Fundamental Laws Of Physics Research Articles

Development of Risk-Based Approaches to Determining the Damageability and Useful Life of Railway Transportation Assets

Modern problems of railway transport in Russia, such as the general technical condition of transportation assets, and relevant issues of their safe operation, substitution of imported equipment and its components, implementation of the programs of technological development give rise to the need to create new equipment and technologies, constructing schemes for long-term development of transport based on new safety requirements and strategic planning. Current level of developments does not allow to completely eliminate damage, failures and accidents regarding railway transportation assets manufactured in accordance with the current regulatory framework. Solving these problems is possible by identifying the actual state of an object regarding cyclic, corrosion, wear and other damage accumulated during operation, which determines the onset of limit states of the basic elements of an asset, taking into account resource recovery technologies at various stages of the life cycle, both in standard (design) operating conditions and beyond them.The article refers to the problems associated with ensuring safe operation of railway transport, with the aim of substantiating based on existing regulatory and technical documents of new approaches to the analysis of damageability, vulnerability of objects and assessment of the risks of accidents and disasters. The development of interaction through a system of new problem statements and regulatory and technical documents, as well as more active involvement in the use and development of the fundamental laws of physics, chemistry, and mechanics of real-life processes in the environment, make it possible to implement new concepts, strategies, and developments of advanced research for technical objects with the use of digital and intelligent technologies.

Practical continuous variable quantum secret sharing scheme based on non-ideal quantum state preparation

Continuous variable quantum secret sharing protocol can guarantee the unconditional security of secret key information based on the fundamental laws of physics. However, the state preparation operation may become non-ideal and imperfect in practical continuous variable quantum secret sharing scheme, which will introduce additional excess noise and affect the security of the scheme. Therefore, it is necessary to analyze it. We propose a practical continuous variable quantum secret sharing protocol based on imperfect state preparation. Specifically, in the proposed scheme, we assume that there are multiple users, and the imperfect state preparation performed by any user is equivalent to the corresponding untrusted third party using a phase insensitive amplifier to amplify the ideal modulator and laser owned by the user. The equivalent excess noise introduced by the imperfect state preparation can be calculated comprehensively and quantitatively through the gain of the corresponding phase insensitive amplifier. The results show that the continuous variable quantum secret sharing scheme is sensitive to the excess noise introduced by the imperfect state preparation operation, which will inevitably reduce its performance and security. Fortunately, the upper bound of the additional excess noise tolerance for the imperfect state preparation is achieved by using the specific gain formula of the phase insensitive amplifier, thus the security risks caused by the imperfect state preparation can be effectively solved. Due to considering the additional excess noise introduced by imperfect state preparation, tighter secret key rate curves can be obtained by the proposed scheme than those by the ideal continuous variable quantum secret sharing protocol. These results indicate that the proposed scheme can improve the practical security of continuous variable quantum secret sharing scheme, and provide a theoretical basis for its practical applications.

PyGpPHs: A Python Package for Bayesian Modeling of Port-Hamiltonian Systems

PyGpPHs is a Python toolbox for physics-informed learning of physical systems. Compared to pure data-driven approaches, it relies on solid physics priors based on the Gaussian process port-Hamiltonian systems (GP-PHS) framework. This foundation guarantees that the learning procedure adheres to the fundamental physical laws governing real-world systems. Utilizing the Bayesian learning method, PyGpPHs enables physics-informed predictions with uncertainty quantification, which are based on the posterior distribution over Hamiltonians. The PyGpPHs toolbox is designed to make Bayesian learning with physics prior accessible to the learning and control community. PyGpPHs can be installed through an open-source link 1.

Higher-order singularities in phase-tracked electromechanical oscillators

Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.

