Arbitrary Point Research Articles

High-energy head-on particle collisions near event horizons: Classification of scenarios

In this paper, we consider head-on collisions of two particles near the event horizon. Particle 1 is outgoing, particle 2 is ingoing. We elucidate the conditions when the energy [Formula: see text] in the center of mass frame can grow unbounded. In doing so, we dispel some misconceptions popular in the literature on high energy collisions near black holes and carry out clear distinction when such a collision happens near a black hole and when this occurs near a white one. If the proper time between the horizon and an arbitrary point outside it for particle 1 is finite, we deal with a white hole. If it is infinite, we deal with a black hole. Particles can be either free or experience the action of a finite force. Our results are complementary to those for the standard BSW effect when particles move in the same direction. The results rely on classification of particles developed in our previous work Ovcharenko and Zaslavskii [Phys. Rev. D 108 (2023) 064029]. The aforementioned article performed the first step towards a building classification of all possible high energy collisions near black/white hole for different types of horizons and nonzero force. In this paper, we perform the second step.

Building a model of oil tank water cooling in the case of fire

The object of this study is the process of liquid combustion in spillage, and the subject is the temperature distribution along the wall of a vertical steel tank when it is heated under the thermal influence of fire and cooled by water. A system of equations describing the water cooling of the wall of a vertical steel tank under the conditions of the thermal effect of a fire spilling a flammable liquid has been constructed. The system consists of a heat balance equation for the tank wall, a heat balance equation for the water film flowing over the wall, and a mass balance equation for the water film. The equations take into account the radiative heat exchange with the flame, the environment, the internal space of the tank, as well as the convective heat exchange with the surrounding air, the vapor-air mixture, and the liquid inside the tank, as well as between the water film and the wall. The joint solution to the system of equations makes it possible to determine the temperature distribution along the tank wall and the water film at an arbitrary time point, as well as to determine the thickness and flow rate of the water film at a certain point. The finite difference method was used to solve the system of heat and mass balance equations. It is shown that the insufficient intensity of water supply for cooling leads to boiling of water from the film, as a result of which the wall temperature in such areas can reach 300 °C. A delay in the supply of water, even with sufficient intensity, could lead to the establishment of a film-like mode of boiling. In such a situation, the water film is thrown away from the wall, as a result of which the part of the wall below the film boiling zone remains without cooling. The practical significance of the built model is the possibility of determining the necessary intensity of water supply for cooling the tank and the limit time for the start of cooling

Determination of Velocities of Thread Axis Points When Interacting with a Direct Large Curvature Taking into Account the Deformation in the Contact Zone

The theoretical study of the process of the movement of the thread, which is deformed in the contact zone with the guide, from the point of view of determining the speed, is of great importance for solving a number of specific applied problems. When determining the speed, it was assumed that the start of the Lagrangian and Euler coordinates coincided. Taking into account that the crumpling of the thread in the contact zone occurs at forces much lower than the forces required to stretch the thread, the thread was considered as non-extensible. To determine the law of the distribution of the speed of the points of the thread, an independent vector, which is always connected to the main triangle, was introduced into consideration. The relationship between the vector of total curvature and the vector of absolute angular velocity is obtained. The obtained values of the speed at an arbitrary point of the axis of the thread as a function of the deformation vector, which determines the degree of twisting of the thread in the contact zone. The obtained results can be used to study various technological processes in the sewing, knitting, and textile industries, where the movement of the thread takes place along the guide surface of great curvature.

Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems

We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter is bounded by data only for fixed polynomial order, mesh, and time. In the absence of dissipation, coupling of the overlapping domains is destabilizing by allowing positive eigenvalues in the system to be integrated in time. This coupling can be stabilized in one space dimension by using the upwind numerical flux. To help provide additional dissipation, we introduce a novel penalty method that applies dissipation at arbitrary points within the overlap region and depends only on the difference between the solutions. We present numerical experiments in one space dimension to illustrate the implementation of the well-posed penalty formulation, and show spectral convergence of the approximations when sufficient dissipation is applied.

Quantum-limited superresolution of two arbitrary incoherent point sources: Beating the resurgence of Rayleigh's curse

Superresolution has been demonstrated to overcome the limitation of Rayleigh's criterion and achieve significant precision improvement in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that, if the photon numbers of two incoherent optical sources are unknown, the precision of superresolution vanishes when the photon numbers are actually different. In this work, we first analyze in detail the estimation precision of the separation for two incoherent optical sources with the same point-spread functions and show that, when the two photon numbers are different but sufficiently close, the superresolution can still be realized but with different precisions. We find the condition on how close the photon numbers need to be to realize the superresolution and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions and show that the competition between the difference of photon numbers, the difference of point-spread functions, and the separation of source locations determines the precision of superresolution. The results exhibit precision limits distinct from that of two identical point-spread functions with equal photon numbers and extend the realizable regimes of quantum superresolution. Finally, the results are illustrated by Gaussian point-spread functions. Published by the American Physical Society 2024

