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We take a fresh look at the relation between generalised Kähler geometry and N = (2 , 2) supersymmetric sigma models in two dimensions formulated in terms of (2, 2) superfields. Dual formulations in terms of different kinds of superfield are combined to give a formulation with a doubled target space and both the original superfield and the dual superfield. For Kähler geometry, we show that this doubled geometry is Donaldson's deformation of the holomorphic cotangent bundle of the original Kähler manifold. This doubled formulation gives an elegant geometric reformulation of the equations of motion. We interpret the equations of motion as the intersection of two Lagrangian submanifolds (or of a Lagrangian submanifold with an isotropic one) in the infinite dimensional symplectic supermanifold which is the analogue of phase space. We then consider further extensions of this formalism, including one in which the geometry is quadrupled, and discuss their geometry. [ABSTRACT FROM AUTHOR]

General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the Drude model. When absorption is included the eikonal becomes complex, with the imaginary part related to the absorption along a ray between emission and observation points. We extend results from the literature to include dispersion in the index of refraction. The complex Hamiltonian splits into a real part that describes the equations of motion and a constraint equation that governs the momentum loss in the system. We work in coordinates which are fully real, with a real metric in physical spacetime. We assume the dust and plasma distributions of the Drude matter to coincide and vary as a power-law 1 / r h . We find that transmission requires h > 1, otherwise exponential absorption occurs along ray paths. We use ray-tracing through strongly absorbing matter near the surface of the compact star, as well as specializing to a point-lens in the weak-field limit with weakly absorbing matter to generate potentially observable light curves for distant observers. In the appropriate limits, our theory reproduces results from the literature. [ABSTRACT FROM AUTHOR]

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description. [ABSTRACT FROM AUTHOR]

The high longitudinal electric fields generated in plasma wakefields are very attractive for a new generation of high gradient plasma based accelerators. On the other hand, the strong transverse fields increase the demand for a proper matching device in order to avoid the spoiling of beam transverse quality. A solution can be provided by the use of a plasma ramp, a region at the plasma injection/extraction with smoothly increasing/decreasing plasma density. The transport of a beam inside a plasma ramp, beside its parameters, depends on the profile of the ramp itself. Establishing the transfer matrix for a plasma ramp represent a very useful tool in order to evaluate the beam evolution in the plasma. In this paper a study of a cosine squared ramp is presented. An approximate solution of the transverse equation of motion is evaluated and exploited to provide a simple transfer matrix for the plasma ramp. The transfer matrix is then employed to demonstrate that this kind of ramp has the effect to minimize the emittance growth due to betatron dephasing. The behavior of a squared cosine plasma ramp will be compared with an experimentally measured plasma ramp profile in order to validate the applicability of the transfer matrix to real cases. [ABSTRACT FROM AUTHOR]

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates or assumptions about the behavior of the rigid body. All the basic quantities and characteristics of a rigid body, as well as the equations of motion and integrals of motion, are obtained from the variational problem by direct and unequivocal calculations within the framework of standard methods of classical mechanics. Several equivalent forms for the equations of motion of rotational degrees of freedom are deduced and discussed on this basis. Using the resulting formulation, we revise some cases of integrability, and discuss a number of peculiar properties, that are not always taken into account when formulating the laws of motion of a rigid body. [ABSTRACT FROM AUTHOR]

After decades, the theoretical study of core-collapse supernova explosions is moving from parameterized, spherically symmetric models to increasingly realistic multidimensional simulations. However, obtaining nucleosynthesis yields based on such multidimensional core-collapse supernova simulations is not straightforward. Frequently, tracer particles are employed. Tracer particles may be tracked in situ during the simulation, but often they are reconstructed in a post-processing step based on the information saved during the hydrodynamic simulation. Reconstruction can be done in a number of ways, and here we compare the approaches of backward and forward integration of the equations of motion to the results based on inline particle trajectories. We find that both methods agree reasonably well with the inline results for isotopes for which a large number of particles contribute. However, for rarer isotopes that are produced only by a small number of particle trajectories, deviations can be large. For our setup, we find that backward integration leads to better agreement with the inline particles by more accurately reproducing the conditions following freeze-out from nuclear statistical equilibrium, because the establishment of nuclear statistical equilibrium erases the need for detailed trajectories at earlier times. Based on our results, if inline tracers are unavailable, we recommend backward reconstruction to the point when nuclear statistical equilibrium was last applied, with an interval between simulation snapshots of at most 1 ms for nucleosynthesis post-processing. [ABSTRACT FROM AUTHOR]