Structure-preserving discretization of fractional vector calculus using discrete exterior calculus

Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractional electromagnetism, and fractional advection-dispersion. In this work, we reformulate a type of fractional vector calculus that uses Caputo fractional partial derivatives and discretize this reformulation using discrete exterior calculus on a cubical complex in the structure-preserving way, meaning that the continuous-level properties curlαgradα=0 and divαcurlα=0 hold exactly on the discrete level. We discuss important properties of our fractional discrete exterior derivatives and verify their second-order convergence in the root mean square error numerically. Our proposed discretization has the potential to provide accurate and stable numerical solutions to fractional partial differential equations and exactly preserve fundamental physics laws on the discrete level regardless of the mesh size.

Topological Descriptors of Molecular Networks via Reverse Degree

Porphyrazine and tetrakis porphyrazine are organic compounds with intricate ring structures. They are made up of four indole rings that fuse together to form a larger cyclic structure. These structures have been extensively studied in physics and chemistry. They exhibit unique electronic and optical properties due to their highly conjugated systems. In several scientific domains, they are used as the building blocks for functional materials, molecular electronics, sensors, and catalysis. In order to derive a topological index from data, molecules are represented as graphs, with atoms acting as nodes and bonds acting as edges. There are many different techniques and algorithms that can be used to determine the topological index. We have used the reverse degree-based methodology for the mentioned structures. Reverse degree-based topological indices evaluate the structural complexity and stability of chemical compounds by adding the reversed atom degree sequence to their molecular networks. In this study, we calculated the reverse degree-based topological indices like the reverse redefined Zagreb indices, the reverse forgotten index, the reverse hyper-Zagreb index, the reverse Balaban index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, and the reverse general Randić index for porphyrazine and tetrakis porphyrazine networks. This research advances our knowledge of the fundamental laws of physics and chemistry by illuminating the complex interrelationships between molecular structure, biological interactions, and chemical reactivity.

Data-driven prediction of the output composition of an atmospheric pressure plasma jet

Cold atmospheric plasma (CAP) in open air hosts numerous chemical species engaged in thousands of chemical reactions. Comprehensive diagnosis of its chemical composition is important across various fields from medicine, where reactive oxygen and nitrogen play key roles, to surface modification. In applications, a centimeter-scale helium–air jet operates for minutes, featuring micrometer-sized streamers and an atmospheric pressure-induced collision frequency in the hundreds of GHz range. To address this intricate multi-scale issue, we introduce a machine learning approach: using a physics-informed neural network (PINN) to tackle the multi-scale complexities inherent in predicting the complete list of species concentrations, gas temperature, and electron temperature of a CAP jet supplied with a mixture of helium and air. Experimental measurements of O3, N2O, and NO2 concentrations downstream of the plasma jet, combined with fundamental physics laws, the conservation of mass and charge, constrain the PINN, enabling it to predict the concentrations of all species that are not available from the experiment, along with gas and electron temperatures. The results, therefore, obey all the physical laws we provided and can have a chemical balance with the measured concentrations. This methodology holds promise for describing and potentially regulating complex systems with limited experimental datasets.

