Momentum Parameter Research Articles

Time evolution of the Von Neumann entropy for a Kerr–Taub–NUT black hole

In this work, we study the evolution of an evaporating black hole, described by the Kerr–Taub–NUT metric, which emits scalar particles. We found that allowing the black hole to radiate massless scalar particles increases the angular momentum loss rate while decreasing the loss rate of the NUT parameter and black hole mass. In fact, it means that angular momentum will disappear faster than the other black hole parameters (mass and NUT parameter) during the evaporation process. We also calculate the time evolution of the mass, angular momentum, and NUT parameter in order to get the evolution of the Von Neumann entropy of the black hole. We found that the entropy follows approximately the so-called Page curve, where the β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} parameter, which quantifies the amount of radiation, affects the evaporation process. Implying that high β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} values accelerate the evaporation process of a Kerr–Taub–NUT black hole.

Spin–Orbit Coupling of the Ellipsoidal Secondary in a Binary Asteroid System

In our solar system, spin–orbit coupling is a common phenomenon in binary asteroid systems, where the mutual orbits are no longer invariant due to exchange of angular momentum between translation and rotation. In this work, dynamical structures in phase space are explored for the problem of spin–orbit coupling by taking advantage of analytical and numerical methods. In particular, the technique of Poincaré sections is adopted to reveal numerical structures, which are dependent on the total angular momentum, the Hamiltonian, mass ratio, and asphericity parameter. Analytical study based on perturbative treatments shows that high-order and/or secondary spin–orbit resonances are responsible for numerical structures arising in Poincaré sections. Analytical solutions are applied to (65803) Didymos, (80218) VO123 and (4383) Suruga to reveal their phase-space structures, showing that there is a high possibility for them to locate inside secondary 1:1 spin–orbit resonance.

Thermodynamic geometry of charged rotating black holes in Einsteinian cubic gravity

We study the thermodynamic geometry of two types of asymptotically anti-de Sitter black holes in four-dimensional Einsteinian cubic gravity, including the uncharged rotating and charged non-rotating black holes, applying the Ruppeiner thermodynamic geometry method. The divergence of the scalar curvature of the Ruppeiner metric ([Formula: see text]) is found to be related to the vanishing of the heat capacity. The stability of the solutions is shown to be affected by the Einsteinian cubic gravity coupling constant [Formula: see text]. In the unstable phase of the rotating black hole, the [Formula: see text] appeared to possess additional diverging points, where the number of these points and the behavior of [Formula: see text] are controlled by the angular momentum parameter. Also, for the charged non-rotating black hole case, we show that depending on the values of [Formula: see text], the solution may enjoy two types of phase transition and [Formula: see text] behaviors. The characteristic behavior of [Formula: see text] of these two types of black holes enabled us to recognize the types of interactions between microscopic degrees of freedom.

Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets.

Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation.

Hawking Temperature Modification and the Physical Dynamics of Black Holes: A Study of the Influence of Internal and Cosmological Variables

<p>The main objective of the study is to develop a model that modifies the traditional Hawking temperature by considering the influence of internal variables such as radius, mass, electric charge, angular momentum, and cosmological constant. The research method involves mathematical analysis and computational modeling based on the modified Hawking temperature equation. The results show that the modified Hawking temperature produces non-linear corrections that show the interaction between black holes and the quantum structure of spacetime. graphical representations visualize the variation of Hawking temperature with changes in area, electric charge, angular momentum, and cosmological parameters. The implications of the research extend to the understanding of the thermal properties of black holes in the context of gravitational and quantum theories. The research identifies gaps in the knowledge of the effects of cosmological parameters on black hole thermodynamics and introduces Hawking temperature modifications that have not been mapped in detail before. The study concludes that the Hawking temperature modification provides a strong foundation for further research in black hole physics, particularly in the effect of physical and cosmological parameters on the thermal properties of black holes.</p>