We present theoretical studies of above threshold ionization (ATI) using sculpted laser pulses. The time-dependent Schrödinger equation is solved to calculate the ATI energy and momentum spectra, and a qualitative understanding of the electron motion after ionization is explored using the simple man's model and a classical model that solves Newton's equation of motion. Results are presented for Gaussian and Airy laser pulses with identical power spectra, but differing spectral phases. The simulations show that the third order spectral phase of the Airy pulse, which can alter the temporal envelope of the electric field, causes changes to the timing of ionization and the dynamics of the rescattering process. Specifically, the use of Airy pulses in the ATI process results in a shift of the Keldysh plateau cutoff to lower energy due to a decreased pondermotive energy of the electron in the laser field, and the side lobes of the Airy laser pulse change the number and timing of rescattering events. This translates into changes to the high-order ATI plateau and intra- and intercycle interference features. Our results also show that laser pulses with identical carrier envelope phases and nearly identical envelopes yield different photoelectron momentum distributions, which are a direct result of the pulse's spectral phase. [ABSTRACT FROM AUTHOR]

Using purely geometrical methods we present a mechanism to solve the scalar field equations of motion (non-minimally coupled with gravity) in a spherically symmetric background. We found that the full set of spacetimes, which are of Petrov type O (conformally flat) and admit a gradient conformal vector field, can be determined completely. It is shown that the full group of scalar field equations reduced to a single equation that depends only on the distance w = r 2 − t 2 leaving the metric function (equivalently the functional form of the scalar field or the potential) freely chosen. Depending on the structure of the metric or the potential V (as a function of φ) a solution can be found either analytically or via numerical integration. We provide physically sound examples and prove that (Anti)-de Sitter fits this scheme. We also reconstruct a recently found solution (Strumia and Tetradis 2022 J. High Energy Phys. JHEP09(2022)203) representing an expanding scalar bubble with metric that has a singularity and corresponds to what is termed as Anti-de Sitter crunch. [ABSTRACT FROM AUTHOR]

The pseudo- PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldyâ€"Wouthuysen transformations. A new spin operator PT symmetric expectation value (called the mean spin operator) for an electron interacting with a time-dependent electromagnetic field is obtained. We show that spin magnetizationâ€"which is the quantity usually measured experimentallyâ€"is not described by the standard spin operator but by this new mean spin operator to properly describe magnetization dynamics in ferromagnetic materials and the corresponding equation of motion is compatible with the phenomenological model of the Landauâ€"Lifshitzâ€"Gilbert equation (LLG). [ABSTRACT FROM AUTHOR]

We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics that contains a maximum observable length scale at the order of the cosmological particle horizon, existing in cosmology. We have started by modifying the classical mechanics which shows non-minimal effects on the equation of motion of a particle. Next, we have provided representation of the deformed quantum mechanical algebra. With this algebra in hand, we have calculated the general form of the path integral propagator in this deformed background. Thereafter, as a most simple case, we have built up the explicit form of the free particle propagator. The modifications to the free particle propagator show some non-trivial effects in this case. Our formalism can be applied to analyze the quantum properties and observations emerging in the context of cosmology. [ABSTRACT FROM AUTHOR]

A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electronâ€"electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view. [ABSTRACT FROM AUTHOR]

We theoretically study thermoelectric transport properties through a triangular triple-quantum-dot (TTQD) structure in the linear response regime using the hierarchical equations of motion approach. It is demonstrated that large Seebeck coefficient can be obtained when properly matching the interdot tunneling strength and magnetic flux at the electronâ€"hole symmetry point, as a result of spin chiral interactions in the TTQD system. We present a systematic investigation of the thermopower (the Seebeck coefficient) dependence on the tunneling strength, magnetic flux, and on-site energy. The Seebeck coefficient shows a clear breakdown of electronâ€"hole symmetry in the vicinity of the Kondo regime, accompanied by the deviation from the semiclassical Mott relation in the Kondo and mixed-valence regimes, which result from the many-body effects of the Kondo correlated induced resonance together with spin chiral interactions. [ABSTRACT FROM AUTHOR]