Compact analogs of the models of vortex flows generated by aircraft flight

The subject of this work is the development of compact analogs of vortex flows models, which are used in the modeling of vortex structures observed during the flight of an aircraft and the motion of a body in a fluid. In particular, two significant misunderstandings prevailing in this area of science are highlighted. The first misunderstanding is that the stationary motion of fluid parcels in a circle is treated as an inviscid vortex. Therefore, any vortex flow model that does not explicitly contain viscosity is considered to describe inviscid vortex motion. It has been proven that this is not so: the stationary viscous motion of fluid parcels in circular orbits corresponds to the self-balance of one force - the force of viscosity. This conclusion, in an explicit form, was made for the first time. This is very important because it changes our ideas about force balance, where two or more forces of different natures must necessarily be present. Overcoming this misunderstanding opens the way for creating compact analogs of existing models of vortex motions. Along the way, one more - the second general misunderstanding in the field of vortex dynamics was eliminated. Wherever we read it, we can see that the compactness of the vortex flow is associated with the compactness of the vorticity field. This is facilitated by the fact that the equations for vorticity and not for velocity are considered. As a result, except for one or two models of vortices, which correspond to the rotation of the entire space, up to infinity, this violates the fundamental law of physics - the law of conservation and transformation of energy. It is about the fact that, as a second misunderstanding, an error is assumed when calculating the kinetic energy of the vortex flows: the Jacobian in cylindrical (polar) coordinates is not considered. As a result, all the mentioned models of vortex flows, which correspond to the hyperbolic law as their asymptotics in the periphery, have infinite kinetic energy. Certainly, this does not correspond to the formation and evolution of compact vortex structures. Therefore, in this work, based on overcoming the aforementioned misunderstandings, many previously obtained models of compact vortex flows, as well as those obtained for the first time, are presented. In particular, this applies to the turbulent vortex flow during the formation of a vortex sheet, which is a compact analog of the Burgers-Rott vortex - both the classical one corresponding to laminar motion and the one consisting of a laminar flow in the core and a turbulent flow on the periphery of the vortex. Research methods are entirely theoretical. Well-known theorems of theoretical mechanics, mathematical theory of field, and calculus of variations, etc. are used. The obtained solutions are compared with the existing corresponding analogs of non-compact flows. Conclusions. Using the methods of calculus of variation, it was possible to show the possibility of the formation of quasi-solid-like rotational motion in a boundary layer of an incompressible fluid. The very presence of viscosity, or rather its taking into account (boundary layer), indicates a possible transition of the flow from plane-parallel motion to the just-mentioned rotational one due to the Kelvin-Helmholtz instability. In addition, two new models of the Burgers-Rott vortex flow were obtained in this study. The first model uses the general solution obtained by Burgers, but this model corresponds to a combined vortex: although the velocity field is continuous, the vorticity field has a discontinuity - at the point of maximum velocity. It is proved that such an approach is quite possible: the equation of motion is satisfied everywhere, i.e., at every point in space, and the tangential stresses are continuous functions. Since the periphery of the Burgers-Rott vortex is an unstable flow, another model is proposed - with a laminar core and a turbulent periphery. Certainly, the motion of fluid parcels in the peripheral region is described by a velocity distribution other than that of Burgers. Finally, the possible use of known models of compact vortex flows to simulate the von Karman vortex street is considered, with an indication of the advantages of these models.

Пифагорейский аргумент разумного замысла вселенной и его критика. Статья 1: Двойная структура пифагорейского аргумента

This article is first in a series of publications on the problem of a special character of fundamental physical laws, which combine two opposite qualities: they are complex enough to allow fine-tuning to life, yet simple enough to be discoverable by emerging intelligent life. In other words, the laws permit the emergence of not just living beings, but those capable of discovering these very laws. How could this be possible? Known laws can be looked at from both logical, objective, and historical, subjective, perspectives. On the one hand – the logical – the successes achieved by physics testify to the adequacy of physical theories, to their conformity to the fabric of the Universe itself. This conformity is fundamentally different from fitting complex formulas to facts, like those implemented by the algorithms of Ptolemy, Copernicus or artificial intelligence. Fits describe only what is already embedded in them, whereas physical theories allow to predict phenomena that have never been observed, often unbeknownst even to the authors of those theories. This predictive power stems from the same qualities as the ability to unambiguously falsify physical theories: the simplicity, universality, precision, and completeness of their mathematical principles. In addition to these qualities, and in addition to the fact that the fundamental physical laws possess numerous symmetries, invariants, and equivalences, they also permit that constructive richness of stable material configurations, that is chemistry, which is a necessary condition of life as we know it. Research of recent decades shows how finely tuned the physical constants are to meet this requirement: even small changes in their values would make chemistry impossible. What is the reason for these amazing Pythagorean qualities of the Universe? Purposeful design of this rational elegance of nature, that is, the intelligent design of the Universe, appears to be the only passable answer to this question, as we intend to demonstrate in this series of publications. On the other hand, the history of science testifies that the belief in the mathematical perfection of nature’s arrangement lies at the origin of modern physics, indicating both the possibility and, without exaggeration, the sacredness of cognition of the Universe. This belief is clearly visible in the worldview of the founders of mathematical physics, as a special, emotionally intense Pythagorean credo, a variant of Christian Platonism. The initial presumption of perfect design may not be recognized by the masses of scientists and philosophers who came later, and it may even be rejected by them verbally, but this does not cancel its status as the foundation of physics: there has been and is no other answer to the question of why the understanding of the Universe is possible and important for humanity. The justification of the assumption of intelligent design as the cause of such specific laws of nature, on the one hand, and, on the other hand, discerning and contemplating the meaning of the Pythagorean credo by granting it the status of a metaphysical working hypothesis, together form a dual objective-subjective logical structure, which the authors designate as the Pythagorean argument, as presented in this article.

