Momentum Research Articles

Reconfigurable structured light generation and its coupling to air–core fiber

Recently, structured light beams have attracted substantial attention in many applications, including optical communications, imaging, optical tweezers, and quantum optics. We propose and experimentally demonstrate a reconfigurable structured light beam generator in order to generate diverse structured light beams with adjustable beam types, beam orders, and beam sizes. By controlling the sizes of generated free-space structured light beams, free-space orbital angular momentum (OAM) beams and vector beams are coupled into an air–core fiber. To verify that our structured light generator enables generating structured light with high beam quality, polarization distributions and mode purity of generated OAM beams and vector beams in both free space and air–core fiber are characterized. Such a structured light generator may pave the way for future applications based on higher-order structured light beams.

Multifield finite strain plasticity: Theory and numerics

Motivated by the inability of classical computational plasticity to fully exploit modern scientific computing, a multifield formulation for finite strain plasticity is presented. This avoids a local integration of the elastoplastic model. In the multifield approach, the balance of linear momentum, the flow relation and the Karush–Kuhn–Tucker constraints are collectively cast in a variational format. In addition to the deformation, both the plastic strain and the consistency parameter are global degrees of freedom in the resulting spatially discrete problem. The ensuing proliferation of global degrees of freedom in the multifield approach is addressed by exploiting the block sparse structure of the algebraic system together with a tailored block matrix solver which can utilise emerging hardware architectures. A series of numerical problems demonstrate the validity, capability and efficiency of the proposed approach.

Pseudogauge freedom and the SO(3) algebra of spin operators

The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local redistribution of such quantities (with global energy, linear momentum, and angular momentum remaining unchanged). This arbitrariness is described in recent literature as the pseudogauge freedom or symmetry. In this letter, we analyze several pseudogauges used to formulate the relativistic hydrodynamics of particles with spin 12 and conclude that the canonical version of the spin tensor has an advantage over other forms as only the canonical definition defines the spin operators that fulfill the SO(3) algebra of angular momentum. This result sheds new light on the results encountered in recent papers demonstrating pseudogauge dependence of various physical quantities. It indicates that for spin-polarization observables, the canonical version is fundamentally better suited for building a connection between theory and experiment.

Variable thermo-physical properties of fluid flow along with exponential stretching; A chemical reaction study

Heat and mass transfer having variable fluid properties has wide range of applications in industrial and engineering processes.The transference of species arises in several processes like oil transport phenomenon, food processing and diffusion of assured medicines in blood (drug delivery). Current research deals with the mixed convection and radiation effects on flow of a non-Newtonian tangent hyperbolic fluid with variable thermo-physical properties and activation energy. Arrhenius kind of chemical reaction is taken along an exponentially stretchable surface. The main focus of the current exploration is to execute shear thinning tangent hyperbolic fluid past an exponentially stretchable surface under the influence of variable viscosity, mixed convection, thermal radiation and activation energy. Transformation approach is opted to attain the non-linear ODE's based on standard conservation laws of mass, linear momentum and energy. Numerical solutions of the governing problem are computed via the shooting technique. Characteristics of the parameters appearing in modeling like radiation parameter, variable viscosity parameter, mixed convection parameter, Williamson parameter, variable conductivity and diffusivity are comprehensively analyzed through graphical behavior.

Conservation and accuracy studies of the LESCM for incompressible fluids

Conservation properties are very important for numerical methods. The presence of non-conservative solutions can result in fictitious sources or sinks that cause alterations in the flow balance. In this paper, the conservation properties and their influences on the accuracy of a newly proposed meshfree Lagrangian-Eulerian stabilized collocation method (LESCM) for the incompressible fluid flow are mathematically derived and numerically validated. The LESCM inspired by the material point method (MPM) is based on the hybrid Lagrangian-Eulerian description, in which the accuracy of the solution on Eulerian nodes and the mapping between Eulerian nodes and Lagrangian particles are highly associated with the conservation properties. On one hand, since the Navier-Stokes equations are solved without any truncation or simplification, the global conservation can be satisfied like most of the numerical methods during the solution on the Eulerian nodes. Moreover, this method can also meet the global conservation for the mass, linear momentum and angular momentum during the mapping process which are detailedly derived in the paper. After that, the energy conservation is evaluated by the corresponding equation. On the other hand, the local conservation properties of the discrete equations as well as the mass and momentums can be satisfied in the LESCM, while most of the numerical methods do not possess this property. Therefore, the conservation properties can be maintained during both the solving and the mapping processes which guarantee the high accuracy, optimal convergence and good stability of the LESCM method. Numerical examples of steady-state flow, shear-driven cavity, dam break and water sloshing problems with complex free surface and breaking waves, demonstrate the high accuracy and efficiency as well as conservation of the LESCM. It also performs very well for fluid flow problems with large Reynolds numbers. This method can be extensively applied to the engineering problems associated with the incompressible free surface flow.

