Physical Solution Research Articles

Physics-informed ConvNet: Learning physical field from a shallow neural network

We introduce a novel methodology for solving nonlinear partial differential equation (PDE) on regular or irregular domains using physics-informed ConvNet, which we call the PICN. The network structure consists of three parts: 1) a convolutional neural network for physical field generation, 2) a pre-trained convolutional layer corresponding to the finite-difference filters to estimate differential fields of the generated physical field, and 3) an interpolation network for loss analysis in irregular geometry domains. From a CNN perspective, the physical field is generated by a deconvolution layer and a convolution layer. Unlike the standard Physics-informed Neural Network (PINN) approach, the convolutions corresponding to the finite-difference filters estimate the spatial gradients forming the physical operator and then construct the PDE residual in a PINN-like loss function. The total loss function involving boundary conditions and the physical constraints in irregular geometry domains can be calculated from an efficient linear interpolation network. The theoretical analysis of PICN convergence is performed on a simplified case for solving a one-dimensional physical field, and several examples of nonlinear PDE of solutions with multifrequency characteristics are executed. The theory and examples confirm the effective learning capability of PICN for the physical field solution with high-frequency components, compared to the standard PINN. A series of numerical cases are performed to validate the current PICN, including the solving (and estimation) of nonlinear physical operator equations and recovering physical information from noisy observations. First, the ability of PICN to solve nonlinear PDE has been verified by executing three nonlinear problems including ODE with sine nonlinearity, PDE involving nonlinear sine-square operators, and Schrödinger equation. The proposed PICN has been assessed by solving some nonlinear PDE on irregular domains such as star-shaped domain, bird-like domain, and starfish domain. Moreover, PICN is applied to identify the thermal diffusivity parameters in an anisotropic heat transfer problem from noisy data, and a denoising display of the temperature field from strong noisy data with standard deviations ranging from 0.1 to 0.4. The numerical results demonstrate the high accuracy approximation and fast convergence performance of PICN. The potential advantage in approximating complex physical field with multi-frequency components indicates that PICN may become an alternative efficient neural network solver in physics-informed machine learning. This paper is adapted from the work originally posted on arXiv.com by the same authors (arXiv:2201.10967, Jan 26, 2022). The data and code accompanying this paper are publicly available at https://github.com/zengzhi2015/PICN.

SiC-on-insulator based lateral power device and it’ s analytical models

This paper proposes the concept of SiC-on-insulator (SiCOI) lateral power device and its analytical models. The SiCOI technology provides dielectric isolation and improves the vertical breakdown. The analytical models provide the physic insight of the surface potential and electric field distributions for both full and partial depletion cases. The optimal breakdown voltage and doping concentration are deduced to analyze the breakdown mechanism qualitatively. The specific on-resistance in the drift region was also calculated to analyze the conduction characteristics. The influences of the structure parameters on the performances of the SiCOI lateral power device are investigated by the analytical model and numerical simulation. The analytical results of the proposed model are well agreement with the numerical results, confirming the validity of the proposed unified analytical model. Both the analytical and numerical results provide the physical explanation and effective solution for optimizing the electric field and improving breakdown voltage for the SiCOI lateral power device.

Continuous and discontinuous compressible flows in a converging–diverging channel solved by physics-informed neural networks without exogenous data

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging–diverging nozzle. This problem represents a typical example described by the Euler equations, a thorough understanding of which serves as a guide for solving more general compressible flows. Given a geometry of the channel, analytical solutions for the steady states do indeed exist, and they depend on the ratio between the back pressure of the outlet and the stagnation pressure of the inlet. Moreover, in the diverging region, the solution may branch into subsonic flow, supersonic flow, or a mixture of both with a discontinuous transition where a normal shock occurs. Classical numerical schemes with shock fitting and capturing methods have been developed to solve this type of problem effectively, whereas the original PINNs are unable to predict the flows correctly. We make a first attempt to exploit the power of PINNs to solve this problem directly by adjusting the weights of different components of the loss function to acquire physical solutions and in the meantime, avoid trivial solutions. With a universal setting yet no exogenous data, we are able to solve this problem accurately; that is, for different given pressure ratios, PINNs provide different branches of solutions at both steady and unsteady states, some of which are discontinuous in nature. For an inverse problem such as unknown specific-heat ratio, it works effectively as well.