Proof-of-Principle Demonstration of Fully Passive Quantum Key Distribution.

Quantum key distribution (QKD) offers information-theoretic security based on the fundamental laws of physics. However, device imperfections, such as those in active modulators, may introduce side-channel leakage, thus compromising practical security. Attempts to remove active modulation, including passive decoy intensity preparation and polarization encoding, have faced theoretical constraints and inadequate security verification, thus hindering the achievement of a fully passive QKD scheme. Recent research [W. Wang et al., Phys. Rev. Lett. 130, 220801 (2023).PRLTAO0031-900710.1103/PhysRevLett.130.220801; 2V. Zapatero et al., Quantum Sci. Technol. 8, 025014 (2023).2058-956510.1088/2058-9565/acbc46] has systematically analyzed the security of a fully passive modulation protocol. Based on this, we utilize the gain-switching technique in combination with the postselection scheme and perform a proof-of-principle demonstration of a fully passive quantum key distribution with polarization encoding at channel losses of 7.2dB, 11.6dB, and 16.7dB. Our work demonstrates the feasibility of active-modulation-free QKD in polarization-encoded systems.

Subduction as a Smoothing Machine: How Multiscale Dissipation Relates Precursor Signals to Fault Geometry

Understanding the process of earthquake preparation is of utmost importance in mitigating the potential damage caused by seismic events. That is why the study of seismic precursors is fundamental. However, the community studying non-seismic precursors relies on measurements, methods, and theories that lack a causal relationship with the earthquakes they claim to predict, generating skepticism among classical seismologists. Nonetheless, in recent years, a group has emerged that seeks to bridge the gap between these communities by applying fundamental laws of physics, such as the application of the second law of thermodynamics in multiscale systems. These systems, characterized by describing irreversible processes, are described by a global parameter called thermodynamic fractal dimension, denoted as D. A decrease in D indicates that the system starts seeking to release excess energy on a macroscopic scale, increasing entropy. It has been found that the decrease in D prior to major earthquakes is related to the increase in the size of microcracks and the emission of electromagnetic signals in localized zones, as well as the decrease in the ratio of large to small earthquakes known as the b-value. However, it is still necessary to elucidate how D, which is also associated with the roughness of surfaces, relates to other rupture parameters such as residual energy, magnitude, or fracture energy. Hence, this work establishes analytical relationships among them. Particularly, it is found that larger magnitude earthquakes with higher residual energy are associated with smoother faults. This indicates that the pre-seismic processes, which give rise to both seismic and non-seismic precursor signals, must also be accompanied by changes in the geometric properties of faults. Therefore, it can be concluded that all types of precursors (seismic or non-seismic), changes in fault smoothness, and the occurrence of earthquakes are different manifestations of the same multiscale dissipative system.

