Particle Equations Research Articles

Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe

For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov’s gravitational-wave models of spacetime and allow the existence of complete integrals of the Hamilton–Jacobi equation for test particles. For all the solutions obtained, the analytical form of the tidal acceleration vector in a strong primordial gravitational wave is obtained. An explicit form of the coordinate transformation, an explicit form of the metric of the primordial gravitational wave of the Bianchi type VI universe, and the form of the tidal acceleration vector in the laboratory synchronous coordinate system are obtained. The synchronous coordinate system is associated with a freely falling observer and allows the observer to separate time and spatial coordinates, as well as to synchronize time at different points in space. The presented mathematical approach can be applied both in the general theory of relativity and in modified theories of gravity.

Generalized Langevin equation for solute dynamics in fluids with time-dependent friction

The generalized Langevin equation (GLE) for a Brownian particle (BP) in a bath under the influence of a moving external harmonic potential is derived. It is assumed that the friction coefficients of the bath particles depend on time. The found GLE has the usual form but its memory kernel is a generalization of the expression known as a Prony series used to approximate a number of memory functions from the literature. Analytical solutions are obtained for the mean and mean squared displacements assuming the overdamped character of motion of the BP.

Interaction of Nanoparticles in Electrolyte Solutions.

The interaction between nanoparticles includes several components; however, the most frequently used are electrostatic, caused by overlapping double electrical layers, and London-van der Waals interactions, caused by quantum and thermodynamic fluctuations of electromagnetic fields. Only these two kinds of interaction are considered below. The electrostatic interaction is calculated based on the linearized Poisson-Boltzmann equation for particles with constant electrical potential of the surfaces (constant ζ potentials). An exact solution of the problem is obtained for both identical particles and particles of different sizes. For the London-van der Waals interaction, the screening of static fluctuations and the retardation of electromagnetic fields for the dispersive part of the interaction are taken into account. The total interaction energy for two particles was calculated for a range of possible nanoparticle sizes from 1 to 103 nm and electrolyte concentration from 10-2 to 10-6 mol/L. The predominance of the London-van der Waals force over the shielded electrostatic repulsion force was found at high electrolyte concentrations in the range from 10-2 to 10-3 mol/L at large interparticle distances.

Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

ABSTRACT This work investigates the evolution of the distribution of charged particles (cosmic rays) due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasi-linear approximation, and by assuming turbulent spectra with power being available only in the sub-gyroscale range, we find that the Fokker–Planck diffusion coefficients Dγγ and Dμμ scale with the Lorentz factor γ as Dγγ ∝ γ−2/3 and Dμμ ∝ γ−8/3. We consider Alfvèn and fast waves in our calculations, and find a universal trend for the momentum diffusion coefficient irrespective of the properties of the small-scale turbulence. Such universality has already been reported regarding the spatial diffusion of the cosmic rays, and, here too, we observe a universality in the momentum diffusion coefficient. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion-type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss, and particle escape on the particle distribution by systematically varying the parameters of the problem. We observe that the effect of the small-scale turbulence is more impactful for the high-energy protons as compared to the electrons and such turbulence is capable of sustaining the energy of the protons from catastrophic radiative loss processes. Such a finding is novel and helps us to enhance our understanding about the hadronic emission processes that are typically considered as a competitor for the leptonic emission for certain astrophysical systems.

Strong decays of {P}_{psi}^N{(4312)}^{+} to J/ψ(ηc)p and {overline{D}}^{left(ast right)}{Lambda}_c within the Bethe-Salpeter framework

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of {P}_{psi}^N{(4312)}^{+} as the overline{D}{Sigma}_c molecular state in isospin- frac{1}{2} . We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a frac{1}{2} baryon. By solving the Bethe-Salpeter equation, we obtain {P}_{psi}^N{(4312)}^{+} as the overline{D}{Sigma}_c molecular state with JP = {left(frac{1}{2}right)}^{-} . Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of {P}_{psi}^N{(4312)}^{+} to J/ψp, ηcp, {overline{D}}^{ast 0}{Lambda}_c^{+} and {overline{D}}^0{Lambda}_c^{+} are calculated to be 0.17, 0.085, 8.8, and 0.026 MeV, respectively, which are roughly consistent with the LHCb experimental measurements and some other theoretical researches. The obtain results indicate the fraction of {overline{D}}^{ast 0}{Lambda}_c^{+} channel amounts to ~ 90% of {P}_{psi}^N{(4312)}^{+} , and is a highly promising channel to be discovered in the near future experiments. Our results favor the interpretation of {P}_{psi}^N{(4312)}^{+} as the overline{D}{Sigma}_c molecular state with JP = {left(frac{1}{2}right)}^{-} and isospin I = frac{1}{2} .

