Dynamics Of Point Particle Research Articles

Superintegrability, symmetry and point particle T-duality

We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more widespread phenomenon in the context of the point particle dynamics than it is in the string one; moreover, it concerns physically very relevant point particle dynamical systems and not just somewhat exotic ones fabricated for the purpose. As a source of T-duality examples, we consider maximally superintegrable spherically symmetric electro-gravitational backgrounds in [Formula: see text] dimensions. We then describe in detail four such spherically symmetric dynamical systems which are all mutually interconnected by a web of point particle T-dualities. In particular, the dynamics of a charged particle scattered by a repulsive Coulomb potential in a flat space is T-dual to the dynamics of the Coulomb scattering in the space of constant negative curvature, but it is also T-dual to the (conformal) Calogero–Moser inverse square dynamics both in flat and hyperbolic spaces. Thus knowing just the Hamiltonian dynamics of the scattered particle cannot give us information about the curvature of the space in which the particle moves.

Self-consistent Spin, Tidal, and Dynamical Equations of Motion in the REBOUNDx Framework

We introduce self-consistent spin, tidal, and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems of which the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code’s performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.

Follow-up analyses of the binary-neutron-star signals GW170817 and GW190425 by using post-Newtonian waveform models

We reanalyze the binary-neutron-star signals, GW170817 and GW190425, focusing on the inspiral regime to avoid uncertainties on waveform modeling in the postinspiral regime. We use post-Newtonian waveform models as templates, which are theoretically rigid and efficiently describe the inspiral regime. We study potential systematic difference in estimates of the binary tidal deformability $\tilde{\Lambda}$ by using different descriptions for the point-particle dynamics and tidal effects. We find that the estimates of $\tilde{\Lambda}$ show no significant systematic difference among three models for the point-particle parts: TF2, TF2g, and TF2+, when they employ the same tidal model. We compare different tidal descriptions given by different post-Newtonian orders in the tidal phase. Our results indicate that the estimates of $\tilde{\Lambda}$ slightly depend on the post-Newtonian order in the tidal phase and an increase in the tidal post-Newtonian order does not lead to a monotonic change in the estimate of $\tilde{\Lambda}$. We also compare the estimate of $\tilde{\Lambda}$ obtained by the post-Newtonian tidal model and numerical-relativity calibrated tidal models. We find that the post-Newtonian model gives slightly larger estimate of $\tilde{\Lambda}$ and wider posterior distribution than the numerical-relativity calibrated models. According to Bayesian model comparison, it is difficult to identify a preference among the post-Newtonian orders by relying on the GW170817 and GW190425 data. Our results indicate no preference among numerical-relativity calibrated tidal models over the post-Newtonian model. Additionally, we present constraints on equation-of-state models for neutron stars with the post-Newtonian model, which show that the GW170817 data disfavor less compact models, though they are slightly weaker constraints than the numerical-relativity calibrated tidal models.

Maxwell’s equations as mechanical law

Electrodynamics and special relativity are so deeply interconnected that it is difficult decide which of them is the logical consequence of the other, without running the risk of circular reasoning. Following the historical development by introducing electromagnetism phenomenologically first, this issue is not resolved but at best minimized, because even the Lorentz force law itself is fundamentally relativistic. Here we propose a derivation of Maxwell’s equations at a beginning graduate level with the goal of circumventing this difficulty. Based on prior work that establishes special relativity independently of any electrodynamic postulates, it is indeed possible to derive Maxwell’s equations from relativity by adding suitable assumptions. The contribution of the present work is to choose these assumptions in such a way that they can be regarded as extensions of the same postulates on which special-relativistic point-particle dynamics itself is based in the first place. The biggest leap is to extend the law of energy- and momentum conservation to the electromagnetic field itself. This hinges on the energy–momentum tensor, and the fact that the latter must account not only for the Lorentz force on a charge, but also for the forces exerted by that same charge on its environment.

Particle Dynamics with Elastic Collision at the Boundary: Existence and Partial Uniqueness of Solutions

We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega $ . Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics into a coupled system of second order ODEs with discontinuous right-hand side. The main contribution of this paper is to develop a precise solution concept for this particle system, and to prove existence of solutions. In this proof we construct a solution by passing to the limit in an auxiliary problem based on the Yosida approximation. In addition to existence of solutions, we establish a partial uniqueness theorem, and show by means of a counterexample that uniqueness of solutions cannot hold in general.