Realizations of Multiassociahedra via Rigidity

AbstractLet $$\Delta _{k}(n)$$ Δ k ( n ) denote the simplicial complex of $$(k+1)$$ ( k + 1 ) -crossing-free subsets of edges in $${\left( {\begin{array}{c}[n]\\ 2\end{array}}\right) }$$ [ n ] 2 . Here $$k,n\in \mathbb {N}$$ k , n ∈ N and $$n\ge 2k+1$$ n ≥ 2 k + 1 . Jonsson (2003) proved that [neglecting the short edges that cannot be part of any $$(k+1)$$ ( k + 1 ) -crossing], $$\Delta _{k}(n)$$ Δ k ( n ) is a shellable sphere of dimension $$k(n-2k-1)-1$$ k ( n - 2 k - 1 ) - 1 , and conjectured it to be polytopal. The same result and question arose in the work of Knutson and Miller (Adv Math 184(1):161-176, 2004) on subword complexes. Despite considerable effort, the only values of (k, n) for which the conjecture is known to hold are $$n\le 2k+3$$ n ≤ 2 k + 3 (Pilaud and Santos, Eur J Comb. 33(4):632–662, 2012. https://doi.org/10.1016/j.ejc.2011.12.003) and (2, 8) (Bokowski and Pilaud, On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon. In: Proceedings of the 21st annual Canadian conference on computational geometry, 2009). Using ideas from rigidity theory and choosing points along the moment curve we realize $$\Delta _{k}(n)$$ Δ k ( n ) as a polytope for $$(k,n)\in \{(2,9), (2,10) , (3,10)\}$$ ( k , n ) ∈ { ( 2 , 9 ) , ( 2 , 10 ) , ( 3 , 10 ) } . We also realize it as a simplicial fan for all $$n\le 13$$ n ≤ 13 and arbitrary k, except the pairs (3, 12) and (3, 13). Finally, we also show that for $$k\ge 3$$ k ≥ 3 and $$n\ge 2k+6$$ n ≥ 2 k + 6 no choice of points can realize $$\Delta _{k}(n)$$ Δ k ( n ) via bar-and-joint rigidity with points along the moment curve or, more generally, via cofactor rigidity with arbitrary points in convex position.

Tortuosity of Delaunay Triangulations and Statistics of Shortest Paths

A tortuosity τ Dln of the Delaunay triangulation on plane and in 3D-space is defined and numerically calculated. This coefficient appears naturally in the porous media studies. The conjecture on the average number of links in the shortest path between two arbitrary points is formulated and statistically studied. The distribution of the number of links in the shortest paths in triangulations of square and disc on R 2 is described.

In-profile monitoring on univariate profile with application to industrial busbar

In the current research on profile monitoring, most studies treat each profile as a whole to design monitoring statistic. These monitoring methods can only detect whether there exist some anomalies in the process after a complete profile sample is collected. This leads to a lag between the occurrence of a shift and the signaling of an alarm, which hinders engineers from promptly intervening in the out-of-control process. To address this limitation, an in-profile monitoring scheme is proposed in this paper, in which the dynamic influence mechanism of covariates on the response variable is considered. In phase-I, a random varying-coefficient model is utilized to model the dynamic time-varying relationship between covariates and the response variable, and the model parameters are estimated. In Phase-II, for the sequential observations generated by the monitored process, a new monitoring scheme based on the generalized likelihood ratio test is designed. This scheme can adapt to within-profile autocorrelation and arbitrary design points. To enhance online computational efficiency, recursive formulas for calculating the charting statistic are developed. Numerical studies demonstrate that the proposed scheme exhibits satisfactory and robust monitoring performance. Finally, an application to industrial busbar running process monitoring is given to demonstrate the implementation of the scheme.

A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields

The flexible rotors within aero-engines operate in complex thermal environments, where temperature influences both the vibration frequency and amplitude. This study establishes a simple thermal flexible rotor dynamics model to rapidly and precisely predict thermo-elastic coupling vibration characteristics within a non-uniform temperature field. The thermal potential energy of the thermal rotor element is derived for any temperature field, and the motion equation is obtained using the Euler-Lagrange equation. Specifically, the generalized vector of an arbitrary point and cross-sectional non-uniform thermal stress of the thermal rotor element are considered in the thermal potential energy. The model's frequency error is less than 1% under identical boundary conditions. Numerical findings indicate that thermal stress, temperature-dependent material properties, and the coupling effect collectively reduce the natural frequency (NF), with thermal stress having a more pronounced impact under axial constraint. Additionally, thermal stress and material decrease the amplitude across a broad range of rotation speeds, contrasting with thermal bending. This model will play a key role in the iterative calculation of thermo-elastic coupling vibration control due to its accuracy and simplicity.