The excitation of toroidicity-induced Alfvén eigenmodes (TAEs) using prescribed external electromagnetic perturbations (hereafter ‘antenna’) acting on a confined toroidal plasma, as well as its nonlinear couplings to other modes in the system, is studied. The antenna is described by an electrostatic potential resembling the target TAE mode structure along with its corresponding parallel electromagnetic potential computed from Ohm’s law. Numerically stable long-time linear simulations are achieved by integrating the antenna within the framework of a mixed representation and pullback scheme (Mishchenko et al 2019 Comput. Phys. Commun. 238 194). By decomposing the plasma electromagnetic potential into symplectic and Hamiltonian parts and using Ohm’s law, the destabilizing contribution of the potential gradient parallel to the magnetic field is cancelled in the equations of motion. Besides evaluating the frequencies and the growth/damping rates of excited modes compared to referenced TAEs, we study the interaction of antenna-driven modes with fast particles and indicate their margins of instability. Furthermore, we show the first nonlinear simulations in the presence of a TAE-like antenna exciting other TAE modes, as well as global Alfvén eigenmodes with different toroidal wave numbers from that of the antenna. [ABSTRACT FROM AUTHOR]

We compute the quantum cohomology of symplectic flag manifolds. Symplectic flag manifolds can be described by non-abelian GLSMs with superpotential. Although the ring relations cannot be directly read off from the equations of motion on the Coulomb branch due to complication introduced by the non-abelian gauge symmetry, it can be shown that they can be extracted from the localization formula in a gauge-invariant form. Our result is general for all symplectic flag manifolds, which reduces to previously established results on symplectic Grassmannians and complete symplectic flag manifolds derived by other means. We also explain why a (0, 2) deformation of the GLSM does not give rise to a deformation of the quantum cohomology. [ABSTRACT FROM AUTHOR]

The spread and scrambling of quantum information is a topic of considerable current interest. Numerous studies suggest that quantum information evolves according to hydrodynamical equations of motion, even though it is a starkly different quantity to better-known hydrodynamical variables such as charge and energy. In this work we show that the well-known memory matrix formalism for traditional hydrodynamics can be applied, with relatively little modification, to the question of operator growth in many-body quantum systems. On a conceptual level, this shores up the connection between information scrambling and hydrodynamics. At a practical level, it provides a framework for calculating quantities related to operator growth like the butterfly velocity and front diffusion constant, and for understanding how these quantities are constrained by microscopic symmetries. We apply this formalism to calculate operator-hydrodynamical coefficients perturbatively in a family of Floquet models. Our formalism allows us to identify the processes affecting information transport that arise from the spatiotemporal symmetries of the model. [ABSTRACT FROM AUTHOR]

By combining the two-particle-irreducible (2PI) effective action common in non-equilibrium quantum field theory with the classical Martinâ€"Siggiaâ€"Rose formalism, self-consistent equations of motion for the first and second cumulants of non-linear classical stochastic processes are constructed. Such dynamical equations for correlation and response functions are important in describing non-equilibrium systems, where equilibrium fluctuationâ€"dissipation relations are unavailable. The method allows to evolve stochastic systems from arbitrary Gaussian initial conditions. In the non-linear case, it is found that the resulting integro-differential equations can be solved with considerably reduced computational effort compared to state-of-the-art stochastic Rungeâ€"Kutta methods. The details of the method are illustrated by several physical examples. [ABSTRACT FROM AUTHOR]

We discuss the limits of the equation of the period of a simple pendulum, T s = 2 π l / g , frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one, taking into account the string’s mass, the bob’s radius, and finite angular displacements. We show that the bob radius and finite angular displacements increase the period of oscillation of the pendulum and, hence, contribute to a positive deviation in the value of g calculated with the simple pendulum formula. On the other hand, the string’s mass decreases the pendulum’s period and induces a negative deviation in the value of g. As a result, it is possible to adapt the pendulum’s characteristics to use the simple pendulum formula and calculate g with accuracy. [ABSTRACT FROM AUTHOR]

The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by neural networks with a limited number of parameters. The training of the networks follows the extreme learning machine idea. We determine laws for different levels of embedding, thus we can represent not only the equation of motion but also the symmetries of different kinds. In the recursive numerical evolution of the system, we require the fulfillment of all the observed laws, within the determined numerical precision. In this way, we can successfully reconstruct both integrable and chaotic motions, as we demonstrate in the example of the gravity pendulum and the double pendulum. [ABSTRACT FROM AUTHOR]