The Influence of Pump-Turbine Specific Speed on Hydraulic Transient Processes

The main porpose of this paper is to perform and present at transient process analysis on the influence of different specific speeds (nq) of the three-model pump-turbines that may implemented at the hydropower pump storage plant (HPSP) Bajina Basta, Serbia. The intention is to analyze the operation regimes along the S-shaped characteristic curve, which creates difficulties in calculations during the load-rejection process. These problems are manifested by an unusual increase in water pressure, followed by an increase in machine vibrations, thus threatening the stability of machine operation. The subject of this research is the four-quadrant (4Q) characteristic curves, presented in the form of Suter curves (the head and momentum parameters (Wh and Wm), in dependence of angle (θ)) for different wicket gate openings, of the three pump-turbine models with different specific speeds (nq = 27, nq = 38 and nq = 50). These 4Q characteristics are used as input data for numerical code developed to calculate the simultaneous load rejection of both pump-turbines. The numerical code is based on the method of characteristics and applied to the test case at HPSP. This is especially relevant when dealing with characteristic S-shaped curves that may lead to serious instability in operation during the transient process. The calculation results show changes in the pressure, speed of rotation and discharge of the machine operation regimes, but the important findings are reflected in further application of the results to determine the parametric flow and speed (Q11 and n11) trajectories of the operating points, where the unstable behavior of a pump-turbine operating in turbine mode is presented and periodically the trajectories also pass through the reverse pump zone.

Unraveling the Photodissociation Branching and Pathways of Methane at 118 nm by Imaging the CH3, CH2, and CH Fragments.

Under irradiation of a vacuum ultraviolet (VUV) photon, methane dissociates and yields multiple fragments. This photochemical behavior is not only of fundamental importance but also with wide-ranging implications in several branches of science. Despite that and numerous previous investigations, the product channel branching is still under debate, and the underlying dissociation mechanisms remain elusive. In this study, the photofragment imaging technique was exploited for the first time to map out the momentum and anisotropy parameter distributions of the CH3, CH2, and CH fragments at the 118 nm photolysis wavelength (10.48 eV photon energy). In conjunction with previously reported results of the H atom fragment at 121.6 nm (10.2 eV), a complete set of product channel branching in both two-body and three-body fragmentations is accurately determined. We concluded that extensive nonadiabatic transitions partake in the processes with two-body fragmentations accounting for more than 90% of overall photodissociation, for which the channel branching values for CH2 + H2 and CH3 + H are about 0.66 and 0.25, respectively. Careful kinematic analysis enables us to untangle the intertwined triple fragmentations into the CH2(X̃ 3B1 and ã 1A1) + H + H and CH(X2Π) + H + H2 channels and to evidence their underlying sequential (or stepwise) mechanisms. With the aid of electronic correlation and prior theoretical calculations of the potential energy surfaces, the most probable or dominant dissociation pathways are elucidated. Comparisons with fragmentary reports in the literature on various photochemical aspects are also documented, and discrepancies are clarified. This comprehensive study benchmarks the VUV photochemistry of methane and advances our understanding of this important process.

Iterative algorithm for a generalized matrix equation with momentum acceleration approach and its convergence analysis

This article discusses a numerical gradient-based method for solving a generalized matrix equation. The iterative method mentioned includes two positive parameters, for which a range is determined to ensure the convergence of the introduced method. It has been shown that the optimal parameters of this method satisfy a constrained optimization problem. Then, specific solutions of this equation, such as the reflexive solution, are examined. Furthermore, to increase the rate of convergence of the proposed method, the idea of momentum is utilized, and a range for the momentum parameter is obtained to ensure the convergence. Finally, the efficiency of this method is investigated through numerical simulations. Additionally, in numerical results section, applications of mentioned matrix equation in image restoration and anti-linear systems are addressed.