Heat rejection effect study on large-scale sodium test facility STELLA-2

The STELLA-2 facility is a large-scale sodium test facility to support the development of PGSFR and is accumulating extensive experiment data. The experiment campaigns of STELLA-2 are mostly planned to be transient and therefore it is very challenging to analyze and quantify the amount of heat loss. In this study, a deliberate heat rejection at arbitrary points to consider the heat loss is discussed and the comparison result between the experiment and code calculation is described. The code calculation with heat loss indicates improvement in prediction and it was verified that the behavior of heat transfer in IHTS loops was mostly influenced by the heat loss. For further study, the heat loss effect on other experiments will be evaluated in the coming years.

Revisiting the fastest way to circle a black hole

The shortest time for a null particle traveling between two arbitrary points outside a static spherically symmetric black hole is revisited. We introduce a functional for the time taken by a null particle in traveling on the path between the two points. By variating the time functional, we analyze the possible path with the shortest travel time for the null particle. It is analytically proven that the Euler–Lagrange equation corresponding to the time-functional for finding the path with the shortest traveling time is equivalent to the geodesics equation. This is in agreement with Hod’s conjecture on the fastest way to circle a black hole. We apply the formalism to the dirty black hole in Einstein-square-root nonlinear electrodynamics-dilaton theory. We calculate explicitly the time measured by an asymptotic observer which is needed for a null particle to circle the dirty black hole. Accordingly, a null particle circling the dirty black hole on an almost circular path of radius infinity achieves the shortest time.

Derivation of full range vapor pressure equation from an arbitrary point

An equation was proposed to obtain the full range of vapor pressures (VPs) for a substance at an arbitrary point of VP data. The basic model is a vapor pressure equation in the form of a reduced Antoine equation derived from the van der Waals equation. Here, Antoine constant C is defined as c by dividing it into gas constant and critical temperature, and is expressed as a polynomial function of reduced temperature. Previously, the exponents were integers, but have been improved to real numbers. Edmister’s formula is a special case in which the Antoine constant C divided by the critical temperature in Chen’s equation is 0. Since this is equivalent to polynomial of c being zero, the intercept can be set to zero. The results, estimated using the derived equation, were compared with VP data for 76 substances. The error rate of the equation using the acentric factor as a variable was 0.49%. This was lower than the 0.50% error rate of the Lee-Kesler method. Meanwhile, by using the correlation between the coefficients, the VP equation can be derived at any one point of VP data other than the acentric factor. For 76 substances, the equation derived from the corresponding VPs at reduced temperatures of 0.25 ∼ 0.95 in increments of 0.05 showed a mean error rate of 0.68%. This can be considered an accuracy equivalent to the Lee-Kesler method, which has the limitation of deriving a VP equation only at the reduced temperature of 0.7.

Optimizing measurement tradeoffs in multiparameter spatial superresolution

The quantum Cramér-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same time are not known. In this paper, we ascertain these optimal measurements for an arbitrary point spread function, in the most relevant regime of a small separation between the sources. Our measurement can be adjusted within a set of tradeoffs, allowing more information to be extracted from the separation or the centroid while ensuring that the total information is the maximum possible. Published by the American Physical Society 2024

EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction With Exogenous Variables.

While exogenous variables have a major impact on performance improvement in time series analysis, interseries correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of multivariate time series could be modeled with complex unknown partial differential equations (PDEs) which play a prominent role in many disciplines of science and engineering. In this article, we propose a continuous-time model for arbitrary-step prediction to learn an unknown PDE system in multivariate time series whose governing equations are parameterized by self-attention and gated recurrent neural networks. The proposed model, exogenous-guided PDE network (EgPDE-Net), takes account of the relationships among the exogenous variables and their effects on the target series. Importantly, the model can be reduced into a regularized ordinary differential equation (ODE) problem with specially designed regularization guidance, which makes the PDE problem tractable to obtain numerical solutions and feasible to predict multiple future values of the target series at arbitrary time points. Extensive experiments demonstrate that our proposed model could achieve competitive accuracy over strong baselines: on average, it outperforms the best baseline by reducing 9.85% on RMSE and 13.98% on MAE for arbitrary-step prediction.