In a recent paper (2022 Eur. J. Phys. 43 035 004) Lineros considers a block (not necessarily initially at rest) which slides down from the top of a frictionless horizontal movable semi-sphere. The author studies the angle at which the block loses contact with the sphere and derives a cubic equation which determines that angle. In this comment, a considerably more elementary derivation of that result is presented. [ABSTRACT FROM AUTHOR]

By using simplified 2D gravitational, non-Lorentz invariant actions constructed from the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a radial observer in Schwarzschild spacetime. We then fully characterize the remnant symmetries corresponding to this near-horizon 2D geometry by solving the motion equations adapted to 2D Milne space. This symmetries, which represent special or privileged diads, acquire the form of uniformly accelerated (Rindler) observers whose constant acceleration is proportional to the black hole mass M. [ABSTRACT FROM AUTHOR]

New characteristics of the Kondo effect, arising from spin chirality induced by the Berry phase in the equilibrium state, are investigated. The analysis is based on the hierarchical equations of motion (HEOM) approach in a triangular triple quantum-dot (TTQD) structure. In the absence of magnetic field, TTQD has four-fold degenerate chiral ground states with degenerate spin chirality. When a perpendicular magnetic field is applied, the chiral interaction is induced by the magnetic flux threading through TTQD and the four-fold degenerate states split into two chiral state pairs. The chiral excited states manifest as chiral splitting of the Kondo peak in the spectral function. The theoretical analysis is confirmed by the numerical computations. Furthermore, under a Zeeman magnetic field B, the chiral Kondo peak splits into four peaks, owing to the splitting of spin freedom. The influence of spin chirality on the Kondo effect signifies an important role of the phase factor. This work provides insight into the quantum transport of strongly correlated electronic systems. [ABSTRACT FROM AUTHOR]

This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local form. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions S ′ . We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all R 3 and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in S ′ . [ABSTRACT FROM AUTHOR]

In this paper, we extend our previous study on the Lemaitre–Tolman (LT) model showing how the prediction of the model changes when the equation of state (EoS) parameter (w) of dark energy (DE) is modified. In the previous study, it was considered that DE was merely constituted by the cosmological constant. In this paper, as in the previous study, we also took into account the effect of angular momentum and dynamical friction (JηLT model) that modifies the evolution of a perturbation, initially moving with the Hubble flow. As a first step, solving the equations of motion, we calculated the relationship between mass, M, and the turn-around radius, R0. If one knows the value of the turn-around radius R0, it is possible to obtain the mass of the studied objects. As a second step, we build up, as in the previous paper, a relationship between the velocity, v, and radius, R. The relation was fitted to data of groups and clusters. Since the relationship v–R depends on the Hubble constant and the mass of the object, we obtained optimized values of the two parameters of the objects studied. The mass decreases of a factor of maximum 25% comparing the JηLT results (for which w = −1) and the case w = −1/3, while the Hubble constant increases going from w = −1 to w = −1/3. Finally, the obtained values of the mass, M, and R0 of the studied objects can put constraints on the DE EoS parameter, w. [ABSTRACT FROM AUTHOR]

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einsteinâ€"Hilbert action reduces to a one-dimensional mechanical model. We have shown in Geiller et al (2021 SciPost Phys. 10 022) that this model exhibits a symmetry under the (2 + 1)-dimensional PoincarĂ© group. Here we extend the PoincarĂ© transformations to the infinite-dimensional BMS3 group. Although the black hole model is not invariant under those extended transformations, we can write it as a geometric action for BMS3, where the configuration space variables are elements of the algebra b m s 3 and the equations of motion transform as coadjoint vectors. The BMS3 symmetry breaks down to its PoincarĂ© subgroup, which arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS2 JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS3 symmetries, provides yet another illustration of the ubiquitous role played by this group. [ABSTRACT FROM AUTHOR]

In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Boseâ€"Einstein condensate to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atomâ€"atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy. [ABSTRACT FROM AUTHOR]