A thermal–kinetic subgrid model for supernova feedback in simulations of galaxy formation

ABSTRACT We present a subgrid model for supernova feedback designed for cosmological simulations of galaxy formation that may include a cold interstellar medium (ISM). The model uses thermal and kinetic channels of energy injection, which are built upon the stochastic kinetic and thermal models for stellar feedback used in the owls and eagle simulations, respectively. In the thermal channel, the energy is distributed statistically isotropically and injected stochastically in large amounts per event, which minimizes spurious radiative energy losses. In the kinetic channel, we inject the energy in small portions by kicking gas particles in pairs in opposite directions. The implementation of kinetic feedback is designed to conserve energy, linear and angular momentum, and is statistically isotropic. To test the model, we run simulations of isolated Milky Way-mass and dwarf galaxies, in which the gas is allowed to cool down to 10 K. Using the thermal and kinetic channels together, we obtain smooth star formation histories and powerful galactic winds with realistic mass loading factors. Furthermore, the model produces spatially resolved star formation rates (SFRs) and velocity dispersions that are in agreement with observations. We vary the numerical resolution by several orders of magnitude and find excellent convergence of the global SFRs and wind mass loading. We show that large thermal energy injections generate a hot phase of the ISM and modulate the star formation by ejecting gas from the disc, while the low-energy kicks increase the turbulent velocity dispersion in the neutral ISM, which in turn helps suppress star formation.

Bounds on energy and angular momentum loss in the full n-body problem

A new bound on the amended potential in an n-body system is derived and applied to the partitioning of energy and angular momentum in a disrupting gravitational aggregate. This result provides analytic insight into how energy and angular momentum can be lost or partitioned between different collections of bodies as they escape from each other. To better understand the possible outcomes in such a situation, some specific numerical tests are also performed for systems of N = 3, 4, 5, 6. The results confirm that disrupting systems always lose energy, with a characteristic stochastic distribution of the lost energy. We also find that the system loses most of its angular momentum, although individual escaping components can retain significant nonzero angular momentum vectors that can be uniformly distributed in space as the number of bodies in the system increases.

A significant study on radioactive cross fluid model with melting boundary near stagnation region

The current research endows the mathematical modeling for the stagnation point flow along with melting nonlinear radiative heat transfer for cross fluid. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, preparation of synthesis, adhesives, etc. A radially stretching sheet has started the flow keeping the assumption of rotational symmetry. Transformation approach is adopted to attain the nonlinear ordinary differential equations based on standard conservation laws of mass, linear momentum and also energy. Numerical solutions of the governing problem are computed via the shooting technique. Characteristics of the parameters appearing in modeling like the melting parameter, power–law index, local Weissenberg number, nonlinear radiation parameter, temperature ratio parameter and Prandtl number are comprehensively analyzed through graphical behavior. In addition, comparative analysis is presented for the cases when the value of free stream velocity overtops the stretching velocity and vice versa. Results are authenticated by taking special cases and excellent compatibility is achieved with the existing literature. The detailed analysis anticipates that the boundary layer structures could be strengthened by growing the melting parameter. Elevation in Weissenberg number caused velocity along with temperature profiles to demonstrate for [Formula: see text]. Further, the temperature behaves oppositely analogous to development in nonlinear radiation parameter besides the temperature ratio parameter.

Spam mail classification using back propagation neural networks

Mail classification methods based on machine learning have been introduced to combat spams. However, few researches focus on the most powerful machine learning model that is neural networks. In this paper, the author trains BP neural networks to detect spams. The inputs of the neural networks are only information about words, punctures, signs, numbers and illegal words. Five neural networks which are different in number of neurons and number of layers are experimented on. All networks apply Rectified Linear Unit (ReLU) functions and Momentum learning technology. The results show that the network with four hidden layers enjoys the best classifying accuracy of 97.0%. In networks with two hidden layers, when the number of neurons in each layer is above 300, the accuracy is between 95.5% and 96.0%; and 100 neurons in each layer result in an accuracy of 93.8%. Although the training only captures information of words, punctures and signs, the networks have achieved high accuracy, and the author suggests that making the computer understand sentences as well as other kinds of improvements can lead to even higher performance.