Structural stability of subsonic steady states to the hydrodynamic model for semiconductors with sonic boundary

The hydrodynamic model for semiconductors with sonic boundary, represented by Euler–Poisson equations, possesses the various physical steady states including interior-subsonic/interior-supersonic/shock-transonic/C 1-smooth-transonic steady states. Since these physical steady states result in some serious singularities at the sonic boundary (their gradients are infinity), this makes that the structural stability for these physical solutions is more difficult and challenging, and has remained open as we know. In this paper, we investigate the structural stability of interior subsonic steady states. Namely, when the doping profiles are as small perturbations, the differences between the corresponding subsonic solutions are also small. To overcome the singularities at the sonic boundary, we propose a novel approach, which combines the weighted multiplier technique, local singularity analysis, monotonicity argument and squeezing skill. Both the result itself and the technique developed here will give us some truly enlightening insights into our follow-up study on the structural stability of the remaining types of solutions. A number of numerical approximations are also carried out, which intuitively confirm our theoretical results.

Reliability–Security Tradeoff Analysis in mmWave Ad Hoc–based CPS

Cyber-physical systems (CPS) offer integrated resolutions for various applications by combining computer and physical components and enabling individual machines to work together for much more excellent benefits. The ad hoc –based CPS provides a promising architecture due to its decentralized nature and destructive-resistance. A growing number of information leakage events in CPSs and the following serious consequences have aroused ubiquitous concern about information security. In this article, we combine physical layer security solutions and millimeter-wave (mmWave) techniques to safeguard the ad hoc network and investigate the reliability-security tradeoff by taking user demands for the network into account, where eavesdroppers attempt to intercept messages. For the secrecy enhancements, we adopt an artificial noise (AN) assisted transmission scheme, in which AN is employed to create non-cancellable interference to eavesdroppers. The reliability and security are correspondingly characterized by the connection outage probability and secrecy outage probability, and their analytical expressions of them are attained through theoretical analysis for the purpose of the tradeoff issue discussion. Our results reveal that secrecy performance in mmWave ad hoc networks gains significant improvement through the use of AN. It also shows that given total transmit power, there exists a tradeoff between reliability and security to achieve optimal outage performance.

Breather patterns and other soliton dynamics in (2+1)-dimensional conformable Broer-Kaup-Kupershmit system

<abstract><p>In this work, the Extended Direct Algebraic Method (EDAM) is utilized to analyze and solve the fractional (2+1)-dimensional Conformable Broer-Kaup-Kupershmit System (CBKKS) and investigate different types of traveling wave solutions and study the soliton like-solutions. Using the suggested method, the fractional nonlinear partial differential equation (FNPDE) is primarily reduced to an integer-order nonlinear ordinary differential equation (NODE) under the traveling wave transformation, yielding an algebraic system of nonlinear equations. The ensuing algebraic systems are then solved to construct some families of soliton-like solutions and many other physical solutions. Some derived solutions are numerically analyzed using suitable values for the related parameters. The discovered soliton solutions grasp vital importance in fluid mechanics as they offer significant insight into the nonlinear behavior of the targeted model, opening the way for a deeper comprehension of complex physical phenomena and offering valuable applications in the associated areas.</p></abstract>

Transition from Small-scale to Large-scale Dynamo in a Supernova-driven, Multiphase Medium