Multipoint Variable parameter compliant control of redundant manipulator based on the equivalent twin model of flexible contact dynamics

To elucidate the dynamic coupling mechanism involved in multipoint/arbitrary point contact during human–robot interactions with redundant manipulators, we introduce a compliant control strategy that adapts to variable parameters. This strategy is based on the flexible contact dynamic equivalent twin system for human–robot interactions. Using the Virtual Elastic Element Representation model for arbitrary point contact dynamics and leveraging the skeleton principle for contact force conversion, we construct a flexible contact dynamic equivalent twin system tailored for redundant manipulators with multipoint/arbitrary point contact capabilities. Within this system, we implement real-time adjustments to the impedance stiffness coefficient in conjunction with the virtual end velocity of the manipulator. We optimize the joint angular velocity of the manipulator while considering the motion allocation of redundant degrees of freedom. This optimization enables multipoint contact variable parameter compliance control for safe human–robot interactions. To validate our approach, we analyze the multipoint contact dynamic model of the redundant manipulator's interaction with humans and assess the feasibility of the variable parameter compliance control method using robot operating system simulations. Ultimately, we verify the effectiveness and practicality of our proposed compliance control method through simulation and experimental results.

A cross-scale material removal prediction model for magnetorheological shear thickening polishing

Conventional polishing methods face significant challenges for achieving excellent performance on complex surfaces. The magnetorheological shear thickening polishing (MRSTP) method, with its dual-stimulus response of shear thickening and magnetization enhancement, offers an effective solution for polishing complex surfaces. However, existing models fail to elucidate the cross-scale material removal mechanisms in MRSTP owing to the coupling of magnetic and flow fields. In this study, a comprehensive model was proposed to address the the challenge of predicting the cross-scale material removal rate (MRR) in MRSTP for complex surfaces. Analytical and finite difference methods were employed to solve the pressure distribution during the MRSTP process using magnetohydrodynamics. By incorporating the pressure distribution, an MRR predictive model was developed for arbitrary points on the workpiece surface based on the indentation theory for active abrasive grains. The material removal mechanism was explored by considering elastic and plastic deformation under fluid pressure. The experimental validation showed a relative error of 14.9 % between the theoretical and experimental MRR. Experiments on aero-engine blade tenons demonstrated that the established MRR model is well suited for application to complex surfaces. This study ultimately reveals the material removal mechanism of MRSTP with coupled magnetic and flow field, providing a new foundation for predicting MRR on complex surfaces.

Evaluation of Traffic Sign Occlusion Rate Based on a 3D Point Cloud Space

The effectiveness of road signs is hindered by obstructions, such as vegetation, mutual obstruction of signs, or the road alignment itself. The traditional evaluation of road sign recognition effectiveness is conducted through in-vehicle field surveys. However, this method has several drawbacks, including discontinuous identification, unclear positioning, incomplete coverage, and being time-consuming. Consequently, it is unable to effectively assess the recognition status of road signs at any arbitrary point within the road space. Therefore, this study employed laser scanning to construct a point-surface model, which was based on a point cloud algorithm and SLAM (Simultaneous Localization and Mapping), integrated LiDAR and inertial navigation system data, and optimized the point model after processing steps such as denoising, resampling, and three-dimensional model construction. Furthermore, a method for assessing the highway sign occlusion rate based on the picking algorithm was proposed. The algorithm was applied to an actual road environment, and the occlusion by other items was simulated. The results demonstrated the effectiveness of the method. This new method provides support for the fast and accurate calculation of road sign occlusion rates, which is of great importance for ensuring the safe traveling of vehicles.

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the W-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the W-boson mass within their radius of convergence in a negligible amount of time.

Bending of composite timber

Technologies and production widely use composite materials now. “Mechanics of deformable solids” was formed as a science based on the study of materials used in the 19th and 20th centuries. Modern composite materials require new theoretical and experimental studies. Determining the stresses and deformations that occur at the points of contact of the matrix with the fibers is a special problem. Composites with a plastic matrix play an important role in modern technology. These materials successfully cope with cracking and significantly slow down the growth of cracks. In this article, the problem of the stress state of a composite beam with an elastic-plastic matrix and elastic fibers located along the axis of the beam is solved. It is assumed that in the zone of contact of the matrix with the fibers, according to the model of Yu. N. Worknov, a constant tangential stress is realized, less than the yield strength of the fiber. One end of the beam is fixed, and a constant force applied to the center of gravity coinciding with the origin of coordinates acts on the second. It is assumed that at the free boundary of the beam and at the points of contact of the beam with the fibers, the stresses reach the plasticity limit. The problem is solved with the help of conservation laws. This makes it possible to find the stress state at an arbitrary point of the section as a calculation of integrals along the outer boundary of the beam and the boundaries of the matrix and fibers.

Spotting, Tracking algorithm and the remoteness

On this paper we present a solution to detect and know if a point M is inside a polygon ( A(k), k∈{1,...,n} ) or outside. We are going to give a very simple, practical and explicit method of the triangulation of a convex polygon (convex polyhedron) after a definition and the concretization of the order relation of the points of a polygon in a plane following a well-chosen orientation in before and an arbitrary point of the vertices of the polygon. In the case where the point M is outside the polygon, a simple optimization method will be applied to determine the distance between the point M and the polygon A(1), ..., A(n) and the point P of the border of the polygon closest to M ”The neighboring Point”.