Unsteady incompressible laminar boundary layer: time and space variable molecular viscosity

The subject of this work is two approaches to describe the laminar unsteady flow of an incompressible fluid in the boundary layer. In the first approach, the viscosity of the fluid and the acceleration with which the plane is set in motion are considered constant. In essence, this is Rayleigh's problem. The solution obtained on the basis of these assumptions asymptotically converges to the well-known self-similar Stokes solution. It is important that the solutions of Stokes and Rayleigh asymptotically at large values of time correspond to the disappearance of shear stresses between the liquid and moving plane after acceleration. A paradox emerges the equations derived by Stokes to describe internal friction indicate the absence of the same friction between a moving body and fluid. Since research using the calculus of variation methods revealed that the molecular viscosity inside the stationary boundary layer should depend on the distance to the moving surface, the corresponding non-steady problem was considered. As a result, as before for the steady case, solutions describing both non-gradient and gradient flows of incompressible fluid in the boundary layer are obtained. The asymptotic analysis of the transition to steady flow testifies the consistency of these solutions. For the case of non-gradient flow, a comparison of the classical solution with the solution corresponding to the extreme fluid flow rate carried by the moving surface is made. It is shown that according to the solution obtained on the basis of the calculus of variation approach, the shear stress on the surface does not disappear anywhere after the motion becomes steady but, as expected, acquires a constant value. The research methods are purely theoretical and the results are analyzed by comparison with available theoretical and experimental data and compliance with the fundamental laws of physics, in particular the law of conservation of energy. These methods are based on the construction of analytical mathematical models, which are differential equations in partial derivatives supplemented with appropriate physical initial and boundary conditions. In addition, Euler's differential equations for the extreme of functional theory are used (in this paper, this is the extreme of fluid flow rate across the cross-section of the boundary layer). When solving these equations, the well-known Fourier method of variable separation is used. Arbitrary functions of time arising during partial integration (by one of the variables – the spatial coordinate) are determined from the conditions of asymptotic convergence of the solutions of non-steady problems to the corresponding solutions of steady problems. Conclusions. The presented results are of fundamental importance for understanding the physics of the flow around aircraft parts, as they indicate the contradiction of the existing idea of the reversibility of direct and inverse problems: the motion of a body in a still fluid and the flow of a fluid around an immobile body.

Artificial Intelligence Enhanced Molecular Simulations.

Molecular simulations, which simulate the motions of particles according to fundamental laws of physics, have been applied to a wide range of fields from physics and materials science to biochemistry and drug discovery. Developed for computationally intensive applications, most molecular simulation software involves significant use of hard-coded derivatives and code reuse across various programming languages. In this Review, we first align the relationship between molecular simulations and artificial intelligence (AI) and reveal the coherence between the two. We then discuss how the AI platform can create new possibilities and deliver new solutions to molecular simulations, from the perspective of algorithms, programming paradigms, and even hardware. Rather than focusing solely on increasingly complex neural network models, we introduce various concepts and techniques brought about by modern AI and explore how they can be transacted to molecular simulations. To this end, we summarized several representative applications of molecular simulations enhanced by AI, including from differentiable programming and high-throughput simulations. Finally, we look ahead to promising directions that may help address existing issues in the current framework of AI-enhanced molecular simulations.

Physics informed neural networks for surrogate modeling of accidental scenarios in nuclear power plants

Licensing the next-generation of nuclear reactor designs requires extensive use of Modeling and Simulation (M&S) to investigate system response to many operational conditions, identify possible accidental scenarios and predict their evolution to undesirable consequences that are to be prevented or mitigated via the deployment of adequate safety barriers. Deep Learning (DL) and Artificial Intelligence (AI) can support M&S computationally by providing surrogates of the complex multi-physics high-fidelity models used for design. However, DL and AI are, generally, low-fidelity ‘black-box’ models that do not assure any structure based on physical laws and constraints, and may, thus, lack interpretability and accuracy of the results. This poses limitations on their credibility and doubts about their adoption for the safety assessment and licensing of novel reactor designs.In this regard, Physics Informed Neural Networks (PINNs) are receiving growing attention for their ability to integrate fundamental physics laws and domain knowledge in the neural networks, thus assuring credible generalization capabilities and credible predictions. This paper presents the use of PINNs as surrogate models for accidental scenarios simulation in Nuclear Power Plants (NPPs). A case study of a Loss of Heat Sink (LOHS) accidental scenario in a Nuclear Battery (NB), a unique class of transportable, plug-and-play microreactors, is considered. A PINN is developed and compared with a Deep Neural Network (DNN). The results show the advantages of PINNs in providing accurate solutions, avoiding overfitting, underfitting and intrinsically ensuring physics-consistent results.