To study properties of magnetohydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a "PNS in a box" simulation model and solve the compressible MHD equation coupled with a nuclear equation of state (EOS) and simplified leptonic transport. As a demonstration, we apply it to two types of PNS model with different internal structures: a fully convective model and a spherical-shell convection model. By varying the spin rate of the models, the rotational dependence of convection and the dynamo that operate inside the PNS is investigated. We find that, as a consequence of turbulent transport by rotating stratified convection, large-scale structures of flow and thermodynamic fields are developed in all models. Depending on the spin rate and the depth of the convection zone, various profiles of the large-scale structures are obtained, which can be physically understood as steady-state solutions to the "mean-field" equation of motion. Additionally to those hydrodynamic structures, a large-scale magnetic component of G is also spontaneously organized in disordered tangled magnetic fields in all models. The higher the spin rate, the stronger the large-scale magnetic component grows. Intriguingly, as an overall trend, the fully convective models have a stronger large-scale magnetic component than that in the spherical-shell convection models. The deeper the convection zone extends, the larger the size of the convective eddies becomes. As a result, rotationally constrained convection seems to be more easily achieved in the fully convective model, resulting in a higher efficiency of the large-scale dynamo there. To gain a better understanding of the origin of the diversity of a neutron star's magnetic field, we need to study the PNS dynamo in a wider parameter range. [ABSTRACT FROM AUTHOR]

The experimental observation of long-lived quantum coherence in the excitation energy transfer (EET) process of the several photosynthetic light-harvesting complexes at low and room temperatures has aroused hot debate. It challenges the common perception in the field of complicated pigment molecular systems and evokes considerable theoretical efforts to seek reasonable explanations. In this work, we investigate the coherent exciton dynamics of the phycoerythrin 545 (PE545) complex. We use the dissipation equation of motion to theoretically investigate the effect of the local pigment vibrations on the population transfer process. The result indicates that the realistic local pigment vibrations do assist the energy transmission. We demonstrate the coherence between different pigment molecules in the PE545 system is an essential ingredient in the EET process among various sites. The coherence makes the excitation energy delocalized, which leads to the redistribution of the excitation among all the chromophores in the steady state. Furthermore, we investigate the effects of the complex high-frequency spectral density function on the exciton dynamics and find that the high-frequency Brownian oscillator model contributes most to the exciton dynamic process. The discussions on the local pigment vibrations of the Brownian oscillator model suggest that the local heterogeneous protein environments and the effects of active vibration modes play a significant role in coherent energy transport. [ABSTRACT FROM AUTHOR]

Non-Hermitian materials can exhibit not only exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is unclear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system. [ABSTRACT FROM AUTHOR]

This paper describes the behavior of a symmetrical gyroscope when it falls down from a certain height over the surface of the earth. The assumptions of the model are that (i) the gravitational acceleration has a constant value and (ii) no aerodynamic or other external forces are exerted on it, thus the expression ‘in vacuum’ is in the title. Using body- and space-fixed reference systems, several formulations are developed to derive the equations of motion. Among them, particular attention was paid to the conservation of the angular momentum in the space-fixed reference system. Closed-form but lengthy analytical expressions were derived for all the three Euler angles, under arbitrary initial conditions. Approximate sinusoidal expressions were derived for an initial lean angle equal to ten degrees. Through computer simulation it is shown that the initial lean angle and the spin of the gyroscope highly influence the variation of its orientation during the free fall. Based on these findings, it was concluded that low spins could cause a considerable change such as one degree in the lean angle at landing, thus may mislead the experimenter who will be cheated measuring a slightly smaller gravitational acceleration. [ABSTRACT FROM AUTHOR]

The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be solved numerically to give a good description of the system’s dynamics. The numerical solution captures complex aspects of the looping pendulum’s behavior, and is in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

We use the Schwinger action principle to obtain the equations of motion in the Koopman–von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems. We show that for velocity-independent forces the Schwinger action principle can be interpreted as a variational principle. [ABSTRACT FROM AUTHOR]

High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated. Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton's principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation. [ABSTRACT FROM AUTHOR]