Magnetic fields are now widely recognized as critical at many scales to galactic dynamics and structure, including multiphase pressure balance, dust processing, and star formation. Using imposed magnetic fields cannot reliably model the interstellar medium's (ISM) dynamical structure nor phase interactions. Dynamos must be modeled. ISM models exist of turbulent magnetic fields using small-scale dynamo (SSD). Others model the large-scale dynamo (LSD) organizing magnetic fields at the scale of the disk or spiral arms. Separately, neither can fully describe the galactic magnetic field dynamics nor topology. We model the LSD and SSD together at a sufficient resolution to use the low explicit Lagrangian resistivity required. The galactic SSD saturates within 20 Myr. We show that the SSD is quite insensitive to the presence of an LSD and is even stronger in the presence of a large-scale shear flow. The LSD grows more slowly in the presence of SSD, saturating after 5 Gyr versus 1–2 Gyr in studies where the SSD is weak or absent. The LSD primarily grows in warm gas in the galactic midplane. Saturation of the LSD occurs due to α-quenching near the midplane as the growing mean-field produces a magnetic α that opposes the kinetic α. The magnetic energy in our models of the LSD shows a slightly sublinear response to increasing resolution, indicating that we are converging toward the physical solution at 1 pc resolution. Clustering supernovae in OB associations increases the growth rates for both the SSD and the LSD, compared to a horizontally uniform supernova distribution.

Biodegradation of petroleum hydrocarbons by fungi strains of Aspergillus sp.-17, Rhizopus sp.-81, Penicillium sp.-94 isolated from oil-contaminated soils of Azerbaijan

Environmental security and biocentric lifestyles are the approaches that today’s man must follow and choose, which cause major environmental problems in modern times and threaten the existence of civilization in the future. The soil ecosystem, which is one of the polluted environments, is polluted naturally and anthropogenically because of oil extraction, transportation and accidents that occurred during this time. Undoubtedly, with the constant increase in the need for oil, land recultivation becomes more urgent than ever for the modern era. Although physical, chemical, and biological solutions are proposed for the recultivation of oil-contaminated soil from oil and oil products in modern times, bioremediation is a more favorable, less capital-intensive, environmentally friendly technology from an ecological and economic point of view. Thus, the main purpose of this study is to determine the ability of micromycetes to biodegrade petroleum hydrocarbons and to determine the advantages of bioremediation of lightly and moderately polluted soils with oil using Aspergillus sp.-17. Rhizopus sp.-81, Penicillium sp.-94 fungal strains with high lipolytic activity. It also mentioned tolerance of oil to different hardnesses.

A Smart System Facilitating Emotional Regulation in Neurodivergent Children

This paper acknowledges the need for a user-centric solution that helps with emotional regulation and stress management in children with ADHD. The paper presents a unique and comprehensive solution that integrates Reinforcement Learning (RL) algorithms to enhance user experience and aid children with ADHD to regulate their emotions and behaviours through a reward-based system. Through careful analysis of existing literature, and user requirements assessment, a comprehensive framework that integrates machine learning algorithms, physical and digital solution components through a user-centric design approach has been proposed. The core objective is to design and develop a sensory regulation system specifically tailored to the requirements of children with ADHD. Through the development of an engaging and impactful sensory regulation system, children can experience social and academic aspects of school positively while also having the opportunity to expand their social circle through inclusive play environments and ultimately improving their daily experiences. This paper aims to address the imminent need for emotional regulation and stress management tools catering to children with ADHD. By incorporating Reinforcement Learning (RL) algorithms with a reward-based interaction, this paper aims to solve critical challenges faced by children with ADHD, like emotional regulation difficulties, stress management, poor social skills, and academic performance issues so that they can lead more holistic lives.

Physical significance and periodic solutions of the high-order good Jaulent-Miodek model in fluid dynamics

<p>Using Whitham modulation theory, this paper examined periodic solutions and the problem of discontinuous initial values for the higher-order good Jaulent-Miodek (JM) equation. The physical significance of the JM equations was discussed by considering the reduction of Euler's equation. Next, the zero- and one-phase periodic solutions of the JM equation, along with the associated Whitham equations, were derived. The analysis included the degeneration of the one-phase periodic solution and the genus-one Whitham equation by examining the limits of the modulus $ m $ of the Jacobi elliptic functions. Additionally, analytical and graphical representations of rarefaction wave solutions and periodic wave patterns were provided, and a solution for discontinuous initial values in the JM equation was presented. The results of this study offer a theoretical foundation for analyzing discontinuous initial values in nonlinear dispersion equations.</p>