COVID infection in 4 steps: Thermodynamic considerations reveal how viral mucosal diffusion, target receptor affinity and furin cleavage act in concert to drive the nature and degree of infection in human COVID-19 disease

We have developed a mechanistic model of SARS-CoV-2 and SARS-CoV infection, exploring the relationship between the viral diffusion in the mucosa and viral affinity for the angiotensin converting enzyme 2 (ACE2) target. Utilising the structural similarity of SARS-CoV and SARS-CoV-2 and a shared viral target receptor (ACE2), but a dramatic difference in upper or lower respiratory tract infectivity, we were able to generate insights into the linkage of mucosal diffusion and target receptor affinity in determining the pathophysiological pathways of these two viruses.Our analysis reveals that for SARS-CoV-2 the higher affinity of ACE2 binding, the faster and more complete the mucosal diffusion in its transport from the upper airway to the region of the ACE2 target on the epithelium. This diffusional process is essential for the presentation of this virus to the furin catalysed highly efficient entry and infection process in the upper respiratory tract epithelial cells. A failure of SARS-CoV to follow this path is associated with lower respiratory tract infection and decreased infectivity. Thus, our analysis supports the view that through tropism SARS-CoV-2 has evolved a highly efficient membrane entry process that can act in concert with a high binding affinity of this virus and its variants for its ACE2 which in turn promotes enhanced movement of the virus from airway to epithelium. In this way ongoing mutations yielding higher affinities of SARS-CoV-2 for the ACE2 target becomes the basis for higher upper respiratory tract infectivity and greater viral spread. It is concluded that SARS-CoV-2 is constrained in the extent of its activities by the fundamental laws of physics and thermodynamics. Laws that describe diffusion and molecular binding. Moreover it can be speculated that the very earliest contact of this virus with the human mucosa defines the pathogenesis of this infection.

High-precision Ramsey-comb spectroscopy on molecular deuterium for tests of molecular quantum theory

Precision spectroscopy of simple, calculable molecules has become an important tool to compare experiments with theory in an effort to test our understanding of the fundamental laws of physics. For this purpose, we have measured the transition frequency of molecular deuterium () with unprecedented accuracy. We use Ramsey-Comb spectroscopy at deep-ultraviolet wavelengths (201 nm) with a two-photon, Doppler-free interrogation scheme. The resulting transition frequency is kHz. The 1-σ uncertainty of 19 kHz represents an improvement of more than two orders of magnitude compared to the best previous measurement. In this paper, we give an extensive description of our methods and the experimental apparatus that we employed. Particular attention is given to aspects that we recently improved, such as the frequency comb laser system, the method of signal recording, and the cryogenic molecular beam apparatus. In combination with future measurements of the ionisation energy of the EF state, our measurement paves the way for an improved determination of the ground state ionisation and dissociation energy of molecular deuterium.

Hybrid modeling for biopharmaceutical processes: advantages, opportunities, and implementation

