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In this work, we have presented a detailed analysis of the event horizon of regular black holes (BHs) in modified gravity known as MOG, the so-called regular MOG BH. The motion of neutral particles around the BH has also been explored. The test particle motion study shows that the positive (negative) values of the MOG parameter mimic the spin of a rotating Kerr BH, providing the same values for the innermost stable pro-grade (retrograde) orbits of the particles in the range of the spin parameter a/M∈(−0.4125,0.6946). The efficiency of energy release from the accretion disk by the Novikov–Thorne model has been calculated, and the efficiency was shown to be linearly proportional to the increase of the MOG parameter α. Moreover, we have developed a new methodology to test gravity theories in strong-field regimes using precision data from twin-peaked quasiperiodic oscillations (QPOs) of objects calculating possible values of upper and lower frequencies. However, it is obtained that the positive MOG parameter can not mimic the spin of Kerr BHs in terms of the same QPO frequencies. We have provided possible ranges for upper and lower frequencies of twin-peak QPOs with the ratio of the upper and lower frequencies of 3:2 around regular MOG BHs in the different models. Moreover, as an example, we provide detailed numerical analysis of the QPO of GRS 1915+105 with the frequencies νU=168±5Hz and νL=113±3Hz. It is shown that the central BH of the QPO object can be a regular MOG BH when the value of the parameter is α=0.2844−0.1317+0.0074 and shines in the orbits located at the distance r/M=7.6322−0.0826+0.0768 from the central BH. It is also shown that the orbits where QPOs shine are located near the innermost stable circular orbit (ISCO) of the test particle. The correlation between the radii of ISCO and the QPO orbits is found, and it can be used as a new theoretical way to determine ISCO radius through observational data from the QPOs around various compact objects.

Viscoelastic fluids impact the locomotion of swimming microorganisms and can be harnessed to devise new types of self-propelling devices. Here we report on experiments demonstrating the use of normal stress differences for propulsion. Rigid dumbbells are rotated by an external magnetic field along their axis of symmetry in a Boger fluid. When the dumbbell is asymmetric (snowman geometry), non-Newtonian normal stress differences lead to net propulsion in the direction of the smaller sphere. The use of a simple model allows to rationalise the experimental results and to predict the dependence of the snowman swimming speed on the size ratio between the two spheres.

This article presents alternative Hamiltonian and Lagrangian formalisms for relativistic mechanics using proper time and proper Lagrangian coordinates in 1 + 1 dimensions as parameters of evolution. The Lagrangian and Hamiltonian formalisms for a hypothetical particle with and without charge are considered based on the relativistic equation for the dynamics and integrals of particle motion. A relativistic invariant law for the conservation of energy and momentum in the Lorentz representation is given. To select various generalized coordinates and momenta, it is possible to modify the Lagrange equations of the second kind due to the relativistic laws of conservation of energy and momentum. An action function is obtained with an explicit dependence on the velocity of the relativistic particles. The angular integral of the particle motion is derived from Hamiltonian mechanics, and the displacement Hamiltonian is obtained from the Hamilton–Jacobi equation. The angular integral of the particle motion θ is an invariant form of the conservation law. It appears only at relativistic intensities and is constant only in a specific case. The Hamilton–Jacobi–Lagrange equation is derived from the Hamilton–Jacobi equation and the Lagrange equation of the second kind. Using relativistic Hamiltonian mechanics, the Euler–Hamilton equation is obtained by expressing the energy balance through the angular integral of the particle motion θ. The given conservation laws show that the angular integral of the particle motion reflects the relativistic Doppler effect for particles in 1 + 1 dimensions. The connection between the integrals of the particle motion and the doubly special theory of relativity is shown. As an example of the applicability of the proposed invariant method, analyses of the motion of relativistic particles in circularly polarized, monochromatic, spatially modulated electromagnetic plane waves and plane laser pulses are given, and comparisons are made with calculations based on the Landau and Lifshitz method. To allow for the analysis of the oscillation of a particle in various fields, a phase-plane method is presented.

Størmer's particles' trapping regions for a planet with an intrinsic dipolar magnetic field are considered, taking into account the ring current which arises due to the trapped particles' drift for the case of the Earth. The influence of the ring current on the particle trapping regions' topology is investigated. It is shown that a critical strength of the ring current exists under which further expansion of the trapping region is no longer possible. Before reaching this limit, the dipole field, although deformed, retains two separated Størmer regions. After transition of critical magnitude, the trapping region opens up, and charged particles, which form the ring current, get the opportunity to leave it, thus decreasing the ring current strength. Numerical calculations have been performed for protons with typical energies of the Earth's radiation belt and ring current. For the Earth's case, the Dst index for the critical ring current strength is calculated.

Rayleigh waves often propagate according to complex mode excitation so that the proper identification and separation of specific modes can be quite difficult or, in some cases, just impossible. Furthermore, the analysis of a single component (i.e., an inversion procedure based on just one objective function) necessarily prevents solving the problems related to the non-uniqueness of the solution. To overcome these issues and define a holistic analysis of Rayleigh waves, we implemented a procedure to acquire data that are useful to define and efficiently invert the three objective functions defined from the three following “objects”: the velocity spectra of the vertical- and radial-components and the Rayleigh-wave particle motion (RPM) frequency-offset data. Two possible implementations are presented. In the first case we consider classical multi-offset (and multi-component) data, while in a second possible approach we exploit the data recorded by a single three-component geophone at a fixed offset from the source. Given the simple field procedures, the method could be particularly useful for the unambiguous geotechnical exploration of large areas, where more complex acquisition procedures, based on the joint acquisition of Rayleigh and Love waves, would not be economically viable. After illustrating the different kinds of data acquisition and the data processing, the results of the proposed methodology are illustrated in a case study. Finally, a series of theoretical and practical aspects are discussed to clarify some issues involved in the overall procedure (data acquisition and processing).