Dual arm coordination of redundant space manipulators mounted on a spacecraft

AbstractThe paper addresses a significant challenge in on-orbit robotics servicing and assembly, which is to overcome the saturation setback of force/torque on robot joint and spacecraft actuators during the post-capture stage while controlling a target spacecraft with uncontrolled large angular and linear momentums. The authors propose a novel solution based on two robust and efficient control algorithms: Optimal Control Allocation (OCA) and Non-linear Model Predictive Control (NMPC). Both algorithms aim to minimize joint torques, spacecraft actuator moments, contact forces, and moments of a compound redundant system that includes a common payload (target spacecraft) grasped by dual n-degree space robotics manipulators mounted on a chaser spacecraft. The OCA algorithm minimizes a quadratic cost function using only the current states and the system dynamics, but the NMPC also considers the future state estimates and the control inputs over a specified prediction horizon. It is computationally more involved but provides superior results in reducing joint torques. The literature to date in application of MPC to robotics mainly focuses on linear models but the dual arm coordination is highly non-linear and there is no MPC application on dual arm coordination. The proposed discretized technique offers exact realizations (of a non-linear model) with elegance and simplicity and yet considers the full non-linear model of the dual arm coordinating system. It is computationally very efficient. The computer simulation results show that the proposed algorithms work efficiently, and the minimum torques, contact forces, and moments are realized. The developed algorithm also is very efficient in tracking problems.

Modelling supernova nebular lines in 3D with extrass

ABSTRACT We present EXplosive TRAnsient Spectral Simulator (extrass), a newly developed code aimed at generating 3D spectra for supernovae in the nebular phase by using modern multidimensional explosion models as input. It is well established that supernovae are asymmetric by nature, and that the morphology is encoded in the line profiles during the nebular phase, months after the explosion. In this work, we use extrass to study one such simulation of a $3.3\, \mathrm{ M}_\odot$ He-core explosion ($M_\text{ejecta}=1.3\, M_\odot$, $E_\text{kin}=1.05\times 10^{51}\,$erg) modelled with the Prometheus-HotB code and evolved to the homologous phase. Our code calculates the energy deposition from the radioactive decay of 56Ni → 56Co → 56Fe and uses this to determine the Non-Local-Thermodynamic-Equilibrium temperature, excitation, and ionization structure across the nebula. From the physical condition solutions we generate the emissivities to construct spectra depending on viewing angles. Our results show large variations in the line profiles with viewing angles, as diagnosed by the first three moments of the line profiles; shifts, widths, and skewness. We compare line profiles from different elements, and study the morphology of line-of-sight slices that determine the flux at each part of a line profile. We find that excitation conditions can sometimes make the momentum vector of the ejecta emitting in the excited states significantly different from that of the bulk of the ejecta of the respective element, thus giving blueshifted lines for bulk receding material, and vice versa. We compare the 3.3 M⊙ He-core model to observations of the Type Ib supernova SN 2007Y.

Multichannel Single-Photon Emissions with On-Demand Momentums by Using Anisotropic Quantum Metasurfaces.

Photon momentums and their control are important for carrying quantum information and increasing information capacities. It is a great challenge to freely control multiple momentums of single photons based on only phase-dependent schemes in isotropic metasurfaces because exact manipulations of interference phases and precise alignments between quantum emitters and metasurfaces are involved. Here, an anisotropic metasurface, in which anisotropic rather than isotropic nanoscatterers are arranged anisotropically, is proposed to freely control multiple momentums of single photons. In the metasurfaces, the phase-independent and phase-dependent schemes are used to independently control spin angular momentums (SAMs) and linear momentums (LMs), respectively. The phase-independent scheme allows robust alignment between quantum emitters and metasurfaces. The anisotropic design amends geometrical phases for oblique emissions, providing larger ranges (up to 53°) for tailoring LMs. In experiments, three-channel single-photon emissions with independent SAMs and LMs are demonstrated. The introduction of anisotropic nanoscatterers and anisotropic arrangements of nanoscatterers is a more general design method for metasurfaces, and it could provide more flexibility to freely and efficiently tailor single-photon emissions.