Process models are mathematical formulations (essentially a set of equations) that try to represent the real system/process in a digital or virtual form. These are derived either based on fundamental physical laws often combined with empirical assumptions or learned based on data. The former has been existing for several decades in chemical and process engineering while the latter has recently received a lot of attention with the emergence of several artificial intelligence/machine learning techniques. Hybrid modeling is an emerging modeling paradigm that explores the synergy between existing these two paradigms, taking advantage of the existing process knowledge (or engineering know-how) and information disseminated by the collected data. Such an approach is especially suitable for systems and industries where data generation is significantly resource intensive while at the same time fundamentally not completely deciphered such as the processes involved in the biopharmaceutical pipeline. This technology could, in fact, be the enabler to meeting the demands and goals of several initiatives such as Quality by design, Process Analytical tools, and Pharma 4.0. In addition, it can aid in different process applications throughout process development and Chemistry, Manufacturing, and Control (CMC) to make it more strategic and efficient. This article focuses on providing a step-by-step guide to the different considerations to be made to develop a reliable and applicable hybrid model. In addition, the article aims at highlighting the need for such tools in the biopharmaceutical industry and summarizes the works that advocate its implications. Subsequently, the key qualities of hybrid modeling that make it a key enabler in the biopharmaceutical industry are elaborated with reference to the literature demonstrating such qualities.

From Behavioral Climate Models and Millennial Data to AGW Reassessment

Context. The so called AGW (Anthropogenic Global Warming), is based on thousands of climate simulations that indicate that human activity is virtually solely responsible for the recent global warming. The climate models used are derived from the meteorological models used for short-term predictions. They are based on the fundamental and empirical physical laws that govern the myriad of atmospheric and oceanic cells integrated by the finite element technique. Numerical approximations, empiricism and the inherent chaos in fluid circulations make these models questionable for validating the anthropogenic principle, given the accuracy required (better than one per thousand) in determining the Earth energy balance. Aims and methods. The purpose is to quantify and simulate behavioral models of weak complexity, without referring to predefined parameters of the underlying physical laws, but relying exclusively on generally accepted historical and paleoclimate series. Results. These models perform global temperature simulations that are consistent with those from the more complex physical models. However, the repartition of contributions in the present warming depends strongly on the retained temperature reconstructions, in particular the magnitudes of the Medieval Warm Period and the Little Ice Age. It also depends on the level of the solar activity series. It results from these observations and climate reconstructions that the anthropogenic principle only holds for climate profiles assuming almost no PCA neither significant variations in solar activity. Otherwise, it reduces to a weak principle where global warming is not only the result of human activity, but is largely due to solar activity.

Parameter identification for a damage phase field model using a physics-informed neural network

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of micro-defect formation using state variables at the macroscopic level. The equations that define the model are derived from fundamental laws of physics and provide important relationships among state variables. Simulations using the model considered in this work produce good qualitative and quantitative results, but many parameters must be adjusted to reproduce certain material behavior. The identification of model parameters is considered by solving an inverse problem that uses pseudo-experimental data to find the best values that fit the data. We apply physics informed neural network and combine some classical estimation methods to identify the material parameters that appear in the damage equation of the model. Our strategy consists of a neural network that acts as an approximating function of the damage evolution with output regularized using the residue of the differential equation. Three stages of optimization seek the best possible values for the neural network and the material parameters. The training alternates between the fitting of only the pseudo-experimental data or the total loss that includes the regularizing terms. We test the robustness of the method to noisy data and its generalization capabilities using a simple physical case for the damage model. This procedure deals better with noisy data in comparison with a more standard PDE-constrained optimization method, and it also provides good approximations of the material parameters and the evolution of damage.

Extension of Noether’s theorem in $${\cal P}{\cal T}$$-symmetry systems and its experimental demonstration in an optical setup

Noether's theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time (PT)-symmetric systems, which exhibit novel quantum properties and have attracted increasing interest. In this work, we extend Noether's theorem to a class of significant PT -symmetric systems for which the eigenvalues of the PT-symmetric Hamiltonian H change from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics. We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT -symmetry unbroken regime, or a chiral symmetry in the PT-symmetry broken regime. In addition, we experimentally investigate the extended Noether's theorem in PT -symmetric single-qubit and two-qubit systems using an optical setup. Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT -symmetry of a system is broken. Furthermore, a novel phenomenon of masking quantum information is first observed in a PT -symmetric two-qubit system. This study not only contributes to full understanding of the relation between symmetry and conservation law in PT -symmetric physics, but also has potential applications in quantum information theory and quantum communication protocols.