Combining multiple sparse measurements with reference data regularization to create spherical directivities applied to voice data

Obtaining high-resolution, spherical phoneme-dependent directivities for voice radiation is beneficial for numerous acoustics applications. This work reports on a spherical interpolation method based on two interleaved measurements using a regularized least-squares fit with reference data. Maximizing the spherical correlation between previously reported results and measured data determines the regularization hyper-parameters to ensure physical solutions. While the resultant spherical directivity patterns show similarities to time-averaged results, distinct radiation characteristics appear, particularly in the range of 630 Hz to 2 kHz.

Facile preparation of durable superhydrophobic DTMS@HKUST-1 wood membrane for continuous oil-water separation in harsh conditions

Manufacturing durable wood membranes that demonstrate both high efficiency and ultra-high flux for continuous oil-water separation utilizing scalable and cost-effective processes remains a serious challenge. In this study, a facile two-step approach is employed to prepare a novel superhydrophobic/oleophilic wood-based MOF (metal-organic framework) membrane. This method involves in-situ anchoring of the octahedral Cu-HKUST-1 (copper benzene-1,3,5-tricarboxylate) onto the wood sponge (WS), which inherently features internal micro-channels. The structure is then modified using the eco-friendly hydrophobic long-chain coupling agent dodecyltrimethoxysilane (DTMS). Due to its unique micro/nanoscale rough surface morphology and low surface energy, the functional wood membrane (DTMS/HKUST-1@WS) exhibited a high contact angle of 162.98±1.10° for water and was able to effectively separate various immiscible oil/water mixtures. Notably, the DTMS/HKUST-1@WS membrane can be integrated into a pump drive system, serving as an advanced filter element for the sustained and efficient oil-water constituents. Results showed that this membrane possesses attractive permeability toward CCl4 (56689.34 L·m−2·h−1) and toluene (47241.12 L·m−2·h−1), achieving separation efficiencies over 99.0%. Furthermore, this novel membrane exhibits remarkable resistance to physical damage, high/low temperatures, and corrosive solutions, thereby showcasing stable superhydrophobic and superoleophilic interfaces suitable for oily wastewater treatment in harsh environments. Thus, this work offers an innovative approach for designing functional wood-based MOF membranes to achieve highly efficient continuous oil-water separation.

Numerical study on heat and flow transfer of biomagnetic fluid with copper nanoparticles over a linear extended sheet under the influence of magnetic dipole and thermal radiation

A steady, two-dimensional flow of biomagnetic fluid namely blood flow with copper nanoparticles across a stretchable sheet that is affected by a strong magnetic field and thermal radiation is investigated in this study. Copper nanoparticles (Cu-NPs) were used for this study because of their important applicability in biomedical research. Thus, the properties of copper nanoparticles render it an antibacterial, antimicrobial, and anti-fungal material. Similarity substitutions were applied to reduce the nonlinear partial differential equations to ordinary differential equations. Utilizing the MATLAB R2018b software bvp4c function technique, the physical solution was established. This model's pertinent dimensions, such as the ferromagnetic parameter, the magnetic field parameter, the radiation parameter, the suction parameter, the ratio parameter, the slip parameter, and the Prandtl Number, were computationally and graphically inspected about the dimensionless velocity, temperature, skin friction, and heat transfer rate. One of the pivotal observations was that a rise in the ferromagnetic parameter and Prandtl number drops the temperature and velocity, correspondingly. A cross-case analysis with the outcome of other published research is also executed for divergent parameter values. Based on the investigations, copper nanoparticles may be advantageous for biomedical purposes and lessen the hemodynamics of stenosis. Owing to the research, copper nanoparticle-concentrated blood exhibits a reduced flow impedance and a larger temperature changeability compared to sheer blood.