Coulomb Problem for Classical Spinning Particles

We consider the motion of a weakly relativistic charged particle with an arbitrary spin in central potential e/r in terms of classical mechanics. We show that the spin–orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The angular velocity of precession depends on the distance of the particle from the centre. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin–orbital interaction. The possible orbits of a quantum particle are determined by the Bohr–Sommerfeld quantization rule. We give examples of orbits corresponding to small quantum numbers, which were obtained by numerical integration of equations of motion. The energies of stationary states are determined by spin–orbital interaction.

Optimal elastostatic cloaks

An elastic cloak hides a hole (or an inhomogeneity) from elastic fields. In this paper, a formulation of the optimal design of elastic cloaks based on the adjoint state method, in which the balance of linear momentum is enforced as a constraint, is presented. The design parameters are the elastic moduli of the cloak, and the objective function is a measure of the distance between the solutions in the physical and in the virtual bodies. Both the elastic medium and the cloak are assumed to be made of isotropic linear elastic materials. However, the proposed formulation can easily be extended to anisotropic solids. In order to guarantee smooth inhomogeneous elastic moduli within the cloak a penalization term is added to the objective function. Mixed finite elements are used for discretizing the weak formulation of the optimization problem. Several numerical examples of optimal elastic cloaks designed for both single and multiple loads are presented. We consider different geometries and loading types and observe that in some cases the optimal elastic cloaks for cloaking holes (cavities) are made of auxetic materials.

Dislocation Motion Induced by Thermally Driven Phase Transformations

AbstractThe interaction of dislocations with phase boundaries is an interesting aspect of the interplay between phase transformation and plasticity at the nano‐scale. We capture this interaction within a phase field framework coupled to discrete dislocation dynamics. In order to regularize the stress and driving force for phase evolution at the dislocation core, a first strain‐gradient elasticity approach is used, which leads to more physical, discretization‐independent numerical solutions.From a mathematical point of view, this results in a system of coupled partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDEs include an equation analogous to the balance of linear momentum, a second‐order tensor‐valued Helmholtz‐type equation for the true stress as well as a time‐dependent Ginzburg‐Landau equation for the evolution of the phase field. The ODEs are the equations of motion of the dislocations. The dislocations are modeled as lamellae with eigenstrain that can evolve with time; the resulting stress field is an outcome of the numerical solution. A parallel framework was developed in order to solve these coupled dynamics problems using the finite element library FEniCS. We show the effect of dislocations on phase microstructure as well as the influence of phase microstructure on the motion of dislocations using an illustrative example of a thermally‐driven planar phase boundary, and its interaction with a single edge dislocation.

New constraints on the Bray conservation-of-momentum natal kick model from multiple distinct observations

ABSTRACT Natal supernova kicks, the linear momentum compact remnants receive during their formation, are an essential part of binary population synthesis (BPS) models. Although these kicks are well supported by evidence, their underlying distributions and incorporation into BPS models are uncertain. In this work, we investigate the nature of natal kicks using a previously proposed analytical prescription where the strength of the kick is given by $v_\text{k}=\alpha \frac{m_\text{ejecta}}{m_\text{remnant}}+\beta \, \mathrm{km\, s}^{-1}$ , for free parameters α and β. We vary the free parameters over large ranges of possible values, comparing these synthetic populations simultaneously against four constraints: the merger rate of compact binary neutron star (BNS) systems, the period–eccentricity distribution of Galactic BNSs, the velocity distribution of single-star pulsars, and the likelihood for low ejecta mass supernovae to produce low-velocity kicks. We find that different samples of the parameter space satisfy each test, and only 1 per cent of the models satisfy all four constraints simultaneously. Although we cannot identify a single best kick model, we report $\alpha =115^{+40}_{-55}\, \mathrm{km\, s}^{-1}, \beta =15^{+10}_{-15}\, \mathrm{km\, s}^{-1}$ as the centre of the region of the parameter space that fulfils all of our constraints, and expect $\beta \ge 0\, \mathrm{km\, s}^{-1}$ as a further constraint. We also suggest further observations that will enable future refinement of the kick model. A sensitive test for the kick model will be the redshift evolution of the BNS merger rate since this is effectively a direct measure of the delay-time distribution for mergers. For our best-fitting values, we find that the peak of the BNS merger rate is the present day.

The biomechanical differences of wearing safety shoes compared with everyday shoes on dynamic balance when tripping over an obstacle

Safety shoes are known to challenge dynamic balance, but the interaction between footwear and trips has not been thoroughly explored. This study investigated the biomechanical differences on dynamic balance during unexpected trip perturbations between safety shoes and everyday shoes. The vertical position of the whole-body center of mass (CoM) and the linear momentum of the swing leg from seven females and sixteen males were analyzed in five subsequent gait cycles. Additionally, the recovery strategies (i.e., the displacement of the foot after tripping) were classified. Wearing safety shoes, the linear momentum of the foot and whole leg increased, and the vertical position of the whole-body CoM was lower after the perturbation. Additionally, the recovery strategy when wearing safety shoes demonstrated a lower displacement of the foot. In conclusion, wearing safety shoes was found to have negative biomechanical effects when having to circumvent a trip, and this potentially increased the risk of falling.

Effect of flow–thermodynamics interactions on the stability of compressible boundary layers: insights from Helmholtz decomposition

Helmholtz decomposition of velocity perturbations is performed in conjunction with linear stability analysis to examine the effects of flow-thermodynamics interactions on the stability of high-speed boundary layers. A corresponding decomposition of the pressure field is also proposed. The contributions of perturbation solenoidal kinetic, dilatational kinetic and internal energy to the various instability modes are examined as a function of Mach number ( $M$ ). As expected, dilatational and pressure field effects play an insignificant part in the first-mode behaviour at all Mach numbers. The second (Mack) mode, however, is dominantly dilatational in nature, and perturbation internal energy is significant compared to perturbation kinetic energy. The observed behaviour is explicated by examining the key processes of production and pressure-dilatation. Production of the second-mode dilatational kinetic energy is mostly due to the solenoidal-dilatational covariance stress tensor interacting with the mean (background) velocity gradient. This cross production component also inhibits the first mode. The dilatational pressure facilitates energy transfer from the kinetic to the internal field in the near‐wall region, whereas the energy transfer away from the wall is mostly due to the solenoidal pressure work. The dilatational characters of the fast and slow modes are also examined. The fast mode is dominantly dilatational at both $M=4$ and $M=6$ , while the nature of the slow mode is dependent on $M$ . Finally, Helmholtz decomposition of the perturbation momentum vector is performed. Interestingly, both first and second modes are dominated by solenoidal components of momentum.

When functionally graded materials meet higher order simplified strain gradient elasticity theory

We investigate the constitutive equations when the functionally graded materials (FGMs) are considered under the strain gradient elasticity theory (SGET). The SGET considered includes both the Helmholtz and bi-Helmholtz types. The constitutive equations become more complicated and contain more terms due to the interaction between the material gradation and the nonlocal effect of the strain gradient. We also derive the governing partial differential equations (PDEs) by the balance law of linear momentum, and the PDEs also appear to be highly complicated. Under the assumption that material gradation is of the exponential form, a simpler set of governing PDEs can be reached. Solutions to those PDEs under the formulation of different modes of crack problems are discussed.

Gait-phase specific transverse-plane momenta generation during pre-planned and late-cued 90 degree turns while walking

Turning while walking is ubiquitous and requires linear and angular momenta generation to redirect the body’s trajectory and rotate towards the new direction of travel. This study examined strategies that healthy young adults used during each gait phase to generate transverse-plane momenta during pre-planned and late-cued 90° turns. During leftward turns, we expected that momenta would be generated most during the gait phases known to generate leftward linear and angular momenta during straight line gait. We found distinct roles of gait phases towards generating momenta during turns that partially supported our hypotheses. Supporting one hypothesis, the change in transverse-plane angular momentum and average moment were greater during double support with the left foot in front vs. other gait phases. Also, the change in leftward linear momentum and average leftward force were greater during right single support vs. other gait phases during straight-line gait and late-cued turns. However, during pre-planned turns, the average leftward force was not significantly greater during right single support vs. other gait phases. Overall, transverse-plane angular momentum generation during turns is similar to its generation during straight-line gait, suggesting that healthy young adults can leverage momenta control strategies used during straight-line gait during turns.