There has been in the past decade a significantly growing interest in the use of flow-induced lift forces for a passive control of particle motion in microchannels. This nonlinear microfluidic technique can be implemented in both Newtonian and non-Newtonian fluids. The motions of rigid particles in confined flows of viscoelastic fluids with and without shear-thinning effects have each been well studied in the literature. However, a comprehensive understanding of particle motion in inelastic shear-thinning fluids is still lacking. We present herein a systematic experimental study of the motion of rigid particles in the Poiseuille flow of pseudoplastic xanthan gum (XG) solutions through straight rectangular microchannels. We find that the number and location of particle equilibrium positions are both a strong function of channel dimension, particle size and XG concentration. We attempt to explain the experimental observations using the competition of inertial and elastic lift forces acting on particles. Our experimental results imply a potentially high throughput separation of rigid particles by size in XG solutions.

A novel hydrocyclone sand washer featured by connecting a cylindrical hydrocyclone and a conical-cylindric hydrocyclone in series was developed to improve the poor grading performance in current machine-made sand processing technology. The former hydroycyclone with a flat bottom was designed to enhance the centrifugal intensity, thereby achieving the pre-grading of fine and coarse particles and ensuring the discharge of most fine mud particles from the overflow pipe. The latter hydrocyclone was designed to achieve the secondary fine separation and therefore reduce the content of fine particles in the underflow product. Firstly, the flow field inside the consecutive hydrocyclones was simulated using an RSM and VOF model. The DPM model was introduced to trace the particle motion trajectory and validate the feasibility of hydrocyclone separation. Then, the experimental study was performed using the control variable method, and the effects of the first-section overflow pipe diameter, the feeding rate, and the mud–sand mixing ratio on the desliming performance were examined. Results show that the content of particles with a diameter of below 75 μm in the second-section underflow drops significantly after the separation in the hydrocyclone sand washer. When the first-section overflow pipe diameter, the feeding rate, and the mud–sand mixing ratio are set to 34 mm, 60 kg/h and 1:1, respectively, the desliming rate of the novel hydrocyclone sand washer can reach 94.31% and the loss rate of quartz sand is only 1.28%.

The charged particle motion for certain configurations of oscillating magnetic fields can be simulated by a Volterra integro-differential equation of the second order with time-periodic coefficients. This paper investigates a simple and accurate scheme for computationally solving these types of integro-differential equations. To start the method, we first reduce the integro-differential equations to equivalent Volterra integral equations of the second kind. Subsequently, the solution of the mentioned Volterra integral equations is estimated by the collocation method based on the local multiquadrics formulated on scattered points. We also expand the proposed method to solve fractional integro-differential equations including non-integer order derivatives. Since the offered method does not need any mesh generations on the solution domain, it can be recognized as a meshless method. To demonstrate the reliability and efficiency of the new technique, several illustrative examples are given. Moreover, the numerical results confirm that the method developed in the current paper in comparison with the method based on the globally supported multiquadrics has much lesser volume computing.

An efficient system for the joint acquisition and analysis of multi-component active and passive seismic data is presented. It is shown how, in spite of the limited field equipment (the system requires just a 4-channel seismograph, one 3-component and four vertical-component geophones), it is nevertheless possible to define up to seven different (but mutually related and complementary) objects used to constrain a multi-objective joint inversion capable of providing a robust subsurface shear-wave velocity ( V S ) profile for both geotechnical and seismic-hazard studies. The presented approach relies on acquisition techniques that require simple and straightforward field procedures useful in particular, but not solely, in the characterization of urban and remote areas where, due to logistical problems, standard acquisition procedures cannot be easily applied. Active data recorded by a single 3-component geophone are processed so to define up to five objective functions: the group-velocity spectra of the three components, the radial-to-vertical spectral ratio and the Rayleigh-wave particle motion frequency curve. Passive data are used to compute two further objects: the horizontal-to-vertical spectral ratio and the phase-velocity dispersion curve obtained via miniature array analysis of microtremors. These seven objects are jointly inverted by means of a multi-objective inversion procedure based on the Pareto criterion. Performances are assessed through a comprehensive field dataset acquired in an urban area of NW-Italy. The consistency of the overall procedure is assessed by comparing the results with the analyses accomplished by considering classical multi-channel active and passive data and methodologies (multi-component MASW, multichannel analysis of surface waves and ESAC, extended spatial auto-correlation).

The recently built China Digital Seismic Network consists of the China National Digital Seismic Network (CNDSN), 31 regional seismic networks and several small aperture arrays with more than 1 000 stations including 850+ broadband stations. It forms a gigantic seismic array that provides an unprecedented opportunity to study the Earth’s deep interior besides its routine task of seismic monitoring. Many modern seismic studies rely on rotation of vertical and horizontal components in order to separate different types of seismic waves. Knowledge of the orientations of the two horizontal components thus is important to perform a correction rotation. We analyzed particle motions of teleseismic P waves recorded by the network and used them to estimate the north-component azimuth of each station. An SNR-weighted-multi-event method was introduced to obtain component azimuths that best explain the P-wave particle motions of all the events recorded at a station. The method provides robust estimates including a measurement error calculated from background noise levels. We found that about one third of the stations have some sort of problems, including misorientation of the two horizontal components, mislabeling and polarity reversal in one or more components. These problems need to be taken into account for any rotation based seismic studies.