Program for quantum wave-packet dynamics with time-dependent potentials (new version announcement)

wavepacket is a program to simulate the dynamics of a wave packet interacting with a time-dependent potential, with the time-dependent Schrödinger equation being solved on a one-, two-, or three-dimensional spatial grid using the split operator method. This new version fixes bugs present in the original program. New version program summaryProgram Title: wavepacketCPC Library link to program files:https://doi.org/10.17632/gnxmkygxrw.1Licensing provisions: GPLv3Programming language: C (iso C99)Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 407–414.Does the new version supersede the previous version?: YesReasons for the new version: Bug fixes.Summary of revisions: This new version fixes bugs in the program wavepacket [1]. In the original version, the function print_wf_bin, used (optionally) to write out the wave function as a binary file, contained a bug that would result in only part of the full wave function being written out when the program was run in parallel.Additionally, negative values of the parameters nt and/or nprint could lead to the program being stuck in an infinite loop. Additional checks have been added to ensure that both these parameters are positive (or zero).Nature of problem: Solves the time-dependent Schrödinger equation for a single particle interacting with a time-dependent potential.Solution method: The wave function is described by its value on a spatial grid and the evolution operator is approximated using the split-operator method [2,3], with the kinetic energy operator calculated using a Fast Fourier Transform.Additional comments including restrictions and unusual features: Simulation can be in one, two, or three dimensions. The fftw [4] implementation of the fast Fourier transform is used, so the corresponding library must be installed. Serial and parallel versions are compiled from the same source files. The parallel version is based on the Message-Passing Interface (mpi) [5].

Motion equations in a Kerr–Newman–de Sitter spacetime: some methods of integration and application to black holes shadowing in Scilab

In this paper, we recall some basic facts about the Kerr–Newman–(anti) de Sitter (KNdS) spacetime and review several formulations and integration methods for the geodesic equation of a test particle in such a spacetime. In particular, we introduce some basic general symplectic integrators in the Hamiltonian formalism and we re-derive the separated motion equations using Carter’s method. After this theoretical background, we explain how to ray-trace a KNdS black hole, equipped with a thin accretion disk, using Scilab. We compare the accuracy and execution time of the previous methods, concluding that the Carter equations is the best one. Then, inspired by Hagihara, we apply Weierstrass’ elliptic functions to the non-rotating case, yielding a fairly fast shadowing program for such a spacetime. We provide some illustrations of the code, including a depiction of the effects of the cosmological constant on shadows and accretion disk, as well as a simulation of M87*.

A Mathematical Approach to the Momentum Equations of Massless Photon and Particle with Relativistic Mass

A Mathematical Approach to the Momentum Equations of Massless Photon and Particle with Relativistic Mass

Degenerate wave-like solutions to the Dirac equation for massive particles

In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like electromagnetic fields corresponding to these solutions. We show that the state of the particles does not depend on the intensity of the electromagnetic fields, but only on their frequency, which is proportional to the mass of the particles and lies in the region of Gamma/X-rays for typical elementary charged particles, such as electrons and protons. We have also calculated the electric current density corresponding to the electromagnetic 4-potentials connected to the degenerate solutions and found that it has the same spatial and temporal dependence on the electromagnetic fields, rotating at an exceptionally high frequency. This result indicates that the degenerate states may occur at locations where matter collapses, e.g., in the central region of a black hole. Finally, we have calculated the spin of the particles described by degenerate spinors and found that it rotates in synchronization with the magnetic field and the current density.

Simulation of DC glow discharge plasma with free-moving dust particles in the radial direction

A self-consistent fluid model is developed to investigate the radial distributions of dusty plasma parameters in a DC glow discharge, in which the extended fluid approach of plasma particles and the transport equations of dust particles are coupled. The electrical interaction between charged dust particles is considered in the model. The time evolution of radial distributions of dust density, plasma density, the radial component of electric field and the forces acting on dust particles when dust density tends to be stable, are obtained and analyzed under different discharge currents and dust particle radii. It is shown that the dust density structure is determined mainly by the radial electrostatic force, thermophoretic force and ion drag force in the discharge tube, and both discharge current and dust particle radius have an obvious effect on the transport processes of dust particles. The dust particles gather in the central region of the discharge tube for low discharge current and small dust radius, then dust voids are formed and become wider when the discharge current and dust radius increase. The plasma parameters in the dust gathering region are obviously affected by the dust particles due to the charging processes of electrons and ions to the dust surface.

Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterized by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.

Role of impurity and thermal noise on the radiation sources in ITER using DT fuel

Abstract In this paper, the time evolution of bremsstrahlung radiation loss, plasma frequency and electron particles density and the relationship between these parameters and black body radiation are investigated. The model used in this work is based on numerical solution of particle and energy balance equations in ITER with DT fuel. The fusion reaction takes places in a plasma of deuterium and tritium heated to millions of degrees. It is expected that at this temperature, the thermal noise could have a significant effect on plasma behavior. This effect is considered in the solution of equations for the first time in this work. In order to attain a proper set of particle and energy balance equations, an appropriate thermal noise term is considered in the set of coupled differential equations. These equations are solved simultaneously by numerical methods. The results of the calculations for bremsstrahlung radiation loss, plasma frequency, intensity of blackbody radiation, absorption coefficient and quality factor show that in the absence of thermal noise blackbody radiation doesn’t occur but in the presence of thermal noise blackbody radiation occurs in times of 55.7 s and 42.73 s for two cases of considering and ignoring impurity respectively. As it can be seen that with the addition of impurities to the system, bremsstrahlung radiation and intensity of blackbody radiation increase while absorption coefficient and quality factor decrease.

Common Features of Free Particle Wave Functions in Curved Space-times

Quantum equations for massless particles of any spin and for massive spin one-half particles are considered in curved space-times. It is demonstrated that in stationary axially symmetric space-times the angular wave functions up to a normalization function are the same as in a Minkowski space-time. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms which depend in a unique form on the ratio of time to space curvatures. For a Dirac spin one-half particle, in addition to these three terms a fourth term which depends on the particle rest mass is added.

Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is less incompatible with quantum mechanics -- should admit energy nonconservations. This paper begins by identifying the conditions for a theory to have an energy-momentum tensor that is not conserved. Then, the trajectory equation for pointlike particles that lose energy is derived, showing that energy nonconservation produces a particular acceleration. As an example, the unimodular theory of gravity is studied. Interestingly, in spherical symmetry, given that there is a generalized Birkhoff theorem and that the energy-momentum tensor divergence is a closed form, the trajectories of test particles that lose energy can be found using well known methods. Finally, limits on the energy nonconservation parameters are set using Solar system observations.

Estimation of the Just Suspension Speed of Mixed Particles in a Solid-Liquid Stirred Tank

Based on the model equation for homogeneous particles, we propose a model equation for just suspension speed for mixed particles. If the correlation equation of Zwietering holds, the just suspension speed of mixed particles [njs,mix(XT)] is given as a function of the volume fraction of particle i (φi) and the just suspension speed of uniform particle i [njs,i(XT)]. njs,mix(XT)=[∑injs,i(XT)20/3φi∑injs,i(XT)10/3φi]3/10 The calculated values using the proposed model equation were in close agreement with the experimental data. Furthermore, the results were in good agreement with the literature data for mixed particles containing four-component system. The study also confirmed the usefulness of the proposed model equation, since the existing correlation equation did not correlate well with the experimental data.

Kaon condensation in skyrmion matter and compact stars

We address the possibility of the appearance of a charged kaon condensate in neutron star cores described within a generalized Skyrme model. Our treatment of strange degrees of freedom is based on the Bound State Approach by Callan and Klebanov, which allows to obtain an in-medium effective potential for the $s$-wave kaon condensate. We predict the onset of kaon condensation at a certain threshold density - whose value depends on the parameters of the model, and ranges between 1.5 and 2.5 times saturation density -, and obtain both the particle fractions and equation of state for dense matter in the kaon condensed phase. Finally, we discuss the effect of such condensates on the mass-radius curves and other observable properties of neutron stars with kaon condensed cores.