A correlational study: Establishing the link between quantum parameters and particle dynamics around Schwarzschild black hole

The field of point particle dynamics is correlated with the study of particle dynamics around the black hole and one can initiate the study of a more complex motion of extended/celestial bodies. In this article, we consider the study of the dynamics of the neutral/charged particles around the quantum corrected-Schwarzschild black hole and Schwarzschild black hole. We investigate Noether symmetries and their conservation laws corresponding to the quantum corrected-Schwarzschild spacetime. We also study the effect of angular momentum, quantum parameters and magnetic field on the dynamics of neutral and charged particles around the quantum corrected-Schwarzschild black hole and Schwarzschild black hole.

Emergent dynamics of the Lohe Hermitian sphere model with frustration

We study emergent dynamics of the Lohe Hermitian sphere (LHS) model, which can be derived from the Lohe tensor model [S.-Y. Ha and H. Park, SIAM J. Appl. Dyn. Syst. 13, 1312–1342 (2020)] as a complex counterpart of the Lohe sphere model. The LHS model describes aggregate dynamics of point particles on the Hermitian sphere HSd lying in Cd+1, and the coupling terms in the LHS model consist of two terms. For an identical ensemble with the same free flow dynamics, we provide a sufficient framework, leading to the complete aggregation in which all point particles form a giant one-point cluster asymptotically. In contrast, for a non-identical ensemble, we also provide a sufficient framework for the practical aggregation. Our sufficient framework is formulated in terms of coupling strengths and initial data. We also provide several numerical examples and compare them with analytical results.

Stochastic modeling for subgrid-scale particle dispersion in large-eddy simulation of inhomogeneous turbulence

We consider Lagrangian modeling of heavy particle motion in inhomogeneous turbulence. The dynamics of point particles is one-way coupled to the large-eddy simulation (LES) of fluid flow. To account for the effect of non-resolved (subgrid) flow scales on particle motion, we propose a model for the fluid velocity along the particle trajectories. The model, based on a stochastic diffusion process, accounts for turbulence anisotropy and utilizes the statistical estimates of subgrid quantities: the velocity components (the r.m.s. and covariance) and the Lagrangian time scales. The turbulent channel flow case is taken for validation. First, we discuss the outcome of an a priori LES study. Then, the proposed subgrid dispersion model is tested in a true LES computation. The resulting velocity statistics, particle concentration profiles, and the deposition velocity are compared against available reference data from direct numerical simulations.

T-duality and T-folds for point particles

We argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, we construct a four-parametric family of four-dimensional electro-gravitational backgrounds such that the dynamics of a charged point particle in those backgrounds is insensitive to a particular permutation of the parameters although this very permutation does alter the background geometry. In particular, we find that a direct product of the Euclidean plane with the two-dimensional Euclidean black hole admits a point-particle T-dual with asymptotically negative curvature. For neutral particles, this point-particle T-duality picture gets slightly modified because the T-duality map is no longer defined everywhere but only on a dense open domain of the space of states. We suggest a possible interpretation of this phenomenon in terms of a point particle T-fold.

Dynamics of particles around the time conformal quantum corrected Schwarzschild black hole

Abstract In this paper, we explore the dynamics of neutral and charged particles in presence/absence of magnetic field around the quantum corrected-Schwarzschild black hole as well as the time conformal quantum corrected-Schwarzschild black hole. We investigate the conditions under which the particles move towards or away from the vicinity of black hole when they collide with other particles. We study the effective potential and effective force in presence/absence of magnetic field graphically. Recently many researchers took interest in point particle dynamics and one can initiate the study of a more complex motion of extended celestial bodies. A major area of interest among these important fields, is the particle motions (neutral and charged) around black hole and naked singularities. In this work we want to show that the quantum corrected-Schwarzschild black hole admits the time conformal factor e ϵ g ( t ) without violating the symmetry structure of the black hole, where ϵ is a small parameter that causes perturbation in the proposed spacetime and g ( t ) is a function of time t . The inception of time conformal factor, re-scales all the conservation laws that hold in the given spacetime. This type of study is important because it tells about the formation of gravitational waves and Hawking radiation. The study of thermal stability, horizons and energy conditions corresponding to the time conformal quantum corrected Schwarzschild spacetime is also explored. Furthermore, we analyze and compare the dynamics of charged and neutral particle around time conformal quantum corrected-Schwarzschild black hole with the time conformal Schwarzschild black hole. The effective force and effective potential with magnetic field and angular momentum are given graphically. The stability of the proposed spacetime is also discussed with the help of Lyapunov exponent.

Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Stringy Newton gravity with H -flux

A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: \[ \begin{array}{lll} {\bf{\nabla}^{2}\Phi}=4\pi G \rho+\bf{H}{\bf{\cdot}}\bf{H}\,, \quad&\qquad\bf{\nabla}\bf{\cdot}\bf{H}=0\,, \quad&\qquad {\bf{\nabla}\bf{\times}\bf{H}}=4\pi G\, \bf{K}\,. \end{array} \] Not only the mass density $\rho$ but also the current density $\mathbf{K}$ is intrinsic to matter. Sourcing $\mathbf{H}$ which is of NS-NS $H$-flux origin, $\mathbf{K}$ is nontrivial if the matter is `stringy'. $\mathbf{H}$ contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e. $\bf{\ddot{x}}=-\bf{\nabla}\Phi$. We define `stringization' analogous to magnetization and discuss regular as well as monopole-like singular solutions.

Einstein-Nordström theory as a frame for a theory of quantum gravity

The Einstein-Nordström theory is proposed as a framework for a theory of quantum gravity, dividing the space of physical reality into a part longer than the radius of a proton and described by Einstein’s classical field theory of gravitation and one smaller than the radius of a proton, for the Yang–Mills theories of elementary particles, with both of them separated by a common event horizon. This division of space is reflected into the division of classical Newtonian point particle dynamics and Helmholtz line vortex dynamics, leading to a non-dimensional number for stable vortex line configurations, as for the stability of the Karman vortex street in classical fluid dynamics, and here for the non-dimensional mass ratio, of the Higgs particle mass to the Planck mass. Setting the vortex core radius of the line vortices equal to the Planck length, Lorentz invariance is broken for energies larger than the Planck energy, whereby the underlying more fundamental symmetry is the Galilei group, establishing a preferred reference system. With the Hamiltonian operator there commuting with the particle number operator, this permits the existence of negative, as well as positive masses.

A WKB approach to the quantum multiband electron dynamics in the kinetic formalism

We derive a WKB-like asymptotic expansion of the multiband Wigner function. The model, derived in the envelope function theory, is designed to describe the dynamics in semiconductor devices when the interband conduction-valence transition cannot be neglected. We derive a hierarchy of equations that to lowest order consist of two HamiltonJacobi equations corresponding to the classical dynamics of point particles with positive and negative kinetic energy. Our methodology is based on the Van Vleck approach and a WKB-like asymptotic expansion procedure is used to reduce the numerical complexity of the Wigner multiband evolution system. An approximate closed-form solution is obtained by an iterative procedure that exploits the different time scales on which the intraband and interband dynamical variables evolve. The interband tunneling mechanism appearing to the first order of the expansion is expressed in a very simple mathematical form. By exploiting the highly oscillating behaviour of the multiband Wigner functions we derive a asymptotic expression of the interband transition probability. The resulting formulation reveals particularly close to the classical description of the particles motion and this formal analogy is useful to gain new physical insight and to profit of the numerical method developed for classical systems. The approximates evolution equations are used to simulate the evolution of the Wigner quasi-distribution function in a IRTD diode.

Waveform systematics for binary neutron star gravitational wave signals: Effects of the point-particle baseline and tidal descriptions

Gravitational wave (GW) astronomy has consolidated its role as a new observational window to reveal the properties of compact binaries in the Universe. In particular, the discovery of the first binary neutron star coalescence, GW170817, led to a number of scientific breakthroughs as the possibility to place constraints on the equation of state of cold matter at supranuclear densities. These constraints and all scientific results based on them require accurate models describing the GW signal to extract the source properties from the measured signal. In this article, we study potential systematic biases during the extraction of source parameters using different descriptions for both, the point-particle dynamics and tidal effects. We find that for the considered cases the mass and spin recovery show almost no systematic bias with respect to the chosen waveform model. However, the extracted tidal effects can be strongly biased, where we find generally that Post-Newtonian approximants predict neutron stars with larger deformability and radii than numerical relativity tuned models. Noteworthy, an increase in the Post-Newtonian order in the tidal phasing does not lead to a monotonic change in the estimated properties. We find that for a signal with strength similar to GW170817, but observed with design sensitivity, the estimated tidal parameters can differ by more than a factor of two depending on the employed tidal description of the waveform approximant. This shows the current need for the development of better waveform models to extract reliably the source properties from upcoming GW detections.

Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids

We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations, and are obtained from standard relativistic hydrodynamics in the limit of infinite or vanishing velocity of light. All dissipative phenomena such as friction and heat conduction are included in our description. Part of our work consists in designing the appropriate coordinate frames for relativistic spacetimes, invariant under Galilean or Carrollian diffeomorphisms. The guide for the former is the dynamics of relativistic point particles, and leads to the Zermelo frame. For the latter, the relevant objects are relativistic instantonic space-filling branes in Randers–Papapetrou backgrounds. We apply our results for obtaining the general first-derivative-order Galilean fluid equations, in particular for incompressible fluids (Navier–Stokes equations) and further illustrate our findings with two applications: Galilean fluids in rotating frames or inflating surfaces and Carrollian conformal fluids on two-dimensional time-dependent geometries. The first is useful in atmospheric physics, while the dynamics emerging in the second is governed by the Robinson–Trautman equation, describing a Calabi flow on the surface, and known to appear when solving Einstein’s equations for algebraically special Ricci-flat or Einstein spacetimes.

Cold Active Motion: How Time-Independent Disorder Affects the Motion of Self-Propelled Agents.

Assemblages of self-propelled particles, often termed active matter, exhibit collective behavior due to competition between neighbor alignment and noise-induced decoherence. However, very little is known of how the quenched (i.e., time-independent) disorder impacts active motion. Here we report on the effects of quenched disorder on the dynamics of self-propelled point particles. We identified three major types of quenched disorder relevant in the context of active matter: random torque, force, and stress. We demonstrate that even in the absence of external fluctuations ("cold active matter"), quenched disorder results in nontrivial dynamic phases not present in their "hot" counterpart. In particular, by analyzing when the equations of motion exhibit a Hamiltonian structure and when attractors may be present, we identify in which scenarios particle trapping, i.e., the asymptotic convergence of particle trajectories to bounded areas in space ("traps"), can and cannot occur. Our study provides new fundamental insights into active systems realized by self-propelled particles on natural and synthetic disordered substrates.

Computational study of radial particle migration and stresslet distributions in particle-laden turbulent pipe flow

.Particle-laden turbulent flows occur in a variety of industrial applications as well as in naturally occurring flows. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we employ a fully-resolved numerical simulation based on a lattice Boltzmann scheme, to investigate turbulent flow with large neutrally buoyant particles in a pipe flow at low Reynolds number and in dilute regimes. The energy input is kept fixed resulting in a Reynolds number based on the friction velocity around 250. Two different particle radii were used giving a particle-pipe diameter ratio of 0.05 and 0.075. The number of particles is kept constant resulting in a volume fraction of 0.54% and 1.83%, respectively. We investigated Eulerian and Lagrangian statistics along with the stresslet exerted by the fluid on the spherical particles. It was observed that the high particle-to-fluid slip velocity close to the wall corresponds locally to events of high energy dissipation, which are not present in the single-phase flow. The migration of particles from the inner to the outer region of the pipe, the dependence of the stresslet on the particle radial positions and a proxy for the fragmentation rate of the particles computed using the stresslet have been investigated.Graphical abstract

Simulation of Finite-Size Particles in Turbulent Flows Using the Lattice Boltzmann Method

Particle laden turbulent flows occur in a variety of industrial applications. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we will present results on the development of numerical algorithms, based on the lattice Boltzmann method, suitable for the study of suspensions of finite-size particles under turbulent flow conditions. The turbulent flow is modeled by the lattice Boltzmann method, and the interaction between particles and carrier fluid is modeled using the bounce-back rule. Direct contact and lubrication force models for particle-particle interactions and particle-wall interaction are taken into account to allow for a full four-way coupled interaction. The accuracy and robustness of the method is discussed by validating the velocity profile in turbulent pipe flow, the sedimentation velocity of spheres in duct flow and the resistance functions of approaching particles. Preliminary results from the turbulent pipe flow simulations with particles show that the angular and axial velocities of the particles are scattered around values of mean axial velocity and shear rate obtained from the Eulerian velocity field.

An effective theory of metrics with maximal proper acceleration

A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point particles should hold, the notion of a generalized metric and a theory of maximal proper acceleration are introduced. A perturbative approach to metrics of maximal proper acceleration is discussed and we show how it provides a consistent theory where the associated Lorentzian metric corresponds to the limit when the maximal proper acceleration goes to infinity. Then several of the physical and kinematical properties of the maximal acceleration metric are investigated, including a discussion of the rudiments of the causal theory and the introduction of the notions of radar distance and celerity function. We discuss the corresponding modification of the Einstein mass-energy relation when the associated Lorentzian geometry is flat. In such a context it is also proved that the physical dispersion relation is relativistic. Two possible physical scenarios where the modified mass–energy relation could be confronted against the experiment are briefly discussed.