Impact of optimizers functions on detection of Melanoma using transfer learning architectures

AbstractEarly diagnosis-treatment of melanoma is very important because of its dangerous nature and rapid spread. When diagnosed correctly and early, the recovery rate of patients increases significantly. Physical methods are not sufficient for diagnosis and classification. The aim of this study is to use a hybrid method that combines different deep learning methods in the classification of melanoma and to investigate the effect of optimizer methods used in deep learning methods on classification performance. In the study, Melanoma detection was carried out from the skin lesions image through a simulation created with the deep learning architectures DenseNet, InceptionV3, ResNet50, InceptionResNetV2 and MobileNet and seven optimizers: SGD, Adam, RmsProp, AdaDelta, AdaGrad, Adamax and Nadam. The results of the study show that SGD has better and more stable performance in terms of convergence rate, training speed and performance than other optimizers. In addition, the momentum parameter added to the structure of the SGD optimizer reduces the oscillation and training time compared to other functions. It was observed that the best melanoma detection among the combined methods was achieved using the DenseNet model and SGD optimizer with a test accuracy of 0.949, test sensitivity 0.9403, and test F score 0.9492.

Stationary Landweber method with momentum acceleration for solving least squares problems

In this article, we proposed an enhancement to the convergence rate of Landweber’s method by incorporating the concept of momentum acceleration. Landweber’s method is commonly used to solve least squares problems of the form minx‖Ax−b‖. Our approach is based on Landweber’s method, which is acknowledged as a particular case of the methodologies outlined in Ding and Chen (2006). Through optimizing the momentum parameter, we were able to demonstrate the superior performance of the momentum-accelerated Landweber method. Specifically, we established that when A is a nonsquare m×n matrix with Rank(A)=n and σmin(A)≠σmax(A), the momentum-accelerated Landweber method with the optimal parameter consistently outperforms the standard Landweber method. Our numerical experiments have confirmed the theoretical findings, demonstrating a notable improvement in the convergence rate of the Landweber method.

Physical and Numerical Experimentation of Water Droplet Collision on a Wall: A Comparison between PLIC and HRIC Schemes for the VOF Transport Equation with High-Speed Imaging

Liquid films are often found in engineering applications with thicknesses ranging from micrometer scales to large scales with a wide range of applications. To optimize such systems, researchers have dedicated themselves to the development of new techniques. To further contribute to this development, the objective of this work is to present the results of the collision of water droplets on a wall by means of experimentation and numerical simulations. For physical experimentation, an injector is used to generate a chain of water droplets that collide with the opposite wall, forming a liquid film. Images of the droplets were obtained using two high-speed recording cameras. The results for different droplet sizes and impact angles are presented and the relationship between the momentum parameter and non-dimensional pool size was established. Modeling such processes is a common challenge in engineering, with different techniques having their advantages and limitations. The simulations in this work were run using the volume of fluid method, which consists of solving a transport equation for the volume fraction of each considered fluid. A correlation was found between the surface tension to momentum transport ratio, Scd, and the non-dimensional pool size for different droplet sizes and impact angles. Regions where partial depositions were most likely to occur were found via physical experiments.

Magnetohydrodynamics tangent hyperbolic nanofluid flow across a vertical stretching surface using Levengberg-Marquardt back propagation artificial neural networks

This analysis uses the Levenberg-Marquardt back propagation artificial neural networks (LM-BP-ANNs) approach to demonstrate the mathematical strategy of neural networks for the simulation of MHD Tangent hyperbolic nanofluid (THNF) flow consisting of motile microorganisms through a vertically extending surface. The fluid flow is being investigated in terms of exponential heat source/sink, thermal radiation, and magnetic field. The modeled equations are relegated to the ordinary system of differential equations by substituting similarity variables. The ND-solve approach is applied for the modeled equations to numerically handle and generate a dataset. Several activities, including testing, verification, and training, are performed by creating a scheme for various fluid problems using reference data sets. The precision of LM-BP-ANNs is evaluated using mean square error, curve fitting error histogram, and the regression analysis plot. Furthermore, graphs are used to analyze flow parameters for concentration, momentum, and energy profiles. It has been observed that the velocity field declines as the magnetic field grows stronger. The THNF model for energy, mass, and momentum equations is tested, authenticated, and trained within an average of 10−9. The LM-BP-ANNs accomplish the highest accuracy, with a target date and absolute error reference values in the 10−4 to 10−5 range.

Dynamic response of clamped metallic thin-walled cylindrical shells under lateral shock loading

A combined experimental and numerical study was carried out to explore the dynamic response of Q235 thin-walled cylindrical shells under lateral shock loading. The machined Q235 specimens were clamped on both sides and subjected to centered lateral simulated shock loading via foam projectile impact tests, with their dynamic deformation evolution, mid-point deflections, and final deformation modes experimentally measured. The mid-point deflections of the impact side are all positive (the direction of deformation is the same as the impact direction) while those of the rear side all exhibit negative values (the direction of deformation is opposite to the impact direction). To further explore this phenomenon, the method of finite element (FE) was employed to simulate the foam projectile impact, with good agreement against experimental measurements achieved. Using the validated numerical model, the effects of impact velocity, length-to-diameter ratio, and thickness-to-diameter ratio on the dynamic response of the thin-walled cylindrical shell were further analyzed. The direction of both side deflections and deformation modes are significantly affected by the impact level and the shell geometries. For the rear side, within the given range of impact momentum and geometric parameters, the numerically predicted deflection varies from −1.775 mm to 2.45 mm. Thereupon, the coupling of indentation and bulge deformation patterns are indicated, and their corresponding contribution changes are considered the main mechanism for determining the final deformation of the thin-walled cylindrical shell's rear side.

On the Convergence of an Adaptive Momentum Method for Adversarial Attacks

Adversarial examples are commonly created by solving a constrained optimization problem, typically using sign-based methods like Fast Gradient Sign Method (FGSM). These attacks can benefit from momentum with a constant parameter, such as Momentum Iterative FGSM (MI-FGSM), to enhance black-box transferability. However, the monotonic time-varying momentum parameter is required to guarantee convergence in theory, creating a theory-practice gap. Additionally, recent work shows that sign-based methods fail to converge to the optimum in several convex settings, exacerbating the issue. To address these concerns, we propose a novel method which incorporates both an innovative adaptive momentum parameter without monotonicity assumptions and an adaptive step-size scheme that replaces the sign operation. Furthermore, we derive a regret upper bound for general convex functions. Experiments on multiple models demonstrate the efficacy of our method in generating adversarial examples with human-imperceptible noise while achieving high attack success rates, indicating its superiority over previous adversarial example generation methods.

Analysis of a Two-Step Gradient Method with Two Momentum Parameters for Strongly Convex Unconstrained Optimization

The paper is devoted to the theoretical and numerical analysis of the two-step method, constructed as a modification of Polyak’s heavy ball method with the inclusion of an additional momentum parameter. For the quadratic case, the convergence conditions are obtained with the use of the first Lyapunov method. For the non-quadratic case, sufficiently smooth strongly convex functions are obtained, and these conditions guarantee local convergence.An approach to finding optimal parameter values based on the solution of a constrained optimization problem is proposed. The effect of an additional parameter on the convergence rate is analyzed. With the use of an ordinary differential equation, equivalent to the method, the damping effect of this parameter on the oscillations, which is typical for the non-monotonic convergence of the heavy ball method, is demonstrated. In different numerical examples for non-quadratic convex and non-convex test functions and machine learning problems (regularized smoothed elastic net regression, logistic regression, and recurrent neural network training), the positive influence of an additional parameter value on the convergence process is demonstrated.

ОТНОСИТЕЛЬНОЕ ЗАПАЗДЫВАНИЕ СИГНАЛОВ В ПРОСТРАНСТВЕ-ВРЕМЕНИ ВРАЩАЮЩИХСЯ УСКОРЯЮЩИХСЯ ЧЕРНЫХ ДЫР

The paper studies a potentially observable effect – relative time delay– on the background of the rotating accelerating black holes, called the C-metric. The C-metric proposed by Griffiths and Podolsky is an exact solution to Einstein's equations. The metric is characterized by mass, angular momentum and acceleration parameter, and is reduced to Kerr's solution when the acceleration parameter is zero. Relative time delay occurs if two light beams come from a variable source located behind a rotating gravitational lens. Passing on opposite sides of the lens, the rays arrive at the observer with a time difference. The time difference arises due to the frame dragging effect. Black holes described by the C-metric have the angular momentum which is necessary to occur the relative time delay. To calculate the relative delay of signals, the Dymnikova method was used. The xpression for the relative delay was expanded into a series to determine the influence of the acceleration parameter of the C-metric. It was found that the relative time delay in the leading order for the C-metric does not depend on the mass of black holes and the acceleration parameter, but depends only on the angular momentum. In the corrections, the relative time delay for the C-metric differs from the corrections to the delay in the Kerr solution by the influence of the free parameter of the C-metric. To estimate the influence of the acceleration parameter on the relative time delay, numerical delay values were obtained for a range of accelerations. Numerical values were calculated by substituting observed data from realistic pulsar–black hole configurations into the expression for the relative signal delay. The obtained numerical estimates show that the magnitude of the relative time delay in the first order is measurable with the capabilities of modern technology. Considering that all previously studied solutions of objects using relative delay had the influ- ence of mass, the numerical values of the delay in the C-metric are significantly different. Therefore, black holes described by the C-metric can be distinguished from previously studied black hole solutions using potential observations of relative time delay. However, the corrections containing the influence of the acceleration parameter are too small to take their influence into account.

DFT2kp: Effective kp models from ab-initio data

The k\cdot pk⋅p method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator \pi= p+ p_{SOC}π=p+pSOC (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of k\cdot pk⋅p effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation UU that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a “hands-on” example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

Codebase release 0.0 for DFT2kp

The k\cdot pk⋅p method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator \pi= p+ p_{SOC}π=p+pSOC (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of k\cdot pk⋅p effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation UU that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a “hands-on” example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

Study of relativistic accretion flow in the [formula omitted] theory of gravity

We present the properties of relativistic, inviscid, low angular momentum, advective accretion flow in a f(R) gravity theory that satisfactorily mimics the asymptotically flat vacuum solutions of the Einstein’s equations. With this, we solve the governing equations describing the accretion flow and obtain the global transonic accretion solutions in terms of flow energy (E), angular momentum (λ) and gravity parameter (A) that determines the effect of f(R) gravity. We observe that depending on the model parameters, flow may contain either single or multiple critical points. We separate the effective domain of the parameter space in λ−E plane that admits accretion solutions possessing multiple critical points and observe that solution of this kind continues to form for wide range of the flow parameters. We examine the modification of the parameter space and reveal that it gradually shrinks with the decrease of A, and ultimately disappears for A=−2.34. Finally, we calculate the disk luminosity (L) considering bremsstrahlung emission process and find that global accretion solutions passing through the inner critical point are more luminous compared to the outer critical point solutions.

Significance of Melting Heat Transfer, Inclined Magnetic Field, and Thermal Radiation on the Dynamics of Williamson Nanofluid Above a Stretching Sheet

This study investigates the melting heat transfer in MHD flow that occurs when the flow is past a stretched sheet. With the use of the boundary layer concept, a set of non-linear ODEs is derived from a system of PDEs of motion and energy. After transforming the non-linear ODEs and their boundary conditions into dimensionless form with the use of appropriate similarity conversions, the equations are then numerically solved by employing the MATLAB inbuilt solver bvp4c method in conjunction with the shooting methodology. Through the use of a variety of charts and tables, the authors analyze and describe in depth the effects that relevant factors have on a variety of flow fields. As melting factor (Me) increases, it is discovered that the effect of Me on fluid temperature and velocity distributions decreases. Williamson parameter and inclined magnetic profile are shown to have decreasing impact on velocity and momentum parameter. After that, the findings are compared with the earlier published findings in limited situations of the issue, and it is discovered that they are in exceptional specify with those findings.