A looping pendulum is a setup that consists of two loads connected by a light string, which in turn is put over a fixed rod, with the lighter load being held by a person, and the heavier close to the rod. When the lighter load is released, experience shows there is an instant when the heavier load stops falling, and the lighter winds around the rod, bringing the system to rest. This setup is used in science demonstrations to prevent a fragile object, such as a ceramic mug, from falling to the ground, using washers as the lighter load. In this paper we propose a mathematical model for this demonstration, which we use to analyze the main parameters that influence the effectiveness of the setup. We find its equations of motion analytically, and use numerical methods to relate relevant parameters (such as falling distance and trajectory) to the initial configuration, determine the conditions that allow the phenomenon to happen, and display results as plots and parameter spaces. Lastly, through careful experimentation we found strong evidence for the validity of our theoretical predictions. We found the looping pendulum to be an extremely useful problem for introductory college physics courses interested in strengthening analytical and computational physics skills, as its construction is easy, inexpensive, and its analysis encompasses various mechanics concepts, solving differential equations numerically, and data collection through video software. [ABSTRACT FROM AUTHOR]

The dynamics of water micro-particles in air can be studied by introducing a viscous force in the equations of the motion, in addition to the weight of the particle and the buoyance force. In this work, by taking account of the buoyance force, the range of the micro-particle is calculated as a function of the angle at which it is released. An analytic-numerical procedure to find the angle giving the maximum range is indicated. The effect of a convective air flow is finally studied. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically analyze the motion of an ellipse rotating on a horizontal floor without slipping. The contact point between the ellipse and the floor is shifted back and forth against the center of gravity of the ellipse depending on its inclination, and the static frictional force is also changed its direction and prevents the ellipse from slipping. The torque due to the normal force exerted on the contact point causes the rotation to be accelerated and decelerated. While the exact form of the equation of motion of the rolling ellipse is nonlinear, we take the linear approximation of small deviations from the vertically standing and horizontally lying states, and its approximate solutions are given by a hyperbolic and a trigonometric function. We will show that the linear approximate solutions are suitable for university students in physics courses to understand the rotational motion of the ellipse, especially the nature of the forces acting on the ellipse. [ABSTRACT FROM AUTHOR]

Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is made of either fractional derivatives or a covariant fractional d'Alembertian. The classical action for each theory is constructed and the equations of motion are derived. Unitarity and renormalizability of theories with a fractional d'Alembertian are also considered. We argue that unitarity and power-counting renormalizability never coexist, although in some cases one-loop unitary and finiteness are possible. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity. [ABSTRACT FROM AUTHOR]

State-of-the-art numerical simulations of quantum electrodynamical (QED) processes in strong laser fields rely on a semiclassical combination of classical equations of motion and QED rates, which are calculated in the locally constant field approximation. However, the latter approximation is unreliable if the amplitude of the fields, a0, is comparable to unity. Furthermore, it cannot, by definition, capture interference effects that give rise to harmonic structure. Here we present an alternative numerical approach, which resolves these two issues by combining cycle-averaged equations of motion and QED rates calculated in the locally monochromatic approximation. We demonstrate that it significantly improves the accuracy of simulations of photon emission across the full range of photon energies and laser intensities, in plane-wave, chirped and focused background fields. [ABSTRACT FROM AUTHOR]

The Landau–Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when influenced by radiation reaction. Until recently, there has been no clear experimental verification. However, aligned crystals have remedied the situation: here, as in Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on a quantitative experimental test of the LL equation by measuring the emission spectra of electrons and positrons penetrating aligned single crystals. The recorded spectra are in remarkable agreement with simulations based on the LL equation of motion with moderate quantum corrections for recoil and, in the case of electrons in axially aligned crystals, spin and reduced radiation intensity. [ABSTRACT FROM AUTHOR]

The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently introduced effective spin foam models, which are particularly numerically efficient. Previous work has raised the concern of a flatness problem in spin foam dynamics, identifying the potential for the dynamics to lead to flat geometries in the small ℏ semiclassical limit. The numerical results presented here expose a rich semiclassical regime, but one that must be understood as an interplay between the various parameters of the spin foam model. In particular, the scale of the triangulation, fixed by the areas of its boundary triangles, the discreteness of the area spectrum, input from loop quantum gravity, and the curvature scales around the bulk triangles, all enter the characterization of the semiclassical regime identified here. In addition to these results on the dynamics, we show that the subtle nature of the semiclassical regime is a generic feature of the path integral quantization of systems with second class constraints. [ABSTRACT FROM AUTHOR]

We present a phase- and spin-dependent manipulation of leakage of a Majorana mode into a double quantum dot. We study the density of states (DOS) to show the effect of phase change factor on the Majorana leakage into (out) of a double quantum dot. The DOS is derived from the Green's function of the quantum dot by the equation of motion method, and exhibits a formant structure when ϕ = 0,2π and a resonance shape when ϕ = 0.5π and 1.5π. Also, it changes more strongly under the spin-polarized coefficient than the non-polarized lead. Such a theoretical model can be modified to explore the spin-dependent effect in the hybrid Majorana quantum dot system. [ABSTRACT FROM AUTHOR]

Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc, are related to multi-scale structure and symmetries of underlying equations of motion. Significantly simplified equations of motion, called toy-models, are traditionally employed in the analysis of such complex systems. In these models, equations are modified preserving just a part of the structure believed to be important. Here we propose a different approach for constructing simplified models, in which instead of simplifying equations one introduces a simplified configuration space: velocity fields are defined on multi-dimensional logarithmic lattices with proper algebraic operations and calculus. Then, the equations of motion retain their exact original form and, therefore, naturally maintain most scaling properties, symmetries and invariants of the original systems. Classification of such models reveals a fascinating relation with renowned mathematical constants such as the golden mean and the plastic number. Using both rigorous and numerical analysis, we describe various properties of solutions in these models, from the basic concepts of existence and uniqueness to the blowup development and turbulent dynamics. In particular, we observe strong robustness of the chaotic blowup scenario in the three-dimensional incompressible Euler equations, as well as the Fourier mode statistics of developed turbulence resembling the full three-dimensional Navier–Stokes system. [ABSTRACT FROM AUTHOR]

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations. [ABSTRACT FROM AUTHOR]

The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of classical equations of motion is derived and the characteristic features of the motion are examined. A specific regime is found with comparable strong field quantum parameters of the beams, when the electron trajectory exhibits ultrashort spike-like features, which bears great significance to the corresponding radiation properties. An analytical expression for the spectral distribution of spontaneous radiation is derived in the framework of the Baier–Katkov semiclassical approximation based on the classical trajectory. All the analytical results are further validated by exact numerical calculations. We consider a non-resonant regime of interaction, when the laser frequencies in the electron rest frame are far from each other, avoiding stimulated emission. Special attention is devoted to settings when the description of radiation via the local constant field approximation fails and to corresponding spectral features. Periodic and non-periodic regimes are considered, when lab frequencies of the laser waves are always commensurate. The sensitivity of spectra with respect to the electron beam spread, focusing and finite duration of the laser beams is explored. [ABSTRACT FROM AUTHOR]

Detection of gravitational waves opened new windows on fundamental physics and it would be natural to search how the role of extra dimensional effects can be traced to gravitational wave physics. In this article, we consider a toy model of five dimensional pure gravity theory compactified on a circle. The resulting four dimensional theory is a scalar-Maxwell theory which is minimally coupled with gravity. By finding the equations of motion for scalar, electric and magnetic fields, we would be able to find exact wave solutions of coupled equations which are zero mode solutions. We also perform perturbation in order to consider non-zero modes of electromagnetic fields. Having these solutions at hand, we study the recombination of scalar-affected electromagnetic waves in a typical Michelson interferometer. In particular, we obtain, up to first order, the change of amplitude of electromagnetic power due to presence of this scalar field which may reveal some signals of extra dimension. [ABSTRACT FROM AUTHOR]

Permanently deformed objects in binary systems can experience complex rotation evolution, arising from the extensively studied effect of spin–orbit coupling as well as more nuanced dynamics arising from spin–spin interactions. The ability of an object to sustain an aspheroidal shape largely determines whether or not it will exhibit nontrivial rotational behavior. In this work, we adopt a simplified model of a gravitationally interacting primary and satellite pair, where each body's quadrupole moment is approximated by two diametrically opposed point masses. After calculating the net gravitational torque on the satellite from the primary, as well as the associated equations of motion, we employ a Hamiltonian formalism that allows for a perturbative treatment of the spin–orbit and retrograde and prograde spin–spin coupling states. By analyzing the resonances individually and collectively, we determine the criteria for resonance overlap and the onset of chaos, as a function of orbital and geometric properties of the binary. We extend the 2D planar geometry to calculate the obliquity evolution. This calculation indicates that satellites in spin–spin resonances undergo precession when inclined out of the plane, but they do not tumble. We apply our resonance overlap criteria to the contact binary system (216) Kleopatra, and find that its satellites, Cleoselene and Alexhelios, may plausibly be exhibiting chaotic rotational dynamics from the overlap of the spin–orbit and retrograde spin–spin resonances. While this model is, by construction, generalizable to any binary system, it will be particularly useful for studies of small bodies in the Solar System, whose irregular shapes make them ideal candidates for exotic rotational states. [ABSTRACT FROM AUTHOR]

Trajectory-based methods are well-developed to approximate steady-state probability distributions for stochastic processes in large-system limits. The trajectories are solutions to equations of motion of Hamiltonian dynamical systems, and are known as eikonals. They also express the leading flow lines along which probability currents balance. The existing eikonal methods for discrete-state processes including chemical reaction networks are based on the Liouville operator that evolves generating functions of the underlying probability distribution. We have previously derived [1, 2] a representation for the generators of such processes that acts directly on the hierarchy of moments of the distribution, rather than on the distribution itself or on its generating function. We show here how in the large-system limit the steady-state condition for that generator reduces to a mapping from eikonals to the ratios of neighboring factorial moments, as a function of the order k of these moments. The construction shows that the boundary values for the moment hierarchy, and thus its whole solution, are anchored in the interior fixed points of the Hamiltonian system, a result familiar from Freidlin–Wenztell theory. The direct derivation of eikonals from the moment representation further illustrates the relation between coherent-state and number fields in Doi–Peliti theory, clarifying the role of canonical transformations in that theory. [ABSTRACT FROM AUTHOR]

We built a simple structure of seven dipole neodymium magnetic balls, a magnetic spinner that easily rotates around its central ball. This proved to be a very simple magnetic oscillator-rotator with a dipole-like field. After capturing videos of its rotating movements in different magnetic fields, video analysis has provided us with the rotation angle-time function of the motion, either in the case of a stationary magnetic field (damped oscillation) or an alternating magnetic field (forced oscillations). We were able to obtain a numerical solution for the differential equation describing the motion, a solution which was in tune with the special phenomena observed. It was especially interesting—and can be utilised in physics education—that the oscillation of the system was very strongly dependent on the initial conditions and seemed to be quite chaotic. The rotation angle, angular speed functions and their representation in phase space have shown the characteristics of chaotic behaviour, especially in the case of coupled oscillations. Thus, this kind of chaotic movement can be demonstrated very simply, even in classroom conditions by the use of such magnetic systems. At the same time, such models might help in the scientific understanding of magnetic nanostructures—their self-assembly and motions in alternating magnetic fields—which is the basis of practical applications such as magnetic hyperthermia. [ABSTRACT FROM AUTHOR]

The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress–energy–momentum tensor for a hyperelastic body are derived from the gauge–invariant action principle first considered by DeWitt. This action is a natural extension of the action for a single relativistic particle. The central object in the Lagrangian treatment is the Landau–Lifshitz radar metric, which is the relativistic version of the right Cauchy–Green deformation tensor. We also introduce relativistic definitions of the deformation gradient, Green strain, and first and second Piola–Kirchhoff stress tensors. A gauge-fixed description of relativistic hyperelasticity is also presented, and the nonrelativistic theory is derived in the limit as the speed of light becomes infinite. [ABSTRACT FROM AUTHOR]

In the present work, we develop a theoretical study for predicting the streaming potential and, therefore, the electric power generation in a system composed of a semi-permeable osmotic membrane inserted in a slit microchannel. Both physical systems are communicated through the forced microcirculation of an electrolyte employing the use of a saline gradient, which is established between the external faces of the membrane, creating the suction force needed to induce a hydrodynamic flow. In this manner, we externally impose a uniform volumetric flow rate to promote simultaneous hydrodynamic and electrokinetic fields, replacing the usual external pressure gradient with an equivalent osmotic pressure force. The viscoelectric effects of the electrolyte solution are included in the present analysis. The resulting non-linear governing equations for the motion are written in dimensionless form and permit us to derive an integro-differential equation for the velocity field, which is solved by an iterative method. With the aid of these previous results, the electric energy, in terms of an electrokinetic streaming potential and the streaming current, is generated for this combined system. This proposed electric power generation technique converts the energy of a saline gradient into electrical energy, avoiding the mechanical use of an external pressure gradient. [ABSTRACT FROM AUTHOR]