Inverse method study based on Characteristic Statistic Algorithm (CSA) with application in estimating core states parameters

In reactor-related scenarios, inverse methods utilizing monitoring data are frequently employed to address issues such as state estimation, accident analysis, and power reconfiguration. These problem-solving approaches can entail converting the original problem into a parameter estimation problem. This paper presents a versatile and scalable framework for solving inverse problems by iterative optimization. To address intricate core parameter problems effectively, we incorporate the CPACT program, a physical thermal engineering solution program. Additionally, we employ the global optimization algorithm known as CSA (Characteristic Statistic Algorithm) to tackle specific challenges associated with nonlinear global optimization. To evaluate the performance of our framework, a numerical simulation model based on the Daya Bay Nuclear Power Plant was used as the test object design as our test subject.

Observing inter-well and intra-well oscillations in buckled nanomechanical systems enabled by image processing

The scanning electron microscope (SEM) recordings of dynamic nano-electromechanical systems (NEMS) are difficult to analyze due to the noise caused by low frame rate, insufficient resolution, and blurriness induced by applied electric potentials. Here, we develop an image processing platform enhanced by the physics of the underlying system to track the motion of buckling NEMS structures in the presence of high noise levels. The algorithm is composed of an image filter, two data filters, and a nonlinear regression model, which utilizes the expected form of the physical solution. The method was applied to the recordings of a NEMS beam about 150 nm wide, undergoing intra- and inter-well post-buckling states with a transition rate of approximately 0.5 Hz. The algorithm can track the dynamical motion of the NEMS and capture the dependency of deflection amplitude on the compressive force on the beam. With the help of the proposed algorithm, the transition from inter-well to intra-well motion is clearly resolved for buckling NEMS imaged under SEM.

Physical multiple shock solutions to the integrability of linear structures of Burgers hierarchy

This work is concerned with the formation of linear structures of components of Burgers' hierarchy. The integrability of some linear systems of two or more parts is investigated. A linear arrangement of five elements is studied by using the Painlevé analysis. The simplified Hirota's method provides a trustworthy cure for the proposed linear design of the five components, where multiple kink solutions are formally derived for this constructed system. Our findings can help many researchers interested in fluid mechanics and plasma physics.

General parallel cosmology

General (tele)parallel Relativity, G∥R, is the relativistic completion of Einstein's theories of gravity. The focus of this article is the derivation of the homogeneous and isotropic solution in G∥R. The first-principles derivation, based on a non-trivial realisation of the symmetry, supersedes and unifies previous constructions of Riemannian and teleparallel cosmologies, and establishes the uniqueness of the physical solution. The constitutive law and the form of the material and inertial source currents is presented in the tensor (Palatini) formalism and adapted to the cosmological background, which exhibits novel features absent in the previously studied, static solutions to the theory. The results are contrasted with those in incomplete theories, such as sitting at the three corners of the geometrical trinity which correspond to particular reference frames in G∥R.

Toward AI grading of student problem solutions in introductory physics: A feasibility study

Toward AI grading of student problem solutions in introductory physics: A feasibility study

Simulation of new waves in applied sciences via Schrödinger equations

The perturbed chiral nonlinear Schrö dinger equation (PCNLSE) reflects the quantum actions such as quantum pictures of Bohm potential and internal self-potential properties. Indeed, this equation introduces the basics of the hidden variable theory in quantum mechanics. Two unified solver methods and exp -expansion technique applied to PCNLSE to present many solitonic solutions in an explicit and effective way. The behaviour of these solutions is of qualitatively different structural natures, relying on physical coefficient parameters. The application of three mathematical techniques to our model system provides us with several possible physical property solutions that account for the majority of many phenomena the model under study attempts to depict. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applicable in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and in a lot other applied sciences. The results of this system's solitary structures are consistent with the characteristics of the nonlinear Schrödinger equation systems used to study dispersive modes and higher-order perturbed systems. For more details about the physical dynamical representation of the presented solutions, we have illustrated them with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approach can be applied to several equations arising in all applied sciences.

A positivity-preserving adaptive-order finite-difference scheme for GRMHD

We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection strategy, but differs in several ways. The approach is a priori and so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems.