Physical Laws Research Articles

Some Aspects of Maxwell’s Equations, Klein-Gordon Equations, and Heat and Mass Transfer Equations in an n-Dimensional Maximally Symmetric Space-Time from the Classical and Quantum Mechanical Standpoints

This manuscript examines Maxwell’s equations, Klein-Gordon equations, and heat and mass transfer equations in n-dimensional maximally symmetric space-time. It investigates these equations in spherical and hyperbolic spaces embedded in higher-dimensional Euclidean and Minkowski spaces. The study focuses on the implications of these geometries and symmetries on the behaviour of the equations, highlighting how specific transformations and parametrizations impact their solutions. The findings reveal the underlying connections between geometric symmetries and physical laws, providing insights into their possible applications in theoretical physics. We touch upon both classical and quantum mechanical aspects of density and velocity evolutions with time in the universe. Quantum mechanical aspects of single and two-particle state evolution and statistical moments of the matter four-current are derived from the quantum Boltzmann equation and Feynman’s path integral method for fields applied to gravity interacting with electrons and positrons.

A multifidelity approach to continual learning for physical systems

We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and the desired output of the model on the current training dataset, limiting catastrophic forgetting. On its own the multifidelity continual learning method shows robust results that limit forgetting across several datasets. Additionally, we show that the multifidelity method can be combined with existing continual learning methods, including replay and memory aware synapses, to further limit catastrophic forgetting. The proposed continual learning method is especially suited for physical problems where the data satisfy the same physical laws on each domain, or for physics-informed neural networks, because in these cases we expect there to be a strong correlation between the output of the previous model and the model on the current training domain.

Newtonian Physics Informed Neural Network (NwPiNN) for Spatio-Temporal Forecast of Visual Data

AbstractMachine intelligence is at great height these days and has been evident with its effective provenance in almost all domains of science and technology. This work will focus on one handy and profound application of machine intelligence-time series forecast, and that too on visual data points, i.e., our objective is to predict future visual data points, given a subtle lag to work on. For the same, we would propose a deep learner, Newtonian physics informed neural network (NwPiNN) with the critical modelling capabilities of the physics informed neural networks, modelled on the laws of Newtonian physics. For computational efficacy, we would work on the gray-scale values of pixels. Since the variation in data pixel values is not only provoked by the pixel gray values but also by the velocity component of each pixel, the final prediction of the model would be a weighted average of the gray value forecast and the kinematics of each pixel, as modelled by the PINN. Besides its’ proposal, NwPiNN is subjected to benchmark visual dataset, and compared with existing models for visual time series forecast, like ConvLSTM, and CNN-LSTM, and in most of the occasions, NwPiNN is found to outperform its preliminaries.

Pulsed Propulsion of Unmanned Aerial Vehicles by Centrifugal Force Modulation—First-Order Theory and Practicability

A novel technique suitable for the propulsion of small unmanned aerial vehicles (UAV) is discussed in this paper. This approach utilizes the rotational energy of airborne gyro rotors and converts it into translational propulsion for the vehicle. The energy conversion is achieved by generating precisely directed centrifugal force pulses through short-duration rotor unbalances. The accurate control of the timing and magnitude of these unbalances is crucial for successful propulsion generation. Our first-order theory of controlled unbalance propulsion (CUP) predicts the potential for achieving high translational accelerations and vehicle velocities up to orbital levels. Power-saving levitation of UAVs can be attained. In this paper, we provide traceable evidence that pulsed centrifugal propulsion is based on well-established laws of physics and can be realized using state-of-the-art technologies.

A Systematic Review of Physical Modelling Techniques, Developments and Applications in Slope Stability Analyses

AbstractAn extensive evaluation of published articles suggests a lack of research on a systematic literature review relating to physical modelling techniques, developments and application in slope stability studies. However, there is growing interest in using physical model tests in slope stability investigations. The present study systematically reviews the methodologies and applications of physical modelling in slope stability research. The Scopus database was used to identify relevant studies which employed physical model tests in slope stability investigations. A combination of fifteen keywords was used to identify relevant articles. A PRISMA-P method for conducting a systematic review was adopted. Articles were screened and analysed, and extracted data were re-organised using an Excel sheet. Data relating to research objectives, physical model test techniques, instrumentation, scaling laws, numerical modelling, results, and findings were extracted and analysed. The systematic review highlights gaps requiring further studies, particularly in slope reinforcements using vegetation and strength deterioration of reinforcements performance under repeated loading exposures. It is found that scholars have not fully addressed the influence of loss of water on pore water regimes and its impact on stability when vegetation is applied as reinforcements. It is also found that the development of slope materials for soil slopes in physical model tests relies on the artificial development of such materials with minimal consideration of their long-term behaviour. Although other options, such as bio-cementation and desiccation techniques, which simulate the natural environment of the slopes, are neglected in slope material development, the present study recommends that future studies consider such techniques.

Quantum counterpart of equipartition theorem in quadratic systems

The equipartition theorem is a fundamental law of classical statistical physics, which states that every degree of freedom contributes kBT/2 to the energy, where T is the temperature and kB is the Boltzmann constant. Recent studies have revealed the existence of a quantum version of the equipartition theorem. In the present work, we focus on how to obtain the quantum counterpart of the generalized equipartition theorem for arbitrary quadratic systems in which the multimode Brownian oscillators interact with multiple reservoirs at the same temperature. An alternative method of deriving the energy of the system is also discussed and compared with the result of the quantum version of the equipartition theorem, after which we conclude that the latter is more reasonable. Our results can be viewed as an indispensable generalization of recent works on a quantum version of the equipartition theorem. Published by the American Physical Society 2024

Windblown sand around obstacles - simulation and validation of deposition patterns

Sand dunes are iconic landmarks of deserts, but can also put human infrastructures at risk, for instance by forming near buildings or roads. We present a simulator of sand erosion and deposition to predict how dunes form around and behind obstacles under wind. Inspired by both computer graphics and geo-sciences, our algorithm couples a fast wind flow simulation with physical laws of sand saltation and avalanching, which suffices to reproduce characteristic patterns of sand deposition. In particular, we validate our approach via a qualitative comparison of the erosion and deposition patterns produced by our simulator against real-world patterns measured by prior work under controlled conditions.

From advanced hydraulic modelling to performance indicator for the efficiency of investments in leakage management of pressurized water systems

IntroductionThe digital transition is meant as the review of processes using digital technologies and strategies to increase efficiency based on a simpler collection of representative data. The process of interest here is the leakage management in systems distributing water. ObjectiveTo develop a novel key performance indicator (KPI) for leakage management considering the needs of ongoing digital transition in the water sector, which is opening a new era in the management of drinking water infrastructures. MethodologyThe novel KPI, named Asset Management Support Indicator, is developed starting from advanced hydraulic modelling and the physical laws governing leakage outflows, in order to be physically based and rational for increasing the efficiency of leakage management activities using representative process data. ResultsThe Asset Management Support Indicator supports effective leakage management strategies by driving towards efficiency, as discussed and demonstrated using several real case studies. ConclusionThe novel indicator is consistent with the digital transition perspective and current need of increasing the efficiency of water utilities, and it is also suitable to be adopted by water authorities to benchmark their performances, because it overcomes the weaknesses of traditional KPIs.

Expert's experience-informed hierarchical kriging method for aerodynamic data modeling

Data-driven models, such as kriging, have gained popularity in aerospace engineering due to their capability of predicting multidimensional, nonlinear aerodynamic characteristics of an aircraft. However, they are still suffering from the problem associated with poor extrapolation capability and physical interpretability, which in turn has great impacts on aerodynamic performance and flight safety. To address this problem, this article proposes to incorporate an empirical aerodynamic model obtained from expert's understanding of aerodynamics in the fitting process of a kriging model. First, empirical aerodynamic models based on expert's understanding and experience are derived. Second, the regression term of a kriging model is replaced by the expert's experience-informed model so that the global trend can be consistent with physical laws and provides extra knowledge in the subregion(s) without training data, especially for the extrapolation region(s). Finally, the expert's experience-informed hierarchical kriging (EEI-HK) model is built in a sequential way. The proposed method is validated with analytical test examples and demonstrated by aerodynamic data modeling of an AGARD-B missile and an FDL-5A hypersonic flight vehicle. Results show that, compared with ordinary and universal kriging models, the proposed EEI-HK model can dramatically improve the prediction accuracy in the extrapolation domain and slightly enhance the interpolation accuracy, with assistance from physical information provided by an empirical model. In consequence, it can be a promising approach for aerodynamic data extrapolation and saving the cost of establishing an aerodynamic database.

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

AbstractWe present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re‐parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi‐variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning‐generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large‐scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state‐of‐the‐art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade‐off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics‐based knowledge.

A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics-guided neural network. In particular, the nonlinear Mori–Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori–Tanaka method in the condition of the small deformation. Notably, this neural-network-based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.

A stochastic world model on gravity for stability inference.

The fact that objects without proper support will fall to the ground is not only a natural phenomenon, but also common sense in mind. Previous studies suggest that humans may infer objects' stability through a world model that performs mental simulations with a priori knowledge of gravity acting upon the objects. Here we measured participants' sensitivity to gravity to investigate how the world model works. We found that the world model on gravity was not a faithful replica of the physical laws, but instead encoded gravity's vertical direction as a Gaussian distribution. The world model with this stochastic feature fit nicely with participants' subjective sense of objects' stability and explained the illusion that taller objects are perceived as more likely to fall. Furthermore, a computational model with reinforcement learning revealed that the stochastic characteristic likely originated from experience-dependent comparisons between predictions formed by internal simulations and the realities observed in the external world, which illustrated the ecological advantage of stochastic representation in balancing accuracy and speed for efficient stability inference. The stochastic world model on gravity provides an example of how a priori knowledge of the physical world is implemented in mind that helps humans operate flexibly in open-ended environments.

A stochastic world model on gravity for stability inference

The fact that objects without proper support will fall to the ground is not only a natural phenomenon, but also common sense in mind. Previous studies suggest that humans may infer objects’ stability through a world model that performs mental simulations with a priori knowledge of gravity acting upon the objects. Here we measured participants’ sensitivity to gravity to investigate how the world model works. We found that the world model on gravity was not a faithful replica of the physical laws, but instead encoded gravity’s vertical direction as a Gaussian distribution. The world model with this stochastic feature fit nicely with participants’ subjective sense of objects’ stability and explained the illusion that taller objects are perceived as more likely to fall. Furthermore, a computational model with reinforcement learning revealed that the stochastic characteristic likely originated from experience-dependent comparisons between predictions formed by internal simulations and the realities observed in the external world, which illustrated the ecological advantage of stochastic representation in balancing accuracy and speed for efficient stability inference. The stochastic world model on gravity provides an example of how a priori knowledge of the physical world is implemented in mind that helps humans operate flexibly in open-ended environments.

Configuration entropy and thermodynamics phase transition of black hole in [formula omitted] gravity

Starting from a d−dimensional black hole (BH) in f(R) gravity, we analyzed the effect of modified gravity on critical point parameters, the difference in number densities, and configuration entropy during the BH phase transition phenomenon. From our investigations, consistent results with charged AdS BH are obtained that is holographic dual of van der Waal’s fluid and hence the BH in modified gravity. The thermodynamic pressure, temperature, and free energy are affected by f(R) gravity. The difference in the number densities of molecules (small and large BHs) and configuration entropy are investigated as a function of reduced temperature (τ̃). The difference in the number densities of BH molecules in f(R) gravity decreases with the increase in τ̃, whereas, Scon increases monotonically and becomes a concave function with the increase in space–time dimensions. The relation between the difference in the number density of BH molecules and space–time dimensions (d) decreases with the increase in dimension d. Finally, using our results, the laws of BH Physics are also discussed.

Peristaltic transport of diethylene glycol-based magnesium aluminate nanofluid under the effects of viscous dissipation and Hall current

ABSTRACT The fundamental importance of peristaltic phenomena in numerous biological systems, including dialysis, heart-lung machines, urine transportation, invertebrate locomotion, and the passage of gallbladder bile into the intestines, persuaded scientists to investigate the different aspects of it over the past few years. In addition, peristaltic pumping is an important consideration in industrial processes including, roller pumps used for the transport of sanitary materials, finger pumps, cell separation, and endoscopes. Keeping such inspirational applications in mind, the present investigation is dedicated to exploring the peristaltic transport of a Cross-magneto nanofluid through a curved geometry in the presence of heat transfer. The inspection of the heat transfer is conducted by utilizing variable viscosity and ohmic heating aspects. This study also retains the characteristics of viscous dissipation, heat generation/absorption, and thermal conductivity of nanofluids. Modeling of the 2D, incompressible Cross nanofluid with peristaltic movement is carried out using a curvilinear coordinate system. The basic equations of the problem are mPodeled in the light of physical laws and then simplified by adopting the lubrication theory. The solutions of the resulting nonlinear system are computed numerically. The outcomes of the related flow parameters on the nanofluid’s temperature, pressure gradient, velocity distribution, heat transfer, streamlines pattern, and stresses at the wall are discussed through graphs. The graphical results depict that the rates of heat transfer are augmented by increasing the curvature parameter, Hartmann number, and nanoparticles’ volume fraction while decreasing the Hall parameter and temperature-dependent viscosity parameter. Moreover, the nanofluid’s temperature increases by improving the values of the heat generation parameter, whereas it decreases for the Hall parameter. Furthermore, a reduction in the axial velocity occurs near the center of the channel, when Hartmann number attains higher values.

Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamics

Abstract Melt pool dynamics in metal additive manufacturing (AM) is critical to process stability, microstructure formation, and final properties of the printed materials. Physics-based simulation including computational fluid dynamics (CFD) is the dominant approach to predict melt pool dynamics. However, the physics-based simulation approaches suffer from the inherent issue of very high computational cost. This paper provides a physics-informed machine learning method by integrating the conventional neural networks with the governing physical laws to predict the melt pool dynamics such as temperature, velocity, and pressure without using any training data on velocity. This approach avoids solving numerically the non-linear Navier-Stokes equation, which significantly reduces the computational cost (if including the cost of velocity data generation). The difficult-to-determine parameters' values of the governing equations can also be inferred through data-driven discovery. In addition, the physics-informed neural network (PINN) architecture has been optimized for efficient model training. The data-efficient PINN model is attributed to the extra penalty by incorporating governing PDEs, initial conditions, and boundary conditions in the PINN model.

Cosmological Consequence of Varying Speed of Light and Gravitational Constant

<p>The speed of light is taken to be a constant in a vacuum. This forms the basic tool for the principle of General Covariance, which asserts that all laws of Physics should take the same form in all frames of reference. Without putting inflation into consideration, the theory of varying speed of light (VSL) would solve basic problems of cosmology in the early universe. Furthermore, the Gravitational constant G that occurred in the Friedmann Equations may not have been real constants in the early universe but have some variation with the universe scale factor. Cosmological models with varying physical constants have been of interest in recent years with few works in the literature. A cosmological solution obtained by incorporating variable speed of light and gravitational constant gives a cosmic model which is free from the initial Big Bang singularity and horizon problem. It is also observed here that the early universe was dominated by dark matter, however, as the scale factor increases, the dark energy become dominant.</p>

Evolutionary neural networks for learning turbulence closure models with explicit expressions

Developing physical closure models with explicit expressions based on a given dataset is essential to science and engineering. For such symbolic regression tasks, biology-inspired evolutionary algorithms are most widely used. However, typical evolutionary algorithms do not utilize any structural information inherent in training data, which limits their performance in finding accurate model structures and coefficients. By combining one evolutionary algorithm, gene expression programing (GEP), with an artificial neural network (ANN) for symbolic regression, we propose a novel evolutionary neural network method, in which candidate expressions are specifically designed so that they can be transformed between the GEP and ANN structures during training iterations. By combining the GEP's global searching and the ANN's gradient optimization capabilities, efficient and robust convergence to accurate models can be achieved. In addition, sparsity-enhancing strategies have been introduced to improve the interpretability of the trained models. The present method has been tested for finding different physical laws and then applied to turbulence modeling problems with different configurations, showing advantages compared to the existing GEP and ANN methods.

Назад в будущее: визуализация развития, проблем и перспектив искусственного интеллекта, Data Science, квантовых вычислений

The paper is designed as a review and analysis of the current situation in the field of information technology (IT). The relevance of the article arises from the need to popularize IT among young people, which is reflected in the documents of the Ministry of Digital Development, Communications and Mass Communications of the Russian Federation, as well as from the high demand for experts in the field of digital technologies and the need to increase the digitalization of Russia. According to GeekBrains (the first programming school in Russia, which appeared in 2010, and the leader in the field of training for digital professions, which operates in 85 regions of the Russian Federation and 21 countries of the world), the number of IT job vacancies in this country will grow up to 2 million by 2027. All large organizations are looking for specialists in different IT branches, which are described in this and the following research paper. In this article, which is the first part of the study, the capabilities and problems of the following advanced technologies are considered: artificial intelligence, Data Science and quantum computing. The concepts of technologies are analyzed from the viewpoints of their everyday use and professional application. The topics are closely related and complement each other in one way or another. The article follows the logic and chronology of events in the global IT sphere. The conclusion contains a description of the author's thought experiment about bringing machine intelligence to life, it accumulates the mentioned technologies while taking into account the laws of physics. The calculations for this experiment are given as well. The materials from one of the GeekBrains's educational shows “The Way to IT” were used, including the GIF animation, which is reproduced only on the website of the “Scientific Visualization” journal.

Deep learning of first-order nonlinear hyperbolic conservation law solvers

In this contribution, we study the numerical approximation of scalar conservation laws by computational optimization of the numerical flux function in a first-order finite volume method. The cell-averaging inherent to finite volume schemes presents a challenge in the design of such numerical flux functions toward achieving high solution accuracy. Dense neural networks, as well as (piecewise) polynomials, serve as function classes for the numerical flux. Using a parametrization of such a function class, we optimize the numerical flux with respect to its solution accuracy on a set of Riemann problems for which we have closed-form solutions. By design, our resulting first-order finite volume schemes are conservative.We show empirically that the proposed schemes can achieve higher accuracy than the Godunov and Enquist-Osher method on a wide range of discretizations.The proposed method can be applied to the inverse problem, i.e., the data-driven synthesis of macroscopic physical laws for real-world flux phenomena.