A prediction model for magnetic particle imaging–based magnetic hyperthermia applied to a brain tumor model

Background and objectiveBrain tumor is a global health concern at the moment. Thus far, the only treatments available are radiotherapy and chemotherapy, which have several drawbacks such as low survival rates and low treatment efficacy due to obstruction of the blood-brain barrier. Magnetic hyperthermia (MH) using magnetic nanoparticles (MNPs) is a promising non-invasive approach that has the potential for tumor treatment in deep tissues. Due to the limitations of the current drug-targeting systems, only a small proportion of the injected MNPs can be delivered to the desired area and the rest are distributed throughout the body. Thus, the application of conventional MH can lead to damage to healthy tissues. MethodsMagnetic particle imaging (MPI)-guided treatment platform for MH is an emerging approach that can be used for spatial localization of MH to arbitrarily selected regions by using the MPI magnetic field gradient. Although the feasibility of this method has been demonstrated experimentally, a multidimensional prediction model, which is of crucial importance for treatment planning, has not yet been developed. Hence, in this study, the time dependent magnetization equation derived by Martsenyuk, Raikher, and Shliomis (which is a macroscopic equation of motion derived from the Fokker-Planck equation for particles with Brownian relaxation mechanism) and the bio-heat equations have been used to develop and investigate a three-dimensional model that predicts specific loss power (SLP), its spatio-thermal resolution (temperature distribution), and the fraction of damage in brain tumors. ResultsBased on the simulation results, the spatio-thermal resolution in focused heating depends, in a complex manner, on several parameters ranging from MNPs properties to magnetic fields characteristics, and coils configuration. However, to achieve a high performance in focused heating, the direction and the relative amplitude of the AC magnetic heating field with respect to the magnetic field gradient are among the most important parameters that need to be optimized. The temperature distribution and fraction of the damage in a simple brain model bearing a tumor were also obtained. ConclusionsThe complexity in the relationship between the MNPs properties and fields parameter imposes a trade-off between the heating efficiency of MNPs and the accuracy (resolution) of the focused heating. Therefore, the system configuration and field parameters should be chosen carefully for each specific treatment scenario. In future, the results of the model are expected to lead to the development of an MPI-guided MH treatment platform for brain tumor therapy. However, for more accurate quantitative results in such a platform, a magnetization dynamics model that takes into account coupled Néel-Brownian relaxation mechanism in the MNPs should be developed.

Study on the Characteristics and Model Optimization of Coal Particle Gas Emission Law.

In order to further clarify the transport mechanism of coalbed methane and to study the gas diffusion law in coal, this paper conducted an experimental study on the desorption law of coal particle gas. On the basis of experiment, the time-varying characteristics of the diffusion coefficient in the process of coal particle gas desorption were analyzed, and the gas diffusion calculation model considering the time-varying diffusion coefficient was obtained by experimental fitting. On this basis, the influence of coal particles with different shapes on the gas desorption law is studied, and the gas diffusion equations of flat and cylindrical coal particles based on time-varying diffusion coefficients are established. The corresponding analytical solutions are obtained by using mathematical and physical methods, and the results are verified. The results show that the larger the adsorption equilibrium pressure is, the larger the gas desorption capacity is. At the initial stage of desorption, the larger the particle size is, the smaller the desorption capacity and desorption speed are. However, after reaching the "limit particle size", the particle size has little influence on the desorption capacity and desorption speed. Under different temperature conditions, the gas desorption amount monotonously increases with time. The higher the temperature is, the greater the desorption amount is. The adsorption constant a value slightly increases with the increase of temperature and then decreases. The adsorption constant b value has a trend of decreasing with the increase of temperature. The research results have very important practical significance for the optimization of the testing method of underground coalbed methane content and the prediction of coal and gas outburst risk.

Hawking radiation as tunneling with pressure and volume of the RN-AdS black hole

In consideration of the thermodynamic pressure and volume, we present a short and direct derivation of Hawking radiation as a tunneling process for the charged particles. Using Parikh's Semi-classical tunneling method and Lagrangian analysis on the action, we provide the geodesic equation of the massive particles via tunneling from the Anit-de Sitter (AdS) black hole. Special attention is given to calculating the imaginary part before and after particles via the horizon as the pressure and volume are considered. The result shows that the emission rates are always related to the change of Bekenstein-Hawking entropy and the exact spectrum is not precisely thermal, which are consistent with the case without pressure and volume.

Black hole information recovery from gravitational waves

We study the classical and quantum black hole information in gravitational waves from a black hole’s history. We review the necessary concepts regarding quantum information in many-body systems to motivate information retrieval and content in gravitational waves. We then show the first step in an optimal information retrieval strategy is to search for information in gravitational waves, compared to searching for correlations in Hawking radiation. We argue a large portion of the information of the initial collapsing state may be in the gravitational waves. Using the Zerilli equation for particles falling radially into Schwarzschild black holes, we then describe a method to retrieve full classical information about infalling sources, including masses, infall times and angles.