicinity of the vertical plate. The explored problem is two-dimensional and incompressible. Governing equations such as continuity, momentum, energy, turbulent kinetic energy (TKE), dissipation rate of TKE, and also turbulent heat and stream functions are generated based on geometry and turbulent flow assumptions. Owing to the lack of analytical methods for solving the highly nonlinear set of partial differential equations, the Crank–Nicolson scheme (CNS) of finite difference approach is employed to find a numerical approximation of the governing turbulent equations. Further, this approach is unconditionally stable, and it helps in the discretization of governing equations, which are kept in the tridiagonal system of algebraic equations and solved using the Thomas algorithm. The obtained numerical results ensure convergence since the stability and compatibility holds good in CNS. The simulated results are examined using tables and graphs to determine how laminar flow differs from that of turbulent flow in terms of velocity, temperature, heat lines, and streamlines with the help of turbulent Prandtl () and Reynolds () numbers. Also, the authors demonstrated the behavior of average momentum and heat transfer rates of laminar and turbulent flows. Additionally, average velocity, kinetic energy, and dissipation rate contours are plotted and discussed including turbulent isotherms, heat lines, and streamlines. It has been noted that the average momentum rate decreased and the heat transfer rate increased with increasing in laminar flow. However, these rates decreased with increasing values in the turbulent flow. Furthermore, streamlines are denser in laminar and turbulent flow conditions at the top and the leading edge of the plate, respectively. Finally, as a particular instance, the outcomes obtained using the LRN k-ϵ model for turbulent flows are compared to the usual laminar flow and noted to be in excellent agreement.

Medium-modifications of g → cc splitting

We study medium-modifications of the gluon splitting into a quark and anti-quark pair. Applying the Baier-Dokshitzer-Mueller-Peigné-Schiff and Zakharov (BDMPS-Z) formalism, we derive a path-integral formula for the in-medium g → qq¯ splitting function in the close-to-eikonal limit. Our analysis shows that there are two qualitatively different medium effects: transverse momentum broadening of qq¯ pairs and enhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium to the parton is at the quark mass scale. In ultra-relativistic heavy-ion collisions, this condition is realized by charm quarks, therefore we focus our numerical analysis on the medium-modifications of g → cc¯ splitting.

Pion and nucleon relativistic electromagnetic four-current distributions

The quantum phase-space approach allows one to define relativistic spatial distributions inside a target with arbitrary spin and arbitrary average momentum. We apply this quasiprobabilistic formalism to the whole electromagnetic four-current operator in the case of spin-0 and spin-$\frac{1}{2}$ targets, study in detail the frame dependence of the corresponding spatial distributions, and compare our results with those from the light-front formalism. While former works focused on the charge distributions, we extend here the investigations to the current distributions. We clarify the role played by the Wigner rotation and argue that electromagnetic properties are most naturally understood in terms of Sachs form factors, contrary to what the light-front formalism previously suggested. Finally, we illustrate our results using the pion and nucleon electromagnetic form factors extracted from experimental data.

Flow induced by a pair of plasma actuators on a circular cylinder in still air under duty-cycle actuation

A pair of surface mounted dielectric-barrier-discharge (DBD) plasma actuators is placed diametrically on a circular cylinder model. The flow field generated by the actuators in steady and duty-cycle actuation modes is measured by particle image velocimetry. Salient features of the flow and vortices are discovered for the duty-cycle actuation modes with frequency ranging from 5 to 1000 Hz and duty-cycle ratio from 0.01 to 0.99. The results are compared with those for continuous steady actuation. For a given duty-cycle ratio, a discrete vortex is generated by each of the DBD actuator in an actuation cycle for low frequencies. Such vortices are created alternately from each side of the cylinder. They interact and move laterally in response to the on-off signals of the actuators. As the frequency increases, the distance between the vortices generated from successive duty-cycles decreases and the lateral motion of the vortices becomes smaller so that the vortices are packed together as a vortex train along a narrow path on each side of the cylinder. As the frequency is further increased, the vortices in the vortex trains lose their individual characteristics and the vortex trains become steady jets. Regardless of the actuation frequency, the direction of the average total momentum of the air is found to be continuously dependent on the duty-cycle ratio. The magnitude of the average total momentum depends on the frequency. An optimum frequency exists for maximum average momentum, which may exceed that in the continuous steady actuation mode.

Flux Eruption Events Drive Angular Momentum Transport in Magnetically Arrested Accretion Flows

We evolve two high-resolution general relativistic magnetohydrodynamic simulations of advection-dominated accretion flows around nonspinning black holes (BHs), each over a duration ∼3 × 105 GM BH/c 3. One model captures the evolution of a weakly magnetized (SANE) disk and the other that of a magnetically arrested disk (MAD). Magnetic flux eruptions in the MAD model push out gas from the disk and launch strong winds with outflow efficiencies at times reaching 10% of the incoming accretion power. Despite the substantial power in these winds, average mass outflow rates remain low out to a radius ∼100GM BH/c 2, only reaching ∼60%–80% of the horizon accretion rate. The average outward angular momentum transport is primarily radial in both modes of accretion, but with a clear distinction: magnetic flux eruption–driven disk winds cause a strong vertical flow of angular momentum in the MAD model, while for the SANE model, the magnetorotational instability (MRI) moves angular momentum mostly equatorially through the disk. Further, we find that the MAD state is highly transitory and nonaxisymmetric, with the accretion mode often changing to a SANE-like state following an eruption before reattaining magnetic flux saturation with time. The Reynolds stress changes directions during such transitions, with the MAD (SANE) state showing an inward (outward) stress, possibly pointing to intermittent MRI-driven accretion in MADs. Pinning down the nature of flux eruptions using next-generation telescopes will be crucial in understanding the flow of mass, magnetic flux, and angular momentum in sub-Eddington accreting BHs like M87* and Sagittarius A*.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.